A Methodology Of Rainfall Data Analysis And Stochastic Rainfall/runoff Synthesis By

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A METHODOLOGY OF RAINFALL DATA ANALYSIS AND STOCHASTIC RAINFALL/RUNOFF SYNTHESIS by Allen Douglas Jones A Thesis Submitted to the Faculty of the SCHOOL OF RENEWABLE NATURAL RESOURCES In Partial Fulfillment of Requirements For the Degree of MASTER OF SCIENCE WITH A MAJOR IN WATERSHED MANAGEMENT In the Graduate College THE UNIVERSITY OF ARIZONA 1981 STATEMENT BY AUTHOR This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the library. Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgement the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: APPROVAL BY THESIS COMMITTEE This thesi has been approved on the date shown below. F r. John L. Thames Thesis Director essor of Watersh d Management Dr. Per Ffolliott Professor of Watershed Management Dif. Edgar J. McCullou Professor of Geosciences Date 14 7i/ Date Date ACKNOWLEDGMENTS I would like to thank Dr. John L. Thames, my thesis director and major advisor, for his guidance and support throughout the duration of my graduate study and the preparation of this paper. Appreciation is also expressed to Dr. Peter F. Ffolliott and Dr. Edgar J. McCullough for their advice and support during the final stages of this thesis. I would like to thank Dr. Louis H. Hekman and Jeffrey Franklin for their help with all of my computer problems and their continuous encouragement. Finally, I would like to express my deepest personal gratitude to my wife, Tracy, for all of the support, encouragement, and patience she has freely given me throughout our marriage. iii TABLE OF CONTENTS Page vi LIST OF FIGURES LIST OF TABLES ix ABSTRACT CHAPTER 1 INTRODUCTION 2 STOCHASTIC PRECIPITATION/RUNOFF MODEL 1 6 Review of Stochastic Models of Precipitation. 6 Precipitation Model 7 Summer Precipitation 8 Winter Precipitation 10 Runoff Determination 12 3 METHODOLOGY FOR DATA ANALYSIS Summer Precipitation Analysis Analysis of Event Interarrival Time Analysis of Rainfall Per Event Winter Precipitation Analysis Fitting Theoretical Distributions 4 STOCHASTIC RAINFALL/RUNOFF MODEL 18 20 22 29 30 35 42 Hanford Stochastic Precipitation/Runoff Model 45 Model Response 61 Model Results 63 5 CONCLUSION 68 APPENDIX A: PROGRAM LISTING OF THE EVENT INTERARRIVAL TIME ANALYSIS (RAIN 1) AND OUTPUT DESCRIBING THE HANFORD DATA 73 APPENDIX B: OUTPUT LISTING FROM RAIN 1 OF THE SEQUENCE OF VALUES FOR CONDUCTING T-TEST GROUPING FOR EVENT INTERARRIVAL TIME 90 iv TABLE OF CONTENTS--Continued Page APPENDIX C: PROGRAM LISTING FOR THE EVENT INTERARRIVAL TIME--GROUPED DATA (RAIN 2) AND OUTPUT DESCRIBING THE HANFORD DATA 102 APPENDIX D: PROGRAM LISTING FOR PRECIPITATION PER EVENT ANALYSIS (RAIN 3) AND OUTPUT DESCRIBING THE HANFORD DATA 114 APPENDIX E: OUTPUT LISTING FROM RAIN 3 OF THE SEQUENCE OF VALUES FOR CONDUCTING T-TEST GROUPING FOR PRECIPITATION PER EVENT 130 APPENDIX F: PROGRAM LISTING FOR PRECIPITATION PER EVENT--GROUPED DATA (RAIN 4) AND OUTPUT DESCRIBING THE HANFORD DATA APPENDIX G: PROGRAM LISTING OF THE WINTER STORM PERIOD ANALYSIS (RAIN 5) AND OUTPUT DESCRIBING THE HANFORD DATA 142 146 APPENDIX H: PROGRAM LISTINGS FOR DEVELOPING THEORETICAL GEMMA, GEOMETRIC, AND EXPONENTIAL DISTRIBUTIONS BASED ON OBSERVED DISTRIBUTION PARAMETERS. INCLUDES SAMPLE OUTPUT DISTRIBUTIONS 160 APPENDIX I: GAMMA FUNCTION [F(N)] TABLES FOR VALUES OF K BETWEEN 0 AND 2 168 APPENDIX J: PROGRAM LISTING OF THE NUMERICAL INTEGRATION ROUTINE 171 APPENDIX K: PROGRAM LISTING OF THE STOCHASTIC RAINFALL/RUNOFF MODEL (RAIN 6) AND THE OUTPUT FOR THE HANFORD SITE 173 LIST OF REFERENCES 197 LIST OF FIGURES Figure 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Page Graphic display of summer precipitation components Graphic display of winter precipitation components showing the difference between the 5-distribution method (2a) and the 3-distribution method (2b) 9 11 Initial abstraction and runoff relations. 3a illustrates components of surface runoff and Ia (after Horton 1945). 3b gives a graphic relation between runoff and Ia (after U. S. Soil Conservation Service 1972) 16 Location of Hanford Meterology Station 25 miles NW of Richland, Washington 19 Distribution of the annual precipitation from 1947 to 1966 for the Hanford Meteorology Station, Washington 21 Flow chart for analysis of the event interarrival time variable (RAIN 1) 25 Monthly average rainfall variations at the Hanford Meteorology Station, Washington for the period 1947 through 1966 28 Flow chart for the rainfall per event variable analysis (RAIN 3) 31 Flow chart for the analysis of variable describing the winter storm periods (RAIN 5) 33 Comparison of actual data and fitted probability distribution function for winter storm interarrival time, DB 46 vi vii Figure 11. Comparison of actual data and fitted probability distribution function for winter storm duration, W 12. 13. Comparison of actual data and fitted probability distribution function for winter storm precipitation amount, RP Page 47 48 Comparison of actual data and fitted probability distribution function for precipitation per event (MAR) 49 Comparison of actual data and fitted probability distribution function for precipitation per event (JUN) 50 Comparison of actual data and fitted probability distribution function for precipitation per event (APR-MAY-JULAUG-SEP-OCT) 51 Comparison of actual data and fitted probability distribution function for event interarrival time (MAR) 52 Comparison of actual data and fitted probability distribution function for event interarrival time (APR-MAY) 53 Comparison of actual data and fitted probability distribution function for event interarrival time (JUN) 54 Comparison of actual data and fitted probability distribution function for event interarrival time (JUL) 55 Comparison of actual data and fitted probability distribution function for event interarrival time (AUG-SEP) 56 21. Comparison of actual data and fitted probability distribution function for event interarrival time (OCT) 57 14. 15. 16. 17. 18. 19. 20. viii Figure 22. Flow chart for the stochastic rainfall runoff model for the Hanford Meteorology Station 23. 24. 25. Page 60 Relative frequency comparisons between the actual and synthetic rainfall per event distributions 62 Relative frequencies of three different curve numbers with an Ia = 0.2S for 500 years of synthetic rainfall at the Hanford Meteorology Station 66 Relative frequencies of three different curve numbers with an Ia = 0.15S for 500 years of synthetic rainfall at the Hanford Meteorology Station 67 LIST OF TABLES Table 1. 2. 3. 4. 5. 6. Page Antecedent rainfall conditions (AMC) and curve numbers (CN) 15 Critical statistic (Ca) for the KolmogorovSmirnov test 37 Final listing of observed distributions of interest and their matching hypothetical distributions 39 Probability distribution functions (Theoretical Distributions) and associated parameter values used in simulating winter precipitation 43 Probability distribution functions (Theoretical Distributions) and associated parameter values used in simulating summer precipitation 44 Comparisons of precipitation characteristics between historical 20 year record and synthesized 5000 value record 64 ix ABSTRACT Precipitation data analysis procedures are presented that allow development of the random variables of interest describing the summer and winter rainfall process in semiarid regions of the West. These procedures include programs that define the variables of event interarrival time and rainfall amount per event and a process of grouping months within these variables. A program for analyzing winter frontal storm activity is presented. Procedures are developed describing the actual distributions of the annual rainfall process. A methodology for fitting theoretical distributions to each of these actual distributions is explained. Climactic data from the Hanford Meteorology StationNW of Richland, Washington is used to develop these procedures. Results of the analysis procedures for the Hanford data are included. The results of the above analysis are incorporated into a stochastic rainfall model that includes a direct surface runoff calculation process. This runoff is calculated using the Soil Conservation Service method. The resulting stochastic model allows a study of the change in watershed practices that can greatly assist in making management decisions concerning possible water harvesting practices on western mine sites. CHAPTER 1 INTRODUCTION Over the years, there has been a growing concern by the public about the physical conditions of surface mined land after strip mining operations have been conducted. This concern has led to the establishment of state and federal regulations which define the condition in which land must be left after the completion of any mining of coal, oil shale, tar sands, or uranium deposits. Reclamation of disturbed land entails three main processes. Once mining activities are completed, the overburden that was removed is replaced and recontoured to conform with the local topography. Stockpiled topsoil is then placed over the newly contoured landscape. Revegetation and opening of the land to its pre-mining use or an economical alternative use completes the normal reclamation process. In most cases, the final step in reclamation is the revegetation of the land. Although problems with revegetation in the semi-arid portions of the western United States include toxicity, salinity, infertility, 1 2 high or low pH (Thames 1977), to mention a few, water is the determining factor in the successful outcome of reclamation efforts. The availability of water for plant growth influences the selection of vegetative species. It also affects decisions concerning establishment of irrigation water supplies, stock ponds, and storage reservoirs. It is important for managers and decision makers to have hydrologic information of the mined area to make intelligent decisions concerning reclamation procedures. Learning (1977) states that it is critical that there be no misallocation of resources associated with the reclamation process. In economic terms, the reclaimed land should be worth more than the cost of reclaiming it. It is essential that managers attempt to minimize overall costs by maximizing the return from the post-mining land. Therefore, in some cases the pre-mining use may not have been the best use for the land and alternative post-mine uses may increase the benefits to man. Since water is a limiting factor in the semi-arid west, one such alternative to assist in maximizing return is runoff agriculture or water harvesting. A water harvesting system consists of artificial methods that collect water in the form of precipitation by making the 3 watershed catchment more impervious, thereby increasing the runoff. This collected water is then stored until it is beneficially used. Cluff and Dutt (1975) list four main methods being used that will increase surfact runoff on a catchment: 1) land surface modification, 2) ground cover modification, 3) chemical treatment, and 4) soil cementation techniques. Researchers at the University of Arizona have been studying different water harvesting systems for several years. Cluff (1975) provides an excellent description of these systems. To make a sound decision whether to use a water harvesting system and if so, which method to use, it is important to have an understanding of the hydrologic parameters associated with the rainfall and runoff phenomenon for the site in question. The purpose of this paper is to present a methodology that will facilitate the evaluation of the water harvesting potential of western mine sites. This methodology consists of a series of procedures that will assist in the analysis of historical rainfall data and the development of a stochastic rainfall/runoff model. Although historical rainfall data from the Hanford Meteorology Station northwest of Richland, Washington 4 were used to develop the data analysis procedures and the stochastic model for that location, the techniques and procedures described within can be applied to any location where 20 years or more of historical daily rainfall data are available. The procedures proposed to facilitate evaluation of the water harvesting potential incorporate six computer programs that have the notation of RAIN 1 through RAIN 6. Each of these programs are written in FORTRAN V language. The six programs are titled: RAIN 1 Monthly event interarrival time dist., RAIN 2 Event interarrival time dist. for grouped months, RAIN 3 Monthly rainfall per event dist., RAIN 4 Rainfall per event dist. for grouped months, RAIN 5 Winter storm period dist., and RAIN 6 Stochastic rainfall/runoff model. The methodology procedures follow the basic steps: 1. Breakdown of historical rainfall data into monthly distributions of rainfall per event and event interarrival time and calculation of statistics for each distribution. 2. Conductance of a student t-test to develop a grouping of statistically non-different months. 5 3. Calculation of distributions and statistics for each of the grouped data sets developed from Step 2. 4. Calculation of distributions and statistics describing the winter storm period. 5. Fitting of a theoretical distribution to each of the distributions that describe the annual rainfall process. 6. Incorporation of the above theoretical distributions describing the annual rainfall process into a stochastic precipitation model which includes an antecedent moisture condition and direct surface runoff subroutine. 7. Analysis of resulting simulated rainfall and runoff. The techniques and procedures described in this paper are not limited to extending one's knowledge of only the water harvesting potential of a site. They may also be used to furnish invaluable information for studies in other hydrologic areas of interest such as: the probability of termination and vegetation establishment of mine spoils, water spreading potential, determination of pond,culvert and channel sizing, sediment yield determination, ground water recharge and contamination, and natural and artificial irrigation needs, to mention a few. CHAPTER 2 STOCHASTIC PRECIPITATION/RUNOFF MODEL Since the advent of high speed computer systems, there has been an acceleration in the development of mathematical methods attempting to describe hydrologic processes. Fleming (1975) gives an excellent account of the historical background behind the simulation techniques used in hydrology and a description of the numerous mathematical methods being utilized today. One category of methods treats a sequence of events as time-dependent and attempts to generate a long hypothetical sequence of events based on the statistical and probability characteristics of past historical record. This form of statistical hydrology is termed stochastic simulation. Review of Stochastic Models of Precipitation An event-based stochastic model was developed by Fogel, Duckstein and Kisiel (1971) to predict precipitation based upon probability distributions of random variables associated with precipitation. These variables of interest were the amount of rainfall per event and the number of events per season. Research continued in the area of 6 7 consecutive summer storms by Duckstein, Fogel and Kieiel (1972) and Duckstein, Fogel and Thames (1973). Attention was later turned to the stochastic modeling of winter precipitation by Duckstein, Fogel and Davis (1975). This model allowed a degree of dependence to exist between present and past events to coincide with frontal storm activity. Both Fischer (1976) and Hekman (1977) utilized the summer and winter procedures for simulating precipitation for studying the hydrologic processes of a stripmined watershed in Arizona and for evaluating timber clearing as a means for increasing water yields, respectively. Precipitation Model In most of the semi-arid regions of the West, precipitation events are generally associated with two types of precipitation; those being the convective-type summer thunderstorms and the cyclonic or frontal-type winter storms. Summer thunderstorms may be considered to occur as independent events while winter storms that develop out of large storm systems, tend to persist and the events often occur in groups or sequences. Modeling precipitation, therefore, requires two different procedures, one for the summer period and one for the winter period. 8 Summer Precipitation The summer convection-type storms can best be simulated by an event-based stochastic method; therefore, the model developed by Fogel, Duckstein and Kisiel (1971) and Duckstein et al. (1972) was used as a basis for the model developed in this paper. Storms are assumed to be independent from one another, with no more than one event occurring per day. The basic time step used throughout the data analysis procedures was one day and all rainfall was expressed on a 24 hour basis. To simulate rainfall, it was necessary to know the form of the empirical cumulative density function (Benjamin and Cornell 1970) underlying the random variables of interest. There were two main random variables of interest in modeling summer rainfall. These were: 1. PT, the amount of precipitation per event and 2. T, event interarrival time. A graphic display of these two input process components is presented in Figure 1. An event was defined as a 24 hour period having a measurable (0.01 inches) amount of rainfall. Two days of consecutive rainfall events are assumed to have a one day interarrival time between them; two rainfall events separated by four dry days would therefore have an interarrival time of five days separating them. 9 PT= .55 PT= .4 1 Fm si T=2 T=I — T5 Time (Days) Figure 1. Graphic display of summer precipitation components. 10 Winter Precipitation The basis for the simulation of winter rainfall in this paper was the stochastic model presented by Duckstein et al. (1975). In this model, precipitation was said to occur in groups. A group being defined as consecutive days of precipitation during which daily amounts exceeded a minimum of 0.01 inches. Consecutive groups separated by no more than a specified number of dry days constitute a sequence. A sequence represents a large frontal storm system and may be composed of many precipitation events. Simulating winter precipitation required the definition of the empirical cumulative density function of .five random variables of interest. These were: 1. ANO, the number of groups per sequence, 2. W, group duration in days, 3. RP, the amount of precipitation per group, 4. D, the number of dry days between groups, and 5. B, the number of dry days between sequences. A graphic display of these five input process components is presented in Figure 2a. There were two implicit assumptions contained in the winter model. First, precipitation was spread evenly over all the days in each group. Second, group precipitation, RP, was independent of group length, W. 11 W=2 AN0=3 1111n1•11. nn•n•• RP=/5 1- 4 (b B=4-1-1 HD=I ) W = 2 I.-s4 W = 2 I.nnnn• IIMM•111n•n n••••n• RP=.75 D B = 4 -'1 Fs DB = - Time (Days) Figure 2. Graphic display of winter precipitation components showing the difference between the 5-distribution method (2a) and the 3-distribution method (2b). 12 For the methodology developed in this paper, winter precipitation type was assumed to be rainfall only. The breakdown of winter precipitation into rain, snow and snowmelt may be accomplished on the basis of daily temperature (Corps of Engineers 1956). Heckman (1977) developed a stochastic model of daily maximum temperature with which a synthetic long term record of temperature could be generated and used in conjunction with the simulated precipitation record. Runoff Determination In attempting to determine the water harvesting potential of a mine site, it is necessary to have an understanding of the runoff potential for the watershed being studied. The majority of western mine sites are located on watersheds that are relatively small and ungaged. Due to these reasons, the U. S. Soil Conservation Service (SCS) method for estimating direct surface runoff (U. S. Soil Conservation Service 1972) was used in the model described in this paper. In using this method, the increment of storm rainfall is converted to a direct surface runoff volume which consists of the sum of surface runoff, the prompt 13 subsurface runoff, and channel runoff (Chow 1964). This runoff value is calculated using the equation: - 0.2S) - (I I + 0.8S (1) 2 where: Q = direct surface runoff in inches, I = storm rainfall in inches, and S = maximum potential difference between rainfall and runoff in inches. The U. S. Soil Conservation Service (1972) also defines: S = 1000 CN 10 (2) where CN is an arbitrary curve number varying from 0 to 100. Substituting Eq. (2) into Eq. (1), [I - 0.2 ( 1000 CN = I + 0.8 ( 1000 CN 10d 2 (3) 10) Therefore, the only estimate required for calculating runoff is the curve number. This curve number is a watershed index that is used to evaluate soil conditions, land use, conservation practices, and the antecedent moisture condition (AMC) at the start of the runoff producing storm. The SCS recognizes three AMC's, depending on the amount of rainfall received in the five day period pre ceding the runoff event. These three conditions are 14 given in Table 1. The basis behind the AMC is that a wet soil (AMC III) will produce a greater runoff than a dry soil (AMC I). AMC II is an average value and convertions between the three conditions are also shown in Table 1. In Equation 3, there are two parameters which determine the amount of runoff that will occur on a watershed given a rainfall (I) amount. The first and the most critical is the curve number. As already stated, this is a watershed indicator relating to the hydrologic soil type and the cover complexes of the watershed. Before using Equation 3, a curve number must be estimated for the study watershed. Soil Conservation Service (1972), Chow (1964), and Schwab (1966) all have excellent descriptions and tables for estimating curve numbers for a given location. The second parameter is the initial abstraction (Ia) which consists mainly of interception, infiltration, and surface storage; all of which occur before runoff begins. Figure 3a shows an illustration describing the components of surface runoff and the initial abstraction as they apply to the SCS equation. A graphic representation is shown in Figure 3b. Here it is seen that the initial abstraction must be satisfied before runoff can occur. 15 Table 1. Antecedent rainfall conditions (AMC) and curve numbers (CN). CN for Condition II Factor to Convert CN from Condition II to Condition I Condition III 10 0.40 2.22 20 0.45 1.85 30 0.50 1.67 40 0.55 1.50 50 0.62 1.40 60 0.67 1.30 70 0.73 1.21 80 0.79 1.14 90 0.87 1.07 100 1.00 1.00 AMC Condition Total 5-day antecedent rainfall in inches General Dormant Growing Description Season Season I Lowest runoff potential II Average Condition III Highest runoff potential >1.1 <0.5 0.5-1.1 From U. S. Soil Conservation Service (1972). 16 ( a ) Depression storage Surface storage Soil surface In f il tr a ti o n (b) Infiltration Curve Initial abstraction (La) b• Time Figure 3. Initial abstraction and runoff relations. 3a illustrates components of surface runoff and Ia (after Horton 1945). 3b gives a graphic relation between runoff and Ia (after U.S. Soil Conservation Service 1972). 17 The general SCS equation was developed for agricultural land with an Ia = 0.2S. However, under many arid and semi-arid conditions the initial abstraction may be less than that of agricultural land due to less vegetation and clearer land surface conditions (Fogel 1981; Kao 1973). Therefore an Ia = 0.15S was utilized in this study as well as, the standard Ia = 0.2S. The current chapter has described the stochastic precipitation models used in this study to simulate summer and winter storm activity. An explanation of the procedure for converting the simulated rainfall amount into runoff (the SCS method) was also discussed. But before a precipitation model can be developed for a given location, it is necessary to be able to analyze historical rainfall data for the site in such a way as to facilitate ease of model development. CHAPTER 3 METHODOLOGY FOR DATA ANALYSIS The ability to simulate precipitation greatly facilitates the prediction of hydrologic responses of a watershed to changes. However, before precipitation can be modeled it is necessary: to define the random variables that describe the precipitation process, group these random variables into groupings of statistically non-different months, estimate parameter values using the method of moments (Benjamin and Cornell 1970), and then fit a theoretical probability distribution to each random variable grouping. Once determined, the fitted theoretical probability distributions can be applied to a precipitation model using the Monte Carlo method (Benjamin and Cornell 1970; Mihran 1972) to simulate a sequence of precipitation events that are based on the probability characteristics of the past historical record. The following discussion will describe the data analysis procedures that were developed using twenty years (1947-1966) of climatic data from the Hanford Meteorology Station northwest of Richland, Washington. Figure 4 shows 18 19 20 the general location of the Hanford Station, which is east of the Cascade Range in south central Washington State. Its exact location is latitude 46° 34' N, longitude 110° 35' W. This region falls within the arid/semi-arid climate classification with an average annual precipitation (based on 20 years of data analyzed ) of 6.86 inches. Figure 5 shows the distribution of annual precipitation for the 20 years of historical data analyzed. The discussion will first analyze the summer precipitation followed by the analysis of the winter storm period. Finally, the procedure for fitting theoretical distributions to random variables will be explained. Summer Precipitation Analysis As stated, there are two random variables of interest that describe summer rainfall. These are PT, the amount of rainfall per event, and T, the event interarrival time. Both random variables are analyzed in a similar manner by using computer programs designed to calculate the actual empirical cumulative density function (CDF) for each month of the year for the period of record. The separation of data into monthly intervals facilitates the determination of periods of similar storm or rainfall activity. The programs also calculate a sequence of values 21 a) 4 - [ 4.) I I o i4-1 V CD Lo kID - I I- cn r--1 0 4) N .1, I H 't Ii es 10 .—. 0 (1, (D (7) 1 1%- 1 I 1 1 1 1 o P 1+4 • oZ -H 0 4-) .4-.) ni C:S1 4..... -H -H 044 -H u) C.) al (1) 3 - u.. O 0:0 » .. .-1 al ' '-40 iti CM - Ul .r-1 -1- ) z (11 z 4-) ni En 1 1 4 tP - 4J0 ,--i f 1 I I _ I I _ 1 I II I CM CO 11•••• ( S 8 II 3UI ) JD9A /U0 14 D 4 I 4-40 d 39Jd 0 -.1 0 CO Q4-1 vr I i E _ (C) CD ID I .-1 Z 0 -H C1) -W Z 7 ..Q 11:1 0 4-1 4-1 I 0 to z mM -H Ts 22 allowing a student t-test to be conducted to determine a statistical grouping of months. Such a grouping facilitates the ease of modeling. As the event interarrival time is being analyzed and groups are made, a determination of months within the summer and winter periods are found. Analysis of Event Interarrival Time For the random variable of event interarrival time, T, RAIN 1 was written to develop the cumulative density functions (CDF) for each month of the year from the actual data. The program inputs the daily precipitation on the basis of month, day and year that event occurred and the amount of rainfall in inches. An event is defined as before and two consecutive events are separated by an interarrival time of one day. The program assumes there is a data file for every day of the year being analyzed. Therefore, missing' data must be represented by a value within the data file. Gray (1970) describes several procedures for estimating missing precipitation data. The program also accounts for the extra day in February during leap year. The CDF for each month is found by first determining the number of days between each event and categorizing the results into classes. Once the data has been processed the probability density'function (PDF) 23 is found for each class and then the CDF is calculated. A table of PDF and CDF values is printed out for each month. Finally, the method of moments (Benjamin and Cornell 1970) is used to calculate the mean (R) and variance (a 2 ). From these values, the Lamda and K values of the gamma distribution are calculated. Statistical equations used to calculate the mean, variance, Lambdaand K-value, respectively, are: 1 • E xi x = n 1=1 a 2 = n-1 1 E x.1 2 - (Ex) 2 /n] i=1 i=1 (4) (5) LAMBDA = a2 (6) -2 K = — a2 (7) Each of these statistical values are used later in the procedures to calculate theoretical distributions. After calculating the CDF tables and statistics, the program develops a sequence of values allowing one to conduct a student t-test comparing each combination (66 total combinations) of any two months. The program calculates the degrees of freedom (f) and the computed 24 t-value (Tf) for each two-month comparison. The Tf is defined as: Tf = X1 - X 2 - ( 111 - 2 ) (8) Si 2 + 3 2 2 1 [/1 2 n2 where p i - 11 2 is assumed equal to zero. n i and n 2 are sample sizes, and S 2 2 are sample variances, and x i and x 2 are sample means. The degrees of freedom associated with the random variable t is given by: f (s12/111 s221n2)2 ( (S 1 2 /n 1 ) n i - 1 2 (S 2 2 /n 2 ) 9 2 n2 - 1 The above case is based on the assumption that a 1 2 and a 2 are not known and cannot be assumed equal (Bethea, 2 Duran, and Boullion 1975). Figure 6 presents a flow chart of the operational logic of the procedures in RAIN 1. A complete computer listing of the program can be found in Appendix A. The results of running RAIN 1 with the Hanford data is also shown in this appendix. This output consists of the twelve monthly CDF tables describing T plus the corresponding statistical values for each distribution. ) 25 I=1 I< DATA I=I+1 (n) CATAGO RI ZE INTERARRIVAL TIME INTO CLASSES • CALCULATE PDF & CDF TABLES FOR EACH MONTH CALCULATE STATISTICS FOR EACH DISTRIBUTION CALCULATE STUDENT T-TES T PARAMETERS STOP Figure 6. Flow chart for analysis of the event interarrival time variable (RAIN 1). 26 Appendix B gives the listing of the sequence of values that allow the conductance of the student t-test on the Hanford data. For each of the two-month comparisons, a student t-test was conducted using a table of tvalues (Bethea, Duran, and Boullion 1975) and a grouping of statistically non-different months was made using the 0.05 level of significance. In conducting this t-test, only those months were grouped together that were found to be statistically non-different (the null hypothesis that the two means are the same was accepted). If a month was found to be rejected from any month of a group then it could not be placed into that grouping. Groups developed within the variable T must consist of consecutive months since an interarrival time period may overlap the boundary between two consecutive months. After completing the t-test for T, the following grouping was found: Group 1 NOV-DEC-JAN-FEB Group 2 MAR-APR-MAY-JUN Group 3 JUL-AUG-SEP Group 4 OCT. When conducting the Kolmogorov-Smirnov test (to be explained later in this chapter) it was later found that Group 2 and Group 3 had to be broken down further for modeling purposes. 27 This grouping process also reveals an appropriate break between the winter period and the summer period with Group 1 (NOV through FEB) representing the winter frontal storm period. This break is also represented in Figure 7, which shows a change in the monthly average rainfall between the months of February-March and OctoberNovember. Further breakdown of groups resulted in the final grouping for the random variable T as: Group 1 NOV-DEC-JAN-FEB Group 2 MAR Group 3 APR-MAY Group 4 JUN Group 5 JUL Group 6 AUG-SEP Group 7 OCT. To derive the CDF's for the grouped data, RAIN 2 was written. A complete computer listing of the program can be found in Appendix C. This program simply finds the CDF and statistics for each of the above seven final interarrival time groups. The CDF tables (output of RAIN 2) are also given in Appendix C. The winter group, Group 1, distribution is not used further since this period is analyzed differently in RAIN 5. 28 / .9 0 JFMAMJJ AS ON D Month of the Year Figure 7. Monthly average rainfall variations at the Hanford Meteorology Station, Washington for the period 1947 through 1966. 29 Now that CDF tables for variable T for the summer period have been determined, it is necessary to describe summer rainfall amount per event, PT. Analysis of Rainfall Per Event The next program, RAIN 3, does essentially the same for rainfall per event, PT, as RAIN I did for event interarrival time. That is, RAIN 3 finds the CDF for each month for the entire data record, calculates the statistical values using Equations 4, 5, 6, and 7, and finally, it calculates the t-test values to facilitate the grouping of statistically non-different months concerning PT. Groups made with the variable PT need not consist of consecutive months since the PT variable does not exhibit the phenomenon of extending beyond one month into the next that T possesses. Figure 8 presents a flow chart of the operational logic represented in RAIN 3. A complete computer listing of the program and output for the Hanford data can be found in Appendix D. A listing of the sequence of values that allow the conductance of the t-test can be found in Appendix E. After running RAIN 3 using the Hanford data and conducting the t-test, the following grouping was found: Group 1 MAR Group 2 JUN Group 3 All other months. 30 However, since the winter months of NOV-DEC-JAN-FEB were analyzed separately, it was necessary to separate this period from Group 3. Therefore, the final grouping for the random variable of PT is: Group 1 MAR Group 2 JUN Group 3 APR MAY-JUL-AUG-SEP-OCT. - In Appendix F, a computer listing of RAIN 4 can be found. This program calculates the CDF for rainfall per event for the final Group 3. The CDF table and its statistical values are also given in this appendix. This program is designed to be run for a single group unlike RAIN 2 which runs for all groups describing T. At this point, we have nine distributions describing the time to the next rainfall event and the amount of rainfall that occurs for each event for the months of March through October. It is now necessary to describe the winter period precipitation process. Winter Precipitation Analysis The winter period of NOV-DEC-JAN-FEB was modeled differently from the remainder of the year due to the greater occurrence of frontal-type storm activity. Frontal storms are characterized by successive days of 31 I=1 I 5 DATA I=I+1 (n) CATAGORIZE PPT AMOUNT/ EVENT/MONTH INTO CLASSES r CALCULATE PDF & CDF TABLES FOR EACH MONTH CALCULATE STATISTICS FOR EACH DISTRIBUTION -- CALCULATE STUDENT T-TEST PARAMETERS STOP Figure 8. Flow chart for the rainfall per event variable analysis (RAIN 3). 32 precipitation associated with a single storm system. For this reason RAIN 5 was developed to analyze climatic data in reference to storm groups and sequences. A storm group is equal to any number of successive days of precipitation while a storm sequence is one or more groups separated by a certain number of dry days. RAIN 5 develops the five distributions that describe frontal-type storms and which were listed in Chapter 2. Reference is made again to Figure 2a which gives a graphic display of these five components. A flow chart of RAIN 5's operational logic is given in Figure 9 and a complete computer listing of the program can be found in Appendix G which includes output describing the Hanford data. The original program was written to analyze data from northern Arizona (Hekman 1977; Hekman 1980). RAIN 5 is a modified version of the original in that its output furnishes a CDF table and statistics for each distribution. These are found in the same manner as described for RAIN 1. Another major difference is in the calculation of a sixth distribution called the interarrival time to the next storm, DB. The sixth distribution was incorporated into RAIN 5 because of the inability to fit theoretical distributions to the variables D, the number of dry days between groups 33 START LOAD WINTER DATA OUTPUT DISTRIBUTIONS STOP GROUP DURATION (STORM LENGTH NO. OF DRY DAYS BETWEEN GROUPS (STORMS) GROUPS PER SEQUENCE NO. OF DRY DAYS BETWEEN SEQUENCES PRECIPITATION PER GROUP (STORM) INTERARRIVAL TIME TO NEXT STORM Figure 9. Flow chart for the analysis of variables describing the winter storm periods (RAIN 5). - 34 and B, the number of dry days between sequences for the Hanford data. Hekman (1977) found that in mountainous regions of Arizona, the dry days between groups principally ranged from one to three days and that a uniform theoretical distribution fitted D. However, the Hanford data did not lend itself to an easy theoretical distribution matchup. The six distributions describing the winter precipitation process at the Hanford site are included in Appendix G. DB is simply the combining of D and B distributions. By grouping these two distributions into one, the distribution describing the number of groups per sequence, ANO, was no longer needed. Therefore, when required as with the Hanford data, the original five distributions describing the winter process can be reduced to only three distributions which define a storm as being the same as a group. These distributions are: 1. W, storm duration in days, 2. DB, interarrival time between storms in days, and 3. RP, precipitation per storm. Figure 2b presents a graphic display of these three input components. Figure 2 allows a comparison of the threeand five-distribution methods. Both procedures are descriptive of the frontal type storm systems of winter precipitation activity. 34 Therefore, for any set of historical data, it is necessary to obtain the six distributions from RAIN 5, and then study the PDF's for D, B, and DB. From this study, the number of dry days between groups that will constitute a new sequence may be determined. RAIN 5 produces a distribution for D with intervals ranging from one to three days. If, for example, a data file produces a PDF for the one day and two day classes that are the same but the third day class is substantially different, then the variable D should be adjusted to range from one to two, and the third day class placed onto the variable B. If normality is not shown in any of the intervals of D, then it may be possible to utilize the variable DB and the three-distribution method for describing the winter precipitation. In summary, from RAIN 1 through RAIN 5 it is possible to develop all the necessary random variables needed to describe the yearly rainfall process for a given location. To model these variables, it is necessary to fit a theoretical or hypothetical distribution to each of the actual variable distribution groups. Then, the hypothetical distributions are used to model the real processes. 35 Theoretical distributions that may be used are a Gamma, Geometric, Exponential, Normal, or any other, that may fit the actual distribution. Appendix H lists three FORTRAN programs that develop a Gamma, Geometric and Exponential distribution based on the actual data statistics (mean, variance, lambda and K). These three hypothetical distributions are generally all that are needed to describe the rainfall process. Fitting Theoretical Distributions Comparison or goodness-of-fit tests can be conducted between the observed and the hypothetical distributions in order to find a theoretical distribution to describe each of the actual distributions. The test used was theKolmogorvSmirnov (K-S) test (Benjamin and Cornell 1970). This test concentrates on the deviations between the hypothesized CDF [Fx(x)] and the observed CDF [F(x)] . The statistics for this test are D = max i=1 [IF (Xi) - Fx (Xi) I] and ( 10 ) C a,n= In words, D is the largest of the absolute values of the n differences between the hypothesized CDF and the observed CDF evaluated at the observed values in the sample. Ca,n is the critical statistic for the K-S test. The k is a tabular value that is dependent on the level of significance (a) 36 chosen and the sample size (n). Table 2 gives a range of k values depending upon the a and n. A significant level of a = 0.05 (k = 1.36) was used in this paper. By knowing the distribution of the D statistic and the critical value C, the performance of an hypothesis test may be conducted. For the K-S test, the hypothesis test states that: H o : F(X) has a specified distribution H 1 : the distribution of F(X) is other than that specified. The form of the operating rule is: Accept H o if D < C. If H o is accepted, then there is no significant difference between the two distributions. When conducting the K-S test, it is possible to have difficulty in finding a hypothetical distribution that will fit a distribution consisting of grouped monthly data. This was the case in fitting distributions to several of the event interarrival time groups of the Hanford data. As stated before, the original grouping developed from the student t-test of RAIN 1 had to be changed. This was due to the failure of fitting hypothetical distributions to several of the groups. For example, the original interarrival time of Group 2 which 37 Table 2. Critical statistic (Ca) for the KolmogorovSmirnov test. Sample Size (n) a= 0.10 Œ = 0.05 a= 0.01 5 0.51 0.56 0.67 10 0.37 0.41 0.49 15 0.30 0.34 0.40 20 0.26 0.29 0.35 25 0.24 0.26 0.32 30 0.22 0.24 0.29 40 0.19 0.21 0.25 n > 40 1.22/ n 1.36/ n 1.63/ n From Benjamin and Cornell (1970). 38 consisted of MAR-APR-MAY-JUN had to be broken up until a distribution could be fitted to each smaller grout). The final breakdown for this example was that MAR and JUN had to be modeled separately from the APR-MAY group. When dealing with the actual distributions, it is sometimes necessary to develop a shifted distribution in order to find an hypothetical distribution to fit the grouped data (Hekman 1980). What this means is that the first interval or class of the actual distribution is taken off and modeled separately from the remaining classes. New statistical parameters are found for all data greater than the interval taken off. These new statistics are used to develop another hypothetical distribution, which is then tested against your shifted actual distribution using the K-S test. When fitting theoretical distributions to the Hanford data, four interarrival time groups were required to be shifted in order to model them. In summary, the hypothetical distributions are developed and actual distributions, if needed, are shifted until K-S test reveals that a theoretical distribution exists that fits each of the random variable distributions describing the data. The results of the K-S testing on the random variables describing the Hanford data is shown in Table 3. This table gives the observed random variable grouping and then the associated theoretical distribution. 39 Table 3. Final listing of observed distributions of interest and their matching hyopthetical distributions. Observed Distribution Hypothetical Distribution Winter Storm Period Inter time to next storm, DB Geometric Duration of storm, W Geometric Precipitation amount for storm, RP Gamma Remainder of the Year Interarrival Time, IT MAR Gamma APR-MAY Shifted Gamma JUN Geometric JUL Shifted Gamma AUG-SEP Shifted Geometric OCT Shifted Geometric Precipitation Per Event, PT MAR Gamma JUN Gamma APR-MAY-JUL-AUG-SEP-OCT Gamma 40 The steps described in this chapter are listed here. 1. Develop monthly distributions describing event interarrival time using RAIN 1 and group statistically non-different months using T-test. 2. Develop distributions of grouped data using RAIN2. 3. Determine winter storm period from grouping developed in Step 2. 4. Fit theoretical distributions to each group describing summer event interarrival time found in Step 2. a) Make any further group breakdowns or shifts of actual distributions, if necessary. b) Rerun RAIN 2, if original grouping is changed. 5. Conduct steps 1, 2, and 4 for precipitation per event using RAIN 3 and RAIN 4. 6. Develop distributions explaining the winter storm period using RAIN 5. 7. Determine the number of dry days between groups that will constitute a new sequence. This is done by studying the PDF developed for the variable D, B, and DB in step 6. 8. Reevaluate RAIN 5 using decision from step 7. 9. Fit theoretical distributions to random variables determined to describe winter precipitation. 41 10. Summarize results from above steps as shown in Table 2. 11. Proceed to rainfall/runoff model development. This chapter has explained the procedures to analyze historical data to the point where theoretical distributions have been found to describe each random variable of interest that in turn describe the annual precipitation process of a location. Once this has been achieved, the stochastic model for rainfall/runoff may be written. CHAPTER 4 STOCHASTIC RAINFALL/RUNOFF MODEL Once all random variables of interest have been determined, groupings have been made, and theoretical distributions statistically fitted to each distribution describing the data, the stochastic rainfall/runoff model may be written. For the Hanford Meteorology Station data, the probability distribution functions and associated parameter values used in sumulating winter and summer precipitation are presented in Tables 4 and 5. The two parameter gamma distribution was used to describe summer rainfall amount per event, PT, summer event interarrival time, T, for the groups of MAR, APR-MAY, and JUL, and winter storm rainfall amount, RP. The probability density function (PDF) for the gamma distribution is: Fx(x) K x K-1 e -Ax F (K) ( 12 ) where K is the shape parameter, Lamda (A) is the scale parameter and r (K) is the gamma function. gppendix I contains tables that list gamma functions values for any K between 0 and 2. The random variable X in Equation 12 represents either T (days), PT or RP. 42 43 Table 4. Probability distribution functions (Theoretical Distribution) and associated parameter values used in simulating winter precipitation. Precipitation Component (Random Variable) Interarrival time to the next storm, DB Duration of storm, W Precipitation amount for the storm, RP Probability Distribution Function Geometric x = 4.5223 Geometric Gamma X Paramater Value = 1.991 = 2.9956 K = 0.5906 44 Table 5. Probability distribution functions (Theoretical Distribution) and associated parameter values used in simulating summer precipitation. Precipitation Component (Random Variable) Precipitation per event For month of MAR Probability Distribution Function Parameter Value Gamma X = 1.1223 K = 0.8372 Gamma X = 4.3553 K = 0.5998 For months of APR-MAY- Gamma JUL-AUG-SEP-OCT X = 5.5109 K = 0.5384 For month of JUN Event interarrival time For month of MAR For months of APR-MAY: 1 day > 1 day Gamma X = 0.1682 K = 0.7241 Fixed Gamma P = 0.300 X = 0.1412 K = 0.8682 For month of JUN For month of JUL: < 31 days 31 day For months of AUG-SEP: 1 day > 1 day For month of OCT: 1 day > 1 day Geometric Gamma x- = 4.959 X = 0.1260 K = 1.0723 Fixed P = 0.895 Fixed Geometric P = 0.228 Fixed Geometric P = 0.379 x = 9.313 x- = 5.517 45 Because the CDF for the gamma distribution is not in closed-form, a simple numerical integration method developed by Hekman (1977) was used to transform the fitted PDF's into tables depicting their respective CDF's. Appendix J gives a program listing of this numerical integration. The geometric distribution was used to describe summer T for the groups of JUN, AUG-SEP and OCT, and as well as the winter distributions of storm interarrival time, DB, and duration of storm, W. The PDF for the geometric distribution is: Fx(x) = (1-p) x- 1 p (1 3 ) where the random variable X represents either T (days), DB (days) or W (days). The parameter p represents the distribution mean (R) and 0

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'... EM2=2=22=222222= .... %% I r 0 .-In. . Aouanbaij anuoia8 nn• Ls 4-) MI rC:S r-1 .P O 0 -.-1 0 0 4-) C11 -r-1 a) $-1 › (4i Q) 04 5P O O • r-i 0-1 44 58 event was calculated using the SCS method described in Chapter 2. The basic steps in generating the synthetic precipitation record are listed below. 1. The calendar day is set equal to zero. 2. The calendar day is checked to determine in which precipitation season the simulation process is currently operating. If winter is indicated, go to step 3; if summer is indicated, go to step 4. 3. The winter procedure is requested. a) Generate the number of days to the next storm (DB). If the calendar day now falls within the summer season, go to step 3e. If the calendar day is greater than the year length, reduce it by the year length. Update antecedent moisture. b) Generate the duration of the storm in days (W) and update calendar. C) Generate storm precipitation (RP) in inches and spread evenly over all the days in the storm. d) Calculate the amount of any surface runoff, store all values generated into appropriate arrays, and go to step 2. 59 e) Set calendar to last day of winter group. 4. The summer procedure is requested. a) Generate event interarrival time (T) in days, increase calendar, and update antecedent moisture. b) Generate rainfall amount. c) Calculate the amount of any surface runoff, store all values generated into appropriate arrays, and go to step 2. The above steps were repeated until 500 years of synthetic precipitation record was obtained. Figure 22 gives a flow chart of RAIN 6's operational logic, while a complete computer listing of the program can be found in Appendix K. As stated, the above program uses athree-distribution method for describing the winter storm period. If using the five-distribution method 3. a) Generate the number of dry days between sequences (B) and increase the calendar by this amount. If the calendar day now falls within the summer season, go to step 3f. If the calendar day is greater than the year length, reduce it by the year length. Update antecedent moisture. 60 Figure 22. Flow chart for the stochastic rainfall/runoff model for the Hanford Meteorology Station. 61 b) Generate the number of groups per sequence (ANO). Generate group length (w) in days, increase calendar, and update antecedent moisture. d) Generate group precipitation (RP) and spread evenly over all the days in the group. Calculate the amount of any surface runoff. e) If all groups in the current sequence have been serviced go to step 2; otherwise, generate the number of dry days between groups (D), increase calendar, update antecedent moisture, and go to 3c. f) Set calendar to last day of winter group. Model Response To determine whether or not the model was indeed representing the actual precipitation process at the Hanford site, two checks were conducted. First, the actual mean annual precipitation for the 20 years of data was compared to the simulated mean produced by the 500 years of synthesized record. The actual mean was 6.86 inches while the simulated annual mean was 7.66 inches. This results in a percent difference of 11.66. Figure 23 compares the relative fraquencies between the actual and 62 ti- o o in •Przzr r Por VIEM Aouenbeid an14 0 1 9 8 0 63 synthetic rainfall per event distributions. As can be seen, the comparison is very good. The second check was to develop 5000 values for each of the twelve distributions describing the precipitation processes and the twelve corresponding distributions. Table 6 lists the historic and synthetic means and variances for the twelve precipitation components. Although there was close agreement between the actual and simulated parameter values, the non-normality of the distributions involved preclude a statement of goodness-of-fit based on these parameter values only. Therefore, the KolmogorovSmirnov test was used to determine the goodness-of-fit between the probability distributions of the precipitation components for the observed and synthesized records. At an a level of 0.05, no distribution pairs could be said to differ. Therefore, the simulation procedure provides a satisfactory representation of actual precipitation events. Model Results The results or output of the stochastic model describing rainfall and runoff at the Hanford site is also given in Appendix K. This output consists of a listing of daily simulated precipitation amounts for any given number of years, and distributions showing synthetic event interarrival time, precipitation per event, and event runoff. • • 64 co al d' • Ln cp .-1 re) re) cm in 0 N • • N en di ri i Lo rn H • CD ri a% cs ro rn I I o co cn n I - I m 1/4s) co o 0 i.0 Ci ri cr) ,-I o (n co h .-I co . , i -v CI N - rH N N O IX k.c) N d' h N Crl • . ce) • -:), rn cr, N ri ri In 1-4 I t.o s k.0 lD • m • 0 I I r .v ni • crn rH • œ til h . o • 0 0 01 cr, cr, al 0 • 0 I n.0 • N I • ri ri N h Cf1 ON *If LL) -r, Ln en CO r,-) . . o') r-- cs . Ln N 01 Ln h 0 d' ce) 111 Cf1 N CD m h N 01 LC) rn Ln -4.. . co . co 0 d' CD ri ri • 0 N 03 rn r i - 0 0 0 0 N LII • dr co h di CO lo h 0 k.0 CD h 0 CD • ,-I N CO ri CO h N CO N 01 N h en k.o IC) 01 Lo 03 I ,--i o o . . . r n 0 o co 0 N . rH Lf) i-i . qp ,--i Ln .,:r es • • N Ln N M cn Cl • ri I en . k.0 co tr) h . . lf) d' 0 . CO d' ri k.0 N 'd' co cr 0 i..0 d' C)I CO • • • LI'l 03 Cf) CO N re) N 0 ri co 0 0 N ce) ri t.fl • N h 1/4D (")1 ✓i h Lf1 0) 01 h 01 ri 0 • • ri CO CO '''ZI. 01 h co cs, k.0 0 0 tfl h CO N ri 0 cf) pl cr% ri CD CD 0 0 in Cf) • • dr L.r1 d CO ri • 0 CO d' d' • ✓H ••••n• ••••••• >4 al l a P.1 4 ..... 2 + D - -... a I D ..- - r=1 cn 1 c..9 4 — Q) a) -H -H - ri +-) Cd cd -H -H }-4 Cd rd Q) 4-) -H •H 4-1 .4--1 Q) (1 ) rs — E-i C..) 0 65 These distributions give both the PDF and CDF values. When concerned with the water harvesting potential of a site, the distribution of main interest is that giving the amount of surface runoff. This model was run using several different curve numbers (80, 70 and 60) and two different initial abstractions (0.2S and 0.15S) to obtain a moderate range of runoff values. Figures 24 and 25 show the relative frequency distribution for each of the combinations of two initial abstractions with the three curve numbers. There was a certain degree of difference between the two different initial abstractions with the Ia = 0.15S being nearly twice the 0.2S value for total number of runoff events. It can be seen that in all six cases the runoff events that were less than 0.05 inches makeup greater than 75 percent of the total events. The higher curve numbers have a larger total number of event runoff. It is relatively simple to see that by increasing the curve number (or initial abstraction) for a given site the total amount of runoff can be greatly increased. One of the main concerns in water harvesting is increased runoff, which is obtained by one or more of the practices mentioned in Chapter 1. 66 CN = 80 Ia = .2S n = 272 .2 .4 .6 .8 Runoff (Inches) CN = 60 LL. 0 .4 > la =.2S n :21 CN= 70 = .2S n = 61 o .2 .4 .2 .4 Runoff (Inches) Figure 24. Relative frequencies of three different curve numbers with an Ia = 0.2S for 500 years of synthetic rainfall at the Hanford Meteorology Station. 67 CN= 80 Ia = .15S n= 499 .2 .4 .6 .8 Runoff (Inches) 0 .6 . CN=.60 CN= 70 LL.. II Ia =.I5S n = 42 a ) .4 la = .I5S n =135 0 .2 .4 .2 .4 Runoff (Inches) Figure 25. Relative frequencies of three different curve numbers with an Ia = 0.15S for 500 years of synthetic rainfall at the Hanford Meteorology Station. CHAPTER 5 CONCLUSION To facilitate the determination of the water harvesting potential on western mine sites, it is important to be able to analyze readily available climatic data for a given location and develop from the data analysis a model that will simulate precipitation and runoff. The series of FORTRAN programs developed for the Hanford site describe a step by step progression toward the final simulation model. Given a sufficient amount of daily climatic data (at lease 20 years) one can quickly obtain a grouping of statistically like months regarding precipitation per event and interarrival time from RAIN 1 and RAIN 3. The t-test that was conducted in RAIN 1 and RAIN 3 results in an initial grouping of months for modeling purposes. However, it may be required to adjust the initial grouping if difficulties arise when fitting hypothetical distributions. When grouping months for the distribution of precipitation per event, it is not necessary to have consecutive months within a group, since what happens in one month does not affect what happens in the adjacent month. In the distribution of interarrival time, however, 68 69 it is necessary to develop the groups with consecutive months. This is due to the overflow effect that interarrival time has from one month to the next. Once the winter period grouping has been found from RAIN 1, the distributions describing the winter period (assuming this period is characterized by frontaltype storms) may be derived from RAIN 5. After all distributions describing the watershed have been fitted to hypothetical distributions, adjustments to RAIN 6 may be made. These adjustments consist mainly of changing the groupings and their corresponding hypothetical distributions. Usually only the Gamma, Geometric, or Exponential distribution will be needed to model precipitation per event, interarrival time, and the winter storm components. Only the Gamma, Geometric, shifted Gamma, and shifted Geometric distributions were required to model the Hanford data. The final output of the stochastic model is a listing of the three distributions: interarrival time, precipitation per event, and runoff for the desired simulated period. The actual mean annual precipitation at the Hanford site for the 20 years of data analyzed was 6.86 inches. The stochastic model produced an average annual rainfall 70 for the 500 simulated years of 7.66 inches. This is a difference of 0.80 inches or 11.66 percent higher than the observed mean. This difference is small and can be attributed in part to inaccuracies in the approximation of the simulated CDF to the observed parameter distribution as well as the failure of the model to predict more accurately the winter storm precipitation. These errors accumulate in the precipitation term. Another source of error in precipitation simulation may have been introduced at the beginning and end of each season. It was necessary to assume specific dates for the transition from summer to winter event simulation. Since the exact change between seasons is never quite that predictable, it is probable that this assumption led to occasional errors in defining observed data event types. Although errors of varying magnitudes do exist in the simulated distributions, in no case are they large enough to cause rejection of the K-S test null hypothesis using acceptable significance levels. Taken as a whole, the simulation procedure provides a satisfactory representation of actual precipitation events. As stated, the runoff distribution produced by the model is dependent on the curve number assigned to the 71 watershed and to a lesser extent upon the initial abstraction value used. Sufficient historical runoff data would allow a sensitivity test to be conducted to obtain a curve number for the watershed. This curve number could then be applied to the model to derive a runoff distribution that better represents the watershed. However, historical runoff data are not often available; therefore, an estimate curve number will be required for the watershed in question. For model development, a series of curve numbers (80, 70, and 60) were used as well as two values of initial abstraction (0.2S and 0.15S). The printouts of the consecutive runs of the model reveals that as the curve number increases or the initial abstraction decreases, the amount of direct surface runoff increases. Most of this increase of runoff is due mainly to the greater number of smaller events. Changes in watershed practices can be studied using this model since any practice that lowers or increases the watershed curve number will produce a different runoff output. Provided adequate data are available, the procedure developed in this study can be applied on other sites. Necessary changes may include redefining the storm sequence 72 scheme for the winter period. Given sufficient data for the model and providing precipitation parameters are appropriately defined, these procedures can be a valuable tool for determination of the hydrologic characteristics of any site. 73 APPENDIX A PROGRAM LISTING OF THE EVENT INTERARRIVAL TIME ANALYSIS (RAIN 1) AND OUTPUT DESCRIBING THE HANFORD DATA. 74 1 2 3 4 5 6 7 PROGRAM RAIN1 (INPUT,OUTPUT.1A 0 E2.1UTPUT,T(PE3) DIMENSION DATA(8),KPPT(40,12),PnF(40).CnF(40) DIMENSION AVE(12), VAR(12), ITOTAL(12) REAL (,LAMDA,MEAN.NUM2 DATA KPPT , PDF,CDF/460 1 0,40*0.,40*0./ C CA•• 8 C 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 C C C C C C C C C C C C C C C C C C C C C 29 30 31 C C 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 C C C C C C C C C C C C C C C C ( C C C C C C C C C C C C C 62 C 63 64 65 66 67 C C*** THIS PROGRAM CALCULATES THE POE , COE AND STATISTICS FOR THE INTERARRIVAL TIME PER MONTH FOR THE PERIOD OF HISTORICAL RECORD BEING ANALIZED. IT ALSO CALCULATES THE COMPUTED T-.VALUE AND THE DEGREES OF FREEDON FOR EVERY COMBINATION OF TWO MONTHS. THIS ALLOWS FOR A VISUAL COMPARISON (T- TEST) TO BE MADE TO SEE WHICH MONTHS ARE STATISTICALLY MON DIFFERENT IN ORDER TO GROUP THEM. - TO ADAPT THIS PROGRAM TO ADJUST THOSE LINES ASSUMES THAT THERE IS ANALIZED. THEREFORE, WITHIN THE DATA FILE. FOR A SPECIFIC DATA RECORD, IT IS NECESSARY MARKED BY THE SYMBOL *ADJUST*. THIS PROGRAM A DATA FILE FOR EVERY DAY OF THE YEAR BEING MISSING DATA MUST BE REPRESENTED BY A VALUE VARIABLE LIST DATA(I) • THE DATA ARRAY DATA(1) • MONTH DATA(2) • DAY DATA(3) • YEAR DATA(7) • PRECIP AMOUNT KPPT • A TWO DIMENSIONAL ARRAY FOR STORAGE OF INTERARRIVAL TIME ON A MONTHLY BASIS IDAY • LAST DAY OF RAIN (DAY • NEW DAY OF RAIN NDAY • NUMBER OF DAYS IN MONTH JDAY • DAYS OF INTERARRIVAL TIME LDAY • COUNTER LMONTH • GROUP NUMBER (OF MONTHS) MMONTH • GROUP NUMBER M • MONTH COUNTER MM • GROUP NUMBER (OF MONTHS) NNDAY • LENGTH OF SKIPPED MONTH NUM2 • MONTH COUNTER NUM3 • COUNTER NUM4 • COUNTER IYEAR • THE YEAR AS AN INTEGER VALUE ILEAP • THE LEAP YEAR VALUE NO LEAP YEAR LEAP • 0 THE YEAR IS A LEA* YEAR LEAP • 1 POE • PROBABILITY DENSITY FUNCTION CDT • CUMULATIVE DENSITY FUCNTInN END • COUNTER REPRESENTING INTERARRIVAL TIME ITOTAL • COUNTER FOR STATISTICS CALCULATION JTOTAL • COUNTER FOR STATISTICS CALCULATION TOTAL • COUNTER FOR STATISTICS CALCULATION AVE • AVERAGE VALUE VAR • VARIANCE LAMOA • STATISTICAL PERAMETER FOR THE GAMMA DISTRIBUTION K • STATISTICAL PERAMETER FOP THE GAMMA DISTRIBUTION C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C NUM2•1. 'DAY.° DO 80 1•1,7305 68 69 70 71 72 73 C 10 C C** C READ(3,10) DATA FORMAT(F4.0,2F3.0,F4.0,2F5.0,2F6.3) IS THE NEW PRECIP EVENT IN THE SAME MONTH AS THE PREVIOUS EVENT IF(DATAII).NE.Num2I Go To 40 *ADJUST* 75 74 75 76 77 7e 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 C C** C 20 C C** C YES. THE NEW PRECIP EVENT IS IN THE SAME MONTH AS THE PREvTOUS ("NE KDAywiNT(DATA(2)+.51 END OF DATA CHECK IF ) I.E0.73051 GO TO 30 C C** C *ADJUST* ARE WE IN A LEAP YEAR IYEAR.INTIDATA(3)4.51 ILEAP*IyEAR/4—(IYEAR-1 ) /4 C C** C HOW LONG IS THE MONTH THAT WE ARE IN IF(DATA)11.E0.1.1 N0AY*31 IFIDATA(11.E0.2.) NDAyw28 IF(DATA(1).E0.2..AND./LEAR.E0.11 NDAy.26 IFIDATA(1).E0.3.) NDAY.31 IFIDATA(11.E0.4.) NOAyw30 IFIDATA(1).E0.5.) NOAyw31 IF(DATA(1).E0.6.1 NDAY.30 IF(DATA(1).E0.7.) NDAy.31 IF(DATA(1).E0.8.) NoAy.31 IFIDATA(1).E0.9.1 NDAyw30 IF(DATA(1).E0.10.) NDAY.31 IF(DATA(1).E0.11.) N0Aym30 IFIDATA(1).E0.12.1 N0Ay.31 C C** C IS THIS pRECIP EVENT mEAluRABLE OR NOT m.INT(DATA(1)+.5) IFIDATA(7).LT.0.011 GO TO 80 C C** C CALCULATE INTERARRIvAL TIME AND STORE IT JOAywKDAy—IDAy INDwJDAy KppT(IND01).KPIDT(IND,m)+1 IDAywKDAy GI TO 80 C 30 C C* • C** C** Cs* C** C 40 C C** C 50 60 C C** C IDAywKDAy WE HAVE MOVED INTO A NEW MONTH WE NOW PROCESS THE END OF THE OLD MONTH AND PROCESS THE REG/NNING OF THE NEW moNTH IF A MONTH HAS No MEASURABLE pRECIP (IT IS SKIPPED) THAN IT IS PROCESSED HERE IN.D.NDAy—IDAy IF(INO.E0.0) GO TO 50 (PP1(IND.m).KPRTIIND,P)+1 END OF DATA CHECK IFII.E0.73051 GO TO 80 IDAywO NUM2*NUM241. IFINUM2.E0.13.1 Ga TO 70 IF(DATA(1).E0.Num2) GO TO 20 M01+1 ARE WE IN A LEAP YEAR IYEAR.INT(DATA(3)4.5) ILEAP*IyEAR/4—(IyEAR-1)/4 C C** C HOW LONG IS THE MONTH THAT WE ARE maw IN IF(NUM2.E0.1.) NDAY•31 IFINUM2.EQ.2.1 N0Ay428 IFINuM2.E0.2..AND.ILEAR.E0.11 NDAY.29 IF(NuM2.E0.3.) NDAY.31 *ADJUST* 76 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 109 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 219 219 220 221 222 223 70 80 C C C C IF(NUM2.E0.4.) NDAY.30 IF(NUM2.E0.5.) NDAY.31 IF(NUM2.E0.6.) NDAY.30 IF(NUM2.E0.7.) NOAY.31 IF(NUM2.E0.8.) NDAY.31 IFINUM2.E0.9.1 NDAY.30 IF(NUM2.E0.10.) NOAY.31 IF(NUM2.E0.11.) N0AY.30 IF(NUM2.E0.12.) NOAY.31 KPPT(NDAY,M).KPPTINDAY,N)+1 GO TO 60 IF(NUM2.E0.13.) NUM2.1. GO TO 20 CONTINUE C** THIS C go 100 110 C C... C 120 C 0.4, Cs. SECTION CALCULATES THE DOF AND CDF DISTRIBUTIONS FOR EACH MCNTH DO 130 I.1,12 ITOTAL(I).0 DO 90 4.1.40 ITOTAL(I).BPDT(J,I)+ITITAL(I) CONTINUE DO 110 J.1,40 IO•,/ PDF(J).ELOAT(OPT(J,I))/ITOTAL(I) IF(IO.E0.1) GO TO 100 CDF(.1).00B(J-1).P0F(J) GO TO 110 CDF(.1).PDF(J) CONTINUE WRITE OUT HEADING AND DISTRIBUTION WRITE(2,1000) I WRITE (2,2000) WRITE(2,3000) JTOTAL.0 TOTAL.O. DO 120 N.1,40 WRITE(2,4000) MoKPPT(M,I),PDF(M),CDF(M) TOTAL.TOTAL.(MB*2).BRPT(M,I) JTOTALs(N.BPPT(M,I)).JTOTAL CONTINUE CALCULATE THE MEAN, VARIANCE, LAMDA, AND K VALUE FOR THE DISTRIBUTION AND WRITE THESE VALUES OUT C 130 C. C C** Co* CI,* C55 AVE(I)*(JTOTAL40.)/(ITOTAL(1).0.) VAR(I).(1OTAL—(JTOTALB*2/1TOTAL(I)))/(ITOTAL(I)-1.) LAMDA.AVE(I)/VAR(I) K.AVE(I)1.02/VAR(I) WRITE(2,5000) ITOTAL(I),JTOTAL WRITE(2,6000) AVE(I),VAR(I) WRITE(2,7000) LAMDA,K CONTINUE THIS SECTION CALCULATES THE DEGREES of FREEDOM AND THE STUDENT T — VALUE FOR EACH COMB/NATION OF TWO MONTHS. A LISTING OF THESE VALUES ARE PRINTED OUT TO FACILITATE THE CONDUCTANCE OF A STUDENT I.—TEST FOR GROUPING OF STATISTICALLY NON—OIFFERENT MONTHS. WRITE(2,8000) N•2 DO 150 N.1,11 DO 140 L04,12 0F.(VAR(J)IITOTAL(J)+V4R(L)/ITOTAL(1))**2/(MVAR(J)/ITCTA CL(.1))."02)/(ITOTAL(J)-1)1.(MAR(L)/ITOTAL(L))**2)/(ITOTAL(1)-1))) T.(AVE(J)—AVE(L))/(SORTMAR(J)/ITOTALIJ))*(VAR(L)/ITOTAL( CL)))) 77 224 225 226 227 228 229 230 231 232 233 234 WRITE(2,1111) J.L. WRITE(2.2222) OF,T WRITE(2,3333) WRITE(2.4444) 140 CONTINUE J*J.1 150 CONTINUE 1000 FORMAT(m1",///p9X, m FREQUENCY DISTRIBUTION OF INTERARRIVAL TIME FO CR MONTH "0. 67,12) FORMAT(1/,10X." INTERARRIVAL"~'OCCURENCE5",8%,"PDF",13WCDF.) FORMAT(13W (DAYS)",/) FORMAT(15X.I2.15X.I4,10X,F7.5.10K,F7.5) FORMAT(//,10X. TOTAL NO. OF OCCURENCES. ".I4.1/,10X." TOTAL NO. 0 CF INTERARRIVAL DAYS ,. ".I5) 6000 FORMAT(/.10X." MEAN. "tf6.3,10)(P.VARIANCE. ,F8.4) 7000 FORMAT(/,10X, * LAMDA. m.F7.4,8X..K. ".F7.4) 8000 FORMAT(n1"olOW . HYPOTHESIS TEST LNVOLVING MEANS (ASSUMPTIONS MADE CARE",/.10W THAT THE ACTUAL VARIANCES ARE NOT KNOWN AND ARE Nnt E CQUAL)",///) 1111 FORMAT(10%,"MONTHS BEING COMPARED"0. 34,12.T38.VS.".1. 44,I2,/) 2222 FORMAT(15WOEGREES FREEDOM.".T33,F7.3./.15WCOMUTED T VALUE.".F7 C.3,/) 3333 FORMAT(15X,NTABULAR T 4444 FORMAT(15X.mRESULTS OF TEST•.•"../15X."IS THERE A SIGNIFICANT DIFfE CRENCE".10WYES".10X,"NO",,f) 2000 3000 4000 5000 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 2 52 STOP END 78 FREQUENCY DISTRIBUTION INTERARRIVAL OF INTERARRIVAL OCCURENCES TIME FOR MONTH POF (DAYS) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 93 27 16 21 13 5 2 2 5 2 .47692 .13846 .08205 .10769 .06667 .02564 .01026 .01026 .02564 .01026 .00513 .01026 .00513 .00513 0.00000 .00513 0.00000 0.00000 0.00000 .00513 0.00000 0.00000 .00513 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 .00513 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1 2 1 1 0 1 0 0 o 1 0 0 1 o o 0 o 0 0 1 o 0 o 0 0 o 0 0 0 0 TOTAL NC. OF CCCURENCES2 195 TOTAL NO. OF INTERARRIVAL DAYS- MEAN-m . LAMDAm 3.179 .2123 VARIANCE. Km .6751 620 14.9742 1 CDF .47692 .61538 .69744 .80513 .87179 .89744 .90769 .91795 .94359 .95385 .95897 .96923 .97436 .97949 .97949 .98462 .98462 .98462 .98462 .98974 .98974 .98974 .99487 .99487 .99487 .99487 .99487 .99447 .99487 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 79 FREQUENCY DISTRIBUTION OF INTERARRIVAL INTERARRIVAL OCCURENCES PDF (DAYS) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 '27 28 29 30 31 32 33 34 35 36 37 38 39 40 78 21 16 9 4 10 .48750 .13125 .10000 .05625 .02500 .06250 .02500 0.00000 .02500 .01250 .01250 .01250 0.00000 .00625 .01250 0.00000 0.00000 0.00000 .00625 .00625 0.00000 .00625 .01250 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 4 0 4 2 2 2 0 1 2 0 0 0 1 1 0 1 2 0 0 0 0 0 0 0 0 0 0 o 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0 0 0 0 0 0 TOTAL NO. OF OCCURENCES• TOTAL NC. OF INTERARRIVAL DAYSs MEAN. LAMDAs .1803 160 VARIANCE* 3.531 Ks TIME FOR MONTH .6367 565 19.5849 2 CDF .48750 .61875 .71875 .77500 .80000 • 86250 .88750 .88750 .91250 . .92500 .93750 .95000 .95000 .95625 .96875 .96875 .96875 .96875 .97500 .98125 .98125 .98750 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.e0000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 80 FREQUENCY DISTRIBUTION OF INTERARRIVAL TIME FOR MONTH INTERARRIVAL OCCURENCES PDF (DAYS) 1 2 3 4 5 6 7 51 26 16 11 5 8 2 5 2 5 2 0 0 2 1 2 0 e 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 .35417 .18056 .11111 .07639 .03472 .05556 .01389 .03472 .01389 .03472 .01389 0.00000 0.00000 .01389 .00694 .01389 0.00000 0.00000 .00694 .01389 0.00000 0.00000 .00694 0.00000 .00694 .00694 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 o 1 2 0 0 1 0 1 1 0 0 27 28 29 30 31 32 33 34 35 36 37 38 39 40 43 o 0 0 0 o 0.00000 0 0 0 0 0 0 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 TOTAL NC. OF OCCURENCES* 144 TOTAL NO. OF INTERARRIVAL DAYS* MEAN* LO D ** VARIANCE• 4.306 .1682 Ks .7241 620 25.6014 3 COF .35417 .53472 .64583 .72222 .75694 .81250 .82639 .86111 .87500 .90972 .92361 .92361 .92361 .93750 .94444 • 95833 .95833 .95833 .96528 .97917 .97917 .97917 .98611 .98611 .99306 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 81 FREQUENCY DISTRI8UTION INTERARRIVAL OF INTERARRIVAL OCCURENCES PDf (DAYS) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 36 19 12 11 4 3 7 4 4 1 3 3 1 2 0 2 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 .30508 .16102 .10169 .09322 .03390 .02542 .05932 .03390 .03390 .00847 .02542 .02542 .00847 .01695 0.00000 .01695 .00847 .00847 .00847 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 .00847 .00847 0.00000 .00847 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 TOTAL NC. OF OCCURENCESe TOTAL NO. OF INTERARRIVAL DAYS- MEAN- .LAMDAIN 5.085 .1552 118 VARIANCEKm TIME .7894 60 0 32.7521 FUR-MONTH 4 COF .30508 .46610 .56780 .66102 .69492 .72034 .77966 .81356 .84746 .85593 .88136 .90678 .91525 .93220 .93220 .94915 .95763 .96610 • 97458 .97458 .97458 .97458 .97458 .97458 .97458 .97458 .98305 .99153 .99153 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 82 FREQUENCY DISTRIBUTION OF INTERARRIVAL INTERARRIVAL OCCURENCES PDF (DAYS) 1 2 3 4 5 6 7 36 19 12 6 8 5 5 a .31579 .16667 .10526 .05263 .07018 .04386 .04386 .00877 .01754 .02632 .00877 .02632 .00877 0.00000 .02632 0.00000 0.00000 0.00000 .01754 .00877 0.00000 .00E177 0.00000 .00877 0.00000 0.00000 .00877 0.00000 .00877 .01754 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1 9 10 2 11 1 3 1 0 3 0 0 0 2 1 0 1 0 1 0 0 1 0 1 2 0 0 0 0 0 0 0 0 0 0 3 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 TOTAL NO. OF CCCURENCES. 114 TOTAL NO. OF INTERARRIVAL DAYS. MEAN. LAMDA. 5.439 .1218 VARIANCE. K. TIME FOR MONTH .6625 620 44.6460 5 CDF .31579 .48246 .58772 .64035 .71053 .75439 .79825 .80702 .82456 •85088 .85965 .88596 .89474 •89474 .92105 .92105 .92105 .92105 .93860 .94737 .94717 .95614 .95614 .96491 .96491 .96491 .97368 .97368 .98246 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 83 FREQUENCY DISTRIBUTION OF INTERARRIVAL INTERARRIVAL OCCURENCES TIME FUR MONTH PDF (DAYS/ 1 2 3 4 5 37 18 15 14 3 7 1 2 2 4 4 1 1 2 1 2 1 1 2 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 .30579 .14876 .12397 .11570 .02479 .05785 .00826 .01653 .01653 .03306 .03306 .00826 .00826 .01653 .00826 .01653 .00826 .00826 .01653 0.00000 0.00000 .00826 .00826 0.00000 0.00000 .00826 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 TOTAL NO. OF OCCURENCESs 121 TOTAL NO. OF INTERARRIVAL DAYS* MEANS 4.959 LAPIDA- .1696 VARIANCE* Km .8409 600 29.2417 6 CDF .30579 .45455 .57851 .69421 .71901 .77686 .78512 .80165 .81818 .85124 .88430 .89256 .90083 .91736 .92562 .94215 .95041 .95868 .97521 .97521 .97521 .98347 .99174 .99174 .99174 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 84 FREQUENCY DISTRIBUTION OF INTERARRIVAL TIME FOR MONTH INTERARRIVAL OCCURENCES PDF (DAYS) 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20 21 22 14 4 3 3 3 1 1 1 2 2 1 2 1 1 1 0 1 2 1 1 1 0 23 1 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 1 0 2 0 1 0 0 6 0 0 0 0 0 0 0 0 0 TCTAL NO. OF OCCURENCESo .24561 .07018 .05263 .05263 .05263 .01754 .01754 .01754 .03509 .03509 .01754 .03509 .01754 .01754 .01754 0.00000 .01754 .03509 .01754 .01754 .01754 0.00000 .01754 .01754 0.00000 .03509 0.00000 .01754 0.00000 0.00000 .10526 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 57 TOTAL NO. OF INTERARRIVAL DAYS MEAN' 10.877 VARIANCES , LAMDA° .1000 Ku 1.0874 620 108.8036 7 CDF .24561 .31579 .36842 .42105 .47368 • 49123 .50877 .52632 .56140 .59649 .61404 .64912 .66667 .68421 .70175 .70175 .71930 .75439 .77193 .78947 .80702 .80702 .82456 .84211 .84211 .87719 .87719 .89474 .89474 .89474 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 85 FREQUENCY DISTRIBUTION OF INTERARRIVAL INTERARRIVAL OCCURENCES TIME FOR MONTH POF (DAYS) 1 17 6 5 5 4 3 2 2 4 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 o 4 1 0 1 1 1 0 1 1 1 1 0 3 1 o 0 1 0 1 0 4 0 0 0 0 o 0 0 o 0 TOTAL NC. OF occuRENcEs. TOTAL NO. OF MEAN- INTERARRIVAL .1046 70 DAYS ° VARIANCE 8.857 LAMDAm .24286 .08571 .07143 .07143 .05714 .04286 .02857 .02857 .05714 0.00000 .05714 .01429 0.00000 .01429 .01429 .01429 0.00000 .01429 .01429 .01429 .01429 0.00000 .04286 .01429 0.00000 0.00000 .01429 0.00000 .01429 0.00000 .05714 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Km 7 • .9267 620 84.6522 8 CDF .24286 .32857 .40000 .47143 .52857 .57143 .60000 .62857 -.68571 .68571 .74286 .75714 .75714 .77143 .78571 • 80000 .80000 .81429 .82857 .84286 .85714 .85714 .90000 .91429 .91429 .91429 .92857 .92857 .94286 .94286 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 86 FREQUENCY DISTRIBUTION OF INTERARRIVAL TIME FOR MONTH INTERARRIVAL OCCURENCES PDF (DAYS) 1 2 3 4 5 6 7 17 6 5 a 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 .22078 .07792 .06494 27 28 29 30 31 32 33 34 35 36 37 38 39 40 TOTAL NC. OF OCCURENCESn a .1039 0 5 3 2 4 1 3 3 2 2 2 1 1 3 2 1 1 .06494 '603896 .02597 .05195 .01299 .03896 .03896 .02597 .02597 .02597 .01299 .01299 .03896 .02597 .01299 .01299 0.00000 .02597 0.00000 0.00000 0.00000 .96104 LAMDA• 7.792 .1491 0.00000 1.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.0000 0 0.00000 77 VARIANCE Kw 0.00000 .97403 .97403 .98701 .98701 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 .01299 0.00000 .01299 0.00000 .01299- TOTAL NO. OF INTERARRIVAL DAYSMEAN n CDF .22078 .29870 .36364 .46753 .53247 .57143 .59740 .64935 .66234 .70130 •74026 .76623 •79221 .81818 .83117 .84416 .88312 .90909 .92208 .93506 .93506 .96104 .96104 .96104 o 2 o o o 1 o 1 o 1 o o o o o o o o o o 26 9 1.1615 600 52.2763 87 FREQUENCY DISTRIBUTION OF INTERARRIVAL TIME FOR MONTH INTERARRIVAL OCCURENCES PDF (DAYS) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 .37857 .18571 .07143 .04286 .07857 .37857 .56429 .63571 .67857 .75714 5 .03571 .79296 2 4 6 3 1 2 0 1 1 0 2 1 1 2 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .01429 .02857 • 04286 .02143 .00714 .01429 0.00000 .00714 .00714 0.00000 .01429 .00714 .00714 .01429 0.00000 .00714 0.00000 .00714 .00714 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 .80714 .83571 .87857 .90000 .90714 .92143 .92143 .92857 .93571 .93571 .95000 .95714 .96429 .97857 .97857 .98571 .98571 .99286 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 INTERARRIVAL DAYS- 620 MEAN ° 4.429 VARIANCE s 27.1295 LAMDA• .1632 CDF 53 26 10 6 11 TOTAL NO. OF OCCURENCES* 140 TOTAL NO. OF 10 Ks .7229 88 FREQUENCY DISTRIBUTION OF INTERARRIVAL INTERARRIVAL OCCURENCES TIME FOR MONTH PDF (DAYS) 1 2 3 4 5 86 30 19 8 8 7 2 4 3 4 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 .46739 .16304 .10326 .04348 .04348 .03804 .01087 .02174 .01630 .02174 .04348 .00543 0.00000 0.00000 .00543 0.00000 .01087 0.00000 0.00000 0.00000 .00543 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 8 1 0 0 1 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 TOTAL NC. OF CCCURENCESs 184 TOTAL NC. OF INTERARRIVAL DAYS e MEAN- LAMDAn 3.261 .2535 VARIANCE* Ks .8266 600 12.8634 11 CDF .46739 .63043 .73370 .77717 .82065 .85870 .86957 .89130 .90761 .92935 .97283 .97826 .97826 .97826 .98370 .98370 .99457 .99457 .99457 .99457 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 89 FREOUENCY DISTRIBUTION OF INTERARRIVAL INTERARRIVAL 00CURENCES TIME FOR MONTH PDF (DAYS) 1 2 3 4 5 6 7 107 36 15 10 15 12 5 .50000 .16822 .07009 .04673 .07009 .05607 .02336 8 1 .00467 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 3 3 1 3 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .01402 .01402 .00467 .01402 .00467 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 .00467 0.00000 0.00000 .00467 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 TOTAL NC. OF C0CURENCESs TOTAL NC. OF INTERARRIVAL DAYSs MEANLAMDA• 2.869 .2917 214 VARIANCE. Km .8370 614 9.8357 12 0DF .50000 .66822 .73832 .78505 .85514 .91121 .93458 .93925 .95327 .96729 .97196 .98598 .99065 .99065 .99065 .99065 .99065 .99065 .99065 .99533 .99533 .99533 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.000,0 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 90 APPENDIX B OUTPUT LISTING FROM RAIN 1 OF THE SEQUENCE OF VALUES FOR CONDUCTING T-TEST GROUPING FOR EVENT INTERARRIVAL TIME. 91 -- HYPOTHESIS TEST INVOLVING MEANS (ASSUMPTIONS MADE ARE THAT THE ACTUAL VARIANCES ARE NOT KNOWN AND ARE NOT EQUAL) MONTHS BEING CCMPARED 1 VS. 2 DEGREES FREEDOM* 318.377 COMUTED T VALUE- n 6788 TABULAR T VALUEs RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 1 VS. MONTHS BEING CCMPARED YES NO YES NO YES NO YES NO YES NO YES NO 3 DEGREES FREEDOM 257.762 COMUTED T VALUE. TABULAR T VALUERESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 1 VS. MONTRS BEING COMPARED 4 DEGREES FREEDOM* 182.280 COMUTED T VALUE- •..3.201 • TABULAR T VALUES RESULTS Of TEST... IS THERE A SIGNIFICANT DIFFERENCE MjNTHS BEING COMPARED 1 VS. 5 DEGREES FREEDOMS 158.118 COMUTED T VALUE. .3.301 TABULAR T VALUEs RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. 6 DEGREES FREEDOM°. 196.128 COMUTED T VALUE* 3.153 TABULAR T VALUE' , RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. DEGREES FREEDOM= 60.568 COMUED T VALUEs.75.463 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 92 MONTHS BEING COMPARED 1 VS. 8 DEGREES FREEDOM* 77.929 COMUTED T VALUE* -5.006 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. YES NO YES NO YES NO YES NO YES NO YES NO 9 DEGREES FREEDOM* 93.695 COMUTED T VALUE* -5.306 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. 10 DEGREES FREEDOM- 243.585 COMUTED T VALUE* -2.401 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. 11 DEGREES FREEDOM* 376.881 COMUTED T VALUE* -.212 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE M3NTHS BEING COMPARED 1 VS. 12 DEGREES FREEDOM* 373.771 .886 COMUTED T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 2 VS. 3 DEGREES FREEDOM* 285.836 COMUTED T VALUE* -1.413 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 93 MONTHS BEING COMPARED 2 V. 4 DEGREES FREEDOM. 212.534 MILTED T VALUE* .2.456 TABULAR T VALUE* RESULTS OF TEST.., IS THERE A SIGNIFICANT DIFFERENCE 2 VS. MONTHS BEING COMPARED YES NO YES NO YES NO YES NO YES NO YES NO 5 DEGREES FREEDOM- 182.038 MILTED T VALUE- .2.660 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 2 VS. MONTHS BEING COMPARED 6 DEGREES FREEDOM- 228.169 COMUTED T VALUE* ••2.366 TABULAR T VALUE* RESLLTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 2 VS. MONTHS BEING COMPARED 7 DEGREES FREEDOM- 63.321 COMUTED T VALUE- •5.154 TABULAR T VALUE• RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED DEGREES 2 VS. 8 83.305 FREEDOM COMUTED T VALUE- -..4.615 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 2 VS. 9 DEGREES FREEDOM' 104.256 COMUTED T VALUE'-4.760 , TABULAR T VALUE.' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 94 MONTHS BEING COMPARED 2 VS. 10 DEGREES FREEDOM' 274.363 COMUTBD T VALUE" .1.596 TABULAR T VALUE" RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 2 VS. YES NO YES NU YES NO YES NO YES NO YES NO 11 DEGREES FREEDOM' 305,813 .617 COMUTED T VALUE" TABULAR T VALUE" RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 2 VS. 12 DEGREES FREEDOM' 272.175 CCMUTED T VALUE" 1.614 TABULAR T VALUE" RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. 4 DEGREES FREEDOM' 235.750 COMUTED T VALUE" .'1.155 TABULAR T VALUE' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 3 VS. 5 DEGREES FREEDOM" 205.430 COMUTED T VALUE" ..•1.502 TABULAR T VALUE" RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. 6 DEGREES FREEDOM' 248.601 qomuTEo T VALUE' 1.008 TABULAR T VALUE" RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 95 MONTHS BEING COMPARED 3 VS. 7 DEGREES FREEDOM* 66.691 COMLTED T VALUE* .4.549 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. YES NO YES NO YES NO YES NO YES NO YES NO 8 DEGREES FREEDOM* 89.842 COMUTED T VALUE* •..3.865 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. 9 DEGREES FREEDOM* 116.761 COMUTED T VALUE* 3.767 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. 10 DEGREES FREEDOM* 281.079 COMUTED T VALUE* ..202 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. 11 DEGREES FREEDOM* 247.650 COMLTED T VALUE* 2.099 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE M3NTHS BEING COMPARED 3 VS. 12 DEGREES FREEDOM* 216.767 COMUTED T VALUE* 3.037 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 96 MONTHS BEING COMPARED 4 VS. 5 DEGREES FREEDOM. 222.158 COMUTED T VALUE. ••433 TABULAR T VALUE. RESULTS OF TEST IS THERE A SIGNIFICANT DIFFERENCE MONT44S BEING COMPARED 4 VS. TES NO_ YES NO YES NO YES NO YES NO YES NO 6 DEGREES FREEDOM. 235.425 COMUTED T VALUE. .175 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 4 VS. 7 DEGREES FREEDOM. 72.734 COMUTED T VALUE. •3.917 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 4 VS. 8 DEGREES FREEDOM. 101.165 COMUTED T VALUE. •3.094 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 4 VS. 9 DEGREES FREEDOM. 136.072 COMUTED T VALUE. •2.768 TABULAR T VALUERESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 4 VS. 10 DEGREES FREEDOM. 239.242 .956 COMUTED T VALUE. TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 97 MONTHS BEING COMPARED 11 DEGREES FREEDOM- 176.213 COMUTED T VALUE. 3.094 TABULAR T VALUE+ RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED MONTHS 4 VS. 4 VS. YES NO YES NO YES NO YES NO YES NO YES NO 12 DEGREES FREEDOM 156.597 COMLTED T VALUE- 3.895 TABULAR T VALUE° RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE BEING CCMPARED 5 VS. 6 DEGREES FREEDOM* 217.499 .603 COMLTED T VALUE. TABULAR T VALUE° RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 5 VS. 7 DEGREES FREEDOM* 79.674 COMUTED T VALUE. *3.586 TABULAR T VALUE u RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 5 VS. 8 DEGREES FREEDOM- 113.649 COMUTED T VALUE ° *2.702 TABULAR T VALUE 0 RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED- . 5 VS. 9 DEGREES FREEDOM m 154.413 T VALU... -2.275 capogo TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 98 MONTHS BEING COMPARED 5 VS. 10 DEGREES F.REEDOM. 210.579 COMUTED T VALUE. 1.320 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 5 VS. YES NO YES NO YES NO YES NO 11 DEGREES FREEDOM. 153.915 COMUTED T VALUE. 3.206 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 5 VS. 12 DEGREES FREEDOM. 140.056 COMUTED T VALUE* 3.884 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 6 VS. 7 DEGREES FREEDOM. 70.550 CCMUTED T VALUE. -4.036 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 6 VS. DEGREES FREEDOM. 97.103 COMLTED T VALUE. -3.236 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 6 VS. YES NO . 9 DEGREES FREEDOM* 129.355 COMUTED T VALUE. -..2.953 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE YES NO 99 MONTHS BEING COMPARED 6 VS. 10 DEGREES FREEDOM' 250.534 .803 COMUTED T VALUE' TABULAR T VALUE' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 6 VS. YES NO YES NO YES NO YES NO YES NO YES NO 11 DEGREES FREEDOM' 189.093 COMUTED T VALUE" 3.042 TABULAR T VALUE' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 6 VS. 12 DEGREES FREEDOM' 166.590 COMUTED T VALUE' 3.896 TABULAR T VALUE' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 7 VS. 8 DEGREES FREEDOM" 112.716 COMLTED T VALUE' 1.144 TABULAR T VALUE' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 7 VS. 9 DEGREES FREEDOM' 94.144 COMUTED T VALUE' 1.918 TABULAR T VALUE" RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 7 VS. 10 DEGREES FREEDOM' 67.666 COMUTED T VALUE' 4.447 TABULAR T VALUE' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 100 MONTHS BEING COMPARED 7 VS. 11 DEGREES FREEDOM' 60.152 COMUTED T VALUE' 5.414 TABULAR T VALUE' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 7 VS. YES NO YES NO YES NO YES NO YES NO YES NO 12 DEGREES FREEDOM' 58.720 COMUTED T VALUE" 5.728 TABULAR T VALUE' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 8 VS. 9 DEGREES FREEDOM' 130.794 COMUTED T VALUE' .775 TABULAR T VALUE' RESLLTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 8 VS. 10 DEGREES FREEDOM' 91.716 COMUTED T VALUE' 3.739 TABULAR T VALUE' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED B VS. 11 DEGREES FREEDOM' 77.111 COMUTED T VALUE' 4.948 TABULAR T VALUE' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 8 VS. 12 DEGREES FREEDOM" 74.310 COMUTED T VALUE' 5.345 TABULAR T VALUE" RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 101 MONTHS BEING COMPARED 9 VS. 10 DEGREES FREEDOM- 120.222 COMUTED T VALUE.' 3.601 TABULAR T VALUERESULTS Of TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 9 VS. YES NO YES NO YES NO YES NO YES NO YES NO 11 DEGREES FREEDOM- 92.052 COMUTED T VALUE- 5.236 TABULAR T VALUERESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 9 VS. 12 DEGREES FREEDOM- 86.497 COMUTED T VALUE. 5.782 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 10 VS. 11 DEGREES FREEDOM- 234.228 COMUTED T VALUE. 2.274 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 10 VS. 12 DEGREES FREEDOM- 205.221 COMUTED T VALUE. 3.185 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 11 VS. 12 DEGREES FREEDOM. 366.587 COMUTED T VALUE- 1.151 TABULAR T VALUE. . RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 102 APPENDIX C PROGRAM LISTING FOR THE EVENT INTERARRIVAL TIME-GROUPED DATA (RAIN 2) AND OUTPUT DESCRIBING THE HANFORD DATA. 103 I. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 66 69 70 71 72 73 PROGRAM RAIN2 (INPUT.OUTPUT,TAPE2•OUTPUT,TAPE3) DIMENSION DATA(9),KPPT(60,7),P0F(60),CDF(60) DIMENSION AVE(7), VAR(7), ITOTAL(7) REAL KipLAMOAgMEAN.NUM2 DATA KPPT,P0F.CDF/420*0.60*0..60•10./ C*** C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C O C C C C C C C C C THIS PROGRAM CALCULATES THE PDF, CDF AND STATISTICS FUR THE INTERARRIVAL TIME ON THE GROUPED MONTHS THE GROUPING DETERMINED FROM THE T...TEST AND LATER ADJUSTMENTS (USING 0.05 SIGNIFICANCE) WAS GROUP SET 1 NOV- DEC..JAN n FEB MAR 2 APR-MAY 3 4 JUN Jul 5 6 . AUG-5ER 7 OCT VARIABLE LIST IDAY • LAST DAY OF RAIN (DAY • NEW DAY OF RAIN NDAY • NUMBER OF DAYS IN MONTH JDAY • DAYS OF INTERARRIVAL TIME LMONTH • GROUP NUMBER (OF MONTHS) NNDAY • LENGTH OF SKIPPED MONTH MM • GROUP NUMBER (OF MONTHS) NUM2 • MONTH COUNTER NUM3 • COUNTER NUM4 • COUNTER ILEAP • THE PRESENT YEAR IS A LEAP YEAR MMONTH • GROUP NUMBER LDAY • COUNTER KPPT • 2 DIMENSIONAL ARRAY FOR STORAGE OF INTERARRIVAL TIME PDF • PROBABILITY DENSITY FUNCTION CDF • CUMULATIVE DENSITY FUCNTION END • COUNTER REPRESENTING INTERARRIVA1 TIME ITOTAL • COUNTER FOR STATISTICS CALCuLlainN JTOTAL • COUNTER FOR STATISTICS CALCULATION TOTAL • COUNTER FOR STATISTICS CALCULATION AVE • AVE-AGE VALUE VAR • VARIANCE LAMOA • STATISTICAL PERAMETER FOR THE GAMMA DISTRIBUTION K • STATISTICAL PERAMETER FOR THE GAMMA DISTRIBUTION NUM2•l. 'DAY.° LMONTH.1 DO 140 1.1,7305 REA0(3,1000) DATA 1000 FORMAT(F4.0,2F3.0,F4.0,2F5.0,2F6.3) MMONTH•LMONTH C C4.1. C WHAT GROUP SET IS THE PRECIP EVENT IN IF(DATA(1).E0.1..OR.DATA(1).E0.2..OR.DATA(1).E0.11..OR.DATA(1).EC. C12.) LMONTH•1 IF(DATA(I).E0.3.) 1MONTH.2 IF(DATA(1).E0.4..OR.DATA(1).E0.5.) LMONTH•3 IF(DATA(1).E0.6.) LMONTH.4 IF(DATA(1).E0.7.) IMONTH•5 IF(DATA(1).E0.11..OR.DATA(1).E0.9.) LMONTH.6 IF(DATA(1).E0.10./ LMONTH.7 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C 104 74 75 76 77 78 79 80 81 82 83 84 85 86 87 de 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 C C** IS THE NEW PRECIP EVENT IN THE SAME MONTH AS THE PREVIOUS EVENT C IF(OATAI1).NE.NUM2) GO TO 30 C C** YES. THE NEW PRECIP EVENT IS IN THE SAME MONTH AS THE PREVIOUS CNE C 10 KDAY.INT(DATA(2)..5) C C** ARE WE IN A LEAP YEAR C IYEAR•INT(DATA(3)+.5) ILEAP.IYEAR/4-(IYEAR-1)/4 C vol. HOW LONG IS THE MONTH THAT WE ARE IN C IF(DATAI1).E0.1.) NDAY.31 IFIDATA(1).E0.2.) NDAY.28 IF(DATA(1).E0.2..ANO.ILEAP.E0.1) NDAY.29 IFID4TAI1).EQ.3.) NOAY.31 IF(DATA(1).E0.4.) NDAY.30 IFCDATAIII.E0.5.1 NOAY.31 IFIDATA(1).E0.6.1 NDAY.30 IFIDATA(I).E0.7.) NOAY.31 IF(DATAIII.E0.8.) N0AY.31 IFIDATA(1).E0.9.) NOAY.30 IF(DATA(1).E0.10.) NDAY-31 IF(DATA(1).EQ.11.) NDAY.30 IF(DATA(1).E0.12.) NDAY.31 C C** IS THIS PRECIP EVENT MEASURABLE OR WIT C IF(CIATA(7).LT.0.01) GO TO 140 C C** CALCULATE INTERARRIVAL TIME AND STORE IT C JDAY.KOAY-IDAY 20 IND.JDAY KPPT(IND,LMONTH)4KPPTIIND.LMONTH)+1 IDAY.KOAY GO TO 140 C C** NO. THE NEW PRECIP EVENT IS IN A DIFFERENT MONTH THAN THE PEEVE CUE ONE ' C LDAY.0 30 NUM3.0 NUM4.0 40 NUM2.NUM24,1. NUM3.NUM34.1 IF(NUM2.E0.13.) NUM2.1. IF(I.E0.7305) GO TO 120 C C** HAS A MONTH BEEN SKIPPED IA ,COMPLETE MONTH WITH NO MEASURABLE PRECIP) C IF(DATA(1).E0.NUM2) GO TO 90 C*** C*0 YES. A MONTH (HO PRECIP) HAS BEEN SKIPPED NUM4.NUM4.1 C** ARE WE IN A LEAP YEAR IYEAR.ENT(DATA(31+.5) IL.EAPIYEARI4-(IYEAR1)/4 C** HOW LONG IS THE MONTH THAT WE ARE IN IFINUM2.E0.1.) MNDAY31 EF(NUM2.EO.2.) NNDAY.28 IF(NUMZ.EQ.2..ANO.ILEAP.EQ.1) NNOAY.29 IF(NUM2.E0.3.) NNDAY.31 IFINUM2.E0.5.) NNOAY.31 £F(NUN2.EQ.7.) NNDAy.31 IF(NUM2.E0.8.) NNDAY•31 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 1/c 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 105 IF(NUM2.E0.4.) NNDAY.30 IF(NUM2.E0.6.) MNDAY.30 IF(NUM2.EQ.9.) NNDAY.30 IFINUM2.E0.10.) NNDAY.31 IF(NUM2.E0.11.) NNDAY.30 IF(NUM2.E0.12.) NNOAY • 31 C** WHAT GROUP SET IS THE PRECIP EVENT IN IFINUM2.E0.1..OR.NUM2.E0.2..OR.NUM2.E0.11..OR.NUP2.E0.12.) Mm.1 IF(NUM2.60.3.) MM.2 IF(NUM2.E0.4..OR.NUM2.E0.5.) MM.3 IF(NUM2.60.6.) mm.4 IF(NUM2.E0.7.) MM•5 IF(NUM2.E0.8..OR.NUM2.E0.9.) mm.6 IFINUM2.60.10.) MM-7 C** ARE WE IN THE SAME GROUP IF(MM.E0.MMONTH) GO TO 50 GO TO 70 IF(NUM3.NE.1) GO TO 60 1DAY.(NDAY-IDAY)+NNDAY.LOAY GO 1 0 40 60 LDAY.NNOATO.DAY GO TO 40 70 IF(NUM3.NE.1) GO TO 80 JOAY.NOAY-IDAY 1.04v.NNOAY INO.JOAY KPPT(IN0.MMONTH).KPPT(INO,MMONTH)+1 MMONTH.MM • GO TO 40 JOAY.I.DAY+NNOAY 80 INO.JDAY KPP1(INOIMMONTH).KPPT(IND,MMONTH)+1 LDAY.NNDAY MMONTH.MM GO TO 40 C*** 50 C** ARE WE IN THE SAME GROUP AND NO MONTH HAS BEEN SKIPPED 90 100 110 120 130 IFUMONTH.EQ.MMONTHI GO TO 100 IF(NUM4.E0.0) GO TO 120 INO.IDAY KPPT(IND.MMONTH).KPPT(IND,MmONTH)+1 NUM3.0 GO TO 130 KDAv.INT(DATA(2)+.5) IFINUM4.E0.0) GO TO 110 IND.LDAY*KDAY KPPT(INO.LMONTH).KPPT(INO,LMONTH)+1 NUM3.0 GO TO 130 JOAT.(NDAY-(DAY)*KDAY IND.JDAY KPPT(INO.LMONTH).KPPT(IND,LMONTH)+1 IDAY.KDAY GO TO 140 INO.NOAY-IDAY IF(IND.E0.0) GO TO 130 KPPT(IND,MMONTH).KPPT(INO.MOONTH)+1 IF(I.E0.7305) GO TO 140 IDAY.0 GO TO 10 140 CONTINUE C** THIS SECTION CALCULATES THE PDF, CDF, AVERAGE, VARIANCE, LAID* O.* AND K VALUES FOR THE GROUPED DATA AND PRINTS THE RESULTS. 106 . 222 DO 190 I.1,7 ITOTAL(I).0 224 DO 150 J.1.40 225 ITOTAL(I)0(PPT1J,1)+ITOTAL(I) 226 150 CONTINUE 227 DO 170 J.1.40 228 - 10.J 229 POF(J).FLOAT(KPPT(J.I))JITOTAL(I) 230 IF(IO.E0.1) GO TO 160 231 CDF(J).CDF(J-.1)+PDF(J) 232 GO TO 170 233 160 CDF(J).PDF4J) 234 170 CONTINUE 235 C 236 WRITE(2,2000) I 237 WRITE(2,3000) 238 WRITE(2.4000) 239 JTOTAL.0 240 TOTAL-0. 241 DO 180 M-1,40 242 '.WRITE(2,5000) MplOPT(M.1),PDF(M).00F(M) 243 - TOTAL.TOTAL.(M**2)..PPT(M,I) 244 JTOTAL.(M.KPPT(M,I)).JTOTAL 24 5 180 CONTINUE 246 C 247 AVE(1).(JTO1AL.0.)/(ITOTAL(I).0.) 248 VAR(/).(TOTAL-(JTOTAL**2/ITOTAL(1)))/(ITOTAL(1)-1.) 249 LAMDA.AVE(I)/VAR(I) 250 K.AVE(I).+2/VAR(I) 251 WRITE(2,6000) ITOTAL(I).JTOTAL 252 WRITE(2,7000) AVE(I),VAR(I) 253 WRITE(2,8000) LAMDA,K 254 190 CONTINUE 255 .0 256 C.... 257 258 2000 FORMAT("1",///,91(.. FREQUENCY DISTRIBUTION OF INTERARRIVAL TIME FO 259 CR GROUP SET"..171,I2) 260 3000 FORMAT(//,10X," INTERARRIVAL",7X..MCCURENCES",9%,"PDF",13X."CDF") 261 4000 FORMAT(13X," (DAYS),/) 262 5000 FORMAT(15X.I2,15X,I4,10X.F7.5,10X,F7.5) 263 6000 FORMAT(/1,1010 TOTAL NO. OF OCCURENCES. ',I4,//,10X." TOTAL NO. 0 264 CF INTERARRIVAL DAYS. ".I5) 265 7000 FORMAT(/,10X," MEAN. ".F6.3.10X."VARIANCE. "IlF13.4) 266 8000 FORMAT(/.10X." LAMDA. ",F7.4) 267 STOP 268 END 223 107 FREQUENCY DISTRIBUTION OF INTERARRIVAL INTERARRTVAL TIME PDF OCCURENCES (DAYS) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 362 111 72 47 39 34 13 .49138 ..14761 .09574 .06250 .05186 .04521 .01729 .01064 .02128 .01197 .01330 .01197 .00266 .00266 •00532 .00133 .00133 .00133 •00399 .00133 .00133 .00266 .00399 0.00000 0.00000 0.00000 0.00000 0.00000 .00133 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 s 16 9 10 9 2 2 4 1 1 1 3 1 1 2 3 o o o o 0 1 o o o o 0 o o 0 o 0 o TOTAL NO. OF OCCURENCES2 752 TOTAL NC. OF INTERARRIVAL MEAN' , LAM0As 3.190 .2299 DAYS' , 2399 VARIANCES Ks .7334 13.8775 FJR GROUP SET CDF .41138 .62899 .72473 .75723 .83910 .88431 .90160 .91223 .93351 .94548 .9587e .97074 .97340 .97606 .98139 .98271 .98404 .98537 .98936 .99069 .99202 .99468 .99867 .99867 .99867 .9 9 867 .9°867 .99867 1.00000 1.00000 1.00010 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1 108 FREQUENCY DISTRIBUTION OF INTERARRIVAL INTERARRIVAL OCCURENCES TIME FOR GROUP SET PDF CDF (DAYS) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 51 .35417 26 .18056 16 .11111 11 .07639 5.03472 .05556 2 .01389 5 .03472 2 .01389 5 .03472 2 .01389 0.00000 0 0.00000 2 .01389 1 .00694 2 .013119 0 0.00000 0 0.00000 .00694 1 2 .01389 0 0.00000 0 0.00000 1 .00694 0 0.00000 •00694 1 .00694 1 0 0.00000 0 0.00000 0 0.00000 0.00000 0 0 0.00000 0.00000 0 0.00000 0 0.00000 0 0.00000 0.00000 0.00000 0 0 0.00000 0.00000 0 0.00000 a o o o o TOTAL NO. OF OCCURENCES0 144 TOTAL NO. OF INTERARRIVAL DAYS. MEAN' 4.306 , LANDA• .1682 VARIANCE. Ks .7241 620 25.6014 .35417 .53472 .64583 .72222 .756 9 4 .81250 .82639 .86111 .87500 .90972 .92361 .92361 .92361 .93750 .94444 .95833 .95833 .95833 .96528 .97917 •97917 .97917 .98611 .98611 .99306 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 2 109 FREQUENCY DISTRIBUTION OF INTERARRIVAL INTERARRIVAL OCCURENCES TIME FOR GROUP SET PDF (DAYS) 1 . 69 38 25 16 13 8 11 6 8 1 4 '7 2 3 2 2 1 2 1 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 o o 1 o o 2 1 2 1 1 o o o o 0 o o 0 o TOTAL NC. OF OCCURENCESs 230 TOTAL NO. OF INTERARRIVAL MEAN. LAPDAs VARIANCE s 5.304 .1381 DAYS* Ks .7326 .30000 .16522 .10870 .06957 .05652 .03478 .04783 .02609 .03478 .00435 .01739 •03043 .00870 .01304 .00870 .00870 .00435 .00870 .00435 .00870 .00435 0.00000 0.00000 .00435 0.00000 0.00000 .00870 .00435 .00170 .00435 .00435 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1220 38.4061 3 CDF .30000 .46522 .57391 .64348 .70000 .73478 .71261 .80870 .84348 .84783 .86522 •89565 .90435 .91739 .92609 .93478 •93913 .94783 .95217 .96087 .96522 .96522 .96522 .96957 .96957 .96957 .97826 .98261 .99130 .99565 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 - 110 FREQUENCY DISTRIBUTION OF INTERARRIVAL INTERARRIVAL OCCURENCES TIME FOR PDF GPOUP SET COF (DAYS) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 37 18 15 14 3 7 1 2 2 4 4 1 1 .30579 .14876 • 12397 .11570 .02479 .05785 .00826 .01653 .01653 .03306 •03306 .00826 .00826 .01653 .00826 .01653 .00826 .00826 .01653 0.00000 0.00000 .00826 •0.0826 0.00000 0.00000 .00826 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2 1 2 1 1 2 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d TOTAL NO. OF GCCURENCESs 121 TOTAL NO. OF INTERARRIVAL MEANLAMDA2 4.959 .1696 DAYS ° VARIANCEK2 .8409 600 29.2417 .30579 .45455 .57851 .69421 .71901 .77686 .78512 .80165 .81819 .85124 .88430 .89256 .90083 .91736 .92562 .94215 .95041 .95868 .97521 .97521 .97521 .98347 .99174 .99174 .99174 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00010 1.00000 1.00000 1.00000 1.00000 1.00000 4 111 FREQUENCY DISTRIBUTION OF /NTERARRIVAL INTERARRIVAL OCCURENCES TIME FOR GROUP SET POF (DAYS) 1 2 3 4 5 6 7 14 4 3 3 3 1 8 1 2 2 1 2 1 1 1 0 1 2 1 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 1 1 1 o 1 1 o 2 o 1 o o .10526. 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0 o o 0 o o o 0.00000 0.00000 0.00000 0 TCTAL NC. OF MEAN' 10.877 LAMDA• 0.00000 6 0 TOTAL NC. OF , .24561 .07018 .05263 .05263 .05263 .01754 .01754 .01754 .03509 .03509 •01754 .03509 .01754 .01754 .01754 0.00000 .01754 .03509 .01754 .01754 .01754 0.00000 .01754 .01754 0.00000 .03509 0.00000 .01754 0.00000 OCCURENCES* INTERARRIVAL .100C 57 DAYS- 620 VARIANCE 108.8036 102 1.0874 CDF .24561 .31579 .36842 .42105 .47368 .49123 .50877 .52632 .56140 .59649 .61404 .64912 •66667 .68421 .70175 .70175 .71930 .75439 .77193 .78947 .80702 .80702 .82456 .84211 .84211 .87719 .87719 .89474 .89474 .89474 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 5 112 FREQUENCY DISTRIUTION INTERARRIVAL OF INTERARRIVAL TIME FOR GROUP SET OCCURENCES POF COF (DAYS) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 34 14 11 11 9 T 5 4 7 3 7 3 1 4 2 3 2 2 1 3 1 2 2 2 1 0 1 1 2 0 0 4 0 0 0 0 0 0 0 0 TOTAL NC. OF CCCURENCESs 149 TOTAL NO. OF INTERARRIVAL DAYS s MEANS LAMOAs 8.188 .1213 VARIANCE* Kg .9929 .22819 .09396 .07383 .07383 .06040 .04698 .03356 .02685 .04698 .02013 .04698 .02(113 .00671 .02685 .01342 .02013 .01342 .01342 .00671 .02013 .00671 .01342 .01342 .01342 .00671 0.00000 .00671 .00671 .01342 0.00000 0.00000 -.02685 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 .22819 .32215 .39597 .46980 .53020 .57718 .61074 .63758 .68456 .70470 .75168 .77181 .77852 .80537 .81879 .83893 .85235 .86577 .87248 .89262 .89933 .91275 .92617 .93960 .94631 .94631 .95302 .95973 .97315 .97315 .97315 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 0.00000 1.00000 1220 67.5203 1.00000 1.00000 6 113 FREQUENCY DISTRIBUTION OF INTERARRIVAL INTERARRIVAL OCCURENCES TIME FOR GROUP SET POF (DAYS) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 53 26 10 6 11 5 2 4 6 3 1 2 0 1 1 0 2 1 1 2 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .37857 .18571 .07143 .04286 .07857 .03571 .01429 .02857 .04286 .02143 .00714 .01429 0.00000 .00714 .00714 0.00000 .01429 .00714 .00714 .01429 0.00000 .00714 0.00000 .00714 .00714 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 TOTAL NO. OF OCCURENCESe 140 TOTAL NC. OF INTERARRIVAL DAYS' MEAN' LAMDA° 4.429 .1632 VARIANCE' Ka .7229 620 27.1295 CDF .37857 .56429 .63571 .67857 .75714 .79286 .80714 .83571 .87857 .90000 .90714 .92143 .92143 .92857 .93571 .93571 .95000 .95714 .96429 .97857 .97857 .98571 .98571 .99286 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 7 114 APPENDIX D PROGRAM LISTING FOR PRECIPITATION PER EVENT ANALYSIS (RAIN 3) AND OUTPUT DESCRIBING THE HANFORD DATA. 115 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 c*** C C C C C C C C C C C C*** C C C C C 27 C 28 29 30 31 32 33 34 35 36 37 38 39 C C C C C C C C C C C C 40 C 41 42 43 C C C 44 C C 45 46 41 C C 48 C 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 C C C C C C C C C C C C*** PROGRAM RAIN3 (INPUT,OUTPUT,TAPE2.0UTPUT,TAPE3) DIMENSION MOOSE (I2,40), PDF (40), COP (40), TOTAL (40). TOTAL2 (4 CO). SSH (40). SSL (40), D4TA(8), AVE(12), VAR(12), TEVENT(12) DIMENSION MOOSE2(40),SH(40),SL(40) REAL K, LAMDA INTEGER TYREVT,TEVENT DATA MOOSE, TOTAL, TOTAL2 / 480.0, 40*0., 40.0./ DATA POP, COE, SSH, SSL / 40*0., 40.0., 40*0., 40*0./ THIS PROGRAM CALCULATES THE POP, COP AND STATISTICS FOR PRECIP/EVENT/MONTH FOR THE PERIOD OF HISTORICAL RECORD BEING ANALIZED. IT ALSO CALCULATES THE COMPUTED T—VALUE AND THE DEGREES OF FREEDOM FOR EVERY COMBINATION OF TWO MONTHS. THIS ALLOWS FOR A VISUAL COMPARISON (I —TEST) TO SEE WHICH MONTHS ARE STATISTICALLY THE SAME IN ORDER TO GROUP THEM. A DISTRIBUTION FOR PRECIP/ EVENT FOR THE ENTIRE HISTORICAL RECORD BEING ANALIZED IS ALSO CALCULATED. . TO ADAPT THIS PROGRAM TO ADJUST THOSE LINES ASSUMES THAT THERE IS ANALIZED. THEREFORE, WITHIN THE DATA FILE. FOR A SPECIFIC DATA RECORD, IT IS NECESSARY MARKED BY THE SYMBOL *ADJUST*. THIS PROGRAM A DATA FILE FOR EVERY DAY OF THE YEAR BEING MISSING DATA MUST BE REPRESENTED BY A VALUE C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C VARIABLE LIST DAUM • THE DATA ARRAY DATA(1) • MONTH DATA(2) • DAY DATA(3) • YEAR ' DATA(7) • PRECIP AMOUNT MOOSE • ARRAY FOR STORAGE OF CATEGORIZED EVENTS MR • COMPONENT FOR CATEGORIZATION OF PRECIP EVENT TOTAL • TOTAL PRECIP FOR THE MONTH TOTAL2 • COUNTER USED IN CALCULATING THE VARIANCE TEVENT • TOTAL NUMBER OF EVENTS/MONTH GRANO.). • SUMMATION OF PRECIP FOR THE ENTIRE PRECIP RECCRD GRAND2 • SUMMATION OF THE SQUARE OF THE PRECIP AMOUNT FOR THE ENTIRE PRECIP REORD TYREVT • SUMMATION OF TOTAL NUMBER OF EVENTS FOR THE PRECIP RECORD MONTH • COUNTER FOR THE MONTH OF THE YEAR SSH(I) • UPPER LIMIT OF PRECIP INTERVAL C SSL(I) • LOWER LIMIT OF PPECIP INTERVAL SL(I) • LOWER LIMIT OF PRECIP INTERVAL SH(I) • UPPER LIMIT OF PRECIP INTERVAL POF(I) • PROBABILITY DENSITY FUNCTION CDF(I) • CUMULATIVE DENSITY FUNCTION AVE • AVERAGE NUMBER OF EVENTS LAmDA • PARAMETER FOR GAMMA DISTRIBUTION K • PARAMETER FOR GAMMA DISTRIBUTION OF • DEGREES OF FREEDOM T • COMPUTED T—VALUE C C C C C C C C C C C C C C C C C C C C C MONTH • 0 MR • 0 C 64 C** 65 66 67 68 69 70 71 72 73 74 75 76 77 78 C..* C** DATA IS READ INTO PROGRAM PRECIP EVENTS ARE CATEGORIZED INTO SIZE CLASSES AND STORED INTO MOOSE SUMMATION OF PRECIP/EVENT AND PRECIP SQUARED ARE FOUND C C 300 DO 10 1.1,7305 READ 13,300 1 DATA FORMAT (F4.0, 2F3.0, F4.0, 2E5.0, 2F6.3) IF(DATA(7).1.7.0.01) GO TO 10 MR.INT (DATA(7)*20.0+0.999999) IF (MR.GT.40) MR.40 MONTH.INT(DATA(1)+.5) MOOSE (MONTHOR).MOOSE(MONTH,MR)+1 TOTAL (MONTH) • TOTAL (MONTH) + DATA(7) TOTAL2 (MONTH) • TOTAL2 (MONTH) + DATA(7)**2 *ADJUST* *ADJUST* 116 79 80 81 82 83 84 85 86 87 88 89 90 91 - 92 93 94 95 96 97 90 99 100 101 ' 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 MOOSE2(MR).MOOSE2(MR)+1 GRANOT.GRANOT.DATA(7) GRANO2•GRAND2+0ATA(7)**2 TYREVT•TYREVT+1 10 CONTINUE DO 30 MM81,40 20 30 40 50 10.MM SH(MM)*FLOAT(I0)*0.05 $ L( )q M)*SH(MM)-0.04 PDF(MM).FL0A1(400SE2(MM))/TYREVT IF(I0.E0.1) GO TO 20 COF(MM).00F(MM•4)+PDF(MM) GO TO 30 CDF(MM).PDF(MM) CONTINUE WRITE(2,40) FORMAT('1",9X.*FREQUENCY DISTRIBUTION OF PRECIP PER EVENT FOR",/,1 COX,*HISTORICAL RECORD BEING ANALIZED*) WRITE(2,2000) DO 50 0.1,40 WRITE (2,3000) SL(K).SH(K),MOOSE2(K),PDF(K),CDF(K) CONTINUE AVEl•GRANOT/TYREVT VAR1.(GRAND2—(GRANDT**2/TYREVT))/(TYREVT-1.) WRITE(2,4000) GRANDTITYREVT WRITE(2,5000) AVE1,VAR1 C** TOTAL NUMBER OF EVENTS/MONTH ARE FOUND DO 100 1.1,12 TEVENT(I).0 DO 60 .1.1,40 TEVENT(I)*MOOSE(I,J)+TEVENT(I) 60 C** CONTINUE PDF CDF DISTRIBUTIONS APE CALCULATED DO 80 Me1,40 10•M SSH(M)*FL0AT(10)*0.05 SSL(M) • SSH(M)-0.04 PDF(M)..FLOAT(MOOSE(I,M))/TEVENT(I) IF (IO.E0.1) GO TO 70 CDF(M).CDF(M-1)+PDF(M) GO TO 80 CDF(M)•PDF(M) 70 80 CONTINUE C** C** C** STATISTICAL PARAMETERS ARE CALCULATED FOR EACH MONTHS DISTRIBUTION THESE INCLUDE THE AVERAGE, VARIANCE, LAMDA AND K VALUES AND THE TOTAL PRECIP AND THE TOTAL NUMBER OP EVENTS 90 WRITE (2,1000) WRITE (2,2000) DO 90 10.1,40 WRITE (2,3000)SSL(K),SSH(K).MOOSE(I,K),P0F(K) , CDF(K 1 AVE(I).TOTAL(I)/TEVENT(I) VAR(1).(TOTAL2(1)—(TOTAL(1)**21TEVENT(1)))/(TEVENT(I)-1.) LAMOA*AVE(I)/VAR(I) K.AVE(1)**2/VAR(1) WRITE (2.4000) TOTAL(I), TEVENT(I) WRITE(2,5000) AVEU), VAR(I) WRITE (2,6000) LAMDA, K 100 CONTINUE C C C** C** C** C** C THIS SECTION CALCULATES THE DEGREES OF FREEDOM AND THE STUDENT A LISTING OF THESE TVALUE FOR EACH COMBINATION OF TWO MONTHS. VALUES ARE PRINTED OUT TO FACILITATE THE CONDUCTANCE OF A STUDENT T—TEST FOR GROUPING OF STATISTICALLY NON—DIFFERENT MONTHS. 117 154 WRI1E120000/ 155 N.2 156 1.1 157 DO 120 M.1,11 158 D0.110 00.412 159 OF.(VAR(J)/TEVENT(J)+VAR(1)/TEVENT(1))**2/(MVAR(J)/TEVEN 160 CT(J))**2)/(TEVENT(J).q)I+MVAR(L)/TEVENT(L))**2)/(TEVENT(L) n 1))) 161 T•(AVE(J).-.AVE(L))/(SORTUVAR(J)/TEVENT(J))+IVAR(L)/TEVEST( 162 C1))1) 163 WRITE(2,1111) JP 164 WRITE(2,2222) OF, T 165 WRITE(2,3333) 166 WRITE(2,4444) 167 110 CONTINUE 168 N.N+1 169 J.J+1 170 120 CONTINUE 171 172 C*** 173 C 174 1000 FORMAT ("1",///p9Xp*FREOUENCY DISTRIBUTION OF PREC1P PER EVENT FCR 175 C MONTH . .. 1 65012/ 1 76 2000 FORMAT1//p1OXp"INTERVAL"PlOXP"OCCURENCES.p6Xp.PDF.,13Xp.COF"p/1 177 3000 FORMAT (8X,F6.2,1X."-",1X.F4.2.8)(.14,142,F7.5,10X,F7.5) 178 4000 FORMAT (HOW' TOTAL PRECIP FOR MONTH • "p F7.1pPfp9X," 179 180 181 182 183 184 185 186 187 188 189 190 191 192 TOTAL NO. C OF EVENTS • ... IS/ 5000 FORMAT ( /p9)(p. MEAN • "p F6.3, 10Xp "VARIANCE. "p F7.4) 6000 FORMAT (1,91," LAMDA • upF7.4, 10X, "K. *p F7.4) 7000 FORMAT("1",10Xp.HYPOTHESIS TEST INVOLVING MEANS (ASSUMPTIONS MADE CARE"p/P1OX," THAT THE ACTUAL VARIANCES ARE NOT KNOWN AND ARE NOT E COUAL)",/,/, 1111 FORMAT(10XpmMUNTHS BEING COMPAREMP134,12,(38,"VS.mp 1 44,12,/) 2222 F0RMAT(15Xp"DEGREES FREEDOM..,T33,F7.3.1,15Xp.COMUTED T VALUE.",F7 Cp30/) 3333 FORMAT(15Xp.TABULAR T VALUE."//) 4444 FORMAT(15Xp.RESULTS OF TESTp..",/p151P . I5 THERE A SIGNIFICANT DIFF CERENCE"PlOXP"TES"PIOXP"NO",//) STOP ENO 118 FRECUENCY DISTRIBUTION OF INTERVAL • .01 .C6 .11 .16 021 .26 .31 .36 .41 .46 .51 .56 .61 .66 .71 .76 .81 .86 .91 .96 1.01 1.06 1.11 1.16 1.21 1.26 1.31 1.36 1.41 1.46 1.51 1.56 1.61 1.66 1.71 1.76 1.81 1.86 1.91 1.96 • • n • • • • • n • • • • n • • • • • • • • • • • • • • • • • • • • • • • • • • TOTAL OCCURENCES .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 PRECIP 91 41 14 7 9 4 6 3 1 o 2 o 1 o o o 1 1 o o o o o o o o o o o o o o o o o o o o o FOR MONTH • LAME)* .106 0 5.1220 • . PER EVENT FOR MONTH POF .50276 .22652 .07735 .03867 .04972 .02210 .03315 .01657 0.00000 .00552 0.00000 .01105 0.00000 .00552 0.00000 0.00000 0.00000 .00552 .00552 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 o TOTAL NO. OF EVENTS MEAN PRECIP • 19.181 181 VARIANCE* Kg .5428 .0207 CDF .50276 .72928 .80663 .84530 .89503 .91713 .95028 .96685 .96685 .97238 .97238 .98343 .98343 .98895 .98895 .98895 .98895 .99448 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1600000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1 119 FREQUENCY DISTRIBUTION OF INTERVAL - .01 .06 .11 .16 .21 .26 .31 .36 .41 .46 .51 .56 .61 .66 .71 .76 .81 .86 .91 .96 1.01 1.06 1.11 1.16 1.21 1.26 1.31 1.36 1.41 1.46 1.51 1.56 1.61 1.66 1.71 1.76 1.81 1.86 1.91 1.96 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * TOTAL OCCURENCES .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 PRECIP • PDF 79 27 13 7 4 2 3 2 2 o o o 1 o 1 o o o 0 0 o o o o o o 0 o o o o 0 0 • o o 0 0 o 0 1 FOR MONTH TOTAL NO. OF EVENTS a MEAN PER EVENT FOR MONTH PRECIP .55634 .19014 .09155 •04930 .02817 .01408 .02113 .01408 .01408 0.00000 0.00000 0.00000 .00704 0.00000 .00704 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 •00704 • 14.350 142 .101 VARIANCE s LAMDA • 2.4419 Ka .2468 .0414 CDF .55634 .74648 .83803 .88732 .91549 .92958 .95070 .96479 .97887 .97887 .97887 .97887 .98592 .98592 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 • 99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 1.00000 2 120 FREQUENCY DISTRIBUTION OF INTERVAL .01 .06 .11 .16 .21 .26 .31 .36 .41 .46 .51 .56 .61 .66 .71 • 76 .81 .86 .91 .96 1.01 1.06 1.11 1.16 1.21 1.26 1.31 1.36 1.41 1.46 1.51 1.56 1.61 1.66 1.71 1.76 1.81 1.86 1.91 1.96 OCCURENCES • n • • • • • • • • • • • • • • • • • .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 1.00 • 1.05 n 1.10 • 1.15 • 1.20 • 1.25 • 1.30 • 1.35 • 1.40 • 1.45 • 1.50 • 1.55 • 1.60 • 1.65 • 1.70 • 1.75 • 1.80 • 1.85 • 1.90 • 1.95 • 2.00 TOTAL PRECIP 71 23 14 10 5 o o o o o 0 , • o o o o o o o o o o o o o o o o o o o o o o . 0 o o FOR MONTH • PDF .55906 .18110 .11024 .07874 .03937 .00787 .00787 .00787 .00787 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1 1 1 1 TOTAL NO. OF EVENTS MEAN PER EVENT FOR MONTH PRECIP • 9.560 127 .075 VARIANCE- LAMDA • 11.1223 Ka .8372 .0068 CDF .55906 .74016 .85039 .92913 .96850 .97638 .98425 .99213 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 3 121 FREQUENCY DISTRIBUTION OF INTERVAL OCCURENCES PD f .01 .05 .06 .10 .11 ..- .15 ..16 - .20 .21 .25 .26 .30 031 .35 .36 -• .40 .41 .45 .46 .... .50 .51 .55 .56 .60 .61 ... .65 .66 n .70 .71 .75 .76 .80 .81 .• .85 .86 •• .90 .91 • .95 .96 1.00 1.01 n 1.05 1.06 • 1.10 1.15 1.11 1.20 1.16 1.21 .• 1.25 1.26 1.30 1.31 ..• 1.35 1.40 1.36 1.41 1.45 1.46 •'. 1.50 1.51 '''. 1.55 1.56 1.60 1.61 .... 1.65 1.70 1.66 1.71 • 1.75 1.76 1.80 1.81 .'• 1.85 1.90 1.86 1.95 1.91 1.96 ..• 2.00 TOTAL PRECIP 58 17 9 7 4 4 1 o o o 1 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o FOR MONTH TOTAL NO. OF EVENTS MEAN a PER EVENT FOR MONTH PRECIP .079 LAMDA • 9.6545 • .57426 .16832 .08911 .06931 .03960 .03960 .00990 0.00000 0.00000 0.00000 .00990 0.00000 0.0000 0 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 o.00000 1.00000 • 8.010 • 101 VARIANCE"' K• COF .7657 .0082 .57426 .74257 .83168 .90099 .94059 .98020 .99010 .99010 .99010 .99010 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 4 122 FREQUENCY DISTRIBUTION OF INTERVAL .01 .06 .11 .16 .21 .26 .31 .36 .41 .46 .51 .56 .61 .66 .71 .76 .81 .86 .91 .96 1.01 1.06 1.11 1.16 1.21 1.26 1.31 1.36 1.41 1.46 1.51 1.56 1.61 1.66 1.71 1.76 1.81 1.86 1.91 1.96 - - - - - - - - - - - - - - - - - - - - TOTAL OCCURENCES .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 PRECIP FCR 49 16 12 3 6 6 4 o o 2 o o o o o o o o o o o o o o o o o o o o o o o o o o o o o MONTH .105 LAMDA • 7.5222 • PER EVENT FOR MONTH PDF .50000 .16327 .12245 .03061 .06122 .06122 0.00000 .04082 0.00000 0.00000 .02041 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 o TOTAL NO. OF EVENTS MEAN • PRECIP • 10.260 98 VARIANCE= Ks .7875 0139 CDF .50000 .66327 .78571 .81633 .87755 .93878 .93878 .97959 .97959 .97959 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 5 123 FREQUENCY DISTRIBUTION OF INTERVAL OCCURENCES .01 - . 05 .06 - .10 . 15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 .11 - .16 .21 .26 .31 .36 .41 .46 .51 .56 .61 .66 .71 .76 .81 .86 .91 .96 1.01 1.06 1.11 1.16 1.21 1.26 1.31 1.36 1.41 1.46 1.51 1.56 1.61 1.66 1.71 1.76 1.81 1.86 1.91 1.96 - - - - - - - - - - - - - - - - - - - 44 16 14 7 3 3 2 2 2 5 1 1 o o o o o o 1 o o o o o o o o o o o o o o o o o o PRECIP TUTAL NO. OF EVENTS • FOR MONTH .138 LAMDA • 4.3553 • PDF .43564 .15842 .13861 .06931 .02970 .02970 .01980 .01980 .01980 • 04950 .00990 0.00000 0.00000 0.00000 .00990 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 .00990 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 o o o TOTAL MEAN PER EVENT FOR MONTH PRECIP • 13.910 101 VARIANCE• Km .5998 .0316 CDF .43564 .59406 .73267 .80198 .83168 .86139 .88119 .90099 .92079 .97030 .98020 .98020 .98020 .98020 .99010 .99010 .99010 .99010 .99010 .99010 .99010 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 6 124 FREQUENCY DISTRIBUTION OF INTERVAL .01 .C6 .11 .16 .21 .26 .31 .36 .41 .46 .51 .56 .61 .66 .71 .76 .81 .86 .91 .96 1.01 1.06 1.11 1.16 1.21 1.26 1.31 1.36 1.41 1.46 1.51 1.56 1.61 1.66 1.71 1.76 1.81 1.86 1.91 1.96 OCCURENCES POP - .05 - .10 - .15 - .20 - .25 - .30 - .35 - .40 - .45 - .50 - .55 - .60 - .65 - .70 .75 - - .80 - • 85 - .90 .95 - - 1.00. - 1.05 - 1.10 - 1.15 - 1.20 - 1.25 - 1.30 - 1.35 - 1.40 - 1.45 - 1.50 - 1.55 - 1.60 - 1.65 - 1.70 - 1.75 - 1.80 - 1.85 - 1.90 - 1.95 - 2.00 TOTAL PRECIP 18 7 3 • LAMDA • .48649 .18919 .08108 .02703 .05405 .05405 .08108 .02703 0.00000 0.00000 0.00000 ' 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1 2 2 3 1 o o 0 o o o o • o o o o o o o o o o o o o o o o o o o o 0. o o o o FOR MONTH TOTAL NO. OF EVENTS MEAN PER EVENT FOR MONTH PRECIP .104 8.5171 • • 3.840 37 VARIANCE• K. .8839 .0122 COP .48649 .67568 .75676 .78378 .83784 .89189 .97297 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 7 125 FREQUENCY DISTRIBUTION OF INTERVAL OCCURENCES - • 05 .10 - - .15 - .20 .21 - .25 .26 - .30 .31 - .35 .36 - .40 .41 - .45 .46 - .50 .51 - .55 .56 • 60 .61 ..- .65 .66 - .70 .71 - .75 .76 •••• .80 .81 - .85 .86 - .90 .91 .... .95 .96 ... 1.00 1.01 -. 1.05 1.06 - 1.10 1.11 - 1.15 1.16 • 1.20 1.21 - 1.25 1.26 - 1.30 1.31 - 1.35 1.36 - 1.40 1.41 - 1.45 1.46 - 1.50 1.51 - 1.55 1.56 .- 1.60 1.61 - 1.65 1.66 - 1.70 1.71 - 1.75 1.76 - 1.80 1.81 - 1.85 1.86 - 1.90 1.91 - 1.95 1.96 .... 2.00 .01 .06 .11 .16 TOTAL 30 8 3 6 2 o 1 0 0 1 0 0 0 o o ' PRECIP 0 0 0 o 0 o 0 0 0 0 o 0 0 o 0 0 0 o 0 0 0 o 0 0 FOR MONTH • .082 LAMDA • 8.0805 • PDF .57692 .15385 .05769 .11538 .03846 .01923 0.00000 .01923 0.00000 0.00000 .01923 6.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1 TOTAL NO. OF EVENTS MEAN PER EVENT FOR MONTH PRECIP 4.270 • 52 VARIANCE* Ks .6635 .0102 CDF .57692 .73077 .78846 .90385 .94231 .96154 .96154 .98077 .98077 .98077 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 8 126 FREQUENCY DISTRIBUTION OF INTERVAL .01 .06 .11 .16 .21 .26 .31 .36 .41 .46 .51 .56 .61 .66 .71 .76 .81 .86 .91 .96 1.01 1.06 1.11 1.16 1.21 1.26 1.31 1.36 1.41 1.46 1.51 1.56 1.61 1.66 1.71 1.76 1.81 1.86 1.91 1.96 OCCURENCES n .05 n .10 •n .15 n .20 • .25 n .30 n .35 • .40 n .45 • .50 n .55 • .60 n .65 n .70 • .75 • .80 • .85 • .90 • .95 n 1.00 n 1.05 n 1.10 n 1.15 n 1.20 n 1.25 • 1.30 n 1.35 • 1.40 n 1.45 n 1.50 n 1.55 • 1.60 • 1.65 • 1.70 • 1.75 n 1.80 n 1.85 n 1.90 • 1.95 n 2.00 TOTAL 33 13 3 4 o 3 1 o o o 1 o o o o o o o o o o o o o o o o o o o o o o o o o o PDF CDF - FOR MONTH • 6.090 PRECIP • PER EVENT FOR MONTH .54098 .21311 .04918 .06557 .01639 .01639 .01639 0.00000 .04918 .01639 0.00000 0.00000 0.00000 .01639 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1 1 1 TOTAL NO. OF EVENTS MEAN PRECIP 61 VARIANCE • .0181 .100 LAMDA • 5.5112 • Ks .5502 .54098 .75410 .80328 .86885 .88525 .90164 .91803 .91803 .96721 .98361 .98361 .98361 .98361 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 9 127 FREQUENCY DISTRIBUTION OF INTERVAL .01 .06 .11 .16 .21 .26 .31 .36 .41 .46 .51 .56 .61 .66 .71 .76 .81 .86 .91 .96 1.01 1.06 1.11 1.16 1.21 1.26 1.31 1.36 1.41 1.46 1.51 1.56 1.61 1.66 1.71 1.76 1.81 1.86 1.91 1.96 - - - - - - - - - - - - - - - - - - - - - - - TOTAL OCCURENCES .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 PRECIP 66 21 8 6 6 2 4 2 2 o 1 o o o o o o o o o o o o o o o o o o 1 o o o o o o 0 o FOR MONTH MEAN • • PDF .54545 .17355 .06612 .04959 .04959 .01653 .03306 .01653 .01653 .00826 .00826 0.00000 .00826 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 .00826 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1 1 TOTAL NO. OF EVENTS • PER EVENT FOR MONTH PRECIP • 13.450 121 .111 VARIANCES .0335 LAMDA • 3.3145 Ka .3684 . 10 CDF .54545 .71901 .78512 .83471 .88430 .90083 .93388 .95041 .96694 .97521 .98347 .98347 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 .99174 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 128 FREQUENCY DISTRIBUTION OF INTERVAL .01 .06 .11 .16 .21 .26 .31 .36 .41 .46 .51 .56 .61 .66 .71 .76 .81 .86 .91 .96 1.01 1.06 1.11 1.16 1.21 1.26 1.31 1.36 1.41 1.46 1.51 1.56 1.61 1.66 1.71 1.76 1.81 1.86 1.91 1.96 - - - - - - - - - - - - - - - - - - - - - - TOTAL OCCURENCES 85 .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 PRECIP 31 14 16 9 9 2 3 • PDF .49419 .18023 .08140 .09302 .05233 .05233 .01163 .01744 .00581 0.00000 .00581 0.00000 • 1 o 1 o .00581 1 o o o o o o o o o o o o o o o o o o o o o o o o o o o FOR MONTH TOTAL NO. OF EVENTS MEAN PER EVENT FOR MONTH PRECIP .099 LAMDA • 8.2420 • 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 • 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 • 17.040 172 VARIANCE. Ka .8165 .0120 11 CDF .49419 .67442 .75581 .84884 .90116 .95349 .96512 .98256 .98837 .98837 .99419 .99419 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 129 FREQUENCY DISTRIBUTION OF INTERVAL .01 .06 .11 .16 .21 .26 .31 .36 .41 .46 .51 .56 .61 .66 .71 .76 .81 • 86 .91 .96 1.01 1.06 1.11 1.16 1.21 1.26 1.31 1.36 1.41 1.46 1.51 1.56 1.61 1.66 1.71 1.76 1.81 1.86 1.91 1.96 . • • •.• • • • • • • • • • • • • • • • • • • • • TOTAL OCCURENCES .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 •95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 • • .• • • • • • • • • • • • PRECIP 110 36 17 15 • 5 7 2 1 0 3 1 1 o o o 0 0 o o o o o o o o o 0 o o o o 0 o o o 0 o o • LAMDA • .087 7.0983 • - 0.00000 • 17.140 198 VARIANCE. Ks • 6145 12 COF 0.00000 0 FOR MONTH PDF .55556 .18182 .08586 ' .07576 .02525 .03535 0.00000 .01010 .00505 0.00000 .01515 .00505 .00505 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 o TOTAL NO. OF EVENTS MEAN PER EVENT FOR MONTH PRECIP .0122 .55556 .73737 .82323 .89899 .92424 .95960 .95960 .96970 .97475 .97475 .98990 .99495 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 130 APPENDIX E OUTPUT LISTING FROM RAIN 3 OF THE SEQUENCE OF VALUES FOR CONDUCTING T-TEST GROUPING FOR PRECIPITATION PER EVENT. 131 HYPOTHESIS TEST INVOLVING MEANS (ASSUMPTIONS MADE ARE THAT THE ACTUAL VARIANCES ARE NOT KNOWN AND ARE NOT EQUAL) M1NTHS MONTHS BEING COMPARED 1 VS. 2 DEGREES FREEDOM- 243.906 COMUTED T VALUE.' .244 TABULAR T VALUERESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE BEING CCMPARED 1 VS. YES NO YES NO YES NO YES NO YES NO YES NO 3 DEGREES FREEDOM e 295.275 COMUTED T VALUE.' 2.371 TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. 4 DEGREES FREEDOM- 275.877 COMUTED T VALUE- 1.906 TABULAR T VALUE u RESULTS OF TEST... IS IHERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. 5 DEGREES FREEDOM.' 234.218 COMUTED T VALUE & .080 TABULAR T VALUE' RESLLTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. 6 DEGREES FREEDOM* 173.501 COMLTED T VALUE' •1.536 TABULAR T VALUE= RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. 7 DEGREES FREEDOM* 63.791 COMUTED T_VALUEs .104 TABULAR T VALUE' RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 132 MONTHS BEING COMPARED 1 VS. DEGREES FREEDOM* 116.789 COMUTED T VALUE' 1.356 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. YES NO YES NO YES NO YES NO YES NO YES NO 9 DEGREES FREEDOM* 109.664 .303 COMUTED T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. 10 DEGREES FREEDOM* 215.011 COMLTED T VALUE* TABLLAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. 11 DEGREES FREEDOM* 335.408 COMUTED T VALUE* .509 TABLLAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 1 VS. 12 DEGREES FREEDOM* 336.872 COMUTED T VALUE* 1.463 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 2 VS. 3 DEGREES FREEDOM* 190.165 COMUTED T VALUE* 1.389 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 133 MONTHS BEING COMPARED 2 VS. 4 DEGREES FREEDOM* 207.855 COMUTED T VALUE- 1.126 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 2 VS. YES NO YES NO YES NO YES NC YES NO YES NO 5 DEGREES FREEDOM* 231.867 COMUTED T VALUE* • n 175 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 2 VS. 6 'DEGREES FREEDOM* 230.915 COMUTED T VALUE- •1.491 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 2 VS . ' 7 DEGREES FREEDOM* 106.594 COMUTED T VALUE- •.109 TABULAR T VALUES RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 2 VS. DEGREES FREEDOM ° 175.422 .858 COMUTED T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 2 VS. 9 DEGREES FREEDOM ° 167.078 .050 COMUTED T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE . 134 MONTHS BEING COMPARED 2 VS. 10 DEGREES FREEDOM- 260.197 COMUTED T VALUEs TABULAR T VALUE. RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 2 VS. YES NO YES NO YES NO YES NO YES NO YES NO 11 DEGREES FREEDOM- 206.919 COMLTED T VALUE= .105 TABULAR T'VALUEs RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 2 VS. 12 DEGREES FREEDOM- 200.486 .771 COMUTED T VALUE* TABULAR T VALUE s RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. 4 DEGREES FREEDOM'. 204.350 MILTED T VALUE- —.347 TABULAR T VALUE s RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 3 VS. 5 DEGREES FREEDOM- 165.513 COMUTED T VALUE- -.2.105 TABULAR T VALUE s RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. 6 DEGREES FREEDOM s 133.862 COMUTED T VALUE- .•-3.262 TABULAR T VALUE° RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 135 MONTHS BEING COMPARED 3 VS. 7 DEGREES FREEDOM- 48.233 COMUTED T VALUE- •1.457 TABULAR T VALUE• RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. YES NO YES NC YES NO YES NO TES NO YES NO 8 DEGREES FREEDOM* 80.193 COMLTED T VALUE* •.434 TABULAR T VALUE° RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. 9 DEGREES FREEDOM* 82.206 COMUTED T VALUE ° •1.312 TABULAR T VALUE° RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED - 3 VS. 10 DEGREES FREEDOM- 164.780 COMUTED T VALUE- •1.974 TABULAR T VALUE° RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. 11 DEGREES FREEDOM- 296.914 COMUTED T VALUE- •2.144 TABULAR T VALUE* / RESULTS Of TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 3 VS. 12 DEGREES FREEDOM ° 315.775 COMUTED T VALUE- •1.053 TABULAR T VALUE° RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 136 MONTHS BEING COMPARED 4 VS. 5 DEGREES FREEDOM* 182.010 COMUTED T VALUE* *1.699 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 4 VS. YES NO YES NO YES NO YES NO YES NO YES NO 6 DEGREES FREEDOM* 148.670 COMUTED T VALUE* *2.941 TABULAR • T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 4 VS. 7 DEGREES FREEDOM* 54.774 COMUTED T VALUE* *1.208 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 4 VS. a DEGREES FREEDOM* 93.982 COMUTED T VALUE* *.169 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 4 VS. 9 DEGREES FREEDOM- 93.172 COMUTED T VALUE* *1.055 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 4 VS. 10 DEGREES FREEDOM* 181.957 COMLTED T VALUE* *1.682 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 137 MONTHS BEING COMPARED 4 VS. 11 DEGREES FREEDOM* 241.438 COMUTED T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 4 VS. YES NO YES NO YES NO YES NO YES NO YES NO 12 DEGREES FREEDOM* 239.180 COMUTED T VALUE* •...607 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 5 VS. 6 DEGREES FREEDOM* 174.321 COMUTED T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MjNTHS BEING COMPARED 5 VS. DEGREES FREEDOM* 68.983 .042 COMUTED T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 5 VS. 8 DEGREES FREEDOM* 119.013 COMUTED T VALUE* 1.229 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 5 VS. 9 DEGREES FREEDOM* 114.861 .232 COMUTED T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFfERENCE 138 MONTHS BEING COMPARED 5 VS. 10 DEGREES FREEDOM* 207.187 COMUTEO T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 5 VS. YES NO YES NO YES NC YES NO YES NO YES NO 11 DEGREES FREEDOM* 189.871 .386 COMUTED T VALUE* TABULAR T VALUE° RESLLTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 5 VS. 12 DEGREES FREEDOM* 182.480 COMUTED T VALUE* 1.270 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 6 VS. 7 DEGREES FREEDOM- 103.356 COMUTED T VALUE- 1.339 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT. DIFFERENCE MONTHS BEING COMPARED 6 VS. DEGREES FREEDOM* 149.551 COMUTED T VALUE ° 2.466 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 6 VS. 9 DEGREES FREEDOM* 151.901 COMUTED T VALUE* 1.534 TABULAR T VALUE° RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 139 MONTHS BEING CCMPARED 6 VS. 10 DEGREES FREEDOM* 215.006 COMUTED T VALUE* 1.093 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 6 VS. YES NO YES NO YES NO YES NO YES NO YES NO 11 DEGREES FREEDOM* 145.389 COMUTED T VALUE* 1.975 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 6 VS. 12 DEGREES FREEDOM* 140.456 CCMUTED T VALUE* 2.643 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED ' 7 VS. 8 DEGREES FREEDOM* 73.205 .946 COMUTED T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MOINTHS BEING COMPARED 7 VS. 9 DEGREES FREEDOM* 87.505 .158 COMUTED T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 7 VS. 10 DEGREES FREEDOM* 100.697 COMUTED T VALUE* ..299 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 140 MONTHS BEING COMPARED 7 VS. 11 DEGREES FREEDOM* 52.403 COMUTED T VALUE* .236 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 7 VS. YES NO YES NO YES NO YES NC YES NO YES NO 12 DEGREES FREEDOM* 50.403 COMUTED T VALUE* .871 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 8 VS. 9 DEGREES FREEDOM* 109.277 COMLTED T VALUE* -.799 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 8 VS. 10 DEGREES FREEDOM* 160.791 COMUTED T VALUE* •-1.336 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 8 VS. 11 DEGREES FREEDOM* 90.544 COMUTED T VALUE* •"1.041 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING CCMPARED 8 VS. 12 DEGREES FREEDOM* 86.002 1.278 COMUTED T VALUE* TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 141 MONTHS BEING COMPARED 9 VS. 10 DEGREES FREEDOM= 156.222 COMUTED T VALUE= .•..472 TABULAR T VALUE= RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 9 VS. YES NO YES NO YES NO YES NO YES NO YES NO 11 DEGREES FREEDOM= 89.817 COMUTED T VALUE= .040 TABULAR T VALUE= RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 9 VS. 12 DEGREES FREEDOM= 86.338 COMLTED T VALUE= .701 TABULAR T VALUE= RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 10 VS. DEGREES FREEDOMCOMUTED T VALUE= 11 180.108 .649 TABULAR T VALUE* RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 10 VS. 12 DEGREES FREEDOM= 174.024 COMUTED T VALUE* 1.336 TABULAR T VALUE= RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE MONTHS BEING COMPARED 11 VS. 12 DEGREES FREEDOM* 361.503 COMLTED T VALUE* 1.091 TABULAR T VALUE= RESULTS OF TEST... IS THERE A SIGNIFICANT DIFFERENCE 142 APPENDIX F PROGRAM LISTING FOR THE PRECIPITATION PER EVENT--GROUPED DATA (RAIN 4) AND OUTPUT DESCRIBING THE HANFORD DATA. 143 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 ” 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 PROGRAM RAIN§ (INPUT.UUTPUT,TAPE2•OUTPUT,TAPE3) DIMENSION MOOSE (12,40), PDF (40), CDF (40). TOTAL (40), TOTAL2 (4 CO). SSH (40), SSL (40), DATA(8). AVE(12), VAR(I2), TEVENT(12) REAL K, LAMDA INTEL,ER TEVENT DATA MOOSE, TOTAL, 1OTAL2 / 480*0, 40*0., 40*0.1 DATA POP, CDF, SS)1, SSL / 40*0., 40*0., 40*0., 40*0.1 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C THIS PROGRAM CALCULATES THE POF, CDF AND STATISTILS FOR PRECIP/EVEMT FOR THE GROUPED DATA CONSISTING OF THE MONTHS APR ..MAY4UL...AUGSEP-..00T. VARIABLE LIST DATA(I) • THE DATA ARRAY DATA(1) • MONTH DATA(2) • DAY DATA) 3) • YEAR DATA(?) • PRECIP AMOUNT MOOSE • ARRAY FOR STORAGE OF CATEGORIZED EVENTS MR • COMPONENT FOR CATEGURIZATION OF PRECIP EVENT TOTAL • TOTAL PRECIP FOR THE MONTH TOTAL2 • COUNTER USED IN CALCULATING THE VARIANCE TEVENT • TOTAL NUMBER OF EVENTS/MONTH SSH(I) • UPPER LIMIT OF PRECIP INTERVAL SSL(I) • LOWER LIMIT OF PRECIP INTERVAL PDF(I) • PROBABILITY DENSITY FUNCTLON CDF(I) • CUMULATIVE DENSITY FUNCTION AVE • AVERAGE NUMBER OF EVENTS VAR • VARIANCE OF EVENTS LAMUA • PARAMETER FOR GAMMA DISTRIBUTION K • PARAMETER FOR GAMMA DISTRIBUTION MONTH • 0 MR • 0 C Cs* C** C** C" DATA IS READ INTO PROGRAM INTO MOOSE PRECIP EVENTS ARE CATEGORIZED INTO SIZE CLASSFS AND STuRkD SUMMATION OF PRECIP/EVENT AND PRECIP SQUARED ARE FOUND DO 10 1.1,7305 READ (3,300) DATA 5 IF(DATA(1).E0.1..OR.DATA(1).E0.2..0R.0ATA(1).E0.3..0R.JATA(1).E0.6 C..OR.DATA(1).E0.11..OR.DATA(1).E0.12.) GO 1010 IF(DATA(7).LT.0.01) GO 10 10 MR.1.4T IDATA(7)*20.0+0.999 999 ) IF (MR.0T.40) MR•40 MOOSE (1,MR)*MUOSE(1,MR)+1 TOTAL(1).TOTAL(1).DATA(7) TOTAL2(1).TOTAL2(1)+DATA(7)**2 10 C C** C 20 C C** C 30 40 CONTINUE TOTAL NUMBER OF EVENTS/MONTH ARE FOUND TEVENT(1)*0 DO 20 J01,40 TEVENT(1)0100Sk(1,J)*TEVENT(1) CONTINUE POP AND COP DISTRIBUTIONS ARE CALCULATED 00 40 11 .1,40 10•M SSH(M).FLOAT(10)*0.05 SSL(MI • SSH(M) -..0.0 4 PDF(M)*FLOAT(MOO5E(1,M))/TEVENT(1) IF (I0.10.1) GO TO 30 CDF(M).CDF(141)4P0F(M) GO TO 40 CDF(11).00F(M) CONTINUE C C C C ,C C C C C C C C C C C C C C C C C C C C C C C C C C C 144 78 79 80 81 62 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 C C** STATISTICAL PARAMETERS ARE CALCULATED FOR EA:H MONTHS DISTRIBUTION. C** THESE INCLUJE THE AVERAGE, VARIANCE, LAPIDA AND K VALUES AND THE C** TOTAL PRECIP AND THE TOTAL NUMBER OF EVENTS C WRITE (2,1000) WRITE (2,2000) DO 50 0.1,40 WRITE (2,3000)SSL(K),5SH(K),MOOSE(1,K).PDF(K),C0F(K) 50 AVE(1).TOTAL(1)/TEVENT(1) VAR(1).(TOTAL2(1)•(TOTAL(1)**2/TEVENT(1)))/(TEVENT(1)...1.) LAMDA.AVE(1)/VAR(1) KmAVE(1)**2/VAR(1) WRITE (2,4000) TOTAL(1), TEVENT(1) WRITE(2,5000) AVEU), UAW WRITE (2,6000) LAMA, K C FORMAT (F4.0, 2F3.0, F4.0, 2F5.0, 2F6.3) 300 1000 FORMAT ("1"09X,*FREOUENCY DISTRIBUTION OF PRECIP PER EVENT FOR",!, ClOWCOMBINED MONTHS OF APR MAY n JUL.-AUGSEP....00T") 2000 FORMAT(///,10X.*INTERVAL*010K,"OCCURENCES *,6 X , "PDF" ,13 WCOF" ,/) 3000 FORMAT.(8X,F6.2,1X.* n ° ,1X,F4.2,8X , I 4,74 2 , F 7 . 5,10 X , F 7 . 5) 4000 FORMAT Wpm TOTAL PRECIP FOR MONTH • 6 . F7.3s//," TOTAL NO. OF EV CENTS • *,I5) 5000 FORMAT (/," MEAN • *, F6.3. 10E, "VARIANCE. ", F7.4) 6000 FORMAT (W. LAMDA • *,F7.4, 10X, "K. ", F7.4) STOP ENO 145 FREQUENCY DISTRIBUTION OF PRECIP PEP EVENT FOR COMBINED MONTHS 3 F-ARR-MAY-JUL-AUG-SEP-0CT INTERVAL .01 .06 .11 .16 .21 .26 .31 .36 .41 .46 .51 .56 .61 .66 .71 .76 .81 .86 .91 • 96 1.01 1.06 1.11 1.16 1.21 1.26 1.31 1.36 1.41 1.46 1.51 1.56 1.61 1.66 1.71 1.76 1.81 1.86 1.91 1.96 TOTAL - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 11CCURE4CES .05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 PRECIP FOR MONTH TOTAL NO. OF EVENTS • MEAN .098 LAMDA • 5.5109 254 82 38 27 21 16 9 .54043 .17447 .09085 .05745 .04468 .03404 .01915 .01702 .01064 .00426 .01064 0.00000 .00213 .00213 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.30000 .00213 0.00000 0.00000 b 5 2 5 o 1 1 o 0 o o o o 0 o o o 0 o o o o o o 1 0 o o o 0.00000 0.00000 0.00000 0.00000 0 o o o 0.00000 0.00000 = 45.920 470 VARIANCE= Ke .53 8 4 PDF .0177 CDF .54043 .71489 .79574 .85319 .89787 .93191 .95106 .96809 .97872 .98298 .99362 .99362 .99574 .99787 .99787 .99787 .99787 .99787 .997b7 .99787 .99787 .99787 .99787 .99787 .99787 .99787 .99787 .99787 .99787 .99787 .99787 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 146 APPENDIX G PROGRAM LISTING OF THE WINTER STORM PERIOD ANALYSIS (RAIN 5) AND OUTPUT DESCRIBING THE HANFORD DATA. 147 I 2 3 4 5 6 7 8 9 PROGRAm RAI15(INKUT,)UTPUT,TAPE1.INPUT,TAPE2.OUTPUT,TAPE3) DIMENSION 0(20) .A 40(2 0).D(3).3(00).RP(60),38(60),DAT ( 5350) DIMEN4IUN DATA(R) , PDF(100).00F(100) REAL LAm0A,K INTEGER GC,GF.SF DATA R,AN0,D.B,RP,OB,UAT,POPPCOF/20*0.,20,0.,300.160*0.,60,0.,6C*0 C..7350*0.,100*0.,100*0./ 11 12 13 14 15 16 17 18 19 20 21 22 23 C C*** C C C C C C C C C C C C C C 24 C 25 26 C C 27 TO THIS PROGRAM ANALIZES THE WINTER FRONTAL TYPE STORM PERIOD BY OEVELuI,IG FROM THE ACTUAL CLIMATIC DATA THE FuLLOW/NG SIX (6) DISTRIBUTLOS... GROUP DURATION IN DAYS (W) NO. LiF GROUPS/SEQUENCE (ANU) NO. OF DRY DAYS BETWEEN GROUPS (D) NO. OF DRY DAYS BET4EEN SEQUENCES (B) PRECIPITATION/GRUUP (RP ) C INTERARRIVAL TIME TO THE NEXT STORM (DB) A STORM GRuUP IS EQUAL TO ANY NC. OF SUCCESSIVE DAYS OF PRECIP. A STORM SEQUENCE IS ONE OR MORE GROUPS SEPERATEu BY NO MORE THAN THREE (3) DRY DAYS. C C C C C C C C C C C C C C C C C C 28 C C 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 5d 59 bo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• GROUP DURATION OR STORM LENGTH (W) ANO(I) • GROUPS/SEQUENCE D(I) • DRY DURATIJN BETKEEN GROUPS S(I) • DRY DURATION BETWEEN SEQUENCES RP(I) • GROUP RAINFALL OR STORM RAINFALL DB(I) • INTERARRIVAL TIME TO NEXT STORM DAUM • AN ARRAY OF THE HISTORICAL DATA OAT (I ) • AN ARRAY WHERE THE WINTER PERIOD DATA IS STORED POF(I) • THE PROBABILITY DENSITY FUNCTION CORM • THE CUMULATIVE DENSITY FUNCTION Na • INTER. SEQUENCE OuRATIJN CuumTER ND • INTER. GROUP DURATION COUNTER mod • INTERARRIVAL TIME TO NEXT STORM COUNTER NNO • GROUPS/SEQUENCE COUNTER GC • DAYS IN GROUPS COUNTER GF • CONTROL COUNTER PG • GROUP PRECIP HISTROGRAM SF • CONTROL COUNTER 391 • THE AVERAGE VALUE OF THE DISTRIBUTION C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C c 148 75 76 77 78 79 80 81 82 83 84 85 86 87 88 69 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 VI • THE VARIANCE OF THE DISTRIBUTION C C LAML.A • A GAMMA PARAMETER FOR THE DISTRIBUTION C C It • A GAMMA PARAMETER FOR fHE DITRIBUTION C C SI • A VARIABLE USED Tu CALCULATE STATISTICS C C C SNI • A VARIABLE USED TO CALCULATE STATISTICS C C SOI • A VARIABLE USED TO CALCULATE STATISTICS C C TUTANO • TOTAL FUR NO. OF GROUPS PER SElUENCE C C TOTB • TOTAL FOR NO. OF DRY DAYS BET4EE4 SEQUENCES C TOTD • TOTAL FOR NO. OF DRY DAYS BETWEEN GROUPS C C C TOTUB • TOTAL FOR INTERARRIVAL TIME TO (HE NEXT STJRM C C TUTRo • TOTAL FOR PRECIPITANON PER GROUP C TOTw • TOTAL FOR GROUP ouRArloN C C JNUM • COUNTER FOR ROUTING CONTROL C C C C 1END • COUNTER FOR ROUTING CONTROL C IND • DUMMY VARIABLE C A • DUMMY VARIABLE C C C C C C C C*** C C C** STORAGE OF wINTER PERIOD PRECIP RECURD C L=0 .A0JuST* DU 60 J.1,19 DO 10 JJ=1,500 READ(3,1) DATA FORMAT(F4.0,2F3.0,F4.0,2F5.0,2F6.3) 1 — IF(DATA(1).E0.11.) GO TO 20 CONTINUE 10 C C** LOAD DATA FOR PORTION OF WINTER PERIOD AT THE END OF THE YEAR C *ADJUST* DU 30 1.1.61 20 •0.4.1 IPCDATA(7).LT..011 OATA(7).0. DATCL1.0ATA171 READ(3.1) DATA CONTINUE 30 C OF THE YEAR C** LOAD DATA FOR PORTION OF WINTER PERIOD AT THE BEGINNING C *ADJUST* OU 50 1•1,59 1F(I.E0.1) GO TO 40 READt3.11 DATA 0.L.1 40 IFIDATA(3).E0.3.1 GO TO 50 IF(DATA(7).LT..01) DATAi71.0. pAr(o.oATA(7) CONTINUE 50 L•L.1 OAT(L)•-10.0 60 OAT(L) -0.O C C*0 PRECIP RECORD HAS NOW BEEN LOADED INTO OAT(L) C DO 70 1.1,5350 IF(DAT(I).E0.0.) DAT(I)•0. 70 CONTINUE C C C C PRECIP RECORD THAT HAS C** THIS SECTION PRINTS GUT THE HISTORICAL WINTER C** BEEN STORED INTO DAT(L) C L •0 LL.0 wRITE(2,1000) PERIOD ",//1 1000 FONmAT(1X."PRECIPITATION RECORD FOR WINTER PRECIP *ADJUST* 00 130 Ie1,14 bRITE(2,1100) I . 0 ,61x."* YEAR ",I2," ",/,1x,"* 1100 FORmAT(1X," wi *",/,1X," C/,1x..* 149 148 149 150 151 152 153 154 155 156 DO 80 90 1200 100 120 J.I,4 G0 TO (80.100,100,110),J L•1.1-41 LL.1.0.30 48ITE(2,1200)(DAT(K),K.L,LL) FORMATI1X,16(F5.2,1X,"I"),/,6X.15(F5.2,1X,"I")) GO TO 120 L.1.L.1 LL.LL*31 157 15 6 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 17d 179 160 181 162 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 GJ TO 90 110 120 1300 130 C CS* L.LL+1 LL.L1.1.24 GO TU 90 CONTINUE WRITE(2,1300) FORMAI(///) LL.LL+1 CONTINUE ARRAY 01 HAS JUST 8EE4 PRINTED C Cs** CS* 140 150 C** VAAIABLE INITIALIZATION L.0 L.0.1 IFIDAT(L)) NO.0 N8 • 0 N08.0 1E40.1 GF.1 SF.1 GC.1 NI41.1 PG.DAT(L) 140.140,153 SEQUENCE AND GROUP TRAFFIC DIRECTOR. 160 LL.I.+1 LLL*1.0.4 JNUM.0 DO 170 I.LL,LLL JNUM.JMU14.1.1 IF(OAT(I).LT.-10.1 GO TO 350 IF(DAT(1).L7.0.) GO TO 383 IF(DAT(I).GT.0.) GO TO 180 170 160 190 CONTINUE GO TO (190,240,240,240,280),J4UM 1 .L.1.1 IF(GF-1) 210.200,210 ZOO 201 202 203 204 205 206 207 208 209 210 211 412 213 214 215 216 217 218 CS* 200 210 C** 220 CONTINUATION OF EXISTING GROUP GC.GC+1 PG.PG+DAT(L) GO TO 160 GF.I IFISF-1) 230.220,230 NE 4 GROUP — SAME SEQUENCE GC.GC.1 00401.0(ND)4.1. 08(NDE4)•08(N08)+1 NNO.NN041 ND.0 N08.0 PG*PG+OAT(L) G3 TO 160 *ADJUS T * *ADJUST* 150 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 24d 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 C** 230 SF*1 GCE 240 Cs* 250 NNJ*1 d ( N8)*(31N8)+1. DBIN00).0d(NO3)+1 PG*PG+DAT(L) N8.0 NOd*0 GO TO 160 1=0.1 IF(GF-1) 200,250,260 NO DATA ENCOUNTERED — END OF GROUP — SAME SEQUENCE GF.0 W(GC/*W(GC(.01. ND*ND4.1 NO0*ND6+1 INO*INT(PG*10.0+0.99999) RP ( IND)*RP(IND)+1. PG-O. 260 C** 270 C** 280 GC•0 GU 10 100 IF(SF-1) 330,270,330 CONTINUATION OF NO DATA — END OF SEQUENCE — ENO OF GROUP TOO 300 310 320 R(GC).w(GC)+1. ANOINN0IwANO(NNO)+1. Nb*N8.1 N08•NOB+1 IND*INTIPG*10.0+0.99999) RP(IND)*RP(INO).01. PG.O. IF(IEND-2) 160,140,420 290 SAME SEQUENCE ND*ND+1 NO8*N08+1 GO TO 160 L*0.1 11.1-1 11.101 IF(DAT(LL)) 340,290,300 IF(SF-1) 330,310,330 GF*0 SF.° Co* INTER—SEQUENCE — 330 N8mN8+1 ND80408+1 GO TO 160 IF(0Af(LL)+10.1 1.1.+JNUM GO TO 370 L•L1 1E10•3 G.. TU 410 340 350 360 370 380 L.L.Jaum GO TO 23 284 285 NEW SEQUENCE 390 400 L*11 1END•2 400 NO DATA 360,390,390 151 286 410 IF(SF-L) 320.310.320 287 288 C*** 289 290 C** THIS SECTION CALCULATES THE DISTRIBUTIONS AND STATISTICS FOR EACH 291 C** OF THE DISTRIBUTIONS LISTED ABOVE 292 293 CI* 015TRIBLTION OF GRJUP (UR STORM) DURATION IN DAYS (W) 294 295 420 S1.0. 296 501.0. 297 SN1.0. 298 TOTW.O. 299 00 430 1•1.20 300 A.FLOAT(I) 301 5NI.5N1•W(I) 302 SI.514111(I)*A 303 S0I.S01+61(I)*A*A 304 430 TOTW.TOTW+W(I) 305 DO 450. 1.1,20 306 307 PDF(I).(W(I))/TOTR 308 IF(IO.E0.11 GO TO 440 309 CDF(I).CDF(1-1)+PO.F(1) 310 GO TU 450 311 440 CDF(I).PDF(I) 312 450 CONTINUE 313 WRITE(2,1400) 314 WRITE(2,1500) 315 1400 F0RMAT("I",9X."FREQUENCY DISTRIBUTION FUR GROUP DURATION IN DAYS ( 316 CW)",//) 317 1500 FORMA((10X,"INTERVAL",8X,"UCCURENCES",8X,"P0F",13X,"C0F"./) 318 DO 460 1.1,20 319 460 WRITE(2,1600) IPW(I),PDF(I),C0F(1) 320 1600 F0RMAT(15X.I2,15X.F5.0,10X.F7.5,10X.F7.5) 321 xel-slismi 322 V1.(S01-(SI*S1)/SN1)/(SN1-1.) 323 LAMDA.X81/V1 324 K.X111**2/V1 325 WRITE(2,1700) TOT4,X81.VI,LAMDA,K 326 1700 F ORMAT ( / /, 10X, *TOTAL NO. OF OCCURENCES• ",F5• 0, /, 10X,"MEAN• t• 3 327 C,10X,"VARIANCE• ",F8.4,/.10,0LAMDA. ",F7.4,8X,.K. *,F7.4) 328 324 C** DISTRIBUTION OF NU. OF GROUPS PER .1E00ENCE (ANO) 330 331 S1.0. 332 S01.0. 333 5N1.0. 334 TOTANO.O. 335 00 470 1.1.20 AFLOAT(I) 336 IMI.41,4NO(1) 337 338 S1.SI.ANO(1).A 53I.S01+441(1)*A*8 339 T0TANO.TOTAN0+4N0(1) 340 470 341 U0 490 1.1,20 342 IW.I PDF(I).(ANO(1))/TOTANO 343 1F( 10.i0.1) GO TU 4 ,80 344 345 10F(I).CDF(I-1)+PDF(I) GO TO 490 346 COF(I).PDF(I) 480 347 490 CONTINUE 348 4RITE(2,1800) 349 4RITE(2,1500) 350 1800 FORMAT ( "1", 9X, "FREQUENCY DISTRIBUTION FOR NO. OF GROUPS PER SEQUEN 351 CCE (ANO)",//) 352 DO 500 1.1,20 353 WRITE(2,1600) l'AMO(II,PDF(1),CDF(I) 354 500 xal•slismi 355 VI.(501-(51*S1)/S41)/(SN1-1.) 356 LAMDA.X81/VI 357 K•X111**2/V1 358 WRITE(2,1700) TOTANO,181,9I,LAMDA,K 359 152 360 361 C** DISTRIBUTION JF NO. OF DRY DAY1, BETWEEN GROUPS (D) 362 363 S1.0. 3 64 SN1.0. 365 S01.0. 3oo TOTD.O. 367 DO 510 1.1,3 368 A.FLUAT(I) 369 SN1.5641+0(1) 370 S1.S1*D(I)*A 371 S01.S014.0(1)*A*A 372 510 TUTD.TOT0.0(1) 373 DO 530 I • 1,3 374 10.1 375 PDF(11.(D(I))/TOTD 376 IF(10.E0.1) GO TO 520 377 COF(I).CDF(I-1)*PDF ( I) 378 GO TO 530 379 520 COF(1).P0F(1) 380 530 CONTINUE 381 wRITE(2,1900) 382 WRITE(2,1500) 383 1900 FORMAT("1".9X,"FREQUENCY DISTRIBUTION FOR ,40. OF DRY DAYS 384 CGROUPS (0)*,//) 385 00 540 I • 1.3 386 540 WRITE(2,1600) I.0(I),PDF(I),C0F(1) 367 X81.51/SNI 388 V1.(541-(51.51)/SNI)/(5N1-1.) 389 LAMDA•X81/Y1 39u K.X81**2/V). 391 WRITE (2,1700) TOTO.X81,V1,LAIDA,R 392 393 C** OISTRIBUTION OF NO. OF DRY DAYS BETWEEN SEQUENCES (8) 394 395 S1.0. 396 SN1•0. 397 S01•0. 398 TOTB.O. 394 DO 550 1.1,50 400 A.FLJAT(I) 401 SI.S1+B(I)*A 402 SNI.S;41+3(1) 403 SQI.S.114.8(1)*A.A 404 TOTB.T01114.8111 550 405 DU 570 1.1,50 406 101 407 PDF(I)*(8(1))/TOTB 408 IF(IO.EO.1) GO TO 560 409 CJF(I).CDF(I-1)+PDF(I) 410 GO TO 570 411 560 CDF(I).PDF(I) 412 CONfINUE 570 413 BRITE(2,2000) 414 WRITE(2,1500) FORMAT(*1 0 ,9)(..FREQUENCY DISTRIBUTION FOR NO. OF DRY DAYS 415 2000 416 CSEQUENCES (8)*,//) 417 DU 580 I.1,50 4RITE(2,1600) 1,8(I),PDF(I),CDF(I) 418 580 x81.51/SNI 419 V1.(501-(51*S1)/SN1)/(SNI-1.) 420 LA1DA.X81/V1 421 K.X81**2/V1 422 WRITE12,17001 TOTB.M11,V1,LAMDA,K 423 424 425 426 427 428 429 430 C** DISTRIBUTION OF PRECIPITATION PER GROUP (OR STORM) 510. SN1.0. 501.0. TOTRP•O. (RP) BETWEEN BETWEEN 153 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 454 460 461 462 463 464 465 466 407 468 464 590 600 610 00 590 1.1.50 A*FLOAT(I) SN1*SNI.I.RP(I) Sl*S1+RP(I)*(A/ (. 0.0-.0.05) SQ1•SQ1+RP(()*(4/10.0-0.05)*(A/10.0-0•05) A•A/10.0 TOTRP*TOTRP+RP(I) DO 610 1.1.50 IO*I PDF(I)*(RP(I))/TOTRP IF(10.E0.1) GO TO 600 CDF(1).00F(I-.1)4.PDF(1) GO TO 610 CDF(1)*P0F(I) CONTINUE WRITE(2,2100) WRITE(2,1500) 2100 F0RMAT("1",4X.*FREOUENCY CI) DO DISTRIBUTION FOR PRECIP PER GROUP (RP)",/ 620 1.1,50 A*FLOAT(I)/10. 620 RRITE(2.2200) AFRP(I),P0F(I).CDF(T) 2200 FORMAT(15X,F3.1,13X,F5.0,10X,F7.5,10X,F75) X8l*S11SN1 V1*(501IS1*S1)/S81)/(SN1-1.) LAMDA*X8I/V1 KRX81**2/VI WRITE(2,1700) TJTRP,X81,V1,L4NDA,K C** DISTRIbUTION OF INTERARRIVAL TIME TO THE NEXT STORM (DB) 31.0. 3810. S01.0. TUTDB*0. oa 630 I*1,50 A - FLOAT )! ) S1s5141)dill*A LN1*SN11.013(1) 470 SQl*S01+08(1)*A*A 471 630 TOTDB*TOTDB+08(I) 472 00 650 1.1.50 473 10*I 474 PDF(1)*(08(I))/TOTOB 475 IFTIO.E0.1) GO TU 640 476 CDF(1).00F ( 1-.1).0P0F(I) 477 GO Ti 650 478 640 COF11)*PDF(1) 479 CONTINUE 650 480 WRITE(2,2300) 481 4RITEC2,1500) 482 2300 FORMAT("1",9Xr"FREOUENCY DISTRIBUTION FOR INTERARRIVAL TIME BETREE 483 CM STORMS",/,10X,"(CUMBINATION 3F D AND B DISTRIBUTIONS)",//) 484 DO 660 1.1.50 WRITE(2,I600) 1.08(1),P0F(1),CDF(1) 485 660 486 xal.slisNI 487 V1*(S01—(SI*S1)/SNIMSNI-1.) 488 LAMDA*X81/V1 489 KRX131**2/V1 RRITE(2,1700) TUTOB,X(11,V1,LAMDA,R 490 STOP 491 070 ENO 492 154 FREQUENCY DISTRIBUTION FOR GROUP OURATION IN GAYS (14) INTERVAL 1 3 4 5 6 7 8 lo 11 12 13 14 15 16 17 18 19 20 OCCURENCFS 158. 92. 42. 22. 13. 3. 2. 0. o. 1. 0. O. 0. o. o. o. o. o. o. o. TOTAL NO. OF OCCURENCES2 333. MEANS 1.991 VARIA4CE2 Ks 2.3212 LAMOA0 1.1659 PDF .47447 .27629 .12613 .0660 7 • 3904 .00901 .00601 0.00000 0.00000 .00300 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.7077 .47447 .75075 .B7686 .94?94 .98198 .99099 .99700 .99700 .99700 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 155 FREWUENCY 0ISTRI3UTIJN INTERVAL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 FjR AU. OF GkljPs PER 3EOUFNCE (AND) UCCURENCES 830 38. 19. 5. 10. 2. 2. O. O. 1. le O. O. O. O. O. O. 0. O. O. TOTAL NU. OF OCCURENCES= 161. MEAN= 2.068 VARIANCE LAMDA• Ka 1.5618 .7551 POE CDF .51553 .23602 .11801 .03106 .06211 .01242 .01242 0.00000 0.00000 .00621 .00621 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2.7391 .51553 .75155 .86957 .90062 .96273 .97516 .98758 .98758 .9875 6 .99379 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 156 FREQUENCY DISTRIBuTioN F0R 40. OF DRY DAYS BETwEEN GROUPS (D) IlTERVAL 1 2 3 OCCURENCES 92. 44. 36. TOTAL NO. OF OCCURENCES= 172. VARIANCE= MEAN= 1.674 K= 4.3677 LAMOAs 2.6065 CDF PDF .53488 .26561 .20930 .6419 .53483 .79170 1.00000 FREOUcNCY DISTRISOTION 1ATERVAL FJR ;ij. OF D,‹t DAY OCCURENCES 8-,ifoittN POF .'_EQUENCEz, GDF 1 0. 2 3 4 5 6 7 0.00000 O. O. 34. 31. 16. 6. 12. 9. 5. 7. 1. 2. 3. 5 1. 1. O. 2. 1. 2. 2. 0.00000 . 0.00000 0000000 .23944 .21831 .11268 .04225 .08451 .06338 .03721 .04930 .00704 .01408 .02113 .03521 .00704 .00704 0.00000 .01408 .00704 .01408 .01408 0.00000 0.00000 0.00000 .00704 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 .00704 0.00000 0.00000 0.00000 0.00000 .23944 .45775 .57042 .6126d .6971d .76056 .79577 .84707 .85211 .86620 .88732 .92254 .9295d .93662 .93662 .95070 .95775 .97183 .98592 .98592 .98792 .98592 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 .99296 1.00000 1.00000 1.00000 . 0.00000 1.00000 . 0.00000 0.00000 0.00000 0.00000 0.00000 1.00000 1.00000 1.00000 1.00000 1.00000 . 0.00000 1.00000 a 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 . o o o . . . 1. o. o. o. O. o. o. O. o. o. o. o. o. o. o. 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 1 . O. o o o. o. o. o o o 45 46 47 48 . 49 50 TOTAL NO. UF OCCUKENCESg 142. MEAN ° 7.972 LANOAm .2756 VARIANCE. K. 2.1974 28.9212 (B) 157 158 - FROWENCT DITRIBUTIu.4 rjk INTERVAL OCCURENCES .1 .2 .3 .4 .5 .6 .7 164. 67. .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 PRECIP 35. 25. 18. 3. 4. 4. 3. 2. 2. 2. o. 1. o. o. O. O. O. 1. o. 1. o. O. o. o. a. O. O. O. O. O. o. O. o. O. o. o. o. O. O. O. O. O. o. o. o. O. O. O. PEk GkJUR PDF .49249 .20120 .10811 .07508 .05405 .00901 .01201 .01201 .00901 .00601 .00601 .00601 0.00000 .00300 0.00000 0.00000 0.00000 0.00000 0.00000 .00300 0.00000 .00300 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 .0.00000 0.00000 0.00000 0.00000 TOTAL NO. OF OCCURENCES* 333. .197 MEAN* LAMDA* 2.9956 VARIANCc* .5906 K. .0658 (RP) CUF .49249 .69369 .H0190 • 87668 .93093 .93994 .95195 .9(3396 .97297 .97848 .98496 .99049 .99099 .99349 .99399 .99399 .99399 .99399 .99399 .99700 .99700 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00030 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00030 1.00000 1.00000 1.00000 1.00030 1.00030 1.00000 159 FREQUENCY DIIIRIBUTILJN (CLMBINATIUN UF D IlTERVAL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 lb 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 INTERARRIvAL PUR AND B DITRIBUTION) L1CCURENCEb PDF 92. 44. 36. 34. 31. 16. 6. 12. 9. 5. 7. 1. 2. 3. 5. 1. 1. O. 2. 1. 2. 2. O. O. O. 1. O. O. O. O. O. O. O. 0 TIME 8ETwEEN STORMS . O. O. O. O. O. O. 1. O. O. O. O. 0. 0. O. O. 0. COF .29299 .14013 .11465 .10828 .04873 .05096 .01911 .03822 .02866 .01592 .02229 .00318 .00637 .00955 .01592 .00318 .00318 0.00000 .00637 .00318 .00637 .00637 0.00000 0.00000 0.00000. .00318 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0 .00000 0.00000 0.00000 0.00000 0.00000 0.00000 .00318 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 TJTAL NO. JF OCCURENCES 2 314. VAR1ANCE2 23.2343 MEAN. 4.522 .d802 Ks LAMDA 2 .1446 .29294 .43312 .54777 .65605 .75478 .80573 .82484 .86306 .89172 .90764 .92994 .93312 .93949 .94904 .96497 .96d15 .97134 .97134 .97771 .98089 .98726 .99363 .99363 .99363 .99363 .99682 .99682 .99682 .99682 .99682 .99682 .99682 .99682 .99682 .99682 .99682 .99682 .99682 .99682 .99682 1.00000 1.00000 1.00300 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 160 APPENDIX H PROGRAM LISTINGS FOR DEVELOPING THEORETICAL GAMMA, GEOMETRIC, AND EXPONENTIAL DISTRIBUTIONS BASED ON OBSERVED DISTRIBUTION PARAMETERS. INCLUDES SAMPLE OUTPUT DISTRIBUTIONS. 161 I. C THIS PROGRAM CALCULATES A THEORETICAL GAMMA DISTRIBUTION C BASED ON THE ACTUAL DISTRIBUTION PARAMETERS OF LAMDA AND K. THIS PROGRAM IS WRITTEN IN FORTRAN IV. C C INPUT CONSISTS OF LOU, K, INPUT LIMIT, AND UNIT SIZE. 5 PROGRAM GAMMA(INPUT,OUTPUT,TAPE2.0UTPUT) DIMENSION CDF(500) DATA ALAM,AK,ALIMpUSIZE/.1632,.7229,26.4./ DO 20 I.1,500 10 15 20 25 30 35 40 45 CDF(I).0.0 20 CONTINUE WRITE(2,1040) 1040 FORMAT(///,5K," GAMMA DISTRIBUTION ***** .) WRITE(2,1000) ALAM,AK 1000 FORMAT(//,1WLAMDA • "pF7.505X,•K • ",F7.5) WRITE(2,1010) ALIM,USIZE 1010 FORMAT(/.1X,.INPUT • ",F4.0,5K..UNIT SIZE • ",F5.3) STEP0USIZE/100.0 TSTEP.ALIM/USIZE L.IFIX(TSTEP) CALL GAMF(AK,G) Rl.ALAM/G R2.AK-1.0 2.0.0 DO 40 J.1,1. DO 30 1 • 1,100 X.FLOAT(1).STEP4USIZE*FLOAT(J .. 1) Z.24.R14.6(ALAM 4 X)**R2).EXP(ALAM*X) 30 CONTINUE COF(J).2 40 CONTINUE DO 50 I.141. CDF(i)=CDF(I)/2 50 CONTINUE WRITE(2.1020) 1020 FORMAT(//p4WINTERVAL",13WPDF ., 12X , CDF" , /) HOLD.0.0 DO 60 I.1,L TOP.FLOAT(I)*USIZE BOT-TOP- US IZE+STEP PDF.CDF(I)-HOLD HOLD.CDF(I) WRITE(2,1030) BOT.TOP,PDF,CDF(I) ",F6.3,5X,F9.7,6X,F9.7) 1030 FORMAT (1X,F6.3," 60 CONTINUE STOP END 1 5 SUBROUTINE GAMF(X,Y) DIMENSION P(7),0(6) P(1) .3.410911E+ 01 P 6 21.-4.93 4 12 7 E 401 P(3).4.300589E+02 P(4).5.5680 731+01 P65 ). • 058522E'03 10 15 P(6).7.7192.41E-01 P(7)0-3.1721 06 E +00 Q(1).2.445514E+02 0(2).-1.017 477 E +03 0(3).1.1616 00 E +03 0(4).2.0512 90 E +03 Q(5).6.608 035 E -01 (.!v.-2.535b73E4.01 1.1 I.IFIX(T) 41.1.0 IF(I2) 30,30,60 30 1.1+1 20 GO T0(40,500 01,1 162 C 0.0 < X < 1.0 25 40 A.AitT 6 474.1.011 T.T+2.0 GO TO 80 C 1.0 ‹. X < 2.0 30 50 A.A/T T.T+1.0 GO TO 80 35 40 C 3.0 <• X 60 DO 70 T.T-1.0 A.AAT 70 CONTINUE C C 2.0 ‹. X < 3.0 C EVALUATE MINIMAX APPROXIMATION FOR GAMMA FUNCTION. 45 50 80 TOP.P(6)670(7) DEN.T+0(6) DO 90 J.1,5 TOP.TOP*74.PW, DEN.DENPT.0(J) 90 CONTINUE Y. ( TOP/DEN)*A RETURN END 163 ***** GAMMA DISTRIBUTION ***** LAPIDA a .16320 INPUT a 26. INTERVAL .010 1.010 2.010 3.010 4.010 5.010 6.010 7.010 8.010 9.010 10.010 11.010 12.010 13.010 14.010 15.010 16.010 17.010 18.010 19.010 20.010 21.010 22.010 23.010 24.010 25.010 • 1.000 n 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 11.000 12.000 13.000 14.000 15.000 16.000 17.000 1d.000 19.000 20.000 21.000 22.000 23.000 24..000 25.000 26.000 • • • • • • • • • • • • • • • • • • • • • • • • K .72290 UNIT SIZE • 1.000 PDF .2101915 .1541914 .1191405 .0943331 .0757688 .0614357 .0501491 .0411417 .0338836 .0279928 .0231848 .0192432 .0160002 .0133242 .0111104 .0092751 .0077510 .0064832 .0054271 • 0045464 .0038112 .0031967 .0026828 .0022527 .0018924 .4,0015904 CDF .2101915 .3643829 .4835234 .5778565 .6536253 .7150610 .7652102 .8063519 .8402355 .8682283 .8914130 .9106562 .9266565 .9399806 .9510910 .9603661 .9681171 .9746003 .9800274 .9845738 .9883850 .9915817 .9942646 .9965173 .9984096 1.0000000 164 C C C C THIS PROGRAM CALCULATES A THEORETICAL GEOMETRIC DISTRIBUTION BASED ON THE ACTUAL DISTRIBUTION MEAN. THIS PROGRAM IS WRITTEN IN FORTRAN IV. INPUT CUNSISTS OF THE DATA MEAN AND THE OUTPUT LIMIT. 5 PROGRAM GEOME(INPUTAOUTPUT.TAPE2•OUTPUT) REAL n DATA M004.306,30/ 10 15 20 WRITEI2,200) GEOMETRIC DISTRIBUTION ***** ..,///1,1X,"DATA MEAN 200 FORMAT("1".* C. *,F7.5,3X,"OUTPUT LIMIT • "..13,//) WRLTE(2,300) 300 FORMATI1WCLASS",BX,"P0F",13WCDF",/) 5.0 DO 10 1.1,L PDF.(1.•1/MPOSIII-1)*(1/M) CDF.CDF+POF WRITE(2,400) I.PDF.CDF 400 FORMAT(11,12.8X,F13.6,8X,F8.6) 10 CONTINUE STO END 165 ***** GEOMETRIC DISTRIBUTION ***** DATA MEAN CLASS 1 2 3 4 5 6 7 a 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 a 4.30600 OUTPUT LIMIT * 30 PDF COE .232234 .178301 .136894 .105102 .080694 .061954 .047566 .036520 .028039 .021527 .016528 .012689 .009743 .007480 .005743 • 004409 .003385 .002599 .001995 .001532 • 001170 .000903 .000693 .000532 .000409 .000314 .000241 .000185 .000142 .000109 .232234 .410536 .547429 .652532 .733226 .795180 .842746 .879266 .907304 .926831 .945359 .958049 .967791 .975271 .981014 .985423 .988608 .991408 .993403 .994935 .996111 .997014 .997708 .998240 .998649 .998963 .999204 .999388 .999530 .999640 166 1 5 C C C C THIS PROGRAM CALCULATES A THEORETICAL EXPONENTIAL DISTRIBUTION BASED ON THE ACTUAL DISTRIBUTION MEAN. THIS PROGRAM IS WRITTEN IN FORTRAN IV. INPUT CONSISTS OF THE DATA MEAN, INPUT LIMIT, AND UNIT SIZE. PROGRAM EXPO ( INPUT,OUTPUT0TAPE2.0UTPUT) DIMENSION CDF(250) REAL "W. DATA MoLt014.306,30.,1./ 10 15 20 25 WRITE(2,100) MoloU 100 FORMAT("1'," EXPONENTIAL D/STRIBUTION "0///,1X,"MEAN • • CoF7.5,3X,"LIMIT • ',F3.0.3X,"UNIT SIZE • ".F3.0,//) • WRITE(2,200) 200 FORMAT(IX,"CLASS",13X,*PDF.,13X,"CDF",/) LN•IFIXIL/U+.91 R.O. DO 10 .1•1,LN R.R+U 10 CDF(.1/.1•.EXP(—R/M) PDF.00F(1) DO 30 I•1,LN C.FLOAT(I)OU IFII.E0.11 GO TO 20 PDF.CDF(1).-CDFII-1/ 20 WRITE(2,300) C,PDF,C0F(1) 300 FORMAT(IX,F5.2,5X,F13.698X,F13.6) 30 CONTINUE STOP END 167 ***** EXPONENTIAL DISTRIBUTION ***** MEAN • 4.30600 CLASS 1.00 2.00 3.00 4.00 5.00 . 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00 30.00 LIMIT • 30. UNIT SIZE • 1. PDF CDF .207239 .164291 .130244 .103252 .081854 .064891 .051443 .040782 .032330 .025630 .020319 .016108 .012770 .010123 .008025 .006362 .005044 .003998 .003170 .002513 .001992 .001579 .001252 .000993 .000787 .000624 .000494 .000392 .000311 .000246 .207239 .371531 .501774 .605026 .686681 .751771 .803214 .843996 .676326 .901956 .922275 .938382 .951152 .961275 .969301 .975663 .980706 .984705 .987875 .990387 .992380 .993959 .995211 .996203 .996990 .997614 .998108 .998500 .998811 .999058 168 APPENDIX I GAMMA FUNCTION [F(N)] TABLES FOR VALUES OF K BETWEEN 0 AND 2. 169 N CO 0 N 0 LO CV h Cl 01 LO LO 0 l D CO CN •re Ln L.0 Ln r-i o -zr h o ,--4 r-1 r-- r--• o Lo co r-1 NCOLn Mr-100 . . . . . 0 •zr M CN H H , -i H H H H N CO CN CN O H L.0 CO In L.0 o N L ,--i H en Y en en co co CN Cr) CO ul en H o o en CO • Ln Cr) Ln N CN H 'V LO N • 01 se en 01 • LC) C) LN H 'V H H CO • lr) Ln • ri ri ri H ri LO Ln CO en CN Q '14 CV Cr) ge CO LD CO 'e co in • rl CN N C CN CO 01 szti CO 'e Cl H Cr) H 0 0 • • • ri ri ri ri Lf) CO CV LD CN H N CO CN Ln co Lo N N N CO LO H 0 CN •ei se 01 Ln M LN H 0 • en r-i ri ri 0 0 LO M N H CO Ln in Ln c-1 L.0 Ln LO CO nr In 0 CV LO H CO CV H Cr) CV Ln H 0 C71 LO Cr) CV CN C Ln ‘(:)" • • • • • LO Cr) CN H H H H H H Q o H N CO H 0 LO •V Cr) •zr •e co in 0 se 0 LO CO CO N H LO N O Q LO • • • • • nr L.0 en N CN H H en 01 H cf' CO CO N cn en LN H 0 • H H H Q o Cr Ln h H o Lo Cr (N LC) 0 Cr) rs- 0 0 CO Cr) LO 0 LO N CV in m LN 01 N Q ¼0 se N H 0 • • • • cNi en N en Ln Lo ln CO 0 Ln 'e 0 0 In 0 Ln Ln h CV Crl Ln -Y Lo o .14 ,--1 cs ) u: Ln 0 H CN y t--- ,--1 h ,--i co 0 Cn 0 M CN -e • •zr . , . . . . . Cl tss se CV (N H H H H H •v 0 h 0 Cr) 01 cf' N Ln CV N 0 N 0 0 N CO LD (N Cr) o Ln 1. 0 CO LO Cr) L..0 Cr) ,--4 1.0 01 H C N .zt' CV H CO Cr) .e LO . . • . . . rl ri H ri H CN (NI se (X) 01 cs 0 0 N CN •zr CN 0 CV N CO •ze CO 01 CO CN ,--i ,..-4 1.0 LO cn co s r--i cs el I-, •14 N ,..1 C) (N cr, Ln .r. ,--1 8 in • • • • • CV CV H H H H H CN Cr) se Ln 1.0 N CO 01 170 tf) 01 CO o V) CI) N 01 . N 1/4.0 a) 0 01 CO CO CO . CO CO . C1 h (Y ) N 01 h 0 Ce 01 V) CO CO CO CO in CO CO N N ‘.0 al Lf) N CD 01 ( r) t.0 N 01 • N CO CO O'N C 01 N 01 N N 01 Cr) Cl • k.0 0 01 H 01 CO • if) CO CO • t0 Cr) Cl tf) CO 0 01 N N 01 CO • 01 01 Cf) 01 CO 1-1 0) ',7t. (Y ) 01 CO k.0 CO CO 01 (f) N • 01 • CO cd o a) • 0 n.o c:n N Cl • CO CO • tf) CO CO 'tzt, N 01 00 01 CO l0 0 01 CO CO N 01 . cr CO 111 01 . CO Ln 01 01 N LO N 01 ri h tf) 01 • 01 01 CO 03 r•-• V) 01 • CO 01 cr C H tf) 01 CO C tf) 0 Ce) 01 C 01 • al 03 N C tr) Cd 01 h If) o 01 Ln Cl Ln re) N 01 • N In 01 01COCO CO CO CO CO CO ri ri ON•zi3OD 01 01 01 01 01 CO CO CO r-4 0 0 01 • H CO tf) CO CO • N CO CO CO l0 CO 01 CO • 03 l0 H 01 • C t.0 h CO CO N h 01 CO h •tt. Cl CO • gzr L0 CO CO • 0 h CO CO 0 LC Cl LO LO 00 cr) co CO LO CO a) 0) N CO ri 01 in h 01 CO • Cl 1"-CO CO . V k.0 tf) N lOrr)COri rf) 0 01 CO C1 01 CO CO • • • CO ri liD 01 • CD 0 0 0 . r--I 01 0 • N 01 r--1 Cl .f) tf) .1' 01 • N cr 01 • 01 h 01 01 4-) 0 tij ( e) rn • CO 01 C 01 h 01 (*el 01 szf' N N 01 01 Lt1 01 CO t.0 N H 01 • Cf) t.0 01 01 • CO CO LD 01 N LO H N C r H Cd 0 a) CO 03 CO Cl 01 .411 01 a) 0 0 0 H k.C) (11 cl" 01 • r•-• Cr a) V rl tr) CYN • Ce) H 01 LO 1!) H cc co 000000 LC) Cr) N • • • • • H H H H H H a) co H a) e) 000 L9 H h • H CO • H H 171 APPENDIX J PROGRAM LISTING OF THE NUMERICAL INTEGRATION ROUTINE. 172 PROGRAM INTEG(OUTPUT,TAPE6.0UTPUT,TAPE7) 1 5 C C INTEG GENERATES A TABULAR1ZED GAMMA COF IN ARRAY P. LAM AMU K ARE THE PARAMETERS OF THE GAMMA DISTRIBUTION. G IS THE VALUE OF THE GAMMA FUNCTION OF K. THIS EXAMPLE PROGRAM PRODUCES A GAMMA COF FOR 0.0 TO 4.0 INCHES THE PROBABILITY OF 4.0 UF PRECIPITATION IN 0.01 INCH INTERVALS. OR LESS INCHES OF PRECIPITATION IS ASSUMED TO EQUAL 1.0. FILE 7 STORES THE GENERATED TABLE. 10 REAL K,LAM DIMENSION P14001 15 20 25 30 35 LAM.2.4851 K.0.6849 G=1.3227 RI.LAM/G R2.K-1.0 2.0.0 DO 20 1 .1,400 DO 10 1.1,100 X.FLOA1111/10000.0+FLOAT1J-11/100.0 2.2 , 121 ,011LAM.X1 4..R21.0 EXPI - LAMAX) 10 CONTINUE P1.11.2 20 CONTINUE DO 30 1.1,400 P ( I).P(I)/2 30 CONTINUE DO 40 1.1,400 •RITE(6,150) Pli) 150 FORMAT11X,F10.7/ 40 CONTINUE WRITE(7) P ENOFILE 7 STOP END 173 APPENDIX K PROGRAM LISTING OF THE STOCHASTIC RAINFALL/RUNOFF MODEL (RAIN 6) AND THE OUTPUT FOR THE HANFORD SITE. 174 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 PROGRAM RAIN6(INPUT,OUTPUT,TAPEleINPUT,TAPE2.0UTPUT) DIMENSION INTER(400,6)OPT(400.3),RUNOF(100).PROB1(366).PROB2(400) C.PRO83(41).SSL(80),SSH(80).PRECIP(500) REAL LAMI.LAM2.LAM3pLAM4,LAM5,LAM6PLAM7 REAL Kl.K2,1,(3,1(4.R50(6.K7 REAL INTER REAL INTVAL INTEGER PRO81,PROB2,PROB3,PRO84 DATA LAM1,LAM2,LAM3.LAM4.LAM5,LAM6,LAM7/.1682,.1412,.1260,2.995tr1 C1.1223,4.3553,5.5109J DATA K1,K2,K3,K4,K5,K60(7/.7241,.0682,1.07230.5906..8372,.5998,.53 C84/ DATA GAMAI.GAMA2.GAMA3,GAMA4,GAMA5,GAMA6.GAMA7/1.2616.1.0956..9f31 CI 1•5112,1•1249,1•4847, 1•6496/ C CT.** C C C C C C C C C C C C C C C C C C C C C C C C C C C 44 C 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 C C C C C C C C C C C C C C C 60 61 C C 62 63 64 65 66 67 68 69 70 C C C C • C C C C C C C C C STOCHASTIC PRECIPITATION MODEL C C C THIS PROGRAM SIMULATES THE FUTURE DAILY PRECIPITATION FOR THE C HANFORD SITE RICHLAND, WASHINGTON. FOR THIS LOCATION C THE CALENDAR YEAR HAS BEEN BROKEN DOWN INTO GROUPS FOR MODELING C PURPOSES IN BOTH THE AREAS OF INTERARRIVAL TIME AND PRECIPITATION C PER EVENT. TWENTY (20) YEARS OF PAST CLIMATIC DATA WERE ANALYZED C MONTHS AND THE TO DETERMINE THE APPROPRIATE GROUPING OF C TO BE USED FOR EACH GROUP. THE WINTER DISTRIBUTIONS HYPOTHETICAL C MONTHS OF NOV—DEC—JAN—FEB ARE MODELED DIFFERENTLY THEN THE C REMAINING MONTHS OF THE YEAR DUE TO THE FRONTAL TYPE OCCURRANCE C USED... OF STORMS. FOP THIS PERIOD, THREE DISTRIBUTIONS ARE C C INTERARRIVAL TIME (DAYS) TO THE NEXT STORM C DURATION (DAYS) OF THE STORM C THE AMOUNT (INCHES) OF PRECIPITATION FOR THE STORM C C THE CALCULATION OF PRECIPITATION DURING THE WINTER PERIOD IS C DONE WITHIN THE SUBPROGRAM WINTER. THE FOLLOWING TABLE SHOWS C THE GROUPING AND DISTRIBUTIONS USED FOR MODELING. C C C C HYPOTHETICAL C DISTRIBUTION WINTER STORM PERIOD C NOV— DEC *JAN*FEB C GEOMETRIC INTERARRIVAL TIME C GEOMETRIC DURATION C GAMMA PRECIP AMOUNT C C REMAINDER OF THE YEAR C INTERARRIVAL TIME C GAMMA MAR C SHIFTED GAMMA APR -.MAY C GEOMETRIC JUN C SHIFTED GAMMA JUL C SHIFTED GEOMETRIC AUG*SEP C SHIFTED GEOMETRIC OCT C C PREC/P PER EVENT GA C GAMMA MAR JUN APR—MAY—JUL—AUG— SEP —OCT GAMMA C ' GAMMA C C C C C C C C C THIS PROGRAM ALSO CALCULATES THE DIRECT SURFACE RUNOFF BY METHOD USING THE SOIL CONSERVATION SERVICE (ICS) METHOD. THIS ALSO CONTAINS A SUBPROGRAM (MOIST) THAT MAINTAINS THE ANTECEDENT RAINFALL CONDITIONS FOR THE FIVE DAYS PRIOR TO THE PRESENT PREC1P EVENT. 175 71 72 73 74 75 76 77 78 79 80 81 82 83 84 88 86 87 Se 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 C C C C C C A RANGE OF CURVE NUMBERS (CM) AND AN INITIAL ABSTRACTION of .15 AND .2 ARE USED IN MULTIPLE RUNS OF THE PROGRAM. THIS PROGRAM OUTPUTS THE DISTRIBUTIONS OF PREDICTED VALUES FOR A 500 YEAR PERIOD FOR INTERARRIVAL TIME, AND RUNOFF. IT ALSO OUTPUTS THE DAILY PRECIPRRECIP/EVENT, AMOUNTS FOR THE FIRST 20 YEARS. C*** C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C*** C*** C C C C C C C C 121 C*** 122 123 124 125 126 C C C C C THE FIRST SECTION DEVELOpEs GAMMA TABLES FOR INTERARRIVAL TIME AND PRECIP PER EVENT DISTRIBuTUINS USING THE LAm0A, K— VALUE AND GAMMA FUNCTION DETERMINED FOR EACH DISTRIBUTION WHICH IS MODELED WITH A GAMMA DISTRIBUTION. f C 128 129 130 131 132 133 134 C C C C C C C C GAMA IS THE NOTATION FOR THE GAMMA FUNCTION FOR THE GROUPS K— VALUE C C*** C C** CALCULATE GAMMA TABLE FOR INTERARRIvAL DIST. FOR GROUP 1 C RI.LAM1/GAMA1 R2AKI-1. z•0. 136 137 138 139 140 141 142 143 C C C C C C LAM IS THE LAmDA PARAMETER FOR THE GAMMA DISTRIBUTION K IS THE K VALUE PARAMETER FOR THE GAMMA DISTRIBUTION (MAR) .-1 IS NOTATION FOR INTERARRIVA1 TIME GROUP 1 (APR—MAT) —2 IS NOTATION FOR INTERARR1vAL TIME GROUP 2 —3 IS NOTATION FOR INTERARRIvAL TIME GROUP 3 (JUL) —4 IS NOTATION FOR WINTER STORM PRECIPITATION (MAR) —5 IS NOTATION FOR PRECip PER EVENT GROUP I —6 IS NOTATION FOR PRECIP PER EVENT GROUP 2 (JUN) —7 Is NOTATION FOR PREcIP PER EVENT GROUP 3 (APP —MAY—JUL—AUG—SEP—OCT) 127 135 C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C VARIABLE LIST ARRAYS INTER • USED TO STORE GAMMA TABLES FOR INTER. TIME PPT • USED TO STORE GAMMA TABLES FOR pRECIP/EvENT PROB1 • USED TO STORE THE NUMBER OF INTER TIME EVENTS PROU • USED TO STORE THE NUMBER OF pRECIP EVENTS P 808 3 • USED TO STORE THE NUMBER OF RUNOFF EVENTS SSL • LOWER LIMIT OF DISTRIBUTION INTERVAL SSH • UPPER LIMIT OF DISTRIBUTION INTERVAL pRECIP • USED TO STORE DAILY PRECIP VALUES LAM • LAmDA PARAMETER FOR THE GAMMA DISTRIBUTION K • K— VALUE PARAMETER FOR THE GAMMA DISTRIBUTION GANA • NOTATION FOR THE GAMMA FUNCTION Ni • NOTATION FOR INTERARRIVAL TIME N2 • NOTATION FOR PRECIP PER EVENT NyDAy • NUMBER OF DAYS IN THE YEAR ILEAp • NOTATION FOR LEAP YEAR TRAIN • YEAAY CUMULATIVE VALUE OF PREc/p RAIN • DAILY RRECIP AMOUNT (INCHES) ICAL • CALENDAR COUNTER Il • COUNTER FOR THE NUMBER OF EVENTS FOR INTER TIME 12 • COUNTER FOR THE NUMBER OF EVENTS FOR pRECIP/EvENT 13 • COUNTER FOR THE NUMBER OF EVENTS FOR RUNOFF RuNoF • AMOUNT OF DIRECT SURFACE RUNOFF (INCHES) ppf • PROBABILITY DENSITY FUNCTION CDF • CUMULATIVE DENSITY FUNCTION CM • SCS CURVE NUMBER C C C C C C C C C C C C - 176 144 145 146 147 148 149 150 151 152 153 154 155 116 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 20$ 206 207 208 209 210 211 212 213 214 00 20 1.1,31 00 10 4.1,100 X.FLOATIJ)/100..FLOATI1-.11 1.Z.R1*((LAMI*X)**R2)*EXP(LAM1*X) 10 CONTINUE INTER(I,2).2 20 CONTINUE DO 30 1.1,31 INTER(1102).INTER(1,2)/2 30 CONTINUE C** CALCULATE GAMMA TABLE FOR INTERARRIVAL 01ST. FOR GROUP 2 R1.LAM2/GAMA2 2.0. DO 50 1.1,60 DO 40 4 .1,100 A.FLOAT(J)/100,4FLOAT(11) Z.I.R1*((LAM2*X)**R2)*E1P(....L4M2*X/ 40 CONTINUE INTER(I,3).Z 50 CONTINUE 00 60 1.1,60 INTER(I,3).INTER(I,3)/2 60 CONTINUE C** CALCULATE GAMMA TABLE FOR INTERARRIVAL DIST. FOR GROUP 3 R1.LAM3/GAMA3 R2.1(3-.1. 2.0. DO 80 1.1/30 DO 70 4.1,100 AnFLOATIJJ/100.+FLOAT(1...1) Z.Z+R1*((L4M3*X)**R2)*EXP(LAM3*A1 70 CONTINUE INTER(I,4).1 80 CONTINUE 00 90 1.1,30 INTER(I,4).INTER(/,4)/1 90 CONTINUE C** CALCULATE GAMMA TABLE FOR WINTER STORM PRECIPITATION R1.LAM4/GAMA4 R2.K4.4. Z.O. DO 110 1.1,400 DO 100 J.1,100 X.FLOAT(J)/10000.4FLOAT(11)/100. Z.L.R1*((LAM4*X)**R2)*EXP(•.LAM4*X) 100 CONTINUE IN1ER(1,5).2 110 CONTINUE DO 120 1.1,400 INTER(1,5).INTER(1,5)/2 120 CONTINUE C** CALCULATE GAMMA TABLE FOR PRECIP PER EVENT FOR GROUP 1 R1.1.AP15/GAMA5 R2.11(51. DO 140 1.1,400 00 130 J.1,100 X.ELOA1(J)/10000.+FL0ATt1-..1)/100. 2.1+R1*((LAM5X)**R2)*EXP(LAN5*X) 130 CONTINUE PPT(I,1).2 140 CONTINUE 177 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 DO 150 1.1,400 PPT(I,1).PPT(I.1)11 150 CONTINUE C C** CALCULATE GAMMA TABLE FOR PRECIP PER EVENT FOR GROUP 2 C RI.LAM6/GAMA6 R2.1(6-1. Z.O. DO 170 1.1,400 00 160 J.1.100 X.FLOAT(J)/10000.4fLOAT(1-1) 1 100. Z.Z+R10((LAM6.0X)**R2)*EXP(-LAN6*X) 160 CONTINUE . PPT(IO2).Z 170 CONTINUE DO 180 1.1,400 PPT(1,2).PPTII.2)/Z 180 CONTINUE C C** CALCULATE GAMMA TABLE FOR PRECIP PER EVENT FOR GROUP 3 C R1.LAM7/GAMA7 R21,1(7-.1. Z.O. DO 200 1.1,400 DO 190 J • 1,100 X.FLOAT(J)110000.+FLOATI1-11/100. Z.Z441*((LAM7+X)**R2)*EXP(-LAM7tX) 190 CONTINUE PPT(I,3)•2 200 CONTINUE DO 210 1.1,400 PPT(1,3).PPT(I,3)/Z 210 CONTINUE C C** ENO OF GAMMA TABLE DEVELOPMENT C C*** C*** C C THIS SECTION CALCULATES THE DAILY PRECIPITATION AMOUNT AND C THE AMOUNT OF RUNOFF C C C C C NI IS NOTATION FOR INTERARRIVAL TIME C c C C C C C C C NI Ni Ni NI NI Ni NI • • • • • • • 1 WINTER GROUP (NOV-DEC-JAN-FEB) 2 MAR ' 3 APR-MAT 4 JUN 5 JUL 6 AUG- SEP C 7 OCT 272 C 273 274 275 276 277 278 279 280 281 282 283 284 285 C N2 IS NOTATION FOR PRECIP PER EVENT C C N2 • 1 MAR C N2 • 2 JUN C N2 • 3 APR-MAY-JUL-AUG-SEP-OCT C C C C C** VARIABLE AND CIUNTER INITIALIZATION C TOTAL•O. ICOUNT.0 C C C C C C C C C C C C C C C c C C C C C C C C C C 178 286 N1.1 287 N2.1 288 11.0 289 12.0 290 13 • 0 291 TRAIN.O. 292 293 ILEAP.0 294 J.1.1 295 NYDAY.365 296 RAIM.O. 297 298 CN•80. 299 A8ST.0.20 300 NCN.INTICM.F.5) 301 ( .0 302 IJI.894.ILEAP 303 NY.' 304 NYN.NY 305 MA.0 306 M8.0 307 MC.0 308 MD.0 309 ME•0 310 MF.0 311 MG.0 312 313 C** HEADING PRINTOUT 314 315 WRITE(2,1) 316 1 FORMAT("1",291s #30X,"' 317 C *",/,30X,"* PREDICTED PRECIPITATION 318 C RECORD *.) 319 WRITE(2,2) 320 2 FORMAT(30X,"* **,/,30)(s* 321 C ,///) 322 323 C** CHECK TO SEE IF EVENT IS IN WINTER PREC1P PERIOD 324 325 IF(M1.E0.20) GO TO 230 220 326 GO TO 240 327 328 C** YES, EVENT IS IN THE WINTER PRECIP PERIOD 329 330 230 CALL WINTER(ICAL,K,M1,CM,ILEAP,PRO81,PR082,PRO83,TRAIMPRUNOF,JJ, CIJ1,11,12,13,PRECIP,RAIM,NYDAY,MY,MA,M8,MC.80,ME,MF,MG,NYM,TOTAL,K 331 CK,INTER) 332 IF(NY.GT.500) GO TO 460 333 334 NYN.NY GO TO 350 335 336 337 C** CALCULATION OF INTERARRIVAL TIME FOR MONTHS OTHER THAN WINTER PRECIP PERIOD 338 339 C** IS EVENT IN THE MONTH OF JUN 340 240 IF(N1.NE.4) GO TO 250 341 342 C** YES, THE EVENT is EN JUN 343 344 X.RANF() 345 P.1. 1 4.959 346 IT.INTICALOG(X)IALOG(1-4))+1.0) 347 IF(IT.GT.30) /T.30 348 GO TO 310 349 350 C** IS EVENT IN THE MONTH OF JULY 351 352 IF(M1.NE.5) GO TO 260 353 250 354 YES, THE EVENT IS IN JULY C** 355 C** THE 31 ST DAY INTERARRI VAL TIME FOR JUL IS MODELED SEPERATELY FROM 356 C** THE REMAINDER OF THE MONTH. THERE IS A 0.895 PERCENT CHANCE CF 357 C** HAVING AN INTERARRIVAL TIME LESS THAN 31 DAYS. 358 359 179 360 X.RANF() 361 IF(X.LT.0.89474) GO TO 320 362 K.31 363 GO TO 340 364 365 C** IS THE EVENT IN OCT 366 367 260 IF(N1.NE.7) GO TO 270 368 369 C** YES, EVENT IS IN OCT 370 C** THE FIRST DAY INTERARRIVAL TIME FOR OCT IS MODELED SEPERATELY FROM 371 C** THE REMAINDER OF THE MONTH. THERE IS A 0.379 PERCENT CHANCE OF 372 C** HAVING A ONE DAY INTERARRIVAL TIME. 373 374 X•RANF() 375 IF(X.GT.0.37857) GO TO 300 376 111 377 GO. TO 310 378 379 C** IS THE EVENT IN APR-MAY 380 381 270 /F(N1.NE.4) GO TO 280 382 383 C** YES, EVENT IS IN APR-MAY 384 C** THE FIRST DAY INTERARRIVAL TIME FOR APR-MAY IS MODELED SEPERATELT 385 C** FROM THE REMAINDER OF THE GROUP. THERE Is A 0.300 PERCENT CHANCE OF cs* HAVING A ONE DAY INTERARRIVAL TIME. .386 387 388 X.RANF() 389 IF(X.GT.0.30000) GO TO 320 390 IT.1 391 GO TO 310 392 393 C** IS THE EVENT IN AUG-SEP 394 395 280 IF(.N1.NE.6) GO TO 320 396 397 C** YES, EVENT IS IN AUG-SEP 398 C** THE FIRST DAY INTERARRIVAL TIME FOR AUG-SEP IS MODELED SEPERATELY 399 C** FROM THE REMAINDER OF THE GROUP. THERE IS A 0.228 PERCENT CHANCE 400 C** OF HAVING A ONE DAY 1NTERARRIVAL TIME. 401 402 X.RANFII 403 IF(X.GT.0.22819) GO TO 290 404 IT.1 405 GO TO 310 406 407 C** THE EVENT IS IN AUG-SEP GROU BUT HAS AN INTERARRIVAL TIME 408 C** GREATER THAN 1 DAY 409 290 x.RANF() 410 P • 1./9.313 411 IT./NTI(ALOG(X)/ALOG11-P))+1.0)+1 412 IFIIT.GT.601 K.60 413 414 GO TO 310 415 416 C** EVENT IS IN OCT 417 X.RANF() 418 300 P.1./5.517 419 IT.INTUALOG(X)/ALOG(1-P))+1.0)41 420 IF(IT.GT.31) 17.31 421 ICAL.ICAL+IT 310 422 K•17 423 GO TO 350 424 425 C** EVENT IS IN MAR, APR-MAY OR JUL GROUP 426 427 X.RANF() 32C 428 00 330 1.1,60 429 IF(NI.E0.5.A140.I.GT.30) GO TO 340 430 IFIN1.E0.2.AND.I.GT.31) GO TO 340 431 180 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 K.I IF(INTER(I,N1).GE.X) GO TO 340 330 CONTINUE 340 IF(N1.E0.4.0R.N1.E0.6) K.K+1 ICAL.ICAL4K Co* WE ARE IN THE SAME YEAR . Co* THE FOLLOWING SEVEN STATEMENTS REPRESENT THE ENO OF EACH INTERAPRIVAL Co* TIME GROUP. 350 IJI.59+ILEAP IJJ.90+ILEAP IJ0.151+ILEAP IJK.181+ILEAP IJI.212+ILEAP IJM.273.1.1LEAP IJN.304+ILEAP Co* DETERMINATION OF WHICH NEW GROUP WE HAVE MOVED INTO. IF(NI.E0.I.AND.ICAL.GT.IJI) IF(N1.E0.2.AND.ICAL.GT.IJJ) IF(N1.E0.3.AND.ICAL.GT.IJO) IF(N1.E0.4.AND.ICAL.GT.IJK) IF(ICAL.E0.1JL.AND.K.E0.31) IF(N1.E0.5.AND.ICAL.GT.IJL) IFINI.E0.6.AND.ICAL.GT.IJM) IF(NI.E0.7.ANO.ICAL.GT.1J4) GO TO 430 GO GO GO GO GO GO GO GO TO 360 TO 370 TO 380 TO 390 TO 400 10 400 10 410 TO 420 Co* THE FOLLOWING STATEMENTS ADJUST THE FINAL PERIOD AT THE END OF AN Co* INTERARRIVAL TIME GROUP BY FINDING WHICH NEW GROUP WE HAVE Co* OVERFLOWED INTO AND THEN BY BACKING UP TO THE END OF THE OLD GROUP. Co* THE ANTECEDENT RAINFALL CONDITION IS UPDATED TO THE END OF THE OLD Co* GROUP. A NEW INTERARRIVAL TIME IS FOUND BY USING THE NEW GROUPS Co* DISTRIBUTION IN THE ABOVE PROCESSES. Co* THE NEW GROUP IS MAR 360 N1.2 IF(MA.E0.1) GO TO 430 K.IJI-(ICAL-K) ICAL.IJI KK.K+KK MA.1 CALL MOIST(K.ICAL.N1,CN,RAIN) GO TO 320 Co* THE NEW GROUP IS APR-MAY 370 N1.3 IF(MB.E0.1) GO TO 430 K.IJJ-I/CAL-K) ICAL.IJJ KK.K+KK M8.1 CALL MOISTIK.ICAL,N1pCN,RAINI GO TO 270 Co* THE NEW GROUP IS JUN 380 NI.. IF(MG.E0.1) GO TO 430 K.IJO-(ICAL-K) ICAL.IJO KK.K+KK MG.1 CALL MOIST(K.ICALOI,CN.RAIN) GO TO 240 181 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 56, 568 569 570 CS* THE NEW GROUP IS JUL 390 N1.5 u(mc.eo.1) GO TO 430 K.IJK—IICAL—K) ICAL.IJK KK.K+KK MC.1 CALL MO/ST(KvICAL,N1sCNIPRAIN) GO TO 250 C** THE NEW GROUP IS AUG—SEP 400 N146 IF(M0.E0.1) GO TO 430 K.IJL—(ICAL nK) ICAL.IJL KK.F4KK M0.1 CALL MOIST(K,ICAL,N1,CN,RAIN) GO TO 280 CS* THE NEW GROUP IS OCT 410 4147 IF(ME.E0.1) GO TO 430 K.IJM—(ICAL—K) ICAL.IJM RK.R.,KK ME-1 CALL MOIST(K,ICAL,N1,CN,RAIN) GO TO 260 Cs* THE NEW GROUP IS THE 4/NTER PER/00 420 N1.1 IF(MF.E0.1) GO TO 430 10.1J)4(ICAL...1() ICAL.IJN MF.1 43C CALL MOIST(K,ICALiN1,CN,RAIN) GO TO 230 CALL MOIST(K,ICAL,N1,CN,RAIN) Il -11+1 PRO81(K).PRO810(141 KX.0 Cs* DETERMINATION OF WHICH PRECIP GROUP WE ARE IN N2.3 IF(ICAL.GT,IJI.AND.ICAL.LT.IJJ) N2.1 I".151+ILEAP IF(ICAL.GT.IKL.ANO.ICAL.LT.IJK) N2.2 Cs* CALCULATION OF PRECIP AMOUNT USING APPROPRIATE GAMMA TA8LE X.RANF() DO 440 J.1,400 L.J IF(PPT(J,N2).GE.X) GO TO 450 44C C** CONTINUE CALCULATION OF PRECIPITATION AMOUNT 45 0 RAIN.FLOAT(L)/100. 12.12+1 182 571 572 C" PLACEMENT OF PRECIP AMOUNT INTO STORAGE AND UPDATE OF TOTAL RAIN 573 PREC/P(ICAL).RAIN 574 PROB2IL).PROB2(1).1 575 TRAIN.TRAIN4RA/N 576 577 C" CALCULATION OF RUNOFF AND STORAGE OF RUNOFF INTO ARRAY 578 579 5.1000./CN10, 580 581 A.RAIN n e2 5 S 582 IF(A.LE.O.) GO TO 220 583 584 585 RUNOF(JJ).(A**2)/(RAIN4.8*S) 586 Lrf•INT(RUNOF(JJ)520.0.99) 587 IF(LJY.LT.1) LJY*1 588 13.13+1 589 PROB3(LJY).PROB3(LJY)41 590 GO TO 220 591 592 593 594 595 C THIS SECTION CALCULATES AND PRINTS OUT THE PDF AND COP D/STR18UTIONS 596 C FOR INTERARRIVAL TIME, PRECIP PER EVENT, AND RUNOFF. 597 598 C"' 599 600 C" DISTRIBUTION OF PREDICTED INTERARRIVAL TIME 601 46C WRITE(2,1000) 602 100C FORMAT(.1.,9X,"FREOUENCY DISTRIBUTION OF INTERARRIVAL TIME",/,,10X 603 C,"INTERARRIVAL",6X,"OCCURENCES",8X,"PDF",13X,"CDF") 604 WRITE(2,2000) 605 2000 FORMAT(138," (DAYS)",) 606 607 PDF.O. 608 CDF.O. 609 DO 470 1.1,73 610 POF.FL0AT(PROB1(I))/FLOAT(I1) 611 COF.P0F+COF 612 WRITE(2,3000) I,PRO81(I),PDF,COF 613 3000 FORMAT(15A,I2,13X.16,7X,F7.5,10X,F7.51 614 47 0 CONTINUE 615 616 C" DISTRIBUTION OF PREDICTED PRECIPITATION 617 618 POF*0. 619 CDF.O. 620 WRITE(2,4000) 621 4000 FORMAT("1",9X."FREQUENCY DISTRIBUTION OF PREC/P EVENTS",//,10X,"/N 622 CTERVAL",8X,"OCCURENCES",8X,"0F",I3X,"C0") 623 DO 490 1.1,50 624 10.1 625 PRO84.0 626 1"(I..•1)4.541 627 N4N+4 628 DO 480 II.M,N 629 P8I1134•PROB4.,PRO82(1I) 630 CONTINUE 48 0 631 (I)*FLOAT(In)40.05 5 54 632 SSL(1)•SSH(1)....0.04 633 PDF.FLOAT(PRO84)/FLOAT(I2) 634 CDF"OF4CDF 635 WRITE (2,5000) SSL(I),SSH(I),PRO84,ROF , COF 636 5000 FORMAT(8X,F6.2,1X."— . ,1A,F 4 .2 ,8 X 116, T 42, F 7 . 5,158,F7.5) 637 490 CONTINUE 638 AVERPT.TOTAL/FLOAT(NTN) 639 WRITE(2,6000) NYNIPTOTAL 640 NUMBER OF YEARS • ",I3,//,10X,"TOTAL AMOUNT 0 6000 FORMAT(//,10X,"T0TAL 641 PRECIP • ",F10.2) CF 642 183 643 644 645 646 647 VRITE(2,7000) I2pAVEPPT 7000 FORMAT(/p1OX,"TOTAL NUMBER OF EVENTS • "pI6p//p1OXP"AVERAGE YEARLY C PRECIP AMOUNT • "PF8.2,//) 0.4. DISTRIBUTION OF PREDICTED RUNOFF 648 649 650 651 652 653 654 655 656 657 659 659 660 661 662 663 664 665' 666 667 668 669 /NTVAL•Op PDF•Op CDF•Op WRITE(2,8000) NCN,ABST 8000 FORMAT("1"p9Xp"FREQUENCY DISTRIBUTION OF RUNOFF CURVE NUMBER C. "P13,//042Xp"INITIAL ABSTRACTION • "pF3.2p"5",//,10X."INTERVALL" CP8XP"OCCURENCES"P8XP"PDF",13Xp"C0F*) DO 500 1.1,40 10.1 SSNII)*FLOAT(/0)*0.05 SSLM.SSN(/)...0.04 POF.FLOAT(PROB3t1))/FLOAT(I3) CDFAPDF+CDF WR/TEt2p9000) SSL(I)PSSN(1),PROB3(1),PDF,CDF 9000 FORMAT(8X,F6.2p1X,—p1X,F4p2p8X014,742,F7p5,758,F7.5) 500 CONTINUE 011o0. STOP END 184 1 2 3 4 5 6 7 B 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 21 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 SUBROUTINE WINTERIICAL,K,N1,CN.ILEAP,PROB1,PR082,PROB3.TRAIN, CRUNOF,JJ./JI.I1,12,I3.PRECIP,RAIN,NYDAY.NY,MA,MB,MC,MD,ME,MF,MG,NY CN.TaTAL,KK,/NTER) DIMENSION RUNOP(100),PROB1(366),PROB2(400),PROB3(41),PRECIP(500) DIMENSION INTER(400,6) REAL INTER REAL MEAN101EAN2 INTEGER DURA1N#PROB1,PRO82,PROB3 DATA MEAN1,MEAN2/4.5223#1.991/ C C C C C C C C C C C C c C C C C C C C C C C C C C C C C C** CI. THIS SUBPROGRAM CALCULATES THE PRECIPITATION AMOUNT AND RUNOFF AMOUNT FOR THE FRONTAL STORM TYPE SYSTEMS OF NOV-DEC- JAN •FEB. THIS IS DONE BY FIRST CALCULATING INTERARRIVAL TIME (R) TO THE NEXT EVENT THAN CALCULATION OF THE DURATION OF THE STORM SYSTEM (DURATN) AND FINALLY BY THE AMOUNT OF PRECIPITATION (RAIN) THAT WILL OCCUR FOR THE STORM DURATION. TOTAL PRECIPITATION IS DIVIDED BY DURATION OF STORM TO FIND THE DAILY PRECIPITATION. THE GEOMETRIC DISTRIBUTION IS USED TO CALCULATE EACH OF THESE PARAMETERS. THE SOIL CONSERVATION SERVICE METHOD OF RUNOFF DETERMINATION IS USED TO CALCULATE DIRECT SURFACE RUNOFF IN INCHES. A RANGE OF CURVE NUMBERS (CM) AND AN INITIAL ABSTRACTION OF .15 AND .2 ARE USED IN MULTIPLE RUNS OF THE PROGRAM. TH/S'SUBROUTINE ALSO PRINTS OUT THE FIRST 20 YEARS OF PREDICTED DAILY PRECIPITAION RECORD. VARIABLE LIST mew. • THE AVERAGE VALUE FOR THE INTERARRIVAL TIME DISTRIBUTION MEAN2 • THE AVERAGE VALUE FOR THE STORM DURATION DISTRIBUTION MEAN3 • THE AVERAGE VALUE FOR THE STORM PRECIP. DISTRIBUTION DURATN • DURATION OF THE STORM (DAYS) OPPT • DAILY PRECIPITATION AMOUNT ' NPPT • PRECIPITATION CLASS NOTATION C C C C C C C C C C C C C C C C C C C C C C C C C C C CALCULATION OF INTERARRIVAL TIME TO NEXT EVENT. UPDATE OF CALENDAR AND CALCULATION OF CURVE NUMBER IN SUBROUTINE MOIST C IC X.RANF11 P.1./MEAN1 K.INT1(ALOG(X)/ALOG(1.•P))+1.0) ICAL•ICAL+KK+K KK.0 C O'S C** C CHECK TO SEE WHETHER THE NEW EVENT IS WITHIN THE WINTER GROUP OR IN A NEW GROUP. /JI•59+ILEAP IJN•304+ILEAP IF(ICAL.GT.IJI.AND.ICAL.LT.IJN) GO TO 90 IF(ICAL.LE.NYDAY) GO TO 40 ICAL•ICAL-NYDAY C C C C C FOR THE THIS SECTION PRINTS OUT THE PREDICTED PRECIPITATION RECORD FIRST 20 YEARS. C C C 61 62 63 64 IFOT.GT.1) GO TO 20 65 L•0 66 LL.0 67 ICOUNT.ICOUN1+1 68 ICOUHT,TRAIN WRITE(2,1) 69 ",1p1X,"* 1 FORMAT(1X," 70 •pF6.3,/.1X,..* RAIN. *",10X,"TOTAL C" 71 0.1.0") 72 P",/,1X,"* YEAR ",I3. C C C C C C 185 73 74 7 5 76 77 78 79 80 81 82 83 84 DO 506 4.1+12 Go TO (503,504,503,501,503,5010503,503001,503,501,503 ) ,3 501 502 1020 503 504 85 86 87 88 89 90 91 92 93 94 95 96 97 9$ 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 505 50t L*L1+1 LL.LL+30 WRITE(2,1020)(PRECIP(KAY),KAY.L+LL, FORMATI1X+16(F5+2,1WI"),/,8X+15(F5.2,1X+"I")) GO TO 506 L•11+1 LL.LL+31 GO TO 502 L*LL+1 IF(ILEAP.E0.1) GO TO 505 LL.LL+28 GO TO 502 LL*LL+29 GO TO 502 CONTINUE 20 TOTAL.TOTkL+TRAIN NY*MY+1 C** CHECK FOR LEAP YEAR ILEAP*NY/4-(NY-1) 1 4 NYDAY•365 IF(ILEAP.E0.1) NYDAY.366 IF(NY.GT+500) GO TO 90 DO 30 11.1,366 PREC/P(II).0+ 30 CONTINUE JJ*0 TRAIN.O. RAIN*0+ MA*0 M8.0 MC.0 MO*0 ME - 0 MF.0 115 16.0 116 C.* CALCULATION OF DURATION OF STORM IN peas 117 118 40 CALL MOIST(KrICAL,N1PCN , RAIN ) 119 K.RANFII 120 P*1./MEAN2 121 DURA1N.INTI(AL0GM/AL0G(1-P)1+1.0) 122 IF((ICAL+DURATN).GT.IJI.AND.ICAL.LE.141) DURATN.IJI.+ICAL 123 IF(DURATN.E0.0) ICAL.ICAL+1 124 IF(DURATN.E0.0) DURATN•1 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 AMOUNT FOR THE STORM OF DURATION LENGTH C** CALCULATION OF PRECIPITAION X*RANF() DO 50 4.1,400 IF(INTER(.1.5).GE.X) GO TO 60 50 CONTINUE 6 0 RAIN.FLOAT(L)1100. AND THE PLACEMENT OF DAILY PREC/P C** CALCULATION OF PREC/PIDAY (OPPT) C** AMOUNT INTO THE STORAGE ARRAY OPPT.RAIN/FLOAT(DURATN) I1*I1+1 Do 70 KKK.1+DURATN PRECIP(ICAL)*OPPT ICAL.ICAL+1 70 CONTINUE 186 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 C** PLACEMENT OF INTERARRUAL TIME PRO81(K).PRO81110+1 I1*I1+(DURATN-1 ) PROB1(1)*PROB1(11+(DURATN-1 ) NPPT.INTOPPT*100.1 IF(NPPT.LT.1) NPPT.1 IF(NPPT.GT.400) NPPT.400 C** C** PLACEMENT OF PRECIPITATION AMOUNT INTO THE STORAGE ARRAY AND UPDATE OF TOTAL PRECIPITATION I2.12+DURATN PROB2(NPPT).PROB2(NPPT1+DURATN TRAIN*TRAIN+RAIN C** C* • CALCULATION OF RUNOFF, PLACEMENT OF RUNOFF AMOUNT INTO STORAGE, AND UPDATE OF ANTECEDENT RAINFALL IN SUBROUTINE MOIST. 5*1000./CN-10. A.OPPT—.2*S IF(A.LE.0.) GO Tr) 10 DO 80 IelyDURATN 170 JJ.JJ+1 171 172 RUNGF(JJ).(A...2)/(OPPT..9.5) LJY=INT(RUNOF(JJ1.4201.66) 13•13.1 173 174 IF(LJY.LT.1) LJY*1 175 176 177 178 179 180 181 182 INTO THE STORAGE ARRAY PROB3(LJY).PR083(LJY)41 CALL MOIST(K,ICAL,N1 , CN , 0PRT) 80 CONTINUE GO TO 10 90 RETURN ENO 187 SUBROUTINE MO/STK.ICAL.N1,CN.RAINI 1 OTHENSION EVENT(5),LE4GTH(5) 2 C*** 3 4 5 THIS SUBROUTINE MAINTAINS A RUNNING ACCOUNT OF THE ANTECEDENT RAINFALL 6 C CONDITIONS TO BE USED IN THE mAIN PROGRAM AND IN SUBROUTINE WINTER C 7 FOR THE CALCULATION OF DIRECT SURFACE RUNOFF. 8 C 9 VARIABLE LIST 10 C EVENT • AN ARRAY TO STORE THE AMOUNT OF PRECIP FOR THE LAST C 11 FIVE PRECIPITATION DAYS 12 C LENGTH • AN ARRAY TO STORE THE NUMBER OF DAYS BETWEEN EACH 13 C OF THE PRECIP EVENTS IN THE ARRAY EVENT 14 C 15 16 c.000 17 18 19 C** THE NEW INTERARRIVAL TIME IS ADDED AND THE THE ARRAYS ARE SHIFTED 20 C** TO ACCOUNT FOR THE NEW EVENT. 21 22 DO 10 1.2,5 23 EVENTIII.EVENT(I-1) 24 LENGTH(1).LENGTH(1-1)+K 25 le CONTINUE 26 27 C** UPDATE THE ARRAYS EVENT AND LENGTH WITH THE NEw PRECIP EVENT. 28 EVENTI1I.RAIN 29 LENGTHIll•t 30 31 32 C** CALCULATION OF THE 5—DAY ANTECEDENT RAINFALL IN INCHES FOR THE 33 CA* PRECIPITATION EVENTS WITHIN THE LAST 5 PRECIP DAYS. 34 H20.0. 35 36 DO 20 1.1,5 37 IF(LENGTH(I).GT.5) GO TO 20 38 H20,0.120+EVENT(I) 39 2E CONTINUE 40 41 CA* CALCULATION OF CURVE NUMBERS USING TABULAR 5—DAY ANTECEDENT 0,4 RAINFALL VALUES OF... 42 43 C** LT 0.7 FOR SOIL CONDITION I 44 C4.1. 0.7-1.3 FOR SOIL CONDITION II 45 GT 1.3 FOR SOIL CONDITION III C** 46 4T 0.1, 48 49 50 51 52 53 54 INITIAL WATERSHED CURVE NUMBER IS 80 IF(H20.LE..7) CH-63.2 IF()120.GT..7.AND.H20.LT.1.3) CP4•80. IF(H20.GE.1.3) CN.91.2 RETURN ENO C • ino 188 ..... o. I., CD fo. 0 CD CD CD Ci -.00 CD CD C) CD C) CD CD CD CD CD CD C) 00000 C) CD CD C> C) CD • • • C) • • • • • • . • • • • • • • • • 0...0 c) a) c) CD C7 Ci C) CD CD CD 0 42 000 Ci 0 -r CD CD 00 1.• CD CD 47 CD CD CD CD CD 0 CD CD CD CD CD CD CD CD CD C) C) CD CD 0 CD CD m CD 0 CD 0 C7 CD CD 0 CD .r CD CD C) CD CD C) C) C) CD C7 CD CD CD P. CD CD CD CD cn C) C) 00 0 CD 0 C) CD C> C) CD CD CD CD Ci 000 CD C) 0 • • • • • • • • • • • • • • • • • o • • • • • • CD CD CD CD Ci MI Q.0 4. CD CD <7 CD CD 0 CD