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Analysis of hydrological data for subsurface drainage design for an arid area in India Prairie, Katherine Anne 1996

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ANALYSIS OF HYDROLOGICAL DATA FOR S U B S U R F A C E DRAINAGE DESIGN FOR AN ARID AREA IN INDIA  by KATHERINE ANNE PRAIRIE  B.Sc. (Geology), University of Alberta, 1983  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE D E G R E E OF MASTER OF SCIENCE  in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMICAL AND BIO-RESOURCE ENGINEERING  We accept this thesis as conforming to the required ^ancj&rd  THE UNIVERSITY OF BRITISH COLUMBIA April 1996  © Katherine Anne Prairie, April 1996  In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Department of Chemical and Bio-Resource Engineering The University of British Columbia Vancouver, Canada  II  ABSTRACT In the semi-arid to arid State of Rajasthan, 90% of the annual rainfall occurs as convective storms during the monsoon season. The suitability of a Markov chain analysis to model rainfall in this region was evaluated. A 5 day transition probability matrix accurately predicts sequences of wet and dry days based solely on the state of the preceding day. Both a daily model and an event-based model were used to describe rainfall pattern and distribution. Although the daily model is a traditional choice, the event-based model produced superior results. The event-based model describes the distribution of rainfall during a storm, the length of dry periods between rainfall events, and rainfall depths. The drainage coefficient derived from the normal value analysis, is 32.26 mm using the daily model, compared with 10.69 and 21.77 mm for the event-based models. The most cost-effective drainage coefficient is 10.69 mm derived from the 0.1 mm threshold event model. The Penman (1963) method best estimated E T over both seasons as well as within each season. C  The Jensen-Haise method, when adjusted by a correction factor of 1.15 for ET ^, produced alfa  comparable estimates of E T . The minimal climatic data required for the Jensen-Haise method C  makes it the most suitable evapotranspiration method for this area. A set of coefficients, ranging from 0.73 to 1.40, was developed to convert pan evaporation measurements to E T * . General crop coefficients for each development stage were determined J H  from the generalized cropping pattern of the Chambal C o m m a n d area. A water balance using effective wet year rainfall and evapotranspiration for the Kharif season was used to calculate the drainage requirement. The drainage requirement for the 178 ha Daglawada test plot is 749.2 and 1165.3 (xlO ) m , for return periods of 5 and 10 years, respectively. 3  3  The leaching requirement of 0.0309, can be met with the Kharif season rainfall expected in wet years with return periods of 5 or more years, and normal years with return periods of 10 or more years.  iii  TABLE OF  CONTENTS  ABSTRACT  ii  TABLE OF CONTENTS  iii  LIST O F T A B L E S  vii  LIST O F FIGURES  viii  ACKNOWLEDGEMENT  ix  1.0  INTRODUCTION  1  1.1  OBJECTIVES  2  2.0  BACKGROUND  3  2.1  SALINITY AND WATERLOGGING PROBLEMS IN INDIA  3  2.2 CHAMBAL COMMAND A R E A  4  2.2.1 Daglawada Test Site 2.3 CLIMATE  6 7  2.3.1 Rainfall. 2.3.2 Evaporation 2.4 SOIL  7 9 12  2.4.1 Soil Classification 2.4.1.1 Chambal Soil Series 2.4.1.2 Kota Soil Series  2.4.2 Salinity  14 14 15  15  2.5 W A T E R T A B L E  17  2.5.1 Waterlogging 2.6 C R O P S  17 18  2.6.1 Kharif season crops 2.6.2 Rabi season crops 3.0  LITERATURE  3.1  S U B S U R F A C E DRAINAGE  20  SALINITY CONTROL  20  3.1.1  REVIEW  18 18 20  3:1.1.1 Source of soluble salts 3.1.1.2 Crop sensitivity to salinity 3.1.1.3 Leaching requirement 3.1.1.4 Salt leaching in the monsoon season 3.1.2  W A T E R TABLE CONTROL  21 21 21 23 24  3.1.2.2 Crop sensitivity to high water table conditions 3.1.2.3 Water balance 3.3 RAINFALL MODELLING  25 25 26  3.3.1 Daily rainfall 3.3.1 Markov Chain Model 3.3.1.1 Transition probability matrix  26 27 28  3.3.2 Rainfall events 3.3.2.1 Event Based Model  29 30  3.3.3 Frequency analysis of extreme events 3.3.3.1 Assumptions in frequency analysis 3.3.3.2 Hydrologic data series 3.3.3.3 Extraordinary values  31 32 32 33  iv  3.3.3.4 Probability distributions 3.3.3.5 Plotting position  34 35  3.3.4.1 Drought analysis  37  3.3.4 Drought  3.4 EFFECTIVE RAINFALL  3.4.1 Factors affecting effective rainfall  38  3.4.1.1 Rainfall pattern and distribution 3.4.1.4 Other factors  38 40  3.4.2.1 Soil water balance models 3.4.2.2 Empirical methods 3.4.2.2.1 U.S. Bureau of Reclamation method 3.4.2.2.2 U S D A - S C S method 3.4.2.2.3 Local methods  41 42 42 42 43  3.4.2 Effective rainfall estimations  3.5  36  38  40  EVAPOTRANSPIRATION  44  3.5.1.1 Temperature 3.5.1.2 W i n d  44 44  3.5.1.2 Other Climatic Factors  45  3.5.2.1 Advection  46  3.5.3.1 Comparison of Grass and Alfalfa Reference Evapotranspiration 3.5.3.2 Conversion between reference E T estimates  46 47  3.5.4.1 3.5.4.2 3.5.4.3 3.5.4.4 3.5.4.5  48 49 50 50 51  3.5.1 Climatic Factors  3.5.2 Crop Factors  3.5.3 Reference Evapotranspiration 3.5.4 Empirical formulae for ET estimation Combination methods Temperature methods Radiation Methods P a n Evaporation Methods Correction coefficients  3.5.5 Studies  3.5.5.1 Arid Regions 3.5.5.2 Semi-Arid Regions 3.5.5.3 Combination studies - Arid and Humid Climates 4.0 M E T H O D S A N D M A T E R I A L S 4.1 DATA  4.1.1 Data assumptions 4.1.2 Analysis Limitations  44  45 46  51  52 53 54 55 55  55 55  4.2 PROGRAMMING AND CALCULATIONS  56  4 . 3 RAINFALL MODELLING  56  4.3.1 Characteristics of the monsoon season 4.3.2 Markov chain analysis 4.3.3 Daily rainfall modelling 4.3.4 Rainfall event modelling 4.2.4.1 Model definition.... 4.2.4.2 Threshold rainfall values 4.2.4.3 Model assumptions  57 57 60 60 60 61 61  4.4 F R E Q U E N C Y ANALYSIS  61  4 . 5 EVAPOTRANSPIRATION CALCULATION METHOD  64  4.4.1 Normal rainfall 4.4.2 Extreme rainfall 4.4.3 Design storm 4.4.4 Wet and dry year rainfall 4.5.1 Time period  48  62 62 63 63 65  V  65 65  4.5.2 10 day moving and fixed averages 4.5.3 Crop coefficients 4.5.3.1 Crop Development Stages 4.5.3.2 Crop Coefficients for each development stage  66 66  4.5.4 Seasonal ET requirements for selected crops 4.5.5 Comparison of estimated seasonal ET with lysimeter data 4.5.6 Pan evaporation coefficient 4.5.7 Crop water requirements for the Daglawada test plot  67 67 58 68  4.5.7.1 Generalized crop coefficient  68  4.5.7.2 Seasonal E T  69  C  4.6 EFFECTIVE RAINFALL  69  4 . 7 W A T E R BALANCE  69  4.7.1 Leaching requirement.  70  5.0 D I S C U S S I O N O F R E S U L T S  71  5.1 RAINFALL MODELLING  71  5.1.1 Characteristics of the monsoon season 5.1.2 Markov chain analysis  71 72  5.1.2.1 Transition probability matrix 5.1.2.2 Stationarity over 5 day intervals 5.1.2.3 Actual v s . predicted 3 and 4 day wet-dry sequences 5.1.2.3.1 Results over all years 5.1.2.3.2 Results of yearly analysis  72 73 73 73 76  5.1.3.1 5.1.3.2 5.1.3.3 5.1.3.4  77 77 78 78  5.1.3 Daily rainfall modelling 1 day rainfall 2 day rainfall 3 day rainfall 4 day rainfall  depths depths depths depths  5.1.4 Rainfall event analysis 5.1.4.1 Randomness of events 5.1.4.2 Number of rainfall events 5.1.4.2.1 Distribution of events within the season 5.1.4.3 Duration of rainfall events.. 5.1.4.3.1 Event duration distribution 5.1.4.4 Rainfall depth 5.1.4.4.1 0.1 m m threshold model 5.1.4.4.1.1 5.1.4.4.1.2 5.1.4.4.1.3 5.1.4.4.1.4  1 2 3 4  day day day day  events events events events  5.1.4.4.2 5.0 m m threshold model 5.1.4.4.2.1 5.1.4.4.2.2 5.1.4.4.2.3 5.1.4.4.2.4  1 2 3 4  day day day day  events events events events  5.1.4.4.3 Probability distribution function 5.1.4.5 Rainfall event depth-duration probability 5.1.4.6 Rainfall Distribution 5.1.4.7 Drought conditions 5.2 F R E Q U E N C Y ANALYSIS  77  80 80 82 82 82 83 83 83 83 83 84 84  85 85 85 85 86  86 86 88 88 88  5.2.1 Annual and monthly rainfall 5.2.2 Number of rain days 5.2.2 Maximum and minimum 1-4 day rainfall depths 5.2.2.1 Normal 1-4 day rainfall depths  5.2.3 Design storm  88 92 92  94  92  vi  94  5.2.4 Wet and dry year rainfall 5.2.4.1 Probability of occurrence 5.2.4.2 1 in 5 wet and dry year rainfall 5.2.4.3 1 in 10 wet and dry year rainfall 5.3 EVAPOTRANSPIRATION  5.3.1 Reference ET. 5.3.2 Comparison of 10 day moving and fixed average measurements 5.3.3 Actual vs. Estimated Seasonal Crop ET 5.3.3.1 Kharif season 5.3.3.2 Rabi Season  5.3.4 ET estimate summary over both seasons 5.3.5 Selection of most appropriate method of estimating ET 5.3.5 Crop water requirements for the Daglawada Test Plot. 5.3.6 Coefficient to convert Class A Pan Evaporation measurements to ET 5.4 EFFECTIVE RAINFALL  5.4.1 Comparison of USD A and 70% effective rainfall 5.5 W A T E R BALANCE  5.5.1 Drainage requirement. 5.5.2 Leaching requirement.  .'  94 98 98 101  101  101 102  102 102  103  109  109 109  112 112  6.0 S U M M A R Y O F M A I N R E S U L T S  113  7.0 C O N C L U S I O N  116  8.0 R E C O M M E N D A T I O N S  119  LITERATURE CITED  120  APPENDIX A  FREQUENTLY USED ABBREVIATIONS AND S Y M B O L S  127  APPENDIX B  CLIMATIC D A T A , K O T A S T A T I O N 1970-1993  130  APPENDIX C  DATA C O R R E C T I O N S A N D ASSUMPTIONS  150  APPENDIX D  F R E Q U E N C Y ANALYSIS METHODS  152  APPENDIX E  EVAPOTRANSPIRATION CALCULATION METHODS  155  APPENDIX F  CHARACTERISTICS OF THE MONSOON SEASON  169  APPENDIX G  R E S U L T S O F M A R K O V CHAIN A N A L Y S I S  172  APPENDIX H  DAILY R A I N F A L L M O D E L L I N G R E S U L T S  217  APPENDIX I  E V E N T - B A S E D M O D E L L I N G R E S U L T S , 0.1 M M T H R E S H O L D  234  APPENDIX J  E V E N T - B A S E D M O D E L L I N G R E S U L T S , 5.0 M M T H R E S H O L D  241  APPENDIX K  FREQUENCY ANALYSIS RESULTS  248  APPENDIX L  C R O P AND EVAPOTRANSPIRATION SUMMARY  261  APPENDIX M  E F F E C T I V E RAINFALL S U M M A R Y  270  104 105 108  LIST OF TABLES TABLE 1 SALINE AND ALKALI AFFECTED AREAS  4  TABLE 2 A V E R A G E CLIMATIC CONDITIONS, KOTA STATION 1 9 7 0 - 1 9 9 3 TABLE3  8  SOILSURVEY, MEHTA(1958)  12  TABLE 4 SOIL CLASSIFICATION SERIES  14  TABLE 5 SOIL PROFILE CHARACTERISTICS  16  TABLE 6 S E L E C T E D C R O P S A L T T O L E R A N C E  22  TABLE 7 S E L E C T E D EVAPOTRANSPIRATION ESTIMATION METHODS  64  TABLE 8 W E T AND DRY DAY CLASSIFICATION AND TRANSITIONAL PROBABILITY, BY MONTH  72  TABLE 9 INDEPENDENCE OF RAINFALL PROBABILITY ON MORE THAN 1 PRECEDING DAY, BY MONTH  75  TABLE 10 INDEPENDENCE OF RAINFALL PROBABILITY ON MORE THAN 1 PRECEDING DAY, BY YEAR  76  TABLE 11 1 - 4 DAY RAINFALL DEPTH, KHARIF SEASON (1970-1993)  79  TABLE 12 CORRELATION OF MODEL MONSOON SEASON CHARACTERISTICS, BY THRESHOLD RAINFALL TABLE 13 CORRELATION OF EVENT-RELATED CHARACTERISTICS, BY THRESHOLD RAINFALL  1  TABLE 14 E V E N T DURATION DISTRIBUTION, BY MONTH  1  81 81 84  TABLE 1 5 INTERARRIVAL TIME BETWEEN SIGNIFICANT RAINFALL E V E N T S , WITHIN SELECTED MONTHS  89  TABLE 16 NORMAL MONTHLY RAINFALL AND NUMBER OF RAIN DAYS  91  1  TABLE 1 7 NORMAL ANNUAL RAINFALL AND NUMBER OF RAIN DAYS  91  TABLE 18 COMPARISON OF MAXIMUM 1-4 DAY RAINFALL DEPTHS, VARIOUS RETURN PERIODS  93  TABLE 1 9 COMPARISON OF NORMAL 1 -4 DAY RAINFALL DEPTHS, VARIOUS RETURN PERIODS TABLE 2 0 ALFALFA v s . GRASS REFERENCE EVAPOTRANSPIRATION  93 101  TABLE 21 COMPARISON OF TOP RANKED E T ESTIMATION METHODS FOR EACH SEASON  103  TABLE 2 2 T O P RANKED E T ESTIMATION METHODS, BOTH SEASONS  105  TABLE 2 3 GENERALIZED CROP INFORMATION FOR T H E DAGLAWADA TEST SITE  106  C  C  TABLE 2 4 C R O P WATER REQUIREMENTS FOR T H E DAGLAWADA TEST SITE  107  TABLE 2 5 MONTHLY AND SEASONAL E T FOR VARIOUS CROP MIX PROPORTIONS C  107  TABLE 2 6 COMPARISON OF E T PAN EVAPORATION AND ADJUSTED JENSEN-HAISE  108  TABLE 2 7 W A T E R BALANCE FOR W E T AND NORMAL RAINFALL, KHARIF SEASON  111  viii  LIST OF FIGURES FIGURE 1 CHAMBAL COMMAND AREA, RAJASTHAN, INDIA FIGURE 2 ANNUAL RAINFALL DISTRIBUTION, KOTA STATION  5 10  FIGURE 3 MONTHLY RAINFALL DISTRIBUTION FOR JULY, KOTA STATION  11  FIGURE 4 ANNUAL POTENTIAL EVAPORATION, KOTA STATION  13  FIGURE 5 GENERALIZED CROPPING PATTERN, CHAMBAL COMMAND AREA  19  FIGURE 6 A V E R A G E ROOT ZONE SALINITY, 4 0 - 3 0 - 2 0 - 1 0 METHOD  23  FIGURE 7 5 DAY INTERVAL TRANSITION PROBABILITY  74  FIGURE 8 RAINFALL DEPTH DISTRIBUTION FOR 3 DAY EVENTS, 0.1 MM THRESHOLD MODEL  87  FIGURE 9 MAXIMUM DRY DAY SEQUENCES, BY YEAR  90  FIGURE 10 RAINFALL INTENSITY CURVES, DAILY MODEL  95  F I G U R E H RAINFALL INTENSITY CURVES, 0.1 MM THRESHOLD MODEL  96  FIGURE 12 RAINFALL INTENSITY CURVES, 5.0 MM THRESHOLD MODEL  97  FIGURE 13 1 IN 5 YEAR RAINFALL, KHARIF SEASON  99  FIGURE 14 1 IN 10 YEAR RAINFALL, KHARIF SEASON  100  FIGURE 15 EFFECTIVE RAINFALL, 5 AND 10 YEAR RETURN PERIODS  110  ix  ACKNOWLEDGEMENT Without the direction and guidance of my committee members, the completion of this research project would not have been possible. I am deeply grateful to Dr. Sie-Tan Chieng for his assistance, patience and support throughout the various stages of this research. I would like to thank Don Reid (Altana Exploration Company, Calgary), Monica Schmidt (Department of Biotechnology, University of British Columbia), Poh Peng Wong (Equity Office, University of British Columbia) for helping me overcome the problems associated with the completion of my thesis in Calgary. I also wish to acknowledge the typing assistance of my son Stephen Taylor. Finally, special thanks is extended to my husband Bill Taylor for his encouragement, support, patience and assistance over the many months of my research.  X  ACKNOWLEDGEMENT Without the direction and guidance of my committee members, the completion of this research project would not have been possible. I am deeply grateful to Dr. Sie-Tan Chieng for his assistance, patience and support throughout the various stages of this research. I would like to thank Don Reid (Altana Exploration Company, Calgary), Monica Schmidt (Department of Biotechnology, University of British Columbia), Poh Peng Wong (Equity Office, University of British Columbia) for helping me overcome the problems associated with the completion of my thesis in Calgary. I also wish to acknowledge the typing assistance of my son Stephen Taylor. Finally, special thanks is extended to my husband Bill Taylor for his encouragement, support, patience and assistance over the many months of my research.  1  1.0  Introduction  In humid areas agricultural drainage, particularly subsurface drainage systems, are designed to remove excess soil water to prevent waterlogging conditions for crop production. In monsoonal, irrigated areas, such as the State of Rajasthan, India, the system has to be designed for waterlogging control during the monsoon season, as well as salinity control for the irrigation period.  Prior to the introduction of subsurface drainage in 1974, both waterlogging and soil salinity were problems affecting many hectares of agricultural land. However, even with the installation of drains, salt accumulation has continued, and high water table levels have remained a problem. During the irrigated Rabi (dry) season in Rajasthan, there is often barely enough water to meet the requirements of the growing crop. Without the application of adequate water to leach salts from the soil, the productivity of the soil is negatively affected, even where subsurface drains have been installed.  Rather than applying excess water throughout the irrigated season, this thesis evaluates whether there is adequate precipitation during the monsoon season to leach salts from the soil prior to the start of the Rabi season. In order to achieve a soil salinity of 2 dSrrf , 1.16 mmd" of excess water 1  1  over the Kharif season is necessary (Chieng, personal communication). The level of soil salinity is based on the salt tolerance of the most sensitive crops grown in the area.  2 1.1  Objectives  The objectives of this thesis research are: 1.  To examine each of the two seasons, Rabi and Kharif, independently in the analysis of weather data and in the determination of a water balance. The results of these analyses are combined to determine the most cost-effective subsurface drainage design.  2.  Current subsurface drain spacings have been based on various drainage coefficients obtained from both published and unpublished reports. A drainage coefficient based on a water balance using the historical climatic records of the Kota station within the Chambal C o m m a n d area, will be examined to improve the design of the subsurface drainage system.  3. To study the rainfall pattern and analysis of its distribution and occurrence. The intensity of the monsoon rains results in significant surface runoff, therefore, effective rainfall will be considered as well as actual rainfall.  4.  To determine the most appropriate method of estimating evapotranspiration for a monsoonal, irrigated area. A coefficient correlating actual pan-evaporation and calculated evapotranspiration will also be investigated. A simple method of estimating evapotranspiration from pan evaporation measurements is desirable as data other than rainfall and pan evaporation, are not routinely collected at weather stations in the Chambal C o m m a n d area.  3 2.0  Background  2.1  Salinity and Waterlogging Problems in India  The population of India is supported primarily by agricultural activities, particularly irrigated agriculture. The number of hectares of agricultural land under irrigation in India more than tripled from 1947 to 1990, increasing from 22 million ha to more than 70 million ha. Approximately 60% of the C h a m b a l C o m m a n d area, representing 229,000 ha, is under irrigation (Chieng, 1993).  Initially, irrigation was developed to allow for the expansion of agricultural activity during the dry, Rabi season. Surface drains were utilized to remove excess irrigation water. However, with the expansion of irrigation into the monsoon season, the surface drainage system was unable to cope with the combined runoff from the monsoon rain and irrigation water. Where once the heavy monsoon rainfall was solely responsible for waterlogged soils, now irrigation water has compounded the problem.  Irrigation practices contributed to increased salinity and waterlogging. Many inadequately planned irrigation projects were developed in areas with soils unsuited to excessive irrigation. Other projects, such as railway and highway development, often had a negative impact on the surface drains and canals. In addition, the locai people found that by blocking the surface drains, pools of water suitable for fish harvesting or irrigation water supplies, were created.  A s a result, almost 7 million ha of land in India is affected by salinity, and approximately 6 million ha experiences waterlogging (Table 1).  4 Table 1  Saline and Alkali affected areas Waterlogged Saline/Alkali (millions of ha) (millions of ha) 0.810 1.295 Uttar Pradesh 0.484 1.214 Gujarat 1.850 0.850 West Bengal 0.348 0.728 Rajasthan 1.090 0.688 Punjab 0.620 0.526 Haryana 0.111 0.534 Maharashtra 0.060 0.404 Orissa 0.010 0.404 Karnataka 0.057 0.224 Madhya Pradesh 0.339 0.042 Andhra Pradesh * 0.117 Bihar * 0.061 Kerala * 0.018 Tamil Nadu * 0.010 J a m m u and Kashmir * 0.001 Delhi 0.040 Other Source: Maheshwari, 1993; C S S R I , 1991 (cited in Chieng, 1993) * Included under Other State  2.2  Chambal Command Area  The lower Chambal Valley lies between 24° 45' - 26 °45' North and 75° 20' -79° 20', encompassing an area of 12,050 sq. km. Within the state of Rajasthan, the districts of Bundi, Kota, Sawai, Madhopur and Bharatpur lie within the valley. The Bundi-Karauli hills form the north-western boundary of the valley from Kota to Dhaulpur. The Chambal Command area represents 385,000 ha of the lower Chambal Valley, and encompasses approximately 60 distinct watersheds.  It lies in the  south-eastern part of Rajasthan between 25 ° and 26 ° north latitude and 75° 30' and 76° 6' east longitude (Figure 1). The primary water source for the Command Area is the Chambal river, one of the tributaries of the Yamuna river. The Kali-Sindh and Parbati streams enter the Valley from the south-eastern plateau, joining the Chambal River within the Valley to form an alluvial plain. This triangular plain, known as the Chambal Plain, lies within the Kota district of Rajasthan. A s the Chambal river continues through the valley in a north-eastern direction, it forms several tributaries including the Kalisindh, Parwatim, Mej and Banas rivers.  5  o o o  CO  6  The elevation of the Chambal Plain ranges from 240 to 270 meters elevation, representing a drop of 600 meters from the south-western plateau. The elevation of the Valley diminishes further, to 150 meters above mean sea level, where the Chambal River meets the Y a m u n a in the north-east. The Bundi-Karauli hills, reaching a maximum height of 650 meters are the highest landforms in the Valley (Sharma, 1979). The elevation of the Chambal Command area ranges from 170 and 260 meters above mean sea level, with a slope of approximately 0.8% (Chieng, 1993).  The city of Kota, at 250 to 270 meters above mean sea level within the Chambal Plain, is of major importance in the state of Rajasthan. The development of hydro, thermal and nuclear power in Kota has allowed it to become a major industrial centre. In the rural district surrounding Kota, 1140 villages with an estimated combined population of 500,000 lie within the Chambal Command area (1985 census, Chieng, 1993).  2.2.1  Daglawada Test Site  A large scale research project has identified 25,000 ha of land with salinity and waterlogging problems in the Chambal Command area. Within this problem area, several test sites, each consisting of a number of test plots, have been established. The test plots are intended to investigate the performance of the subsurface drainage system and to aid in the determination of optimal drain spacing, drain depth and filter materials, for large-scale subsurface drainage system installation.  The Daglawada test site encompasses approximately 178 ha, and it is located approximately 20 km east of Kota. It is representative of the Chambal Command area in terms of soil type and condition, cropping pattern and irrigation practice. The site includes 20 test plots, evaluating a combination of drain depths (1.0 and 1.3 m) and drain spacings (15, 30, 40 and 60 m) with and without fabric envelope (filter).  7  2.3  Climate  The sub-tropical climate of the Chambal Command area is generally classified as arid to semi-arid. The region experiences three distinct seasons, the Kharif (monsoon), Rabi (dry winter) and Zaid (hot dry summer). The Zaid season begins in March and ends with the sudden onset of monsoon rain in the month of June. The monsoon (Kharif) season tapers off in October followed by the dry Rabi season.  During the Zaid season, the average temperature climbs from approximately 23 °C to a high of almost 34 °C in May, the warmest month of the year. It is not uncommon for temperatures in May to reach 49 °C , with an average maximum day time temperature of 41.83 °C (Table 2). By the end of April, hot, dry winds from the south-west begin, with average daily wind speeds in excess of 6 ms" . 1  Average daily humidity lies below 30 % throughout the Zaid season.  In contrast, winter (Rabi season) temperatures may reach a low of 4 °C. The average minimum day time temperature for the month of January, the coldest month of the year is 6.38 °C. On average, the mean day time temperature for the Rabi season is 17.17°C, with humidity of 40 to 55% (Table 2). Winds are generally from the north-west and north with an average speed of less than 3 ms" during 1  the Rabi season, although wind direction during this period is variable.  During the Kharif season, winds are predominantly from the south-west and west, with an average wind speed of approximately 8 ms' during July, tapering off to approximately 4 m s in August. 1  1  Mean day time temperature during the height of the monsoon in July and August, is 28.5 °C (Table 2). Humidity reaches almost 90% during August and September.  2.3.1  Rainfall  In temperate climates, the rainfall pattern tends to follow a normal distribution. Such a distribution allows the use of univariate statistics such as the mean, median and mode to characterize the rainfall. However, in arid and semi-arid areas, such statistics are not representative of actual rainfall.  8  a> ^  «  CO CO  |CM  TJ  "re c 2  I  CD CO  CO  CO  CO  E E  Q  c .2 re o a. re > co  o  O CO  -I  in  co  \°. in  \a>  -o E c S  CO  m co  co  CO CO  in  CO  I CO I  0  CM CM  *1  oi  1 oil  Si  co o  CO  ai  Icri  CO  c\i  O)  co co  E  >> Q .  re  o  CO  w  Q  CO CD  in  CO  cn cn T—  |cp  = > 5. _ — ro — co rg e £ \  co  CM  m  CM  CM  CO CO  SI  co co  | CM  CO  co  CD  I  o ro>  c o re +J to re o ^ to c o  X TJ  co led  CM  in  in  m  o IS  CO  2  B  CO  CO CM  CM  co  CD  w  re E co  I co  Pi  co  £51 co  m o  I CM  in  co  co  IS  CD  TJ  c o u  Ico  CM CO CO  « E 5 co  CO  13  co  I  CO  CO CO  oo o  m co I  iri  CM CO  CM  O)  2  CM CO  CM O  CO  >  <  CD O  CD CO CM CM  IS  I  CM  .a re  c o 5  re  re  O U  a  9  Annual rainfall varies considerably in the Chambal Command, from 309.10 mm to a high of 1506.80 mm (Appendix B). The mean is a poor indicator of annual rainfall, as the rainfall ranges from 40 to 194 % of the mean value of 777.67 mm (Figure 2). The annual distribution, strongly influenced by the extreme values, has the characteristics of an arid or semi-arid area as described by Jones (1981). It is positively skewed; the mode is less than the median value; both the mode and the median values are less than the mean; and the majority (59%) of the annual values fall below the mean rainfall.  The distribution of rainfall throughout the year is also very different from that experienced in temperate climates. From the sudden onset of the summer monsoon rain in the month of June until its departure in late September or early October, the Chambal C o m m a n d area receives approximately 90% of the total annual rainfall. During the Zaid season, little or no rain is recorded. From 1970 - 1993 the maximum rainfall for this season was 40 mm, with less than 11 mm of rain recorded in 64% of the years (Appendix B). Most of the rainfall outside of the Kharif season falls in November, although there may be some small contribution from December to February.  The seasonal, monthly and daily rainfall depths for June through September, exhibit more variability than the annual rainfall (Figure 3). Monsoonal storms are typically of short duration with intense rainfall, although many of the storms are of much lower intensity. The storms are interspersed with dry periods of 1 or more days. A s a result, daily rainfall depths ranging from 0 mm to 174 mm have been recorded during the Kharif season (Appendix B).  2.3.2  Evaporation  The annual potential evaporation has an estimated mean value of 2486 mm, with actual evaporation values varying from 64 to 133% of the mean (Appendix B and Figure 4). The distribution of annual evaporation values more closely follows a normal distribution than rainfall. However, as with the rainfall distribution, the extreme values have a strong influence. Potential evaporation is highest during the months of April and May during the hot, dry Zaid season. Maximum evaporation occurs  10  (0 >-  E E r(O  r--  co £= 'ca s  tz C C C O  E  (JA/IUUI) ||eju;ecj  ai o  11  12  during May, the warmest month of the Zaid season, with mean daily evaporation rates reaching a high of 15.25 mmd" (Table 2). During all months of the year, except for the height of the monsoon 1  season, mean daily evaporation rates exceed mean daily rainfall rates (Table 2).  2.4  Soil  The soils of the Chambal Command area were first classified by Mehta (1958, cited by Sharma, 1979) into two broad categories based on colour. The categories were further subdivided into 3 groups relating to the presence and depth of a kankar layer (Table 3). The soil survey was conducted in 1951-1957, prior to the development of irrigation and drainage in the area.  Table 3  S o i l S u r v e y , M e h t a (1958)  Soil Type Grey, without kankar layer Grey, with kankar layer below 1.2 m Grey, with kankar layer above 1.2 m Brown, without kankar layer Brown, with kankar layer below 1.2 m Brown, with kankar layer above 1.2m  % of A r e a 67.4 2.1 2.4 24.7 2.5 0.9  Source: Chieng, 1993  The high evaporation, low humidity and low rainfall of the region result in high evaporation rates from the upper layers of the soil, causing calcium carbonate concretions to accumulate, forming the restrictive kankar layer. Silicate particles (30%) are bound tightly together with magnesium carbonate (35%), a combination of aluminum, iron, sodium, potassium and trace elements (10%) and water (20%) to form the concretions (Bhatnagar, 1990).  Soil surveys conducted since 1958 indicate that calcium carbonate concretions (kankar grits) may be found at depths other than 1.2 m, and do not lead to a restrictive layer. However, all of the hard-pan layers in the Chambal Command area, regardless of depth, contain kankar grits (Chieng, 1993).  13  14  2.4.1  Soil Classification  A detailed soil survey was conducted from 1968 to 1981, resulting in the definition of eight soil series based on soil colour, texture, and presence and depth of a kankar layer (Table 4). A more recent survey was completed in 1993 for ten drainage blocks selected from within the Chambal C o m m a n d area. The Chambal, and Kota soil series and their variations, were found to be the most common. Although the Sultanpur and Bundi soils occur in small amounts, they are often important on a local level.  Table 4  Soil Classification Series  Soil Series Chambal Chambal Variant Kota Kota Variant Sultanpur Bundi Guda Alod  % of Chambal Command area (approx.) 63.0 5.0 23.0 5.5 1.0 1.5 1.0 1.0  Source: Chieng, 1993  2.4.1.1 Chambal Soil Series The most common soil in the Chambal Command area is the Chambal soil series (63%). These level to gently sloping soils (0-2% slope) are primarily comprised of fine textured montmorillonite clay. This deep, hard, mostly calcareous soil exhibits a slow permeability down to 120 cm. Below this point, the soils are non-saline to saline and non-sodicto sodic. A detailed description of the soil profile characteristics is given in Table 5.  15  The Chambal variant is similar to the Chambal soil series, although it is far less common (5%). The physical and chemical characteristics of the two soils is very similar except for the absence of calcium carbonate in the Chambal variant.  2.4.1.2 K o t a S o i l S e r i e s The second most common soil in the Chambal Command area is the Kota soil series (23%). Like the Chambal soil series, these soils exhibit a level to gentle slope of 0-2%. The soil profile is deep to very deep and is comprised mainly of non-calcareous clay loam to clay soils. Permeability throughout the profile is slow to moderately slow. A detailed description of the soil profile characteristics is given in Table 5. The Kota variant is similar in character to the Kota soil series, except for the presence of calcium carbonate in the Kota variant. It is less common than the Kota series, encompassing less than 6% of the Chambal Command area.  2.4.2  Salinity  With the introduction of irrigation to the Chambal Command area in the 1960's, soil salinity became problematic. The World Bank (1974, cited in Chieng, 1993) reported that by 1972, soil salinity in varying degrees, was a problem over approximately 20,000 ha, or 5% of the command area.  Irrigation water applied in the Chambal Command area has an average electrical conductivity (ECi) of 0.3 d S m " and total dissolved solids of 200-250 ppm (Chieng, 1993). This water is of excellent 1  quality with low salinity, however it is of some concern with respect to soil sodicity according to the F A O irrigation water quality criteria (Ayers and Westcot, 1985).  Salinization in the Chambal Command area is primarily due to low salt efflux from the root zone and salinization from groundwater. During the irrigated season, there is little or no rainfall and evaporation rates are high. A s there is often barely enough water to irrigate, the application of water in excess of plant needs is not practised. Irrigation has led to increased groundwater recharge  16  co  cm)  ^—  IO T  m  "  CN  o  CM CD  O) LO  ~  CM  CN  CO CN  1^ CN  Tl-  T  CO  m  CN  O) CM  CO CM  LO  CM CD  LO  T—  CM  CO  CO  Tt  LO  o>  in  CD LO CM  LO  ries rof  cu I O  CD  0.  03 +J O  O  CO  \S  CO  T— T 1 -  to  CO IO  o  CO  Tt  ,_: CD  in  o  CM  CO  CM  Ti-  CN  en  in  r~  CO  CO  b  CO  CD CM  cn co  Tf  cn  CM CO  T—  LO CO  o  CO  ^—  T—  m b  CO  •9  o in o  CM  CD  b  co b b  CD LO  b  CD CO  -a" o  CD  CM  00  O  od  cn  b  o  co  b  CD  CD  LO  cn  Tf  CO  b  co  CO  CM  co  T  T—  b  CM  CO CN  LO  CO  b  CM  CM  LO  o  O  T1Tf  CO  CM CM  cn  Tt  CM  cu  a o 1  Ti-  o ©  LO  d  ed b  CM  m Tf  CO  CM  Ti-  ,  LO  CN  ro  o  ~  m CM  in o  cn  o m b  co cn  CO  CM  ~  CO T—  IO  E  o  *~  CD  CN  in  in  T—  o  CM  T _  CM  CM LO  m m co co  o in  CO  CM  T—  CN  CM CO  CO  o  b  b  Tl"  00  CM  o  o  co  CM  o  o  _co I O  ba Seri >rofi  T—  T-  o  co IO  CD  ^—  c  •9 O  o  CD  o  ro  o ©  2  JZ  co  o  LO  b  Tf  CM  CM  ^—  o  CL  o "co  CN CN  in  CO CM  CM  CN  CM  in  ^—  LO  Tt  co CM  Tl-  o  CM  CO LO  co  m Tf  m  CD CM CM  LO  T—  cn  b  ^—  LO  CM T  ~ b  CO  co oo •st oo CM  CM CO  co  CO  CO  b  c: o  r*co  LO  o b  00 co ~  CO  CM  T  b  o  b  b  CO  co  CO  o  CM  CM  CO  o  u  0-  o to CO O  d  CO to 0_ i  JZ  o  E, CD  X O CL  CO  d  LU  UJ o d  UJ  o  CO  E  ssiu  to  E,  nesi  E.  o  -I  E  CO  O  2  .2  £  <u  co to  § 1  CU  odi um  CO  CO  'to  E o  >  •c>  ale ium  o o  T3 >s  OJO  JZ  5" c>  CO  o  CO  N  o o  ch. catio ns (m  'in  >^  o  arbon  u  •o  CD +J O  mic  haracter  O  o 3 >»  o  ieq/10  •c?  CO  1  Cha acteri  w  to >>  CO  u zz  ysi cal  CO  L.  CO  oo b b  CO  o  CO  CN  O b b  o  "5  b  Tf  CO  o  Q.  CM  O  ist  'C CD  co co  CM  emlical Chara  to  LO  ravity  zz  CO  CM  Tf  o  CO  Dep1  to o  CN CN  LO  pec  E  o  ulk den  cu  anc  (0  8§  •= -2  CO  cn cn c  CO  0  O CO _ X CO  !c  3  O  n  o  CO  — co LU O)  E S  o  x:  o  o >< co co x to 0_ 1 LU O LU  O  o 3  o to  17  resulting in a significant rise in the water table depth. A s the saline groundwater evaporates, salts accumulate in the root zone.  Salts also rise upward into the root zone by capillary action. Potential capillary rise investigated under laboratory conditions of the clay loam was found to range from 91 to 132 c m (Joshi, 1993). Field investigations are being undertaken.  2.5  Water Table  A good supply of groundwater is located in the deeper alluvial deposits of the soil profile. A s the clay content of the soil increases toward the south-west of the Chambal C o m m a n d area, the aquifer diminishes. The overall gradient of the groundwater for the region is sloped towards the Chambal River (Darra, 1993, cited in Chieng, 1993).  Water table monitoring wells were established in each of the test plots in the Chambal Command area. Data for June 1993 to January 1994 collected from wells in drainage zone B near Kota, indicate a median water table height of 650 mm below the surface. The water table height during this 6 month period fluctuated from a depth of more than 1300 mm to 0 mm from the ground surface.  2.5.1  Waterlogging  Waterlogging had affected approximately 161,000 ha of land in the Chambal Command area by the 1970's. Potential and actual waterlogged areas increased from 79,000 ha in 1964 to 161,000 ha in 1971 (Chambal Drainage Master Plan, 1978, cited in Chieng, 1993).  In this thesis, waterlogged areas are defined as those in which the water table is within 1.5 metres of the surface. In potential waterlogged areas, the water table lies between 2-3 metres from the surface. All areas with a water table below 3 metres from the surface by the end of March, are considered to be safe from waterlogging.  18  2.6  Crops  The development of irrigation in India has had a dramatic effect on the timing and type of crops grown. Gradually the shift has been made from dry farming to irrigation dependent agriculture in both the Kharif and Rabi seasons.  Prior to the introduction of irrigation, approximately 70 and 35 % of the land was left fallow during the Kharif and Rabi seasons, respectively (Darra, 1993). The percent of fallow land has steadily decreased to the present level of approximately 50 % during the Kharif season, and 5 % during the Rabi season (Chieng, 1993).  2.6.1  Kharif season crops  Prior to irrigation development, sorghum, maize and some pulses were the primary crops. The main Kharif crops at present are soybean, paddy rice, sorghum, maize, sesame, pigeon pea and sugarcane (Haroon, 1993, cited in Chieng, 1993).  Crops are generally sown between the start of the monsoon season and the middle of July (Figure 5). Harvesting begins toward the end of October, continuing through to early December.  2.6.2  Rabi season crops  The main Rabi crops are mustard, wheat, barley, gram and berseem. Prior to the development of irrigation, the main Rabi season crops were wheat, linseed, gram, and a combination of other crops. Mustard has increased dramatically from less than 1 % of the area, to approximately 50 %, making it the predominant Rabi crop.  Rabi crops are sown from the middle of October through to the end of November. Harvesting generally takes place from late February through to the end March or early April.  19  20  3.0  Literature review  3.1 Subsurface drainage Extensive literature exists on the use of subsurface drainage to control the water table for salinity control in arid areas, and waterlogging control in humid areas. In monsoonal irrigated areas it is necessary for both salinity control and the prevention of waterlogged soils.  The drainage coefficient, or amount of water which a system must remove from an area over a 24 hour period, differs with the purpose of subsurface drainage.  A drainage system for salinity control must be able to remove excess water applied to meet the leaching requirement. It must also be able to maintain the water table at a minimum depth, in order to prevent upward movement of soluble salts.  To prevent waterlogged soils, the drainage system must have the capacity to remove precipitation in excess of the crop evapotranspiration demand.  3.1.1  Salinity control  All irrigation water carries small, but significant amounts of dissolved salts into the soil profile. The concentration of soluble salts increases as pure water is removed from the root zone by the evapotranspiration process.  Salt accumulation in the root zone reduces crop yield at concentrations above the tolerance level of the crop. High salt concentrations make it more difficult for plants to take-up water, due to the increased osmotic pressure exerted by the soil solution. Over time, the crop becomes water stressed, and its growth rate diminishes.  21  3.1.1.1 Source of soluble salts Soil salinization is the result of excessive concentrations of soluble salts, such as chloride (CI"), sodium (Na ) and calcium ( C a ) , that are easily transported by water. Soluble salts are introduced +  ++  into the soil profile primarily through the application of irrigation water, the dissolution of salt deposits in the soil, agricultural drainage from higher areas and shallow water tables. Other sources include fertilizers, agricultural amendments, weathering soil minerals, and rain (Smedema and Rycroft, 1983).  Crops deplete water first from the upper portions of the root zone. The salts left behind are leached into deeper levels of the root zone, with each subsequent irrigation water application. A s a result, soil water salinity increases with depth, with salinity near that of the irrigation water, at the top of the root zone (FAO/Unesco, 1973).  3.1.1.2 Crop sensitivity to salinity Agricultural crops exhibit a wide range of salt tolerances. Many of the crops commonly grown in the Chambal C o m m a n d area are sensitive, or moderately sensitive to soil salinity ( E C ) (Table 6). e  During the Kharif season, approximately 2 5 % of the crops (gram, maize, paddy rice, groundnut and sugarcane) will suffer a significant yield reduction when cultivated under saline soil conditions. The majority of crops grown during the Rabi season are moderately tolerant of soil salinity.  3.1.1.3 Leaching requirement The removal of accumulated salts in the root zone is accomplished through the application of irrigation water in excess of crop water requirements. The water removes accumulated salt as it percolates through the root zone, and is removed from the soil profile through subsurface drains.  22  Table 6  Selected Crop Salt Tolerance Crop  Sensitivity*  Yield potential as influenced by soil salinity ( E C ) 50% 75% 100% 90% 1  e  Rabi crops: Wheat Mustard (Safflower) G r a m (field beans) Barley  <6.0 <5.5 1.0  <8.0  Kharif crops: <5.0 Soybean <3.0 Paddy rice <4.0 Sorghum <1.5 Maize 1.0 G r a m , black and green <3.0 Groundnut Sugarcane 1 1 Ayers and Westcot, 1985 ( E C Doorenbos and K a s s a m , 1979  e  7.5 6.0 1.5 10.0  9.5 7.5 2.3 13.0  13.0 10.0 3.6 18.0  moderately tolerant moderately tolerant sensitive moderately tolerant  5.5 4.0 5.0 2.5 1.5 3.5 3.0  6.0 5.0 7.0 4.0 2.3 4.0 5.0  7.5 7.0 11.0 6.0 3.6 5.0 8.5 —  moderately moderately moderately moderately sensitive moderately moderately  1  I  .  tolerant sensitive tolerant sensitive sensitive sensitive  values in mmhos.cm )  Leaching effectiveness is related to the soil type and its drainage properties (Bouwer, 1969). In sandy soils, leaching efficiency can be as high as 100%. With swelling heavy clays, it can be as low as 30% (Doorenbos and Pruitt, 1977).  The drainage coefficient for salinity control is determined from the leaching requirement and the evapotranspiration demand. The leaching requirement is dependent on the irrigation water salinity, and the salt tolerance of the crops. The leaching fraction is that portion of irrigation water percolating through the entire root zone, removing salts to the region below the root zone.  The conventional method of calculating the leaching requirement is based on the input water quality and the output drainage water quality. This method assumes soil water depletion occurs evenly throughout the root zone (FAO/Unesco, 1973). In addition, soil salinity is assumed to remain constant, reflecting steady state conditions. Therefore within the root zone, the contribution of salts from precipitation and dissolution processes and the removal of salts by crops are considered negligible ( A S C E , 1990).  23  An alternative method is based on the soil water salinity as it relates to the 40-30-20-10 pattern of crop water use in the root zone (Figure 6). Crops are assumed to take 4 0 % of their water requirement from the top quarter of the root zone. In each of the subsequent quarters moving downward in the root zone, 10% less water is depleted. Field measurements support this pattern, under normal irrigation conditions (Burman and Pochop, 1994; Ayers and Westcot, 1985).  Figure 6  Average root zone salinity, 40-30-20-10 method  SOIL S U R F A C E LFo , ECswo 25%  Total root zone depth  25%  25%  25%  |  0.40 E T  1  0.30 E T  |  0.20 E T f  0.10 E T  LFi , E C  LF2 , E C  SW  s w  i  2  L F , EC , 3  LF4,  S  EC  S W  4  E T = evapotranspiration LF1.4 = leaching fraction at the bottom of each quarter; L F = leaching fraction at surface E C . = soil water salinity at bottom of each quarter; E C o = soil water salinity at surface 0  s w 1  4  s w  Source: Ayers and Westcot, 1985  3.1.1.4 Salt leaching in the monsoon season In semi-arid and arid areas there is often a shortage of water in the irrigated season. A s a result, insufficient irrigation water is applied to meet the leaching requirement. Therefore, leaching of accumulated salts from the root zone must occur in the monsoon season. The monsoon season is characterized by low evapotranspiration rates and high rainfall amounts. Under these conditions, rainfall that infiltrates into the root zone can be used to leach the salts. This  24  will result in low soil salinity at the start of the irrigated season, when crops are most sensitive to salinity. Salt accumulation would not reach critical levels until the later part of the growing season, when crops are not as sensitive to soil water salinity (Ayers and Westcot, 1985).  3.1.2  Water table c o n t r o l  In arid and semi-arid areas, shallow water table conditions exist during the monsoon season. A s the water table rises, the air content of the soil diminishes as the pore spaces are filled with water. A reduction of 5 - 1 0 % in the volume of air-filled pore space results in anaerobic conditions (Smedema and Rycroft, 1983).  Anaerobic conditions impair crop respiration and results in the accumulation of toxic levels of carbon dioxide. Toxic concentrations of reduced iron and manganese compounds, sulphides and organic gases are also possible. A s a result, root growth is stunted and the roots are less able to absorb nutrients from soil water. The early stages of crop growth are more sensitive to waterlogging conditions, event those of short duration, than later well-developed stages.  High intensity rainfall during the monsoon season, results in a rise of the water table. High water table conditions over a short period of time will have less of an effect on crops than persistent waterlogging. Therefore, the rate at which the water table drops is important.  Early stages of crop development are more sensitive to waterlogging conditions, even those of short duration, than later well-developed stages. Throughout the crop development stages, higher temperatures serve to intensify the reaction to a high water table, as the crops require higher amounts of oxygen under such conditions.  3.1.2.1 Water table a n d salinity  High water table conditions increase soil water salinity, and reduce the effectiveness of leaching. With a rise in the water table, dissolved salts in the groundwater are introduced into the root zone. In  25  low lying areas, with insufficient natural drainage, the salt concentration of groundwater may be 1.5 to 2 times that of the root zone soil water (FAO/Unesco, 1973).  A water table at a depth of 3 m or more from the surface will contribute salts to the root zone (FAO/Unesco, 1973). With the depletion of soil water from the unsaturated zone, groundwater moves upward through capillary flow, depositing salts in the root zone. Upward capillary flow increases as the distance from the root zone to the water table decreases.  Talsma (1963, cited in van Schilfgaarde, 1974) recommends water table depths of 120 cm to 190 cm, for light-textured soils and medium-textured soils respectively, based on a review of available information. The physical properties of the soil affect the rate of capillary flow, and the critical water table depth The highest capillary flow occurs in loam soil, with the most flow resistance in clay soils. The critical water table depth also varies with groundwater salinity, crop tolerance and the climate of the region.  3.1.2.2 Crop sensitivity to high water table conditions Many crops grown in the Chambal Command area are sensitive to a high water table. Peas and pulses are very sensitive to waterlogging conditions, whereas rice exhibits a high tolerance. Maize is sensitive to a groundwater table at 50 cm below the soil surface, while wheat, barley and peas moderately tolerate these conditions, and sugarcane has a high tolerance (FAO/Unesco, 1973).  3.1.2.3 Water balance Subsurface drainage in monsoonal areas, is used to prevent fluctuating water table conditions. A water balance is necessary to determine the amount of excess water which must be drained. The water balance calculation method using precipitation and evapotranspiration, developed by Thornthwaite and Mather (1955), has been used extensively throughout the world.  26 The water balance over a period of 3 to 5 days is normally the most critical in the drainage coefficient determination. A drainage system may be capable of removing excess water resulting from a single high intensity storm, but fail if the rainfall event occurs over several days. Intermediate periods of 1.5 to 2 days are important for shallow subsurface drainage systems and storms of less than 6 hours duration (Smedema and Rycroft, 1983).  3.3  Rainfall modelling  Rainfall models are important in semi-arid and arid zones where records of adequate length necessary to determine the true characteristics of the monsoon season rainfall are often lacking. A s rainfall is the limiting factor in crop development, rainfall modelling is an important tool in agricultural planning and drainage design.  Most rainfall models are based on the assumption that daily, monthly and annual rainfall follow a normal distribution. In semi-arid and arid monsoonal areas however, the distribution is seldom normal. Rainfall is a highly variable, intermittent process during the monsoon season, and rainfall occurrences tend to be persistent. This introduces a complexity to the modelling of rainfall events in such areas, but also makes modelling that much more important.  3.3.1  Daily rainfall  The determination of available water during the monsoon season is dependent on the amount of rainfall and the pattern of rainfall occurrence. In many arid and semi-arid zones, a pattern emerges in the daily rainfall probability within the monsoon season when records of adequate length are examined. A n analysis of 73 years of rainfall data in Tucson, Arizona showed that the daily rainfall probability exhibited a distinct pattern within the four month rainy season (Smith and Schreiber, 1973; Lane and Osborn, 1972).  27  3.3.1  Markov Chain Model  Gabriel and Neumann (1962) were the first to model the sequence of wet and dry days recorded over 27 years in Tel Aviv, Israel with a simple first-order, two state Markov chain. Since that time, Markov chain models have been used extensively in work in arid and semi-arid regions as they provide a reasonable fit to the observed monsoonal rainfall pattern.  A Markov chain is a two stage, discrete model which provides the probability of rain on a given day and the probable rainfall depth. Markov chains base the probability of a wet day on the occurrence or non-occurrence of rain on one or more previous days. A wet or rain day may be described as a day on which any rain is recorded; or alternatively, a day on which rainfall above a threshold value is recorded.  The expected amount of rain is obtained from a probability distribution of rainfall depth. Under most conditions, a g a m m a distribution provides an adequate fit to rainfall depth on wet days (Maidment, 1993). A n exponential distribution, which requires less complex calculations may be used as an alternative to the gamma distribution (Todorovic and Woolhiser, 1975).  Markov chain models are often selected over other models due to their flexibility and ease of use. Different orders and number of states can be selected depending on the specific needs of the location. Rainfall modelling generally requires only a simple, two-state Markov chain:  X(r) = 0 and,X(f) = 1  if day f is dry, t=U...t„ if day  [Eq. 1]  t has rain, t=t-,...t  n  where X(f) is a discrete-value process representing two states, wet and dry, for each day within the period U to t„..  A first-order Markov chain assumes the probability of occurrence of a wet or dry state on day r is dependent only on the state of the preceding day:  28  P [X(f) = x, | X ( M ) ] ,  t=t ...tn 1  [Eq. 2]  where P is the probability of occurrence, x is the value of the state (0 or 1) on day f in the n day t  process X(r). If the probability is dependent on the previous 2 days, then a second-order Markov chain model is assumed. Higher orders of Markov chains are possible for those rainfall patterns dependent on more than two preceding days.  In practice, first and second order chains are used as they provide an adequate fit to the data, and are preferred due to their ease of use (Coe and Stern, 1982). In arid and semi-arid areas, first-order, two-state Markov chains have been found to provide a reasonable fit to the seasonal analysis of rainfall distribution patterns (Smith and Schreiber, 1973; Osborn and Lane, 1972; Gabriel and Neumann, 1962).  3.3.1.1 Transition probability matrix A two-state Markov chain analysis is based on a matrix containing the probability of occurrence of combinations or transitions of wet and dry states on successive days over a fixed time interval. The resulting transition probability matrix contains the following probabilities:  Poo P10  P01 P11  where P is the probability of occurrence of a wet or dry state on a given day conditional on the state of the preceding day. The matrix elements represent the probabilities of dry-dry ( P ) , dry-wet ( P ) , 00  01  wet-dry ( P ) and wet-wet (Pn) 2 day sequences over the interval. 10  In semi-arid regions, the dry season is generally excluded from the analysis and a single transition probability matrix is calculated for the entire rainy season or a portion of the season. The transition probabilities are assumed to be consistent or stationary within the selected interval. A further  29  assumption is that the probabilities exhibit stationarity from one year to the next. Gabriel and Neumann (1962) assuming stationarity over the entire rainy season, reported a reasonable fit to the data collected at Tel Aviv, Israel.  However, the assumption of stationarity over an entire season has been challenged by the results of studies from various parts of the world. Significant variation in rainfall probability within a given month of the rainy season has been reported. Several transition probabilities, corresponding to smaller stationary portions of the season such as 5 and 10 day periods, have been successfully applied to regions exhibiting non-stationarity (Jackson, 1981; Heermann et al, 1968). This is similar to using a different Markov chain to model each of the time periods.  Stern and C o e (1984) report however, that in regions dominated by convective storm precipitation, the rainfall process may not exhibit stationarity even over a period a s short a s 5 days. Transition probabilities which change smoothly overtime often provide better results in arid and semi-arid regions (Coe and Stern, 1982; Smith and Schreiber, 1973). A fourier series may be used to model the transition probabilities as a continuous function of time (Feyerherm and Bark, 1965).  The complex calculations required to model transition probabilities which vary over small time intervals are not practical for field use. A simple model using constant probabilities over a number of days, a month or a season is preferable. In assessing whether Markov chain analysis is appropriate to a given area, a model based on a single seasonal transition probability matrix may predict the fit of a more realistic, variable probability model (Gabriel and Neumann, 1962).  3.3.2  Rainfall e v e n t s  The predominant form of precipitation in semi-arid zones are convective storms, which occur intermittently, often clustered in groups. Many of the stations in these zones record a single 24 hour rainfall depth only. This aggregated rainfall information does not provide the detail necessary to determine the characteristics of individual rainstorms.  30  The intermittent nature of precipitation in semi-arid and arid regions does not fit well in traditional rainfall models based on equally spaced time intervals such as days or months. An alternative approach is the modelling of rainfall events. An event is defined as successive rainy days, which occur between dry intervals. Convective storms generally produce rainfall events consisting of one or more rainy days, randomly distributed throughout the season. Dry intervals of 1 to more than 30 days in duration exist between rainfall events.  Models based on events, have been found to provide satisfactory results in semi-arid and arid zones especially when rainfall depth is limited to daily measurements. These stochastic models focus on rainfall event duration, rainfall depth per event and the distribution of events throughout the monsoon season. Event based models have the advantage of being easily extended to other stations in the region, as they do not depend on spatial uniformity. A n event based probabilistic approach, however, is more complex than the analysis routinely carried out in temperate regions.  Rainfall depths on successive rainy days within an event are an important factor in drainage design. Drainage systems are designed to remove a specific magnitude of water, up to a maximum amount. Several days of rainfall below this maximum amount may strain the system and produce failure. A pattern of rainfall depths over the duration of an event often emerge.  3.3.2.1 E v e n t B a s e d M o d e l Early work on event based models was directed at the determination of runoff, rather than the characterization of monsoonal rainfall (Todorovic and Yevjevich, 1969; Fogel and Duckstein, 1969) Duckstein et al (1972) defined event based models as those models that describe two or more random variables, such as the number of events per monsoon season and the rainfall magnitude for each event, and their distribution functions.  Bogardi et al (1988) presented a practical procedure to analyze rainfall events under semi-arid climatic conditions in central Tanzania. Probability distribution functions were fitted to four random  31  variables: events per rainy season, duration of rainfall events, rainfall depth per event, and the interarrival time between rainfall events. They reported satisfactory results assuming an independent random process, although convective storm series are generally not purely random sequences (Fogel and Duckstein, 1982). Application of such an assumption reduces the computational complexity of the model, while retaining the accuracy required in practice.  A Poisson probability density function (pdf) has been found to adequately describe the number of events per rainy season under a number of semi-arid and arid conditions (Bogardi et al, 1988; Duckstein et al, 1972). Geometric pdf's adequately describe the duration of rainfall events (Bogardi et al, 1988; Fogel and Duckstein, 1969). A negative binomial distribution provides a reasonable fit to the interarrival time between events (Bogardi et al, 1988).  Bogardi et al, (1988) found it was necessary to separate rainfall depths into various duration classes, as rainfall depth and duration were directly related. Their study indicated that rainfall depths for events of more than 5 days were best described by a log Pearson type III distribution, while depths for events of 1 day were fit to a negative binomial distribution.  3.3.3  Frequency analysis of extreme events  Extreme events such as intense storms, floods and droughts are important considerations in drainage design. A n event, for this purpose, may be defined as a single rain storm, 24 hour rainfall, or a sequence of dry or rainy days. In semi-arid and arid monsoonal areas where mean climatic values are often meaningless, information regarding extreme events is important to agricultural planning.  The objective of frequency analysis of hydrologic data is to relate the magnitude of extreme events to their frequency of occurrence through the use of probability distributions. These distributions are based on the inverse relationship between the magnitude of an extreme event and its frequency of  32  occurrence. Estimates of the risk of extreme drought or flood conditions can be determined using long rainfall records, although the true probability of such extreme events cannot be predicted.  Most project areas however, do not have rainfall records of adequate length. A probability distribution that reasonably accounts for the recorded rainfall information must be used to extrapolate beyond the available data. From the distribution, the average recurrence interval or return period for events equalling or exceeding a given rainfall amount can be determined. The maximum return period which can be calculated from rainfall data at a single station is limited by the length of the record. Generally a minimum of 30 years of data from a single station is necessary to estimate rainfall with a return period of 100 years (National Research Council Canada, 1989).  3.3.3.1 Assumptions in frequency analysis Several assumptions are inherent in extreme value analysis. Annual maxima and minima for consecutive years are assumed to be independent and identically distributed. A lack of independence introduces a random error with respect to the estimated exceedence probability. In practice annual, rather than daily precipitation most closely meets the independence requirement (Mockus, 1960). However, persistent trends of above- or below-average annual rainfall exhibit a degree of dependence which may increase the variance in the frequency analysis (Zhang, 1982).  A further assumption is that the hydrologic system is stochastic. In addition, the system must be comprised of random precipitation depths, independent with respect to both time and space (Maidment, 1993).  3.3.3.2 Hydrologic data series A complete, partial or extreme value data series is commonly used in frequency analysis. A complete data series includes all rainfall values and provides an estimate of probability. A partial  33 duration data series includes only those values exceeding a threshold value. The resulting data series is known as an exceedence series.  Extreme event analysis is generally applied to either an extreme value or partial duration data series. An extreme data series is comprised of a single maximum or minimum value for each equally spaced time period. This series is known as an annual series if one value is selected for each year of the record. A partial duration series, includes only those events above a threshold value. Thus, a single year may contribute more than one value, with values from other years excluded from the series.  A partial duration series may be preferable in semi-arid and arid areas where the maximum value for a given year may be less than the second largest value of another year. In such a series, the maximum rainfall in drought years which may be exceptionally low compared to maximum values in average years, is excluded. The use of a partial duration series requires a more complex analysis method. In addition, a successful analysis requires the use of an appropriate threshold limit, which is not always easy to determine.  In practice, analyses utilizing either type of data series provide comparable results, if more than 15 years of rainfall data is available. The National Environment Research Council (1975) reports that an annual maximum series may provide more efficient results as both magnitude and a time interval are indicated, whereas annual exceedence values indicate magnitude only.  3.3.3.3 Extraordinary values Extraordinarily high and low values, common in semi-arid and arid monsoonal areas often have a recurrence interval which greatly exceeds the one calculated by flood frequency analysis. S o m e engineers use their personal judgement to determine whether such values should be excluded from the analysis or shifted to a position closer to the probability curve. The U.S. Water Resources Council (1982) suggest that high outliers, defined by a skewness-based test, be removed from the  34 analysis if they are considered to be extraordinary values based on historical information. If such information is unavailable, the outliers are retained. Extraordinarily low values are eliminated from the frequency analysis.  Since the true probability of such extraordinary events is unknown, deleting these values or shifting their position may adversely affect the analysis. Zhang (1982) reports that the inclusion of extraordinary events decreases the random error in frequency analyses. A graphical curve-fitting technique rather than a computed best-fit curve may provide better results when outliers are present in the frequency analysis. This allows the curve to be adjusted so that it is not excessively influenced by extraordinary values (Dunne and Leopold, 1988).  3.3.3.4 Probability distributions Several families of probability distributions are in common use in hydrology. These include the normal/lognormal family, the extreme value family and the exponential/Pearson/log-Pearson type 3 family. The choice of distribution is generally based on a judgement as to which curve provides the best fit to the rainfall data, unless a specific recommendation for the region exists. Countries such as the United Kingdom and the United States have adopted as standard, the Extreme value type II and log Pearson type III methods, respectively ( N E R C , 1975; Benson, 1968).  The normal distribution is not well-suited to semi-arid or arid areas as the annual and daily rainfall is generally positively skewed. Instead, the data may follow a log-normal distribution, with two or three parameters. Hazen (1914) first introduced the two parameter log-normal distribution to hydrological applications. The incorporation of a third, lower bound parameter, which is subtracted from each value before the logarithm is calculated, improves the flexibility of the log-normal distribution.  Extreme value distributions are based on the probability distribution of the largest or smallest values of a random variable, such as rainfall depth. First introduced by Fisher and Tippett (1928), the extreme value distribution was developed into the Type I, II and III forms by Gumbel (1941), Frechet  35  (1927), and Weibull (1939), respectively. The Type I and Type II distributions have been used extensively in flood frequency studies, while the Type III distribution is commonly applied to drought analysis. The equation for the extreme value type I or Gumbel distribution is contained in Appendix D. A General Extreme Value distribution, developed by Jenkinson (1955) has become more popular 4  in recent years. It is a single extreme value distribution in which each of the Type I, II and III forms is a special case. The Pearson Type III and the log Pearson Type III distributions, derived by Pearson (1902) assume a number of different shapes depending on the parameters used. Their flexibility makes them wellsuited to hydrological analysis of random rainfall events. However, the Pearson distributions are limited to the prediction of shorter return periods when extraordinarily high values are present (Reich, 1973). The equation for the log Pearson Type III distribution is contained in Appendix D.  3.3.3.5 Plotting position Foster (1934) introduced the term plotting position to indicate the exceedence probability or recurrence interval of extreme events. When extreme values are plotted using one of the available plotting position formulae which depend on rank and sample size, the return period of an extreme event of a given magnitude can be determined graphically. The return period is defined as the reciprocal value of the plotting position.  Hazen (1914) first introduced a formula to calculate the plotting position, which has since been modified by a number of authors:  P(X > x ) = m - 0 . 5 n m  [Eq. 3]  where P is the exceedence probability or plotting position of the value, m is the rank of the value in descending order and n is the total number of values.  36  Each of the formulae show similar results within the middle range of values, but may differ considerably in the plotting position of the largest and smallest values.  The plotting position formula developed by Weibull (1939) is the most practical and widely accepted. The formula generates probability-unbiased plotting positions such that each position is equal to the average exceedence probability of the ranked observations:  P(X > x ) = m  m n + 1  [Eq. 4]  where P is the exceedence probability or plotting position of the value, m is the rank of the value in descending order and n is the total number of values. Cunnane (1978) argues that a quantile-unbiased method with minimum variance is preferable. A quantile-unbiased method, applied to a sufficiently large number of equally sized samples, results in a distribution line through the average value of the plotting positions. Cunnane recommended a formula which provides better results than the Weibull formula, when the largest values of a sample are important:  P(X > x ) = m  m - 0.40 n + 0.2  [ E q . 5]  For the Gumbel extreme value distribution the plotting position formula developed by Gringorten (1963 ) provides optimal results for the largest values:  P(X > x ) = m  3.3.4  m - 0.44 n + 0.12  [Eq. 6]  Drought  The extreme lack of rainfall, or drought, is a common occurrence in semi-arid and arid regions. Agricultural drought is based on the depletion of soil moisture in the root zone such that crop yield is adversely affected.  37 A number of states in India have attempted to establish criteria for drought conditions for various climatic conditions. Seasonal rainfall below set limits, rainfall deficit levels and variable rainfall within a season have all been used to define drought (Sikka, 1973).  In semi-arid and arid regions, the characterization of drought is often related to the total monsoon rainfall. A s a very dry season preceding the monsoon depletes all soil moisture, there is always a water deficit prior to the onset of the monsoon. Without adequate replenishment from rainfall, crop failure during the monsoon season is certain. Irrigated crops grown during the dry season are also affected as the supply of irrigation water is dependent on the monsoon rains stored in the reservoirs.  3.3.4.1 Drought analysis The pattern and distribution of rainfall throughout the season is often more important than the total rainfall to the determination of drought conditions. Prolonged dry periods randomly distributed between rainfall events can result in drought conditions. In arid and semi-arid regions, studies indicate that the length of dry day sequences may provide an indication of drought conditions (Gupta and Duckstein, 1975).  Hershfield et al (1973) used the frequency distribution of dry day sequences between rainfall events as an indicator of reliable precipitation in the mid-latitude eastern region of the United States. The authors cautioned that other information must be considered to determine the occurrence and severity of drought conditions. The soil moisture capacity, soil moisture content, and the water-use pattern of the crops, are all important factors in addition to the length of dry day sequences.  Gupta and Duckstein (1975) applied extreme value analysis to the maximum dry day sequences. Extreme frequency analysis of dry day sequences and the minimum annual rainfall provides information on the recurrence interval of extreme drought.  38  3.4  Effective rainfall  Dastane (1974) presents a overview of effective rainfall definitions, which differ with the hydrological application. In conventional hydrology, effective rainfall is considered to be that portion of total rainfall that contributes to runoff. Conversely, effective rainfall for agricultural purposes is considered to be that portion of total rainfall which satisfies evapotranspiration (ET) requirements (Burman 1980, 1983; A S C E , 1990; Burman and Pochop, 1994).  Surface runoff and deep percolation losses do not contribute to crop water requirements, nor do they serve to reduce E T . Although deep percolation is excluded from effective rainfall, it may be beneficial to crops. The percolation of water through the root zone may remove excess salt, thereby reducing the leaching requirement. Water temporarily stored in surface depressions and plantintercepted rainfall are generally included as part of effective rainfall. The water may infiltrate the soil over time, or evaporate into the atmosphere so that E T is reduced.  Intercepted water which evaporates directly into the atmosphere from plant surfaces is excluded from effective rainfall by some authors (Burman and Pochop,1994). Effective rainfall is restricted to that portion of total rainfall which infiltrates into the soil profile at a point in a field, without contributing to deep percolation. Although water evaporating into the atmosphere from plant surfaces reduces E T , it occurs downwind from the interception point (Burman et al, 1975).  3.4.1  Factors affecting effective rainfall  3.4.1.1 Rainfall pattern and distribution In arid and semi-arid regions of India, there is little or no moisture stored in the soil root zone prior to the onset of the monsoon season. The monsoon rains are the only source of plant-available soil water; however, much of the rainfall is not effective.  39  The intensity, depth and duration of rainfall events are related to the magnitude of effective rainfall. The high intensity, short duration rainfall events of substantial depth characteristic of convective storms in semi-arid and arid regions result in large surface runoff.  Of equal importance is the distribution of rainfall events throughout the monsoon season. If the soil moisture in the root zone is depleted between rainfall events, the surface runoff and deep percolation losses are reduced. However, large magnitude rainfall events with short dry periods between events do not allow adequate time for plants to take-up available soil water.  The timing of rainfall events with respect to crop growth stage is also important. Rainfall just before harvesting is for most crops a waste, and is considered ineffective.  3.4.1.2 Soil characteristics  Soils have a limited water intake rate and moisture holding capacity. The amount of water held by the soil between its field capacity and the wilting point, is the portion available for uptake by plant roots.  Soils with high infiltration rates and permeability are able to intake more water and reduce surfacerunoff. Both infiltration and permeability are related to the texture, structure and compactness of the soil.  The plant-available soil water stored in the soil profile depends upon its depth, texture, structure and organic matter content. Values range from 200 mm/m for heavy textured soils, to 60 mm/m for coarse textured soils. Fine textured soils with deep soil profile have more storage capacity, thereby increasing effective rainfall.  3.4.1.3 Crop factors  40  Under conditions of high crop water requirements or evapotranspiration (ET), the moisture in the soil root zone is depleted rapidly. This allows more rainfall to infiltrate the soil profile, increasing effective rainfall.  The type of crop and its growing stage, together with climatic conditions, are directly related to evapotranspiration rates. A s the rooting depth increases and the crop matures, more water is required, increasing evapotranspiration. Deep-rooted crops take-up soil moisture from deeper levels of the root zone, further increasing the proportion of effective rainfall.  3.4.1.4 Other factors Management practices which influence runoff, infiltration, permeability and soil water holding capacity also influence the amount of effective rainfall. Surface ruts and channels, or soil compaction resulting from poor field management, increase surface runoff rates.  The topography also impacts surface runoff. In areas with little or no gradient, water that has an opportunity to pond at the surface, may infiltrate into the soil over time. A s the gradient increases, more rainfall is lost to surface runoff.  3.4.2  Effective rainfall estimations  Several methods of effective rainfall estimation, based on direct measurement, empirical formulae and the soil water balance, have been developed. Dastane (1974) provides an comprehensive overview of all of the methods, including the relative merits of each.  Although direct measurement techniques often provide the best information with regard to effective rainfall, historical data is seldom available. In the absence of direct field measurements, empirical methods and soil water balance methods are commonly used to estimate effective rainfall.  41  3.4.2.1 Soil water balance models Soil water balance models ( S W B M ) are considered to provide the best estimates of effective rainfall for a specific location. They incorporate all of the processes of the hydrologic cycle which contribute to soil water storage in the soil profile. These models are therefore, easily adapted to the climate and soil conditions of any location. However, many are complex and difficult to apply, especially if there is a lack of data.  Several models have been developed which simulate the soil moisture balance, which consider rainfall and irrigation as inputs to soil water. Interception, runoff and deep percolation in excess of actual field capacity represent losses to the balance. A n estimation of evapotranspiration is used to determine the soil water depletion. Often the models use methods to estimate the various components that were developed for other purposes.  One of the more common soil water balance models, known as the S P A W model was developed by Saxton et al (1974). The model simulates the soil water balance using rainfall, actual evapotranspiration, infiltration and the redistribution of soil moisture. Each of the components is considered separately on a daily basis, together with the previous day's soil water balance, to determine the effective rainfall.  Both interception and evaporation from water stored in surface depressions are taken into account in the S P A W model. Interception losses up to a maximum value, are subtracted from actual evapotranspiration regardless of the stage of crop growth. In the early crop growth stages, the interception loss is assumed to account for evaporation from water stored in surface depressions.  42  3.4.2.2 Empirical methods  3.4.2.2.1  U.S. Bureau of Reclamation method  Stamm (1967) developed a method of effective rainfall estimation for the arid and semi-arid areas of the Western United States. Monthly effective rainfall is calculated as a percentage of incremental rainfall amounts, for the 5 driest consecutive years only.  The simplicity of this method has resulted in widespread use throughout the world. Dastane (1974) reports that the U.S. Bureau of Reclamation method is not appropriate for most areas. The method does not incorporate soil and crop information, rainfall frequency and distribution, or the degree of aridity, raising questions as to its accuracy.  3.4.2.2.2  USDA-SCS method  The U S D A - S C S (1970) presented an effective rainfall estimation method which relates average monthly effective rainfall to average monthly evapotranspiration and the normal depth of depletion prior to irrigation:  R = f(D)[1.25 R,  0 8 2 4  e  - 2.93][10  0 0 0 0 9 5 5 ETc  ]  [Eq. 7]  where R = effective rainfall, R = mean monthly rainfall, E T = E T for the crop, D = normal depth of e  t  C  depletion prior to rainfall/irrigation. The relationship is based on measurements of daily soil water storage, rainfall and evapotranspiration over a 50 year period. A total of 22 stations located in arid to humid climates in the United States contributed to the results.  This method is often recommended in areas where a daily water balance simulation is not practical ( A S C E , 1990). However, as it does not take into account either soil infiltration rates nor rainfall  43  intensity, it is only applicable in areas with high soil infiltration rates relative to the intensity of rainfall (Patwardhan et al, 1990; Dastane, 1974).  Patwardhan et al (1990) compared the results of the U S D A - S C S method with a soil water balance model. The U S D A - S C S method produced effective rainfall estimates comparable to the S W B M for well-drained soils, but did not perform as well with poorly drained soils. The method produced less accurate estimates under both soil conditions, when rainfall exceeded the mean annual event.  The discrepancy between the effective rainfall estimated by each method was considered to be related to several weaknesses in the U S D A - S C S method. The U S D A - S C S method is not sensitive to soil type and does not account for carry-over soil water. In addition, event frequencies and local climatic characteristics are not explicitly incorporated into the method.  3.4.2.2.3  Local methods  Dastane (1974) discusses several methods, based on practical experience, developed locally in India. The effective rainfall for rice is generally considered separately from other crops. Dastane (1974) provides an overview of the methods. The estimates vary in accuracy, with some appropriate for preliminary planning only.  Many of the methods are based on a set percentage of rainfall or an amount above or below a threshold rainfall value. Fifty to 80% of the total rainfall is considered effective for rice, with 70% of average seasonal rainfall used as effective rainfall for other crops (Dastane, 1974). Smith (1991) estimates effective rainfall as 70 to 90% of mean monthly rainfall of 120 mm or less for use with the F A O computer program developed for irrigation and planning purposes ( C R O P W A T ) .  44 3.5  Evapotranspiration  The term evapotranspiration (ET) is commonly used to describe the water requirement of crops. It refers to the transpiration component, as well as the evaporation of water from soil, water surface and plant canopy.  A n accurate measure of evapotranspiration is essential to the planning and design of both irrigation and drainage systems. Evapotranspiration determined directly through tanks, lysimeters, water balance or other methods provide the best prediction of crop water requirements. However, such data is seldom available over a long enough time period to be useful. Estimations obtained from empirical formulae, based on climatic data and calibrated to the local area, are often relied upon in the planning of water resource projects.  3.5.1  Climatic Factors  Evapotranspiration is affected by several climatic factors, including precipitation, temperature, wind speed, and sunlight hours and intensity.  3.5.1.1 Temperature Temperature is considered to be the major factor influencing E T in crops. Temperature has a direct influence on transpiration, but it also indirectly affects transpiration through its effect on plant growth. Under conditions of lower or higher than average temperatures, crop growth is retarded or stopped completely (USDA, 1970).  3.5.1.2 Wind Evaporation from land and plant surfaces is accelerated by wind, therefore it is an important factor in the determination of E T . Most wind measurements represent average wind speeds over a 24 hour period. A s day and night wind speeds differ significantly, the use of daily average wind speeds in  45  empirical E T formulae often results in a poor estimate of E T . Under conditions of stronger daytime wind, often experienced during the Rabi season, E T estimates tend to be underestimated.  In the absence of actual day to night wind ratios, an approximation of 2.0 is often recommended. Based on this approximation, a correction factor of 1.33 is used to obtain day time wind speeds from mean 24 hour wind speed measurements (Doorenbos and Pruitt ,1977).  Rao et al (1981) however, found that the day-night ratio differed dramatically between the monsoon and dry periods. The study, conducted over a two year period in the state of Maharashtra, suggests that the day-night ratio during the monsoon season varied between 1.0 and 1.4. During the hot, dry season, the ratio increased to between 1.8 and 3.8.  3.5.1.2 Other Climatic Factors In areas with low relative humidity, higher crop water requirements can be expected. Dry air promotes both evaporation and transpiration, while they are suppressed under conditions of high humidity.  E T processes require energy in the form of sunshine. Thus, crop E T requirements are directly proportional to the number of daily sunshine hours. A s areas of higher latitude receive much more sunshine during summer months than those closer to the equator, latitude is also an important factor.  3.5.2  Crop Factors  Seasonal crop E T is affected by the length of the growing season. Also of importance, is the length of each crop development stage. Crops require more water in their mid-season development stage, between the time they reach effective ground cover until they begin to mature.  46  The length of the mid-season development stage and the growing season vary depending on the time of year. Generally, those crops planted in warm summer months will have shorter growing seasons.  3.5.2.1 Advection In arid irrigated areas, sensible heat advection becomes an additional source of energy for ET processes. Sensible heat is transferred from drier areas into the irrigated areas, where it is converted into latent heat. The aerodynamic roughness of the crop affects the amount of sensible heat advection that occurs.  3.5.3  Reference Evapotranspiration  Empirical formulae are designed to calculate reference ET or potential ET. The relationship between reference ET (ET ) and crop ET (ETr) is defined as: r  ET = k ET C  c  r  [Eq. 8]  Reference ET estimates are generally based either on grass, 8 to 15 cm tall (Doorenbos and Pruitt, 1977) or alfalfa, 30 to 50 cm tall (ASCE, 1990). In each case the crop is assumed to be well-watered and actively growing.  3.5.3.1 Comparison of Grass and Alfalfa Reference Evapotranspiration The ET requirement of alfalfa is 13 to 20% more than that of grass (ASCE, 1990). Factors such as the canopy density, leaf resistance, aerodynamic roughness and root system account for the difference between grass and alfalfa ET rates.  The dense ground cover provided by alfalfa leaves absorbs more incoming solar radiation than grass, preventing excessive drying of the soil. In addition, alfalfa leaves have a lower leaf resistance  47  to water vapour diffusion than blades of grass. In areas where sensible heat advection is a factor, alfalfa may provide better crop ET estimates as the aerodynamic roughness of its leaves is more similar to other agricultural crops than grass.  Under conditions of unlimited soil water supply, ET reaches maximum or potential rates. As the soil water is depleted, the ET rate decreases. The extensive root system of alfalfa occupies a greater volume of soil than that of grass roots, minimizing ET rate changes due to soil water depletion (Wright and Jensen 1972; A S C E , 1990).  The main disadvantage of alfalfa as a reference crop is its change in height throughout the growing season. Grass provides a more consistent reference as it can be clipped to a constant height (Burman and Pochop, 1994).  3.5.3.2 C o n v e r s i o n between reference E T estimates In order to compare grass and alfalfa ET estimations, it is necessary to convert from one to the other. The conversion of alfalfa based estimates to grass and vice versa can produce questionable results due to lack of local calibration. The differences in cultivation practices and climate make conversion factors determined for one area not easily applied to other regions (Burman and Pochop, 1994).  Doorenbos and Pruitt (1977) recommend a factor of 1.15 to convert grass ET estimates to alfalfa in arid and semi-arid regions, under conditions of predominately light to moderate wind. Studies in semi-arid regions have found alfalfa ET is reasonably estimated as 1.15 the ET of grass (Allen and Pruitt, 1986; Hussein and El Daw, 1989). Saeed (1986) reported a conversion factor of 1.2 produced better results under the arid conditions of central Saudi Arabia.  48  3.5.4  Empirical formulae for ET estimation  Extensive research on empirical formulae has been conducted since 1948, when P e n m a n introduced the first E T formula relating various climatic factors.  Empirical formulae are classified into combination, radiation, temperature and pan evaporation methods based on the required climatic factors. Combination methods require the greatest number of climatic parameters, while temperature methods require the least.  E T formulae are recommended for specific climatic regimes depending on the location and climatic conditions under which the equation was developed. S o m e combination methods however, can be applied to any area (Allen, 1986). The equations for those methods suitable for estimating E T in semi-arid and arid climates are contained in Appendix E.  3.5.4.1 Combination methods The P e n m a n equation, developed in 1948, was based on aerodynamic and energy components. It has undergone several modifications to the present. Allen (1986), provides a comprehensive overview of the variations in the Penman equation.  Wright and Jensen (1972) modified the original Penman equation to estimate alfalfa reference ET, based on work in Kimberly, Idaho. The Kimberly-Penman method introduced new wind function coefficients and a revised saturation deficit method.  Wright (1982) refined the Kimberly-Penman 1972 equation, introducing varying coefficients for the wind function. Sensible heat advection, which exhibits seasonal variation, is better estimated with a varying wind function. A set of crop coefficients were compiled for use with alfalfa reference E T based on the studies at Kimberly Idaho.  49  Monteith (1965) incorporated aerodynamic and canopy resistance factors into the original Penman equation to create a new alfalfa reference method. Thorn and Oliver (1977) further refined the Penman-Monteith equation to account for varying surface roughness. It is unclear as to how the Monteith equation was adapted from a forest canopy to agricultural crop E T . However, the use of the Penman-Monteith method for agricultural application has gained widespread acceptance.  Doorenbos and Pruitt (1977) developed the grass reference F A O Penman, and the F A O Corrected Penman. The corrected version, uses solar radiation, wind and humidity to refine the E T estimate.  3.5.4.2 Temperature m e t h o d s Thornwaite (1948) correlated mean monthly air temperature with E T . The correlation, based on water balance studies in valleys of east-central U S A , allows for the estimation of E T with temperature and latitude data only. The conditions under which this correlation is valid do not occur in arid or semi-arid areas except during short post-rainfall periods. The Thornwaite equation only applies to areas where a standard albedo can be applied to the evaporating surface, and advection is not a factor.  U S D A - S C S (1970) introduced the Blaney-Criddle method, which is based solely on temperature and daylight hours. Rather than a grass or alfalfa based set of crop coefficients, the S C S Blaney-Criddle relies on a coefficient combining climatic and crop factors, to convert reference E T to crop E T .  Doorenbos and Pruitt (1977), modified the original S C S Blaney-Criddle equation to create a grass reference method, known as the F A O Blaney-Criddle. This method uses standard grass coefficients rather than the original S C S coefficients. It can be adjusted to various climatic zones through correction factors.  50  Hargreaves and Samani (1982;1985) revised an earlier radiation method (Hargreaves, 1974) to eliminate the need for radiation information. The new method, based on research in Arizona, is a minimal data method requiring temperature alone.  3.5.4.3 Radiation Methods Turc (1961) developed a radiation method which estimates potential rather than reference E T . The equation was based on research in western Europe and is best suited for areas with similar climates.  Jensen-Haise (1963) and the modified Jensen-Haise (Jensen et al, 1971) provide estimates of alfalfa reference E T . It provides reasonable estimates for arid and semi-arid regions.  The Priestly-Taylor (1972) method was designed primarily for humid regions, and does not give adequate E T estimations for arid or semi-arid areas. A reference crop for this method was not indicated.  Hargreaves (1974) introduced a method of estimating E T using radiation and temperature information, based on 15 years of research conducted in Cochocton, Ohio. Grass was used as the reference in the estimation of crop E T in this humid area.  The F A O Radiation method (Doorenbos and Pruitt, 1977) is a modification of the Makkinik (1957) radiation method. This method was designed to provide grass reference E T estimates for a wide range of climatic regimes, through the use of correction factors.  3.5.4.4 Pan Evaporation Methods Christiansen (1968) and Christiansen and Hargreaves (1969) developed a method of estimating E T from Class A pan evaporation and climatic data. The pan coefficients, relating evaporation to E T , are based on regression equations.  51  The F A O P a n evaporation method (Doorenbos and Pruitt, 1977) estimates E T from both Class A pan and Colorado sunken pan evaporation measurements. Pan coefficients, dependent on wind, fetch and humidity, are presented in tabular form.  3.5.4.5 Correction coefficients Correction coefficients are used in the F A O radiation, Blaney-Criddle, Corrected Penman and Pan methods to account for different climatic conditions. Doorenbos and Pruitt (1977) presented a number of "look-up" tables in the F A O - 2 4 document which provide these coefficients. A number of mathematical representations of these "look-up" tables have been developed which allow for computerized calculation of E T using the F A O methods.  Frevert et al (1983) developed correction coefficient regression equations for each of the 4 methods. These correction coefficients agree closely with values in the original F A O - 2 4 tables.  Allen and Pruitt (1991) found that the results of Frevert et al (1983) for all methods but the F A O Radiation method deviated from the F A O - 2 4 tables by up to 10%. The accuracy of the correction factor equations for the F A O Penman, Blaney-Criddle and Pan methods was improved through the introduction of additional parameters. The resulting equations provide an accurate representation of the original F A O - 2 4 tables.  Snyder (1992) derived a Class A pan coefficient for use with the F A O Pan method, based on the regression equation developed by Cuenca (1989). The number of terms in the regressions equation were minimized to create a simpler equation.  3.5.5  Studies  Studies comparing various E T methods from areas with climates similar to the Rajasthan area were examined. In general, the E T studies tend to be focused on the irrigated dry season rather than the  52 monsoon season. Studies comparing methods which could be used over both a humid and a semiarid or arid area were not common.  3.5.5.1 Arid Regions A comparison of ET methods under extremely arid conditions was conducted by Salih and Sendil (1984) in central Saudi Arabia. Lysimeter measurements for alfalfa were compared to ET estimates calculated with Jensen-Haise, Modified Penman, Class A Pan, Hargreaves, Penman, S C S BlaneyCriddle, FAO Blaney-Criddle and a local version of the Blaney-Criddle equation. The Jensen-Haise and Class A Pan methods were ranked first and second, respectively, although the authors were not confident of the validity of the pan evaporation measurements. The Hargreaves method was ranked third, while the Modified Penman method was ranked fourth . The Blaney-Criddle methods were 1  ranked lowest, with the local version of the Blaney-Criddle equation resulting in the least accurate estimate.  Although the Jensen-Haise method produced the most accurate estimates, E T  JH  underestimated  ET ifaifa by as much as 20%. The authors recommended adjusting E T , based on the results of their a  JH  work and earlier work in the same area as follows:  ET  alfa  , = 1.16 E T - 0 . 3 7 fa  JH  [Eq. 9]  Saeed (1986) conducted a similar study in the same region of central Saudi Arabia from 1981 -1983. In this study, the S C S Blaney-Criddle, FAO Blaney-Criddle, Jensen-Haise, Turc, Hargreaves (1974) and Pan Evaporation methods were investigated. The Jensen-Haise method provided a good estimate of ET during the October to March (winter) period, but underestimated ET during the summer months by as much as 33%. The Turc and Hargreaves methods resulted in fair estimates  1  The version of the Penman equation was not indicated.  53  during the winter months, but also underestimated E T during the summer period. Both versions of the Blaney-Criddle method underestimated E T throughout the year.  An evaluation of minimal data E T methods in Arizona was reported by Samani and Pessarakli (1986). The Jensen-Haise, Modified Jensen-Haise, Hargreaves (1974), Hargreaves-Samani (1982; 1985), Modified P e n m a n (Hansen et al, 1980) and S C S Blaney-Criddle, Class A P a n were compared. The authors ranked the methods in descending order as follows: Hargreaves, P a n , Hargreaves-Samani, P e n m a n , Jensen-Haise and Modified Jensen-Haise, and S C S Blaney-Criddle. While the Hargreaves, Pan and Hargreaves-Samani methods were within 1% of the actual ET, the S C S Blaney-Criddle method underestimated E T values by 2 1 % .  The E T comparison study conducted by Al-Sha'lan.and Salih (1987) in central Saudi Arabia is the most comprehensive report on the estimation of E T in an arid area. Twenty-three empirical methods were compared, over two 12 month periods, using 5 different rating criteria. The Jensen-Haise, class A pan, Ivanov, adjusted class A pan, Behnke-Maxey and Stephens-Stewart methods were ranked one to six respectively using a combined rating criteria. The Makkink, local Blaney-Criddle (described by Salih and Sendil, 1984), S C S Blaney-Criddle, Turc, and Ostromecki and Oliver methods resulted in the least accurate estimates, respectively.  3.5.5.2 S e m i - A r i d R e g i o n s A comparison of E T estimation methods in the flat central plains of the Sudan was reported by Hussein and El Daw (1989). The Jensen-Haise, Hargreaves, F A O - P e n m a n and F A O - C l a s s A evaporation pan methods were selected for comparison against actual evapotranspiration data. . The Hargreaves method produced reasonable estimates. The Jensen-Haise and F A O - C l a s s A pan methods overestimated E T ; the F A O Penman method, uncorrected and corrected versions, resulted in an underestimation of E T . Use of the original Penman (1948) wind function in the F A O - P e n m a n equation resulted in a more accurate estimate of E T . The application of the correction factor developed by Frevert et al. (1983), further improved the estimate.  54 3.5.5.3 Combination studies - Arid and Humid Climates Allen (1986) reported on the variations of the Penman combination equation and evaluated the performance of each form over a 3 year period. The evaluation included arid (Kimberly, Idaho) and humid (Coshocton, Ohio) locations, as well as a Mediterranean climate (Davis, California). The 1982 Kimberly Penman performed well in the arid area for which it was developed, with good results from the F A O corrected Penman and Penman-Monteith methods. The Penman-Monteith, 1963 Penman and Priestly-Taylor methods all produced reasonable estimates at the humid site. The PenmanMonteith, and F A O Corrected Penman performed well at all 3 locations; the Penman-Monteith produced the most consistent results between the 3 locations. The 1982 Kimberly-Penman produced good results in both the arid and humid areas when E T estimates were adjusted downward to convert from alfalfa to grass.  55  4.0  Methods and Materials  4.1  Data  Climatic data for the Chambal Command area is collected at several weather stations throughout the watershed. Data collected at the Kota station was used for this study as it is the closest station to the Daglawada test plot. The method of data collection was determined by the weather station in Kota, based solely on the local need for weather information. The author had no input into the method of collection or the level of detail recorded.  4.1.1  Data assumptions  The data obtained from the Kota station in Rajasthan, India posed some problems. Within the climatic data, there is no distinction between true zero values and zero as a missing value. It is not known whether this lack of distinction is due to faulty record-keeping at the station, or if the problem was introduced when the paper records were entered into database/spreadsheet software at the station. A s access to the original paper records was not possible, assumptions as to when a zero value was reasonable were necessary in order to analyze the data (Appendix C).  In addition, some of the measures were entered in error. All climatic values were subjected to a reasonableness test, and obvious errors were corrected (Appendix C).  4.1.2  Analysis Limitations  Measurements of such climatic data as minimum and maximum humidity, sunshine hours and wind speed were routinely taken only in some years. In addition, measurements for an entire month or more within those years were neglected. A s a result, many calculations are based on a single month's data, even though 24 years of data were collected.  56  Rainfall data for 1981 and 1982 have been excluded from all rainfall modelling, effective rainfall and water balance calculations. The rainfall data for the Kharif season months of these years is incomplete. The data has been included in evapotranspiration calculations, and general climatic information where possible.  The analysis is further limited by the lack of detailed data. Rainfall was recorded once every 24 hours, without detail as to the pattern of rain throughout the day. It is therefore impossible to determine whether the rain fell continuously over 24 hours, or whether there were one or more short duration rain storms. Throughout this thesis, daily recorded rainfall is assumed to have occurred as one continuous storm over a 24 hour period.  4.2  Programming and calculations  All necessary programs were written in the S A S programming and procedural language contained in B A S E S A S for Windows, version 6.10. Statistical analyses were completed using both B A S E and S T A T S A S , version 6.10. S o m e data was summarized in Microsoft Excel for Windows, version 6.0. A complete set of programs is available from the Bio-Resource Engineering Program, Department of Chemical and Bio-Resource Engineering, the University of British Columbia.  The programs require a minimum of a 386 D X personal computer with 8 mb of ram, with Windows 3.1 or higher, B A S E and S T A T S A S for Windows, version 6.08 or higher. A 486 computer with 16 mb of ram provides better processing times. With minor modifications, the programs can be run in a main frame environment.  4.3  Rainfall Modelling  Rainfall modelling was conducted over the monsoon season months only. The emphasis is on 1-4 day rainfall depths due to its significance in subsurface drainage design.  57  4.3.1  Characteristics of the monsoon season  The monsoon season was characterized through a number of measures. All measures were based on a portion of the Kharif season between a defined start and end date, referred to as the model monsoon season. The start of the season was defined as the first June rainfall of at least 0.1 m m d ' . The first rainfall in 1  June of 5.0 mmd" or more was also determined for comparison purposes. 1  The annual monsoon cycle was defined as the time between the start of two subsequent model monsoon seasons.  The end of the season was defined as the date on which total rainfall from the start of the season reached 90% of the yearly total. The 90% cut-off was a consistent measure that allowed for comparison between years. It was based on the average percentage of annual rainfall recorded during June through September for the Chambal Command area (Appendix B).  The length of the monsoon season was defined as the period between the start and end of the model monsoon season.  Days within the model monsoon season, with at least 0.1 mm of recorded rain were considered rain days.  Persistence was evaluated using a cumulative departure from the mean model monsoon season rainfall. This allowed for the determination of independence between successive monsoon seasons, or alternatively, the recognition of trends.  4.3.2  Markov chain analysis  The suitability of a first-order, two state Markov chain analysis to predict the daily probability of rainfall over the Kharif season months of June to September was examined. The model monsoon  58  season period was not considered suitable for this analysis, as it is biased toward wet day sequences due to the definition of the start and end dates.  The probability of rainfall on a given day was based solely on the occurrence or non-occurrence of rain on the previous day. Wet days were defined as those which recorded a minimum of 0.1 mm of rain, and were assigned a value of 1. All other days were considered dry days, and were assigned a value of 0.  Fixed intervals of 5 and 10 days and 1 month were selected for evaluation. A transition probability matrix for each month of the Kharif season, and for 10 and 5 day fixed intervals within each month was calculated. Intervals ending on the 31st day of July and August were included in the preceding 5 and 10 day interval periods. The number of wet-wet, wet-dry, dry-dry and dry-wet sequences for each interval were summed over all years of data, providing corresponding P-n, Pio, P  0 0  and P  0 1  matrix values for the interval:  P n = number of occurrences of X(n = 1 and X(t-1) = 1  [Eq. 10]  total number of occurrences of X(r) = 1  Pm = number of occurrences of Xffl = 1 and X(t-1) = 0  [Eq. 11]  total number of occurrences of X(r) = 1  Poo = number of occurrences of X(f) = 0 and X(t-1) = 0  [Eq. 12]  total number of occurrences of X(f) = 0  Pm = number of occurrences of X(n = 0 and X(t-1) = 1  [Eq. 13]  total number of occurrences of X(r) = 0 where X(r) is the represents the state (wet = 1, dry = 0) of day f in the interval.  Stationarity over each interval and between years was evaluated. Variation in the values of P , P01, 0 0  P11 and P i o within the interval, was used as an indication of stationarity over the interval. For each of  59  the years (1970 - 1980, 1983-1993) the probability values over 5 day intervals were calculated and compared.  The occurrence of each combination of wet and dry days, over 3 and 4 days within the interval, was predicted from the transition probability matrix. More than 1 day preceding the last day of the sequence was assumed not to influence the outcome. For example:  and  Predicted (wet-dry-dry-wet) = Actual (wet-dry-dry) P i 0  [Eq. 14]  Predicted (dry-wet-dry-wet) = Actual (dry-wet-dry) P  0 1  [Eq. 15]  where Predicted is the number of occurrences of the bracketed combination of wet and dry states over a 4 day period within the interval, recorded over all years; Actual is the observed number of occurrences of the bracketed combination of wet and dry states over a 3 day period within the interval, recorded over all years; and P i is the probability of occurrence of a wet state preceded by a 0  dry state, calculated over all years for the interval.  A chi-square test of independence was used to verify the assumption that the probability of rain was not dependent on more than 1 preceding day. Two levels of significance, 5 and 10% were used to evaluate independence. The interval with the best fit of actual to predicted 3 and 4 day wet and dry state combinations was selected as the most appropriate for Markov chain analysis in this region of India.  The results of the Markov chain analysis were verified against each of the years of available rainfall data (1970-1980, 1983-1993). For each year, the predicted and actual 3 and 4 wet and dry state combinations for the selected interval were compared. The transition probability matrix generated from all years of data for the selected interval was applied to each year. A chi-square test of independence with 5 and 10% levels of significance was used to evaluate the results.  60  4.3.3  Daily rainfall modelling  The rainfall depth distribution over 1-4 day periods from June to September were determined. Moving totals of daily recorded rainfall were used to determine the 2-4 day rainfall depths. Missing rainfall data within a 1-4 day period resulted in the exclusion of that period from the analysis. All periods were recorded in the month in which in the period ended.  4.3.4  Rainfall event modelling  An event-based model for rainfall pattern and distribution was developed from rainfall event depth and duration, and interarrival times. The model was applied to the model monsoon season rather than to the months of June through September. The inclusion of 90% of the monsoon season rainfall within the model monsoon season, ensures that all relevant events are included in the model. It also eliminates the introduction of extraordinary interarrival times resulting from the departure of the monsoon rains prior to September.  4.2.4.1 Model definition Rainfall events were defined as consecutive days of rainfall, while interarrival times were defined as the consecutive dry days between rainfall events. Missing values in the data collected at the Kota station were treated as the end of a rainfall event or dry day sequence. Events were reported on the date in which they ended.  Events were characterized by rainfall depth and event duration. In addition, the rainfall depth of each day over the event was examined for pattern.  Probability distribution functions were fitted to sample data wherever possible.  61  4.2.4.2 Threshold rainfall values Two event-based models were developed with different rainfall threshold values. The first model included all successive days with at least 0.1 mm of rain as part of a rainfall event. The second model defined a rainfall event as successive days with 5.0 mm or more recorded rain.  The selection of 5.0 m m of rain was considered the threshold for significant rainfall, given that evaporation rates meet or exceed 5.0 mmd" throughout the Kharif season. The start of the model 1  monsoon season for the 5.0 mm threshold model was set to the first day in June with 5.0 mm or more recorded rainfall.  4.2.4.3 Model assumptions Event-based modelling assumes the rainfall events in the monsoon season are part of a random process. The parameters describing the monsoon season, and the rainfall events throughout the season are therefore assumed to be independent.  The assumption of independence was tested using a correlation analysis. Relationships between the monsoon season measures and between the event-related measures were examined.  Successive rainfall events and interarrival times were each subjected to a pairwise correlation to ensure independence.  4.4  Frequency analysis  For each analysis, the sample data were ranked and exceedence and non-exceedence values determined from the Weibull formula (Appendix D). The Weibull formula was selected as it is suitable to both the Gumbel and Log Pearson Type III distributions. The Gumbel and Log Pearson type III probability distributions were selected as they are the most commonly used distributions for hydrologic data. The equations for both distributions are contained  62  in Appendix D. The Gumbel probability distribution curve was constructed from the sample moments for the data series. The frequency factor method was used to determine the Log Pearson Type III probability distribution curve. Values with return periods of 2, 3, 4, 5, 10, 15, 25 and 50 years were determined from the equation for each curve. The standard normal variable (z) and reduced variate were used to linearize the graph for the Log Pearson Type III and Gumbel distributions, respectively. The logarithms of the data were plotted against the Log Pearson Type III probability distribution. The fit of the distribution to the sample data was judged graphically to ensure that extraordinary values did not bias the distribution. More weight was given to the fit of the curve against data values with non-exceedence values of 0.900 or less, representing a return period of 10 years. Values for each return period were selected from the curve providing the best fit to the data.  4.4.1  Normal rainfall  A complete duration data series was generated for each month of the Kharif season for total rainfall depth, and number of rain days. An annual rainfall series was also generated from the available data. A data series for each of the daily, 0.1 and 5.0 event models was generated for rainfall depths over 1-4 days for the Kharif season.  4.4.2  Extreme rainfall  The maximum daily rainfall for each year was compared to the total annual rainfall to determine if an annual exceedence series was more appropriate than an annual maximum series. With the exception of 2 years with less than 500 mm of rain, each of the years had maximum rainfall depths in excess of 75 mmd" (Appendix B). A n exceedence series would draw heavily from the years with 1  more than 1000 mm of rain if a threshold value of 75 mmd" were applied. A n extreme value series 1  was therefore considered to be more representative of the years of available data.  63  A single maximum and minimum rainfall depth over 1-4 days from the daily model, and the 0.1 and 5.0 mm threshold event-based models, were selected for each year. For the daily model, minimum values were selected from rainfall depths of greater than 0.0 mm.  4.4.3  Design storm  Depth-duration-frequency curves and intensity-duration-frequency curves were constructed from the results of the extreme value analysis for 1-4 day rainfall from the daily and event-based models. A set of curves for return periods of 2, 5 10, 15 and 25 years were generated from the G u m b e l probability distribution. Straight lines were drawn through the values to allow for extrapolation and.  4.4.4  Wet and dry year rainfall  Wet and dry year rainfall was calculated from maximum and minimum daily rainfall over the Kharif season. The rainfall contribution from months outside the Kharif season was not considered. The pattern of rainfall throughout the Kharif season indicates that rainfall does not occur on every day. The number of rain (wet) days for the season was determined from the results of the Markov chain analysis. The interval for which the wet and dry day sequences predicted by the Markov chain most closely fit the actual sequences was selected. For each interval the number of rain days was calculated as follows:  # of rain days = P(X(f) = 1) (# of days in interval)  [Eq. 16]  where P(X(f) = 1) is the probability of occurrence of a wet day within the interval calculated over all available years of data. Daily rainfall depths from the extreme value analysis for the 0.1 mm threshold event model were assumed to have occurred on each rain day. The rainfall depths with return periods of 5 and 10 years were selected from the best-fit probability distribution.  64  Wet year rainfall was calculated using the maximum daily rainfall depth with return periods of 5 and 10 years. Dry year rainfall was calculated from the minimum daily rainfall depth. 'In each case, the total rainfall depth for each month of the monsoon season was calculated as follows:  Monthly rainfall = Z [(rainfall depth) (# of rain days)]  [Eq. 17]  where the monthly rainfall is the sum of total rainfall for each interval within the month; rainfall depth is the maximum or minimum daily rainfall value generated from the extreme value analysis; and the # of rain days is calculated from the probability of rain within a given interval.  4.5  Evapotranspiration calculation method  Based on the results of other studies in semi-arid and arid environments, several E T estimation methods were selected (Table 7). The E T formula for each method is contained in Appendix E. In addition, an adjusted version of the Modified Jensen-Haise method (1.15 adjustment factor) was evaluated.  Table 7  Selected Evapotranspiration Estimation Methods Time period Daily Daily Daily Daily Daily Daily  Combination  Penman (1963) Kimberly-Penman (1972) Kimberly-Penman (1982) F A O - 2 4 Penman (c=1) F A O - 2 4 Corrected Penman Penman-Monteith  Reference crop Grass Alfalfa Alfalfa Grass Grass Alfalfa  Radiation  F A O - 2 4 Radiation Method Modified Jensen-Haise  Grass Alfalfa  5 days 5 days  Temperature  F A O Blaney-Criddle Hargreaves, 1985  Grass Grass  5 days 10 days  Grass Grass  Monthly 5 days  Type of method  Method  Christiansen F A O Pan Minimum recommended time period ( A S C E , 1990)  Pan Evaporation  1  65  4.5.1  Time period  Although the combination methods were designed to estimate E T on a daily basis, the radiation, temperature and pan evaporation methods are limited in their ability to estimate E T over short periods of time. For each of these methods, E T estimates were calculated over the minimum recommended time periods (Table 7).  Moving averages based on 5 and 10 day periods were calculated wherever 5 or 10 days of consecutive climatic values were recorded. Monthly averages were based on all climatic data for each month over the 1970-1993 time period.  4.5.2  10 day moving and fixed averages  In the field, both farmers and researchers find it easier to calculate 10 day fixed, rather than moving average values for E T calculations.  Ten day averages of temperature, humidity, wind speed, sunshine hours, and solar radiation were calculated using each of the two methods. Fixed 10 day averages were calculated on the 10 , 2 0 th  th  and 3 0 of each month. Moving averages were generated over each consecutive 10 day period with th  recorded climatic data. A correlation analysis of the monthly average of each measure using fixed and moving average values was completed on the irrigated months of November to February, inclusive.  4.5.3  Crop coefficients  Grass reference crop coefficients were selected for the typical crops grown in the Chambal Command Area (Appendix L). They were selected over alfalfa reference coefficients owing to the availability of coefficients for the crops grown in the Chambal Command area. A conversion factor of 0.85 for alfalfa to grass reference E T was applied.  66  4.5.3.1 Crop Development Stages Initial, development, mid-season and late season crop development stages, as defined by Doorenbos and Pruitt (1977), were determined. The length of some crop stages were adjusted, based on the actual growing season length reported by Chieng (1993). Stage lengths were also compared against those reported by Subramaniam (1989) for Maharastra, India, wherever possible.  4.5.3.2 Crop Coefficients for each development stage For each crop development stage, an appropriate grass reference crop coefficient ( k c ) was selected. Coefficients for the initial crop stage were based on the curves relating initial k c to the interval between significant rainfall or irrigation and grass reference E T published by Doorenbos and Pruitt (1977). The k factors for fallow land were determined from the same curves.  Reference E T from the selected methods were averaged to give a single E T  g r a s s  for each month.  Significant rainfall was assumed to be 5.0 mmd" for the Kharif season. Interarrival times from the 1  5.0 mm threshold event model with a probability of occurrence of 70% were selected for each month (Table 15). The interval between irrigation water applications in the Rabi season is 20 days (Chieng, 1993).  Crop coefficients for the mid-season and last season (end) stages were taken from published tables (Doorenbos and Pruitt, 1977). Development stage and late season stage coefficients were calculated as follows, based on the procedure for the development of a crop coefficient curve described by Doorenbos and Pruitt (1977):  k o development stage  = k c mid-season - k  k c late season stage  = k mid-season - k c late season (end) c  c  initial  [Eq. 18]  [Eq.19]  67  4.5.4  Seasonal ET requirements for selected crops  For each of the crops for which lysimeter data was available, a seasonal ET value was calculated. Soybean, sorghum and groundnut, grown in the Kharif season represent 74.26% of the sown area . 2  Wheat, mustard and gram, grown in the Rabi season represent 86.72% of the sown area.  The actual sowing date for each crop as reported by Chieng (1993) was used as the start of the initial stage. The length of each development stage was converted into a number of days per month, and the grass reference ET for that month was multiplied by the appropriate coefficient. The seasonal ET value for each crop was then summed over the 4 development stages.  4.5.5  Comparison of estimated seasonal ET with lysimeter data  Seasonal E T measurements were calculated over all years of available data. For some of the C  methods, the necessary information was present only in 1 year. ETi i ter, for crops other than wheat yS me  and sorghum, was based on 2 - 3 years of lysimeter measurements. Comparisons were not necessarily made between the same years.  The variation reported in E T between 2 different periods for wheat and sorghum indicates that 2 - 3 C  years of data may not accurately reflect average E T requirements. Lysimeter measured E T for C  C  sorghum was 717.90 mm for 1982-83, whereas the 1978-1983 average was 548.70 mm. Lysimeter measurements for wheat varied between 414.30 and 527.10 mm for the same two periods (Chieng, 1993).  Estimated seasonal ET for the selected crops were compared with actual seasonal ET|y ter to C  Sime  determine the most appropriate ET estimation method. The results were ranked according to the ratio of estimated E T to ETi eter for each crop, the crops of each season, and all of the crops. C  2  ysim  The sown area excludes fallow land of 44.06% and 4.43% in the Kharif and Rabi seasons respectively.  68  Both a weighted and unweighted ratio was calculated to rank the ET methods over all of the crops within each season. The methods were also ranked using unweighted and weighted ratios of ET  C  totalled over the crops of both seasons. The weighting factor was based on the percentage of crop grown, assuming 100% of the area was sown (Figure 5).  4.5.6  Pan evaporation coefficient  Reference ET was calculated from available data using the most appropriate ET estimation method. A comparison of pan evaporation rates and ET was used to determined a suitable coefficient to r  convert evaporation to ET for each month. r  Coefficients were based on the ratio of pan evaporation to ET adjusted to eliminate the effect of r  extraordinary values.  4.5.7  Crop water requirements for the Daglawada test plot  4.5.7.1 Generalized crop coefficient A set of generalized crop coefficients for each season was determined for the calculation of ET for C  the Daglawada test plot. Based on the generalized cropping pattern of the Chambal Command area (Figure 5), and crop information (Appendix L), an average weighted coefficient and length for each development stage was determined (Table 10). A set of coefficients was also determined for various proportions of dry crop to rice.  A general sowing date was selected for each season, based on the date by which at least 60% of the crops are sown. July 8 and November 1 were selected as the start of the growing season for the th  st  Kharif and Rabi seasons, respectively. The general sowing date for the Rabi season was moved from October 12th, at which point the majority of the crops were sown, to November 1st to eliminate overlap between Kharif and Rabi crops.  69  4.5.7.2 Seasonal E T  C  S o m e farmers in this area are planting rice during the monsoon season (Chieng, personal communication). A s the k c values for rice are much higher than those for other Kharif crops except during the mid-season development stage, this practice can dramatically increase the crop E T requirement. Therefore, a number of values of seasonal E T based on 0 - 1 0 0 % rice were estimated C  for the Daglawada test plot.  4.6  Effective rainfall  Effective rainfall was calculated for normal Kharif season rainfall, and for the 1 in 5 and 1 in 10 wet years. All rainfall during a dry year is assumed to be effective. The U S D A - S C S formula was used in the calculation of effective rainfall (Section 3.4.2.2.2). Normal depth of depletion prior to rainfall was assumed to be 75 mm. Soils were assumed to be welldrained, assisted by sub-surface drainage system. E T was calculated using E T C  p a n  values and the  generalized crop information for the Daglawada test site. A comparison of the U S D A - S C S effective rainfall with the 70% method for India (Section 3.4.2.2.2) was completed to determine if such a method would be suitable for broad planning purposes.  4.7  Water balance  A simple water balance over the monsoon period was completed to determine the drainage coefficient. Rainfall amounts in excess of E T or E T | were assumed to recharge the groundwater. C  soi  The soil profile was assumed to be dry at the start of the Kharif season. A water balance was completed over the interval used in the calculation of the 1 in 5 and 1 in 10 wet and dry years, using effective rainfall. Normal effective rainfall depths were also examined. E T was calculated from E T  p a n  values and the generalized crop information for each interval.  C  70  4.7.1  Leaching requirement  The leaching requirement for average soil salinity conditions was determined for the irrigated season using the conventional method:  LR =  EC  /  W  (5 ( E C ) e  [Eq. 20]  - EC ) W  where LR is the minimum leaching requirement with surface irrigation, E C is the salinity of the W  applied irrigation water in dSm" , and E C is the average soil salinity tolerated by the cop. 1  e  The depth of water necessary to meet both E T c and the leaching requirement on an annual basis was determined using the following equation:  AW =  ( E T - rain)/ (1 - LR)  [Eq. 21]  C  where A W is the depth of applied water (mm/year), E T is the total annual crop water requirement C  (mm/year), rain is the amount of rainfall (mm) and LR is the leaching fraction.  The electrical conductivity of the Irrigation water ( E ) is 0.3 dSm" . Average salinity tolerance was 1  c  based on the most sensitive crops, giving an E C of 2.0 dSm" at a 90% 1  e  yield potential.  71  5.0  Discussion of results  5.1  Rainfall modelling  5.1.1  Characteristics of the monsoon season  The monsoon season begins suddenly in June and tapers off in October. In 55 % of the years of recorded monsoon rainfall, the first rainfall was between the 1st and the 9th day of June. With the exception of 1 year, the start of the monsoon occurred prior to the 15th of June. In many years (36.36%), the first rainfall event was of less than 5 mm, with a subsequent event of 5 mm or more within 1 to 6 days (Appendix F).  The annual cycle, the time between the onset of successive monsoon seasons, ranges from 354 to 383 days In 70% of the recorded years, the length of the annual monsoon cycle is between 360 and 370 days, inclusive (Appendix F).  The end of the model monsoon season was defined as the date on which accumulated monsoon rainfall reached 90% of annual rainfall. In 6 8 . 1 % of the years, the model monsoon season ended on or before the 2 3  rd  of September. By October 2 0 , a further 22.7% of the years had reached 90% of th  the monsoon rainfall (Appendix F).  The length of the model monsoon season, measured as the number of days between the start and end of the model monsoon season, varied from 58 to 169 days. A length of 80 and 100 days, was recorded in 50 % of the years from 1970 - 1993 (Appendix F).  Significant variation was evident in the number of days with more than 0.1 mm of recorded rainfall. Between 24 and 57 days of rainfall were recorded within the model monsoon season. In 5 5 % of the years, less than 40 days of rainfall occurred, with more than 50 rain days recorded in 9% of the years examined between 1970 - 1993(Appendix F).  72  A degree of persistence is evident in the monsoon rainfall. The cumulative departure from the mean rainfall indicates that the monsoon rainfall from year to year is not independent (Appendix F). Trends of greater and less than average rainfall over 5 - 6 years, for the model monsoon season, appear throughout the period of 1970 to 1993. The length of record is insufficient to indicate a longterm pattern. In addition, the lack of rainfall information in 1981 and 1982 makes it difficult to be certain of the length of trend between 1978 and 1986.  5.1.2  Markov chain analysis  5.1.2.1 Transition probability matrix The number of wet and dry days within each month varies over the Kharif season, resulting in significantly different monthly transition probabilities. The probability of a wet-wet sequence (P-n) varies from 0.426 in June to 0.687 in August (Table 8). The transition probabilities calculated over 5 and 10 day periods varied significantly within each month (Table 8). This variation indicates non-stationarity over monthly intervals, making a single  Table 8  Wet and dry day classification and transitional probability, by preceding day, by month Transitional Probability Period  month 10 day 5 day month July 10 day 5 day August month 10 day 5 day September month 10 day 5 day P n = probability of wet P i = probability of dry June  a  b  Interval  0  Pn (Range) 0.426 0.267- 0.515 0.176-0.600 0.663 0.560 - 0.750 0.550 - 0.830 0.687 0.654 - 0.743 0.647 - 0.797 0.571 0.429 - 0.634 0.273 - 0.700 - wet sequence occurrence - wet sequence occurrence a  P  b  (Range) 0.147 0.079 - 0.240 0.043 - 0.241 0.260 0.208 - 0.303 0.178-0.310 0.303 0.256 - 0.356 0.208 - 0.380 0.123 0.063 - 0.254 0.040 - 0.371  73  transition probability matrix for each month unsuitable. The wide range of values in the 5 day interval transition probability matrix indicates non-stationarity over 10 day periods.  5.1.2.2 Stationarity over 5 day intervals The transition probabilities for some successive 5 day intervals, most notably P n over the period from July 25 to August 25, exhibit a near stationary trend (Figure 7). In the month of June, the probabilities vary significantly, becoming more consistent toward the end of the month. The trend is consistent with the onset of the monsoon rains in early June. Similarly, the non-stationary transition probability trend over the month of September is consistent with diminishing monsoon rains. Varying degrees of stationarity is evident in the transition probabilities within 5 day intervals. The trend is similar to that exhibited by successive 5 day periods. However, during the months of June and September probabilities are more consistent, especially with respect to dry-wet and dry-dry sequences. The 5 day transition probability matrix for each year does not exhibit stationarity. The probability values range from 0.0 to 1.0 in each interval throughout the season, regardless of the month (Appendix G ) . This result is consistent with the pattern of drought and flood conditions from year to year experienced in semi-arid and arid monsoonal areas.  5.1.2.3 Actual vs. predicted 3 and 4 day wet-dry sequences  5.1.2.3.1  Results over all years  Use of the monthly transition probability matrix in the calculation of 3 and 4 day wet-dry sequences resulted in poor prediction of actual wet and dry day sequences. The chi-square test of independence of rain on the second preceding day was not significant at the 5 and 10% level. Rain was independent of the second and third preceding days, at 5% significance for only September (Table 9).  74  aauajjnaoo jo A)!i!qeqoj<j  75  A reasonable prediction of actual wet and dry day sequences resulted from the application of a separate transition probability matrix to each 10 day interval. The chi-square test of independence of rain on the second preceding day was significant at the 5 and 10% levels in 75 and 58.3% of the intervals, respectively . At the 5 and 10% significance levels, the probability of rain was independent of the second and third preceding days, in 66.7 and 7 5 % of the intervals.(Table 9). The 5 day interval transition probability matrix provided the best predictions of actual wet and dry day sequences. The percentage of intervals found to be independent of the second preceding day at both the 5 and 10% significance level, was 83.3 and 75 %, respectively. The percentage increased slightly to 87.5 and 79.2% in the test of independence on the second and third preceding days. In all months but September, the 5 day interval transition probability matrix met or exceeded the results of the 10 day interval analysis (Table 9).  Table 9  Independence of rainfall probability on more than 1 preceding day, by month  Interval  Month  Percentage of the interval for which Chi-squares were significant Independent of second and Independent of second third preced ing days precedin g day  1  3  2  (%]  (% P=5% June  0.0 66.7 83.3 0.0 66.7 66.7 0.0 66.7 100.0 0.0 100.0 83.3  month 10 day 5 day month 10 day 5 day  July  4  month 10 day 5 day September month 10 day 5 day 0.0 month Total 75.0 10 day 83.3 5 day Fixed intervals H = P(x |x . ,x,. ) = P(x»|x». ); x with 2 d.f. H = P ( x | x , x . , x . ) = P(x |x -i); x with 6 d.f. % at 5% significance % at 10% significance  August  1  2  2  0  t  t  1  2  1  3  2  0  4  5  2  t  M  t  2  t  3  t  t  P=10% 0.0 66.7 66.7 0.0 0.0 66.7 0.0 66.7 100 0 100.0 66.7 3  0.0 58.3 75.0  P=10%  P=5% 0.0 66.7 83.3 0.0 66.7 83.3  0.0 66.7 83.3  0.0 100.0 100.0 100.0 100.0 83.3  0.0 66.7 83.3 0.0 100.0 83.3  75.0 66.7 87.5  0.0 75.0 79.2  0.0 66.7 66.7  76  5.1.2.3.2  Results of yearly analysis  The 5 day interval transition probability generated from rainfall occurrences recorded in all years provided reasonable predictions of actual wet and dry day sequences in the Kharif season for each year. Dependence on the annual rainfall was not evident. The percentage of intervals independent of the second preceding day ranged from 50.0 to 87.5% at the 10% significance level. The percentage increased slightly to 70.8 to 100.0% at the 10% significance level in the test of independence on the second and third preceding days (Table 10).  Table 10  Independence of rainfall probability on more than 1 preceding day, by year Percentage of the 5 day intervals for which Chi-squares were significant Independent of second and Independent of second third preced ing days precedin g day (%) (% P=10% P=5% P=10% P=S% 95.8 100.0 70.8 87.5 91.7 100.0 75.0 84.5 100.0 100.0 79.2 87.5 87.5 95.8 79.2 83.3 100.0 100.0 83.3 91.7 79.2 91.7 75.0 75.0 83.3 91.7 54.2 62.5 70.8 79.2 58.3 66.7 87.5 91.7 75.0 79.2 87.5 87.5 62.5 75.0 95.8 95.8 87.5 95.8 91.7 95.8 75.0 83.3 91.7 95.8 66.7 83.3 100.0 100.0 75.0 83.3 87.5 87.5 54.2 75.0 79.2 83.3 58.3 70.8 83.3 95.8 70.8 70.8 83.3 87.5 70.8 79.2 87.5 91.7 58.3 75.0 83.3 83.3 66.7 79.2 91.7 91.7 79.2 91.7 70.8 79.2 50.0 54.2  Year  Annual rainfall, sorted (mm)  J  1972 1987 1980 1989 1979 1992 1983 1990 1970 1993 1991 1984 1985 1986 1973 1988 1976 1977 1978 1975 1974 1971  309.10 469.10 561.10 562.10 574.00 634.00 640.50 656.10 681.80 713.82 722.70 724.30 725.40 791.30 804.50 848.80 900.10 986.70 991.60 1011.00 1294.00 1506.80 1  H = P(x |x,. ,x . ) = P ( x , | x . i ) ; x  2  0  2  t  4  t  2  t  with 2 d.f.  Ho = P(x |xt_i,x,.2,Xt. ) = P(x |xt. ); x with 6 d.f. 2  t  3  1  3  % at 5% significance x at 10% significance 2  2  2  1  t  1  4  77  5.1.3  Daily rainfall modelling  5.1.3.1 1 day rainfall depths Over a 24 hour period, rainfall depths in excess of 100 mm are recorded during the months of June through October (Table 2). The maximum 24 hour rainfall depth recorded at the Kota station is 174.00 mm occurring in July, 1970 (Appendix B). In both July and September, 3% of the daily rainfall depths exceeded 100 mm, with 1% of the 1 day rainfall in June in excess of this magnitude (Table 11).  Daily rainfall depths of less than 10 mm are the most common throughout the Kharif season. At the start of the active monsoon period, 86% of the daily rainfall is less than 20 mm, with a further 7% of the rainfall depths between 20 and 50 mm. During July and August, daily rainfall of more than 20 mm becomes more common, with 2 0 % of the depths recorded at 20 to 50 m m . This trend continues into September, with rainfall depths of between 20 and 50 mm occurring over 14% of the month (Table 11 and Appendix H).  5.1.3.2 2 day rainfall depths The distribution of precipitation over 2 day intervals in June, is very similar to the 1 day rainfall depths for that month. The majority of the 2 day rainfall depths (80%) are less than 20 m m , with 9 1 % of the month recording rainfall depths of 40 mm or less (Table 11).  September also shows a similar pattern in its 1 and 2 day rainfall depths. Depths of less than 20 mm account for 66% of the 2 day rainfall totals with 50 mm or less rainfall over 89% of the month (Table 11).  During the months of July and August, the number of 2 day rainfall depths of 20 mm or less falls to 55%. Two day rainfall depths of less than 70 mm and 60 mm account for 90% of July and August,  78  respectively. In each of these two months, 10% or more of the 2 day rainfall depths are greater than 60 mm, with 4 % of the depths exceeding 100 mm (Table 11 and Appendix H).  5.1.3.3 3 day rainfall depths The majority of 3 day rainfall depths in June were less than 30 mm (85%), with only 9% of the depths totalling more than 50 m m . Similarly, 3 day depths in September were predominantly less than 30 mm (75%), with 12% of the total depths in excess of 50 mm (Table 11).  At the height of the monsoon, approximately 24% of the 3 day rainfall depths exceed 50 mm. Rainfall depths in excess of 100 mm over a 3 day interval occur over 8 and 6% of July and August, respectively (Table 11).  5.1.3.4 4 day rainfall depths During the month of June, 70% of the 4 day rainfall depths are less than 20 mm in magnitude. A s with 3 day intervals for this month, 90% of the 4 day rainfall depths are less than 50 mm (Table 11).  The distribution of rainfall over four day intervals in September, also shows a trend similar to that exhibited over 3 day intervals. The majority of the 4 day rainfall depths (75% ) fall below 30 mm, with 26% of the depths recorded between 30 and 70 mm (Table 11).  During the months of July and August, 4 day rainfall depths of less than 20 mm decrease by approximately 50% as compared to June. In July, 90% of the depths are less than 110 mm, with 29% of those exceeding 50 mm. Similarly, 90% of the 4 day depths in August are less than 100 m m , with 3 5 % of those exceeding 50 mm (Table 11, and Appendix H).  79  2  intervals  o I*  o  IO T-  en en en  10  ro CD CO CC .C  a  CO TJ  75  o o o  o o o o  o  d  d d  d  d d d  o o o q d  d d  d  d d d  d  o o o o o  o o o o d d d  d d d  >. co  •a  Tt I  d  d d  o o o o d d d d  CM O E  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  d d d d  d d  CO CD CD  1o  o o o o o o  o o o o o o  o CM T — o o o o d d o d d  o CO CM o o o d d o do d  o CM o o o o d d o d d  o CM T — o o o o d d o d d  o CM CM o  •*— o CM CO o  90-1  o o  CO o 00  o CO o IO i  co o  • o9 Tt o  t o CO o  CO 1 C M o o  o d  d  d d  d d d  d  d d d  d d d d  d d o do d  d  CO  d d  O co  i | 28  d o do d  •a co  o  o  o o o o d d d d  o  o o CO o o  o  Mo o o C d o d d d  o d d d d  co o o CM o d d  — r  c  _C0 ca H  o  c5  CO - o  o o q o d d d d  CM o o d d  C M CM O O d d  o CM q CM c o o d d  o d d  O o Tt Tt C d q d q d q d CM o  co  q q o d d d d  co Tt CM o o o d d d d  M co co C CM d CM d d d  M Tt CO o C d d o do do  Om o C o Tt d d d o d o  o Mo CO c q C q d d o d d  O Tt CM q C d q d q d q d  o Oc o CM c o o C  co o CM CO o  o co CM Tt o o q  CO in D CO q C  o CM CM CM d d o do do  T—  o d o d d d  d o d o d d  q d d  Tt o CO o  Tt  h- CM o CD o  Tt Tt o T— c  d d d  CO CM  d  co CM  T—  d d o d  d  q d d d  o co E  co o m in in CM m d d m d d  CO co Tt co o d d d d  CM CDm CM  o in co  O mC CM oo CO d Tt d dCM dco  —m in co 1 d d CO dco dTt  1 1  d 3 "5 3 T— —)-j <  1 "5.I CO CO CO c:  I  CO CO  .2  #  CO o  J) c c  c: — co o cn _ E  S  CM i_ >  d d d d  co o co  o  o E  p  CO c  TJ  c <"  E « O o C CM co Tt TJ TJ d Tt d dCM dCO  O  "* CO c  1 =i £ Q.1 CDQ. 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CO 3 o r*.  c o  o o o o o o o o  CO CO CO  o o q o o q d d d d  0 o • oil en o CO  CO  o o d o q d d d  o o d d d d  o T— o o q q q d d d d  a. o  u  o d d q d d  o  o o q o o d d d d  T- CM T—  (0  O Tt O O q C  (31 mo m  T— o o o o q q o d d d  Qo  CO N 'C  O CM T — CM O O  T—  o o q q o d d d  1o CO Tt  •o  O 00 co CD C CO C M CO CO Tt Tt m  o  A  I«  CM Tt m CM  CO  o io i Q  Tt r~- O O )Tt CM O CO Tt CM  CD cn m co Tt co CM co  f  co o  CO  80  5.1.4  Rainfall event analysis  5.1.4.1 Randomness of events The number of rainfall events is independent of all other parameters in the model, with the degree of independence varying with the definition of a rain day. Pairwise relationships between current and preceding rainfall event duration, rainfall depth and interarrival times were not evident (Table 12). A weak relationship between total monsoon rainfall depth and the number of rain days exists for rainfall 0.1 mm or more. The number of rainfall events and the length of the monsoon season also exhibits a weak relationship. A significant correlation is apparent between the total number of dry days and the maximum interarrival time (Table 12). Rain days defined by a threshold value of 5.0 mm show a weak relationship with the total monsoon rainfall. The length of the monsoon season and the maximum interarrival time is also characterized by a weak relationship. A significant correlation is evident between the total number of dry days and the maximum interarrival time (Table 12). The results indicate the assumption of randomness with respect to the events of the monsoon season is valid. The correlation between the length of the monsoon season and the number of rain days is consistent with the definition of the monsoon season used in this model. A relationship between the duration of rainfall events and the total rainfall depth of that event is expected (Table 13). As the maximum interarrival time is expected to occur under drought conditions, a relationship between the number of dry days and the maximum interarrival time is expected.  81  Table 12  Correlation of model monsoon season characteristics, by threshold rainfall Number of rain days  Number of rainfall events  Maximum interarrival time  Length of annual cycle  Characteristic >0.1 mm 0.47  >5.0 mm 0.63  >0.1 mm 0.21  >5.0 mm 0.25  £0.1 mm -0.15  >5.0 mm -0.19  >0.1 mm -0.07  Total monsoon rainfall depth (mm) -0.43 0.52 0.65 0.09 0.47 0.37 0.27 Length of the monsoon season (days) ni 0.13 0.03 -0.19 -0.36 -0.10 -0.08 Length of the annual cycle (days) -0.22 0.93 0.89 0.23 0.31 0.33 0.15 Total number of dry days (days) Note: correlation measured by Pearson correlation coefficients ni = not investigated threshold rainfall values of 0.1 and 5.0 mm as defined in the 2 event-based models 1  Table 13  Correlation of event-related characteristics, by threshold rainfall  Characteristic  Rainfall depth of event (mm) >0.1 mm 0.79  >5.0 mm 0.78  Duration of rainfall event (days) >5.0 >0.1 mm mm ni ni  1  Interarrival time (days) >0.1 mm -0.10  >5.0 mm -0.05  Duration of rainfall event (days) ni ni -0.05 -0.10 -0.07 -0.06 Interarrival time (days) -0.07 -0.06 0.03 -0.01 0.03 0.00 Duration of preceding rainfall event (days) ni ni 0.03 0.00 0.09 -0.02 Rainfall depth of preceding event (mm) -0.06 -0.03 ni ni ni Preceding interarrival ni time (days) Note: correlation measured by Pearson correlation coefficients ni = not investigated threshold rainfall values of 0.1 and 5.0 mm as defined in the 2 event-based models 1  >5.0 mm -0.07 -0.42  ni -0.05  1  82 5.1.4.2 Number of rainfall events The distribution of the number of rainfall events per season is similar for both the 0.1 mm and 5 mm threshold models. In each case, between 10 and 16 rainfall events were recorded in approximately 55% of the model monsoon seasons. The distribution is described by a Poisson probability density function, with reasonable accuracy for both models (Appendix I, J). The Poisson density function is given by:  Un) = (e - X  n  )l n!  [Eq. 22]  where X is estimated by the mean number of rainfall events, e is the natural logarithm base and n is the total number of events.  5.1.4.2.1  Distribution of events within the season  Most of the events within the season occur at the height of the monsoon season, during the months of July and August. Approximately 63 - 6 5 % of all events, regardless of duration or threshold rainfall definition, occur during this period. A further 20 - 2 3 % of the events occur during the month of June (Table 14).  5.1.4.3 Duration of rainfall events Rainfall events of 1 day in iength are the most common, in both the 0.1 mm and 5.0 mm rainfall threshold models. This result is consistent with the general character of convective storms. However, longer periods of consecutive rain days occur throughout the season. The maximum rainfall event is 16 days, and 11 days for the 0.1 and 5.0 mm threshold models respectively (Appendix I, J).  The definition of a rain day using a 0.1 mm threshold results in approximately 82% of the events occurring over 4 days or less. The 5.0 mm threshold model results in 95.3% of the events occurring  83  over 4 days or less. The probability of rainfall events of more than 2 days decreases significantly as the duration increases.  The duration of rainfall events was fitted to a geometric probability distribution function (pdf) given by:  fQ) = pqT  1  [Eq. 23]  where j is the duration of the event in days, p is the probability of occurrence, and q = 1-p.  5.1.4.3.1  Event duration distribution  Events of more than 7 days occur only during the months of July and August, in both the 0.1 mm and 5.0 mm threshold models. One day events are the most common throughout the season, especially in June when they comprise 70 and 82% of all events in the 0.1 and 5.0 mm models, respectively. In July and August, 1-3 day events are commonly encountered. In September, 4-6 day events are common in the 0.1 mm threshold model (Table 14).  5.1.4.4 Rainfall depth  5.1.4.4.1  0.1 mm threshold model  5.1.4.4.1.1  1 day events  One day rainfall event depths of 5.0 mm or less, are common. More than 70% of all of the 1 day events in this model, are of less than 15 mm in depth (Appendix I).  5.1.4.4.1.2  2 day events  The most common total depths recorded for a 2 day event range between 0.1-10.0 mm and 20.0 25.0 mm (Appendix I).  84  Table 14  Event duration distribution, by month Event probability, categorized by event duration (days) 7 6 >8 5 4 3 2 1  Month  Total # Of events  1  0.1 mm threshold 0.70 0.41 0.33 0.32  June July August September  0.17 0.21 0.18 0.24  0.06 0.11 0.22 0.08  0.03 0.04 0.07 0.11  0.03 0.07 0.05 0.13  0.00 0.04 0.05 0.11  0.01 0.01 0.03 0.03  0.00 0.10 0.06 0.00  71 97 95 38  5.0 mm threshold 0.00 0.07 0.02 0.82 June 0.01 0.28 0.09 0.53 July 0.08 0.23 0.14 0.52 August 0.05 0.32 0.03 0.54 September total number of events from 1970-1993 recorded in which the event ends 1  60 0.00 0.00 0.00 0.00 102 0.02 0.01 0.02 0.04 96 0.00 0.01 0.00 0.02 37 0.00 0.00 0.00 0.05 for each month; events are reported in the month  Rainfall depths of less than 10.0 mm are recorded on each day of the event in approximately 50% of the events. Rainfall depths are not significantly different between the first and second day of the event (Appendix I).  5.1.4.4.1.3  3 day events  The total rainfall depths recorded over 3 day events exhibit significant variation. Approximately 2 8 % of the events are in the range of 15.0 - 25.0 mm. however a substantial number of events have depths of 45.0 - 50.0 mm and 60.0 - 65.0 mm (Appendix I). The rainfall depth is similar on the first 2 days of the event, tapering off slightly on the third day. Approximately 50% of the events have rainfall depths of less than 10 mm on each of the 3 days. The highest depths are commonly recorded on the second day of the event (Appendix I).  5.1.4.4.1.4  4 day events  Approximately 3 3 % of the 4 day event depths occur within the ranges of 75.0 - 80.0 m m and 120.0 mm or more, using the 0.1 mm threshold. The distribution of rainfall depths varies between 5.0 mm to more than 120.0 mm (Appendix I).  85  The first 2 days of the event commonly receive less than 10.0 mm of rain. The rainfall depth increases over the third and fourth days, with more than 4 5 % of the events recording rainfall depths of greater than 20 m m . Rainfall depths in excess of 50 mm occur in approximately 2 5 % of the events on the last 2 days of the event (Appendix I).  5.1.4.4.2  5.0 mm threshold model  5.1.4.4.2.1  1 day events  Approximately 5 3 % of all 1 day events have rainfall depths of 5.0 - 1 5 . 0 mm. Rainfall depths of 15.0 - 30.0 mm are recorded in a further 26% of these events (Appendix J).  5.1.4.4.2.2  2 day events  Approximately 39% 2 day event depths range between 20.0 - 35.0 mm, with a variable distribution over other depths. Depths of 85.0 mm to more than 120.0 mm are recorded in a significant number of events (Appendix J). The rainfall depth over each of the 2 days is consistent, with depths of less than 20.0 mm commonly recorded (Appendix J).  5.1.4.4.2.3  3 day events  The 5.0 mm threshold model results in 3 day event depths which are more variable than the 0.1 mm model. A high proportion of events occur within various depth ranges from 35.0 - 65.0 mm to more than 120.0 mm (Appendix J) Rainfall depths vary significantly over the 3 days of the event in the 5.0 mm threshold model. Rainfall depths of less than 15.0 mm are recorded on the first day in more than 6 0 % of the events. On the second day of the event, rainfall depths of 20.0 - 40.0 mm are recorded in 30% of the events. The rainfall depth decreases slightly on the third day of the event, with approximately half of the days receiving less than 20.0 mm of rain (Appendix J).  86 5.1.4.4.2.4  4 day events  The most common rainfall depth, occurring in approximately 46% of the 5.0 m m threshold events, is 120.0 mm or more. The remaining events are included in equal proportions in a number of depth ranges (Appendix J). The rainfall distribution over 4 day events in the 5.0 mm model, differs from that of the 0.1 mm model. The first and last days of the event commonly receive less than 15.0 mm of rainfall. During the second day of the event, rainfall depths of more than 30.0 mm are recorded in approximately 50% of the events. The highest daily rainfall depths are recorded on the second day of the event. On the third day, the rainfall depth tapers slightly, with approximately 50% of the events receiving between 10.0 and 25.0 mm of rain on that day (Appendix J).  5.1.4.4.3  Probability distribution function  A geometric probability distribution function (pdf) provides a general fit to the 1 day event depths. It does not however, account for the variable number of events with depths in excess of 40 m m . The variable probability of 2 day event rainfall depths over a large range of values cannot be defined by a distribution function. The 3 and 4 day events are also not adequately described by a pdf. The total rainfall depth is highly variable and near random in nature (Figure 8).  5.1.4.5 Rainfall event depth-duration probability The relationship between rainfall depth and duration requires the consideration of the rainfall event duration probability in the determination of the most probable rainfall depth. The conditional probability of rainfall event depth, indicates rainfall events of 1 day with a rainfall depth of less than 10.0 mm are the most common, using the 0.1 mm threshold. Similar results are obtained in the 5.0 m m threshold model (Appendix J).  87  88  5.1.4.6 Rainfall Distribution Throughout the Kharif season, rainfall events are interspersed with dry intervals, or interarrival time periods. Interarrival times of 1 - 2 days in length are common, although dry intervals of 15 days or more also occur within the model monsoon season (Appendix J). Interarrival times of more than 30 days may occur as the monsoon rains taper in September and October. Generally, interarrival times of this magnitude are reported as a result of the definition applied to the end of the model monsoon season.  The distribution of interarrival times between significant rainfall events does not vary significantly over the model monsoon season. Interarrival times during July are of 1 - 2 days in length more than half of the time. During June, August and September 3 day interarrival times are also common. Throughout the model monsoon season, approximately 7 0 % or more of all interarrival times are of 5 days or less (Table 15).  5.1.4.7 Drought conditions When the year is examined on a continuous basis, rather than by individual months, drought conditions over the 1970 - 1993 period emerge (Figure 9). The maximum sequence of dry days reached in a single year was 283 days which began in September of 1972. This 9 month interval without rain followed a model monsoon season in which only approximately 282 m m of rain was recorded (Appendix F).  5.2  Frequency analysis  5.2.1  Annual and monthly rainfall  The monthly rainfall data is more accurately modelled with the Log-Pearson Type III probability distribution. Although both methods provide similar rainfall values for return periods of less than 10 years, the Log Pearson Type III distribution gives a better estimate of rainfall amounts for higher return periods.  89  Table 15 Interarrival time (days) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 > 15 1  2  3  Interarrival time between significant rainfall events , within selected months 1  June Cum. P. 10 0.26 0.46 8 0.64 7 0.64 0 0.64 0 3 0.72 0.74 1 1 0.77 0.82 2 0.87 2 1 0.90 0.90 0 1 0.92 0.95 1 1.00 2 1.00 0 J  #  July Cum. P. 0.32 32 0.52 21 9 0.61 0.66 5 0.75 9 0.77 2 0.80 3 0.84 4 0.86 2 0 0.86 0.88 2 0.89 1 0.91 2 0.92 1 0 0.92 1.00 8  #  August Cum. 25 17 14 6 8 5 4 1 4 1 0 3 2 0 1 5  P. 0.26 0.44 0.58 0.65 0.73 0.78 0.82 0.83 0.88 0.89 0.89 0.92 0.94 0.94 0.95 1.00  #  Se ptember Cum. P. 0.38 14 0.46 3 0.51 2 0.62 4 0.70 3 0.73 1 0.76 1 0.76 0 0.81 2 0.86 2 0.89 1 0.92 1 0.95 1 0.95 0 0.95 0 1.00 2  37 96 39 101 Total Significant rainfall events are defined as successive days of 5.0 mm or more rainfall Number of interarrival time periods (dry periods between rainfall events) recorded from 1970 1993 for each month Cumulative probability of occurrence of the specified interarrival time length  (sXep) i|)6u3| aouanbas Aep AIQ  91  Table 16 Return period  Normal monthly rainfall and number of rain days Jun.  Total rainfall (mm) 55.04 2  (years)  1  3  4  Jul.  1  #of rain days  Aug.  1  Total #of Total rainfall rain rainfall (mm) days (mm) 13.40 276.14 5.65 225.62 4  4  Sept.  1  #of rain days 15.01 4  Kharif s e a s o n  1  Total #of rainfall rain (mm) days 6.03 88.46 4  2  #of Total rain rainfall days (mm) 645.25 40.09 4  3  87.39  7.66  291.03  15.74  316.02  16.75  138.85  8.13  833.28  48.30  4  111.49  8.90  334.98  17.06  335.78  17.78  171.27  9.53  953.52  53.27  5  130.78  9.77  368.34  17.96  347.96  18.49  194.33  10.57  1041.41  56.79  20.42  254.64  13.63  1292.64  66.36  10  193.51  12.09  470.17  20.22  374.33  15  231.83  13.22  529.41  21.29  384.37  21.41  282.64  15.32  1428.25  71.24  25  281.42  14.45  604.36  22.43  393.40  22.54  311.37  17.38  1590.55  76.80  50  350.44  15.83  707.25  23.71  401.25  23.94  340.64  20.05  1799.58  83.52  Frequency analysis of complete duration series of monthly rainfall and rain days; Monthly rainfall values from Log Pearson Type III distribution Kharif season = sum of Jun.-Sept. rainfall for given return period Monthly rain days (defined as days on which at least 0.1 mm of rain is recorded); values from Log Pearson Type III distribution  Table 17  Normal annual rainfall and number of rain days Annual  Return period (years)  Total rainfall (mm)  1  # of rain days'  1  2  2  733.93  40.50  3  845.25  45.15  4  916.50  48.00  5  969.24  50.03  10  1125.03  55.76  15  1212.93  58.83  25  1321.88  62.49  50  1467.91  67.19  Frequency analysis results of complete duration series of annual rainfall and rain days Annual rainfall; Values from G u m b e l distribution Annual rain days (defined as days on which at least 0.1 m m of rain is recorded); Values from Log Pearson Type III distribution  92  Both the G u m b e l and Log-Pearson Type III probability distributions provide a reasonable fit to the annual data series. However, for return periods of less than 10 years the Gumbel distribution provides a better estimate. Annual rainfall depths for return periods of more than 5 years are underestimated by both methods. A s a result the total Kharif season rainfall calculated from monthly rainfall is higher than the annual rainfall for return periods of more than 5 years (Table 16, and Table 17).  5.2.2  Number of rain days  The Log Pearson Type III distribution provides the most reasonable fit to the number of rain days for both the monthly and annual data series. The number of rain days per month s u m m e d over the Kharif season results in higher values than the annual total number of rain days (Table 16 and Table 17).  5.2.2  Maximum and minimum 1-4 day rainfall depths  Maximum and minimum rainfall depths for each return period were selected from the Gumbel and Log Pearson Type III probability distribution curves, respectively. The fit of the curves was based primarily on 1 to 2 day rainfall depths as the sample data was the most reliable over this period for all three models. Maximum and minimum rainfall depths for various return periods were significantly higher for the daily model than for the event-based models (Table 18 and Appendix K). The high daily rainfall depths result from 6 extraordinary values of more than 110.00 mmd" . Each of these rainfall depths 1  occur within periods of 3 or more successive days of rain. Results for 3 and 4 day rainfall depths for the 5.0 mm model are not reliable, due to a lack of data. In many years, 3 and 4 day rainfall events did not occur.  5.2.2.1 Normal 1-4 day rainfall depths Normal rainfall depths for each return period were selected from the Gumbel probability distribution  93  c c  TT  O)  TT  TT  x—  ^~  cn  E  Al LO CO  ^_  Q Al b E  Tf  >>  to  TJ O 'd  TO  Q  cu Q.  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E  1  LO Al  2  >. re  co' 00 00 cn o  i~-  C  cu  CN  CO CN  |  Al  a  CD TT  o  d  O LO  TJ  CN  CM ItD 00  IS  to*  o  CD  IS  LO  00 CD CM CO  re >  o  CM CD  L O JAl C  3 O  CO  oo  co co*  °. E  to  CM CD X—  CO  b CM  TJ O  oo  00 CO LO  CD  to  T—  CO  CN CN  CD TT  CD  •<r  Tf  CO LO  E  Al  \—  LO CN CO  CN  cn  8  CN  LO  oo  1  Tt- 00  O  00 00  ff  51  oo  d Al  TJ  T—  CO  ;  Al  o  CN  re  CO  LO CO  CD  >.  Q  JQ  CO CM  O LO LO CO  00 r-: o  C  >l  COE "x c o 3 to 0 'C TO * TJ re E a. Al E E o o ">, TO _cu  CM  \—  d  T—  o E E  >. re  E  CN  CO  o LO* O)  TJ  TJ  CM  cn  T  2  LO  00 TT r--: b cri  CO  CO  C  CN  CN  CM CO  cn r-~: b  •o  1  co h-  *~  , >»  cu  cn c\i  CO CN  LO  >< ^—  aj > T»  LO CO  CN  IS  \° LO TT  c  E  1  s  t  TT O  IR  ICM* CM  b  CN  CD  00  Tf  I?  I CM  18  CD  oo  CO LO  O  c  CM  c o to 'C  s  re a  CN  E o o  CD  CO CO  LO CO CN  CD  ICM  o  CN  c "O  n  re — I  3  C  LO CN  to oj  m CU CU a  a.  >  94  curves, respectively. The fit of the curve was based primarily on 1 to 2 day rainfall depths as the sample data was the most reliable over this period for all three models. Normal 1 day rainfall depths for various return periods calculated from the daily model were higher than from the event-based models (Table 19). The rainfall depths in the daily model are lower than the 5.0 mm event model over 2-4 days due to the inclusion of dry days in moving 2-4 day rainfall depths. In contrast, the 5.0 event-based model includes only those days on which rainfall in excess of the threshold value is recorded.  5.2.3  Design storm  Rainfall depth-duration-frequency curves for each of the models exhibit significantly different storm profiles (Appendix K). The rainfall intensity for a return period of 5 years ranges from approximately 40 mm/hr from the daily model, to 10 mm/hr from the 0.1 mm model (Figure 10, Figure 11 .Figure 12). Rainfall intensity of this magnitude would results in significant runoff given the slow to moderately slow permeability, characteristic of the soils in the Chambal command area (Table 5).  5.2.4  Wet and dry year rainfall  5.2.4.1 Probability of occurrence The probability of occurrence of either the 1 in 5 or 1 in 10 year maximum daily rainfall depth (44.23 and 55.07mm, respectively) is less than 6.0%. The conditional probability of a 1 day event with rainfall depth of this magnitude is less than 2.0% (Appendix I). The probability of occurrence of daily rainfall depths of 0.71 mm and 0.35 mm used in the 1 in 5 and 1 in 10 dry year calculations, is based on the probability of rainfall depths of less than 5.0 mm. The probability of occurrence of a 1 day event of this magnitude is 42.6%, with a conditional probability of 19.0% (Appendix I).  o a)  D_  c  a>  (jq/iuiu) A)isu3)ui ||ejiije>j  S2  tn  co <u a>  ro  12  roro a>  <u >>  >. in CM  >. >.  o  •  ® M  CM io  < 1  97  TJ  O <5  a. c  (0 co  fll  % tr  >* CM  >. ID  8>  •  (•JH/uiw) Aijsuajui iiejuieu  CO  s>  <  CO  co  >.  >. io  k0) ro  o  ®  ro a>  CM  98  A total of 44 days of rain for the Kharif season is generated from the probability of a wet day within 5 day intervals. This total is slightly higher than the 1 in 2 normal number of rain days (40.09) for the season (Table 16). The occurrence of 44 rain days during the Kharif season is therefore, very likely.  5.2.4.2 1 in 5 wet and dry year rainfall The daily maximum rainfall depth based on the 0.1 mm threshold event model is 44.23 mm for a 5 year return period (Table 18). The daily minimum rainfall depth from the same model is 0.71 mm for a 10 year return period (Appendix K). The 1 in 5 wet year seasonal rainfall of 1946.12 mm is more than 300% of the 1 in 2 normal seasonal rainfall (645.25 mm) (Figure 13 and Appendix K). It exceeds the highest recorded annual rainfall (1506.80 mm) by approximately 30%. The 1 in 5 dry year Kharif season rainfall of 31.24 represents approximately 5% of the normal rainfall (Figure 13 and Appendix K). It represents approximately 10% of the lowest annual recorded rainfall of 309.10 mm.  5.2.4.3 1 in 10 wet and dry year rainfall The daily maximum rainfall depth based on the 0.1 mm threshold event model is 55.07 mm for a 10 year return period (Table 18). The daily minimum rainfall depth from the same model is 0.35 mm for a 10 year return period (Appendix K). The 1 in 10 wet year seasonal rainfall of 2423.08 mm is approximately 375% of the 1 in 2 normal seasonal rainfall (645.25 mm) (Figure 14 and Appendix K). It exceeds the highest recorded annual rainfall (1506.80 mm) by approximately 60%. The 1 in 10 dry year seasonal rainfall of 15.40 is insignificant compared to normal rainfall (Figure 14 and Appendix K). It represents approximately 5% of the lowest annual recorded rainfall of 309.10 mm.  99  (luui) iiejujeu  (wiu) iiejiuey  101  5.3  Evapotranspiration  5.3.1  Reference ET  The mean alfalfa reference E T (ET | if ) rates exceed mean grass reference E T ( E T a  fa  a  grass  ) rates  throughout the year, by an average of approximately 29%. During April and May, the warmest months of the year, E T | a  falfa  is more than 36% higher than ET  graS  s (Table 20).  E T rates for both alfalfa and grass reference vary significantly between the methods, particularly r  during the months of May - July inclusive. E T rates for May range from 7.02 -18.20 mmd" for grass 1  r  reference and 10.29 - 23.03 mmd" for alfalfa reference (Appendix L). 1  Table 20  Alfalfa vs. grass reference evapotranspiration E T , averaged by reference crop (mmd' ) Mean E T s s all methods Grass Alfalfa % reference reference Difference 3.42 27.89 4.35 3.14 5.15 29.95 4.65 ' 6.64 6.95 28.68 6.34 8.90 10.60 36.69 14.29 9.05 13.20 11.22 37.14 17.85 11.54 31.09 10.33 15.00 9.44 30.46 8.49 12.21 4.83 25.22 6.05 4.52 5.14 29.20 6.60 4.68 6.58 18.69 6.44 7.91 4.33 23.77 4.09 5.37 3.46 25.05 3.25 4.33 r  1  gra  Month  2  1  Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec. % difference = E T allfalfa/ETgrass Adjustment factor for alfalfa to grass of 0.85  1  2  5.3.2  Comparison of 10 day moving and fixed average measurements  Analysis of 10 day moving and fixed average measurements (Appendix L) indicates the two methods produce similar results. Overall differences are within ± 2% for the irrigated months of November through March, although the variation within individual months lies between 0.008% and 17.55%.  102  A fixed average calculation method provides an adequate estimate for preliminary planning purposes.  5.3.3  Actual vs. Estimated Seasonal Crop ET  Many of the methods estimate seasonal E T more accurately for some crops than for others. The C  estimated crop coefficients, necessary due to lack of local information, may account for some of the variation.  5.3.3.1 Kharif season  5 ranked methods estimated E T to within 10% of seasonal ETi i ter  For Kharif crops the top  yS  C  me  measures. Weighted and unweighted ranking results were similar. The Penman-Monteith, original Penman and Kimberly-Penman (1982) and the adjusted Jensen-Haise methods provided the most accurate estimates over weighted Kharif season crops (Table 21).  The top 5 weighted ranked methods were predominantly comprised of combination methods. All but 2 of the top ranked methods were based on alfalfa reference. The pan evaporation methods and the temperature methods significantly underestimated ET for each crop (Appendix L). C  The accuracy of the E T estimates from each method varied with the crop. Estimates of seasonal C  groundnut E T were overestimated by the combination methods by as much as 18%. However, C  these same methods produced estimates of within 7% of ET|y ter for soybean and sorghum Sime  (Appendix L).  5.3.3.2 Rabi Season Seasonal E T was estimated to within 7% of C  ETiimeter by the top 5 weighted ranked results. yS  Weighted and unweighted rankings produced similar results. The most accurate estimates were  103  produced from the F A O radiation, Penman and F A O corrected Penman methods and the adjusted Jensen-Haise method (Table 21).  The top 5 ranked methods included combination, radiation and temperature methods, the majority of which were grass reference. The pan evaporation methods consistently underestimated seasonal ET . C  The seasonal E T was overestimated for both gram and mustard by most of the combination C  methods. The Penman-Monteith method estimate was 39% greater than the ETi eter measure for ysim  gram, and 2 1 % higher for mustard. The seasonal E T estimates for wheat were underestimated by C  all methods except Penman-Monteith.  Table 21  Comparison of top ranked E T estimation methods for each season C  Kharif season E T estimates Top 5 methods Rank He ET| | ter Penman (1963) 1 0.99 Penman-Monteith 1 1.01 Adjusted Jensen-Haise 0.99 1 Kimberly-Penman (1982) 2 0.97 Kimberly-Penman (1972) 3 1.04 F A O Corrected Penman 4 1.06 average ratio weighted over all selected crops Modified Jensen-Haise * 1.15 C  vs  2  5.3.4  me  Rabi Season E T estimates Top 5 Methods Rank ETc ET| i ter 1.02 F A O Radiation 1 1.03 F A O Corrected Penman 2 3 1.05 Penman (1963) 0.94 F A O Blaney-Criddle 4 Adjusted Jensen-Haise 4 0.94 5 1.07 F A O Penman (c=1) for the season C  VS  me  2  ET estimate summary over both seasons  Alfalfa reference E T methods performed well in both seasons. Although only 4 alfalfa reference E T methods were included in the analysis, they were within the top 5 methods in the Kharif and Rabi seasons.  The Kimberly-Penman (1972), Kimberly-Penman (1982) and F A O Radiation methods were ranked among the top 5 methods over both seasons. However none of these methods consistently ranked in the top 5 for both the Rabi and Kharif season crops.  104  The Penman ET estimates were within 2% of ETi eter in the weighted average over all crops C  ysim  (Table 22). The estimates were within 1% and 5% of ETi ,eter for Kharif and Rabi season crops, ysirr  respectively (Table 21).  The FAO Corrected Penman estimates were within 5% of ETi eter in the weighted average over all ysim  crops (Table 22). The estimates were within 6% and 3% of ETi eter for Kharif and Rabi season ysim  crops, respectively (Table 21).  The adjusted Jensen-Haise ET estimates were within 3% of ETi imeter in the weighted average over C  yS  all crops (Table 22). The estimates were within 1% and 6% of ETi ter for Kharif and Rabi season ysirne  crops, respectively (Table 21).  5.3.5  Selection of most appropriate method of estimating ET  The selection of an ET method for the Chambal Command area requires consideration of both the accuracy of the method and the amount of climatic data required. Although both the Penman and FAO Corrected Penman methods performed well over both season, these combination methods require a number of climatic parameters.  Of the minimal data methods, the FAO Radiation and FAO Blaney-Criddle estimates are inconsistent over both seasons. The modified Jensen-Haise estimates of ET adjusted upward by 15%, C  performed consistently over both seasons.  The Penman (1963) and adjusted Jensen-Haise methods are the most suitable methods of estimating ET for this region. The Penman (1963) method is the preferred choice if the required data is available. The modified Jensen-Haise method adjusted upward by 15% provides a reasonable estimate of ETi imeter for both Kharif and Rabi season crops. It is the most suitable method for this yS  region when only minimal climatic data is available as this method requires only temperature data.  105  Table 22  Top ranked E T estimation methods, both seasons C  Top 5 Methods  Rank  Penman (1963) 1 Adjusted Jensen-Haise 2 F A O corrected Penman 3 Kimberly-Penman (1972) 4 F A O Radiation 4 Kimberly-Penman (1982) 5 average ratio weighted over all selected crops modified Jensen-Haise * 1.15 2  1 2  5.3.5  1.02 0.97 1.05 1.07 0.93 0.92  Crop water requirements for the Daglawada Test Plot  E T for the sown area of the test plot is 5 3 % higher for the Kharif season crops than for the Rabi C  season crops (Table 24). Seasonal E T was calculated from the general crop mix of 87% mixed dry 0  crop and 13% rice (Figure 5, using the general crop coefficients (Table 23). With different proportions of rice to mixed dry crop the seasonal E T changes significantly. The seasonal E T C  C  increases from 600.60 mm to 892.86 mm as the proportion of rice increases from 0 to 100% (Table 25).  Seasonal E T weighted by the proportion of mixed crops to fallow land (general cropping pattern) is C  29% higher during the Kharif season than the Rabi season (Table 24).  Rabi season E T is reasonably estimated by the crop water requirements as only approximately 4 % C  of the land is left fallow. However, E T for the Kharif season is 21 % higher than the weighted C  seasonal E T including evaporation from fallow land. C  106  CO  00  CO  CJ) CJ) CJ)  CD CO co  c co CO T J  CO T J CO CO  O) CO  CO  o o  125 c  CO  o  CO  co to co CO  ro  E a.  +± to,  o  o o  C CO CO T J  CO  >  CO  Id CO  TJ  _>>  o O  co  3  —}  00 CO oo 00  m O)  ro Q  TJ  O) CD CD  c CO CO  c co co  CO T J  o m CD  2 •  c o  3  OtS  o> ^ ~ T  ^  o c Q. O TJ CO N  1  E CO  S  X  ^»  I  Q.I a o o O °  a  CO  c  CO  (5  o  X3.  co  CO CO CO  to  CO  0 0  E  > t CO  3  >  w  "Q. O  a g o  ;  o " O  CO CO CO M-  C  CO CO CD CO  -c . _ irj ec -O 9i _c co CO  S * a: °> cfc 5- vo cz > ii O  CO CM  °  03 CO  **- co cc X TJ TJ  E  CO O )  rz cz  2 o o  o w <o  107  Table 24  Crop water requirements for the Daglawada test site Mean ET grass  Month  1  c  1  (mmd" )  1 1  Kharif season Jul. Aug. Sept. Oct.  ET  Esoil  C  ET + ET oii  ET jce  C  (100% fallow)  3  (100% mixed crops)  r  100% rice  S  ET jce •*" E T i | r  (weighted)  SO  5  (weighted)  4  2  117.29 151.52 191.26 152.54  115.63 86.31 87.04 35.57  116.35 122.79 145.34 94.46  236.08 210.33 202.85 211.69  183.01 155.69 151.82 134.09  612.61  324.55  478.93  860.95  624.61  59.49 90.31 126.31 116.12 36.05  28.97 27.67 27.08 30.32 33.94  58.14 87.53 121.91 112.32 34.46  147.98 428.28 Total Note: all ET values in mm unless otherwise indicated  414.37  8.28 6.18 6.44 6.75  0  Total' Rabiseason Nov. Dec. Jan. Feb. Mar.  4.94 3.75 3.67 4.90 6.44  B  ETg 2  3 4  5  6  7 8  rass  = ETJH*  assumes 0% fallow; generalized crop kc and growing stage lengths for 87% dry crop and 13% rice k factor for each month contained in Appendix L weighted ET for mixed crops and fallow (Figure 5) weighted ET for 100% rice on sown portion, and fallow land (Figure 5) portion of October for crops is 28 days; 31 days are used for fallow ET for November of 31.91 m m was excluded to prevent overlap with Rabi season portion of March for crops is 3 days; 31 days are used for fallow  Table 25  Monthly and seasonal E T for various crop mix proportions C  E T by month (mm) Crop mix Oct. Sept. Rice Jul. Aug. Dry crop (%) (%) 139.17 191.26 117.29 152.88 100.0 0.0 148.83 158.13 193.19 10.0 127.73 90.0 157.40 195.13 131.21 158.81 87.0 13.0 163.41 193.19 138.66 164.80 80.0 20.0 195.13 187.05 149.35 168.32 70.0 30.0 190.76 173.70 195.13 40.0 160.04 60.0 195.15 197.06 50.0 171.14 180.98 50.0 198.99 198.32 181.82 186.48 40.0 60.0 200.48 191.86 198.99 70.0 192.51 30.0 206.29 197.23 200.92 80.0 204.77 20.0 208.79 200.92 216.03 204.89 10.0 90.0 211.69 202.85 100.0 236.08 210.33 0.0 Note: E T calculated from adjusted Jensen-Haise method mixture of dry crops as indicated in Figure 5 C  Nov.  Seasonal E T (mm)  C  1  C  1  4.15 8.50 12.90 13.19 31.48 36.77 31.91  600.60 627.88 642.55 660.07 699.84 723.77 752.82 778.51 797.03 840.68 867.39 892.86  108 5.3.6  Coefficient to convert Class A Pan Evaporation measurements to ET  The coefficient relating pan evaporation rates and E T calculated from the adjusted Jensen-Haise r  method was difficult to define. Very little data was available for some months, especially July, August and October. Although evaporation were averaged over 5 day periods in order to correspond with the adjusted Jensen-Haise method ( E T * ) , significant variation in evaporation rates was evident JH  (Table 26)..  Manual adjustment of the ratio of daily pan evaporation rates to E T resulted in some improvement r  of the coefficient. The selected monthly coefficients produce reasonable estimates of E T over the r  normal range of evaporation rates for each month. E T is over- or underestimated for extraordinary r  values of evaporation.  Table 26 Month  Comparison of ET pan evaporation and adjusted Jensen-Haise Coeff.  1  #of days  Pan evaporation 2  Mean  Mean  ETJH*  ET  4  5  pan (mmd ) mean" r (mmd ) 3.67 3.66 3.40 0.32 1.08 82 Jan. 4.97 4.91 4.78 1.10 1.02 81 Feb. 6.80 6.44 3.16 0.89 93 7.30 Mar. 9.10 9.11 11.58 3.17 0.79 85 Apr. 10.53 10.28 14.10 6.61 0.73 83 May 10.34 10.01 13.78 6.98 0.75 64 Jun. 9.17 8.29 11.25 0.95 30 9.61 Jul. 7.63 6.18 5.87 4.07 1.30 12 Aug. 6.50 6.33 50 4.64 0.47 Sept. 1.40 6.40 6.79 0.53 23 4.78 Oct. 1.34 4.77 4.95 0.22 47 3.97 Nov. 1.20 3.71 3.75 0.25 62 3.75 Dec. 1.16 coefficient to convert pan evaporation to E T number of days in the month with both pan evaporation and E T * values pan evaporation values averaged over 5 day periods adjusted Jensen-Haise E T , calculated over 5 day periods ETpan = pan evaporation * coefficient 1  2  c  1  1  2  J H  3  4  ETpan " E T J H * 7  HO: m - u.2 = 0; m = mean ETJH*, H2 = mean E T  p a n  Mean difference (mmd' ) 0.02 -0.62 0.36 -0.01 0.25 0.21 0.88 1.45 0.17 -0.06 -0.04 -0.38 6  1  Paired t test (p values) 0.79 0.50 0.02 0.93 0.16 0.22 0.14 0.12 0.21 0.62 0.51 0.63 7  109  The mean values for E T estimated from pan evaporation rates is significantly different from ETJH* r  for the months of July and August (Table 26). Without additional data, the coefficients for these months cannot be improved. However, the coefficients are suitable for planning and modelling purposes.  5.4  Effective rainfall  5.4.1  Comparison of USDA and 70% effective rainfall  The effective rainfall resulting from the U S D A method for the 1 in 5 and 1 in 10 wet years, is approximately 55 - 57% of the total rainfall (Figure 15). The 70% effective rainfall method represents a 13 - 1 5 % increase over the U S D A estimated rainfall (Appendix M). U S D A estimates of effective rainfall for normal Kharif season rainfall with return periods of 5 and 10 years, is approximately 60 - 66% of the total rainfall (Figure 15). The U S D A method is more suitable to this region than the 70% method commonly applied. Daily rainfall depths are commonly less than 5.0 mm, most of which would be effective. The 70% method underestimates the effective portion of these rainfall depths, while overestimating the effective portion of higher rainfall depths (Appendix M).  5.5  Water balance  The water balance was calculated for 5 day fixed intervals from evapotranspiration and total and effective rainfall for the Kharif season. The adjusted Jensen-Haise method and the general crop coefficients (general cropping pattern) were used to determine E T for each 5 day interval. Effective C  rainfall was calculated from total rainfall depth for each interval using the U S D A method. The use of effective rather than total rainfall significantly reduces the amount of rainfall in excess of evapotranspiration requirements. A s expected, groundwater recharge is highest during the months  110  m  CO  •5  >.  we ive  we am  >.  to c  I  I  1  !  0  ,cu  "5  CO 01  CS cu  >- cCO  >. 1 •  0 c  &  i_  J5  0  ive  03 <U c CO  ain  1  CO CD  "S  .2  2= cu  1  CO TJ O  cu Q.  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In September, the effective rainfall is less than E T  C  for most of the month. The water balance calculated from effective wet year rainfall and E T does not significantly change C  between the 1 in 5 and 1 in 10 wet years. However, groundwater recharge for a 1 in 10 normal year is approximately 2 0 % of the 1 in 5 wet year rainfall (Table 27).  5.5.1  Drainage requirement  O v e r the Kharif season, excess effective rainfall of 420.91 and 654.66 m m is estimated for the 1 in 5 and 1 in 10 wet years, respectively (Table 27). For the 178 ha Daglawada test plot, a total of 749.2 and 1165.3 (xlO ) m of excess water must be drained, for return periods of 5 and 10 years, 3  3  respectively. The drainage requirement for a 1 in 10 normal year rainfall is 82.98 m m , or 147.7 (xlO ) m (Table 3  3  27). The 1 in 5 normal year rainfall results in a groundwater deficit over the Kharif season. A drainage coefficient of 10.69 mmd" based on the 0.1 mm threshold event model would adequately 1  remove excess water over 5 day intervals for each of the rainfall conditions (1 in 5 and 1 in 10 normal and wet years).  5.5.2  Leaching requirement  The leaching requirement is 0.0309, expressed as a fraction. To meet the leaching requirement within the main monsoon period (July to September), a value of 0.49 mmd" , or 164.45 mm of 1  water is required, based on E T and rainfall for the Rabi and Kharif seasons. In each of the 1 in 5 C  and 1 in 10 wet years, the leaching requirement can be met during the monsoon season.  113  6.0  S u m m a r y of M a i n R e s u l t s  Markov chain analysis The actual wet and dry day sequences were accurately predicted by the Markov chain analysis, using a 5 day transition probability matrix. Transition probabilities over 5 day fixed intervals demonstrate a reasonable stationarity, although stationarity between years is not evident. The results from the 10 day transition probability matrix were reasonable for some months of the Kharif season. Stationarity over 10 day fixed intervals is evident only over portions of July and August. A monthly or seasonal transition probability matrix is not suitable to this region. Daily and event-based rainfall models Event-based modelling is well suited to semi-arid and arid regions, where storms often occur in clusters. The event-based model provides information regarding rainfall pattern and distribution that is not evident from the daily rainfall model. In addition, the model is not limited by daily rainfall records. The random nature of the rainfall pattern and distribution within the monsoon season was confirmed through correlation analysis. Dependence between rainfall depth and duration and between maximum interarrival times and total dry days was evident. Such dependence is expected and not inconsistent with an assumption of randomness with respect to rainfall events. The event-based model provides information regarding storm behaviour over 2 or more successive days. Although the daily model gives total rainfall over 2-4 day periods, information regarding rainfall during that period is not available. Interarrival times give an indication of the amount of time available for drainage of excess water from the soil profile. The interarrival times between significant rainfall events provides valuable information for irrigation planning. In addition, maximum dry day sequences may be a useful measurement of drought conditions.  114  Design storm The depth-duration-frequency curves for the daily and event-based rainfall models produced significantly different results. The hourly rainfall intensity values ranged from 10.0 - 40.0 mm/hr from the 0.1 threshold event and the daily model, respectively. Wet and Dry year models The probability of rain over 5 day fixed intervals and the maximum and minimum 1 day rainfall from the 0.1 threshold event model were used to construct wet and dry year models. The probability of occurrence of the annual rainfall modelled in these scenarios is very small. The annual wet and dry year rainfall with a return period of 5 years is 1946.12 and 31.24 mm, respectively. The wet year rainfall is approximately 30% greater than the highest annual rainfall recorded from 1970-1993. The dry year rainfall is approximately 10% of the lowest annual rainfall for the same period. Evapotranspiration The estimation of E T was very successful, despite limited available data. The top 5 ranked C  methods over both seasons, Penman (1963), F A O Corrected Penman, adjusted Jensen-Haise, F A O Radiation and Kimberly Penman (1972 and 1982), were within 8% of seasonal  ETi imeter yS  • The best  estimation methods ftir each season were very different with only 3 methods, Penman (1963), F A O Corrected P e n m a n and adjusted Jensen-Haise ranking in the top 5 of each season. In addition, the results for many of the methods were inconsistent within a season. The Penman (1963) method results in the most accurate estimation of E T and is the appropriate choice when adequate data is available. The Modified Jensen-Haise method, provides reasonable estimates of E T , when adjusted upward by 15%. This method is the most appropriate choice when only minimal climatic data is available. Crop water requirements are accurately estimated from the general crop coefficients for the Daglawada test plot. E T values increase significantly as the proportion of rice to dry mixed crops C  increases.  115  The monthly coefficient relating pan evaporation to E T produces reasonable results. The lack of data, and extraordinary values resulted in poor correlation between pan evaporation and JensenHaise calculated E T rates in some months. Effective rainfall The rainfall intensity determined from the design storm analysis indicates much of the rainfall is lost to surface runoff. The effective wet year rainfall as calculated from the U S D A - S C S method, is approximately 55 - 57% of the actual rainfall. The effective normal year rainfall is approximately 60 - 66% of actual rainfall, using the same method. The 70% method commonly used in India overestimates effective rainfall, and is not well-suited to this region. Water balance The water balance calculated from effective rainfall indicates that groundwater recharge is highest at the height of the monsoon season. Excess rainfall of 82.98 mm is produced during the Kharif season of a 1 in 10 normal year, which is approximately 2 0 % of the excess rainfall produced during a 1 in 5 wet year. Drainage coefficient The drainage coefficient for the Daglawada test plot is 10.69 mmd" based on the 1 in 5 normal daily 1  rainfall from the 0.1 mm threshold event model. The coefficient increases to 16.33 mmd" for a 10 1  year return period. Leaching requirement The leaching requirement, based on the average E C (2.0 dSm" ) of the most sensitive crops, is 1  e  0.0309. To meet the leaching requirement, 164.45 mm of leaching water is required.  116  7.0  Conclusion  Rainfall modelling in semi-arid and arid areas is necessary as the average values are not representative of actual conditions.  The design of a sub-surface drainage system requires accurate information regarding rainfall over 1 or more days. Traditionally, daily rainfall modelling has been used. However, such models do not adequately characterize the monsoon season rainfall. They do not provide information as to the pattern and distribution of rainfall over the season; Nor do they provide details concerning the distribution of rainfall over 2 or more days.  Event-based modelling is a flexible alternative to daily modelling. Events are defined as successive days of rainfall over a specified threshold value, with dry days or interarrival times between them. Although the event-based model described by Bogardi et al (1988) cannot be rigidly applied to this region, an adaptation of the model makes it a valuable tool in sub-surface drainage design and irrigation planning.  Event-based modelling helps to overcome the difficulty in characterizing storms from daily rainfall measurements. A rain storm may be a few hours in length, but a single daily reading means the storm is assumed to have occurred over 24 hours. The problem is exaggerated when the storm straddles the daily recording time. In this case, the storm is actually recorded on each of 2 days, and is then assumed to have occurred over 48 hours.  It is probable that a portion of rainfall depths of 5.0 mmd" or less, commonly recorded, are due to 1  the problem of a single daily measure. Rainfall depths of this magnitude may be part of a rain storm occurring before or after the daily recording time.  Event-based modelling characterizes the event, rather than individual storms. It is well suited to subsurface drainage design where the rainfall over 1-4 days is more important than the rainfall of a single storm. A waterlogged root zone resulting from a single storm will drain before the crops are affected. However, several days of storms of significant rainfall depth will result in a failure of the sub-surface drainage system, and damage to the crops.  117  Significant rainfall events are separated by dry day intervals of 5 or less days 70% of the time. Most of the dry-day intervals are of 1 - 2 days in length. Such dry intervals allow for system recovery after rain storms. The use of a daily model measuring rainfall depths over 1-4 day periods is difficult to defend. A 4 day period does not represent a 4 day rainfall event. One or more of the days within the period may not have recorded rainfall. This is a highly probable occurrence given that approximately 4 5 % of events (0.1 mm threshold) are 1 day in duration, and dry intervals of 1 - 2 days are common. Additionally, events of 3 days or less account for almost 80% of all events. The modelling of design storms is also better achieved through event-based models. Daily rainfall modelling results in an poor estimates of rainfall intensity, depth and duration. The measured period may lie in the middle of a storm of significant length, when rainfall depths are at their highest. The hourly rainfall intensity determined from the daily rainfall model is 4 times higher than the results of the event-based model (0.1 mm threshold). The overestimation of maximum rainfall depths results in the overdesign of sub-surface drainage systems. The daily maximum rainfall depth used to construct the 1 in 5 wet year model is approximately 34% of the 1 day maximum calculated from the daily model. Effective, rather than actual rainfall is an important consideration in the determination of a drainage coefficient. Much of the rainfall occurring during storms of significant magnitude is lost to surface runoff. The use of actual rainfall would result in an overestimation of the drainage coefficient by as much as 47%. The drainage coefficient was determined from a water balance using effective rainfall and crop water requirements. The crop water requirements were estimated from a set of general crop coefficients and a coefficient to convert pan evaporation rates to evapotranspiration. A s pan evaporation rates are commonly measured in the Chambal Command area, while other climatic data is not, evapotranspiration from pan evaporation provides the most information. A set of general crop  118  coefficients allows for consistent modelling over any interval length, based on the general cropping pattern. The resulting drainage coefficients, for 5 and 10 year return periods did not differ significantly. Since the probability of occurrence of the 1 in 5 and 1 in 10 wet year rainfall is extremely low, basing the sub-surface drainage design on this scenario is not necessary. The most appropriate and costeffective drainage coefficient of 10.69 mmd" , based on the 1 in 10 effective normal rainfall. A s 1 1  day rainfall events followed by 1-2 dry days are common, this drainage coefficient is adequate to meet the 1 in 5 maximum daily rainfall of 44.23 mm. The leaching requirement of 0.0309 can be easily met with the Kharif season rainfall occurring in wet years with return periods of 5 and 10 years. However, the 164.45 mm of necessary excess water is not available in normal rainfall years with return periods of 2, 5 and 10 years, considered here to approximate average conditions. The persistence evident in the Kharif season rainfall from 1970-1993, indicates that over 5 year periods drier than average conditions exist. During such periods, soil salinity would increase to levels which would adversely affect crops. The dry year models based on minimum daily rainfall depths are not adequate to describe drought conditions nor the recurrence interval of same. The failure of the Kharif season rainfall to meet leaching requirements would occur in years in which seasonal effective rainfall is less than approximately 700 mm. Of the 22 years with recorded Kharif season rainfall, 4 1 % are below 700 mm in total rainfall. Consideration of effective rainfall only would result in a higher failure rate.  119  8.0 •  Recommendations Comparison of the event-based model results on data from other stations in the Chambal Command area. A model that accurately represents the region rather than a single station is highly desirable.  •  A study of rainfall depths of 10.0 mm or less to determine if such events are part of larger storms. A comparison of daily rainfall depths of 10.0 mm or less with hourly data would aid in the determination of an appropriate threshold value for event-based modelling.  •  Comparison of the rainfall intensity values with hourly data to determine if the event-based design storm based on the 0.1 mm threshold value is accurate.  •  Comparison of estimates of E T from pan evaporation using the monthly coefficient with actual E T for a variety of crops grown in the Chambal command area.  •  Determination of effective rainfall using soil water balance to determine if effective rainfall calculated by the U S D A - S C S method is appropriate to this region of India.  •  Analysis of drought conditions based on the maximum dry-day intervals to determine appropriate dry year rainfall for various return periods.  120 LITERATURE CITED Al-Sha'lan, S A . and A . M . Salih. 1987. Evapotranspiration estimates in extremely arid areas. J . Irrig. Drain. Eng. 113(4): 565-574. Allen, R . G . 1986. A Penman for all seasons. J . Irrig. Drain. Eng. 112(4): 348-368. Allen, R . G . and W . O . Pruitt. 1986. Rational use of the F A O Blaney-Criddle formula. J . Irrig. Drain. Eng. 112(2): 139-155. Allen, R . G . and W . O . Pruitt. 1991 F A O - 2 4 reference evapotranspiration factors. J . Irrig. Drain. E n g . 117(5): 758-773. Allen, R . G . et al. 1989. Operational estimates of evapotranspiration. Agron. J . 81: 650-662. A S C E (Am. S o c . of Civil Engineers). 1990. Evapotranspiration and Irrigation Water Requirements. No. 70. M . E . Jensen, R.D. Burman and R . G . Allen (eds.). Ayers, R . S . and Westcot, D.W. 1985. Water Quality for Agriculture. F A O . Irrigation and Drainage Paper 29, 1976, revised 1985. F A O , R o m e . Benson, M.A. 1968. Uniform flood frequency estimating methods for federal agencies. Water Resour. R e s . 4(5): 891-908. Bhatnagar, D.K. 1990. Saline and Alkaline Soils of India. Directorate of Extension, Ministry of Agriculture, Government of India, cited in S T . Chieng, Analysis of subsurface drainage design criteria, Chambal C o m m a n d , Rajasthan, India, Unpublished, 1993. Bogardi, J . J . , L. Duckstein, O . H . R u m a m b a . 1988. Practical generation of synthetic rainfall event time series in a semi-arid climatic zone. J . Hydrol. 103(1988): 357-373. Bouwer, H. 1969. Salt balance, irrigation efficiency, and drainage design. A S C E , Proc. 95(IR1):153-170. Brunt, D. 1932. Notes on radiation in the atmosphere. Quart. J . Roy. Meteor. S o c . 58:389-418. Budyko, M.I. 1956. The heat balance of the earth's surface (translated by N A . Stepanova, 1958). U.S. Dep. C o m . Weather Bur. PB131692. Burman, R.D., J.L. Wright and M.E. Jensen. 1975. Changes in climate and estimated evaporation across a large irrigated area in'ldaho. Trans, of the A S A E 18(6): 1089-1091, 1093. Burman, R.D. et al. 1980. Design and Operation of Farm Irrigation Systems. 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R e s . 18(4): 859-864.  APPENDIX A Frequently used abbreviations and symbols  128  Appendix A  Frequently used abbreviations and symbols Abbreviation  Definition  Cum.  cumulative  d.f.  degrees of freedom  evap  Class A pan evaporation  ET  evapotranspiration  ETaifaifa  alfalfa reference evapotranspiration  (mmd )  ET  crop evapotranspiration  (mmd )  ETJH  reference evapotranspiration, Jensen-Haise method  (mmd"  ETJH*  reference evapotranspiration, adjusted Jensen-Haise (1.15 E T )  (mmd"  ETiysimeter  lysimeter measured crop evapotranspiration  (mmd"  ETpan  evapotranspiration calculated from pan evaporation measurements  (mmd"')  ET  reference crop evapotranspiration  (mmd"  ETsoii  evaporation from fallow land  (mmd  hmax  maximum relative humidity in percent  hmean  mean relative humidity in percent  hmin  minimum relative humidity in percent  k  crop coefficient  C  (mmd ) 1  1  1  JH  r  c  P.  probability  pdf  probability distribution function  R  e  effective rainfall  (mm)  R  t  total rainfall  (mm)  sunhr  sunshine hours  (hrs.)  Tmax  maximum daily air temperature  (°C)  Tmean  mean daily air temperature  (°C)  Tmin  minimum daily air temperature  (°C)  129  wind  wind speed at 2 meters over 24 hrs G l o s s a r y of Hindi W o r d s  Kharif  Monsoon season, June -October  Rabi  Irrigated season, October - March  Zaid  Dry season, March - mid-June  (ms ) 1  130  APPENDIX B SUMMARY OF CLIMATIC DATA, KOTA STATION, 1970-1993  131  Appendix B  Summary of climatic data, Kota station, 1970 -1993  Table B-1  Temperature summary  Month Jan.  Year 1971 1972  9.50  0.40 0.00  Maximum  Minimum  Std. dev. 2.42  22.62  25.80  15.50  2.91  24.36  28.80  21.50  1.64  29.50  19.00  2.63  1.99  4.96  14.00  -0.50  3.93  1974  5.22  12.40  1.00  3.06  24.03  32.00  18.50  2.70  21.96  26.90  19.00  2.07  5.26  10.50  1.70  2.57  1976  8.37  13.30  4.00  2.56  24.65  27.00  19.50  2.22  1977  6.78  14.40  0.00  3.98  23.90  32.50  17.00  3.70  1978  6.61  12.80  2.50  2.77  23.64  28.20  20.30  1.95  1979  8.99  14.20  4.20  3.06  24.09  29.50  18.60  2.78  1992  7.10  15.00  3.00  3.70  23.26  27.00  19.00  2.34  1993  8.05  12.00  5.00  2.15  23.55  29.00  18.00  2.77  1971  7.49  13.00  1.00  3.38  27.79  33.30  20.70  3.34  1972  6.19  14.40  0.90  3.85  24.16  32.30  17.00  3.72  1973  8.31  15.60  2.40  3.45  28.12  36.50  21.50  3.96  1974  6.69  12.30  0.50  3.60  25.31  32.60  18.00  4.12  1975  7.45  14.50  1.10  3.45  24.85  31.00  20.30  2.85  1976  10.09  15.60  5.70  2.56  26.52  32.60  19.00  3.34  1977  9.31  15.90  4.00  3.46  27.40  38.30  22.00  3.45  3.99  23.69  32.00  13.70  4.23  1.00  3.36  25.04  31.00  20.50  2.96  23.97  33.00  20.00  2.97  1979  9.21 8.57  16.50 14.50  2.40  8.43  14.00  5.00  2.25  1993  10.57  18.00  4.00  3.49  27.54  35.00  22.00  3.82  1971  12.23  19.50  5.40  4.58  33.18  40.30  24.40  5.01  20.40  4.20  4.31  33.77  39.50  25.50  4.06  4.44  32.91  40.30  25.00  4.11  1992  1972  Apr.  4.89  9.20  Mean  1973  1978  Mar.  3.91  Maximum daily temperature (°C)  23.65  1975  Feb.  Minimum daily temperature (°C) Std. dev. Minimum Maximum Mean  13.18  1973  14.01  25.70  6.50  1974  15.75  24.00  10.20  3.73  34.50  39.00  25.20  3.35  1975  12.18  17.50  6.50  3.23  31.68  36.10  26.20  2.79  1976  15.11  22.20  10.70  2.98  32.19  37.00  27.00  2.43  1977  15.08  20.80  9.50  3.42  34.68  40.50  28.60  3.52  1978  13.38  18.70  8.90  2.69  31.02  35.40  25.30  2.58  1979  13.82  23.00  5.20  4.15  31.01  36.70  21.00  3.88  1992  16.26  25.00  11.00  3.65  32.28  37.00  28.00  2.49  1993  13.27  26.00  9.00  3.62  29.87  35.00  23.00  3.11  1970  21.87  41.80  12.20  5.06  38.80  45.60  1.80  7.61  1971  20.83  26.00  16.50  2.29  40.23  43.50  34.00  2.58  1972  18.42  25.00  13.80  3.07  37.23  39.80  31.60  1.73  1973  23.30  30.00  13.50  2.99  40.67  44.40  36.00  2.63  1975  19.05  26.50  12.70  3.50  38.40  42.00  32.50  2.25  1976  21.04  25.50  14.60  3.35  37.37  41.10  31.30  2.89  1977  22.24  28.30  13.30  3.29  37.45  40.60  32.70  2.29  1978  21.44  27.00  15.50  3.26  37.66  42.00  14.00  5.15  1979  21.72  29.50  16.20  3.43  39.10  44.20  32.00  3.07  1992  20.38  25.00  17.50  1.98  37.07  43.50  31.00  2.92  1993  19.87  30.00  12.00  4.26  37.80  44.00  32.00  3.86  132 Table B-1  Month  Continued  Year  Minimum daily temperature (°C) Std. dev. Minimum Maximum Mean 3.01 21.50 32.50 26.77 2.77 17.50 28.00 23.44 2.75 18.20 28.00 23.42 2.60 21.90 33.80 28.32 2.44 20.50 30.50 26.26 2.25 21.50 29.50 26.16 3.63 19.00 31.70 25.22 2.49 22.70 31.40 28.34 2.97 19.70 30.00 24.06 3.05 18.00 32.00 22.91 3.41 18.00 34.00 27.55  May  1970 1971 1972 1973 1975 1976 1977 1978 1979 1992 1993  Jun.  1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1992 1993  25.73 24.43 25.21 28.83 27.44 25.51 25.94 27.26 27.61 27.74 29.03 28.56  29.50 28.80 29.50 34.00 31.20 30.50 31.00 30.90 32.00 32.80 35.00 35.40  21.00 19.50 19.50 24.80 21.20 20.00 22.00 22.00 22.70 23.60 23.00 23.40  Jul.  1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1992 1993  24.42 22.52 23.65 25.72 25.56 24.17  26.50 25.00 26.40 30.00 31.00 26.00  22.50 20.80 20.50 23.30 22.30 21.60  26.11 25.49 25.34 26.27 27.31 25.82  29.50 27.30 26.70 30.30 31.00 28.00  22.50 24.00 23.50 22.00 24.00 22.80  1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1992 1993  23.25 22.21 22.49 24.76 24.65 23.57 24.23 24.45 24.48 24.40 25.05 25.39  24.70 24.00 25.80 26.70 27.00 26.10 26.00 26.60 26.50 27.10 27.00 27.50  22.00 19.80 20.00 22.70 21.50 21.50 23.00 22.20 22.40 22.00 24.00 23.50  Aug.  Maximum daily temperature (°C) Mean  Maximum  Minimum  Std. dev.  43.24 40.73 42.09 43.09 41.90 40.76 39.69 43.38 39.80 41.59 43.84  46.00 43.40 45.50 46.00 44.50 43.30 43.40 45.30 43.50 44.50 47.00  39.00 37.00 36.00 35.80 38.50 37.20 36.50 40.70 34.20 33.00 41.00  1.50 1.71 2.09 2.38 1.30 1.51 2.02 1.29 2.46 2.18 1.62  2.24 2.01 2.84 1.99 2.59 2.56 2.72 2.63 2.66 2.75 2.80 3.94  39.19 36.31 41.07 39.74 39.67 38.62 36.96 38.42 39.15 40.86 43.00 40.00  42.50 42.40 45.00 45.70 44.00 43.50 43.10 44.50 44.50 46.00 47.00 47.10  32.70 27.00 34.50 32.00 34.00 31.50 26.50 30.00 29.70 32.90 38.00 31.20  1.06 1.13 1.30  34.39 30.68 35.22 33.28 33.90 32.64  37.00 36.00 38.50 42.40 42.10 36.50 41.30  30.50 24.70 27.60  35.20 35.00 41.00 41.00 39.00  29.00 27.00 28.00 31.00 26.80 28.40 26.50 26.00 26.00  2.25 3.17 2.49 2.92 2.23 2.85 4.08 4.45 4.35 3.13 2.38 4.46 1.81 2.91 1.88 3.51 4.34 2.57 3.03 2.13 1.50 3.87 4.42 2.90  34.50 34.20 40.60 34.70 35.10 36.50 34.20 33.50 33.00 36.60 38.00 36.00  21.50 26.50 27.50 26.00 25.50 26.20 25.20 25.70 28.00 28.00 26.00 24.00  2.29 1.58 3.37 1.87 2.14 2.18 1.90 2.06 1.41 2.02 2.36 3.00  1.55 2.19 .1.17 1.74 0.83 0.85 1.93 2.42 1.33  34.95 31.47 31.68 34.75 35.66 33.18  0.71 0.96 1.38 1.02 1.34 1.02 0.67 0.89  31.60 31.11 31.94 31.18 31.86 31.57 31.03 31.06  1.07 1.36 0.91 1.21  30.65 32.23 30.71 32.16  •  133 Table B-1  Month  Continued  Year  Mean  Minimum daily temperature (°C) Std. dev. Minimum Maximum  Maximum daily temperature (°C) Mean  Maximum  Minimum  Std. dev.  35.00  0.50 23.60 30.50 27.50 32.00 28.00 28.00 26.50 25.60 33.00 28.00 28.00  5.94 2.91 2.36 1.84 2.05 1.60 2.38 2.04 2.61 1.37 2.11 1.87  20.60 19.10 11.50 21.70 20.00 20.10 19.00 20.00 21.00 18.90 17.00 21.50  0.71 1.27 4.38 0.83 1.29 1.52 2.79 1.58 0.79 2.29 2.89 0.87  30.83 32.32 34.22 31.22 35.31 31.47 32.62 31.60 32.61 35.49 31.80 32.27  34.30 36.20 42.00 34.50 39.00 34.00 38.80 35.50 36.00 37.70 37.00  1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1992 1993  22.16 20.90 18.39 23.87 23.18 22.98 22.93 22.97 22.77 23.03 22.03 23.14  23.50 23.70 23.50 25.50 25.00 28.80 35.00 25.40 24.60 26.90 27.00 24.00  Oct.  1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1992 1993  16.65 15.68 13.67 16.97 19.38 18.15 17.60 18.19 16.87 20.04 17.84 17.37  21.00 21.20 17.50 24.00 24.30 22.60 21.50 22.80 25.40 23.50 22.00 22.40  12.50 9.00 9.20 11.70 13.40 10.50 12.00 14.50 12.20 17.00 13.00 12.00  2.56 3.69 2.14 3.60 3.89 3.86 2.37 2.46 3.91 1.69 2.46 2.47  35.00 32.75 34.82 32.22 32.65 32.15 34.76 35.22 34.39 34.86 31.16 34.45  37.00 36.00 38.50 35.20 36.60 35.00 38.80 36.90 36.00 37.10 35.00 36.80  33.00 27.80 26.00 20.50 24.00 24.00 32.20 30.50 30.50 27.90 22.00 27.80  0.95 1.98 3.28 2.93 3.10 2.51 1.47 1.30 1.20 2.02 2.85 1.98  Nov.  1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1992 1993  7.25 8.01 8.61 8.49 9.89 8.20 16.48 14.76 13.90 16.70 11.42 11.63  11.00 15.00 13.40 11.00 15.80 13.50 20.00 19.00 20.30 20.20 19.00 17.00  2.10 5.30 5.70 4.00 5.00 4.30 11.00 10.90 5.10 13.00 7.00 0.00  2.50 2.12 1.57 1.95 3.30 2.21 2.55 2.01 3.52 2.13 3.06 3.64  30.00 30.07 30.97 29.82 29.34 28.52 28.63 30.79 30.47 28.56 27.63 30.39  37.50 32.50 33.10 32.80 32.50 31.70 33.50 36.10 35.00 34.40 31.00 35.00  24.90 28.50 24.40 27.20 25.50 23.50 18.00 22.50 24.00 20.00 22.00 27.20  2.84 1.09 2.79 1.42 2.31 2.51 4.61 3.57 3.08 5.14 2.43 2.22  1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1992 1993  5.14 3.85 5.37 6.34 6.47 6.15 8.55 9.16 8.29 10.81 8.03 7.05  9.00 7.50 10.20 12.00 13.70 11.10 15.40 14.60 16.50 15.80 11.00 10.50  2.30 0.00 2.00 0.50 2.00 4.00 4.50 3.90 3.00 7.50 5.00 4.00  1.73 1.82 2.30 3.12 3.09 1.45 3.12 2.47 3.12 2.07 1.81 2.19  26.02 25.29 25.53 23.74 23.97 26.20 24.23 26.34 24.62 24.39 24.74 25.92  28.50 28.00 30.50 28.00 28.80 29.00 28.90 30.00 27.60 27.70 26.00 31.00  22.00 23.00 20.70 20.00 18.60 24.00 22.00 19.70 18.50 21.00 22.00 21.80  1.59 1.40 2.15 2.42 2.78 1.25 1.75 2.67 2.17 1.60 1.21 2.31  Sept.  Dec.  134  Table B-2  Humidity summary Maximum daily humidity (%)  Minimum daily humidity (%) Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec.  Year 1971 1993 1971 1971 1970 1971 1970 1971 1970 1971 1970 1970 1970 1970 1970 1970  Mean 33.19 6.50 20.29 10.90 8.86 15.13 17.97 18.65 41.17 51.03 52.39 79.06 65.00 26.87 16.30 23.77  Maximum 64.00 6.50 38.00 23.00 18.00 40.00 39.00 37.00 91.00 98.00 95.00 95.00 96.00 70.00 28.00 44.00  Minimum 13.00 6.50 4.00 4.00 2.00 8.00 7.00 5.00 17.00 32.00 29.00 60.00 47.00 14.00 10.00 9.00  Std. Dev. 13.11 0.00 9.97 4.47 3.80 7.42 7.40 8.53 17.64 20.66 14.92 9.67 12.80 12.05 5.13 10.87  Mean 80.39 2.00 61.14 44.39 26.93 34.03 36.39 41.84 62.93 72.80 76.03 89.55 87.97 71.65 71.52 73.45  Maximum 97.00 2.00 90.00 74.00 59.00 71.00 64.00 78.00 85.00 93.00 92.00 97.00 96.00 92.00 89.00 91.00  Minimum 61.00 2.00 32.00 16.00 15.00 • 21.00 17.00 10.00 37.00 53.00 59.00 80.00 66.00 47.00 43.00 39.00  Std. dev. 10.55 0.00 15.04 15.11 8.99 12.66 10.73 17.75 12.67 12.23 8.16 4.33 5.71 12.62 12.15 15.28  135  Table B-3  Wind speed summary Daily wind speed (ms ) Std. dev Maximum Minimum 1  Month Jan.  Feb.  Mar.  Apr.  May  Jun.  Jul. Aug. Sept. Oct. Nov. Dec.  Year  Mean  1971  2.80  8.90  1.40  1.40  1992  2.06  4.30  1.10  0.82  1993  2.01  4.10  1.00  0.65  1971  2.96  6.10  0.60  1.20  1992  2.60  5.10  1.60  0.77  1993  2.57  5.00  1.10  1.19  1971  3.06  6.30  1.90  1.00  1992  3.24  5.70  0.90  1.29  1993  3.27  6.30  1.10  1.21  1970  4.91  10.80  3.20  1.48  1971  5.05  10.80  2.30  2.02  1992  3.20  5.90  1.20  1.15  1970  7.68  13.40  4.00  2.63  1971  6.90  11.30  3.10  2.29  1992  4.59  9.30  2.50  1.68  1970  9.48  16.80  4.80  2.80  1971  9.39  16.30  2.30  3.16  1992  5.79  10.20  2.50  2.37  1970  9.24  13.80  3.10  3.00  1992  5.38  8.70  2.40  1.54  1970  5.45  10.30  2.60  1.99  1992  3.61  8.00  1.50  1.22  1970  4.75  9.50  1.60  1.91  1992  2.61  6.20  0.90  1.05 0.91  1970  2.85  5.10  1.80  1992  1.95  5.30  0.70  1.16  1970  1.71  2.90  1.10  0.39  1992  1.51  2.90  0.90  0.55  1970  1.85  2.90  1.10  0.60  6.60  0.30|  1992  1.53  1.07  136  Table B-4  Sunshine summary  Month Jan.  Feb.  Mar.  Apr.  May  Jun.  Jul. Aug. Sept. Oct. Nov. Dec.  Year 1971 1992 1993 1971 1992 1993 1971 1992 1993 1970 1971 1992 1970 1971 1992 1970 1971 1992 1970 1970 1970 1992 1970 1992 1970 1992 1970 1992  Daily sunshine hours Mean Maximum Minimum Std. dev. 1.82 2.70 10.00 8.85 1.59 2.00 9.50 8.34 0.90 6.50 10.00 8.96 0.42 9.00 10.80 10.38 1.34 4.50 10.50 9.39 1.65 4.00 10.50 9.16 0.41 8.70 10.60 9.87 1.09 6.00 10.00 8.60 1.81 1.50 10.30 9.19 2.52 2.90 16.60 9.72 0.92 8.60 11.90 10.28 1.04 6.00 11.00 10.17 2.27 4.00 12.20 9.48 1.69 5.50 12.10 10.10 1.19 6.00 11.00 9.80 3.60 0.20 12.40 8.27 3.46 0.50 11,70 7.78 1.28 6.50 11.70 10.24 3.68 0.40 12.00 7.71 2.97 0.90 11.70 4.35 3.30 1.00 10.10 6.09 2.20 2.80 10.40 8.10 0.76 7.60 11.00 10.18 1.59 4.30 10.50 9.33 0.27 9.70 10.70 10.26 0.73 7.50 12.00 9.46 0.36 9.00 10.20 9.76 0.94 4.30 9.40 8.40  Table B-5  Pan evaporation summary Monthly pan evaporation (mm)  Daily pan evaporation (mmd") 1  Month Jan.  Year  Minimum Std. dev  Total  Mean  % of mean 92.38  1971  2.79  3.85  0.72  0.66  86.38  93.51  1972  2.52  3.80  0.90  0.53  78.10  93.51  83.52  1973  3.49  6.90  2.60  0.84  108.30  115.82  1974 1975  3.14  6.80  1.80  97.40  2.61  3.00  2.00  i.to 0.25  93.51 93.51  80.80  93.51  86.41  1976  2.72  5.80  1.30  0.95  84.40  93.51  90.26  1977  2.82  4.90  0.00  1.05  87.40  93.51  93.47  4.00  1.60  0.55  86.84  93.51  92.87  97.90  93.51  104.69  84.90  93.51  90.79  1978  Feb.  Mean  Maximum  2.80  1979  3.16  6.00  1.60  0.93  1980  2.93  4.50  1.50  0.59  104.16  1981  4.14  6.20  1.10  1.22  128.30  93.51  137.20  1984  3.33  5.70  1.70  0.97  103.10  93.51  110.26  1985  2.69  3.60  1.60  0.54  83.40  93.51  89.19  1986  2.28  3.70  0.70  0.67  70.70  93.51  75.61  1987  2.87  4.00  1.50  0.54  89.00  93.51  95.18  1988  2.19  4.00  1.30  0.68  67.90  93.51  72.61  1989  2.72  3.90  1.70  0.47  84.30  93.51  90.15  1.33  132.60  93.51  141.80  1990  4.28  7.30  2.00  1991  3.98  5.20  1.90  0.73  123.50  93.51  132.07  1992  3.50  5.30  .1.40  0.90  108.40  93.51  115.92  1993  3.71  5.50  1.80  0.81  114.90  93.51  122.87  1971  4.62  8.68  2.55  1.27  129.33  121.30  106.62  1972  3.84  7.10  0.80  1.38  111.40  121.30  91.84  1973  4.91  12.80  3.30  1.85  137.50  121.30  113.36  1974  4.04  5.40  2.50  0.80  113.00  121.30  93.16  2.50  0.83  107.20  121.30  88.38  121.30  95.80  1975  3.83  6.00  1976  4.01  6.40  1.70  1.31  116.20  1977  3.76  6.20  1.40  0.89  105.40  121.30  86.89  1978  3.71  6.70  1.50  1.07  104.00  121.30  85.74  1979  3.76  5.40  2.00  0.93  105.30  121.30  86.81  1980  4.50  7.80  2.70  1.38  130.40  121.30  107.50  1981  5.63  8.10  3.80  1.27  157.60  121.30  129.93  1983  5.24  8.30  2.60  1.52  125.70  121.30  103.63  129.90  121.30  107.09  138.70  121.30  114.34 81.70  1984  4.48  9.80  2.40  1.41  1985  4.95  9.50  2.50  1.91  1986  3.54  6.30  1.00  1.21  99.10  121.30  1987  4.19  9.10  2.20  1.36  117.40  121.30  96.78  1988  4.50  7.20  2.20  1.30  130.40  121.30  107.50  1989  4.41  5.50  2.70  0.72  123.50  121.30  101.81  1990  4.43  6.00  1.70  1.07  123.90  121.30  102.14  0.75  116.70  121.30  96.21  1991  4.17  5.60  2.40  1992  4.57  8.80  2.10  1.35  132.60  121.30  109.32  1993  5.34  8.00  2.40  1.68  149.60  121.30  123.33  Table B - 5  Continued Monthly pan evaporation (mm)  Daily pan evaporation (mmd' ) 1  Month Mar.  Year 1971  7.74  Maximum 11.81  Minimum Std. dev 4.63  1.77  Total  Mean  % of mean  239.97  220.41  108.87 99.59  1972  7.08  11.50  4.80  1.76  219.50  220.41  1973  7.49  13.70  3.80  2.24  232.20  220.41  105.35  1974 1975  7.08 6.23  12.20 8.80  3.40  219.49  220.41 220.41  99.58  1976  6.61  9.70  4.10 3.90  1.96 1.25  1977  6.58  10.30  1978  0.64  6.40  1979  6.92  1980  10.73  1981 1983  Apr.  Mean  7.49 9.16  220.41  87.56 93.01  203.90  220.41  92.51  19.93  220.41  9.04  1.75  214.50  220.41  97.32  3.30  5.60  332.50  220.41  150.86  3.90  1.52  232.30  220.41  105.39  2.67  283.90  220.41  128.81 124.36  1.32  193.00 205.00  3.80  1.58  0.00  1.75  11.20  3.60  24.40 11.20 16.50  4.80  1984  8.84  14.80  3.20  2.83  274.10  220.41  1985  7.55  11.90  3.30  2.18  233.90  220.41  106.12  1986  5.91  9.50  2.60  1.41  183.30  220.41  83.16  1987  7.03  12.00  3.50  2.22  217.90  220.41  98.86  1988  7.84  12.70  1.90  2.30  243.10  220.41  110.29  1989  5.65  6.90  3.70  220.41  79.44  6.22  9.20  3.80  0.77 1.42  175.10  1990  192.80  220.41  87.47  1991  8.04  12.60  4.10  2.24  249.30  220.41  113.11  1992  7.07  9.30  4.00  1.20  219.10  220.41  99.41 125.27  1993  8.91  13.40  4.80  2.46  276.11  220.41  1970  10.97  18.57  7.08  2.96  318.14  348.25  91.35  1971  12.12  18.16  8.91  2.50  363.53  348.25  104.39  1972  9.71  15.30  3.10  2.29  291.20  348.25  83.62  1973  11.92  16.60  9.20  2.10  357.50  348.25  102.66  1975  8.72  11.90  7.50  1.12  261.50  348.25  75.09  3.70  2.79  304.70  348.25  87.49 76.96  1976  10.16  16.60  1977  8.93  13.20  4.90  1.99  268.00  348.25  1978  10.05  17.60  0.00  2.93  301.60  348.25  86.60  1979  12.35  19.61  7.10  3.19  370.61  348.25  106.42  1980  13.91  28.90  7.70  4.45  417.20  . 348.25  119.80  1981  14.74  21.10  8.90  3.76  427.60  348.25  122.79  1983  10.79  17.30  2.30  3.92  323.60  348.25  92.92  498.30  348.25  143.09 95.22  1984  16.61  32.30  8.80  5.41  1985  11.05  16.70  5.40  2.80  331.60  348.25  1986  9.86  16.10  6.80  2.40  295.70  348.25  84.91  1987  15.67  26.00  7.80  4.75  454.35  348.25  130.47  1988  11.42  17.50  7.50  2.07  342.60  348.25  98.38  1989  9.74  14.30  5.00  2.39  292.10  348.25  83.88  1990  12.52  18.50  7.30  3.22  375.70  348.25  107.88  1991  11.18  15.10  4.80  2.53  335.40  348.25  96.31  348.25  105.04  348.25  127.52  1992  12.19  17.90  8.30  2.19  365.80  1993  14.80  25.20  6.60  4.17  444.10  Table B-5  Continued Monthly pan evaporation (mm)  Daily pan evaporation (mmd ) 1  Month May  Year 1970 1971  15.41 13.21  Maximum 43.41 20.72  Minimum Std. dev 6.19 8.84  Total  Mean  % of mean  6.22  477.70  467.35  102.21  3.19  409.41  467.35  87.60 88.14  1972  13.29  21.70  7.30  3.73  411.90  467.35  1973  15.58  3.84  482.90  467.35  103.33  13.58  23.90 22.60  4.90  1975  8.30  3.16  420.90  467.35  90.06  1976  13.76  20.70  7.50  2.73  426.50  467.35  91.26  1977  10.40  16.10  6.80  2.42  322.42  467.35  68.99  1978  15.63  19.10  11.10  2.26  484.50  467.35  103.67  1979  12.37  18.00  7.30  2.57  383.41  467.35  82.04  3.93  543.60  467.35  116.32  3.11  589.00  467.35  126.03  4.74  512.80  467.35  109.73 113.66 91.88  1980  17.54  29.20  9.60  1981  19.00  23.10  8.10  1983  16.54  29.40  7.90  1984  17.14  34.50  9.20  4.69  531.20  467.35  1985  13.85  19.50  9.40  2.54  429.40  467.35  1986  11.81  17.80  5.90  2.98  366.10  467.35  78.34  1987  19.49  26.40  14.00  2.97  604.20  467.35  129.28  1988  16.75  21.30  10.10  3.09  519.20  467.35  111.09  1989  13.16  16.20  8.10  1.82  407.90  467.35  87.28  1990  15.14  19.40  8.10  2.91  469.20  467.35  100.40  1991  15.66  19.50  12.30  1.89  485.40  467.35  103.86  8.60  2.84  432.20  467.35  92.48  467.35  148.37  1992 Jun.  Mean  13.94  21.00  1993  22.37  28.70  6.30  3.35  693.41  1970  12.79  42.14  3.91  6.53  383.63  377.57  101.61  1971  10.24  17.63  0.00  4.74  307.07  377.57  81.33  1972  12.41  17.10  5.00  3.53  372.20  377.57  98.58  1973  13.27  19.70  1.20  3.72  398.20  377.57  105.46  1974  12.75  24.50  7.80  3.26  382.60  377.57  101.33  3.81  320.30  377.57  84.83 83.12 79.48  1975  10.68  17.90  0.00  1976  10.46  15.23  0.00  3.66  313.84  377.57  1977  10.00  17.90  0.00  4.35  300.10  377.57  1978  10.95  18.50  0.00  5.18  328.60  377.57  87.03  1979  13.74  26.40  5.90  4.63  412.11  377.57  109.15  1980  13.86  31.90  0.00  7.61  415.70  377.57  110.10  1981  21.91  27.40  16.10  3.69  153.40  377.57  40.63  1983  17.41  24.60  5.70  5.26  522.40  377.57  138.36  1984  14.29  24.60  1.50  5.28  428.80  377.57  113.57 110.34  1985  13.89  19.30  5.80  3.22  416.60  377.57  1986  12.44  20.20  4.60  4.65  373.10  377.57  98.82  1987  13.56  19.70  3.80  4.91  406.70  377.57  107,72  1988  10.86  18.30  0.00  5.86  325.70  377.57  86.26  1989  11.45  17.10  7.90  2.47  343.40  377.57  90.95  1990  13.16  18.40  2.50  3.52  394.80  377.57  104.56  1991  14.94  21.80  5.70  3.50  448.30  377.57  118.73  1992  16.41  20.20  3.70  3.11  492.40  377.57  130.41  1993  7.34  23.50  0.00  6.40  220.10  377.57  58.29  Table B-5  Continued Monthly pan evaporation (mm)  Daily pan evaporation (mmd") 1  Month Jul.  Year 1970 1971  8.72 3.59  Maximum  Minimum Std. dev  Total  Mean  % of mean 121.98  23.64  1.62  4.00  270.30  221.60  13.31  0.00  3.28  111.19  221.60  50.18  221.60  134.43  221.60  74.28  1972  9.61  15.60  3.00  2.87  297.90  1973 1974  5.31 4.83  12.80 13.30  0.30 0.00  3.11 4.46  164.60 149.70  1975  3.80  7.90  0.00  2.59  117.90  221.60 221.60  67.55 53.20  1976  7.05  14.25  0.00  3.74  218.51  221.60  98.61  1977  3.57  12.60  0.00  3.00  110.70  221.60  49.95  1978  3.35  7.90  0.00  2.34  103.90  221.60  46.89  1979  7.75  22.70  0.00  6.32  240.40  221.60  108.48  1980 1983  6.49  12.90  0.00  3.33  201.20  221.60  90.79  6.45  14.10  0.10  3.75  200.10  221.60  90.30  1984  8.43  18.50  0.50  3.51  261.20  221.60  117.87  1985  8.51  17.00  0.90  4.33  263.80  221.60  119.04  4.00  152.00  221.60  68.59  1986  Aug.  Mean  4.90  13.30  0.00  1987  13.52  20.50  5.80  4.15  419.20  221.60  189.17  1988  4.65  10.30  0.00  2.54  144.30  221.60  65.12  1989  7.14  10.50  0.00  2.43  221.20  221.60  99.82  1990  5.42  10.00  0.00  2.91  168.10  221.60  75.86  1991  9.25  23.40  0.00  6.08  286.90  221.60  129.47  1992  10.51  19.50  0.00  5.91  325.70  221.60  146.98  1993  7.31  17.10  0.00  4.82  226.50  221.60  102.21  1970  4.67  0.69  4.21  144.71  142.16  101.79  1971  4.69  25.12 9.83  0.00  2.09  145.46  142.16  102.32  1972  4.88  12.70  0.00  3.51  151.20  142.16  106.36  1973  3.39  7.70  0.00  2.02  105.10  142.16  73.93  1974  3.77  8.80  0.00  2.48  116.80  142.16  82.16  1975  3.21  7.70  0.00  2.28  99.50  142.16  69.99  1976  4.12  7.95  0.00  1.59  127.64  142.16  89.79  2.04  101.20  142.16  71.19 51.63  1977  3.26  6.70  0.00  1978  2.37  5.60  0.00  1.89  73.40  142.16  1979  5.45  13.60  0.00  2.57  168.90  142.16  118.81  1980  4.67  10.60  0.00  2.64  144.90  142.16  101.93  1983  5.29  24.00  0.10  4.64  164.10  142.16  115.43  1984  5.90  16.80  0.50  4.33  182.80  142.16  128.59  1985  3.86  7.80  0.20  1.85  119.80  142.16  84.27  0.80  1.58  105.00  142.16  73.86 271.45  1986  3.39  6.80  1987  12.45  21.90  0.00  5.81  385.90  142.16  1988  3.44  5.40  0.30  1.44  106.60  142.16  74.99  1989  4.04  8.40  0.00  2.25  125.30  142.16  88.14  1990  4.08  7.30  0.00  1.98  126.40  142.16  88.91  1991  3.83  8.20  0.00  2.64  118.80  142.16  83.57  1992  3.42  9.70  0.00  2.42  106.10  142.16  74.63  6.71  14.10  0.00  3.62  208.00  142.16  146.31  1993  -  Table B-5  Continued Monthly pan evaporation (mm)  Daily pan evaporation (mmd") 1  Month Sept.  Year  Minimum Std. dev 0.88  6.85  151.83  4.51  1.86  160.60  151.83  105.78  1.82 1.27  102.44 187.30  151.83  67.47  0.00  1.63  107.40  151.83 151.83  123.36 70.74  0.00  2.03  151.46  151.83  99.76  6.70  0.00  1.81  111.05  151.83  73.14  7.50  0.00  1.70  133.20  151.83  87.73  151.83  167.33  1.99  0.23  3.98  0.00  5.35  11.90  1.50  1973 1974 1975  3.41 6.24  7.80 8.50  0.10 3.00  3.58  7.60  1976  5.05  9.17  3.70  1971 1972  1978  4.44  % of mean  139.56  0.35  4.65  Mean  Total  151.83  11.25  1970  1977  91.92  1979  8.47  26.90  5.70  3.84  254.06  1980  7.14  12.70  0.00  2.65  214.20  151.83  141.08  1983  5.91  16.20  1.10  2.70  177.40  151.83  116.84  1984  5.32  15.00  1.30  2.83  159.50  151.83  105.05  1985  4.56  6.50  1.60  1.36  136.90  151.83  90.17  1986  5.67  9.00  3.70  1.18  170.20  151.83  112.10  1987  8.08  13.20  1.00  2.80  242.40  151.83  159.65  1988  4.76  6.80  0.00  1.44  142.80  151.83  94.05  1989  5.79  8.10  2.90  1.20  173.60  151.83  114.34  1990  5.10  9.10  0.00  2.12  152.90  151.83  100.70  1.79  148.10  151.83  97.54 93.33  1991  Oct.  Mean  Maximum  4.94  6.80  0.00  1992  4.72  7.60  1.00  1.37  141.70  151.83  1993  4.22  9.90  0.60  2.56  126.70  151.83  83.45  1970  0.00  0.00  0.00  0.00  0.00  159.49  0.00  1971  0.00  0.00  0.00  0.00  0.00  159.49  0.00  1972  5.24  8.30  2.90  1.05  162.30  159.49  101.76  1973  4.19  6.70  1.10  1.61  129.80  159.49  81.38  1.94  130.30  159.49  81.70  1.15  125.80  159.49  78.88 113.06  1974  4.20  7.10  0.00  1975  4.06  6.00  0.00  1976  5.82  8.36  2.90  1.51  180.32  159.49  1977  4.68  7.00  2.20  0.86  145.10  159.49  90.98  1978  5.21  6.80  3.00  0.96  161.40  159.49  101.20  1979  6.65  9.00  3.70  1.29  206.30  159.49  129.35  10.10  3.20  1.70  201.70  159.49  126.47  1.35  101.50  159.49  63.64 84.64 94.55  1980 1982  6.51 5.97  7.70  2.90  1983  4.35  6.80  0.10  1.68  135.00  159.49  1984  4.86  8.60  0.50  1.71  150.80  159.49  1985  3.05  6.00  0.10  1.45  94.50  159.49  59.25  1986  5.50  8.80  3.80  1.31  170.50  159.49  106.90  1987  4.94  10.70  1.10  2.10  153.10  159.49  95.99  1988  3.83  4.90  0.20  0.93  118.70  159.49  74.42  1.02  187.30  159.49  117.44  1989  6.04  7.60  3.70  1990  7.10  9.30  4.90  1.27  220.10  159.49  138.00  1991  5.57  7.60  3.50  0.97  172.80  159.49  108.35  1992  4.24  5.80  0.00  1.50  131.50  159.49  82.45  1993  6.85  11.50  3.70  1.98  212.40  159.49  133.17  Table B-5  Continued Monthly pan evaporation (mm)  Daily pan evaporation (mmd") 1  Month Nov.  Year 1970  3.25  Maximum 5.59  Minimum Std. dev 0.00  1.46  Total  Mean  % of mean  97.55  114.33  85.32 74.17  1971  2.83  4.20  0.00  1.22  84.80  114.33  1972  4.17  8.10  2.20  1.04  125.00  114.33  109.33  1973  3.42  5.60  0.60  1.19  102.50  114.33  89.65  1974  3.53  4.60  2.50  0.51  105.80  114.33  92.54  1975  3.45  5.70  2.40  0.65  103.50  114.33  90.53  1976  3.11  5.46  0.00  1.39  93.35  114.33  81.65  1977  4.90  0.93 0.97  114.33  97.35  6.40  1.00 1.90  111.30  1978  3.71 4.21  126.20  114.33  110.38  1979  3.02  7.30  0.00  2.23  90.70  114.33  79.33  114.33  129.97  1980  4.95  8.40  3.00  1.33  148.60  1983  4.25  9.20  1.30  1.83  127.50  114.33  111.52  1984  3.71  5.10  0.80  0.97  111.30  114.33  97.35  1985  3.19  5.90  1.80  0.80  95.80  114.33  83.79  1986  3.71  5.70  2.20  0.83  111.20  114.33  97.26  1987  2.54  5.30  0.50  1.09  76.30  114.33  66.74  1988  3.12  4.10  1.80  0.64  93.70  114.33  1989  4.11  6.70  1.90  1.02  123.30  114.33  81.96 107.85  1990  5.11  6.80  2.30  0.95  153.20  114.33  134.00  4.70  7.80  1.00  1.47  141.00  114.33  123.33  0.75  121.60  114.33  106.36 149.57  1991 1992 Dec.  Mean  4.05  5.50  2.30  1993  5.70  10.10  2.10  1.84  171.00  114.33  1970  2.92  4.48  1.98  0.58  90.54  91.45  99.00  1971  2.54  3.50  1.80  0.49  78.60  91.45  85.95  1972  2.68  4.30  1.60  0.59  83.20  91.45  90.98  .1973  2.36  3.80  0.70  0.71  73.30  91.45  80.15  72.00  91.45  78.73  89.30  91.45  97.65  1974  2.32  3.10  1.60  0.39  1975  2.88  5.40  0.50  0.93  1976  3.48  30.01  1.50  4.98  107.99  91.45  118.09  1977  2.54  3.80  1.10  0.73  78.60  91.45  85.95  1978  2.56  3.50  0.60  0.64  79.40  91.45  86.82  1979  2.46  4.70  0.00  0.93  73.80  91.45  80.70  1980  3.69  5.60  1.60  1.03  114.30  91.45  124.99  1982  2.94  5.70  0.30  1.39  85.20  91.45  93.17  0.79  109.60  91.45  119.85  0.83  81.10  91.45  88.68  1983  3.54  6.10  2.20  1984  2.62  4.60  1.30  1985  2.59  7.90  1.20  1.18  80.30  91.45  87.81  1986  2.70  5.40  1.40  0.74  83.70  91.45  91.53  1987  1.79  3.30  0.30  0.73  55.50  91.45  60.69  1988  2.25  3.10  1.50  0.40  69.60  91.45  76.11  1989  3.16  4.10  2.10  0.51  98.10  91.45  107.27  1990  4.39  8.70  2.20  1.41  136.20  91.45  148.93  1.35  124.60  91.45  136.25  7.30  1.00  1991  4.02  1992  3.58  6.80  1.10  1.23  111.00  91.45  121.38  1993  3.91  14.10  0.40  2.96  121.20  91.45  132.53  Table B-6  Rainfall s u m m a r y Monthly rainfall (mm)  Daily rainfall (mmd ) 1  Month Jan.  Year  Maximum Minimum  Std. dev.  % of mean  Mean  Total  46.95  1971  0.03  1.00  0.00  0.18  1.00  2.13  1972  0.00  0.00  0.00  coo  0.00  2.13  0.00  1973  0.00  0.00  0.00  0.00  0.00  2.13  0.00  1974  0.00  0.00  0.00  0.00  2.13  0.00  1975  0.02  0.70  0.00 0.00  0.13  0.70  2.13  32.86  1976  0.45  9.80  0.00  1.85  13.80  2.13  647.89  0.21 0.00  5.20  0.00  0.94  6.50  2.13  305.16  0.00  0.00  0.00  0.00  2.13  0.00  0.00  0.00  0.00  2.13 2.13  0.00 0.00  1977 1978 1979  0.00  0.00  1980  0.00  0.00  0.00  0.00  0.00  1981  0.13  2.00  0.00  0.45  4.00  2.13  187.79  1984  0.18  3.60  0.00  0.71  5.70  2.13  267.61  1985  0.13  4.00  0.00  0.72  4.00  2.13  187.79  1986  0.00  0.00  0.00  0.00  0.00  2.13  0.00  1987  0.00  0.00  0.00  0.00  0.00  2.13  0.00  1988  0.00  0.00  0.00  0.00  0.00  2.13  0.00  0.35  10.80  0.00  1.94  10.80  2.13  507.04  0.00  0.00  0.00  0.00  0.00 0.00  2.13 2.13  0.00 0.00  0.00  2.13  0.00 0.00  1989 1990  Feb.  Mean  1991  0.00  0.00  0.00  0.00  1992  0.00  0.00  0.00  0.00  1993  0.00  0.00  0.00  0.00  0.00  2.13  1971  0.07  2.00  0.00  0.38  2.00  5.55  36.04  1972  0.32  9.20  0.00  1.71  9.20  5.55  165.77  1973  0.00  0.00  0.00  0.00  0.00  5.55  0.00  1974  0.00  0.00  0.00  0.00  0.00  5.55  0.00  0.00  0.00  0.00  5.55  0.00  0.00  5.55  0.00  1975  0.00  0.00 0.00  0.00  0.00  0.18  3.00  0.00  0.63  5.10  5.55  91.89  0.53  10.80  0.00  2.15  14.80  5.55  266.67  1979  0.10  2.80  0.00  0.53  2.80  5.55  50.45  1980  0.03  1.00  0.00  0.19  1.00  5.55  18.02  1981  0.00  0.00  0.00  0.00  0.00  5.55  0.00  0.00  0.00  0.00  5.55  0.00 0.00  1976  0.00  1977 1978  1983  0.00  0.00  1984  0.00  0.00  0.00  0.00  0.00  5.55  1985  0.00  0.00  0.00  0.00  0.00  5.55  0.00  1986  2.23  58.10  0.00  10.98  62.30  5.55  1122.52  1987  0.00  0.00  0.00  0.00  0.00  5.55  0.00  1988  0.00  0.00  0.00  0.00  0.00  5.55  0.00  1989  0.00  0.00  0.00  0.00  0.00  5.55  0.00  1990  0.69  6.60  0.00  1.66  19.30  5.55  347.75  1991  0.00  0.00  0.00  0.00  0.00  5.55  0.00  1992  0.00  0.00  0.00  0.00  0.00  5.55  0.00  1993  0.00  0.00  0.00  0.00  0.00  5.55  0.00  Table B-6  Continued Monthly rainfall (mm)  Daily rainfall (mmd ) 1  Month Mar.  Year 1971 1972 1973 1974  0.00 0.00 0.00 0.00  Maximum Minimum  Std. dev.  Mean  Total  % of mean  0.00  0.00  0.00  0.00  1.87  0.00  0.00  0.00  0.00  0.00  1.87  0.00  0.00  0.00  0.00  1.87  0.00  0.00  0.00  1.87  0.00 21.39 0.00  0.00 0.00  0.00  1975  0.01  0.40  0.00  0.07  0.40  1.87  1976  0.00  0.00  0.00  0.00  0.00  1.87  1977  0.00  0.00  0.00  0.00  0.00  1.87  0.00  1978  0.34  10.60  0.00  1.90  10.60  1.87  566.84  1979  0.27  8.00  0.00  1.44  8.40  1.87  449.20  1980  0.02  0.70  0.00  0.13  0.70  1.87  37.43  1981  0.10  2.80  0.00  0.50  3.10  1.87  165.78  1983  0.00  0.00  0.00  0.00  0.00  1.87  0.00  0.00  0.00  0.00  0.00  1.87  0.00  1.87  26.74 0.00  1984  Apr.  Mean  0.00  1985  0.02  0.50  0.00  0.09  0.50  1986  0.00  0.00  0.00  0.00  0.00  1.87  1987  0.00  0.00  0.00  0.00  0.00  1.87  0.00  1988  0.30  5.70  0.00  1.12  9.40  1.87  502.67  1989  0.18  3.20  0.00  0.72  5.70  1.87  304.81  1990  0.00  0.00  0.00  0.00  0.00  1.87  0.00  1991  0.00  0.00  0.00  0.00  0.00  1.87  0.00  1992  0.00  0.00  0.00  0.00  0.00  1.87  0.00  1993  0.12  3.60  0.00  0.65  3.60  1.87  192.51  1970  0.00  0.00  0.00  0.00  0.00  2.01  0.00  1971  0.00  0.00  0.00  0.00  0.00  2.01  0.00  1972  0.00  0.00  0.00  0.00  0.00  2.01  0.00  1973  0.00  0.00  0.00  0.00  0.00  2.01  0.00  1975  0.00  0.00  0.00  0.00  0.00  2.01  0.00  1976  0.04  1.10  0.00  0.20  1.30  2.01  64.68  1977  0.41  8.20  0.00  1.64  12.20  2.01  606.97 0.00 0.00  1978  0.00  0.00  0.00  0.00  0.00  2.01  1979  0.00  0.00  0.00  0.00  0.00  2.01  1980  0.00  0.00  0.00  0.00  0.00  2.01  0.00  1981  0.11  3.20  0.00  0.58  3.20  2.01  159.20  1983  0.25  6.90  0.00  1.26  7.40  2.01  368.16  1984  0.00  0.00  0.00  0.00  0.00  2.01  0.00  1985  0.11  3.20  0.00  0.58  3.20  2.01  159.20  1986  0.00  0.00  0.00  0.00  0.00  2.01  0.00  0.00  2.01  0.00  1987  0.00  0.00  0.00  0.00  1988  0.05  0.80  0.00  0.20  1.60  2.01  79.60  1989  0.00  0.00  0.00  0.00  0.00  2.01  0.00  1990  0.00  0.00  0.00  0.00  0.00  2.01  0.00  1991  0.55  14.00  0.00  2.56  16.60  2.01  825.87  1992  0.00  0.00  0.00  0.00  0.00  2.01  0.00  0.00  2.01 |  0.00  1993  0.00  0.00  0.00  0.00  Table B-6  Continued Monthly rainfall (mm)  Daily rainfall (mmd ) -1  Month May  Year  Mean  1970 1971  0.88  7.60  2.01  378.11  1.04  17.60  0.00  3.32  32.30  9.66  334.37  0.00  0.00  0.00  9.66  0.00  0.00  0.00  9.66  0.00  9.66  53.83  0.00 0.00  0.00  1975  0.17  5.20  0.00  0.93  5.20  1976  0.71  18.20  0.00  3.31  21.90  9.66  226.71  1977  0.84  11.00  0.00  2.35  26.00  9.66  269.15  1978  0.00  0.00  0.00  0.00  0.00  9.66  0.00  1979  0.97  21.80  0.00  3.97  30.00  9.66  310.56  1980  0.19  6.00  0.00  1.08  6.00  9.66  62.11  1981  0.10  1.50  0.00  0.37  3.00  9.66  31.06  1983  1.25  28.60  0.00  5.29  38.70  9.66  400.62  1984  0.00  0.00  0.00  0.00  0.00  9.66  0.00  0.00  0.00  0.00  9.66  0.00  0.00  9.66  0.00  0.00  1985  0.00  1986  Jun.  % of mean  Mean  Total  0.00  0.00  1973  Std. dev.  4.40  0.00  1972  Maximum Minimum  0.25  0.00 0.00  0.00  0.00  1987  0.07  2.30  0.00  0.41  2.30  9.66  23.81  1988  0.04  1.10  0.00  0.20  1.10  9.66  11.39  1989  0.00  0.00  0.00  0.00  0.00  9.66  0.00  1990  0.42  9.10  0.00  1.71  13.10  9.66  135.61  1991  0.00  0.00  0.00  0.00  0.00  9.66  0.00  1992  0.60  9.40  0.00  2.32  18.60  9.66  192.55  1993  0.00  0.00  0.00  0.00  0.00  9.66  0.00  80.00  144.38  1970  3.85  79.00  0.00  14.69  115.50  1971  7.28  56.10  0.00  14.62  218.50  80.00  273.13 37.88  1972  1.01  7.60  0.00  2.22  30.30  80.00  1973  0.47  14.00  0.00  2.56  14.00  80.00  17.50  1974  1.01  12.40  0.00  2.88  30.20  80.00  37.75  3.74  37.20  0.00  9.95  112.30  80.00  140.38  3.18  24.80  0.00  6.48  95.30  80.00  119.13  80.00  157.75 198.00  1975 1976  •  1977  4.21  78.00  0.00  14.44  126.20  1978  5.28  67.60  0.00  13.40  158.40  80.00  1979  0.85  13.20  0.00  2.60  25.40  80.00  31.75  1980  6.81  127.00  0.00  23.72  204.30  80.00  255.38  1981  0.00  0.00  0.00  0.00  0.00  80.00  0.00  1983  1.00  10.20  0.00  2.83  29.90  80.00  37.38  1984  0.40  12.00  0.00  2.19  12.00  80.00  15.00  1.73  14.10  80.00  17.63 52.38  1985  0.47  7.80  0.00  1986  1.40  18.20  0.00  4.14  41.90  80.00  1987  1.77  24.30  0.00  5.29  53.20  80.00  66.50  1988  7.33  62.00  0.00  17.35  219.80  80.00  274.75  1989  1.80  19.80  0.00  4.52  54.10  80.00  67.63  1990  2.89  50.50  0.00  9.70  86.80  80.00  108.50  1991  0.39  11.70  0.00  2.14  11.70  80.00  14.63  0.00 0.00  0.55  3.00  80.00  3.75  103.02  80.00  128.78  1992 1993  0.10 3.43  3.00 14.20  5.15  Table B - 6  Continued Monthly rainfall (mm)  Daily rainfall (mmd") 1  Month Jul.  Year 1970  5.86  Maximum Minimum Std. dev.  Total  Mean  % of mean  76.00  0.00  16.50  181.60  260.13  69.81  36.34  568.00  260.13  218.35  5.74  64.20  260.13  24.68  260.13  142.20  1971  18.32  174.00  0.00  1972  2.07  21.40  0.00  1973 1974  11.93  100.60  0.00  21.21  0.00  657.60  260.13  252.80  1975  9.31  171.20 92.20  26.22 36.87  369.90  0.00  19.26  288.70  260.13  110.98  1976  7.16  86.50  0.00  19.55  222.00  260.13  85.34  1977  11.66  53.60  0.00  15.05  361.40  260.13  138.93  1978  10.36  94.60  0.00  22.71  321.30  260.13  123.52  1979  10.60  122.50  0.00  28.77  328.70  260.13  126.36  32.00  0.00  8.34  148.80  260.13  57.20  25.70  0.00  7.97  176.20  260.13  67.74  14.08  161.60  260.13  62.12  202.20  260.13  77.73  1980 1983 1984  Aug.  Mean  4.80 5.68 5.21  67.00  0.00  1985 1986  6.52 15.07  49.30 96.10  0.00 0.00  13.37 23.23  467.30  260.13  1987  2.44  34.30  0.00  7.09  75.50  260.13  179.64 29.02  1988  6.64  40.70  0.00  10.67  205.70  260.13  79.08  1989  3.65  42.70  0.00  10.03  113.30  260.13  43.56  1990  6.03  66.60  0.00  13.64  186.80  260.13  71.81  1991  9.08  123.60  0.00  24.49  260.13  108.25  1992  3.42  46.40  0.00  9.48  281.60 105.90  260.13  40.71  13.29  234.40  260.13  90.11  1993  7.56  51.00  0.00  1970  7.33  43.00  0.00  11.94  227.30  265.76  85.53  1971  8.00  87.20  0.00  17.57  247.90  265.76  93.28  1972  6.04  37.20  0.00  10.12  187.20  265.76  70.44  1973  9.50  71.70  0.00  16.96  294.60  265.76  110.85  1974  12.06  93.60  0.00  23.53  373.80  265.76  140.65  1975  12.56  80.40  0.00  19.78  389.30  265.76  146.49  16.81  303.40  265.76  114.16 100.32  1976  9.79  88.30  0.00  1977  8.60  72.20  0.00  17.27  266.60  265.76  1978  13.23  167.40  0.00  30.80  410.10  265.76  154.31  1979  2.12  24.60  0.00  5.12  65.60  265.76  24.68  1980  3.90  35.00  0.00  8.98  120.90  265.76  45.49  1983  7.31  65.70  0.00  15.56  226.70  265.76  85.30  1984  10.45  85.50  0.00  19.71  324.00  265.76  121.91  1985  9.33  68.80  0.00  15.91  289.10  265.76  108.78  17.90  217.80  265.76  81.95  9.50  181.80  265.76  68.41  1986 1987  . 7.03 5.86  87.00  0.00  38.30  0.00  1988  9.51  75.90  0.00  18.81  294.70  265.76  110.89  1989  11.68  115.50  0.00  25.10  362.00  265.76  136.21  1990  7.78  91.50  0.00  17.75  241.20  265.76  90.76  1991  9.22  63.80  0.00  18.02  285.80  265.76  107.54  1992  11.51  101.00  0.00  22.43  356.70  265.76  134.22  180.30  265.76  67.84  1993  5.82  69.90  0.00  14.36  Table B-6  Continued Monthly rainfall (mTl)  Daily rainfall (mmd ) 1  Month Sept.  Year 1970  4.73  Maximum Minimum 53.50  0.00  Std. dev.  Mean  Total  % of mean  10.69  141.80  103.30  137.27  103.30  399.71  1971  13.76  135.90  0.00  33.47  412.90  1972  0.61  11.40  0.00  2.39  18.20  103.30  17.62  1973 1974  3.72 0.13  26.20 2.80  0.00  7.51 0.55  111.60 4.00  103.30  108.03  0.00  103.30  3.87  1975  4.39  69.20  0.00  13.04  131.80  103.30  127.59  1976  3.65  36.10  0.00  9.92  109.60  103.30  106.10  1977  5.86  57.00  0.00  13.20  175.70  103.30  170.09  1978  2.11  44.80  0.00  8.66  63.40  103.30  61.37  1979  0.00  0.00  0.00  0.00  0.00  103.30  0.00  11.04  70.50  103.30  68.25  1980  2.35  60.00  0.00  1983  3.53  50.70  10.06  106.00  103.30  102.61  31.29  221.00  103.30  213.94  4.43  76.40  103.30  73.96 1.94  1984  7.37  167.90  0.00 0.00  1985  2.55  15.40  0.00  1986  0.07  2.00  0.00  0.37  2.00  103.30  1987  2.35  43.40  0.00  9.01  70.50  103.30  68.25  1988  2.52  44.40  0.00  8.49  75.50  103.30  73.09  1989  0.27  6.10  0.00  1.13  8.10  103.30  7.84  1990  3.45  17.00  0.00  5.71  103.60  103.30  100.29  1991  4.11  71.80  0.00  14.21  123.40  103.30  119.46  0.00  5.16  60.20  103.30  58.28  9.19  186.30  103.30  180.35  1992 Oct.  Mean  2.01  20.80  1993  6.21  31.00  0.00  1970  0.26  8.00  0.00  1.44  8.00  32.02  24.98  1971  0.68  13.80  0.00  2.74  21.20  32.02  66.21  1972  0.00  0.00  0.00  0.00  0.00  32.02  0.00  1973  0.35  10.80  0.00  1.94  10.80  32.02  33.73  1974  7.30 2.66  139.60 47.80  0.00 0.00  27.42 9.09  226.20  32.02 32.02  706.43  82.60  0.00  0.00  0.00  32.02  0.00 0.00 0.00  1975 1976  0.00  0.00  257.96  1977  0.00  0.00  0.00  0.00  0.00  32.02  1978  0.00  0.00  0.00  0.00  0.00  32.02  1979  0.00  0.00  0.00  0.00  0.00  32.02  0.00  1980  0.12  3.70  0.00  0.66  3.70  32.02  11.56  1982  0.00  0.00  0.00  0.00  0.00  32.02  0.00  1983  1.79  35.00  0.00  7.09  55.60  32.02  173.64  1984  0.00  0.00  0.00  0.00  0.00  32.02  0.00  32.02  335.42  1985  3.46  43.80  0.00  9.80  107.40  1986  0.00  0.00  0.00  0.00  0.00  32.02  0.00  1987  1.68  27.10  0.00  6.51  52.10  32.02  162.71  1988  1.32  34.30  0.00  6.18  41.00  32.02  128.04  1989  0.00  0.00  0.00  0.00  0.00  32.02  0.00  1990  0.00  0.00  0.00  0.00  0.00  32.02  0.00  0.00  COO  0.00  32.02  0.00 279.83 19.36  1991  0.00  0.00  1992  2.89  63.50  0.00  12.20  89.60  32.02  1993  0.20  3.40  0.00  0.70  6.20  32.02  Table B-6  Continued Monthly rainfall (mm)  Daily rainfall (mmd ) 1  Month Nov.  Year 1970  0.00  Maximum Minimum 0.00  Std. dev. 0.00  0.00  11.81  0.00  3.00  11.81  25.40  0.00  11.81  0.00  0.00  11.81  0.00  0.00  0.00 0.00  11.81 11.81  0.00 0.00  1971  0.10  3.00  0.00  1972  0.00  0.00  0.00  0.00  1973 1974 1975  0.00  1976 1977  0.00 0.00  % of mean  Mean  Total  0.00  0.55  0.00  0.00 0.00  0.00  0.00 0.00  4.43  85.40  0.00  16.03  132.80  11.81  1124.47  0.23  7.00  0.00  1.28  7.00  11.81  59.27  1978  0.09  2.60  0.00  0.47  2.60  11.81  22.02  1979  3.69  32.90  0.00  8.61  110.80  11.81  938.19  1980  0.00  0.00  0.00  0.00  0.00  11.81  0.00  0.00  0.00  0.00  0.00  11.81  0.00  0.00  0.00  11.81  0.00 0.00  1983 1984  Dec.  Mean  0.00 0.00  0.00 0.00  0.00  0.00  1985  0.00  0.00  0.00  0.00  0.00  11.81  1986  0.00  0.00  0.00  0.00  0.00  11.81  0.00  1987  0.00  0.00  0.00  0.00  0.00  11.81  0.00  1988  0.00  0.00  0.00  0.00  11.81  0.00  1989  0.00  0.00  0.00  0.00  0.00 0.00  11.81  0.00  1990  0.00  0.00  0.00  coo  0.00  11.81  0.00  1991  0.12  3.60  0.00  0.66  3.60  11.81  30.48  1992  0.00  0.00  0.00  0.00  0.00  11.81  0.00  0.00  0.00  11.81  0.00  1993  0.00  0.00  0.00  1970  0.00  0.00  0.00  0.00  0.00  4.51  0.00  1971  0.00  0.00  0.00  0.00  0.00  4.51  0.00  1972  0.00  0.00  0.00  0.00  0.00  4.51  0.00  1973  0.12  3.60  0.00  0.65  3.60  4.51  79.82  1974  0.07  2.20  0.00  0.40  2.20  4.51  48.78  1975  0.00  0.00  0.00  0.00  0.00  4.51  0.00  0.00  0.00  0.00  4.51  0.00  0.00  0.00  4.51  0.00 230.60  1976  0.00  0.00  1977  0.00  0.00  0.00  1978  0.34  8.80  0.00  1.60  10.40  4.51  1979  0.08  1.50  0.00  0.31  2.30  4.51  51.00  1980  0.17  4.20  0.00  0.77  5.20  4.51  115.30  1982  0.00  0.00  0.00  0.00  0.00  4.51  0.00  1983  0.00  0.00  0.00  0.00  0.00  4.51  0.00  0.00  0.00  0.00  0.00  4.51  0.00 631.93  1984  0.00  1985  0.92  28.50  0.00  5.12  28.50  4.51  1986  0.00  0.00  0.00  0.00  0.00  4.51  0.00  1987  1.09  33.70  0.00  6.05  33.70  4.51  747.23  1988  0.00  0.00  0.00  0.00  0.00  4.51  0.00  1989  0.26  8.00  0.00  1.44  8.00  4.51  177.38  1990  0.17  5.30  0.00  0.95  5.30  4.51  117.52  0.00  0.00  0.00  4.51  0.00  0.00  0.00  4.51  0.00  0.00  4.51  0.00  1991 1992 1993  0.00 0.00 0.00  0.00 0.00 0.00  0.00 0.00  0.00  149  T a b l e B-7  A n n u a l rainfall a n d e v a p o r a t i o n s u m m a r y Annual rainfall  Year  1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993  Total  681.80 1506.80 309.10 804.50 1294.00 1011.00 900.10 986.70 991.60 574.00 561.10 640.50 724.30 725.40 791.30 469.10 848.80 562.00 656.10 722.70 634.00 713.82  Mean  777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67 777.67  %of mean  87.67 193.76 39.75 103.45 166.39 130.00 115.74 126.88 127.51 73.81 72.15 82.36 93.14 93.28 101.75 60.32 109.15 72.27 84.37 92.93 81.53 91.79  Daily rainfall depths (mm) 75-100 < 100 (days) (days)  2 1 0 1 3 2 3 1 2 0 0 0 1 0 2 0 1 0 1 0 0 0  0 4 0 1 2 0 0 0 1 2 1 0 1 0 0 0 0 1 0 1 1 0  Annual potential evaporation Total  1922.13 1962.59 2464.50 2394.34 1574.39 2027.10 2329.91 1945.17 2002.97 2617.99 2949.20 2682.10 2912.10 2424.70 2180.60 3221.95 2304.60 2355.10 2645.90 2750.80 2688.10 2964.02  Mean  2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65 2423.65  %of mean  79.31 80.98 101.69 98.79 64.96 83.64 96.13 80.26 82.64 108.02 121.68 110.66 120.15 100.04 89.97 132.94 95.09 97.17 109.17 113.50 110.91 122.30  APPENDIX C DATA CORRECTIONS AND ASSUMPTIONS  Appendix C  Data corrections and assumptions  Table C-1  Assumptions applied to data collected at Kota station  Climatic Measure' tmax tmin  Assumption 0 values missing 0 values missing  Conditions all months, all years 1980-1991 inclusive May-Oct. incl., all years Apr. 1974 3  a  0 0 0 0 0 0  hmax hmin wind sunhr evap rain  values values values values values values  missing missing missing missing missing missing  all months, all years all months, all years all months, all years all months, all years all months, all years Apr. - May incl., 1974 Nov. and Dec. 1-2 incl., 1982 Jan. and Feb. 1-4 incl., 1983 a  a  a  Parameter not measured during this period  Table C-2  Corrections applied to data collected at Kota station  Date (mm-dd-yy) 04/13/70 07/03/70 07/19/70 11/06/70 12/18/70 02/25/72 10/28/73 03/24/76 04/23/76 10/07/76 04/23/78 04/17/79 07/24/79 05/15/79 09/25/79 04/26/87  Climatic Measure tmin evap tmin hmax tmax tmax tmax tmin tmax evap tmax tmax tmin evap evap evap  Original value  Corrected value  1  1.8 87.2 6.0 1.0 2.4 7.0 0.5 115.3 410.3 80.03 14.0 373.5 263.7 133.1 83.6 187.5  41.8 8.72 26.0 missing 24.0 27.0 30.5 11.5 41.0 8.00 41.0 37.4 26.4 13.31 8.36 18.75  Refer to Appendix A for explanation of abbreviations and units of climatic measures  APPENDIX D FREQUENCY ANALYSIS CALCULATION METHODS  153  Appendix D  1.0  Frequency Analysis Calculation methods  Weibull plotting position (1939)  P(X>x) = m / ( N + 1) where m  ranked (ascending) position, m = 1,2,3 ...N total number of values  N  2.0  Equation D-1  Reduced variate y = -ln[ln(T/(T-1)] where T  Equation D-2  return period; T = 1/P probability; P = P ( X > x ) , for maxima P = P(X < x) , for minima  3.0  Gumbel probability distribution (Gumbel, 1954) x = u + a y , for maxima  Equation D-3  x = u - a y , for minima  Equation D-4  T  T  T  T  where x  T  u  magnitude of extreme event, with a return period T mode^of the distribution; u = x - 0.5772a, for maximum distributions u = x + 0.5772a, for maximum distributions mean value  a  slope of the distribution a = (>/6/7i)Sx  Sx  standard deviation reduced variate for return period T  154  4.0  Log Pearson Type III probability distribution  x = 10 T  Equation D-5  y T  where x  T  y  T  magnitude of the extreme event, with a return period T log of the magnitude of extreme event, with a returnperiod T; y = y + K s , for maxima y = y - K s , for minima T  T  T  y  K  T  y  T  y  mean value; y = logx  frequency factor"; K = z + (z -1)k+1/3(z -6z)k - ( z - 1 ) k + z k + 1/3 k 2  3  2  T  2  w, z, k  3  4  5  intermediate variables; z = w-  2.515517 + 0.802853 w +0.010328 w  2  1 + 1.432788 w + 0.189269 w + 0.001308 w 2  w = [In (1 / P ) ] ' 2  1  2  k = C /6 s  C P  n  Kite (1977)  s  coefficient of skewness exceedence probability; P = 1/T (0 < P < 0.5) P = 1/(1-T) (P > 0.5)  3  APPENDIX E EVAPOTRANSPIRATION CALCULATION METHODS  156  Appendix E  Evapotranspiration calculation methods  1.0  Combination Methods  1.1  General form of the Penman Equation (1963) A-ETO = [A/(A+y)] (R - G) + [y/(A+y)] 6.43 Wf(e - e )  [Equation E-1]  0  n  where A.ET  z  z  evapotranspiration  (MJm  slope of vapour pressure and temperature relationship  (kPa°C )  net radiation  ( ( M J m d~ )  G  soil heat flux  (MJm  Y  psychrometric coefficient  (kPa°C )  wind function  (ms )  vapour saturation deficit  (kPa)  0  d" )  2  1  -1  A  R  n  W  f  e° - e z  z  2  2  1  d" ) 1  -1  1  The forms of the Penman Equation differ in the calculation of the wind function (W ), net radiation (R ) and vapour saturation deficit method (Table 1). f  n  Table 1.  Summary of parameters used in various forms of the Penman Equation Wind Function (Wf)  Method  Net Radiation (R ) n  Vapour saturation deficit method (e °-e ) 1  z  Doorenbos and Pruitt (1977) Doorenbos and Pruitt (1977) Wright (1982)  method 3  Doorenbos and Pruitt Doorenbos and Pruitt (1977) (1977) Doorenbos and Pruitt Doorenbos and Pruitt FAO-24 Penman, (1977) (1977) corrected All vapour saturation deficit methods are taken from A S C E , 1990 Correction factor taken from Allen and Pruitt, 1991  method 1  Penman (1963)  Jensen (1974)  1972 Kimberly Penman 1982 Kimberly Penman F A O - 2 4 Penman  Wright and Jensen (1972) Wright (1982)  2  1  2  z  method 3 method 3  method 1  157  1.2  Penman - Monteith Combination Method (Monteith, 1981) A.ET = [A (R - G) + pc [e ° - e j / r j / A+y* n  where XET  p  [Equation E-2]  z  evapotranspiration, alfalfa reference  ( M J m d" )  slope of vapour pressure and temperature relationship  (kPa°C )  net radiation  ( ( M J m d" )  G  soil heat flux  ( M J m ' d" )  P  air density  (kgm )  specific heat at constant pressure  (kJkg" °C )  A  R  c r  n  p  2  2  1  2  1  _3  1  aerodynamic resistance; r = {ln[(z - d)/Zom] ln[(zp - d)/z ]}/[(0.41) u ]  a  1  1  (sm"')  2  a  z  w  z  p  z  o m  w  ov  height of wind speed measurement  (cm)  height of humidity and temperature measurements  (cm)  roughness length for momentum; z = 0.123h  (cm)  mean crop canopy'"  (cm)  roughness length for vapour transfer; 0.1 Z m  (cm)  displacement height of crop; d = 2/3h  (cm)  o m  'c  z  o v  Zov  d  d  c  —  0  0  Y*  psychrometric constant modified by the ratio of resistance to atmospheric resistance; Y* = y (1 + r /r )  (kPa°C~ )  canopy resistance; r = 100/(0.5 LAI)  (sm"')  0  r  c  1  a  c  LAI  leaf area index; LAI = 1.5 ln(h ) - 1.4  (cm) iv  c  u  d  mean daytime wind speed at 2 meters  (ms")  mean crop canopy of 50 cm used for the Daglawada Test Plot Equation for alfalfa with a mean canopy height of more than 3 cm, with periodic harvesting  158  2.0  Temperature methods  2.1  Blaney-Criddle, FAO-24 Method (Doorenbos and Pruitt, 1977) ET =a+bf  [Equation E-3]  Q  where ET  evapotranspiration, grass reference  0  a, b  (mm d ) 1  coefficients ; a = 0.0043 RH in-n/N -1.41 v  m  b = 0.908 + -0.483x10" R H + 0.749 (n/N) + 0.0768 log(U +1) -0.38 x 10" R H ( n / N ) - 0.433 x 1 0 ^ R H U + 0.281 log(U + 1) log(n/N + 1) - 0.00975 log(U +1) log(RH +1) log(n/N + 1) 2  m i n  2  2  d  min  m i n  d  d  2  d  f  Blaney-Criddle factor f = p(.46T + 8.13)  p  mean monthly percent of yearly daytime hours  T  mean temperature  RH in  minimum relative humidity in percent  n/N  ratio of actual to maximum sunshine hours  U  mean daytime wind speed at 2 meters  m  2.2  d  (°C)  (ms')  Hargreaves (Hargreaves and Samani, 1982,1985; Hargreaves et al., 1985) X E T = 0.0023 R T D 0  where A,ET  a  1/2  (T + 17.8)  [Equation E-4]  evapotranspiration, grass reference  (MJm  TD  difference between mean monthly maximum and minimum temperature  (°C)  R  extraterrestrial radiation  (MJm~ d~ )  mean temperature  (°C)  0  a  T  v  min  Allen and Pruitt, 1991  2  2  d" ) 1  1  159  3.0  Radiation Methods  3.1  FAO-24 Radiation Method (Doorenbos and Pruitt, 1977) [Equation E-5]  ET =a+b{[A/(A+y)]R } 0  where ET  s  (mm d" )  evapotranspiration, grass reference  0  a,b  1  constants ; a = -0.3 b = 1.066 - 0.13 x 10" R H n + 0 . 0 4 5 U - 0 . 2 0 X 1 0 " RHmean U - 0.315x10"" R H 2  m e a  d  3  d  m e a n  -0.11 x 10" Ud 2  RHmean  mean relative humidity in percent  R  solar radiation  (mmd ) 1  s  A  slope of vapour pressure and temperature relationship  (kPa°C )  y  psychrometric coefficient  (kPa°C )  mean daytime wind speed at 2 meters  (ms )  U  3.2  d  1  1  1  Modified Jensen-Haise (1971)  XET = C (T - T ) R r  where A.ET C  x  T  [Equation E-6]  s  evapotranspiration, alfalfa reference  r  Ci C C 2  H  2  1  H  constants; d = 38 - (2 Elev/305) C = 7.3  (m) (°C) (kPa)  2  C  x  T s  Allen and Pruitt, 1991  H  = 5.0 / [e°CTx) - e ° ( T ) ] n  intercept of the temperature axis; T  R  2  temperature coefficient; C = 1/(Ci + C C )  T  T  T  ( M J m d' )  (°C)  = {-2.5 - 1 . 4 [ e ( T x ) - e ° ( T ) } - Elev/550 0  x  n  mean temperature  (°C)  solar radiation  (MJm% ) 1  e°(Tx)  saturation vapour pressure at mean maximum temperature for the warmest month " of the year  (kPa)  e°(T )  saturation vapour pressure at mean minimum temperature for the warmest month of the year  (kPa)  Elev  elevation above sea level  (m)  v  n  Warmest month of the year for Kota station during the years 1970 - 1993 is May  161  4.0  Pan Evaporation Methods  4.1  FAO-24 Pan Evaporation Method ET  — 0  [Equation E-7]  kp Epan  where ET  0  Epan  kp  evapotranspiration, grass reference  (mmd )  pan evaporation  (mmd )  1  1  pan coefficient "; k = 0.482 + 0.024 log(Fetch) - 0.376 x 10" U + 0.0045*RH Vl  3  p  d  m e a n  Fetch  windward side distance of ground c o v e r  U  mean daytime wind speed at 2 meters  d  RH ean  Christiansen-Hargreaves ET  (ms"')  mean relative humidity in percent  m  4.2  (m)  IX  0  Pan Evaporation Method (1969) [Equation E-8]  - 0.755 Epan Cj2 CW2 CH2 CS2  where ET  0  Epan  evapotranspiration, grass reference  (mmd )  pan evaporation  (mm)  1  CT2, C 2 , C 2 , C coefficients C = 0.862 + 0.179 (T/T ) - 0.041 ( T / T r W  H  S 2  T 2  co  C  W 2  C  S 2  C  = 1.189 - 0.240 (Ud/Wo) - 0.051 (U A/V ) D  0  = 0.499 + 0.620 ( R H  H 2  S , T o, Wo, 0  constants  0  RH  m  o  =  0.60  S =  0.80 Too = 20 ° C 0  v m K  0  = 0.904 + 0.0080 (S/S ) + 0.088 ( S / S )  - 0.119 ( R H Rmo>  co  Snyder (1993) Fetch of 100 m assumed for the Kota station  m e  0  m e a  n/RHmo)  an/RH r m o  2  2  162  W Ud RHmean S  0  = 6.7 kmh"  1  mean daytime wind speed at 2 meters mean relative humidity, in percent percentage of possible sunshine hours in a day, expressed decimally  (kmh ) 1  5.0  Common Parameters  5.1  Atmospheric and thermodynamic parameters  5.1.1  Latent heat of vaporization (ASCE, 1990) X = 2.501 - 0.002361 T where T  5.1.2  (MJkg ) 1  mean temperature  (°C)  Psychrometric coefficient (ASCE, 1990) y = c P /0.622 X  (kPa°C" ) 1  p  where cp  specific heat at constant pressure  P  atmospheric pressure P = 101.3 (288 - 0.01 Elev) /288  X g  (kJkg" °C ) 1  1  (kPa) s / ( a R )  latent heat of vaporization  (MJkg )  acceleration of gravity; g = 9.8 m s '  (ms' )  the lapse rate a = 0.0065 K m " , for saturated air;  (Km )  specific gas constant for dry air; R = 287.0 Jkg" K"  (Jkg" K )  1  1  1  a  1  1  R  1  5.1.3  1  1  1  Slope of vapour pressure and temperature relationship (ASCE, 1990) A = 0.200*(0.00738 T + 0.8072) - 0.000116  (kPa°C )  mean temperature  (°C)  7  1  where T 5.1.4  Soil heat flux  x  G = 4.2 (T where i T  i+1  - Tj_i)/At  (MJmV)  time period mean temperature for the period i  (°C)  As soil heat flux is relatively small compared to other terms in ET calculations, G is assumed to be 0 (Burman, 1995)  x  164  5.1.5  (days)  time in days between the midpoints of the 2 time periods  At  Dew point temperature (ASCE, 1990) T = (116.9 + 237.3 ln(e ))/(16.78 - ln(e ))  (°C)  actual vapour pressure  (kPa)  d  where e  a  g  a  5.2  Solar and Net Radiation Estimates  5.2.1  Extraterrestrial radiation (Duffie and Beckman, 1980) R =  (24(60)/7i)G d *[(w )sin((())sin(8)+cos((|))cos(8)sin(w )] sc  r  s  s  (MJm" d" ) 2  1  where solar c o n s t a n t ' ;  G  x  G  (MJm" min" ) 2  1  = 0.0820 sc  declination 8 = 0.4093*sin(27t)*((284+J)/365) d  (radians)  relative distance of the earth from the sun d =1 + 0.033cos(27t J/365)  r  r  sunset hour angle  Wc  (radians)  w = cos-1 (-tan((|>)tan(8)) s  location latitude, positive for north latitudes and negative for south latitudes J 5.2.2  (radians)  day of the year (1-366)  Solar radiation (Doorenbos and Pruitt, 1977) R = (a+b(n/N))R s  (MJnrf d~ ) 2  a  1  where a,b  constants  n/N  ratio between actual measured bright sunshine hours to maximum possible sunshine hours  XM  A s evaluated by the International Association of Meteorology and Atmospheric Physics (IAMAP) (London and Frohlich, 1982, cited in ASCE 1990) Values for a and b were taken from the experimentally determined constants for the radiation equation for a latitude of 24°, reported in Appendix VI, Doorenbos and Pruitt (1977); a = 0.28; b = 0.49 xi  x i i  165  5.2.3  Clear sky solar radiation (Doorenbos and Pruitt, 1977)  R = 0.75 R so  (MJrrrV)  a  where extraterrestrial radiation  5.2.4  (MJm d ) 2  1  Net long wave radiation  5.2.4.1 FAO 24 method R = (1 - cx)R - R n  s  where a  (MJm" d ) 2  b  1  albedo  xiii  net thermal radiation for clear skies or partly cloudy conditions; R = [0.9*(Rs/R )+b] * R b  ?  so  b 0  net outgoing long-wave radiation on a clear day Rbo <bo = s aT  b0  :  1  4  constant XIV.  b ,1  net emittance expression (Brunt (1932) e^^+b^e/ ] 2  a1,b1 CT  x v  coefficients Stefan-Boltzmann constant a = 4.903x10"  (MJm" d~ K )  mean temperature  (°K)  2  2  4  9  T R  s  solar radiation  (MJm" d )  R  s 0  clear sky solar radiation  (MJm" d )  e  d  vapour pressure at dew point temperature  2  2  1  1  (kPa)  ™ Albedo is set to 0.23, representing an average value of the full cover range of most green field crops (ASCE, 1990) value taken from Doorenbos and Pruitt (1977); b = 0.1 xiv  ™ The regression coefficients ai and b^ are assigned the general values for arid areas suggested by Budyko (1956) presented in table 3.3 (ASCE, 1990); ai = 0.39; b, = 0.158  166  5.2.4.2 Wright, 1982 method R = (1 - a ) R - R n  where a  s  (MJm" d~ ) 2  b  1  albedo a = 0.29 + 0.06 sin[30 (m + 0.0333 N + 2.25)]  m  month (1-12)  N  the day of the month (1 -31)  R  b  net thermal radiation for clear skies or partly cloudy conditions; Rb = [a (Rs/Rso) + b] R b 0  R  b 0  net outgoing long-wave radiation on a clear day Rbo = E CTT 1  a,b  constants; for R / R values > 0.7 a = 1.126 b = -0.07 for Rs/Rso values < 0.7 a = 1.017 b = -0.06 s  e  4  s o  net emittance expression (Brunt (1932)  1  a^b-i  coefficients; a = 0.26+0.1 exp{-[0.0154(30m+N-207)] } 2  i  ^=0.139 a  Stefan-Bbltzmann constant a = 4.903x10"  (MJm" d" K )  mean temperature  (°K)  2  2  9  T R  s  solar radiation  (MJm~ d )  R  s o  clear sky solar radiation  (MJm" d )  vapour pressure at dew point temperature  (kPa)  e  d  2  2  1  1  4  167  5.3.0  Vapour pressure  5.3.1  Saturation vapour pressure (Tetens, 1930; Murray, 1967) e = exp [(16.78 T -116.9) / ( T + 237.3)] s  where T  5.3.2  mean temperature  (kPa)  (°C)  Actual vapour pressure (ASCE 1990) e  = e  a  [RH  s  m a x  - RH  m i n  / 2) / 1 0 0 ]  (kPa)  where e  5.3.3  saturation vapour pressure  s  (kPa)  RHmax  maximum relative humidity in percent  RHmin  minimum relative humidity in percent  Vapour pressure deficit method 1 (ASCE 1990) (e ° - e ) = e ° ( T ) - e ° ( T d ) 2  z  where e°(T)  vapour pressure at temperature  (kPa)  e°(T )  vapour pressure at dew point temperature  (kPa)  d  5.3.4  Vapour pressure deficit method 3 (ASCE 1990) (e ° 2  = [e°(T) + e ° ( T ) ] / 2 - e°(T ) d  where °(Tx)  vapour pressure at maximum daily temperature  (kPa)  e°(T )  vapour pressure at minimum daily temperature  (kPa)  e°(T )  vapour pressure at dew point temperature  (kPa)  e  n  d  5.4.0  Aerodynamic parameters  5.4.1  Original Wind function (Jensen, 1974) W = 1 + 0.536 u f  where u d  d  mean daytime wind speed at 2 meters  -D  (ms  168  5.4.2  Wright and Jensen (1972) wind function W = 0.75 + 0.993 u f  where u  mean daytime wind speed at 2 meters  d  5.4.3  (ms ) 1  FAO-24, Doorenbos and Pruitt (1977) W = 1 + 0.864*u f  where u  2  mean daytime wind speed at 2 meters  d  5.4.4  2  (ms ) 1  Wright (1982) wind function W  f  where u  = a +bw*u w  d  mean daytime wind speed at 2 meters  d  a ,bw  (ms ) 1  coefficients  w  a =0.4 + 1.4 exp{-[(J - 173) / 58] } bw = 0.007 + 0.004 exp{-[(J - 243) / 80] } 2  w  2  J  5.4.5  calendar day of the year (1 -366)  Daytime wind speed U = [2 U d  where U /U d  U4 2  n  2 4  ( U / U )] / (1 + U /U ) d  n  d  n  (ms ) 1  ratio of daytime to nightime wind speeds, estimated at 2.0 (Doorenbos and Pruitt, 1977) 24 hour average wind speed  (ms ) 1  169  APPENDIX F CHARACTERISTICS OF THE MONSOON SEASON  170  Appendix F  Characteristics of the monsoon season  Table F-1  Summary of monsoon season characteristics  Year  Start date  1  Annual cycle Model monsoon season length Rain days Length Total End First (days) rainfall (number) (days) significant date (mm) rainfall — 37 632.00 103 17-Jun 12-Sep 365 44 1382.90 99 8-Sep 1-Jun 374 24 281.70 83 9-Jun 31-Aug 369 40 739.30 91 13-Jun 12-Sep 360 36 1207.80 125 9-Jun 11-Oct 361 57 912.30 101 9-Jun 13-Sep 369 56 838.80 169 7-Jun 23-Nov 369 41 888.10 86 11-Jun 5-Sep 366 41 907.20 81 1-Sep 12-Jun 367 37 530.00 167 15-Jun 28-Nov 361 39 534.00 3-Sep 86 13-Jun 48 — 593.70 10-Oct 121 11-Jun 368 26 676.40 84 13-Jun 5-Sep 354 42 689.20 9-Oct 129 2-Jun 383 29 722.60 58 20-Jun 17-Aug 354 28 433.10 19-Oct 132 9-Jun 363 42 794.70 109 23-Sep 6-Jun 360 26 516.90 87 7-JUn 27-Aug 377 38 597.40 94 19-Jun 15-Sep 367 26 682.50 80 15-Jun 3-Sep 359 28 125 589.40 11-Oct 14-Jun 370 44 657.62 99 13-Jun 20-Sep 3  4  5  6  Annual rainfall (mm)  2  1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 2 3  4 5  6  1-Jun 1-Jun 9-Jun 13-Jun 8-Jun 4-Jun 7-Jun 11-Jun 12-Jun 14-Jun 9-Jun 11-Jun 13-Jun 2-Jun 20-Jun 9-Jun 6-Jun 1-Jun 13-Jun 15-Jun 8-Jun 13-Jun  Defined Defined Defined season Defined Defined Number  681.80 1506.80 309.10 804.50 1294.00 1011.00 900.10 986.70 991.60 574.00 561.10 640.50 724.30 725.40 791.30 469.10 848.80 562.00 656.10 722.70 634.00 713,82  as the first day of June with > 0.1 mm of recorded rain as > 5.0 mm of rainfall as the day on which 90% of yearly rainfall is recorded after the start of the monsoon as the number of days between the start and end dates as the number of days between successive monsoon season start dates of days with > 0.1 mm of recorded rain, within the defined monsoon season  171  c rs cu E E o  c o o (0  c o E  cu  •a o E o  3 t  co Q.  cu  •u cu > Zi  « 3 E 3  o  3 O)  (LULU)  ueaiu  UIOJJ  sjn^iedap aAi)e|nuino  cu o  APPENDIX G MARKOV CHAIN ANALYSIS RESULTS  AiHjqeqoJd  Table G-1 5 day  Transition probabilities over fixed 5 day intervals, by year  Interval 1-5  6-10  P01  P11  Poi  September  August  July  June  Year  P11  Pd  P«  P11  Poi  0.50  0.50  0.67  0.67  0.00  1.00  0.33  0.50  0.00  0.50  0.00  0.00  0.33  0.50  0.00  1.00  0.67  1970  0.50  0.00  1.00  1.00  1971  0.50  0.33  0.25  1972  0.00  0.00  0.33  1973  0.00  0.00  0.25  0.00  0.25  1974  0.00  0.00  0.25  0.00  0.50  0.67  0.00  0.00  1975  0.25  0.00  1.00  0.67  0.33  1.00  0.67  0.50  1976  0.00  0.00  0.20  0.00  0.00  1.00  1.00  0.67  1.00  1.00  1977  0.00  0.00  0.00  0.80  0.00  1.00  1978  0.00  0.00  0.00  0.80  0.00  0.00  0.25  0.00  1979  0.00  0.00  0.00  0.00  1.00  0.75  0.00  0.00  1980  0.00  0.00  0.25  0.00  1.00  1.00  0.33  1.00 1.00  0.50  0.67  1.00  0.50  0.50  0.00  1.00  0.67  1.00  0.75  0.50  1.00  0.50  0.00  0.00  1.00  0.75  0.50  0.67  0.00  0.00  0.00  0.00  0.33  0.00  0.00  0.00  1987  0.00  0.00  0.33  0.00  0.00  0.00  0.25  0.00  1988  0.00  0.00  1.00  0.33  0.33  0.50  0.00  0.00  1989  0.00  0.50  0.50  0.33  0.00  0.00  0.50  0.00  0.50  0.00  1983  0.00  0.00  1984  0.00  1985  0.33  1986  1990  0.00  0.00  1.00  1.00  1.00  1.00  1991  0.00  0.00  0.00  0.00  0.00  0.50  1.00  0.67  1992  0.00  0.00  0.00  0.00  0.67  0.00  0.25  1.00  0.00  0.50  0.67  1.00  1.00  1993  0.00  0.00  0.50  1970  0.00  0.00  0.25  0.00  0.50  1.00  1.00  0.75  1971  0.25  0.00  0.67  0.00  0.25  0.00  0.00  1.00  1972  0.25  1.00  0.33  0.50  0.50  1.00  0.00  0.00  1973  0.00  0.00  0.67  0.00  0.50  0.33  0.00  0.75  1974  0.33  0.50  0.20  0.00  0.50  0.67  0.00  0.00  1975  0.25  0.00  0.50  0.67  1.00  0.75  1.00  0.33  1976  0.50  1.00  0.00  0.75  1.00  0.50  0.00  0.80  1977  0.00  0.00  0.50  0.67  0.00  0.80  0.33  0.00  0.67  0.00  0.00  0.00  1978  0.00  0.00  1.00  1.00  1979  0.00  0.00  0.33  1.00  1.00  0.75  0.00  0.00  1980  0.25  0.00  1.00  0.67  0.00  0.75  0.00  0.00 0.33  1983  0.00  0.00  0.00  0.67  0.25  0.00  0.50  1984  0.00  0.00  0.50  0.33  0.25  0.00  0.00  0.50  1985  0.00  0.00  0.00  0.00  1.00  1.00  0.00  0.00  0.67  0.00  0.00  1986  0.00  0.00  0.25  1.00  0.50  1987  0.25  0.00  0.33  0.50  0.33  0.50  0.00  0.00  1988  0.25  0.00  0.00  0.00  0.00  0.50  0.25  0.00  1989  0.50  0.00  0.25  0.00  1.00  0.67  0.00  0.00  1990  0.00  0.00  0.00  0.00  0.50  0.67  1.00  0.75  1991  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.33  0.50  0.00  0.67  0.33  0.00  0.67  1.00  0.33  1992  0.25  0.00  0.00  1993  0.00  0.00  0.50  Table G-1 5 day  Continued  Interval 11-15  16-20  P01  P11  P01  September  August  July  June  Year  P11  P11  P01  P01  P11  1970  0.00  0.00  0.00  0.50  1.00  0.75  0.00  0.80  1971  0.00  0.00  0.25  0.00  1.00  0.50  0.33  0.00  0.00  0.00  0.00  0.00  0.00  1972  0.00  0.00  0.00  1973  0.25  0.00  1.00  1.00  0.50  0.67  0.33  0.50  1974  0.00  0.00  1.00  0.75  1.00  0.00  0.00  0.00  0.00  1.00  0.00  1.00  1975  0.00  0.00  1.00  0.75  1976  0.00  0.00  1.00  0.67  0.25  1.00  0.25  0.00  1977  0.50  0.67  1.00  0.67  0.00  0.00  0.50  0.00  1978  0.33  0.50  0.00  0.80  1.00  0.67  0.00  0.00  0.00  0.00  1979  0.25  1.00  0.00  1.00  0.50  0.67  1980  0.50  0.00  0.00  0.75  0.00  0.00  0.00  0.00  1983  0.67  0.00  1.00  0.67  1.00  0.75  0.00  0.00  1984  0.25  0.00  0.00  0.00  0.00  0.50  0.00  0.00 0.00  1985  0.25  0.00  0.33  0.50  1.00  0.75  0.25  1986  0.00  0.00  0.00  0.00  0.33  0.50  0.00  0.00  1987  0.25  0.00  0.33  0.50  0.00  0.00  0.00  0.00  0.00  0.50  0.67  0.00  0.00  1988  0.00  0.00  0.67  1989  0.00  0.00  0.00  0.00  0.00  1.00  0.00  0.00  1990  0.25  0.00  0.25  0.00  0.25  0.00  0.25  0.00  1991  0.20  0.00  0.20  0.00  0.00  0.00  0.00  0.00 0.00  1992  0.00  0.00  0.25  0.00  0.50  0.33  0.00  1993  0.33  1.00  0.33  0.50  0.00  0.00  0.00  0.80  0.50  0.33  0.00  0.00  1970  0.25  0.00  0.00  0.00  1971  0.00  0.00  0.67  0.00  0.50  0.67  0.00  0.00  1972  0.00  0.00  0.00  0.00  1.00  1.00  0.00  0.00  0.00  0.00  0.00  1973  0.00  0.00  1.00  0.75  0.25  1974  0.00  0.00  0.00  1.00  0.20  0.00  0.00  0.00  1975  0.25  1.00  0.00  1.00  0.00  1.00  0.33  0.00  1976  0.67  0.50  0.33  0.00  0.00  0.80  0.00  0.00  1977  0.00  0.00  0.00  0.75  0.00  0.00  0.00  0.50  1978  0.50  1.00  0.25  0.00  0.50  0.67  0.33  0.50  1979  0.00  0.00  1.00  0.75  0.00  0.00  0.00  0.00 0.00  1980  0.33  0.00  0.00  0.00  0.20  0.00  0.00  1983  0.00  0.00  0.50  0.33  1.00  0.67  0.20  0.00  1984  0.00  0.00  0.33  1.00  1.00  1.00  0.00  0.00 0.00  1985  0.00  0.00  1986  0.20  0.00  1987  0.25  0.00  0.00  1.00  0.50  0.00  1.00  1.00  0.67  0.50  0.00  0.00  0.25  0.00  0.25  0.00  0.33  0.50  0.67  0.50  0.25  1988  0.33  0.50  0.33  1.00  0.25  0.00  1989  0.25  0.00  0.25  0.00  0.50  0.33  0.00  0.00  1990  0.25  0.00  1.00  0.33  0.50  0.33  0.50  0.67  0.50  1.00  0.00  0.00  1991  0.00  0.00  0.50  , 0.67  1992  0.00  0.00  0.25  0.00  1.00  0.75  0.25  0.00  1993  0.00  0.80  1.00  0.75  0.50  0.67  0.20  0.00  Table G-1 5 day  Continued  21-25  26-31  June  Year  Interval  Poi  0.00  September  August  July P11  Poi  P11  P11  Poi  Poi  P11  0.00  0.25  0.00  0.33  0.50  1970  0.00  0.00  1971  0.67  0.00  1.00  1.00  0.50  0.67  0.00  0.00  1972  0.67  0.00  0.00  0.00  0.33  0.50  0.00  0.00  1973  0.00  0.00  0.00  0.75  1.00  0.80  0.33  0.50  1974  0.20  0.00  0.00  1.00  0.00  0.80  0.20  0.00  1975  0.00  0.50  1.00  0.75  0.00  0.75  0.00  0.00  1976  0.00  0.50  0.50  0.67  0.25  1.00  0.00  0.00  0.20  0.00  0.00  0.00  1977  0.50  0.00  0.67  0.50  1978  0.50  0.33  0.25  1.00  1.00  0.75  0.00  0.00  1979  1.00  0.67  0.00  0.00  0.00  0.00  0.00  0.00  1980  1.00  0.75  0.25  0.00  0.33  0.50  0.00  0.00  1983  0.25  0.00  0.50  1.00  1.00  0.33  0.00  0.00  1984  0.00  0.00  0.00  0.00  1.00  0.75  0.00  0.00  1985  0.00  0.00  0.50  1.00  0.25  0.00  0.33  1.00  1986  0.00  0.80  0.00  1.00  0.00  0.00  0.00  0.00  1987  0.25  0.00  0.00  0.00  1.00  1.00  0.25  0.00  1988  0.50  0.00  0.00  1.00  0.33  1.00  1.00  0.50  1989  0.25  0.00  1.00  0.67  0.33  1.00  0.20  0.00  0.67  0.00  0.00  0.50  0.00  1990  0.25  0.00  0.20  1991  0.00  0.00  0.00  1.00  1.00  0.75  0.00  0.00  1992  0.00  0.00  1.00  0.67  0.20  0.00  0.00  0.00  1993  0.67  0.50  0.00  0.00  0.00  0.00  0.50  0.67  1970  1.00  0.00  0.20  0.00  0.25  1.00  0.25  0.00  1.00  1.00  0.00  0.83  0.67  0.67  0.25  0.00  1972  1.00  0.67  0.00  0.00  0.33  0.67  0.00  0.00  1973  0.00  0.00  0.00  0.00  1.00  1.00  0.00  0.00  1974  0.00  0.50  0.00  0.50  0.00  0.00  0.33  0.00  1975  0.25  1.00  0.00  0.00  0.50  1.00  0.00  0.00  1976  0.00  0.00  0.50  0.50  1.00  0.80  0.00  0.00  1977  0.00  1.00  1.00  0.80  0.00  1.00  0.00  0.00  0.00  1.00  0.00  0.00  1971  1978  0.67  0.50  0.50  0.50  1979  0.33  0.00  0.00  0.00  0.00  0.00  0.00  0.00  1980  0.50  0.67  1.00  1.00  . 0.25  0.50  0.00  0.00  0.00  0.00  0.00  1983  0.25  1.00  0.00  0.83  0.20  1984  0.00  0.00  0.00  0.00  0.25  0.00  0.00  0.00  1985  0.00  0.00  0.50  0.75  0.17  0.00  0.00  0.75  0.00  0.00  0.25  0.00  1986  0.00  0.00  0.00  1.00  1987  0.25  0.00  0.00  0.00  1.00  0.80  0.00  0.00  1988  1.00  0.33  1.00  0.50  0.00  0.75  0.00  0.00  0.83  0.00  0.00  0.00  0.00  0.50  0.00  0.33  1.00  0.00  0.50  0.20  1.00  0.00  0.00  0.00  0.00  0.33  0.67  0.33  0.67  0.00  0.00  1992  0.00  0.00  1.00  0.25  0,25  0.50  0.00  0.00  1993  0.50  0.33  0.25  0.50  0.00  0.00  0.00  0.00  1989  0.25  1990 1991  Table G-2  Markov Chain Analysis, monthly  Month - Jun. Sequence dry-dry dry-wet wet-dry wet-wet  Actual™  Transition probability  446.00 77.00 78.00 58.00  P P P Pn  0 0  0 1  1 0  = = = =  0.853 0.147 0.574 0.426  Test of Independence: second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual  Predicted™' 379.50 65.52 44.16 32.84 66.52 11.48 33.26 24.74  389.00 56.00 48.00 29.00 57.00 21.00 29.00 29.00 12.93 0.002  Chi-square 0.24 1.38 0.33 0.45 1.36 7.89 0.55 0.74  with 2 d.f.  Test of Independence: second and third preceding days Sequence dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet Chi-square sum Prob.  Actual  Predicted  342.00 47.00 36.00 20.00 33.00 15.00 15.00 14.00 47.00 9.00 12.00 9.00 23.00 6.00 14.00 15.00  331.70 57.27 32.12 23.88 40.93 7.07 16.63 12.37 47.76 8.24 12.04 8.96 24.73 4.27 16.63 12.37  15.96 0.002  with 6 d.f.  Chi-square 0.32 1.84 0.47 0.63 1.54 8.91 0.16 0.22 0.01 0.07 0.00 0.00 0.12 0.70 0.42 0.56  Number of occurrences of the indicated combination of wet and dry states in the interval Number of occurrences predicted by the Markov Chain analysis  Table G-2 Month - Jul  Continued  Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  285.00 100.00 100.00 197.00  Transition probability Poo= Poi = P = Pn = 1 0  0.740 0.260 0.337 0.663  Test of Independencersecond preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet  Chi-square sum Prob.  Actual  Predicted 211.00 74.03 33.67 66.33 74.03 25.97 66.33 130.70  225.00 60.00 42.00 58.00 60.00 40.00 58.00 139.00  18.51 0.000  Chi-square 0.93 2.66 2.06 1.05 2.66 7.57 1.05 0.53  with 2 d.f.  Test of Independence: second and third preceding days Sequence dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet Chi-square sum Prob.  Actual  Predicted  184.00 40.00 25.00 35.00 28.00 14.00 22.00 36.00 41.00 20.00 17.00 23.00 32.00 26.00 36.00 103.00  165.80 58.18 20.20 39.80 31.09 10.91 19.53 38.47 45.16 15.84 13.47 26.53 42.94 15.06 46.80 92.20  28.40 0.000  with 6 d.f.  Chi-square 1.99 5.68 1.14 0.58 0.31 0.88 0.31 0.16 0.38 1.09 0.93 0.47 2.79 7.94 2.49 1.27  Table G-2 Month - Aug  Continued  Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  242.00 105.00 105.00 230.00  Transition probability Poo= 0.697 P01 = 0.303 Pio=  0.313  P n = 0.687  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  168.8 73.23 32.91 72.09 73.23 31.77 72.09 157.9  181.0 61.00 34.00 71.00 61.00 44.00 71.00 159.0 9.75 0.008  Chi-square 0.89 2.04 0.04 0.02 2.04 4.71 0.02 0.01  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  133.00 48.00 18.00 43.00 20.00 14.00 17.00 54.00 48.00 13.00 16.00 28.00 41.00 30.00 54.00 105.0  126.20 54.77 19.12 41.88 23.71 10.29 22.25 48.75 42.54 18.46 13.79 30.21 49.52 21.48 49.84 109.2  Chi-square sum Prob.  13.20 0.040  with 6 d.f.  Chi-square 0.36 0.84 0.07 0.03 0.58 1.34 1.24 0.57 0.70 1.61 0.35 0.16 1.46 3.38 0.35 0.16  Table G-2 Month - Sep  Continued  Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  450.00 63.00 63.00 84.00  Transition probability P = Poi = P = P11 = 0 0  1 0  0.877 0.123 0.429 0.571  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual  Predicted 394.70 55.26 27.00 36.00 55.26 7.74 36.00 48.00  401.00 49.00 28.00 35.00 49.00 14.00 35.00 49.00 6.70 0.035  Chi-square 0.10 0.71 0.04 0.03 0.71 5.07 0.03 0.02  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  361.00 40.00 24.00 25.00 23.00 5.00 14.00 21.00 40.00 9.00 4.00 10.00 26.00 9.00 21.00 28.00  Chi-square sum Prob.  12.37 0.054  Predicted 351.80 49.25 21.00 28.00 24.56 3.44 15.00 20.00 42.98 6.02 6.00 8.00 30.70 4.30 21.00 28.00 with 6 d.f.  Chi-square 0.24 1.74 0.43 0.32 0.10 0.71 0.07 0.05 0.21 1.48 0.67 0.50 0.72 5.14 0.00 0.00  Table G-3 Month - Jun  Markov chain analysis -10 day intervals 1-10 Sequence  Actual  dry-dry dry-wet wet-dry* wet-wet  174.00 15.00 22.00 8.00  Transition probability Poo= P01 = Pio= Pn =  0.921 0.079 0.733 0.267  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual 156.00 14.00 11.00 5.00 18.00 1.00 10.00 3.00 0.46 0.793  Predicted 156.50 13.49 11.73 4.27 17.49 1.51 9.53 3.47  Chi-square 0.00 0.02 0.05 0.13 0.01 0.17 0.02 0.06  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  140.0 11.00 9.00 4.00 9.00 0.00 5.00 2.00 16.00 3.00 2.00 1.00 8.00 1.00 5.00 1.00  139.0 11.98 9.53 3.47 8.29 0.71 5.13 1.87 17.49 1.51 2.20 0.80 8.29 0.71 4.40 1.60  Chi-square sum Prob.  3.09 0.797  with 6 d.f.  Chi-square 0.01 0.08 0.03 0.08 0.06 0.71 0.00 0.01 0.13 1.48 0.02 0.05 0.01 0.11 0.08 0.23  Table G-3 Month - Jun  Continued 10-20 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  155.00 25.00 24.00 16.00  Transition probability P = P = P = Pn = 00  01  10  0.861 0.139 0.600 0.400  Test of Independence-second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual 133.00 21.00 16.00 8.00 22.00 4.00 8.00 8.00 1.17 0.558  Predicted 132.60 21.39 14.40 9.60 22.39 3.61 9.60 6.40  Chi-square 0.00 0.01 0.18 0.27 0.01 0.04 0.27 0.40  with 2 d.f.  Test of Independence: second and third preceding days Sequence dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet Chi-square sum Prob.  Actual 112.0 20.00 13.00 8.00 15.00 3.00 5.00 3.00 21.00 1.00 3.00 0.00 7.00 1.00 3.00 5.00 5.65 0.463  Predicted 113.7 18.33 12.60 8.40 15.50 2.50 4.80 3.20 18.94 3.06 1.80 1.20 6.89 1.11 4.80 3.20 with 6 d.f.  Chi-square 0.02 0.15 0.01 0.02 0.02 0.10 0.01 0.01 0.22 1.38 0.80 1.20 0.00 0.01 0.68 1.01  Table G-3 Continued Month - Jun 20-30 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  117.00 37.00 32.00 34.00  Transition probability P = Poi= P = Pn = 0 0  1 0  0.760 0.240 0.485 0.515  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual  Predicted  100.00 21.00 21.00 16.00 17.00 16.00 11.00 18.00 16.07 0.000  91.93 29.07 17.94 19.06 25.07 7.93 14.06 14.94  Chi-square 0.71 2.24 0.52 0.49 2.60 8.22 0.67 0.63  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry'-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  90.00 16.00 14.00 8.00 9.00 12.00 5.00 9.00 10.00 5.00 7.00 8.00 8.00 4.00 6.00 9.00  80.53 25.47 10.67 11.33 15.95 5.05 6.79 7.21 11.40 3.60 7.27 7.73 9.12 2.88 7.27 7.73  Chi-square sum Prob.  21.92 0.001  with 6 d.f.  Chi-square 1.11 3.52 1.04 0.98 3.03 9.59 0.47 0.44 0.17 0.54 0.01 0.01 0.14 0.43 0.22 0.21  Table G-3 Month - Jul  Continued 1-10 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  99.00 37.00 37.00 47.00  Transition probability Poo= P = P = Pn = 0 1  1 0  0.728 0.272 0.440 0.560  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  72.07 26.93 15.86 20.14 26.93 10.07 21.14 26.86  77.00 22.00 17.00 19.00 22.00 15.00 20.00 28.00 4.82 0.090  Chi-square 0.34 0.90 0.08 0.06 0.90 2.42 0.06 0.05  with 2 d.f.  Test of Independence: second and third preceding days Sequence dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet Chi-square sum Prob.  Actual 64.00 16.00 10.00 10.00 11.00 5.00 8.00 12.00 13.00 6.00 7.00 9.00 11.00 10.00 12.00 16.00 7.27 0.297  Predicted 58.24 21.76 8.81 11.19 11.65 4.35 8.81 11.19 13.83 5.17 7.05 8.95 15.29 5.71 12.33 15.67 with 6 d.f.  Chi-square 0.57 1.53 0.16 0.13 0.04 0.10 0.07 0.06 0.05 0.13 0.00 0.00 1.20 3.22 0.01 0.01  Table G-3 Month - Jul  Continued 10-20  Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  83.00 36.00 35.00 66.00  Transition probability Poo= 0.697  P01 = 0.303 P i o = 0.347  P n = 0.653  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual  Predicted 58.59 25.41 13.51 25.49 24.41 10.59 21.49 40.51  62.00 22.00 18.00 21.00 21.00 14.00 17.00 45.00 5.94 0.051  Chi-square 0.20 0.46 1.49 0.79 0.48 1.10 0.94 0.50  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  48.00 15.00 12.00 13.00 12.00 6.00 9.00 13.00 14.00 7.00 6.00 8.00 9.00 8.00 8.00 32.00  43.94 19.06 8.66 16.34 12.55 5.45 7.62 14.38 14.65 6.35 4.85 9.15 11.86 5.14 13.86 26.14  Chi-square sum Prob.  10.25 0.115  with 6 d.f.  Chi-square 0.37 0.86 1.29 0.68 0.02 0.06 0.25 0.13 0.03 0.07 0.27 0.14 0.69 1.59 2.48 1.31  Table G-3 Month - Jul  Continued 20-31 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  103.00 27.00 28.00 84.00  Transition probability Poo= Poi = P = Pn = i 0  0.792 0.208 0.250 0.750  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual  Predicted 80.82 21.18 6.25 18.75 22.18 5.82 21.75 65.25  86.00 16.00 7.00 18.00 17.00 11.00 21.00 66.00 7.59 0.022  Chi-square 0.33 1.27 0.09 0.03 1.21 4.62 0.03 0.01  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  72.00 9.00 3.00 12.00 5.00 3.00 5.00 11.00 14.00 7.00 4.00 6.00 12.00 8.00 16.00 55.00  64.18 16.82 3.75 11.25 6.34 1.66 4.00 12.00 16.64 4.36 2.50 7.50 15.85 4.15 17.75 53.25  Chi-square sum Prob.  14.43 0.025  with 6 d.f.  Chi-square 0.95 3.64 0.15 0.05 0.28 1.08 0.25 0.08 0.42 1.60 0.90 0.30 0.93 3.56 0.17 0.06  Table G-3 Month - Aug  Continued 1-10 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  65.00 36.00 40.00 79.00  Transition probability Poo= P01 = Pio= Pn =  0.644 0.356 0.336 0.664  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual  Predicted  Chi-square  42.00 22.00 13.00 23.00 23.00 14.00 27.00 56.00  41.19 22.81 12.10 23.90 23.81 13.19 27.90 55.10  0.02 0.03 0.07 0.03 0.03 0.05 0.03 0.01  0.27 0.875  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  29.00 15.00 7.00 16.00 6.00 4.00 6.00 19.00 13.00 7.00 6.00 7.00 17.00 10.00 21.00 37.00  28.32 15.68 7.73 15.27 6.44 3.56 8.40 16.60 12.87 7.13 4.37 8.63 17.38 9.62 19.50 38.50  Chi-square sum Prob.  2.39 0.881  with 6 d.f.  Chi-square 0.02 0.03 0.07 0.04 0.03 0.05 0.69 0.35 0.00 0.00 0.61 0.31 0.01 0.01 0.12 0.06  Table G-3 Month - Aug  Continued 10-20 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  78.00 35.00 37.00 70.00  Transition probability P = Poi = P = Pn = 0 0  1 0  0.690 0.310 0.346 0.654  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  53.84 24.16 11.41 21.59 24.16 10.84 25.59 48.41  60.00 18.00 11.00 22.00 18.00 17.00 26.00 48.00 7.38 0.025  Chi-square 0.70 1.57 0.01 0.01 1.57 3.50 0.01 0.00  with 2 d.f.  ndence: second and third preceding days Sequence  Actual  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  48.00 13.00 6.00 10.00 6.00 6.00 7.00 18.00 12.00 5.00 5.00 12.00 12.00 11.00 19.00 30.00  Chi-square sum Prob.  8.89 0.180  Predicted 42.11 18.89 5.53 10.47 8.28 3.72 8.64 16.36 11.73 5.27 5.88 11.12 15.88 7.12 16.94 32.06 with 6 d.f.  Chi-square 0.82 1.84 0.04 0.02 0.63 1.40 0.31 0.17 0.01 0.01 0.13 0.07 0.95 2.11 0.25 0.13  Table G-3 Month - Aug  Continued 20-31 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  99.00 34.00 28.00 81.00  Transition probability Poo= PM = P = Pn = 1 0  0.744 0.256 0.257 0.743  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  74.44 25.56 9.25 26.75 24.56 8.44 18.75 54.25  79.00 21.00 10.00 26.00 20.00 13.00 18.00 55.00 4.53 0.104  Chi-square 0.28 0.81 0.06 0.02 0.85 2.47 0.03 0.01  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  56.00 20.00 5.00 17.00 8.00 4.00 4.00 17.00 23.00 1.00 5.00 9.00 12.00 9.00 14.00 38.00  Chi-square sum Prob.  10.84 0.093  Predicted 56.57 19.43 5.65 16.35 8.93 3.07 5.39 15.61 17.86 6.14 3.60 10.40 15.63 5.37 13.36 38.64 with 6 d.f.  Chi-square 0.01 0.02 0.08 0.03 0.10 0.28 0.36 0.12 1.48 4.30 0.55 0.19 0.84 2.46 0.03 0.01  Table G-3 Month - Sep  Continued 1-10 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  103.00 35.00 30.00 52.00  Transition probability Poo= P01 = P = Pn = 1 0  0.746 0.254 0.366 0.634  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  82.10 27.90 11.71 20.29 20.90 7.10 18.29 31.71  85.00 25.00 12.00 20.00 18.00 10.00 18.00 32.00 2.01 0.367  Chi-square 0.10 0.30 0.01 0.00 0.40 1.18 0.00 0.00  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  71.00 20.00 10.00 15.00 8.00 4.00 5.00 14.00 14.00 5.00 2.00 5.00 10.00 6.00 13.00 18.00  67.92 23.08 9.15 15.85 8.96 3.04 6.95 12.05 14.18 4.82 2.56 4.44 11.94 4.06 11.34 19.66  Chi-square sum Prob.  3.77 0.707  with 6 d.f.  Chi-square 0.14 0.41 0.08 0.05 0.10 0.30 0.55 0.32 0.00 0.01 0.12 0.07 0.32 0.93 0.24 0.14  Table G-3 Month - Sep  Continued 10-20 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  167.00 16.00 17.00 20.00  Transition probability Poo=  0.913  Poi = 0.087 P i o = 0.459 P n = 0.541  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual 151.00 14.00 7.00 9.00 16.00 2.00 10.00 11.00 0.20 0.907  Predicted 150.60 14.43 7.35 8.65 16.43 1.57 9.65 11.35  Chi-square 0.00 0.01 0.02 0.01 0.01 0.12 0.01 0.01  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  137.00 11.00 6.00 5.00 6.00 1.00 5.00 4.00 14.00 3.00 1.00 4.00 10.00 1.00 5.00 7.00  Chi-square sum Prob.  4.38 0.625  Predicted 135.10 12.94 5.05 5.95 6.39 0.61 4.14 4.86 15.51 1.49 2.30 2.70 10.04 0.96 5.51 6.49 with 6 d.f.  Chi-square 0.03 0.29 0.18 0.15 0.02 0.25 0.18 0.15 0.15 1.54 0.73 0.62 0.00 0.00 0.05 0.04  Table G-3 Month - Sep  Continued 20-30 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  180.00 12.00 16.00 12.00  Transition probability P = Pm = P = Pn = 0 0  i 0  0.938 0.063 0.571 0.429  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual 165.00 10.00 9.00 6.00 15.00 2.00 7.00 6.00 1.08 0.584  164.10 10.94 8.57 6.43 15.94 1.06 7.43 5.57  Chi-square 0.01 0.08 0.02 0.03 0.06 0.83 0.02 0.03  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  153.00 9.00 8.00 5.00 9.00 0.00 4.00 3.00 12.00 1.00 1.00 1.00 6.00 2.00 3.00 3.00  Chi-square sum Prob.  5.85 0.440  Predicted 151.09 10.13 7.43 5.57 8.44 0.56 4.00 3.00 12.19 0.81 1.14 0.86 7.50 0.50 3.43 2.57 with 6 d.f.  Chi-square 0.01 0.13 0.04 0.06 0.04 0.56 0.00 0.00 0.00 0.04 0.02 0.02 0.30 4.50 0.05 0.07  Table G-4 Month - Jun  Markov chain analysis, 5 day intervals 1-5 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  Transition probability  88.00 4.00 14.00 3.00  P Poi P Pn 0 0  1 0  = = = =  0.957 0.043 0.824 0.176  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  75.57 3.43 4.94 1.06 12.43 0.57 8.24 1.76  76.00 3.00 4.00 2.00 12.00 1.00 9.00 1.00 1.83 0.401  Chi-square 0.00 0.06 0.18 0.84 0.02 0.33 0.07 0.33  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  65.00 2.00 2.00 1.00 3.00 0.00 4.00 1.00 11.00 1.00 2.00 1.00 8.00 1.00 5.00 0.00  64.09 2.91 2.47 0.53 2.87 0.13 4.12 0.88 11.48 0.52 2.47 0.53 8.61 0.39 4.12 0.88  Chi-square sum Prob.  3.99 0.678  with 6 d.f.  Chi-square 0.01 0.29 0.09 0.42 0.01 0.13 0.00 0.02 0.02 0.44 0.09 0.42 0.04 0.95 0.19 0.88  Table G-4 Month - Jun  Continued 6-10 Sequence  Transition probability  Actual  dry-dry dry-wet wet-dry wet-wet  86.00 11.00 8.00 5.00  P  0 0  = 0.887  P01 = 0.113 P i o = 0.615  P n = 0.385  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  80.68 10.32 6.15 3.85 5.32 0.68 1.85 1.15  80.00 11.00 7.00 3.00 6.00 0.00 1.00 2.00 2.13 0.345  Chi-square 0.01 0.04 0.12 0.19 0.09 0.68 0.39 0.62  with 2 d.f.  Test of Independence: second and third preceding days Sequence dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet Chi-square sum Prob.  Actual 75.00 9.00 7.00 3.00 6.00 0.00 1.00 1.00 5.00 2.00 0.00 0.00 0.00 0.00 0.00 1.00 4.88 0.559  Predicted 74.47 9.53 6.15 3.85 5.32 0.68. 1.23 0.77 6.21 0.79 0.00. 0.00. 0.00. 0.00. 0.62 0.38 with 6 d.f.  Chi-square 0.00 0.03 0.12 0.19 0.09 0.68 0.04 0.07 0.23 1.83 0.00 0.00 0.00 0.00 0.62 0.98  Table G-4 Month - Jun  Continued 11-15 Sequence  Transition probability  Actual  dry-dry dry-wet wet-dry wet-wet  77.00 14.00 13.00 6.00  P = Poi = Pio= P11 = 0 0  0.846 0.154 0.684 0.316  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual  1  Predicted 62.62 11.38 8.89 4.11 14.38 2.62 4.11 1.89  62.00 12.00 9.00 4.00 15.00 2.00 4.00 2.00 0.22 0.895  Chi-square 0.01 0.03 0.00 0.00 0.03 0.14 0.00 0.01  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  54.00 11.00 8.00 4.00 10.00 2.00 2.00 2.00 8.00 1.00 1.00 0.00 5.00 0.00 2.00 0.00  55.00 10.00 8.21 3.79 10.15 1.85 2.74 1.26 7.62 1.38 0.68 0.32 4.23 0.77 1.37 0.63  Chi-square sum Prob.  3.20 0.784  with 6 d.f.  Chi-square 0.02 0.10 0.01 0.01 0.00 0.01 0.20 0.43 0.02 0.11 0.15 0.32 0.14 0.77 0.29 0.63  Table G-4 Month - Jun  Continued 16-20 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  78.00 11.00 11.00 10.00  Transition probability P  0 0  = 0.876  P01 = 0.124  P i o = 0.524 P n = 0.476  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual  Predicted 70.11 9.89 5.76 5.24 7.89 1.11 5.24 4.76  71.00 9.00 7.00 4.00 7.00 2.00 4.00 6.00 2.07 0.355  Chi-square 0.01 0.08 0.27 0.29 0.10 0.71 0.29 0.32  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  58.00 9.00 5.00 4.00 5.00 1.00 3.00 1.00 13.00 0.00 2.00 0.00 2.00 1.00 1.00 5.00  58.72 8.28 4.71 4.29 5.26 0.74 2.10 1.90 11.39 1.61 1.05 0.95 2.63 0.37 3.14 2.86  Chi-square sum Prob.  8.97 0.175  with 6 d.f.  Chi-square 0.01 0.06 0.02 0.02 0.01 0.09 0.39 0.43 0.23 1.61 0.87 0.95 0.15 1.07 1.46 1.61  Table G-4 Month - Jun  Continued 21-25 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  60.00 19.00 18.00 13.00  Transition probability P = Poi = P = Pn = 0 0  1 0  0.759 0.241 0.581 0.419  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  49.37 15.63 9.29 6.71 10.63 3.37 8.71 6.29  52.00 13.00 11.00 5.00 8.00 6.00 7.00 8.00 4.85 0.089  Chi-square 0.14 0.44 0.31 0.44 0.65 2.06 0.34 0.46  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  46.00 10.00 8.00 3.00 4.00 4.00 2.00 4.00 6.00 3.00 3.00 2.00 4.00 2.00 5.00 4.00  42.53 13.47 6.39 4.61 6.08 1.92 3.48 2.52 6.84 2.16 2.90 2.10 4.56 1.44 5.23 3.77  Chi-square sum Prob.  7.34 0.290  with 6 d.f.  Chi-square 0.28 0.89 0.41 0.56 0.71 2.24 0.63 0.88 0.10 0.32 0.00 0.00 0.07 0.21 0.01 0.01  Table G-4 Month - Jun  Continued 26-30 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  57.00 18.00 14.00 21.00  Transition probability P = P01 = Pio= Pn = 0 0  0.760 0.240 0.400 0.600  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  42.56 13.44 8.40 12.60 14.44 4.56 5.60 8.40  48.00 8.00 10.00 11.00 9.00 10.00 4.00 10.00 12.71 0.002  Chi-square 0.70 2.20 0.30 0.20 2.05 6.49 0.46 0.30  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  44.00 6.00 6.00 5.00 5.00 8.00 3.00 5.00 4.00 2.00 4.00 6.00 4.00 2.00 1.00 5.00  38.00 12.00 4.40 6.60 9.88 3.12 3.20 4.80 4.56 1.44 4.00 6.00 4.56 1.44 2.40 3.60  Chi-square sum Prob.  16.92 0.010  with 6 d.f.  Chi-square 0.95 3.00 0.58 0.39 2.41 7.63 0.01 0.01 0.07 0.22 0.00 0.00 0.07 0.22 0.82 0.54  Table G-4 Month - Jul  Continued 1-5 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  47.00 19.00 19.00 25.00  Transition probability Poo= Poi = P = Pn = 1 0  0.712 0.288 0.432 0.568  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  33.47 13.53 8.20 10.80 13.53 5.47 10.80 14.20  37.00 10.00 11.00 8.00 10.00 9.00 8.00 17.00 7.44 0.024  Chi-square 0.37 0.92 0.95 0.72 0.92 2.28 0.72 0.55  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  29.00 8.00 5.00 4.00 7.00 3.00 3.00 8.00 8.00 2.00 6.00 4.00 3.00 6.00 5.00 9.00  26.35 10.65 3.89 5.11 7.12 2.88 4.75 6.25 7.12 2.88 4.32 5.68 6.41 2.59 6.05 7.95  Chi-square sum Prob.  10.78 0.096  with 6 d.f.  Chi-square 0.27 0.66 0.32 0.24 0.00 0.01 0.64 0.49 0.11 0.27 0.66 0.50 1.81 4.49 0.18 0.14  Table G-4 Month - Jul  Continued 6-10 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  52.00 18.00 18.00 22.00  Transition probability Poo= Poi = P = Pn = 1 0  0.743 0.257 0.450 0.550  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  38.63 13.37 7.65 9.35 13.37 4.63 10.35 12.65  40.00 12.00 6.00 11.00 12.00 6.00 12.00 11.00 1.86 0.394  Chi-square 0.05 0.14 0.36 0.29 0.14 0.41 0.26 0.22  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  35.00 8.00 5.00 6.00 4.00 2.00 5.00 4.00 5.00 4.00 1.00 5.00 8.00 4.00 7.00 7.00  31.94 11.06 4.95 6.05 4.46 1.54 4.05 4.95 6.69 2.3t 2.70 3.30 8.91 3.09 6.30 7.70  Chi-square sum Prob.  5.83 0.442  with 6 d.f.  Chi-square 0.29 0.85 0.00 0.00 0.05 0.14 0.22 0.18 0.43 1.23 1.07 0.88 0.09 0.27 0.08 0.06  Table G-4 Month - Jul  Continued 11-15 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  43.00 18.00 17.00 32.00  Transition probability P = Poi = P = Pn = 0 0  1 0  0.705 0.295 0.347 0.653  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual  Predicted 32.43 13.57 6.94 13.06 10.57 4.43 10.06 18.94  35.00 11.00 8.00 12.00 8.00 7.00 9.00 20.00 3.24 0.198  Chi-square 0.20 0.49 0.16 0.09 0.63 1.50 0.11 0.06  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  27.00 8.00 7.00 6.00 3.00 4.00 7.00 6.00 8.00 3.00 1.00 6.00 5.00 3.00 2.00 14.00  24.67 10.33 4.51 8.49 4.93 2.07 4.51 8.49 7.75 3.25 2.43 4.57 5.64 2.36 5.55 10.45  Chi-square sum Prob.  12.56 0.051  with 6 d.f.  Chi-square 0.22 0.52 1.37 0.73 0.76 1.81 1.37 0.73 0.01 0.02 0.84 0.45 0.07 0.17 2.27 1.21  Table G-4 Month - Jul  Continued 16-20 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  40.00 18.00 18.00 34.00  Transition probability P = Poi = P = Pn = 0 0  1 0  0.690 0.310 0.346 0.654  Test of Independence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  26.21 11.79 6.58 12.42 13.79 6.21 11.42 21.58  27.00 11.00 10.00 9.00 13.00 7.00 8.00 25.00 4.52 0.104  Chi-square 0.02 0.05 1.78 0.94 0.05 0.10 1.03 0.54  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  21.00 7.00 5.00 7.00 9.00 2.00 2.00 7.00 6.00 4.00 5.00 2.00 4.00 5.00 6.00 18.00  19.31 8.69 4.15 7.85 7.59 3.41 3.12 5.88 6.90 3.10 2.42 4.58 6.21 2.79 8.31 15.69  Chi-square sum Prob.  10.28 0.114  with 6 d.f.  Chi-square 0.15 0.33 0.17 0.09 0.26 0.59 0.40 0.21 0.12 0.26 2.74 1.45 0.78 1.74 0.64 0.34  Table G-4 Month - Jul  Continued 21-25 Sequence  Transition probability  Actual  dry-dry dry-wet wet-dry wet-wet  43.00 14.00 9.00 44.00  Poo= Poi = Pio= Pn =  0.754 0.246 0.170 0.830  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  34.70 11.30 1.87 9.13 8.30 2.70 7.13 34.87  35.00 11.00 2.00 9.00 8.00 3.00 7.00 35.00 0.07 0.966  Chi-square 0.00 0.01 0.01 0.00 0.01 0.03 0.00 0.00  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  29.00 5.00 2.00 8.00 3.00 0.00 0.00 8.00 6.00 6.00 0.00 1.00 5.00 3.00 7.00 27.00  25.65 8.35 1.70 8.30 2.26 0.74 1.36 6.64 9.05 2.95 0.17 0.83 6.04 1.96 5.77 28.23  Chi-square sum Prob.  9.89 0.129  with 6 d.f.  Chi-square 0.44 1.34 0.05 0.01 0.24 0.74 1.36 0.28 1.03 3.16 0.17 0.03 0.18 0.55 0.26 0.05  Table G-4 Month - Jul  Continued 26-31 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  60.00 13.00 19.00 40.00  Transition probability Poo= Poi = P = Pn = 1 0  0.822 0.178 0.322 0.678  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  46.03 9.97 4.51 9.49 13.97 3.03 14.49 30.51  51.00 5.00 5.00 9.00 9.00 8.00 14.00 31.00 13.06 0.001  Chi-square 0.54 2.48 0.05 0.03 1.77 8.17 0.02 0.01  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  43.00 4.00 1.00 4.00 2.00 3.00 5.00 3.00 8.00 1.00 4.00 5.00 7.00 5.00 9.00 28.00  38.63 8.37 1.61 3.39 4.11 0.89 2.58 5.42 7.40 1.60 2.90 6.10 9.86 2.14 11.92 25.08  Chi-square sum Prob.  19.17 0.004  with 6 d.f.  Chi-square 0.49 2.28 0.23 0.11 1.08 5.00 2.28 1.08 0.05 0.23 0.42 0.20 0.83 3.84 0.71 0.34  Table G-4 Month - Aug  Continued 1-5 Sequence  Aptual  dry-dry dry-wet wet-dry wet-wet  34.00 17.00 19.00 40.00  Transition probability P = Pm = P = Pn = 0 0  1 0  0.667 0.333 0.322 0.678  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  22.00 11.00 5.47 11.53 12.00 6.00 13.53 28.47  24.00 9.00 6.00 11.00 10.00 8.00 13.00 29.00 1.65 0.438  Chi-square 0.18 0.36 0.05 0.02 0.33 0.67 0.02 0.01  with 2 d.f.  ndence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  18.00 6.00 4.00 7.00 2.00 3.00 4.00 9.00 6.00 3.00 2.00 4.00 8.00 5.00 9.00 20.00  16.00 8.00 3.54 7.46 3.33 1.67 4.19 8.81 6.00 3.00 1.93 4.07 8.67 4.33 9.34 19.66  Chi-square sum Prob.  2.62 0.854  with 6 d.f.  Chi-square 0.25 0.50 0.06 0.03 0.53 1.07 0.01 0.00 0.00 0.00 0.00 0.00 0.05 0.10 0.01 0.01  Table G-4 Month - Aug  Continued 6-10 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  31.00 19.00 21.00 39.00  Transition probability P = Poi = P = Pn = 0 0  1 0  0.620 0.380 0.350 0.650  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  19.22 11.78 6.65 12.35 11.78 7.22 14.35 26.65  18.00 13.00 7.00 12.00 13.00 6.00 14.00 27.00 0.58 0.749  Chi-square 0.08 0.13 0.02 0.01 0.13 0.21 0.01 0.00  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  11.00 9.00 3.00 9.00 4.00 1.00 2.00 10.00 7.00 4.00 4.00 3.00 9.00 5.00 12.00 17.00  12.40 7.60 4.20 7.80 3.10 1.90 4.20 7.80 6.82 4.18 2.45 4.55 8.68 5.32 10.15 18.85  Chi-square sum Prob.  5.47 0.484  with 6 d.f.  Chi-square 0.16 0.26 0.34 0.18 0.26 0.43 1.15 0.62 0.00 0.01 0.98 0.53 0.01 0.02 0.34 0.18  Table G-4 Month - Aug  Continued 11-15 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  44.00 15.00 18.00 33.00  Transition probability P = Poi = P = Pn = 0 0  1 0  0.746 0.254 0.353 0.647  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  32.07 10.93 4.94 9.06 11.93 4.07 13.06 23.94  35.00 8.00 4.00 10.00 9.00 7.00 14.00 23.00 4.27 0.118  Chi-square 0.27 0.79 0.18 0.10 0.72 2.11 0.07 0.04  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  27.00 5.00 2.00 6.00 2.00 3.00 3.00 8.00 8.00 3.00 2.00 4.00 7.00 4.00 11.00 15.00  23.86 8.14 2.82 5.18 3.73 1.27 3.88 7.12 8.20 2.80 2.12 3.88 8.20 2.80 9.18 16.82  Chi-square sum Prob.  6.74 0.346  with 6 d.f.  Chi-square 0.41 1.21 0.24 0.13 0.80 2.35 0.20 0.11 0.01 0.01 0.01 0.00 0.18 0.52 0.36 0.20  Table G-4 Month - Aug  Continued 16-20 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  34.00 20.00 19.00 37.00  Transition probability P = Poi = Pio= Pn = 0 0  0.630 0.370 0.339 0.661  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  22.04 12.96 6.45 12.55 11.96 7.04 12.55 24.45  25.00 10.00 7.00 12.00 9.00 10.00 12.00 25.00 3.17 0.205  Chi-square 0.40 0.68 0.05 0.02 0.73 1.25 0.02 0.01  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  21.00 8.00 4.00 4.00 4.00 3.00 4.00 10.00 4.00 2.00 3.00 8.00 5.00 7.00 8.00 15.00  18.26 10.74 2.71 5.29 4.41 2.59 4.75 9.25 3.78 2.22 3.73 7.27 7.56 4.44 7.80 15.20  Chi-square sum Prob.  4.91 0.556  with 6 d.f.  Chi-square 0.41 0.70 0.61 0.31 0.04 0.06 0.12 0.06 0.01 0.02 0.14 0.07 0.86 1.47 0.00 0.00  Table G-4 Month - Aug  Continued 21-25 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  42.00 19.00 16.00 34.00  Transition probability P = Poi = P = Pn = 0 0  1 0  0.689 0.311 0.320 0.680  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  29.61 13.39 6.72 14.28 12.39 5.61 9.28 19.72  32.00 11.00 8.00 13.00 10.00 8.00 8.00 21.00 2.72 0.256  Chi-square 0.19 0.43 0.24 0.11 0.46 1.02 0.18 0.08  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  20.00 11.00 4.00 9.00 5.00 4.00 0.00 7.00 12.00 0.00 4.00 4.00 5.00 4.00 8.00 14.00  21.34 9.66 4.16 8.84 6.20 2.80 2.24 4.76 8.26 3.74 2.56 5.44 6.20 2.80 7.04 14.96  Chi-square sum Prob.  11.87 0.065  with 6 d.f.  Chi-square 0.08 0.19 0.01 0.00 0.23 0.51 2.24 1.05 1.69 3.74 0.81 0.38 0.23 0.51 0.13 0.06  Table G-4 Month - Aug  Continued 26-31 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  57.00 15.00 12.00 47.00  Transition probability Poo= Poi = Pio= Pn =  0.792 0.208 0.203 0.797  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  45.13 11.88 3.05 11.95 11.88 3.13 8.95 35.05  47.00 10.00 2.00 13.00 10.00 5.00 10.00 34.00 2.40 0.301  Chi-square 0.08 0.30 0.36 0.09 0.30 1.13 0.12 0.03  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  36.00 9.00 1.00 8.00 3.00 0.00 4.00 10.00 11.00 1.00 1.00 5.00 7.00 5.00 6.00 24.00  35.63 9.38 1.83 7.17 2.38 0.63 2.85 11.15 9.50 2.50 1.22 4.78 9.50 2.50 6.10 23.90  Chi-square sum Prob.  6.21 0.400  with 6 d.f.  Chi-square 0.00 0.02 0.38 0.10 0.16 0.63 0.47 0.12 0.24 0.90 0.04 0.01 0.66 2.50 0.00 0.00  Table G-4 Month - Sep  Continued 1-5 Sequence  Actual  dry-dry dry-wet wet-dry wet-wet  44.00 26.00 12.00 28.00  Transition probability Poo= Poi = Pio= P11 =  0.629 0.371 0.300 0.700  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual  Predicted 35.83 21.17 6.00 14.00 8.17 4.83 6.00 14.00  35.00 22.00 7.00 13.00 9.00 4.00 5.00 15.00 0.75 0.686  Chi-square 0.02 0.03 0.17 0.07 0.08 0.14 0.17 0.07  with 2 d.f.  ndence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  29.00 18.00 7.00 11.00 6.00 2.00 3.00 9.00 6.00 4.00 0.00 2.00 3.00 2.00 2.00 6.00  29.54 17.46 5.40 12.60 5.03 2.97 3.60 8.40 6.29 3.71 0.60 1.40 3.14 1.86 2.40 5.60  Chi-square sum Prob.  2.36 0.884  with 6 d.f.  Chi-square 0.01 0.02 0.47 0.20 0.19 0.32 0.10 0.04 0.01 0.02 0.60 0.26 0.01 0.01 0.07 0.03  Table G-4 Month - Sep  Continued 6-10 Sequence  Transition probability  Actual  dry-dry dry-wet wet-dry wet-wet  P = Poi = P = P11 =  59.00 9.00 18.00 24.00  0 0  1 0  0.868 0.132 0.429 0.571  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  45.99 7.01 5.14 6.86 13.01 1.99 12.86 17.14  50.00 3.00 5.00 7.00 9.00 6.00 13.00 17.00 12.02 0.002  Chi-square 0.35 2.30 0.00 0.00 1.24 8.12 0.00 0.00  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  42.00 2.00 3.00 4.00 2.00 2.00 2.00 5.00 8.00 1.00 2.00 3.00 7.00 4.00 11.00 12.00  38.18 5.82 3.00 4.00 3.47 0.53 3.00 4.00 7.81 1.19 2.14 2.86 9.54 1.46 9.86 13.14  Chi-square sum Prob.  13.59 0.035  with 6 d.f.  Chi-square 0.38 2.51 0.00 0.00 0.62 4.08 0.33 0.25 0.00 0.03 0.01 0.01 0.68 4.45 0.13 0.10  Table G-4 Month - Sep  Continued 11-15 Sequence  Transition probability  Actual  dry-dry dry-wet wet-dry wet-wet  81.00 7.00 9.00 14.00  P = Poi= Pio= Pn = 0 0  0.920 0.080 0.391 0.609  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  71.80 6.20 3.13 4.87 9.20 0.80 5.87 9.13  73.00 5.00 4.00 4.00 8.00 2.00 5.00 10.00 2.84 0.241  Chi-square 0.02 0.23 0.24 0.16 0.16 1.82 0.13 0.08  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  67.00 4.00 3.00 1.00 4.00 1.00 2.00 3.00 6.00 1.00 1.00 3.00 4.00 1.00 3.00 7.00  65.35 5.65 1.57 2.43 4.60 0.40 1.96 3.04 6.44 0.56 1.57 2.43 4.60 0.40 3.91 6.09  Chi-square sum Prob.  5.73 0.454  with 6 d.f.  Chi-square 0.04 0.48 1.32 0.85 0.08 0.91 0.00 0.00 0.03 0.35 0.20 0.13 0.08 0.91 0.21 0.14  Table G-4 Month - Sep  Continued 16-20 Sequence  Transition probability  Actual  dry-dry dry-wet wet-dry wet-wet  P = Poi = Pio= Pn =  86.00 9.00 8.00 6.00  0 0  0.905 0.095 0.571 0.429  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  78.76 8.24 4.57 3.43 7.24 0.76 3.43 2.57  78.00 9.00 3.00 5.00 8.00 0.00 5.00 1.00 3.86 0.145  Chi-square 0.01 0.07 0.54 0.72 0.08 0.76 0.72 0.96  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  70.00 7.00 3.00 4.00 2.00 0.00 3.00 1.00 8.00 2.00 0.00 1.00 6.00 0.00 2.00 0.00  69.71 7.29 4.00 3.00 1.81 0.19 2.29 1.71 9.05 0.95 0.57 0.43 5.43 0.57 1.14 0.86  Chi-square sum Prob.  6.08 0.414  with 6 d.f.  Chi-square 0.00 0.01 0.25 0.33 0.02 0.19 0.22 0.30 0.12 1.17 0.57 0.76 0.06 0.57 0.64 0.86  Table G-4 Month - Sep  Continued 21-25 Sequence  Transition probability  Actual  dry-dry dry-wet wet-dry wet-wet  85.00 8.00 8.00 9.00  Poo= Poi = Pio= Pn=  0.914 0.086 0.471 0.529  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Predicted  Actual  78.60 7.40 4.24 4.76 6.40 0.60 3.76 4.24  79.00 7.00 3.00 6.00 6.00 1.00 5.00 3.00 1.76 0.415  Chi-square 0.00 0.02 0.36 0.32 0.02 0.26 0.41 0.36  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  74.00 6.00 3.00 5.00 3.00 0.00 4.00 3.00 5.00 1.00 0.00 1.00 3.00 1.00 1.00 0.00  73.12 6.88 3.76 4.24 2.74 0.26 3.29 3.71 5.48 0.52 0.47 0.53 3.66 0.34 0.47 0.53  Chi-square sum Prob.  4.86 0.561  with 6 d.f.  Chi-square 0.01 0.11 0.16 0.14 0.02 0.26 0.15 0.13 0.04 0.45 0.47 0.42 0.12 1.25 0.60 0.53  Table G-4 Month - Sep  Continued 26-30 Sequence  Transition probability  Actual  dry-dry dry-wet wet-dry wet-wet  95.00 4.00 8.00 3.00  P = Poi = P = Pn = 0 0  1 0  0.960 0.040 0.727 0.273  Test of lndependence:second preceding day Sequence dry-dry-dry dry-dry-wet dry-wet-dry dry-wet-wet wet-dry-dry wet-dry-wet wet-wet-dry wet-wet-wet Chi-square sum Prob.  Actual  Predicted 85.40 3.60 4.36 1.64 9.60 0.40 3.64 1.36  86.00 3.00 6.00 0.00 9.00 1.00 2.00 3.00 5.97 0.051  Chi-square 0.00 0.10 0.61 1.64 0.04 0.88 0.74 1.96  with 2 d.f.  Test of Independence: second and third preceding days Sequence  Actual  Predicted  dry-dry-dry-dry dry-dry-dry-wet dry-dry-wet-dry dry-dry-wet-wet dry-wet-dry-dry dry-wet-dry-wet dry-wet-wet-dry dry-wet-wet-wet wet-dry-dry-dry wet-dry-dry-wet wet-dry-wet-dry wet-dry-wet-wet wet-wet-dry-dry wet-wet-dry-wet wet-wet-wet-dry wet-wet-wet-wet  79.00 3.00 5.00 0.00 6.00 0.00 0.00 0.00 7.00 0.00 1.00 0.00 3.00 1.00 2.00 3.00  78.69 3.31 3.64 1.36 5.76 0.24 0.00 0.00 6.72 0.28 0.73 0.27 3.84 0.16 3.64 1.36  Chi-square sum Prob.  10.06 0.122  with 6 d.f.  Chi-square 0.00 0.03 0.51 1.36 0.01 0.24 0.00 0.00 0.01 0.28 0.10 0.27 0.18 4.35 0.74 1.96  217  APPENDIX H DAILY RAINFALL MODELLING RESULTS  218  '*|h-|CO|0|^|h-|'r-Hf)|^|CO|lOllDCOCOCO  CD  co CO  T3 O E  2! O)  ca  —  T3 CO  •a o  •o  E  .2  a cu  S  c  c  TJ C  X  2 c>.a c a Q TJ <5  cu  Q. Q. <  .Q  ca  °?  220 U)  _ o ra 'E O  N l M t  s  n  in  221  Tr|o)|rM|^|rM|CMlcolcn|coco I*- LO  a  m  222  U) (O O 11  * o| ra 'E  O-l  ,°  to  T—  o  CM  Q. '  a •a 0) 0  oil  n CM  o  o o  CO  ra >-  3  (O p  IM (N IO  (M N  O  O  IO  223  _ o ra 'E  1 a.  224  3  — o ra ™ o  3 <  CO  150 |  Total # of periods  225  CO  CO  IO  TT  r--  CN  CO  in  TT  o  CO  CM  CO  CO  CO  CN  o CM  •o  CM  in  CN  <o  CM  CN  h~  CM  CN  LO  30-40  2 day rainfall, categorized by depth (mm)  40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 | 100-110 | 110-120 | 120-130 | 130-140  140-150 |  ge  CO  CO  in  in  CM  CN  CM  CM  CM  CM  co  CN  IO  20-30  CN  CM  co  |  CM  CO  CN  co  CM  CM  Tf  CO  CO  oo  CM  10-20  c CO  o o  CO  CO  CO  CO  CN  CN  LO  CM  CO  CO  CM  IO  CO  o  a> o  d r-O)  Sept.  Month  Year  o  rCO  CN fOl  CO fO)  TT i o  rcn  CO  co co  cn  co l-~ cn  O CO cn  CO oo CO  TT L O oo O)  co cn  CO co cn  1^  00 cn  oo 00 cn  O) oo O)  o  o> o>  o  CN O) CO  CO cn cn  Total |  V  226  _ o  2  Q.  a •a >>  cu o  TJ  E  a T3  to"  JZ Q. CU TJ  c  2  >< ca  TJ  CO  X a>  n  co  a-  CO  150 |  Total # of periods  227  CM  00  CN  CM  LO cn o CO o CM CM  CM  CO CN IO  t  cn  CO  CO  CN  CN  CN  in  CN  cn  CN  CM  r~  CO  CM  CM  CN  CN CO  CN  CO  o  CN CM  | 30-40 | 40-50 | 50-60 | 60-70 |  70-80  | 80-90 ] 90-100 | 100-110 | 110-120 | 120-130 j 130-140 | 140-150 |  CM  CN  CO  CM  CO  CN  CN CN  CN CO CM  CO CO  co  CM LO  co CM  CN  CM  LO CO  T—  CM  CN  CM LO  co  co  CM CM  CM CO  o  CO  CM  CN  CN  't  CM  CO  r-- to  CM LO co oo  r~  10-20  |  CM  CO CO CO  00  LO 00  CO  LO 00  CM  LO r--  P~ o  to  CO CO  CO LO  20-30  3 day rainfall, categorized by depth (mm)  ge  CD  CO CN LO r- LO o o LO CO CN CM CN CM CM CO CN CN CM CO  LO  *-  o  CN CO  oo cn o CN co LO CO o CN CO 10 CO r~- 00 cn o co O) O) h- r- 00 00 00 CO co co oo oo O) hr - l-~ cn 0 ) G) cn o> o> o> cn O) cn cn cn cn cn 0 ) 0 ) O) O) cn O) o cn  Month  Year  5>  3 ->  Total |  V  228  _  O  £ 2.  229  at _  n  TJ O  'E  a cu  TJ >, .Q TJ  cu N  'E o ra  cu  T3 CD 3 C  o E E o d  O  o  CM C)  CO I  n  ca  Q. (U  CO  230  _ o ra 'E  2  Q.  a •a >. .a ~u a N O O) • V  c 'ra >N  ra •o  cu  TJ O  E ca  TJ  «T a.  JZ +-< cu  TJ  1 c  2 > co  TJ  X  CO  Q-  231  at f  ra 'E "S •>  232  UI  _ra o'E ai  2 2.  <  233  V) "D O  ra 'E  £ 2.  234  APPENDIX I RAINFALL EVENT MODEL RESULTS, 0.1 MM THRESHOLD  235  (%) A)!i;qeqojd aAueiniuno  236  A);suap A)!i;qeqoJd  237  00  CO  ° to  co  co  co  CM  co  oo  * c « S> o cu r-  ** >  CM  to  CM CO CO  CN  co  CM CM  CM  CO CN  co  CD  CM  o  co co CN  to CO  co  CN  E E CO  00  CM  CN  CO  CN CO*  CM  CN CN CN  CO  co  > cu  CO  cu  LO  Q.  CO  CO  in  >>  CM  CO CO >NT3  o  CL CU  •8 £  TJ  CM  S  CN U»  CM §  CM  II ~  CM II  c E  c  .2 = c •s o 2 *- *=  to  1 3  T  C  (J  CM CM II  cu "P  *  n  co  i  CO  1  ' i  >  | B  « i co x 5 05  CD  CO  tO  1^(0  to  0 tz cu  W  238  CL  CO o o o o d d  CO o o d  CO LO y— o d d  CO to o d  r-o o d  o  oo o o d  CO o o d  CO LO o d  r-- CO co LO o d d  CO LO O d  CN  t—  CO  T—  co o o o o d d  o o d  CO LO ^— o \— d o  CO  <c—  O d  o T—  o d  c  o o CO >> CQ "O CL  d  T—  CN  CN  r-~ o o d  cn o o d  CO o o d  CO CO o CN ^— T — O o o d d d  o m o o  LO CN O O  LO LO o CN o o T— T— o o o  CN  i—  r-  CO CN o d  CO CN O d  ^—  oo CO CO — CO CO CO o oo CN o 0 0 ^— CO T— o o o o d d d d d d d d  co d 00  00  ven  to  o tt  T—  cu  CL  CO o o d  CO CO o T— o o d d  CO O O d  cn CO 0 0 o T— o o o o d d d  ro o d  CO o o d  CO o o d  fo o d  00  o o d  oo o o d  LO LO CN o O o O  LO CN o o  LO o CN o o o o  LO CN o o  LO o IN o O O o  o LO o d  LO CN o d  LO CN O d  o LO o d  LO CN O d  LO CN o d  CO  1—  1—  f—  •c—  CN  \—  r~- o o T— o o d d  CO O o T— o o d d  CO  o o d  C  o o o tn  CO ><  TO  13 CL CO  in  E E  o  tt  CD  T3 C  o co CN o o d d  co CN o d  o CD CO CN T — o O O o d d d  ho o d  CO o o d  CN LO o d  co o d  T—  CN CO t— co  CN  co o o d  o o  •o  V)  >»  o  c  CL  2 3 CP  CN  + J  c o  >  T—  LO CN o o  ve  2  CN  03 T3 CM CL  d  T  CN LO T — o o d d  r-T—  o d  o d  CC  o  o  CO c  r-- co CD LO  re  •  \—  CL  o  CN CO O O  CN LO o o  CO CN o o  CO CO CO CN x— T — o O O o o O o o o  o  ro o d  CO  T—  T—  o o  o o  00  o o d  ; I  TJ c O  JQ  o  > ro &  ': £g ro o  i l l  o  TJ  o.  00 m  CD  o  c re  CO LO  ve  4-  > N  CS T3 T—  CL  CO CN  00  d  d  00 T  -  T—  d  LO  CJ) f— LO CN CO LO LO CO CO \ — CN CN o o o o o o o d d d d d d d  T—  o d  : o ro • o c:  • . zj  o o d  : J= TJ  CD  iQ.r !•§ | : c «> > a> <u : > JZ TI ui— CO . c CO > o £ a> a> > > > to co o 1  LO CO oo r-- LO LO CN in LO CN + J  <#O tt  re 0£  IN  00  T—  J  ven  00  "re  CD  roroQ ° ° 1 .^•^ E  E .c  re  a. cu  LO o  o  d  I  1  LO  LO o  d  LO o  LO o  LO o LO 1 LO o LO d LO o LO CN CN CO CO •sr CN CN CO CO T  LO LO o1 LO  o CO LO LO  LO o LO o LO o 1^ 00 00 CO 1 • • 1 • o LO o LO oi LO CO CO r~ CO co  LO o ^— o T— T—  o LO o 1 a> i 1 O o LO o O) O)  LO o T— C N o T— T— CN 1 1 1 LO o LO o T — T — CU cn  1ro 5 ro !5 _§ -9 -S JS S 2 -5 ra o I—  Table 1-3  Rainfall depth of 2 day events by day, 0.1 mm threshold  Depth (mm)  Day of event, categorized by depth Day 2 Day 1 Cum. % Number Number Cum. °/a  23 0.1-5 8 5-10 10-15 12 5 15-20 20-25 3 25-30 2 30-35 2 35-40 40-45 1 45-50 2 ge 50 Cumulative percent  39.7 53.4 74.1 82.8 87.9 91.4 94.8 96.6 100.0  18 12 7 6 6 2 2  31.0 51.7 63.8 74.1 84.5 87.9 91.4  3  96.6  2  100.0  1  Table 1-4  Rainfall depth of 3 day events by day, 0.1 mm threshold Day of event, categorized by depth  Depth (mm)  Day 1 Number Cum. "ft  13 0.1-5 7 5-10 6 10-15 4 15-20 3 20-25 25-30 4 30-35 2 35-40 40-45 45-50 1 ge 50 Cumulative percent 1  1  32.5 50.0 65.0 75.0 82.5 92.5 97.5 100.0  Day 2 Number Cum. %  15 4 6 3 2 1 2 1 2 2 2  37.5 47.5 62.5 70.0 75.0 77.5 82.5 85.0 90.0 95.0 100  Day Number  3 Cum. %  18 4 7 2 2 2  45.0 55.0 72.5 77.5 82.5 87.5  1  90.0  2 2  95.0 100.0  240  co  CM  LO LO  Q "  00  CM  CM  o o  CM  LO  I-a E 3 CM  oo  o d o  CM  LO LO  TJ O  9>  E E  Q-  I*  ca  a  'l  cu N  >i  C  c> u c> u ca.  co  CO  o  O)CO T3  co  cu c oo  CN1  c u CM O > cu c>. a o Q >»l , <° Q  o o  CM  I-a E  co  TJ  I oqo»|  a cu  TJ  00 00  o o  E 3 IO  c  C M  co  co  OH  cu cu  E 3  Q01 >  3  a | CO  H  LO I  o  o LO LO  E  3  o  241  APPENDIX J RAINFALL EVENT MODEL RESULTS, 5.0 MM THRESHOLD  242  (%) A)!i;qeqojd  9A!JB|niuno  243  (U "O  BQ .  -q  ~rjj  T  Xjisusp A)!|iqeqojd  244  CO CO CN CM  to ~ c  O cu  10  >. ca TJ_  CM  C  o TJ  Jx  Si TJ  o  9>  CO  TJ  co  cu N  'C O O) cu  E E o  CN  CN  co in  CN  CN  re u  ui  CN  co  CN  cu > cu  CO  cu  CN  Q.  a  cu  5  E z  cu TJ C  CN  CO  m  >.  CN  CO co  at  03  TJ  CM CM  ^ oo  m  CD  " co  ©  c 2 II •2 M =  CM  '5  3 S-^i > > 7 3  CU  Si ca  a. cu Q  c"  1  * i  *: o o c TJ c c  g co c.E-o a>  03 X £ CO co to  2 2  CO  o CO II  10 CO CD  c  5  CD  CO  245  •  T J  C O  0)  Tt  CO  CO  o o  o o  CO  CO  o o  o o  d  d  d  d  d  d  d  ^_  T  Oi  m m  o T  o o  —  T  Oi Oi  CO  d  d  T—  o  _  Oi o o> o q  •«- •>-  co  —  CO  Oi  o o d d  Q.  r-  CO  O O  1 1  LL  q d  d  d  •>-  -*—  m  c  o  tt > cu •  fx. T J  C  hO  o  O  ^— o  d  d  o  CO ^— o  CO  co  o  o  o  T— o  d  d  d  d  d  T  —  CO  co  T  —  d  d  d  CO  o  o  00  o  oo  00  o  O  o  d  oo  o  o  o o  ^— o  d  d  d  co  00  T—  d  d  d  o  o  co  o  o  o  d  d  d  d  co  CO  oo  T— ^  CO  oo  o  o  o  ^—  o  o T J  9>  T J  d  d  CN  CO  *!—  d  o o  T  o o  q d  T—  —  q d  q d  q d  _  d  CO  T  —  00  T  00  —  CO  T—  4— o c  tt  c 0  r— r o  T J  3  CM  CD  n*  1  C  CN  oo CN  oo o  o  o  CN O  d  d  CM CO  o  o  o  o  d  d  d  d  o  d  CN  oo CD  ^—  o  CN  co  T—  T—  o d  co  o  o  t— C N o O  d  d  d  m  m m  CN CO  CO  00  o  co o  h~ o  X—  d  d  d  d  CN  T—  CN  o  co o  CO o  CO o  CO o  h-  d  d  d  d  d  T—  T—  q d  q d  o  o  o  o  o  o  o  o  o  o  o  o  aj ra  T—  d  o  T J  >. ro  d  o  CO  CO  IO  T J  CO  o  CO  E E p  C CU > a>  _  — T— T  ve  (0  T  w  V)  o  >» CO 1 1 u CL  o o d d  d  Oi Oi  d  m  T— —  o o o o o o o o d d d d d d d d  O o o d d d  o d  o d  CO  00 00 ra o  OI  a  CM  W  o  tt  >>  CO  _  CO  T  o  oo  ^_  CM  CN  T3 o  rx  o  ^_  oo  c  •  co  in  ve  o  o  T J  m o  r>- o  r— o  o  o  co T—  CO  o  o o o  o  co  co  o  ^—  T—  o  ^—  o  hO O  o  o o o o O o  o o  T—  o  CO  o o  o o o  CO  CO  o o  o o  d  d  .1  C o  O m  o  T J  C to  in o  >»  Q. 0)  co T J  rx  CD  o  CO  CN CN  d  O d  CO  cn co  CM  CO  d  d  Oi CO o o  CM  in o  d  cn CN  r-  o  d  Oi  •<—  CO  Oi C O CN o O o  co  CO  o  o o  d  d  d  d  d  d  m  T  f-  o  CN O  T—  o  d  d  d  CO  m  CN  00  o o  x:  o o  "co  (A i n  Oi c o ^—  ^—  Oi m  —  T  c *> a> cu > x: i ro-" »- E o £1  —  | l 5^  C tt c>u o  •s CO £ >  2 cjo CoO o o $>  CN  -J 0)  (0  H  "O  4i |  T J  ro  s  Q.  0) Q  c f=  m  o I  in  o  I  o  CN  in  CN  ir> O  CN  o  CO  1  IO CN  m  CO  o  co  o in  co  in o  •*  o  m I  m  m  o  o in  mi m  m I  co  m  co  o  1  CO  o  h-  1  m  CO  in 1  o r»  o  co •  in  m  co  o  1  co  o m Oi • 1 in o c o Oi  o o  m o  T—  *7 o 1  o  T— T—  m  T— T—  1  m  m o o Oi •«—  1  o  T—  o  CM T— 1  in  o  CM cu  f f i CO  o r-  cora_ •S -8 & 2 S "5  0_ 0- — I  Rainfall depth of 2 day events by day, 5.0 mm threshold  Table J-3  Depth (mm)  Day of event, categorized by depth Day 2 Day 1 Cum. % Number Number Cum %'  Table J-4  21.9 45.2 57.5 67.1 69.9 78.1 82.2 86.3 90.4 100.0  16 17 9 7 2 6 3 3 3 7  23.3 43.8 58.9 68.5 74.0 78.1 83.6 86.3 90.4 100.0  17 5-10 15 10-15 11 15-20 7 20-25 25-30 4 3 30-35 35-40 4 2 40-45 3 45-50 7 ge 50 Cumulative percent  Rainfall depth of 3 day events by day, 5.0 mm threshold  Day of event, categorized by depth Depth (mm)  Day 1 Number Cum. %'  10 5-10 7 10-15 15-20 3 20-25 25-30 1 2 30-35 2 35-40 1 40-45 1 ge 50 Cumulative percent 1  37.0 63.0 74.1 77.8 85.2 92.6 96.3 100.0  Day 2 Number Cum. %  4 4 4 4 1 2 1 1 6  14.8 29.6 44.4 59.3 63.0 70.4 74.1 77.8 100.0  Day 3 Number Cum. %  8 4 2 4 2  29.6 44.4 51.9 66.7 74.1  1 1 5  77.8 81.5 100.0  247  00  o  d  co  d o  CO  m m co in I"* CO m CD  o  CM  o  co o  Q. CO  tn  Q TJ  E E o  ui > rs  TJ  >.  S3  cu N  o  cu co o  cu > cu  cu > cu  >. ca TJ  co CO  o o  o CD  O O  co O  CM  >. (0  Q  C  I in m  CD  CO  I-a  Q  E 3  12 CM  co  Q.  cu  TJ  I  C 'co 0£  ,IQw  C <•>  o t_  cu C L C D  > 3  0)  n cs I-  m • o  m CM  1° CM  in o m • • m  E 3  o  APPENDIX K FREQUENCY ANALYSIS RESULTS  249  Appendix K  Frequency analysis results  Table K-1  Annual rainfall and rain days, ranked  F  Rank  1  2  3  4  1  1-F  Z  Reduced variate  z*  Total rainfall # of rain days (mm) 4  1  0.04  0.96  3.11  1.71  1506.80  64  2  0.09  0.91  2.40  1.36  1294.00  57  3  0.13  0.87  1.97  1.12  1011.00  53 52  4  0.17  0.83  1.66  0.94  991.60  5  0.22  0.78  1.41  0.78  986.70  52  6  0.26  0.74  1.20  0.64  900.10  48  7  0.30  0.70  1.01  0.51  848.80  48  8  0.35  0.65  0.85  0.39  804.50  45  9  0.39  0.61  0.70  0.28  791.30  45  10  0.43  0.57  0.56  0.16  725.40  44  11  0.48  0.52  0.43  0.05  724.30  43  12  0.52  0.48  0.30  -0.05  722.70  42  13  0.57  0.43  0.18  -0.16  713.82  42  14  0.61  0.39  0.06  -0.28  681.80  37  15  0.65  0.35  -0.05  -0.39  656.10  36  16  0.70  0.30  -0.17  -0.51  640.50  33  17  0.74  0.26  -0.30  -0.64  634.00  31  18  0.78  0.22  -0.42  -0.78  574.00  30  19  0.83  0.17  -0.56  -0.94  562.00  29  20  0.87  0.13  -0.71  -1.12  561.10  28  21  0.91  0.09  -0.89  -1.36  469.10  28  22  0.96  0.04  -1.14  -1.71  309.10  28  F = Exceedence probability 1-F = Non-exceedence probability z = standard normal variable rain days are defined as those days on which at least 0.1 mm of rain is recorded  250  SIto IS  o 52 = d co cu cu  to  CO  o  to  r-^  CO  co  CJ>  oo m  co  I oo  co  la  f  CD LO od  I CD 00  to to  to  TJ  <o  o o  o 12 = S2  CD  Si E 3  ICM CO  CD CO leg  to I co  CO  to  o  CO  I CD  CO  CM  o  C TJ C  CO CD  co 15  cu  CN  Si  CD  |r»-  I  CO  ICM  E 3  ra  o  3  c c co_ c o  "P. -  to  0  —  1 CM  co 5 e I * « 2 =  CO  «  'C  to  TJ  Si co Si o  TJ  CU  «  co'|  CM  o co  ICM  cu O  c 2  co  CM  or  TJ  Si  O  to  cu  te.  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 co 3 . 2 So  F — I  CM CD O  CO  08  W 3 •C TJ  cu cu a  3  0)  2 "S E 5 o ~E coil u  cu  X  CO CD CN CM ltd  CO CM | I CD CM co CM CM  £1  E  cu E 2 •* -<  -2 » .E -Q 2 TJ cu  E  .a ca  f  15 CO  to  co  CO  = cu  Si  3 CO  C  S2  o  CM O CD I  3  o  — co  =  fl *i to  TJ  a>  ll CU  E o c zz  |  IO  CM  CN  TJ  CN  T!  o to  -—-  1 CM  II CM  m  TJ W S3  CO  .2 co a> £ Q.  -CI  in 0  tn  O  to  259  Table K-15  1 in 5 dry and wet year sumary  Month Interval P. of wet # of rain days day 1 0.16 1-5 Jun. 1 0.12 6-10 1 11-15 0.17 1 0.19 16-20 1 21-25 0.28 2 26-30 0.32 2 1-5 0.40 Jul. 6-10 0.36 2 2 11-15 0.45 16-20 0.47 2 0.48 2 21-25 26-31 0.45 3 3 1-5 0.54 Aug. 3 6-10 0.55 0.46 2 11-15 16-20 0.51 3 21-25 0.45 2 0.45 3 26-31 1-5 0.36 2 Sept. 0.38 2 6-10 11-15 0.21 1 1.00 16-20 0.13 1.00 21-25 0.15 0.10 1.00 26-30 1  2  1  2  3  4  5  3  1 in 5 dry year 1 in 5 wet year Cum. rainfall Total rainfall Total rainfall Cum. rainfall (mm) (mm) (mm) (mm) 0.71 0.71 44.23 44.23 1.42 0.71 88.46 44.23 2.13 0.71 132.69 44.23 2.84 0.71 176.92 44.23 3.55 0.71 221.15 44.23 4.97 1.42 309.61 88.46 6.39 1.42 398.07 88.46 7.81 1.42 486.53 88.46 9.23 1.42 574.99 88.46 10.65 1.42 663.45 88.46 12.07 1.42 751.91 88.46 14.20 2.13 884.60 132.69 16.33 2.13 1017.29 132.69 18.46 2.13 132.69 1149.98 19.88 1.42 1238.44 88.46 22.01 2.13 1371.13 132.69 23.43 1.42 1459.59 88.46 25.56 2.13 1592.28 132.69 26.98 1.42 1680.74 88.46 28.40 1769.20 1.42 88.46 29.11 1813.43 0.71 44.23 29.82 0.71 1857.66 44.23 30.53 0.71 1901.89 44.23 31.24 0.71 44.23 1946.12 4  5  31.24 1946.12 44 Total Fixed intervals total # of rain days/total # of days, in each interval from 1970 - 1993 (P. of wet day) * (# of days) for each interval [1 day maximum rainfall depth (0.1 mm model)] * (# of rain days in the interval) [1 day minimum rainfall depth (0.1 mm model)] * (# of rain days in the interval)  260  Table K-16  Month  1 in 10 wet and dry year summary  Interval P. of wet # of rain days day 1 0.16 1-5 1 0.12 6-10 1 0.17 11-15 1 0.19 16-20 1 0.28 21-25 2 0.32 26-30 0.40 2 1-5 2 0.36 6-10 0.45 2 11-15 2 0.47 16-20 2 0.48 21-25 3 0.45 26-31 3 0.54 1-5 3 0.55 6-10 2 0.46 11-15 3 0.51 16-20 2 21-25 0.45 3 0.45 26-31 0.36 2 1-5 0.38 2 6-10 0.21 1 11-15 1 16-20 0.13 0.15 1 21-25 0.10 1 26-30 1  2  June  July  August  Sept.  1  2  3  4  5  3  1 in 10 dry year 1 in 10 wet year Cum. rainfall Total rainfall Cum. rainfall Total rainfall (mm) (mm) (mm) (mm) 0.35 0.35 55.07 55.07 0.70 0.35 110.14 55.07 1.05 0.35 165.21 55.07 1.40 0.35 220.28 55.07 1.75 0.35 275.35 55.07 2.45 0.70 385.49 110.14 3.15 0.70 495.63 110.14 3.85 0.70 605.77 110.14 4.55 0.70 715.91 110.14 5.25 0.70 826.05 110.14 5.95 0.70 936.19 110.14 7.00 1.05 1101.40 165.21 8.05 1.05 1266.61 165.21 9.10 1.05 1431.82 165.21 9.80 0.70 1541.96 110.14 10.85 1.05 1707.17 165.21 11.55 0.70 1817.31 110.14 12.60 1.05 1982.52 165.21 13.30 0.70 2092.66 110.14 14.00 0.70 2202.80 110.14 14.35 0.35 2257.87 55.07 14.70 0.35 2312.94 55.07 15.05 0.35 2368.01 55.07 15.40 0.35 2423.08 55.07 4  5  15.40 2423.08 44 Total Fixed intervals total # of rain days/total # of days, in each interval from 1970 - 1993 (P. of wet day) * (# of days) for each interval [1 day maximum rainfall depth (0.1 mm model)] * (# of rain days in the interval) [1 day minimum rainfall depth (0.1 mm model)] * (# of rain days in the interval)  APPENDIX L CROP AND EVAPOTRANSPIRATION SUMMARY  262  c o TJ  a> •*-» re cn  CO  c o E  cu  >.  CU  CO  cu cn  CD CM  o  2  la  cu > <  CD CO  d  2 CD >  co  TJ  TJ  ^ * re  CD  X # !—  M  1 1 .2 2  >. re  o «" > cu  ° c o  .£  «  §.  2 o  o  x  it 2  TJ  CD  CO  O o U o  re o fc CD E ho co ° •§ c oos o CO *3 CO co II TJ T  o  CD D_  CO  4-1  cu E 2 ca  a.  II  —  CD O  -O  §  CO  o o CO c u cu c u° i c O) CO cZ CO ° c £ !CO JCO t re o CD o a > o cu > CO > O E Q  JZ  cu r-  CD  LO  P o  1 ^ cu a. ja Q. re < H  CD  O CD  o  TJ  °-  O  "a  > 5  EL w  2  TJ  cn c  urs lar  to c  >. CO  cu o  c io  > <  1  <  <  Jr-  CO  CO  263  Table L-2  Crop information and coefficients, selected crops  Crop  Sowing Date 3  Growing Season (days)  Initial  Crop Development Stage Late Development Mid-Season  Length (days)  Length K (days)  3  Length (days)  Length (days)  d c  Kharif Season 8-Jul 7-Jul 18-Jul 20-Jul 7-Jul  Soybean Groundnut Sorghum Maize Paddy Rice  100 106 110 115 125  30° 35° 40° 30° 35°  0.48 0.48 0.48 0.48 1.15  15 20 20 20 20  0.74 0.72 0.74 0.80 1.10  50 30 30 50 50  1.00 0.95 1.00 1.10 1.05  15 25 20 15 20  0.72 0.78 0.78 0.83 0.95  25 20  0.70 0.73  30  0.67  Rabi Season 45 1.10 40° 0.65 132 20 0.20 12-Oct Mustard 60 1.10 30° 0.67 20 0.23 131 1-Nov Gram (Chickpea) 50 1.10 2 5 0.67 15 0.23 120 15-Nov Wheat Chieng, 1993 Development stage length from Subramaniam (1989) Development stage length adapted from Doorenbos and Pruitt (1977) K c values from Doorenbos and Pruitt (1977) unless otherwise noted K c value averaged between Doorenbos and Pruitt (1977) and Subramaniam (1989) e  e  e  D  a  b c  d e  Table L-3  Summary of k factors for relevant months  ET k factor Frequency of grass irrigation/rain (mmd" ) (days) 0.28 3.42 20 Jan. 5.15 0.22 20 Feb. 0.18 6.95 20 Mar. 0.41 11.54 6 Jun. 0.48 9.44 5 Jul. 0.61 4.83 5 Aug. 0.58 5.14 5 Sep. 0.20 6.58 20 Oct. 0.23 4.33 20 Nov. 0.28 3.46 20 Dec. mean ETgrass averaged over all methods Doorenbos and Pruitt, 1977 Month  1  c  1  1  2  2  264 CO CN CN co CN CO oo l l O odi  c  CD CO  co  CO  co  CO co  co o  CO  CN CN  loo I  c  CD •*-» CO  'C c J= co O Q.  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