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A‘urm'l; _ '4 $533» van-$134,; ”"9 I .3‘ 731 ‘5 "(533 \ A I “egg: “fig: quv ’ “‘fh‘uj‘ q 7%:L..4.‘ J a . , ‘43 , "r 9-,.‘II 1933‘ . ”NOTE... ; .v‘ I!“ I . .an :. a”. H 1?; ‘fiu. l-' "-v 7:333 I figéf’j’f'y w: .— ifé-jt". " n" nhflifii’m ‘ 3:23.919 ”—- Date Illlll'llllllllllllIlll'llllllllllllllll 3 1293 00910 8618 This is to certify that the dissertation entitled MODELING INFILTRATION USING TINE-TO—PONDING AND A STORM GENERATOR APPROACH presented by Tien—Yin Chou has been accepted towards fulfillment of the requirements for DOCTOR degree in PHILOSOPHY jimjfim Joe T. Ritchie Major professor November 9 , 1990 MSU is an Affirmative Action/Equal Opportunity Institution 0— 12771 _— 1 Michigan State University l LIBRARY “l PLACE IN RETURN BOX to remove this c TO AVOID FINES return on or before date DATE DUE DATE DU heckout from your record. due. E DATE DUE I a “ha—— ‘53.; 1‘ if: u. v—v—vwv _1' MSU Is An Affirmative Action/Equal 0p if! i portuni'ty Institution czbthpna-et MODELING INFILTRATION USING TIME-TO-PONDING AND A STORM GENERATOR APPROACH BY Tien-Yin Chou A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Resource Development 1990 ABSTRACT MODELING INFILTRATION USING TIME-TO-PONDING AND A STORM GENERATOR APPROACH BY TIEN-YIN CHOU Soil productivity is largely determined by the biological, physical, and chemical properties and processes in concert with climate and resource management inputs. Mathematical or physical models are effective for describing the influences of soil erosion and management systems on long- term productivity. Research on developing and applying a functional model of infiltration into a soil profile under rainfall or irrigation conditions is important in both hydrology and agriculture. To provide a rational basis for infiltration prediction during rainfall or irrigation, a nonlinear model was used in this study to calculate cumulative infiltration based on time-to-ponding approach. The cumulative infiltration amount at ponding is a function of water application rate, saturated conductivity, saturated soil water content, antecedent soil water content, and macroscopic capillary length. Soil management practices such as crop types, tillage methods and surface residue cover also influence soil properties and infiltration capacity. To make this infiltration model functional for strategic applications where it is difficult to obtain or use short- period rainfall data, a relatively simple storm generator was used to generate daily precipitation and to disaggregate it into a discrete number of storms of varying intensity patterns. The generated outcome distribution of rainfall was used as input to the physically based time—to-ponding model. A field study was conducted on a loamy sand (Eutric Glossoboralf) soil in Michigan with corn and potatoes under various tillage, surface residue, and wheel traffictconditions to determine values of the soil properties needed for the infiltration model. Time-to-ponding was observed for various water application rates using a sprinkling infiltrometer under a variety of soil management situations. Time to ponding curves were established for each management combination of crop, tillage and wheel traffic conditions. The time-to-ponding approach appears to be a good infiltration predictor under complex rainfall patterns and different soil management conditions. Using the ponding curves, with known soil hydraulic properties, the point source (or localized) runoff are predictable under any type of rainfall or irrigation patterns. This point source runoff is a critical input for the assessment of water erosion. ACKNOWLEDGMENTS I wish to express my sincere gratitude and appreciation to my advisor Dr. Joe T. Ritchie. I believe I was one of the most fortunate Ph.D. student at Michigan State University because of my advisor, who has been continuously supported, encouraged and guided me for the past four years. I learned not only the knowledge in various scientific fields but also important was the emotion for real world application by those researches output from different fields. I also wish to thank Dr. Eckhart Dersch for his patiently advice and serving on my committee. I am grateful to Dr. George Merva for his genuine interest in my research and his inputs for this document. My appreciation is also given to Dr. DennisiGilliland for contributing immensely to my research for storm generator analysis. I would like to express my appreciation and thanks to Dr. Francis Pierce for the time, energy and valuable suggestion for my research. I thank Dr. Vincent Bralts for accepting my late offer to become a member of my committee and appreciate his helpful suggestions regarding improvement of this document. I would like to credit and thank Dr. Ian White for his contribution of the development of time-to-ponding model. I iv also appreciate Dr. Pat 8. Crowley for sharing the interest in this study, and made available the sprinkling infiltrometer equipment and a fruitful summer field study in Montcalm county. I was lucky enough to become one of Dr. Ritchie's graduate student and brought me into the Nowlin Chair Group. I haveibeentguided, motivated, and.challenged.by'many scholars in the group and also developed good friendships with each of them. Specially thanks for Sharlene Rhines, Liliana Nunez, Frederic Dadoun and Marc McNabnay for their contribution to my completion for this document. I wish to dedicate this work.to my parents for their love and support for me. I gratefully thank to my brother Tyan-Shu and my sister-in-law Tswei-Ping, for their support and encouragement. My deepest appreciation is given to my wife for her understanding, support and persistence contributed greatly to the completion of my degree. LIST LIST LIST LIST I. II. III. IV. TABLE OF CONTENTS OF TABLES . . . . . . . . . . . . . . . . . . . OF FIGURES . . . . . . . . . . . . . . . . . . . OF SYMBOLS . O O O O O O O O O O O O O O O O O 0 OF TILLAGE ACRONYMS . . . . . . . . . . . . . . INTRODUCTION . . . . . . . . . . . . . . . . . LITERATURE REVIEW . . . . . . . . . . . . . . . A. B. Rainstorm Generator . . . . . . . . . . . . 1. Precipitation Occurrence . . . . . . . 2. Individual Rainstorm Occurrence . . . . 3. Disaggregation Modeling for Storm Intensity Pattern . . . . . . . . . . Infiltration Model Using Time-to—ponding Approach . . . . . . . . . . . . . . . . . 1. Quasi-Analytic Theory 0 Rainfall Infiltration . . . . . . . . . . . . . 2. Approximate Solutions . . . . . . . . . 3. Time-to-ponding . . . . . . . . . . . . 4. Soil Management Effect on Infiltration DEVELOPMENT OF THE RAINSTORM GENERATOR . . . . A. Rainstorm Occurrences in One Wet Day . . . . B. Amount and Distribution of Individual Storms C. Joint Probability Distribution of Storm Duration and Amount . . . . . . . . . . . . . . . . . . D. Peak Storm Intensity . . . . . . . . . . . . E. Disaggregation for Storm Rainfall Intensity Patterns . . . . . . . . . . . . . . . . . TIME-TO-PONDING MODEL DEVELOPMENT . . . . . . . A. Pre-ponding . . . . . . . . . . . . . . . . B. Ponding . . . . . . . . . . . . . . . . . . C. Post-ponding . . . . . . . . . . . . . . . . FIELD MEASUREMENT OF TIME-TO-PONDING . . . . . A. Sprinkling Infiltrometer . . . . . . . . . . B. Field Procedure . . . . . . . . . . . . . . vi viii ix xiii H oasimox 11 13 16 19 21 23 27 27 34 37 41 45 56 57 58 60 62 62 65 C. Ponding Curves . . . . . . . . . . . . . . . VI. RESULTS AND DISCUSSION . . . . . . . . . . . . A. Rainstorm Generator . . . . . . . . . . . . B. Field Measurements of time-to-ponding . . . C. Some Limitations of Time-to-ponding Model . D. Demonstration of Use of Ponding Curves and Simplified Storm Patterns . . . . . . . . . E. Example of Runoff Prediction for One Rainstorm . . . . . . . . . . . . . . . . . VII. SUMMARY AND CONCLUSIONS . . . . . . . . . . . . APPENDIX 1. Fortran source code for observed storm intensity calculation from rain gauge data record 0 O O O O O O O O O O O O O O O O O O I 0 APPENDIX 2. Fortran source code for time-to-ponding calculation for sprinkling infiltrometer experiment 0 O O O O O O O O O O O O O O O O O 0 APPENDIX 3. Fortran source code for bulk density and initial water content calculation for sprinkling infiltrometer experiment . . . . . . APPENDIX 4. Soil water content estimation from texture and bulk density . . . . . . . . . . . . APPENDIX 5 Optimization Complex program for best- fit ponding curves estimation . . . . . . . . . APPENDIX 6. Fortran source code of storm generator program 0 O D O O O O O O O O O O O 0 O O O 0 0 APPENDIX 7. Field measurement and derived soil properties from ponding curves for infiltrometer experiment . . . . . . . . . . . . . . . ... . . APPENDIX 8. Field measured residue cover, initial water content, and bulk density for sprinkling infiltrometer experiment . . . . . . . . . . . . APPENDIX 9. Field measured ponding time and water applied depth at ponding for sprinkling infiltrometer experiment . . . . . . . . . . . . BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . vii 69 70 70 74 83 84 95 104 110 112 116 120 122 129 132 134 155 164 LIST OF TABLES Table 1. Monthly statistics for observed 30 years rainstorm record (1956-1985) for Deer-Sloan Watershed station #10, Michigan. . . . . . . . . . 29 Table 2. Example calculation of storm intensity pattern for an observed storm record from Deer- Sloan Watershed station #10, Michigan on July 11,1985. . . . . . . . . . . . . . . . . . . . . . 46 Table 3. Simulated output from double exponential distribution for normalized storm time (T*) and intensity (Int*) with 10 equal time increments for Deer-Sloan Watershed station #10 on July 11, 1985. . . . . . . . . . . . . . . . . . . . . . . 51 Table 4. Simulated output for real storm time and intensity with 10 equal time increments for Deer- Sloan Watershed station #10 on July 11, 1985. . . 52 Table 5. Simulated output for real storm time and intensity with peak intensity and 10 equal time increments for Deer-Sloan Watershed station #10 on July 11, 1985. . . . . . . . . . . . . . . . . . . 53 Table 6. Monthly statistics for simulated 30 years rainstorm record for Deer-Sloan Watershed station #10, Michigan. . . . . . . . . . . . . . . . . . . 73 Table 7. Field measurements of time-to-ponding for soil with potato and corn crops with various tillage and surface residue treatments for Montcalm County, Michigan. . . . . . . . . . . . . 76 Table 8. Calculated runoff (mm) from cumulative infiltration and cumulative rainstorm amounts for different surface treatment of a paratilled soil with a potato crop with wheel track condition. . 103 viii LIST OF FIGURES Figure 1. Cumulative Density Function (CDF) for 30 years (1956-1985) observed storm event number on one wet day from Deer-Sloan Watershed station #10, Michigan. Separate CDF are shown for each months analyzed. . . . . . . . . . . . . . . . . Figure 2. Cumulative Density Function (CDF) for simulated storm event number on one wet day using geometric distribution functions for Deer-Sloan Watershed station #10, Michigan. Separate CDF are shown for each months simulated. . . . . . . . . . Figure 3. Geometric distribution coefficients for simulated storm event number on one wet day for Deer-Sloan Watershed stations #10 and #18, Michigan. . . . . . . . . . . . . . . . . . . . . Figure 4. Cumulative Density Function (CDF) for 30 years (1956-1985) observed individual storm amounts from Deer-Sloan Watershed station #10, Michigan. Separate CDF are shown for each months analyzed. . . . . . . . . . . . . . . . . . . . . Figure 5. Cumulative Density Function (CDF) for simulated individual storm amount using gamma distribution functions for Deer-Sloan Watershed station #10, Michigan. Separate CDF are shown for each months simulated. . . . . . . . . . . . . . . Figure 6. Regression for 30 years (1956-1985) observed individual storm duration and amount for April from Deer-Slone Watershed station #10, Michigan. . . . . . . . . . . . . . . . . . . . . Figure 7. Regression for 30 years (1956-1985) observed individual storm duration and amount for July from Deer-Slone Watershed station #10, Michigan. . . . . . . . . . . . . . . . . . . . . Figure 8. Cumulative Density Function (CDF) for 30 years (1956-1985) observed peak intensity for individual rainstorm amount classes from Deer- Sloan Watershed station #10, Michigan. . . . . . . Figure 9. Cumulative Density Function (CDF) for simulated peak intensity for individual rainstorm amount classes using exponential distribution functions for Deer-Sloan Watershed station #10, Michigan. . . . . . . . . . . . . . . . . . . . . Figure 10. Exponential distribution co fficients for simulated peak intensity for individual rainstorm amount classes for Deer-Sloan Watershed ix 31 32 33 35 36 39 40 42 43 station #10, Michigan. . . . . . . . . . . . . . . Figure 11. Observed storm intensity of one rainstorm event on July 11, 1985 from Deer-Sloan Watershed station #10, Michigan. . . . . . . . . . Figure 12. Observed and simulated normalized storm intensity for one rainstorm event on July 11, 1985 from Deer-Sloan Watershed station #10, Michigan. . Figure 13. A comparison of simulated storm intensities with peak intensity and 10 equal time increments for one rainstorm event on July 11, 1985 for Deer-Sloan Watershed station #10, Michigan. . . . . . . . . . . . . . . . . . . . Figure 14. Schematic diagram of sprinkling infiltrometer used for field time-to-ponding measurement. . . . . . . . . . . . . . . . . . . . Figure 15. Flow chart of the rainstorm generator used in this study. . . . . . . . . . . . . . . . . . . . . . . Figure 16. Mean bulk density of surface soil for various crop and tillage plots (MB: moldboard, DP: disc plow, NT: no till, PP: paraplow). The bar above each mean shows one standard deviation. . . Figure 17. Best-fit ponding curves derived from observed time—to-ponding data for corn plots with various tillage and wheel track conditions. . . . . . . . . . . . . . . . . . . . Figure 18. Best-fit ponding curves derived from observed time-to-ponding data for potato plots with various tillage and wheel track conditions. . Figure 19. Surface residue effects on best-fit ponding curves derived from observed time-to- ponding data for potato plots with paraplowed soil and various wheel track conditions . . . . . . . . Figure 20. Influence of initial soil water content on best-fit ponding curves derived from observed time-to-ponding data for potato plots with moldboard plowed soil and various wheel track condition. . . . . . . . . . . . . . . . . . . . . Figure 21. Four types of assumed rainfall distributions for a 30 mm rain in 1.5 hour as a demonstration for infiltration prediction. . . . . . . . . . . . . . . . . . . . Figure 22. Ponding curves for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic conditions with type A rainfall distribution. . . . . . . . . . . . . . Figure 23. Ponding curves for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic conditions with type B rainfall distribution. . . . . . . . . . . . . . Figure 24. Ponding curves for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic conditions with type X 44 47 48 55 63 72 77 78 79 81 82 86 87 88 C rainfall distribution. . . . . . . . . . . . . . 89 Figure 25. Ponding curves for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic conditions with type D rainfall distribution. . . . . . . . . . . . . . 90 Figure 26. Calculated cumulative infiltration amount and cumulative rainfall amount for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic conditions with type A rainfall distribution. . . . . . . . . . . . . . . . . . . 91 Figure 27. Calculated cumulative infiltration amount and cumulative rainfall amount for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic conditions with type B rainfall distribution. . . . . . . . . . . . . . . . . . . 92 Figure 28. Calculated cumulative infiltration amount and cumulative rainfall amount for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic conditions with type C rainfall distribution. . . . . . . . . . . . . . . . . . . 93 Figure 29. Calculated cumulative infiltration amount and cumulative rainfall amount for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic conditions with type D rainfall distribution. . . . . . . . . . . . . . . . . . . 94 Figure 30. Ponding curves for paraplowed soil with a potato crop under wheel track condition for various surface residue treatments and observed rainstorm on July 11, 1985 from Deer-Sloan Watershed station #10, Michigan. . . . . . . . . . 97 Figure 31. Calculated cumulative infiltration amount and cumulative rainfall amount for paraplowed soil with a potato crop under wheel track condition for various surface residue treatments and an observed rainstorm. . . . . . . 98 Figure 32. Ponding curves for paraplowed soil with a potato crop under wheel track condition for various surface residue treatments and simulated rainstorm using peak intensity on July 11, 1985 from Deer-Sloan Watershed station #10, Michigan. . 99 Figure 33. Calculated cumulative infiltration amount and cumulative rainfall amount for paraplowed soil with a potato crop under wheel track condition for various surface residue treatments and a simulated rainstorm using peak intensity. . . . . . . . . . . . . . . . . . . . 100 Figure 34. Ponding curves for paraplowed soil with a potato crop under wheel track condition for various surface residue treatments and simulated xi rainstorm using 10 equal increments on July 11, 1985 from Deer-Sloan Watershed station #10, Michigan. . . . . . . . . . . . . . . . . . . . 101 Figure 35. Calculated cumulative infiltration amount and cumulative rainfall amount for paraplowed soil with a potato crop under wheel track condition for various surface residue treatments and a simulated rainstorm using 10 equal time increments. . . . . . . . . . . . . . 102 xii P[w/w] P[W/d] a, qz 3 LIST OF SYMBOLS probabilities of wet day following a wet day. probabilities of wet day following a dry day. coefficients for gamma distribution function. flux, volume of water moving through the soil in the z-direction (L/T). hydraulic head (L). soil-water hydraulic conductivity (L/T). saturated hydraulic conductivity (L/T). soil water pressure potential (L). volumetric soil water content (Lflnf). saturated soil water content (Lzflf). initial soil water content (L543). reference soil water content (Lzflf). soil sorptivity (L/TJ). soil-water diffusivity (IE/T). flux-concentration relation for constant pressure boundary condition (L/T). surface water flux (L/T). ponding time (T). xiii H 'o 0» 1P 3" cumulative infiltration amount at ponding (L). cumulative infiltration amount post ponding (L). rainfall rate (L/T). cumulative rainfall amount at ponding (L). macroscopic capillary length (L). runoff rate (L/T). xiv CMW CDW CDN CNW CNN PMW PMN PPW PPN LIST OF TILLAGE ACRONYMS Corn, moldboard plowed, wheel track Corn, moldboard plowed, non-wheel track Corn, disk plowed, wheel track Corn, disk plowed, non-wheel track Corn, no—tilled, wheel track Corn, no-tilled, non-wheel track Potato, Potato, Potato, Potato, moldboard plowed, wheel track moldboard plowed, non-wheel track paratill, wheel track paratill, non-wheel track I . INTRODUCTION Soil.is.a‘valuable natural resource that needeprotection from excessive erosion if long term crop productivity is to be maintained. The ability ix: predict long-term soil productivity in a variety of agricultural management and soil, climate, and plant growth scenarios will allow the assessment of the consequences of various environmental and agricultural policies. IEquations that predict soil erosion are widely used tools for dealing with soil conservation issues. Rainfall- runoff models are needed to predict soil infiltration and runoff under different rainfall patterns and soil management. There are several modeling approaches commonly used to simulate infiltration ranging from. complex solutions describing water movement in soil to empirical models that must be fitted using measured infiltration data. The more useful models contain variables that are difficult to measure because they have no physical significance (Mein and Larson, 1973; Reeves and Miller, 1975; Parlange et al., 1985). In several presently used model of crop growth and hydrology, the curve number technique is used for runoff prediction. In 1954 the Conservation Service (SCS) developed 2 this unique procedure for estimating direct runoff from storm rainfall. This procedure, which is frequently referred to as the curve number technique, has proven to be a very useful tool for evaluating effects of changes in land use and treatment on direct runoff. The advantage for the curve number technique is that it requires only the daily rainfall inputs and estimates total runoff somewhat reliably for a season. The limitation of the curve number technique is that it does not accurately predict runoff for individual storm, and it requires empirical inputs which have little physical meaning and are not measurable in the field“ ZMany researchers (Hawkins, 1978: Jackson et. al., 1976) have expressed concern that the curve number procedure does not reproduce measured runoff from specific storm rainfall because time was not incorporated in this method for estimating runoff. Smith in 1978 found that the curve number technique can not be extended to predict infiltration patterns within a storm, and that the procedure can not respond to differences in rainfall intensity. During a rainfall event there are periods of heavy downpour and periods of light drizzle. When the rainfall intensity is heavy, the ground surface usually becomes ponded. When rainfall intensity is low, there is usually no surface ponding. There are two distinct stages of infiltration during a rainfall event - a stage in which the ground surface is ponded with water and a stage without surface ponding. Under a ponded surface the infiltration process is independent of 3 the effect of the time distribution of rainfall. The rate of infiltration reaches its maximum capacity and is referred to as the infiltration capacity. Without surface ponding, all the rain infiltrates into the soil. The rate of infiltration equals the rainfall intensity, which is less than the infiltration capacity. Many infiltration models have been formulated to describe the infiltration process with the surface ponded. If the time that separates the non ponded and ponded can be determined, the difficulty involved in modeling infiltration during a nonsteady state rainfall is reduced. Analysis of infiltration data also requires equations that are physically based to insure their applicability for predictive use. That is, they showed fit observations accurately and the parameters used in the equations should not change with different initial and boundary conditions. Under these conditions infiltration concept can be used with confidence to obtain soil properties, e.g. sorptivity and saturated conductivity by measurement of the time to ponding under condition of variable rainfall rates (Broadbridge and White, 1987). To adopt point source runoff estimation procedures based on infiltration concepts, one major obstacle is the difficulty in obtaining and using short-period or "break-point" rainfall intensity data (Brakensiek et al., 1981). Physically based infiltration models are quite sensitive to the distribution of total storm rainfall within time increments as short as 5 minute (Woolhiser and Osborn, 1985). Although infiltration 4 models allow improved prediction of infiltration, Their practical use has been limited, primarily because of the lack of rainfall intensity. Woolhiser and Osborn (1985) suggested that if parameter-efficient techniques can be developed to disaggregate the commonly available daily rainfall into intermittent rainfall intensities within the day, simulated rainfall intensity could provide input for physically-based runoff models. This study was designed to develop methodology to (1) predict the infiltration of water into soil using a infiltration capacity concept, and to (2) to generate a reasonable pattern of rainfall intensity for use with the infiltration equation when only daily rainfall amount is known. The specific objectives of this study were: 1. To develop a parameter efficient model to disaggregate daily precipitation into individual storms, and to further disaggregate the storms into short period intensity patterns. 2. To examine a time-to-ponding approach for infiltration and runoff prediction under variable rainfall patterns and for various soil management practices. 3. To conduct field studies. to evaluate the soil properties needed in the time-to-ponding equation and how they are influenced by various types of soil management. 5 4. To determine the sensitivity of the model to the measured variations in the soil type, tillage and residue management, and rainstorm characteristics. II. LITERATURE REVIEW A. Rainstorm Generator To use the time-to-ponding infiltration equation for computing infiltration and thus runoff, rainfall input data must be in the form of breakpoint data. The form is called breakpoint because the data results from numerical differentiation. of ‘the tcumulative ‘time ‘versus cumulative rainfall depth curve at the changes in slope, or breakpoint. Using observed weather data has many limitations. Short time rainfall records can be difficult to obtain for a particular location (Carey and Haan, 1978; Mean et al., 1976: Jones et al., 1972; Richardson, 1985) and few sites have hourly rainfall records of 15 or more years duration. Sites with rainfall intensity data often have periods of missing records due to instrument failure. Also, development of data for a long period at a particular location is time consuming, but is needed for developing rainstorm generators. Disaggregation of daily precipitation into rainfall intensity patterns ‘with. properties similar' t0> those obtained from analysis of observed breakpoint data can provide the information needed for analysis of infiltration where only 7 daily rainfall records are available. The following sections provide a brief background and describe the method used in deriving approximate rainfall intensity data. 1. Precipitation Occurrence The first step in generating sequences of daily rainfall is to determine the occurrence of wet and dry days (Srikanthan and McMahon, 1985) . Markov chain models have been commonly employed to generate the wet and dry sequences” Gabriel and.Nuemann (1962) used a first order Markov chain to model rainfall occurrence at Tel Aviv. Green (1964) described the characteristics of the discrete daily rainfall sequence which results from a continuous, two-state Markov process. In an investigation of Monte Carlo methods, Wiser (1965, 1966) found.that.a Markov model should be satisfactory if event persistence lasts only from one period to the next. Several modified models to account for extended persistence were proposed. Adamowski and Smith (1972) determined that a first order Markov model was adequate, but not entirely accurate, as a generator of daily rainfall occurrence. Periods of 5 to 6 days, 8 to 10 days, and 16 days were noted in the variance spectrum that were not accounted for by the Markov chain. Since the publication of Green (1964), a number of studies have examined the probabilistic character of both daily rainfall and short-term event rainfall. Daily 8 rainfall models were described by Roldan and Woolhiser (1982), Yevjevich and Dyer (1983), and Richardson and Wright (1984). Short-term event rainfall models were examined for use in hydrologic applications by Howard (1976), Di Toro and Small (1979), Loganathan and Delleur (1984) Cordova and Rodriquez-Iturbe (1985), and others. Among those daily precipitation simulations, Richardson and Wright (1984) developed a model (WGEN) that simulates daily rainfall, maximum and minimum temperature, and solar radiation. Rainfall occurrence is simulated using a first order Markov chain model. Rainfall amount on a wet day was determined using a two coefficients gamma generation procedure described by Haan (1977). Simulation coefficients for the Markov probabilities of wet day following a wet day (P[w/w]) and. wet day following a dry day (P[w/d]) and gamma distribution (a and B) were estimated for 13 unique seasons within a calendar year. 2. Individual Rainstorm Occurrence Markov models have also been applied to a generation of short term. rainfall sequences. Pattison (1965) produced synthetic hourly rainfall amount for the Stanford Watershed Model. His model was a mixed, first and second order Markov model. A transition probability matrix determined the amount of rainfall in an hour, 9 based on the amount of rainfall occurring in the previous hour. Nguyen and Rousselle (1981) represented the hourly rainfall sequenceiwith first.and second order, two state, Markov chains. Their second order model described the sequence of wet hours only slightly better than the first order model. Rainfall depth of individual rain hours within a storm sequence were assumed to be independent and distributed exponentially. The probabilities of accumulated rainfall within the storm were calculated with a function describing the distribution of the sum of a random number of exponentially distributed random variables. Srikanthan and McMahon (1983) generated rainfall on hourly and six-minute intervals. Their procedure was to generate daily wet-dry sequences using transition probability matrices (TPM). Several methods of generating hourly rainfall rates on wet days were tested. The best model was a two-state Markov chain with two separate hourly TPM conditioned on a critical daily rainfall depth. Croley et al. (1978) presented a six season, exponentially distributed interarrival time model to simulate hourly precipitation. Intrastorm structure was described in terms of storm segments. Storms segments were characterized by duration, peak hour, and rainfall accumulation. Normalized hyetographs of storms were used 10 to simulate hourly rainfall within a storm. Raudkivi and Lawgun (1973) noted a serious limitation of Markov chain models. They found that these models only reproduce transitions which have been observed in the historic record and the extreme events may be inadequately represented. They modeled rainfall as a time dependent autoregressive series with a random component. Rainfall was simulated in 10-minute time units. With the increased focus on short-term, event-scale precipitation, additional attempts to establish links between the continuous and discrete occurrence models have appeared. In particular, methods have been developed to estimate the statistical properties of event precipitation when only daily records are available. The increased focus on event models has led to the recognition that rainfall in many areas does not follow the Markov property. Events may exhibit temporal dependence, as represented in the point process cluster models of Kavvas and Delleur (1981), Waymire et al. (1984), and Smith and Karr (1983). The sequential simulation of rainstorms is but one method of obtaining short term sequences. These sequences can also be obtained through disaggregation of large time interval rainfall depths. 11 3. Disaggregation Modeling for Storm Intensity Pattern Several investigators have. developed stochastic models of short-time storm intensity patterns at a single point (Pattison, 1965: Grace.and Eagleson, 1966; Raudkivi and Lawgun, 1973; Knisel and Snyder, 1975; Nguyen and Rousselle, 1981). A review of this work reveals that the models either were not designed to accommodate intervals of less than an hour or they require a large number of empirically determined coefficients that make them difficult to use in other locations. Most of them focus on the disaggregation of annual to seasonal, seasonal to monthly, and monthly to daily amounts. Hershenhorn and Woolhiser (1987) reviewed rainfall disaggregation methods proposed by Betson, et al. (1980) and Srikanthan and McMahon (1985), found both methods need large numbers of transition probability estimates. Hershenhorn and Woolhiser (1987) disaggregated daily rainfall into one or more individual storms and then disaggregated the individual storms into rainfall intensity patterns. The disaggregated data included starting time of each storm event on wet days as well as the time-intensity data within each event. The accumulated storm precipitation process was nondimensionalized by dividing the precipitation at any time by the total storm precipitation, and the elapsed time by the total duration. The process was divided into 10 equal dimensionless time increments, and the depth increments 12 were rescaled to range between 0 and 1 by dividing each increment by the fraction of the precipitation that occurred between the beginning of that time period and the end of the storm. Flanagan, et al. (1987) studied the influence of storm pattern (time to peak intensity and the maximum intensity) on runoff, and erosion loss using a programmable rainfall simulator. Six rainfall patterns and three maximum intensities were used. The storm patterns were constant, triangular, and compound consisting of four straight line segments. All patterns could be described fairly well by a double exponential function. The double exponential function or distribution describes rainfall intensity as exponentially increasing with time until peak intensity is reached and then exponentially decreasing with time until the end of the storm. The water Erosion Prediction Project (WEPP) User Requirements (Foster and Lane, 1987) suggested that the maximum information required to represent a simulated storm consists of the following: (a) storm amount, (b) average intensity, (c) ratio of peak intensity to average intensity, and (d) time to peak intensity. Examination of appropriate functions to describe a rainfall intensity pattern, given this information, suggest consideration of a triangular distribution and a double exponential distribution. 13 Nicks.and.Lane (1989) demonstrated.that.the rainfall depth-duration-frequency relationship produced by a weather generator they produced for WEPP, is sensitive to the peak storm intensity, and the duration of the event. Although the disaggregated intensity pattern does not fit the observed intensity pattern, the calculated runoff agreed quite well with measured runoff. When using the disaggregated intensity patterns as input to their calibrated infiltration-runoff model, the model could explain some 90% of the variance in runoff computed using the observed rainfall intensity patterns. B. Infiltration Model Using Time-to-ponding Approach Infiltration is controlled primarily by the factors governing water movement in the soil. The basic relationship for describing soil water movement was derived from experiments by Darcy in 1856. He found that the flow rates in porous materials is directly proportional to the hydraulic gradient, or, for the one—dimensional case: q2 = -K (dH/dz) [2.1] where: qi = flux, or volume of water moving through the soil in the z-direction per unit area per unit time (L/t). H = hydraulic head (L). dH/dz = hydraulic gradient in the z direction. 14 K = hydraulic conductivity (L/t). A second relationship needed to describe water movement in soil is the principle of conservation of mass for the soil water system: dO/dt = - v'q [2.2] where: 8 = volumetric soil water content (LAM?) t = time (t) q = flux vector <1 || del operator = d/ax + a/dy + 6/62. Combining equations [2.1] and [2.2] yields the general equation of flow in porous media, or Richards' equation, which can be expressed as: dO/dt = -v (-KvH) [2.3] Richards' equation indicates that soil water movement, and thus infiltration, depends on the hydraulic conductivity and the hydraulic gradient of the soil. The hydraulic gradient depends on the force of gravity plus the capillary suction exerted by the soil. Both hydraulic conductivity and capillary suction are functions of the water content of the soil. 15 When hydraulic conductivity and capillary suction are single-valued functions of water content, equation [2.3] can be written as (Philip, 1969): de/dt = v (ova) + dK/dz [2.4] K(dT/d0) = diffusivity (If/t). where: D 2 = flow direction, taken as positive upward (L). Hanks and Bowers (1963) studied the influence of the shapes of the soil water characteristic curve (suction versus water content) and the hydraulic conductivity and water content relationship in infiltration. ‘Phey showed. that variations in the soil-water'diffusivity at low water’contents have negligible effect on infiltration from a ponded water surface. However, variations in either the diffusivity or soil water characteristic at water contents near saturation have a strong influence on predicted infiltration. Thus, errors in measuring soil hydraulic properties have greater impact for water contents near saturation than for drier conditions as far as infiltration is concerned (Skaggs and Khaleel, 1982). 16 1. Quasi-Analytic Theory of Rainfall Infiltration The infiltration process can be calculated for most initial and boundary conditions by solving the governing differential equations using numerical methods. These solutions provide a physically consistent means of quantifying infiltration in terms of the soil properties governing movement of water and air. Developing and applying quasi-analytical descriptions of the transport of water in soil during rainfall has received considerable attention for the past 30 years. A common approach to rainfall infiltration treats rainfall as a flux boundary condition and assumes that flow in the soil can be described by Darcy's Equation (Rubin, 1966: Smith, 1972: White et al., 1979). Numerical solutions for the highly nonlinear flow equation that result from this procedure have been available since the pioneering work of Rubin and Steinhardt (1963). Their study has led to finite-difference solutions for a variety of complex conditions (Whisler and Klute, 1967: Smith, 1972; Smith, 1982). The desire to produce solutions that are appropriate for field use has led to the application of simplified models of soil-water movement (Mein and Larson, 1973; Braester, 1973; Swartzendruber, 1974:.Ahuja and Romkens, 1974; Chu, 1978). Parlange (1972) removed the necessity for these simplified models when he introduced a general and integral solution method. Philip and Knight (1974) improved this method by 17 producing quasi-analytical solutions of the flow equation to any desired accuracy through the use of a concept called the flux-concentration relation (Philip, 1973). The use of such quasi-analytical solutions has the advantage of a physical-based in situ process which may be used for the measurement.of soil hydrauliijroperties. All parameters in the theory are found from soil properties and need to be determined only once for each soil type. Other empirical infiltration equations require new'coefficients for each set of soil conditions. This theory also describes the change of water-pressure potential profile or the water-content profile of the soil surface with time during rainfall. Despite its attendant assumptions and simplifications, the theory has proven to adequately describe water movement into uniform, stable, nondisturbed field soils during rainfall. It also provided a rational basis for making approximations that are readily'useable in field studies. The infiltration model of Parlange et al. (1985,1988) is an example of a mechanistic model, in that it characterizes infiltration as a function of several field-measurable variables: initial and saturated volumetric soil water content (6n and 68, respectively), depth of ponding (h), and infiltration rate (q). The functional relationship of these variables and infiltration parameters is g = f(Ks, 8, 6n, 6 s, t), where 18 K,| and S are saturated conductivity and sorptivity respectively. Broadbridge and White (1987) described physically reasonable, analytic solutions to a nonlinear model of constant-rate rainfall infiltration. In their model, soil-water hydraulic properties were simply varied from those of the slightly nonlinear Burgers' equation to those of the popular Green-Ampt model. At the limit when soil-water diffusivity and hydraulic conductivity approach the properties of a Green-Ampt-like model, their analytic solution reduces exactly to the Parlange and Smith (1976) approximation: 1.1,, = 0.5 . ln{ [R.(1:p) / [ R.(rp) - 1 1 } [2.5] where L.is time-averaged dimensionless rainfall rate at ponding, R. is dimensionless rainfall rate which equals to {[R(t)-Kn]/[Ks-Kn] ) , and 1,, is dimensionless ponding time, K; is the saturated conductivity. Comparison of the exact solution with approximations derived from the quasi-analytic approach gave good agreement for the same general form: In, = M - 1n { [mtrpi / [ mop) - 11 } [2.6] Here the factor M is a soil specific property determined by the "shape" of the soil-water diffusivity function and 19 lies in the approximate range 0.55 s M s 0.66. Broadbridge and White (1987) found that equation [2.6] described both exact solutions and experimental observations. 2. Approximate Solutions With the limited number and scope of exact solutions, approximations must be sought for the integral solution. These approximations involve simplifications for the various flux-concentration relations, short-time approximations, and assumptions about the nature of the soil hydraulic properties. These approximate solutions were confined to consider only time to incipient ponding, and recognized that such approximations also apply to the water potential and water content profiles. From White et al. (1982), short-time, gravity-free approximations can be used for the early stages of rainfall infiltration provided the time t 5 t@, where in uniform soils: t, = { $268.6.) / [2(93-9nl'Ks] } / V0 [2.7] where 68 and On are volumetric saturated and initial soil water content, respectively, S is soil sorptivity, K8 is saturated hydraulic conductivity, and Vb is water flux. Inn uniform soils, by combining the short time approximation and the assumption that the flux 20 concentration relation for the flux boundary condition equals that for the constant pressure boundary condition, equation [2.7] can be written as (Perroux et a1, 1981): t 2 vamp); iron) dt = s (o,Y)/2 [2.8] 0 where tp is the ponding time, and ll‘ is soil water pressure potential which for constant rate is t.D = saw/f”) / 2ov02 [2.9] Equation [2.8] and [2.9] involve the recognition that 52mm“) = 210,0(6 - 6n) 1((Y) d‘P/Fc [2.10] For the delta function diffusivity soil equation [2.7] is exact: for a soil with constant soil-water diffusivity, D(6), the factor 1/2 in [2.8] is replaced by (n/4)Z. Fc is the flux-concentration relation for constant-pressure boundary conditions. For‘Vyflg 2 5, equation [2.7] is in good agreement with the full solution of constant rainfall rate (Broadbridge and White, 1987). 21 3. Time-to-ponding For one-dimensional downward infiltration from a water-ponded surface into a uniform nonswelling soil, the literature abounds with single-form equations for expressing the cumulative quantity I of water infiltrated versus time t after the initial and instantaneous ponding of the water, where I is the volume of water per unit cross-sectional bulk area of soil. Most of these infiltration equations (Green and Ampt, 1911; Philip, 1957, 1969: Philip and Knight, 1974: Parlange, 1975: Brutsaert, 1977: Parlange et al., 1982; Swartzendruber, 1987) have some kind of basis in physical-mathematical flow theory that leads to I o: t”2 and near-zero times and ,with dI/dt approaching the constant, sated hydraulic conductivity K at large times. Time-to-ponding has received considerable attention because of its importance in hydrologic and agricultural processes. Broadbridge and White (1987) defined the time-to-ponding as that moment during rainfall or sprinkler irrigation when free water first appears at the soil surface. This time marks a period beyond which both runoff and erosion may be initiated. They followed Rubin's (1966) work and predicted the time-to-incipient- ponding, t which is defined as the time at which the pl water pressure potential at the soil surface, To, becomes zero, i.e. ‘Po(tp) = 0. The time-course of ‘Po during rainfall or irrigation can be measured in the field 22 (Clothier et al., 1981; White et al., 1982; Zegelin and White, 1982; Hamilton et al., 1983). Surface runoff will not occur until '0 = 0. Infiltration depends on the rainfall rate as well as soil conditions. If the rainfall rate, R, is less than 1% for a deep homogeneous soil, infiltration will continue indefinitely at a rate equal to the rainfall rate without ponding at the surface. The water content of the soil in this case will not reach saturation at any point but approaches a value that depends on rainfall intensity. For soils with restricting layers, infiltration at R < K; ‘will not always continue indefinitely without surface ponding. Thus, surface ponding and runoff may occur*’as a result of the soil properties of the restricting layer, its initial water content, and its lower'boundary condition, as well as the rate of drainage in the lateral direction. For the case of rainfall rate greater than saturated conductivity (R > Ks), water infiltrates initially at the application rate. After some time, the infiltration capacity falls below' R, surface jponding’ begins, and. water' becomes available for runoff. The time to surface ponding decreases with increasing R, and the infiltration rate- time relationships are clearly dependent on the rainfall intensity. Quantitative descriptions of tp for variable rainfall rates, R(t), have been available for some time 23 (Parlange and Smith, 1976; Chu,1978; Morel-Seytoux, 1974; Broadbridge and White, 1987). The only restriction on R(t) is that it should not produce hysteretic flow. White et al. (1989) used a nondimensional, analytic approximation for time-to-incipient-ponding, t that pl proved to be quite accurate even for variable rainfall rates. Sensitivity tests employing the approximation showed that tp is hydrologically robust whenever the rainfall rate at ponding is greater than twice the soil- saturated hydraulic conductivity. 4. Soil Management Effect on Infiltration Tillage, residue placement, cover crop, and other cultural conditions are known to influence infiltration (Mannering' and. Meyer, 1963). Tillage 'may increase (Burwell and Larson, 1969) or decrease (Ehlers, 1975) infiltration and may increase or decrease (Allmaras, 1967) soil water storage depending on climatic conditions and soil properties. Infiltration into homogeneous or layered soils with flat stable surfaces is generally well understood and can be satisfactorily modeled on a wide variety of soil types (Mein and Larson, 1971; Moore and Larson, 1979) . The infiltration-runoff behavior of soils with disturbed surfaces, e.g., tilled soils, however, is poorly understood. A model to predict infiltration into these soils would be a valuable tool in developing 24 solutions to count the effect of tillage, residue cover and crop management. Tillage affects the soil surface directly by altering residue placement, random roughness, fillable porosity, bulk density, size and stability of aggregates, and runoff patterns in a non-uniform way (Johnson and Moldenhauer, 1979; Burwell and Larson, 1969; Lindstrom et al., 1981; Klute, 1982). Tillage can destroy surface crusts, and change soil structure and pore size distribution as well as remove weeds and the competition for soil water. Additionally, tillage can create compaction at the surface through the action of wheel traffic. Soil surface roughness is an important property of tillage systems because it forms the soil-atmosphere interface and influences the exchange of energy and mass between them. Roughness may also influence soil water storage because of the temporary storage of water in surface depressions. It is a means of keeping ponded water on the land and allowing it to infiltrate. Roughness condition indexes have been measured and have been shown to be highly related to several hydrologic phenomenon, including depression storage (Mitchell and Jones, 1976). The process in quantifying depression storage from microrelief elevation data was difficult to generalize for use in hydrologic models and requires modification for sloping lands. A model was developed by 25 Linden (1979) which defined the upper limit to depression storage as a function of a "roughness index" (RR) and the general land slope (L). The model analysis did not result in a simple functional relationship but could be expressed in general as: D = f (RR,L) [2.11] where D is the upper limit to depression storage, RR is the roughness index (standard deviation of height measurements) and L is the land slope. Depression storage has a maximum value of about 10 mm and decreases as roughness and land slope increases (Linden, 1979). Another important factor influencing infiltration of water into the soil profile is the initial water content, The higher the initial water content, the lower the initial infiltration rate. The dependence on initial water content decreases with time. If infiltration continues indefinitely, the infiltration rate will eventually approach the saturated hydraulic conductivity, 1%, regardless of the initial water content. Infiltration. rates are Ihigher’ at IOW' initial water contents because of higher hydraulic gradients and more available storage volume (Skaggs and Khaleel, 1982). Philip (1969) showed that for all times during infiltration, the*wetting front advances:more rapidly for higher initial water contents. An important non-soil surface condition that affects both preponded and ponded infiltration is the degree to 26 which the soil surface is protected by vegetative cover or residue. Mulches and crop residues placed or left on the surface of the soil protect the soil surface from direct droplet impact, thqupreventing' r retarding crust formation. ‘The quantity and quality of the residues both determine the extent of soil protection and the rate of material decomposition. These are determined by the crop type and tillage method. Burwell et al. (1968) reported that the percentage of the soil covered with residue was more important than random roughness, porosity, or the amount of residue in explaining the differences in the amounts of energy needed to induce runoff. Stein et al. (1986) calculated that the placement of residue on a field can increase overall infiltration by absorbing and retarding runoff in critical pathways more than the absolute amount can. III. DEVELOPMENT OF THE RAINSTORM GENERATOR A rainstorm event is defined for use in this analysis as any period in which the rainfall intensity is greater than or equal to 0.25 mm (0.01 inch) per hour, and does not contain an intervening period of zero intensity exceeding 10 minutes in duration. Any period of greater than 10 minutes, in which no precipitation is measured, signifies the end of a storm event. Given.past.weather raingauge breakpoint data from 1956 to 1985 (30 years weather records from the Deer-Sloan Watershed raingauge stations #10 and #18, Michigan), stochastic models were developed to simulate the number of rainstorm events per wet day and the amount, duration, and peak intensity of each rainstorm occurrence. A final step was to disaggregate the storms into intensity patterns. A. Rainstorm Occurrences in One Wet Day Raingauge data were collected at station #10 from the Deer-Sloan Watershed for 30 years. In this study, only the data from the months of April to September were used because it is the growing season for crop in this area and the existence of frozen soils complicates the process. 27 28 Precipitation records for each day were broken at midnight. The data set consisted of 2145 storms observed from 1956 to 1985 during the period of April to September. A Fortran source code for observed storm intensity calculation from raingauge data record is listed in Appendix 1. Some general statistics describing the complete storm data set of rainstorms per wet.day, amount, duration.and.peak intensity of each rainstorm are presented in Table 1. Because the groups differ statistically, they were separated by month. The first step in disaggregating daily rainfall into one or more individual storms was to generate the number of storms, N}, given the conditional probability of a wet day following a dry day, P[w/d], and a dry day following a wet day P[d/w]. The parameters of P[w/d] and P[d/w] for each month fromHApril to September'were.derived from recorded data. Any day containing one or more rainstorms where the total precipitation exceeds 0.25 mm was counted as a wet day. A uniform distributed random number was generated each day to determine a wet or dry day using the first-order Markov Chain model. Point precipitation was assumed to be a random time series of discrete storm events which under certain restrictions was assumed to be mutually independent (Eagleson, 1978). In this study, the number of rainstorm events in one wet day and the daily rainfall amount were assumed to be independent. Pearson's correlation coefficient was used to test the assumption. 'The coefficients were less than 0.3 for 29 Table 1. Monthly statistics for observed 30 years rainstorm record (1956-1985) for Deer-Sloan Watershed station #10, Michigan. Mean St.d. Min Max Apr. (470 rainstorms) Rainstorma per wet day 3.13 1.94 1 00 12.00 Amount per rainstorm (mm) 3.30 6.86 0.25 106.17 Duration per rainstorm (hr) 1.28 1.48 0.05 11.33 Max. Rate per rainstorm (mm/hr) 11.43 25.15 0 25 243.84 May (367 rainstorms) Rainstorms per wet day 3.01 2.02 1 00 12.00 Amount per rainstorm (mm) 4.06 6.60 0.25 44.20 Duration per rainstorm (hr) 1.36 1.58 0.02 11.30 Max. Rate per rainstorm (mm/hr) 16.26 34.80 0 25 365 76 June (370 rainstorms) Rainstorms per wet day 2.62 1.68 1 00 9.00 Amount per rainstorm (mm) 5.08 7.87 0.25 68.83 Duration per rainstorm (hr) 1.06 1.34 0.02 15.98 Max. Rate per rainstorm (mm/hr) 27.94 47.50 0 25 365 76 July (228 rainstorms) Rainstorms per wet day 2.37 1.46 1 00 7.00 Amount per rainstorm (mm) 6.35 9.65 0.25 86.36 Duration per rainstorm (hr) 1.08 1.12 0.05 7.35 Hex. Rate per rainstorm (mm/hr) 34.80 49.78 0 25 228.60 Aug. (329 rainstorms) Rainstorms per wet day 2.47 1.69 1.00 11.00 Amount per rainstorm (mm) 5.33 8.38 0.25 64.77 Duration per rainstorm (hr) 1.03 1.03 0.02 6.87 Max. Rate per rainstorm (mm/hr) 32.26 51.05 0.25 304.80 Sep. (381 rainstorms) Rainstorms per wet day 2.97 2.15 1.00 13.00 Amount per rainstorm (mm) 4.06 6.10 0.25 $4.61 Duration per rainstorm (hr) 1.13 1.17 0.02 7.15 Max. Rate per rainstorm (mm/hr) 19.81 32.77 0.25 167.64 30 most of the monthly data sets, supporting the assumption of independence. To perform curve fitting with probability and cumulative distribution functions, four discrete distribution functions (binomial, geometric, hypergeometric, and uniform) were compared to obtain the marginal distribution of the number of storms on one wet day. The geometric probability mass function was found to give a good fit to the observed distribution. This cumulative probability function can be written as P{Nj = n} = F{n} = p - (1-p)“", n = 1,2,--- [3.1] where p is the geometric probability coefficient. Figures 1 and 2 respectively show the observed and simulated distribution for number of storms on one wet day for each month. The chi-square goodness-of-fit test indicated that the positive hypothesis cannot be rejected at the 95% level for each month. Each month's value p for the geometric distribution is graphed in Figure 3 for the station #10 and station #18 data sets. Both stations show a similar monthly pattern on storm event number on one wet day; April, May, and September have the tendency of higher storm event number while summer season (June, July, and August) show a lower possibility for storm event on one wet day. The number of storms on one wet day was generated by the inverse function: 31 T l i I i i i l 1.00“ f - - flat;‘;;—a ‘7:— - -i //r’ ,,l/ q 0.80- 4425’" - 1 xf/gd" : « /fl:j ’ /¢;? .4 0.60— ,9” 74/ — Ll.— _, /" ”// .., o r . Q I I I / 'l I”///)( "l 0.40" /// a" / / —‘ .. é/ ,// / ., //// x-x Apr ‘ o’/ / '1 4 V / 13“? May .4 / 0.20“ X 9 -~’> My“ .. . a—e Jm 1 ‘ awe Aug ‘ ' 9-9 Sep 1 C100 r i l l i i 1 i l 2 .3 4i 5 6 i7 8 Storm Event Number on One Wet Doy Figure 1. Cumulative Density Function (CDF) for 30 years (1956-1985) observed storm event number on one wet day from Deer-Sloan ‘Watershed station #10, Michigan. Separate CDF are shown for each months analyzed. 32 1.00- 4 C180— ClBOe U— . Q —t C) Ou40“ o 1 QM x— —>< Aor . ‘1‘"? May 0.20"" O -O U'Uv'w 4 a—a dd ‘ G-El Aug ' o-o Seo C100 l i i i 7 l l i l 2 3 4 5 6 7 8 torm Event Number on One Wet Dcy Figure 2. Cumulative Density Function (CDF) for simulated storm event number on one wet day using geometric distribution functions for Deer-Sloan Watershed station #10, Michigan. Separate CDF are shown for each months simulated. 33 Station #10 ‘ Station #18 SS _ :ssssssssi sags/2,2222% ‘ $§§§§MIAMQESNSSNSE @fl%é¢/%éégéé $§§§§§§§§§§§§ géggéégévg §§N§§§§§§§§§§§ @¢§%§¢é¢wgflé m§V§N§§m§N§M swam §§§Q§§§§§§ Jun Jul Aug Sep Moy Eggflg 5. no a ‘—1 4 fl 1 .4 no no mm 0 2:22:88 8:3an 036880 _ 3. 2 .I 0. no Apr Geometric distribution coefficients for 3. simulated storm event number on one wet day for Deer-Sloan Watershed stations #10 and #18, Michigan. Figure 34 1% = 1 + [ log U / log (1-p) ] [3.2] where U is a generated random number. B. Amount and Distribution of Individual Storms Individual amounts, A, of Ni storms on one wet day are assumed to be independent random variables. While this assumption may not be strictly valid, it makes the problem tractable, and gives reasonable results. Four continuous distributions (exponential, gamma, lognormal, and weibull) were compared to obtain the marginal distribution of storm amount. The two-parameter gamma distribution had the maximum likelihood function value and minimum Akaike Information Criterion, or AIC (Akaike, 1974), and therefore was selected as the best choice. 'The marginal distribution of storm amount is written as: P{ANj s a} = F{a} = 1 - P(b;a/c) / F(b) [3.3] where a is the precipitation amount of N5 storm, and b and c are distribution parameters for shape and scale, respectively, for the gamma distribution. Figures 4 and 5 show the observed and simulated storm amount distributions, respectively. The rainstorms occurred on summer season have a higher possibility of higher storm amount than those on other months. 35 u. C) C) i -- AP. 1 . -«- May . 0.20-l -- Jun _ 1 —- Jul ‘ ‘ -- Aug 1 ‘ --- Sep 1 0.00 T T l I T 7 j I T I T T I I I I 7— T I T 1’ T I I r I I I l 0.0 10.0 20.0 30.0 40.0 50.0 60.0 Individual Storm Amount (mm) Figure 4. Cumulative Density Function (CDF) for 30 years (1956-1985) observed individual storm amounts from Deer-Sloan Watershed station #10, Michigan. Separate CDF are shown for each months analyzed. 36 r/ L‘- 4 I”??? . Q “Ill. . O 431% . 0.40—11 — .11 . .i‘i -- 40' . .1? —— May . 0.20‘ “ OUT“. -4 'l -- Jul 1 -l __. Aug cl 1 ..- Sep 1 0.00 I I I I I I T r I l’ I I I I T—I I—_I I ‘l I I T I rW—Tfi I 0.0 10.0 20.0 30.0 40.0 50.0 60.0 Individual Storm Amount (mm) Figure 5. Cumulative Density Function (CDF) for simulated individual storm.amount using gamma distribution functions for Deer-Sloan Watershed station #10, Michigan. Separate CDF are shown for each months simulated. 37 The Chi-square goodness-of—fit test showed that the null hypothesis cannot be rejected at the 95% level for each monthly data set. C. Joint Probability Distribution of Storm Duration and Amount After individual storm amounts were obtained by the Gamma distribution, it was necessary to simulate the durations D”j associated with each event amount, A“. The joint density function of event amount and duration can be written as a product of the conditional and marginal density functions: f(A,,j s a, DNj s d) = f(A,,j s x) - f(DNJ. I AM.) [3.4] Many researchers have suggested that DNj and ANj are jointly dependent for most rainfall events (Woolhiser and Osborn, 1985). In identifying a form for the conditional distribution, it was assumed that the distribution of the duration, given a particular amount, was the same for all events. To define two new random variables: let a' = logea, and d' = loged. Assume that the conditional density of d', given a', is normal, with an expected value function which is a linear function of a': E[d'|a'] = a + e- a' [3.5] 38 Linear regression functions were obtained from the above equation. Figures 6 and 7 show the regression lines of data sets from station #10 for April and July, respectively: Using a correlation ratio test (Kendall and Stuart, 1979) to test the hypothesis of linearity of the regression, the hypothesis cannot be rejected at 95% level. To test the hypothesis that the conditional density of d', given a', is normal, the values of a' were separated into four classes based on.magnitude, and a chi-square test was run on the residuals, a' - E[a'], for each class. The positive hypothesis could not be rejected at 95% level in each case. The conditional density can be written as: f(DM' I AM') = a + B ° a' + e [3.6] where e is the standard error of the estimate. The storm duration can be obtained by the transformation: DNj = exp(DNj') [3-7] 39 3i) ‘ I ‘ l ‘ l ' l r l i i A C 20‘ .. g .- -:, .,. ,1 .C d I " 7 u/ v // 1 C 1.0“ l I: ' O I a I " 1 ._ q a , l .. 4" it . 8 E O O-J x i g g : h :I" x -< 3 . I y “is x l‘ ‘l‘ C) . l J f3 g.“ .. . i I: " ‘I' I I E -4.0~ ! i i 1:, .. ‘ - ‘ a L. l. , 53 . i i ' . ! a 9 —2.0— g . g; .. . . _. o l ‘ '. . g} u I x _J 3—313— . . ‘ 4 -i -4.0 l I i Y i 1 l r l I -213 -4.0 013 1.0 21) 313 4nO Loge (Storm Amount (mm)) Figure 6. Regression for 30 years (1956—1985) observed individual storm duration and amount for April from Deer-Slone Watershed station #10, Michigan. 40 3.0 I I I I I I I f I I r A f: 2.0— ‘ ,. 'C q . 7 -i V " 3‘ ‘1 I '5" x ‘ " l” C 1.0— . ,. . -. ’,/:,..= .9 ' -": 3'..." :223”:’~’2 4—J ‘ x ‘ :x 21’4", ”, x .. " s’. «,L:. x E 0.0— i i . ‘ ,. ,.;g;c’w . _. :3 1 § it : "1’::’:P”7.u.ua . O -i " g !’,f;1:4’ 10‘ n x " I x 1 g ,i’:3:?f ‘ I a':: I “ x l E —i.o— ~;:;;’g , . . _ . . _ 0 d g! a 1'! u ’3: E x x I .4 -¢—J : : x ‘ ‘ I 1: £9 —2.o— : : ' .. * — o . . H J g l — — I ——l _] 3.0 ‘4-0 i . l . l T l T l . i -2.0 —1.0 0.0 1.0 2.0 3.0 4.0 Loge (Storm Amount (mm)) Figure 7 . Regression for 3 0 years (1956-1985) observed individual storm duration and amount for July from Deer-Slone Watershed station #10, Michigan. 41 D. Peak Storm Intensity Empirical distribution functions for the peak intensity, r were found to be described best by exponential pl distributions in varying storm amount classes. P{rp s r} = 1 - exp(-r/p) [3.8] Figures 8 and 9 show the observed and simulated peak intensities for each storm amount class. Higher storm amount classes have the tendency of higher peak intensity. Figure 10 shows that the parameters, p, are described by a linear pattern within varying classes. Chi-square tests were performed for each class and none could be rejected at 95% level. The peak intensity can be estimated by the inverse function within a known storm amount class: I5 = -p ' log U [3.9] where U is a uniform random variable from 0 to 1. The time from the beginning of the storm to the peak intensity, tp, was estimated by fitting the normalized time scale distribution. 42 ' I I I I I I T I I I I I I I F I I 1.00— ,_-----------;,-,....—- /- -- M .. " /”’.-—-——"’/.--'_: —————— :7’ ‘ - /.-/ / ’,—->Z'”’ ’ ’ a ’ “ . / . '/ ’,’ - ‘l ' /’ (j ’ I / II '4 i / ’r // // 0.80! i l'./ ” // I, —-( at l. [I /J I' // // '1 .t I ,. ,,I ,’ . i l I / - 4‘ I], I// I, .4 . . , Cl60—' I .4 ./ I — LL. q: I] ,// // Q ‘ 'r/ /' /7 / -4 o I: J] I /' I/ I "c I] It //' / .1 0.40-‘1 I // / r // —l ‘1 Ir // I // .J 4. {I / I], [I - - - Rain <5mm 4 l I / o .- l I / -—- Rain <10mm 0.20-' 1,, 1"] -—- Rain <15mnn. I l i/ o “i {1 fl,’ - - Rain <20mm “Igf/ —-- Rain <25mm‘ ‘1 '1’ . -i " j -- Rain >25mm 0.00 I I T I I f fi I II 1' I I T I I I 7 0.0 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 Max. Intensity (mm/hr) Figure 8. Cumulative Density Function (CDF) for 30 years (1956-1985) observed peak intensity for individual rainstorm amount classes from Deer-Sloan Watershed station #10, Michigan. 43 CDF CL40— _ -4 ["1/ / . ‘1 .I I! '/ ,’ Rom 25mm‘ ooorlmrwwwmwws 0.0 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0 360.0 Mox. Intensity (mm/hr) Figure 9. Cumulative Density Function (CDF) for simulated peak intensity for individual rainstorm amount classes using exponential distribution functions for Deer- Sloan Watershed station #10, Michigan. 44 — . filliJ'llld q _ a a q — a I £44, // // -/ ./fi///a,,/4,/ .4 4.4%??? I y//////////V/////V 7??? 77/5/52 r. /%A,/.A..//A//C 42/» 47.4,. ./ // M/MA M//////./ I 7/////////////7é7/7/x7/49/6 I 7 42,4. MAI/L 4a,. 47401.4? m2V////WW/ ,7/V/é/V/7/Z I . ,,.4.d./2, 4,4,4. r WM/ 727/? 3am. I 734.4,... .29 437/??? I W- — q d u — 4 d A d u .— 4 o. o. o. o. o. o. o. O O O O O O O 2 O 8 6 4 2 140i) 220508 8:32.35 BEESQQ 5—310 .3 2 > 15—20 20-25 10—15 <5 Rainstorm Amount (mm) Figure 10. tensity for individual rainstorm amount Exponential distribution coefficients for classes for Deer-Sloan Watershed station #10, Michigan. in lated peak ' S 1mu 45 E. Disaggregation for Storm Rainfall Intensity Patterns Sample calculations for a storm event occurring on July 11, 1984, are summarized in Table 2. The total was 17.5 mm (A) and occurred in 1.283 hour (D) from station #10 raingauge data. The rainfall rates are graphed in Figure 11. Column 1 from'Table 2 is the cumulative time (hr) from the start of the storm and column 4 is the cumulative storm depth (mm) at the given times. Column 8 is the storm intensity calculated from columns 2 and 3. A dimensionless process can be defined by the normalization of storm and intensity. A normalized time scale was developed by dividing each period of storm duration (t) by the total storm duration (D) and intensity values were normalized by the average intensity. The result is called a normalized time, T*, and normalized intensity pattern, Int*. These values are given in column 7 and 9 in Table 2, respectively. The normalized time until the peak intensity, is 0.14 from Table 2, and the normalized peak intensity, is 6.56 for the example data. Thus, the intensity pattern within a storm can be described by the dimensionless stochastic process { Int*(t*); 0 s t* s 1 }. This process of intensity over the time scale (Int* versus T*) was fit to a double exponential function as shown in Figure 12. 46 Table 2. Example calculation of storm intensity pattern for an observed storm record from Deer—Sloan Watershed station #10, Michigan on July 11,1985. Time(hr) Duration Amt(mm) Cum. Amt(mm) Amt* Cum. Dur.(hr) Dur* Int(mm/hr) Int* 0.000 0.000 0.000 0.000 0 0.000 0 0 0 0.000 0.066 0.254 0.254 0.0145 0.066 0.0514 3.848 0.2817 0.066 0.050 0.762 1.016 0.0580 0.116 0.0904 15.240 1.1157 0.116 0.034 1.016 2.032 0.1159 0.150 0.1169 29.882 2.1876 0.150 0.016 1.270 3.302 0.1884 0.166 0.1294 79.375 5.8108 0.166 0.017 1.524 4.826 0.2754 0.183 0.1426 89.647 6.5627 0.183 0.017 0.508 5.334 0.3043 0.200 0.1559 29.882 2.1876 0.200 0.016 0.508 5.842 0.3333 0.216 0.1684 31.750 2.3243 0.216 0.017 0.508 6.350 0.3623 0.233 0.1816 29.882 2.1876 0.233 0.050 0.762 7.112 0.4058 0.283 0.2206 15.240 1.1157 0.283 0.017 0.762 7.874 0.4493 0.300 0.2338 44.824 3.2814 0.300 0.033 0.762 8.636 0.4928 0.333 0.2595 23.091 1.6904 0.333 0.017 0.508 9.144 0.5217 0.350 0.2728 29.882 2.1876 0.350 0.033 0.508 9.652 0.5507 0.383 0.2985 15.394 1.1269 0.383 0.050 0.508 10.160 0.5797 0.433 0.3375 10.160 0.7438 0.433 0.017 0.762 10.922 0.6232 0.450 0.3507 44.824 3.2814 0.450 0.050 0.508 11.430 0.6522 0.500 0.3897 10.160 0.7438 0.500 0.033 0.762 12.192 0.6957 0.533 0.4154 23.091 1.6904 0.533 0.067 0.762 12.954 0.7391 0.600 0.4677 11.373 0.8326 0.600 0.033 0.254 13.208 0.7536 0.633 0.4934 7.697 0.5635 0.633 0.100 0.508 13.716 0.7826 0.733 0.5713 5.080 0.3719 0.733 0.100 1.016 14.732 0.8406 0.833 0.6493 10.160 0.7438 0.833 0.050 0.508 15.240 0.8696 0.883 0.6882 10.160 0.7438 0.883 0.017 0.762 16.002 0.9130 0.900 0.7015 44.824 3.2814 0.900 0.033 0.762 16.764 0.9565 0.933 0.7272 23.091 1.6904 0.933 0.100 0.254 17.018 0.9710 1.033 0.8051 2.540 0.1859 1.033 0.100 0.254 17.272 0.9855 1.133 0.8831 2.540 0.1859 1.133 0.150 0.254 17.526 1.0000 1.283 1.0000 1.693 0.1240 1.283 0.000 0.000 0.000 0.0000 47 ’C‘ 100 I I I I I I I I I . _C . \\. 902 F — E . l . E 80— J — i3~ 70d — .5 1 g C 60d 3 £3 « . E. 50- — d 1'] a E 40- 1] 1 fl — .9 ‘ :1 ' 3 ‘ 30" 1' i 1 1 ‘ (I). a r ‘Lfl Ii I '1 U 1 ‘ —1 .- cu 20- J I I“ > . 1 . a LL10 I _ m 10— I . _Q -I <3 0 r . I r r I I I I ()0 C12 041 C16 C38 1 0 1.2 Time (hr) Figure 11. Observed storm intensity of one rainstorm event on July 11, 1985 from Deer-Sloan Watershed station #10, Michigan. 48 8.0 Y I I I T I ‘l I I I I 1' T I I I T I I H Observed . - - Simuiated .\‘ O I <1 Normalized Intensity (INT*) I I I I I m r I I 012 013 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Normalized Time (T*) Figure 12. Observed and simulated normalized storm intensity for one rainstorm event on July ll, 1985 from Deer-Sloan Watershed station #10, Michigan. 49 A double exponential function fitted to the normalized intensity pattern is then: [: a ebt 0 s t s tp dt [3.10] tp s t s 1.0 i(t) = , c e which is an equation with four parameters (a,b,c,d) to be determined. If the area under the curve defined by equation [3.10] from 0.0 to tp is assumed to be equal to tp, then the area under the curve from tp to 1.0 is 1.0 - tp. Using this assumption and the fact that i(t=tp)==jw, equation [3.10] can be rewritten as: o b(t'tp) 1.p e 0 s t s tp d(tp-t) 1p e tp s t s 1.0 i(t) = [3.11] which is now an equation with two parameters (b,d) to be determined. If I(t) is defined as the integral of i(t), then: tP b(t-tp) I(tp) = 11p e dt = tp [3.12] o and 1 0 d(tp-t) I(1.0)= 1 ip e tp dt = 1 - t [3.13] 50 Evaluation of these integral results in two equations: 1 - ebtp = btp / ip [3.14] and - e‘“‘"‘” = d(1-tp) / ip [3.15] which must be solved for b and d. With the above assumptions i(O) is equal to i(1.0) so that d = b tp / (l-tp). Now, equation [3.14] need only be solved for b for the entire solution” 'The integral I(t) of equation [3.10] and [3.11] can be written as i(t) = a/b (em-1) 0 s t s tp E [3.16] -c/d (emtp'U-l) tp s t s 1.0 where, from above a=ipe°btp, c=ipedtp, and 0.0 s I(t) s 1.0. Dividing this dimensionless process into n equal-time increments, the storm intensity pattern can be calculated by inverting the process function. Tables 3 and 4 and Figure 13 show the results for n=10 equal time increments. Note that the peak intensity in Table 4 is 37.1 mm/hr rather than 89.6 mm/hr from the observed one. 'This is because the intensity is averaged over the period and the average intensity is always less than the instantaneous maximum. A way of eliminating this error requires another value, the duration for the peak intensity (Dip). The results of combining the intensity pattern with.peak intensity and duration are shown on Table 5 Table 3. Simulated distribution for normalized storm time (T*) intensity (Int*) with 10 equal time increments for Deer-Sloan Watershed station #10 on July 11, 51 output from double T* Int* 0.000 0.044 0.100 1.528 0.143 6.930 0.200 2.722 0.300 1.996 0.400 1.464 0.500 1.074 0.600 0.788 0.700 0.578 0.800 0.424 0.900 0.311 1.000 0.228 exponential and 1985. Table 4. 52 Simulated output for real storm time and intensity with 10 equal time increments for Deer-Sloan Watershed station #10 on July 11, 1985. Time (hr) Intensity (mm/hr) 0.000 0.601 0.128 20.872 0.257 37.180 0.385 27.265 0.513 19.998 0.642 14.670 0.777 10.764 0.898 7.895 1.026 5.792 1.155 4.248 1.283 3.114 53 Table 5. Simulated output for real storm time and intensity with peak intensity and 10 equal time increments for Deer-Sloan Watershed station #10 on July 11, 1985. L Time (hr) Intensity(mm/hr) 0.000 0.601 0.128 20.872 0.166 94.660 0.183 42.629 0.257 37.180 0.385 27.265 0.513 19.998 0.642 14.670 0.770 10.764 0.898 7.895 1.026 5.792 1.155 4.248 1.283 3.114 54 and Figure 13 with peak intensity simulated. The maximum intensity is 94.6 mm/hr for this calculation. Both simulated outputs fit reasonably' well with. the observed intensity pattern. But the simulation with peak intensity produced better fit to the observed storm intensity. 55 ’2? 100 I I I I I I I I Ir I I I .C 1 "I —— Peak \ 90- 'l — 5000! more. E . j, E 80~ II V - II I :3; 70- :1 m 1 II C _ i <0 60 :1 *1 ‘ l .fi 50— h . [I E 40~ I ‘1 O J 1 “-1 +1 I . I 00 30- I I 73 1 E ‘ I _2 20~ f—“—*‘ ~—-—— 2 . I ~——— 3 10— l L_“—] .5. 1 T 5"— m 0 T“ r r r Y I T I I | I 1’ C30 C12 041 C16 C38 1 0 1 2 Time (hr) Figure 13. A comparison of simulated storm intensities with peak intensity and 10 equal time increments for one rainstorm event on July 11, 1985 for Deer-Sloan Watershed station #10, Michigan. IV. TIME-TO-PONDING MODEL DEVELOPMENT Mathematical representations of water flow in porous media involves assumptions that usually idealize or simplify the complexity of the real system. The principal simplifying assumptions of the time-to-ponding model used in this study are as follows: 1. The soil is assumed to be uniform and there is with depth no surface storage and detention storage. 2. The air phase is assumed to move freely, thus the water table is assumed to be deep and air pressure changes under infiltration are neglected. 3. Soil hysteretic behavior and raindrop impact are neglected, soil is nonswelling and nonhydrophobic. From those assumptions listed above, infiltration during an irrigation application or a rainfall event can be divided into tondistinct cases or stages: a stage in which the ground surface is ponded with water and a stage without surface pondingu During an unsteady rainfall the infiltration process may change from one stage to another and shift back to the original stage. Under a ponded surface the infiltration process is independent of the effect of the time distribution 56 in pc SI 57 of rainfall. At this point the infiltration rate reaches its maximum capacity and is referred to as the infiltration capacity. At this stage rainfall excess is computed as the difference between rainfall rate and infiltration capacity. Without surfacejpondingy all the rainfall infiltrates into the soil. The infiltration rate equals the rainfall intensity, which is less than the infiltration capacity, and rainfall excess is zero. The mathematical equations used in the infiltration component are presented below. A. Dre-ponding Assume a soil system with uniform hydraulic properties and initially uniform volumetric water content 6n and pressure potential V". The rainfall rate rb(t) is time,t)dependent. Before ponding, all the rainfall infiltrates into the soil, the cumulative soil infiltration amount (Ip) is equal to the cumulative rainfall amount, and no excess water occurs on the soil surface. Initially, when time equals zero: t=0; 6=6n,!=Yn:z>0. where z is the vertical one dimension positive downwards. Darcy's equation describes the flux density V(Y,t) as: V(T,t) = - K(T) aT/dz + K(T). [4.1] 58 As t >0, the boundary condition is: V0(t) = -K(v) dY/az + K(Y); where Y = Y0(t); 6 = 60(t): z = 0. Here Y0(t) and 60(t) are measured at the soil surface. B. Ponding Ponding time (tp) is the ‘moment during rainfall or irrigation application when the soil-surface pressure potential first becomes zero (Y0(t) = 0). At this point, water begins to accumulate on the soil surface. This marks the beginning of'ponding and decline of the infiltration.rate. The cumulative infiltration amount at ponding «“9 is equal to the cumulative rainfall or irrigation amount (R5). The time to ponding is a function of saturated hydraulic conductivity (Kq), saturated soil water content.(63), antecedent soil water content (6") or reference soil water content (6,), soil sorptivity (Sn), macroscopic capillary length (Ac), and rainfall rate (:5) at ponding time. The time to ponding is described in the following equation: Ip = R = 0.55- (an / Ks) - ln[ rp / (rp - 1(8)] [4.2] p = m- Ac- ln[ rp / (rp - Ks) ] [4.3] where m is calculated from 59 m=I<0.-6.)/(6.-6.II"5-(es-6.) [4.41 The parameter Ac in [4.3] is termed the macroscopic capillary length that provides a scaling length to simplify the treatment of soil-water flow (Philip, 1985). It depends weakly on the hydraulic properties. For stable soils, the range of m values are within the range of 0.50 s m < 0.66 (Broadbridge and White, 1987). In laboratory studies conducted.by White and Broadbridge (1988) on.dry repacked soil samples, m was found to be close to 0.5. For field situations where there is evidence that hydraulic properties are different from those of repacked soils, m is expected to be close to 0.6. Where the hydraulic properties are unknown, it is reasonable to take:m = 0.55. This assumption will generate errors of no more than i 10% in predicting the time-to- ponding. White and Sully (1987) described a simple method to estimate itc in the field. Their method was based on the equation 2 Ac=o.55-sr/[(es-6r)-Ks] [4.5] Where Sr is the sorptivity at a reference soil water content (6r). The sorptivity is a measure of the ability of the porous media to absorb a wetting liquid (Philip, 1969). The larger the sorptivity value, the greater the volume of liquid that can be absorbed and the more rapidly it is absorbed. 60 C. Post-ponding Once ponding starts on the soil surface, rainfall is partitioned into infiltration and runoff. Total infiltration amount (I) at any time (t) during this stage is no longer controlled.by the rainfall rate (Rubin, 1966) but by the water flux (Vb) at the soil surface. I = 1p + I“p = 0.55- (sf/Ks) . ln[ v0 / (v0 - Ks) ] [4.6] =m-lc-1n[vo/(vo-Ks)] [4.7] where I",is the cumulative infiltration amount post-ponding. The cumulative infiltration can be described as a function of time: [(I-Ip)/(m'lc)J-{[(t-tp)‘Ks]/(m°lc)} .1.1 . . ___ expt p/(m c)] _ expt l/(m lc)1 [4.8] where tp is the ponding time, and both infiltration rate (V5) and runoff rate (R0) can be described as: Vo(t) Ks / { l - EXP[ -I / (m ' Ac) ]} [4.9] Ro(t) rp(t) - Vo(t) [4.10] When surface storage is considered, the runoff is computed as the excess water generated from the infiltration model minus the maximum depression storage. The concept of depression storage used in this model is the maximum amount of 61 water that can be retained on the surface that will eventually infiltrate. The retention volume on the surface can be computed from microrelief data or it can be evaluated for rainstorms that start abruptly with intensities in excess of infiltration capacityu A. reasonable assumption for' the capacity of this storage volume as a function of random roughness (RR) and the general land slope LIwas developed from concepts of Linden. The accumulated rainstorm less the mass infiltration, in the interval between the beginning of rainstorm excess and the start of direct runoff, is equal to depression storage plus the amount of detention required to initiate runoff. With the storm intensity and the three stage time to ponding approach, a model for infiltration is complete. The necessary input soil properties are Kg, S for each soil nl condition, the rainfall intensity r and the initial water pl content of surface soil. Since K3 is a soil property associated only with the microporous space in a soil, it may be relatively uniform over a large area of similar soil type. Soils having similar mineral composition and organic matter content may well have similar Ks value. V. FIELD MEASUREMENT OF TIME-TO-PONDING Field experiments were conducted to provide data for model development and'verificationn Fifty sets of field tests were conducted on Montcalm loamy sand (Eutric Glossoboralf) in Michigan with corn (C) and potato (P) crops under different tillage and wheel traffic conditions. Soil texture, bulk density, initial soil water content, and surface crop residue were measured on each plot. Tillage systems included moldboard plow (M), disc plowed (D), and no till (N) for corn and moldboard plow and paraplow (P) for potato. A. Sprinkling Infiltrometer Time-to-ponding was determined with minimal disturbance to soil surface conditions by the use of a sprinkling infiltrometer (Figure 14). This infiltrometer satisfies the criteria for the design of a sprinkling simulator as set forth by Bubenzer (1979) with irrigation characteristics substituted for rainfall characteristics. The modified Bubenzer criteria are: 1) Drop size distribution similar to that of sprinkler irrigation: 2) drop velocity at impact near sprinkler irrigation drop velocity: 3) intensity corresponding to 62 63 BYPASS LINE i l -—'W f——_' l ' “ i I . 30¢ POVERBJW° I ma ”CR0 3 :Lfiz ; VATER ': I A ' . ' OAT! ‘ML‘JES\' . I . . (”a ”U l ‘ \.-. FIL- \ A = VALVE CYCLE! m— '3: V f . v , .- . I Tim 1 I I . \‘ \ L i I \ \ I Hose GATE VALVES AIR ”mm : VALVE i SOLENOID VALVES 3 was: i I I ' \ ' F—_‘ SPRAY aoou ,/ . .. LO O 0' r Y: 9919.! , --: r -. or +5 "I“. I. (IV/0F! ;_ I I I I 95mm ‘ ' I \ ‘\ I EVER Figure 14. Schematic diagram of sprinkling infiltrometer used for field time-to-ponding measurement. 64 sprinkler irrigation: 4) uniform application and random drop size distribution: 5) total energy applied near that of sprinkler irrigation; and 6) reproducible patterns of application like sprinkler irrigation. The infiltrometer consists of six nozzles mounted on a horizontal boom that is supported about 1 m above the soil surface» The boom is divided into two sections, each carrying three nozzles, 1.37 m apart. Each section is about 3.7 m long and made of square steel tubing connected by a quick-coupler. The boom is seated on two tripods and a center support which are adjustable so that the boom can be make parallel to the terrain. A polypropylene tank (1230 L) supplies water to the system and the 4 kw gas generator supplies power to the pump and the timing circuit. A by-pass line and gate valve are used to control the nozzle pressure and two additional gate valves allow the tank to be filled from a nearby lake or stream. A 80 meter hose extends the water supply to the spray boom. solenoids and spray nozzles. The boom, water tank, generator, pump, and control unit are transported on a trailer. The six nozzles mounted on the boom are controlled by separate solenoid valves that allow the application of different sprinkling rates to multiple sites simultaneously. Two Full-Jet nozzles, Spraying Systems 1/4 HH 12W and 1/4 HR 10 W, were selected for the infiltrometer. Both nozzles distribute medium to large sized droplets in a uniform circular'pattern. Finer control over low rates is achieved.by 65 using the smaller nozzle (10W). The infiltrometer is started up each time from a static pressure of 82 kPa, controlled by the by-pass line and gate valve near the pump. The rate of application is regulated by timers which control the solenoid valves on each nozzleu .Application rates used in the field ranged from 10 to 95 mm/hr and were achieved by controlling the off time of the nozzle while the on time is held constant at about 0.6 s for each nozzle. The actual rate of application is determined after the test is completed by dividing the application depth by the total elapsed time. 'The appearance of small puddles, 1 to 3 cm, in diameter, was chosen as an indicator'of the occurrence ofjponding. 'Time-to- ponding was recorded under each nozzle, and the application rate and cumulative amount at time-to-ponding from.each.nozzle was measured.by catching water in three small containers below the nozzles on the ground. B. Field Procedure Experimental sites were chosen near the edge of a field were a trailer with a water tank could be easily parked. At the site, any leaves and weeds that interfered with the discharge pattern of the nozzle were removed, but the residue was left in place. In the corn crop when plants were tall, the end tripod and center supports were set up among the plants. The boom section was lifted over the plants and attached.to the tripod and center support. The second tripods was placed at the end of the plot, and the second section 66 installed. Circular observation areas were located side-by- side under the nozzle pattern and the boom height adjusted so that water from the nozzles would not overlap. Three cups were placed in a triangle within the observation area so that an average application rate could be obtained. Before the nozzles were turned on, the air from the hose and boom was purged. Each combination of treatments contained three to five replicates. Measurements were made before and after each infiltrometer application to determine the changes in soil properties and the time-to-ponding under variable application rates. After the time to ponding was determined, the water was turned off and the final time noted. The volume in the cups was measured and the application rate and the total water infiltrated at ponding was calculated. A Fortran source code for calculation of the water application rate and time-to- ponding from field operation of sprinkling infiltrometer is listed in Appendix 2. Soil samples taken in the field was used to determine soil texture, and bulk density. Residue cover for each plot was also measured before each rainfall application. Soil water content was determined.immediately before and after'each rainfall application from samples obtained at the surface. The texture and bulk density of each sample was measured in the laboratory. A Fortran source code for crop residue, bulk density, and initial water content calculation for each plot is listed in Appendix 3. The bulk density and texture data 67 were used to estimate the saturated water content assuming that it was equal to 85% of the total porosity (Ritchie, Ratliff and Cassel, 1987). A, Fortran source code for saturated water content calculation is listed in Appendix 4. Fifty sprinkling infiltrometer tests were performed in the summer of 1989, under four tillage practices and two crops. Ten tests were done on each soil x tillage x crop combination. A sprinkling infiltrometer test plot consisted of one target row section, about 10 m in length, and two adjacent row sections, used for access and observation. An average of two infiltrometer tests were performed per day. A different crop x tillage treatment was tested each day so as to get maximum variability in soil water over a season and similar average values between treatments. Field experiments were carried on three field sites. Field #1, Montcalm sandy loam (Eutric Glossoboralf, coarse- loamy, mixed) is located.NE1/4, SW1/4, Section 18, T9N, R7W’of the Michigan meridian, southeast of Greenville in Montcalm County. Moldboard and disk plowed plots were installed in this field that had been in corn for three years. Moldboard plow ia a primary tillage implement which cuts, partially or completely inverts a layer of soil to bury surface materials, and pulverized the soil. Disk plow is also a primary tillage implement with individually mounted concave disk blades which cut, partially or completely invert a layer of soil to bury surface material, and pulverize the soil. The disking was done on May 1 and the moldboard plowing was done on May 8. 68 The corn was planted on May 9. One half of the furrows were wheel tracks. The field was irrigated by a center pivot system and application were scheduled through the Michigan Energy Conservation Program. The period of sprinkling infiltrometer and soil testing was between June 28 and August 3, during which time 16.9 to 33.2 cm of water was added to the field since tillage. Field #2, Montcalm loamy sand, is located about 200 m from field #1, in an alfalfa field which had been established for five years. The alfalfa in a small section was killed with 2,4 D and Roundup and it was planted with corn on May 9. All of the corn received some damage from.deer grazing; These no-till plots were irrigated by the same center pivot as in field #1, and one half of the furrows were wheel track furrow. Field #3, Montcalm loamy sand, is located NW1/4, SEl/4, SW1/4, Section 8, T11N, R7W of the Michigan meridian, west of Entrican in Montcalm county on the Michigan State University Potato Fanm. A moldboard tillage plot area and a paratill over moldboard tillage plot area were established in 1989 on a section which had been in soybeans the year before, with a fall rye cover crop plowed under on May 1. The paratill operation was done on May 18, as was the planting of the potatoes. On June 8, the plots were hilled. These plots were irrigated by a fixed sprinkler irrigation set. One half the furrows were wheel tracks. The period of sprinkling infiltrometer and soil testing was between June 30 and August 69 7, during which time 12.6 cm of water was added to the field after hilling. C. Ponding Curves Ponding curves were established for each management combination of crop x tillage x wheel traffic condition by plotting the water application rate (rp) versus cumulative infiltration amount (Ip) at ponding for each plot. The soil parameters such as saturated conductivity, Ks, capillary length , Ac, and sorptivity, Sn were determined by best-fitting [4.2] and [4.3] to the ponding curves. Appendix 5 lists a Complex algorithm.programnwhich.was used for finding the best- fit ponding curve for each plot. For many continous system application it has been found that the very straightforward method using Euler's formula for numerical integration is not only adequate but preferred. The program for implementing the Complex algorithm was modified from "Optimization Techniques with Fortran" by James L. Kuester and Joe H. Mize, chapter 10. Field observed ‘time-to-ponding' data and. plot soil. water content were used as input for optimization process to find the least square error of soil physical properties K5 and Sn from [4.2] and [4.3]. With known soil hydraulic properties, prediction of infiltration and runoff under any type of rainfall pattern was possible. VI. RESULTS AND DISCUSSION A. Rainstorm Generator To make the time-to-ponding model functional for practical strategic applications, a relatively simple rainstorm generator is needed to generate storm intensities data when short-time period precipitation records are not available. A parameter-efficient way to simulate the number of storm events in a day and the individual storm intensity patterns is needed. The objective here was to develop a simple model to simulate the number of storm rainfall events per day and the amount, duration, and short time intensity pattern of each event. A stochastic storm model was defined that consists of a geometric marginal probability distribution for the storm event, a two-parameter Gamma marginal distribution for the event amount, and an exponential conditional distribution for the peak intensity for a given amount. A joint distribution of storm event depth and duration ‘was constructed. .A stochastic model for the dimensionless accumulated storm process was proposed. The dimensionless process was divided into 10 equal time increments, and the intensities were 70 71 rescaled to be normalized by the average intensity. This sequence of rescaled increments was found to be best-fit by a double exponential function. The process of this rainstorm generator simulation is shown in Figure 15. The simulated 30 years rainstorm data set output analysis is shown in Table 6. A Fortran source code for this storm generator is listed in Appendix 6. The simulated storm characteristics match reasonably well with the observed rainstorm data set from Table 1. An analysis of observed storms data at the Deer-Sloan Watershed stations #10 and #18 in southeastern. Michigan suggests that the proposed model structure provides an acceptable approximation for storm rainfall. The number of parameters in this approach is few when compared with alternative methods, yet the approach does an adequate job of simulating storm intensities. The simulation procedure developed requires 10 parameters for each month. The simulated.distribution.of numbers of storms during one wet day and storm amounts, duration, and peak intensity compared favorably with observed data. The number of model parameters could. be reduced. by approximating' gamma, geometric, and exponential parameter as seasonal power series functions. The seasonal variation of the model structure and parameter values were also investigated in this study. flow of Jth Month of kth Year P[wlw) a P[wld)4\ Markov Chain Model for jth Month Parameter p for 1th Month Rainstorm events number from arameters o 8 c Iarm )th Month 72 0 III. F or wet dry day YES geometric distribution J Rainstorm amount from gamma distribution .-.r.ametersa 8&8 ror jth Month Rainstorm duration from linear regression Parameter 2. for rainstorm amount grouo Parameters to’, io'. a a Figure 15. in this study. Max. Rate from exponential distribution Caiouiate ID' 4 Break paint data from double exponential I distribution 1 YES and o Simu. \ear Flow chart of the rainstorm generator used 73 Table 6. Monthly statistics for simulated 30 years rainstorm record for Deer-Sloan Watershed station #10, Michigan. Mean St.d. Min Max Apr. (448 rainstorms) Rainstorms per wet day 3.11 2.31 1.00 11.00 Amount per rainstorm (mm) 3.32 2.99 0.27 19.53 Duration per rainstorm (hr) 1 52 1 51 0.14 10 80 Max. Rate per rainstorm (mm/hr) 19.55 31 32 0.56 218 57 May (383 rainstorms) Rainstorms per wet day 3.16 2.42 1 00 13.00 Amount per rainstorm (mm) 4.73 5.76 0.25 35.69 Duration per rainstorm (hr) 1.71 2.11 0.06 18.40 Max. Rate per rainstorm (mm/hr) 27.49 43.90 0 51 357.97 June (352 rainstorms) Rainstorms per wet day 2.57 1.91 1.00 12 00 Amount per rainstorm (mm) 5.72 6.64 0.25 45 64 Duration per rainstorm (hr) 1.23 1.27 0.05 11 46 Max. Rate per rainstorm (anhr) 32.12 46.75 0 28 264.20 July (252 rainstorms) Rainstorms per wet day 2.54 1.73 1.00 9.00 Amount per rainstorm (mm) 6.58 8.62 0.27 53.33 Duration per rainstorm (hr) 1 20 1.28 0.07 9.29 Max. Rate per rainstorm (mm/hr) 35.07 57.92 0.77 373.19 Aug. (329 rainstorms) Rainstorms per wet day 2. . . Amount per rainstorm (mm) 5.91 7.34 0.26 46.15 Duration per rainstorm (hr) 1. Max. Rate per rainstorm (mm/hr) 35. Sep. (406 rainstorms) Rainstorms per wet day 3 Amount per rainstorm (mm) 4. Duration per rainstorm (hr) 1.34 Max. Rate per rainstorm (mm/hr) 28.36 46.08 74 The developed model provides a source of storm event data that can be used as input for the time-to-ponding infiltration model. Further research should be done to examine spatial variations in disaggregation structure and parameters, and criteria governing model transferability should be developed. B. Field Measurements of time-to-ponding To determine the kind of variation expected for infiltration.calculations as related to tillage, a field study to measure time-to-ponding using an sprinkling infiltrometer was conducted on a loamy sand (Eutric Glossoboralf) soil in Michigan with corn and potatoes under different tillage and wheel traffic conditions to determine values of the properties needed for this model. Time to ponding curves were established for each management combination of crop, tillage and wheel traffic conditions. Values for the soil properties needed for the model were derived from best-fit ponding curves.Several sets of field time-to-ponding measurements (five plots for each combination of crop x tillage x wheel track combination) were made during the growing season of 1989. Appendice 7 to 9 show the results of field measurement and derived soil properties for each plot. The measured residue cover, initial water content, and bulk density are listed in Table 7 columns 2 to 4. The saturated water content was estimated from the texture and bulk density of each site. Appendix 8 shows the field measured bulk density and initial water content for each plot. Bulk density for plots with 75 wheel track conditions were higher than that of non-wheel track conditions except for the no till system (Figure 16). Reduced macropore space was associated with higher bulk densities, that diminished the K3 values. Appendix 9 shows the observed ponding time and the water applied depth at ponding time from each nozzle for the infiltrometer experiment. Ponding curves for each plot can be established by the best-fit data set using the modified Complex optimization program. Examples of ponding curves for the corn (CMW2, CMN5, CDWS, CDNS, CNWS, CNNS) and potato (PMW2, PMN2, PPW6, PPN2) plots for each tillage x wheel track treatments are shown in Figures 17 and 18, respectively, by best-fitted time-to-ponding model: IP = R = 0.55. (an / Ks) - ln[ rp / (I:p - 1(3)] [6.1] =m- Ac° ln[ rp/ (rp-Ks) ] [6.2] where m is calculated from m=[(Os-6n)/(Os-6r)]1'5-(Gs-6r) [6.3] Noted here is the r2 for each best-fitted ponding curve as shown in column 8 from Table 7. Example runs for corn under moldboard plow and disc plow and potato under moldboard and paraplow produced 1:2 values between 0.546 to 0.756. The corn with no tillage had low r2 because few points were collected in the field experiment. From the model above, 76 Table 7. Field measurements of time-to-ponding for soil with potato and corn crops with various tillage and surface residue treatments for Montcalm County, Michigan. Exp . Re: idue 6 M g/ 2123 asst mfijhr mmshr r2 CMW2 3 11.5 1.47 37.8 6.45 12.42 .68 CMNS 3 10.9 1.28 43.9 20.90 13.06 .74 CDWS 1 7.9 1.58 34.3 7.80 13.86 .55 CDN5 10 12.9 1.35 41.7 20.63 10.41 .57 CNWS 72 7.6 1.44 38.8 53.81 14.27 .07 CNNS 73 17.5 1.43 39.1 41.91 21.52 .48 PMWZ 7 16.0 1.60 33.7 13.50 10.20 .76 PMNZ 7 14.2 1.30 43.3 14.74 12.88 .70 PMN4 0 10.8 1.33 42.3 7.03 15.19 .53 PMNS 20 5.9 1.32 42.7 6.88 22.34 .91 PPWl 25 7.0 1.56 35.0 16.33 17.76 .49 PPW6 0 14.2 1.58 34.3 12.21 11.64 .72 PPNl 33 6.5 1.34 42.0 13.74 20.10 .83 PPN2 0 10.9 1.29 43.6 19.88 11.67 .65 77 1.70— J ZZZ Wheel Trock 1.651 E3 Non—Wheel Trock T o 1.55- = $2? \ « a 2 3 1.50— % T g 3'} _ ¢ . : _/i .5 1.45 . % _. T S g g 1.40- ,7" % I 3b. 7/ C] 1‘351 ' : Eéjggg y/ls5d fig? ":5 . 4 § i/\\i /§§i "~— / T 3 30a at. ' A ‘ u\\ fit? FISi ‘33 1' W \\ \ \i \\ I 25: \ ”xi \\ k. \i - I ~ xx s, as 1 20 KL. 1A?“ “ [\fl . ‘3‘} AEN ' Corn,MB CornDP Corn,NT to,MB Pototo,PP Figure 16. Mean bulk density of surface soil for various crop and tillage plots (MB: moldboard, DP: disc plow, NT: no till, PP: paraplow). The bar above each mean shows one standard deviation. 77 * mfiN 4\ WNW-N. \\\.\\...\\\\\\M. . TWVWWZ/é/é? .. max-Revs T WWV%/// g 41.14 4 VN \\ NNRmNNRwV \NI. TI.\\\\ %\\\\\\\\\\\M\\\\I\ T WH/V/ 4NNVIIV\ 44444.4 K \\\.\\\\\\.L -K m n. 1...???ég k i C e m m Rex-N d _ e n .n . W? W N _ . _ . _ ._ . _ . _ ._IJ _ . 3 4... no .3 no .3 no .3 no .3 no .3 nu 7” .b .b no so A” A“ .3 1o 7_ .2 AmEo\3 38.60 423m Corn,ME3 Corn,0P Corn,NT Pototo,MB PototoPP Figure 16. disc DP: The bar above each mean Mean bulk density of surface soil for various crop and tillage plots (MB: moldboard, plow, NT: no till, PP: paraplow). shows one standard deviation. Woter Application Rote (mm/hr) Figure 1]. 78 1 20 .IVII I I I I I I I I I I T r I I I I r I I I I I I «'3‘; . .4 ‘Il ._ 0 . i? ‘2 -I d ' ‘ A 1 CO “ 21x13 0 ° __ d l l a 1m: J (In .4 . l... ‘. . 80 ii n . —4 '.| \- \’ _ l l3 . l \l ‘. -I . ‘l‘ .- .\\ o «i “giro \\\ A 6 q 60 "" \i\ ‘1'“ x ‘\\ ~~~~ o -: ‘ K3 ‘”‘_ o o. - \\ \ ‘ _ - ‘ ~ J “.0 ‘ ‘ £0 7 ....................... .1 40 — ‘\ " 20 O {I I I l’ T I I I I r I I T I I I I I f I I I I I O 5 10 i5 20 25 Cumulative Woter Applied o't Ponding (mm) tillage and wheel track conditions. Best-fit ponding curves derived from observed time-to-ponding data for corn plots with various I‘“'Kl \Ju .l. C.‘ .‘.'-' CDN CGQ CMN C-‘I W C7 if: CT 3‘." CC?- COW CMN CMW 79 120 (I I I r I I I r I T I I I I T I r I I I I I I I (j j I — PMW : i . l. -- PMN . E ~ l‘ PPN ~ V j i o PMW j cu 80— i'. A PMN _ 6 ‘ E; /< P-D‘N : or. ‘ I)?“ v PPN C 1' - .9 . ‘5 : .9 _ E}. J L1 .1 < u L .4 B "'8 -°-x- J‘Zx.§.9 _________________ O h _____________ III 3 . 25 Cumulative Water Applied ot Ponding (mm) Figure 18 . Best-f it ponding curves derived from observed time-to-ponding data for potato plots with various tillage and wheel track conditions. 80 the constant state tail on the X axis at large values of cumulative infiltration of each ponding curve represent the Ks values. Wheel track compaction reduced K; in the moldboard plow and disc plow system. The derived KS values were highest for the no till system. The influence of surface residue on the ponding curves is shown in Figure 19 as an example for potato under paraplow tillage system (PPWl, PPW6, PPNl, and PPN2). Surface residue shifted the ponding curves to the right indicating time-to- ponding was delayed and soil sorptivity was higher. This can be explained by the tendency for the residue to retain water without infiltrating the soil. Drier initial soil water conditions had the same tendency to delay time-to-ponding and increase sorptivity as shown in Figure 20 for potato with moldboard tillage. Soil sorptivity and.macroscopic capillary length are key factors in these changes. There are several direct management benefits in using time to ponding to predict soil infiltration. For sprinkler irrigation, controlling the irrigation rate or keeping the application rate lower than the ponding time curve can help reduce runoff so that water enters the root zone slowly and minimizes any preferential flow below the root zone (Clothier et al., 1981). This can help lower or prevent movement of fertilizers and pesticides to groundwater. Also, the best soil management for erosion prevention can be determined by knowing the possibility of rainstorm intensity. 81 120 If I I I T I I I I I I I I I T I I I I I I I r I f: ‘ l \ —- PPW w/Resi.J .C j I I' —- PF’W Bore : E iOO~ l ‘ - - PPN w/Resi- E I I f0 -— PPN Bore " V d ‘ ‘. o PPW w/Resi.: CD 80— ’ I - PPW Sore — '6 ‘ iI \‘\ x PPN vv/Pesi.1 C: 'i "I“ \“ 7 9971 bore : 'i c so- \ - O .l .. :3 . . 8 q . L; 40— — E I . <1 4 xx v . L. _ _ __ 1 _ _ _"__ __d Q 20. _ y 46 ——————————————————— 3 - . O I I j 7 fir I I I I . I I I T T T I I I I I I r I O 5 i0 15 20 25 Cumulative Wcter Applied ot Ponding (mm) Figure 19. Surface residue effects on best-fit ponding curves derived from observed time-to-ponding data for potato plots with paraplowed soil and various wheel track conditions . 82 ~ 1" i —- 9V: 5.9% ‘ ' ‘ —— 0 - 108‘” . l‘\ l‘ V’ - . /o 100— ‘l ‘ -- 0v:142% 4 ll \ a o (5.97.) ‘ ‘.\ X C- (10.8%) 80: ||\‘a \o X /4 A ’10?) \O‘éoL'o l l l l l l l l l l 1 #1 l l l l 1 l Water Application Rate (mm/hr). C) O I 40-1 4 20- _ O I I I I I I I I I I I j I I I I I I r I I I I 0 g 10 15 20 25 Cumulative Water Applied at Ponding (mm) Figure 20. Influence of initial soil water content on best-fit ponding curves derived from observed time-to- ponding data for potato plots with moldboard plowed soil and various wheel track condition. 83 C. Some Limitations of Time-to-ponding Model There are several factors related to the time-to-ponding model that affect its prediction capability. The model developed was only one-dimensional. Thus, it neglects the roughness of the tilled soil surface. Ignoring the roughness implies that the entire soil surface smooth, which is usually not true. This assumption also ignores the horizontal flow that can occur on these rough surfaces. Ignoring the flow that occurs in other than the vertical direction could lead to underprediction of infiltration. Another limitation of this one-dimensional model is that only one form.ofidiffusivity and conductivity is allowed and the upper boundary condition is limited to a constant flux density. Some further generalizations may be possible, for example, and initial profile of piecewise step functions and perhaps other forms. This would allow simulation of cyclic conditions. The spatial variability of soil properties is a common problem in dealing with soil properties. For example, the bulk density and initial water content of a plot was characterized by measurements made on averaging 10 soil cores obtained from each plot. This assumes that the core samples were uniformly representative of the plot. The major difficulty in applying the theory of time-to- ponding to a field experiment lies in the identification and measurement of the necessary hydraulic properties. Under certain conditions the heterogeneity of field soils may be such that a meaningful Darcy scale on which to apply the 84 theory may not exist. Where it does, field variability usually means that the characterization of the site by its basic hydraulic properties on a useful scale is a lengthy and not economically feasible operation. Because of this, rapid techniques must be used for site characterization or basic parameters must be expressed in terms of more readily measured soil-water properties. Although the soil hydraulic parameters in the model are all measurable, or based on measurable quantities, they proved difficult to determine accurately in many cases in the field experiment. This is not unusual for soil properties. For example, saturated hydraulic conductivity and sorptivity are characteristically subject to high variability for natural soils. The properties of tilled soils vary both spatially and temporally, and are ignored in the calculations. Considering the difficulties involved, the results of best-fitted ponding curves and soil properties under different soil management still indicates that the time—to-ponding model has good potential in predicting infiltration into soils. D. Demonstration of Use of Ponding Curves and Simplified Storm Patterns Consider four types of rainfall rate distribution in which a total amount of 30 mm of rain falls in 1.5 hour (Figure 21) . A moldboard tilled potato crop under wheel traffic conditions with surface residue management was examined for the prediction of surface runoff. As shown in 85 Figures 22 to 29, infiltration and runoff are influenced by rainfall distribution patterns as well as soil management. Figures 22 to 25 show the ponding curve derived from residue surface and bare surface with and without wheel track. The intersection of the ponding curve and rainfall pattern on the rate versus cumulative amount graph represents the time-to- ponding. For rainfall type A, the ponding curve of PMN with surface residue treatment has no intersection with storm distribution. Thus all rainfall would infiltrate and no surface runoff would occur for this treatment. The wheel- track with bare surface treatment had the lowest cumulative infiltration amount and thus the highest runoff} For rainfall type B and C, runoff occurred for each treatment. For rainfall type D, a constant rate, only the wheel-track treatments ponding curves intersect with rainfall distribution. Cumulative infiltration amount can be calculated from the model as a function of time (Figures 26 to 29). The runoff can.be calculated from the difference between cumulative rainfall and infiltration amount“ This demonstration shows the sensitivity of the overall model to both rainfall patterns and soil properties. The time-to-ponding curves appear to be a good infiltration-runoff process predictor under variable rainfall patterns and different management conditions. The model proved to be capable of predicting differences in infiltration and runoff due to management condition of the soil by differences in soil properties. 86 Four Types of Roinfoll Distribution (30 mm during 1.5 hr) f I I I I I Type A Type B N (D \I O U“! C) 01 O l I l l F 100- Type C Type D Roinfoll Roto (mm/hr) Bi 1 N 01 (J1 O l 1 O I r l.5 CLO CLS 1.0 1.5 Time (hr) C) (3 9’ on C) Figure 21. Four types of wassumed rainfall distributions for a 30 mm rain in 1.5 hour as a demonstration for infiltration prediction. 87 ‘I‘ I T‘ r T f T I I I r I I I l I I I I I I I r I r r r r I J ‘ ll‘ . —- Roinfoll A 100.0 g i ‘ \\ - - PMN w/Resi?‘ l ‘ “ \ —- PMN Bore ‘ f: - I I ‘ \ I M ' J: .. ‘ l ‘ \ ~ - Pull w/RESH \ 800- l l “ \\ —- PMW Bore — E ‘ l i \ ‘ r— -l i ‘ \ - C i i \ v 4 \ \\ \ \\ C1 G) 60.0“ \ \\ \\ "‘ O .J \ \ \\\ _, : 40.0“ \\ \\ \ ‘ ‘ ‘ ~ - O \\ Q ~ ‘ ~ . w- ‘ \ \ “‘= .E ‘ \ \ ~~~~~ i~ ‘ o l \ ‘”**r: --------------------- [r 200~ \\ -~--__~- _ .. \ ----- . \\ ......... 1 0.0 r I I I I I I I I I T I I I r I I I T 7 I r I I I I I I T 0.0 5.0 10.0 15.0 20.0 25.0 30.0 Cumulotive Roinfoll Amount (mm) Figure 22. Ponding curves for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic distribution. conditions with type A rainfall 88 III I I‘ I I I r I I I I T I I I r I I I I I I I I I .I I r I I ‘ ll ' —— Romfoll B * 100.0— li '. —— PMN w/Resi.‘ 1 l I “ \\ -— PMN Bore <:‘ I‘ ‘ -- PMW’w/Remu L i i i i \ PMW B \ 800- l l | \\ . ore . E d i \\ \ q E ‘ l \ ‘\ . V ‘I I \\ \“L Q) 60.0-i I \ \ d *4 ‘ l ‘ x O . \ ‘\ . Oi . \\ \ \‘\‘ ‘ g 430.0" \ \\\ ‘~_‘“~~ ‘1 H— d \ \ \\ ~~~j .E ‘ \ ‘5 _________ l O .1 ‘ —_: ————— -— ——————— 01 20.0- \\ ‘ - - - , ..... -l \\ -------- 1J————‘ \‘ ~~~~~ J, 0.0 T F T I I I I I I I I I I I I r I I I T 7 I r I I I I I I I7 0.0 5.0 10.0 15.0 20.0 25.C 30.0 Cumulotive Roinfcll Amount (mm) Figure 23. Ponding curves for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic distribution. conditions with type B rainfall 89 [r I‘ r I 1" I I I I I I I I I I I I I I I I I I T I I I I I I " 1 I ‘ \ '1 100.0- I 1 I \ - “ ‘ t \ a I l . \ .. e : 1 1 1 x . .C \ 80.0- ‘ I 1 \ q .1 I \ d E ‘ 1 . ‘ I E ‘1 I \ \\ d v ‘ I \\ \\ 60.0‘ I \ \ —1 (D 4 \ \\ q 6 \ \ \‘ < 4 \ \ \\ (I 4 \ \\ a“ q : 40.0“ \ \\ ~ ~~~~~ fl 0 d \\ ‘ ~~~dL_.: W. \ \\\ ~ ‘ .E ‘ \\ “~~L‘—.,___ —- PMW Bore O .1 ‘ ‘ ~ DH‘H ’" : [z _ \ d -- .....w,.~ ‘ : 3 : . .E 10.0- - U -l // // q CY. ‘ / / d -4 / // q C) d / / --— D‘ " an: d :3- 5.0— / / ~ 41» 5...- .- _o_ J //// - - PMW w/Resw g j / —- PMW Bore . 5 ‘ — Roinfoll A ‘ o 0.0 I I I I I I I I T I r I r T 0() C32 0x1 (16 CL8 1.0 1.2 1.4 Time (hr) Figure 26. Calculated cumulative infiltration amount and cumulative rainfall amount for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic conditions with type A rainfall distribution. 92 A E 30.0 I I I I F I I I I I 4 E Z -— ROInfOll 8 q V - —- PMW Bore « “E 25 O; - - PMW w/Resl. , , , _ 8 . ‘ -— .3121?! Bore ’ ‘ '1 . / fr“ ~ I 3.3 -+ . .E 10.0-4 - 0 ~ I a ‘ d (D . -1 3 5.0— — ‘3 ~ . :3 ‘ I E j 4 5 O O . I . I I I I I . l . I . I 01) (12 0‘1 (16 C)8 1 0 1 2 1 4 Time (hr) Figure 28. Calculated cumulative infiltration amount and cumulative rainfall amount for moldboard tilled soil with.a potato crop with various surface residue treatments and wheel traffic conditions with type C rainfall distribution. 94 E 30.0 I I f I r I I I I I T I T I d E ' — Roinfoll D . V 1 _. PMW Bore ’33 g 25.0; - - PMW w/Resi. ’ ' _: <2 I , , I t I . .< I q c 20.0- .q .9 I . 1e; : ,/; E 15 o~ ///’ L E d // .. 52 I / I E 10.0-J /// - U .4 // d; C: ‘ / 1 .. / cu I / J. E 5.0— O '1 .9: q E I C) 013 I I I I I I I I . I I I I r I (10 022 01$ (16 C18 1.0 1.2 1.4 Time (hr) Figure 29. Calculated cumulative infiltration amount and cumulative rainfall amount for moldboard tilled soil with a potato crop with various surface residue treatments and wheel traffic conditions with type D rainfall distribution. 95 Applying this model to individual rainfall events involves relatively simple calculations. The field measurements suggest that setting up time-to-ponding families of'curves for variable soil management.to predict infiltration and runoff prediction is possible. There are useful applications of this model for in sprinkler irrigation assessment. Management of both the surface soil and.sprinkler application rates.permit.controlled water entry under unsaturated conditions. There are several direct benefits in being able to predict tp. Keeping Y0I< O, or keeping the application time less than tp, should help maintain soil surface structure; it efficiently places water in the root zone by minimizing any preferential flow under saturated conditions below the root zone, thus decreasing the possibility of leaching of fertilizers and pesticides to groundwater. E. Example of Runoff Prediction for One Rainstorm As an example for linkage between rainstorm generator and time-to-ponding approach for long-term infiltration and runoff prediction, the observed and simulated rainstorm on July 11, 1985 from, Deer-Sloan.‘Watershed, Michigan. are shown from Figures 30 to 35. The ponding curves of paratilled potato crop with surface residue (PPWl) and bare surface treatments (PPW6) were established by derived field experiment from Table 7. The observed rainstorm rate has five intersections with the ponding curve of both treatments (Figure 30). Five 96 ponding times and five non-ponding time can be observed from the graph. The cumulative infiltration amount can be calculated from [4.8] with derived soil physical properties and rainfall intensity. Figure 31 shows the calculated results of cumulative rainfall and infiltration amount. The difference between cumulative rainfall and infiltration is runoff (Table 8). Figures 32 shows the simulated rainstorm with peak intensity appearing at normalized time .17 during rainstorm process. The calculated runoff from Figure 33 for both treatments are higher than the results from Figure 31. Figure 34 shows the ponding curve intersect with 10 equal time increments simulated rainstorm. Without a peak intensity simulation, the calculated runoff (Figure 35 and Table 8) is lower than the results from Figure 33. Soil surface storage is an important property of infiltration and runoff process because of the temporary storage of excess water in surface depressions without runoff initiation. A model of surface depressions has been developed by Linden in 1979 and was used in developing a functional relationship for the upper limit to depression storage as a function of roughness RR and the general land slope L. The decreasing of runoff by presence of surface residue indicates the influence of residue cover. 97 120-F‘TI—‘TLI I f I I I I I I I I I I I T r I I r T I I' I ‘ . i ——- Stornw ‘ ’2? . j I sma w/ Refidue : < \‘ B-U Bore _ E ‘I ‘ E ‘ ‘ V _: >\ -4 o-‘j- -1 m . C Q) —1 -4—J u .E . E i O -+-J '1 m i C . . 5 ttW**¢-¢+¢-A-fis Q: EDD-00688880090134 “l j] I I I I f I rj 20 25 Cumulative Amount (mm) Figure 30. Ponding curves for paraplowed soil with a potato crop under ‘wheel track condition for various surface residue treatments and observed rainstorm on July 11, 1985 from Deer-Sloan Watershed station #10, Michigan. Cumulative Amount (mm) 98 I r Storm —_- w/ Refldue Bore —. fl-— —.-—fl-—— fl.- u.- Figure 31. r Ou4 (16 Time (hr) (18 1.0 1.2 Calculated cumulative infiltration amount and cumulative rainfall amount for paraplowed soil with a potato crop under 'wheel track condition for various surface residue treatments and an observed rainstorm. 99 120_—61—+I I I l I I I I l I I I I l . l I I r T I I r l ' l -—— Stornw i ’T‘ d ' l ans w/ Rescue L. . . \ B .C B-CJ are _ . I \ 100d . ‘ I l E ' ‘1 E ‘ '- l j >\ . ' I\ f: .. El \ ‘l m 1 2 R 1 g 60- 1 \q .1 ‘E I e; X 1 _ \ Ex -I E 4'0"4 (:1 AA I .4 5 4 a 515‘ -l I a 1 TI; 4 sea Mfitfi'bg :‘I .1 .E 20" ' 8889133 :- é'kfi-o-a-aa-a-m-{g O ‘ BEER-”355‘El'3GOD-aaaaasaaara-aaaaaaaaa-a‘oagn Q: q 1 O“ “I l I . I I I I I . I I I I I rI I I I I I I I I I O 5 10 15 20 25 Cumulative Amount (mm) Figure 32. Ponding curves for paraplowed soil with a potato crop under wheel track condition for various surface residue treatments and simulated rainstorm using peak intensity on July 11, 1985 from Deer-Sloan Watershed station #10, Michigan. 100 I 1 I I r I I I I I Y I 22- — Storm ‘ ——- w/ Remdue 4 - - Bore 1-1. 4--.] __l._1....1__\1--1_ .‘ It ,1“ 1-1-4-1 ._1_._1 Cumulative Amount (mm) :13 L__L_ 1-..l_._1.___I-1 Figure 33. Calculated cumulative infiltration amount and cumulative rainfall amount for paraplowed soil with a potato crop under wheel track condition for various surface residue treatments and a simulated rainstorm using peak intensity. 101 120q—BT‘?I f r I I I I I I I r I I I I I 1 r I I fiT r T '. 1 —- Storm " 4 . . .J '. 1‘ (Ir-A w/ Resndue d 100- ' 1 a {I Bore ._ d 1 4 \ Rainstorm Intensity (mm/hr) Cumulotive Amount (mm) Figure 34. Ponding curves for paraplowed soil with a potato crop under wheel track condition for various surface residue treatments and simulated rainstorm using 10 equal increments on July 11, 1985 from Deer-Sloan Watershed station #10, Michigan. .Cumulotive Amount (mm) Figure 35. 102 22- .4 20s .J 18- 16— 14— c4 12‘ d 10- ' I I — Storm —- w/ ReQdue -- Bore 1 Time (hr) Calculated cumulative infiltration amount and cumulative rainfall amount for paraplowed soil with a potato crop under wheel -track condition for various surface residue treatments and a simulated rainstorm using 10 equal time increments. 103 Table 8. Calculated runoff (mm) from cumulative infiltration and cumulative rainstorm amounts for different surface treatment. of’ a jparatilled soil with a potato crop with wheel track condition. soil condition Residue cover Bare surface storm intensity Observed storm 1.18 2.76 Simulated storm 2.32 5.00 with peak intensity Simulated storm 0.77 2.57 with 10 increments VII. SUMMARY AND CONCLUSIONS Soil infiltration profoundly influences runoff and soil erosion. The research discussed for this study used a physical-based infiltration model to assess the effects of irrigation and variable rainfall rate patterns on the hydrologic behavior for different types of soil management. A field study was conducted at three sites in Michigan to determine soil properties needed for assessment of infiltration. Field time-to-ponding was measured for various water application rates using a sprinkling infiltrometer for a variety of soil management and initial conditions. Soil parameters were derived from best-fit ponding curves to predict soil infiltration. The soil properties needed for predicting time to ponding were sorptivity, S(Bs,6n), and hydraulic conductivity at field saturation, Ky. The model consists basically of equations to predict the time of surface ponding and the infiltration rate under variable rainfall patterns or sprinkling irrigation applications. The ease and speed with which sprinkler infiltrometer'can be used in the field suggests that their use for measuring soil hydraulic properties is probably more appropriate and 104 105 less variable than taking cores for laboratory measurements. The analytic expression for time-to-ponding in the inverse sense can be used to determine the soil sorptivity, hydraulic conductivity, and point source runoff during rainfall. These properties are proportional to the characteristic mean pore size of soils which is affected by cultivation and.management. Thus, the model provides a rational basis for estimating water infiltration under different management conditions. The rainstorm generator developed in this study required relatively few parameters to disaggregate the daily precipitation into individual storm event and intensity patterns. Thirty years rain gauge data from Deer-Sloan Watershed, Michigan was used to evaluate the number of variables needed to make the model workg .A first—order Markov chain was used for prediction of wet or dry day. For a wet day, the number of rainstorm events and the amount, duration, peak intensity and short-period intensity pattern of each event were disaggregated from stochastic distributions. Marginal and conditional distributions were fitted to simulate the peak intensity pattern of each storm. A multivariate double exponential model for dimensionless storm event was used 'to «disaggregate. individual storms into short-period rainfall intensities. Thus, given a simulated storm amount, duration, and ratio of peak distribution, approximate storm intensity patterns were developed” .An analysis of 30 years of storms observed at the Deer-Sloan Watershed station #10 in Michigan suggests that the proposed model structure provided 106 an acceptable prediction of storms from April to September. The rainstorm generator provided the required information for the time-to-ponding infiltration model. A case study was used to demonstrate the sensitivity of point source runoff estimation from different rainfall patterns. The relationship of point source runoff to rainfall intensity was greatly affected by soil hydraulic properties, which were influenced by soil management, residue cover, and initial soil water content. The decreasing of runoff by the presence of surface residue cover indicated that infiltration is not just a physical process, but a biophysical one. The mulching material, crop residue left on the surface, and.plant roots protect surface soil from the impact of raindrop erosion and increase the absorption of applied water. Soil management techniques, especially‘ tillage, have been linked to 'the creation of low-permeability surface soil, which reduce infiltration capacity and increase runoff and soil erosion on these agricultural soils. Heavy wheel track tillage practices increase the opportunity from movement of surface-applied chemicals to runoff'water“while.decreasing'the opportunity for leaching because of reduced infiltration capacity. The time-to-ponding model has several noteworthy features. ‘First, it represents the actual infiltration process and therefore predicts infiltration as a function of measurable soil characteristics, currently for a rather limited conditions but potentially for a wider range. Empirical infiltration equations and models, on the other 107 hand, require the use of fitted parameters. Second, applying the model to individual rainfall events involves very simple calculations comparable to those with common infiltration equations. There is a difference between modeling infiltration for a steady rain and modeling infiltration for an unsteady rain. For a steady rain, infiltration starts with an unponded surface and later changes to a stage with surface ponding, which lasts until the end of the rainfall event. There is at most one ponding time in a steady rain. For an unsteady rainfall event, there may be several periods when the rainfall intensity exceeds the infiltration rate. The infiltration process may change from one stage to another and shift back to the original stage in a recurrent style. Though the time-to- ponding infiltration model used in this study is a simplified representation of the infiltration process in the field. Because of the practical limitations and difficulties often attendant to evaluating more that several constants by least squares fitting, particularly when the numerical data contain experimental error, it is expected that the least number of parameters required will be most useful for the least squares fitting process. Therefore for describing and fitting field measurements of time-to-ponding data, the infiltration estimation procedure used in this study offers a useful and reasonable simplicity. The sorptivity and hydraulic conductivity are both well defined physical properties. 108 The results of this study has suggested the need for other research to make the system work under many practical conditions. The following suggestion are made for further research need: 1. The criteria governing storm generator transferability, and the sensitivity of point source runoff hydrographs to various types of rainfall data input. If the distribution functions and coefficients have linear spatial variation, the storm generator model will be able to apply to other location. Sensitivity of derived quantities, such as peak runoff rate or volumes to the structure of disaggregation. :models, may lead. to further simplifications of this storm generator. The actual situation at the soil surface during rainfall is undoubtedly much more complex than the infiltration model assumed in this study. The runoff or rainfall significance of water at the ponding stage observed in this investigation requires further study. Uptakes associated with the commencement of ponding are important where even localized runoff is to be prevented during a rainstorm. On the other hand, when runoff relatively far from the source of applied water is of primary interest. It should be pointed out that this study was concerned with rainfall infiltration 109 into soil, the structure of which was affected but little by water percolation or by raindrop impacts. Such. considerations ‘were ‘necessary’ in. order' to throw some light on the purely hydrodynamic aspects of the rain infiltration phenomenon. EDI further field situations the effects of soil structure transformations must also be taken into account. This infiltration model assumes a homogeneous soil profile and a uniform distribution of initial soil water content. The movement of water in the soil is assumed to be in the form of an advancing wetting front, and the diffusion of soil moisture is neglected. But this equation is one of the best models available to describe infiltration during an unsteady rainfall event. The assumption of a homogeneous soil profile and a uniform.distribution of initial soil water content needs further study to explore the potential of the time-to-approach in modeling infiltration during a rainfall event. APPENDICES APPENDIX 1 Fortran source code for observed storm intensity calculation from rain gauge data record. 110 APPENDIX 1. Fortran source code for observed storm 00000 0 101 intensity calculation from rain gauge data record. PROGRAM RAINSTORM program to read in raingauge data record and out put individual storm intensiy patterns for 30 years Heather files from Deer-Sloan Watershed station #10, Michigan character*1 cd OPEN(11,FILE='d10data.txt',STATUS='0LD') OPEN(12,FILE='d10apr.wth',STATUS='UNKNOUN') OPEN(13,FILE='d10may.uth',STATUS='UNKNOHN') OPEN(14,FILE='d10jun.ch',STATUS='UNKNOHN') OPEN<15,F1LE='d10jul.wth',STATUS='UNKNOHN') OPEN(16,F1LE='d10aug.wth',STATUS='UNKNOHN') OPEN<17,FILE='d1OSep.wth',STATUS='UNKNOWN') OPEN(18,FILE='d100ct.wth',STATUS='UNKNOWN') OPEN(19,FILE='d10all.wth',STATUS='UNKNOHN') dcount=0. iswtchsI m=0 d=0 y=0 read(11,101,end=999)cd,sta,m1,d1,y1,starth1,startm1,dur1,amount if(m1.lt.4..or.m1.gt.10.) goto 10 if(starth1.ge.24.) starth1=starth1~24. fornat2mm ) +container(g) : ',\) S‘UHV-fi 1800 format(10x,' Height of container (9) : ',\) 1900 format(10x,' weight of wet soil+container(g) : ',\) 2000 format(10x,' Height of dry soil+container(g) : ',\) call clear write (*,'(15x,A,/,A,A,A,/,A)') & 'Calculation Completed', 8. ' Output file is “', outfname,"", & ' Inpdt data stores in “INPUTF2"' close (10) close (13) end APPENDIX 4 Soil water content estimation from texture and bulk density. 120 APPENDIX 4. Soil water content estimation from texture nnnnnn annnnnnn d nnnn nnnn nnn n 65 and bulk density PROGRAM SOILU PROGRAM TO CALCULATE SOIL HATER CONTENT FROM SOIL TEXTURE BY Dr. J. RITCHIE AND JIMMY T. CHOU, FEB. 22, 1988 A87, PSS BUILDING, MICHIGAN STATE UNIVERSITY, MI 48824 (517) 353-8537 REAL LOLM,LOLC CLAY : CLAY CONTENT(X) SAND : SAND CONTENT(X) 0C : ORGANIC CARBON 0F : FIELD BULK DENSITY RFU : ROCK FRAGMENTS BY HEIGHT (X) write(*,*)' Please input clay content (2): ' read (*,*)clay write(*,*)' Please input sand content (1): ' read (*,*)sand silt-100.-sand-CLAY if (silt .lt. 0.) then write (*,*) ' wrong data, Please re-input ' goto 111 endif write(*,*)' Please input Bulk Density (g/cm**3):' read (*,*) 0F write(*,*)' Please input organic carbon content (X):' read (*,*) 0C write(*,*)' Please input rock fragments by weight (%):' read (*,*) RFw ASSUME THE ORGANIC MATTER CONTENT IS 1.72 TIMES ORGANIC CARBON IF THERE IS NO ORGANIC CARBON DATA, ASSUME OC=0. IF(OC.LT.0.) OC=0. OM8OC*1.72 IF(SAND.LE.75)GOTO 62 LOLM=0.188-0.00168*SAND PLEXUM=0.423°0.00381*SAND GOTO 65 LOLM80.0362+0.00444*CLAY IF(SILT.LT.70)GOTO 63 LOLM80.05+0.000244*CLAY**2. PLEXUM80.1079+0.0005004*SILT IF (SAND.GT.80.) DM= 1.709- 0.01134*CLAY IF(SAND.GE.20..AND.SAND.LE.80.) THEN DM81.118+0.00816*SAND+CLAY*(0.00834-0.36056/(SILT+CLAY)) ENDIF IF (SAND.LT.20.) 0M8 1.45314 ' 0.00433*SAND DFC : CACULATED BULK DENSITY DFC=(OM*0.224 + (100-OM)*DM) I100. IF THERE IS NO DATA ON BULK DENSITY, USE THE CALCULATED VALUE SAVE FIELD MEASURED DF TO DFO AS AN OUTPUT DFO8DF IF(DF.LT.0.01) DF=DFC 1.221 APPENDIX 4 (cont'd) nnnnn nnnnn 000 no C 999 LOLC : CALCULATED SOIL'HATER LOWER LIMIT PLEXHC : CALCULATED SOIL'HATER EXTRACTABLE DULC : CALCULATED SOIL-HATER DRAINED UPPER LIMIT SATC : CALCULATED SOIL-HATER SATURATION DULC'LOLM+PLEXHM-0.17*(DM-DF)+0.0023*OM PLEXHC8PLEXUM+0.035*(DM-DF)+0.0055*0M LOLC=DULC'PLEXHC ADJUST THE SOIL-HATER BY ROCK FRAGMENTS (RFH) RFV :ROCK FRAGMENTS BY VOLUME (X) SV :SOIL VOLUME EXCLUDING ROCK FRAGMENTS(X) IF (RFU.GT.0.) THEN RFV8100./(1+2.65*((100.-RFU)/(RFU*DF))) SV=100.-RFV LOLC8LOLC*SV/100. DULC=DULC*SV/100. ENDIF ASSUME SATC EQUAL TO 85% OF SOIL POROSITY SATC8.85*(1-DF/2.65) IF(SATC-DULC.LT.0.015) SATC=DULC+0.015 URITE(*,'(l,3(A,F6.3),/)') ' Lower Limit :',lolc, +' Drained Upper Limit :',dulc,' Saturated Content :',satc write (*.*) 'Another set of data 7 (Y or N)‘ read (*,'(A)') answer if (answer .eq. 'Y' .or. answer .eq. Ty.) goto 111 STOP END APPENDIX 5 Optimization Complex program for best-fit ponding curves estimation. 122 APPENDIX 5 Optimization Complex program for best-fit (Dr)r3r)f)f)f)firifif3flf)r3f)f)f)(3(3CIFIfirif)f)fir)r)f)C)fIf)f)f)f3C)r!r)r,f)r)fif3f3fififlfi ponding curves estimation PROGRAM ESTIMATE **********i******.**i*******i***************************************** This is a parameter estimation fortran program developed to * estimate the soil infiltration parameters (moisture status and * saturated hydraulic conductivity) using the Complex (non'linear * optimization) algorithm by M.J. Box (Kuester, J.L. and J.H. Mize* 1973) Optimization Techniques with Fortran * ***********t****************it**************************************** Complex algorithm adapted from Kuester and Mize, pp. 375-380. * ********************************************************************** Description of parameters: N 8 number of explicit independent variables; defined in main program M 8 number of sets of constraints; defined in main program K 8 number of points in the complex; defined in main program ITMAX 8 maximum number of iterations; defined in main program IC 8 number of implicit variables; defined in main program ALPHA 8 reflection factor; defined in main program BETA 8 convergence parameter; defined in main program GAMMA 8 convergence iteration; defined in main program DELTA 8 explicit constraint violation correction; defined in main program IPRINT 8 code to control printing of intermediate iterations. IPRINT81 causes intermediate values to print on each iteration. IPRINT80 suppresses printing until final solution is obtained. Defined in main program. X 8 independent variables; define initial values in main program R 8 random numbers between 0 and 1; defined in main program F 8 objective function; defined in subroutine FUNC IT 8 iteration index; defined in subroutine CONSX IEVZ 8 index of point with maximum function value; defined in subroutine CONSX IEV1 8 index point with minimum function value; defined in subroutines CONSX and CHECK G 8 lower constraint; defined in subroutine CONST H 8 upper constraint; defined in subroutine CONST XC 8 centroid; defined in subroutine CENTR l 8 point index; defined in subroutine COMSX KODE 8 key used to determine if implicit constraints are provided; defined in subroutines CONSX and CHECK K1 8 Do loop limit; defined in subroutine CONSX The user-supplied subroutines are: FUNC - specifies the objective functions CONST - specifies the explicit and implicit constraints The dimensions are: X(K,M), R(K,N), F(K), G(M), H(M), XC(N) **********************i**iti******itiii*i*********.****ifi***t************* DIMENSION X(10,10), R(10,10), F(10), C(10), H(10), XC(10) INTEGER GAMMA character*12 file(0:8) OPEN (150,FILE8're.out',ACCESS8'SEOUENTIAL',STATUS8'UNKNONN') open (90,file8're.in',status8'unknown') write (*,'(//,10x,A,//)') 'COMPLEX PROGRAM FOR BEST FITTNESS' write (*,*) 'Please input the estimated variables number (3-10):' read (*,'(i2)') n write (90,*) n file(0) 8 'Ks' do 1000 ifile 8 1,n~1 write (*,'(A,i2,A)') 'File name for ',ifile,‘ data set:' read (*,'(A)') file(ifile) .1223 APPENDIX 5 (cont'd) 1000 2000 101 100 010 011 50 20 01B 014 015 016 300 30 017 999 write (90,'(A)') file(ifile) ifilen8ifile+9 open (ifilen,file8file(ifile),status='old') continue a 8 n R810 itmax81000 ic80 iprint80 alpha81.3 beta8.00001 gamma85 DELTA80.00001 write (*,*) 'Initial value for Ks (mm/hr):' read (*,*) x(1,1) write (90,*) x(1,1) do 2000 ifile 8 2,n write (*,'(A,i2,A)') 'Initial value for ',ifile-1,‘ m.ca:' read (*,*) x(1,ifile) write (90,*) x(1,ifile) continue DO 100 II=Z,K DO 101 JJ81,N CALL RANDN (YFL) R(II,JJ) 3 YFL CONTINUE CONTINUE URITE (150,010) roath (4X,'PARAMETER ESTIMATION BY THE COMPLEX nernoo',//, +1X,'ESTIMATION OF INFILTRATION MODEL (TIME'TO-PONDING) ',///, + 1X,'PARAMETERS') URITE (150,011) N,M,K,ITMAX,IC,ALPHA,BETA,GAMMA,DELTA FORMAT (/,3X,'N8',I2,3X,'M8',I2,3X,'K8',IZ,3X,'ITMAX8',I3, +3X,'IC8',I2,/,3X,'ALPHA8',F5.2,3X,'BETA8',F10.5,3X,'GAMMA8', +IZ,3X,'DELTA8',F6.4) write (*,'(/,15x,A,/)') 'Program is running I' CALL cowsx (N,M,K,ITMAX,ALPHA,BETA,GAMMA,DELTA,X,R,F,IT, + IEV2,G,H,XC,IPRINT) IF (IT-ITMAX) 20.20.30 NRITE (150,018) IT FORMAT (//,1X,'FINAL ITERATION: ',IS) NRITE (150,014) F(IEV2) write (*,14) f(iev2) FORMAT (//,1X,'FINAL VALUE OF THE FUNCTION (r square) =',F8.4) HRITE (150,015) write (',15) FORMAT (/,1X,'FINAL X VALUES') DO 300 J81,N NRITE (150,016) J,X(IEV2,J),file(j'1) write (',16) j,x(iev2,j),file(j-1) FORMAT (3X,'X(',IZ,') s ',F8.2,3x,A) CONTINUE GOTO 999 NRITE (150,017) IT FORMAT (1X,'The number of iterations has exceeded',l3, + '. Program is terminated.') write (*,'(//,15x,A)') 'Program completed' write (*,'(15x,A)') 'Output file is "re.out"' write (*,'(15x,A)') 'Input data stores in "re.in"' STOP END SUBROUTINE CONSX is called from the main program and C c *ififlflflhflttfiiti‘kflttififliiii******"***********i*t***************** C C coordinates all special purpose subroutines (CHECK, 124 APPENDIX 5 (cont'd) (1 CENTR, FUNC, and CONST). ***i***”************t*******************************i********** 000000006 10 20 30 40 000 GOO 000 O 50 021 100 SUBROUTINE CONSX (N, M, K, ITMAX, ALPHA, BETA, GAMMA, DELTA, X, R, F, + IT, IEVZ, G, H ,XC, IPRINT) IT 8 ITERATION INDEX IEV1 8 INDEX OF POINT HITH MINIMUM FUNCTION VALUE IEVZ 8 INDEX OF POINT UITH MAXIMUM FUNCTION VALUE I 8 POINT INDEX KODE 8 CONTROL KEY USED TO DETERMINE IF IMPLICIT CONSTRAINTS ARE PROVIDED K1 8 DO LOOP LIMIT DIMENSION X(10,10), R(10,10), F(10), C(10), H(10), XC(10) INTEGER GAMMA IT 8 1 KODE 8 0 IF (M-N) 20,20,10 KODE 8 1 CONTINUE DO 40 II8Z,K DO 30 J81,N X(II,J) 8 0.0 CONTINUE CALCULATE COMPLEX POINTS AND CHECK AGAINST CONSTRAINTS DO 65 II82,K DO 50 J81,N I8II CALL CONST (N,M,K,X,G,H,I) X(II,J) 8 G(J) + R(II.J)*(H(J)°G(J)) CONTINUE K1 8 II CALL CHECK (N, M, K, X, G, H, I, KODE, XC ,DELTA, K1) IF (II 2) 51,51,55 HRITE (150,018) FORMAT (/,1X,'COORDINATES OF INITIAL COMPLEX') O- HRITE (150,019) (IO, J, X(IO,J), J81,N) FORMAT (1X, 3(3X, 'XC(', I2,',',I2, ') 8 ' ,F8.2)) IF (IPRINT) 56, 65 ,56 NRITE (150,019) (II, J, X(II,J), J81,N) CONTINUE K1 8 K 00 70 I81,K CALL ruuc (N,M,K,X,F,I) CONTINUE KOUNT 8 1 IA 8 0 FIND POINT UITH LONEST FUNCTION VALUE IF (IPRINT) 72, 80, 72 HRITE (150, 021) (J, F(J), J81 ,K) FORMAT (I, 1X, 'VALUES OF THE FUNCTION“ ,/, + 1X ,3(3X, 'F(', I2, ') 8 ' ,F8. 2)) IEV1 8 1 DO 100 ICM82, K IF (F(IEV1) F(ICM)) 100, 100, 90 IEV1 8 ICM CONTINUE F(ITEMP)=F(IEV1) FIND POINT NITH HIGHEST FUNCTION VALUE IEVZ 8 1 JAZES APPENDIX 5 (Cont'd) 110 120 r)r)r) 130 140 CIVIC) 150 160 (if)?! C C C C C C C 170 180 190 200 210 215 220 230 023 024 025 026 228 240 OD 120 ICM82,K IF (F(IEV2)°F(ICM)) 110,110,120 IEV2 8 ICM CONTINUE CHECK CONVERGENCE CRITERIA IF (F(IEV2)'(F(IEV1)*BETA)) 140,130,130 KOUNT 8 1 GO TO 150 KOUNT 8 KOUNT + 1 IF (KOUNT-GAMMA) 150,240,240 REPLACE POINT HITH LOHEST FUNCTION CALL CENTR (u,n,x,xsv1,1,xc,x,x1) 00 160 41:1,» X(IEV1,JJ) 8 (1.0+ALPHA)*(XC(JJ))-ALPHA*(X(IEV1,JJ)) I - 15v1 CALL CHECK (N,M,K,X,G,H,I,KODE,XC,DELTA,K1) CALL ruwc (N,M,K,X,F,I) REPLACE NEH POINT IF IT REPEATS AS LOHEST FUNCTION VALUE ICOUNT8O 15v . 1 00 190 1cn=2,x IF (F(IEV)-F(ICM)) 190,190,180 15v . ICM CONTINUE IF (IEV-IEVI) 220,200,220 00 210 JJ81,N X(IEV1,JJ)8(X(IEV1,JJ) + XC(JJ))/2.0 CONTINUE 1-1£v1 CALL CHECK (N,M,K,X,G,H,I,KODE,XC,DELTA,K1) CALL FUNC (u,w,x,x,r,1) ICOUNT8ICOUNT+1 IF (ICOUNT-S) 170,170,215 IF (F(ITEMP).GE.F(IEV1)) CALL HELP(N,M,K,X,F,IEV1, + R,G,N,KODE,XC,DELTA,K1) CONTINUE 1r (IPRINT) 230,228,230 HRITE (150,023) 11 FORMAT (//,1X,'ITERATION uunasn ',15) HRITE (150,024) FORMAT (/,1X,'COORDINATES or CORRECTED poxnr') HRITE (150,019) (IEV1,JC,X(IEV1,JC), JC81,N) HRITE (150,021) (1,5(1), 1=1,x) HRITE (150,025) roanxr (/.1x,'cooaoxuxrss or THE CENTROID') HRITE (150,026) (JC,XC(JC), JC81,N) FORMAT (1X,3(3X,'X(',IZ,') 8 ',F14.6)) 11 - 11 + 1 1r (IT-ITMAX) 80,80,240 mum: £00 ******i***************i********************i********************* Subroutine CHECK checks all points against explicit and implicit constraints and applies correction if violations are found. * i * *************************i*************************************** 10 SUBROUTINE CHECK (N,M,K,X,G,H,I,KODE,XC,DELTA,K1) DIMENSION X(10,10). C(10), H(10), XC(10) KT 8 0 1136 APPENDIX 5 (cont'd) r)r)r) 20 30 50 f)f)f) (I 60 90 100 110 fififlf5f) 10 r1r5r1r1r1 1000 001 CALL CONST (N,M,K,X,G,H,I) CHECK AGAINST EXPLICIT CONSTRAINTS 00 50 4:1,N IF (X(1.J)-G(J)) 20.20.30 X(I,J) . 0(1) + DELTA 00 TO 50 IF (H(J)-X(I.J)) 40,40,50 X(I,J) - H(J) - DELTA CONTINUE IF (KODE) 110,110,60 CHECK AGAINST THE IMPLICIT CONSTRAINTS NR 8 N + 1 00 100 J8NN,M CALL CONST (N,M,K,X,G,H,I) IF (X(I,J)-G(J)) 80,70,70 IF (H(J)°X(I,J)) 80,100,100 IEV1 8 I KT 8 1 CALL CENTR (N,M,K,IEV1,I,XC,X,K1) DO 90 JJ81,N X(I,JJ) 8 (X(I,JJ) + XC(JJ))/2.0 CONTINUE CONTINUE IF (KT) 110,110,10 RETURN END ***fittitiiflfitiiititfit*tifi**it****i************i*************** Subroutine CENTR calculates the centroid of points. * ****.******itfi****.*****i*****************************it*****i susROUTTNE CENTR (N,M,K,IEV1,I,XC,X,K1) DIMENSION X(10,10), XC(10) 00 20 1:1,N XC(J) . 0.0 00 10 IL81,K1 XC(J) - XC(J) + X(IL,J) RK . K1 XC(J) = (XC(J)-X(IEV1,J))/(RK-1.0) RETURN END *fii*fitttfitififiififiiiiiii***ifii***************i********************** SLbroutine FUNC specifies objective function (user supplied).* *Nii...***********flii*******i*****i**************************i**** susROUTTNE FUNC (N,M,K,X,F,I) DIMENSION x<10,10), F(10) iend 8 n+8 do 1000 irewind 8 10,iend rewind irewind continue icount80 srys80. sry80. see-O. se80. sery80. do 002 im810,iend read (im,*,end8002) junk,cumw,rate icount8icount+1 127 APPENDIX 5 (cont'd) 002 r1r1r1r1r1r) r1r1r) 1000 iforx 8 im -10 +2 yrate8x(i,1)/(1-exp(-cumw/x(i,iforx))) diff 8rate-yrate srys8srys+rate**2 sry8sry+rate ses8ses+diff**2 se8se+diff sery8sery+diff*rate goto 001 continue siys8srys/icount-(sry/icount)**2 sies8ses/icount-(se/icount)**2 siyes8serylicount'(sry/icount)*(se/icount) f(i)8((siys-siyes)**2)/(siys*(siys+sies-2*siyes)) RETURN END i*t...*i****************t*t***iit********************************it Subroutine CONST specifies explicit and implicit constraint * limits (user supplied), order explicit constraints first. * *******i********t******************t******************************* SUBROUTINE CONST (N,M,K,X,G,H,I) DIMENSION X(10,10), C(10), H(10) CONSTRAINTS ON Ks, m.Cr G(1)815.0 N(1)820.00 do 1000 iconst 8 2,n 0(iconst) 8 1.0 N(iconst) 8 50.0 continue RETURN END c *******fi****fi*********t**i********************************************* C C Subroutine RANDN generates a uniform random number on the interval 0-1. c ******.**i*****fi**i***********ii*****************************i********* C C SUBROUTINE RANDN(YFL) DIMENSION K(4) DATA K/2510,7692,2456,3765/ K(4) 8 3*K(4)+K(2) K(3) 8 3*K(3)+K(1) K(2)83*K(2) K(1) 8 3*K(1) I8K(1)/1000 K(1)8K(1)'I*1000 K(Z)8K(2) + I I 8 K(2)/100 K(2)=K(2)'100*I K(3) 8 K(3)*I I 8 K(3)/1000 K(3)8K(3)'I*1000 K(4)8K(4)+I I 8 K(4)/100 K(4)=K(4)'100*I YFL8(((FLOAT(K(1))*.001+FL0AT(K(2)))*.01+FLOAT(K(3)))*.001+FLOAT *(K(4)))*.01 RETURN END c ***i**fi************it******iNi**********************t************** C Subroutine HELP will identify a new complex point when the 128 APPENDIX 5 (cont 'd) minimum point is not able to get out of the complex for some C C reasons.* c itiiiiitt*tiititititfltittttitfitiiit*****************ii'i‘tiiitiitt'k*** C SUBROUTINE HELP(N,M,K,X,F,IEV1,R,G,H,KOOE,XC,DELTA,K1) DIMENSION x<10,10), R(10,10), 5(10), C(10), H(10) DO 10 J81,N CALL RANDN(YFL) R(IEV1,J)8YFL CALL CONST(N,M,K,X,G,H,I) X(IEV1,J)=G(J) + R(IEV1,J)*(H(J)'G(J)) 10 CONTINUE CALL CHECK(N,M,K,X,G,H,IEV1,KODE,XC,DELTA,K1) CALL FUNC(N,M,K,X,F,IEV1) RETURN END APPENDIX 6 Fortran source code of storm generator program. 1239 APPENDIX 6. Fortran source code of storm generator program PROGRAM STORM_GEN C c rainstorm generator c REAL wa(6),PwD(6),A(6),B(6),P1,P2,P3,P4,PS,P6,RN,LDURA,DURA(20), + RNNOR,AMOUNT(20),PEAK(20),IP(20),TP(20) INTEGER PP,ID,IM,IY,LIMONTH(6),EVENTN,LYEAR C C OPEN (12,FILE8'georanapr.d',status='old') OPEN (13,FlLE8'gamranapr.d{,status='old') OPEN (14,FILE8'norranapr.d',status='old') OPEN (15,FILE8‘simuapr.wth',status='unknown') OPEN (16,FILE8'simuapr.eve',status='unknown') OPEN (22,FILE8'georanmay.d',status='old') OPEN (23,FILE8'gamranmay.d',status='old') OPEN (24,FILE8'norranmay.d',status='old') OPEN (25,FILE8'simumay.wth',status='unknown') OPEN (26,FILE8'simumay.eve',status='unknown') OPEN (32,FILE8'georanjun.d',status='old') OPEN (33,FILE8'gamranjun.d',status='old') OPEN (34,FILE8'norranjun.d',status='old') OPEN (35,FILE8'simujun.wth',status='unknown') OPEN (36,FILE8'simujun.eve',status='unknown') OPEN (42,FILE8'georanjul.d',statUS8'old') OPEN (43,FILE='gamranjul.d',status='old') OPEN (44,FILE8'norranjul.d',status='old') OPEN (45,FILE8'simujul.wth',statUS8'unknown') OPEN (46,FILE8'simujul.eve',status8'unknown') OPEN (52,FILE8'georanaug.d',statUS8'old') OPEN (53,FILE8'gamranaug.d',status='old') OPEN (54,FILE8'norranaug.d',status8'old') OPEN (55,FILE8'simuaug.wth',status8'unknown') OPEN (56,FILE8'simuaug.eve',statUS8'unknown') OPEN (62,FILE8'georansep.d',statUS8'old') OPEN (63,FILE8'gamransep.d',status8'old') OPEN (64,FILE8'norransep.d',status8'old') OPEN (65,FILE8'simusep.wth',status8'unknown') OPEN (66,FILE8'simusep.eve',status8'unknown') PHH(1)8.467 PHD(1)8.107 PHH(2)8.402 PHD(2)8.090 PHH(3)8.340 PHD(3)8.123 PHH(4)8.234 PHD(4)8.103 PHH(5)8.406 PHD(5)8.099 PHH(6)8.352 PHD(6)8.108 A(1)8-.354 B(1)8.526 A(2)8'.449 B(2)8.526 A(3)8'.734 B(3)8.424 A(4)8'.687 B(4)8.371 A(5)8'.687 B(5)8.381 A(6)8'.547 0(6)8.445 P186.B 113C) appendix 6 (CONT'D) 10 20 30 40 101 100 3000 2000 1000 P2841. P3862.1 P4884.9 P5894.5 P68126. LYEAR 8 30 LIMONTH(1)830 LIMONTH(2)=31 LIMONTH(3)830 LIMONTH(4)831 LIMONTH(5)=31 LIMONTH(6)830 DO 1000 IY81,LYEAR PP80 DO 2000 IM81,6 ireve8im*10 + 2 iramo=im*10 + 3 irnor8im*10 + 4 iout8imr10 + 5 iouteve8im*10 + 6 DO 3000 ID81,LIMONTH(IM) CALL RANDOM(RN) IF (((PP.GT.0) .AND. (RN.GT.PHH(IM))) .OR. * ((PP.LE.0) .AND. (RN.GT.PHD(IM)))) THEN PP 8 0 ELSE PP 8 1 READ (ireve,*) JUNK,EVENTN IF (EVENTN .LT. 1) GOTO 10 DD 100 I81,EVENTN READ (iramo,*) JUNK, AMOUNT(I) IF (AMOUNT(I) .LT. 0.254) GOTO 20 READ (irnor,*) JUNK, RNNOR LDURA 8 A(IM) + B(IM) * LOG(AMOUNT(I)) + RNNOR DURA(I) 8 EXP(LDURA) IF (DURA(I) .LE. 0.) GOTO 30 IF (AMOUNT(I) .LT. 5.) P8P1 IF (AMOUNT(I) .GE. 5. .AND. AMOUNT(I) .LT. 10.) P8P2 IF (AMOUNT(I) .GE. 10. .AND. AMOUNT(I) .LT. 15.) P8P3 IF (AMOUNT(I) .GE. 15. .AND. AMOUNT(I) .LT. 20.) P8P4 IF (AMOUNT(I) .GE. 20. .AND. AMOUNT(I) .LT. 25.) P8P5 IF (AMOUNT(I) .GE. 25.) P8P6 CALL RANDOM(RN) PEAK(I) 8 -P * LOG(RN) IF (PEAK(I) .LT. AMOUNT(I) .OR. PEAK(I) .GT. 400.) GOTo 40 IP(I) 8 PEAK(I) / (AMOUNT(I)/DURA(I)) CALL RANDOM(RN) TP(I) 8 RN HRITE (iout,101) IY,IM+3,ID,I,AMOUNT(I),DURA(I),PEAK(I), + IP(I),TP(I) if (i.eq.eventn) then write(iouteve,101) iy,im#3,id,i endif FORMAT (4IS,3F10.2,2F10.3) CONTINUE ENDIF continue continue continue STOP END 131 APPENDIX 6 (cont'd) subroutine random(ranf) REAL INTEGER ranf TEMP DIMENSION K(4) K/2510,7692,2456,3765/ DATA K(4) K(3) K(Z) K(1) TEMP K(1) K(Z) TEMP K(Z) K(3) TEMP K(3) K(4) TEMP K(4) RANF + return END 3*K(4)+K(2) 3*K(3)+K(1) 3*K(2) 3*K(1) K(1)/1000 K(1)'TEMP*1000 K(Z) * TEMP K(2)/100 K(2)-100*TEMP K(3)+TEMP K(3)/1000 K(3)-TEMP*1000 K(4)+TEMP K(4)/100 K(4)-100*TEMP (((FLOAT(K(1))*.001+FLOAT(K(2)))*.01+FLOAT(K(3)))*.001+ FLOAT(K(4)))*.01 APPENDIX 7 Field measurement and derived soil properties from ponding curves for infiltrometer experiment. 132 APPENDIX 7. Field measurement and derived soil properties from ponding curves for infiltrometer experiment 2 5“ 133 APPENDIX 7 (cont'd) APPENDIX 8 Field measured residue cover, initial water content, and bulk density for sprinkling infiltrometer experiment 134 APPENDIX 8. Field measured residue cover, initial water content, and bulk density for sprinkling infiltrometer experiment. CMN680 26 June 1989 RESIDUE READING : -1 Crop Residue (X): 7 Depth to layer 8 : 12.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 CON HETS+CON DRYS+CON <2MM CV 80 1 602.00 835.00 528.00 14.10 1105.40 1041.80 -1.00 8.36 1.35 2 656.00 750.00 511.00 13.80 1003.20 946.50 -1.00 9.37 1.54 Total Sample 0v(%): 8.86 BD(g/cm**3): 1.45 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON CV 80 1- 1 154.6 241.2 237.9 5.50 1.39 1- 2 154.5 249.7 245.4 7.17 1.51 2- 1 153.9 259.1 253.8 8.83 1.67 2' 2 -1.0 -1.0 -1.0 .00 .00 3- 1 153.7 256.0 251.9 6.83 1.64 3' 2 -1.0 -1.0 -1.0 .00 .00 4- 1 -1.0 -1.0 -1.0 .00 .00 4- 2 153.7 255.0 251.0 6.67 1.62 5- 1 155.1 253.4 249.6 6.33 1.58 5- 2 -1.0 -1.0 -1.0 .00 .00 0v(X): 6.89 Std: 1.11 BD(g/cm**3): 1.57 Std: .10 Remarks : None CDN4BD 28 June 1989 RESIDUE READING : -1 Crop Residue (X): ? Depth to layer B : 12.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 CON HETS+CON DRYS+CON <2MM 0v BO 1 575.00 790.00 275.00 14.10 800.40 739.30 '1.00 12.47 1.48 2 590.00 740.00 425.00 14.30 939.60 854.90 '1.00 14.73 1.46 Total Sample 0v(X): 13.60 80(9/cm**3): 1.47 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0v BD 1- 1 156.8 250.1 243.2 11.50 1.44 1- 2 155.5 245.8 238.0 13.00 1.38 2- 1 156.6 252.1 243.9 13.67 1.45 2- 2 156.5 252.8 245.1 12.83 1.48 3- 1 155.4 249.0 241.9 11.83 1.44 3- 2 155.2 251.1 243.7 12.33 1.48 4- 1 156.4 248.5 241.1 12.33 1.41 4- 2 156.3 252.9 244.4 14.17 1.47 5- 1 155.4 249.8 241.1 14.50 1.43 APPENDIX 8 (cont'd) 5- 2 156.4 OV(X): 242.4 12.90 234.7 135 12.83 1.31 Std: .97 BO(g/cm**3): 1.43 Remarks : Leaks in Grossman samples. CDHZBD RESIDUE READING : '1 Crop Residue (X): 7 Depth to layer B : 12.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: Std: 28 June 1989 SET INIV FINALV1 FINALV2 CON HETS+CON DRYS+CON <2MM 0v 1 605.00 670.00 510.00 14.40 1024.20 942.50 -1.00 14.21 2 605.00 670.00 510.00 14.40 1024.20 942.50 -1.00 14.21 Total Sample 0v(X): 14.21 BD(g/cm**3): 1.61 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON NETS+CON DRYS+CON 0v BD 1- 1 155.4 257.7 249.5 13.67 1.57 1- 2 156.4 251.9 244.5 12.33 1.47 2- 1 156.0 254.5 247.0 12.50 1.52 2- 2 155.2 254.8 247.8 11.67 1.54 3- 1 156.6 255.7 248.4 12.17 1.53 3- 2 156.8 261.4 253.9 12.50 1.62 4- 1 155.6 255.8 248.2 12.67 1.54 4- 2 156.9 250.6 243.4 12.00 1.44 5- 1 156.7 254.7 247.4 12.17 1.51 5- 2 155.1 253.8 246.2 12.67 1.52 0v(X): 12.43 Std: .53 BD(g/cm**3): 1.53 Std: Remarks : None CMH6BD 26 June 1989 RESIDUE READING : 0 Crop Residue (X): .00 Depth to layer 8 : 12.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 CON HETS+CON DRYS+CON <2MM 1 625.00 505.00 939.00 28.10 1302.90 1209.20 -1.00 2 580.00 790.00 338.00 14.00 882.80 827.70 -1.00 Total Sample 0v(X): 10.75 BD(g/cm**3): 1.46 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0v BD 1- 1 -1.0 -1.0 -1.0 .00 .00 1- 2 155.1 268.1 264.1 6.67 1.82 2~ 1 154.4 291.2 285.8 9.00 2.19 2- 2 153.9 288.9 281.1 13.00 2.12 3- 1 153.8 245.2 239.6 9.33 1.43 0v 11.44 10.05 .05 80 1.61 1.61 .05 80 1.44 1.48 136 APPENDIX 8 (cont'd) 3- 2 154.3 268.6 262.7 9.83 1.81 4- 1 154.5 238.6 234.6 6.67 1.34 4- 2 155.2 240.8 236.2 7.67 1.35 5- 1 155.2 247.0 241.0 10.00 1.43 5- 2 155.3 252.3 245.3 11.67 1.50 0v(X): 9.31 Std: 2.14 BD(g/cm**3): 1.66 Std: .33 Remarks : None CNNZBD 29 JUNE 1989 RESIDUE READING : 40 Crop Residue (X): 66.67 Depth to layer B : 99.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 CON HETS+CON DRYS+CON <2MM 0v BD 1 590.00 795.00 290.00 14.10 772.70 734.50 -1.00 7.72 1.46 2 528.00 690.00 420.00 14.20 820.70 783.40 -1.00 6.41 1.32 Total Sample 0v(X): 7.06 BD(g/cm**3): 1.39 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0v BD 1- 1 155.1 232.5 226.5 10.00 1.19 1- 2 156.0 238.2 234.3 6.50 1.31 2- 1 155.5 241.1 236.9 7.00 1.36 2- 2 155.8 248.1 244.0 6.83 1.47 3- 1 154.9 246.5 242.1 7.33 1.45 3- 2 155.1 235.7 231.3 7.33 1.27 4- 1 145.6 247.5 244.1 5.67 1.64 4- 2 155.1 244.8 240.7 6.83 1.43 5- 1 156.1 245.1 241.1 6.67 1.42 5- 2 155.2 239.2 234.9 7.17 1.33 0v(X): 7.13 Std: 1.12 BD(g/cm**3): 1.39 Std: .13 Remarks : NONE CNN3BD 29 JUNE 1989 RESIDUE READING : 43 Crop Residue (X): 71.67 Depth to layer B : 99.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 CON HETS+CON DRYS+CON <2MM 0v BD 1 535.00 675.00 410.00 14.40 857.90 827.80 -1.00 5.47 1.48 2 460.00 682.00 320.00 14.20 807.20 774.30 -1.00 6.07 1.40 Total Sample 0v(X): 5.77 BD(g/Cm**3): 1.44 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0V BD APPENDIX 8 (Cont'd) 137 1- 1 155.3 246.1 242.5 6.00 1.45 1- 2 154.8 247.0 243.6 5.67 1.48 2- 1 156.4 234.1 229.8 7.17 1.22 2- 2 156.2 241.3 237.0 7.17 1.35 3- 1 155.0 236.7 232.8 6.50 1.30 3- 2 156.3 250.4 246.8 6.00 1.51 4- 1 154.9 247.1 243.6 5.83 1.48 4- 2 154.6 245.7 242.3 5.67 1.46 5- 1 155.2 238.7 235.6 5.17 1.34 5- 2 154.7 243.8 239.6 7.00 1.42 0v(X): 6.22 Std: .70 BD(g/cm**3): 1.40 Std: .09 Remarks : NONE CDNSBD 24 JULY 89 Crop Residue (X): 10.00 Depth to layer 8 : 10.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS*CON DRYS+CON 0v BO 1- 1 155.4 243.8 235.2 14.33 1.33 1- 2 156.4 249.3 240.8 14.17 1.41 2- 1 -1.0 -1.0 -1.0 .00 .00 2- 2 -1.0 -1.0 -1.0 .00 .00 3- 1 156.6 244.1 237.4 11.17 1.35 3- 2 156.8 242.1 235.7 10.67 1.31 4- 1 155.6 238.7 232.0 11.17 1.27 4- 2 156.9 239.0 232.4 11.00 1.26 5- 1 156.7 248.5 239.6 14.83 1.38 5- 2 155.1 254.4 245.0 15.67 1.50 0v(X): 12.88 Std: 2.06 BD(g/cm**3): 1.35 Std: .08 Remarks : NONE CNw4 24 JULY 1989 Crop Residue (X): 88.33 Depth to layer B : 99.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0v BD 1- 1 155.1 249.5 243.1 10.67 1.47 1- 2 155.1 250.8 243.2 12.67 1.47 2- 1 154.4 251.7 244.8 11.50 1.51 2- 2 153.9 256.3 248.8 12.50 1.58 3- 1 153.8 250.0 242.4 12.67 1.48 3- 2 154.3 250.5 243.4 11.83 1.48 4- 1 154.5 251.7 245.0 11.17 1.51 4- 2 155.2 244.6 238.5 10.17 1.39 5- 1 155.2 251.4 244.0 12.33 1.48 5- 2 155.3 244.0 237.2 11.33 1.36 0v(X): 11.68 Std: .87 BD(g/cm**3): 1.47 Std: .06 Remarks : DEER TRACKS APPENDIX 8 (Cont'd) CNN48D Crop Residue (X): 66.67 Depth to layer B : 99.0 inch 138 24 JULY 1989 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1- 1 1° 2 2° 1 2° 2 3° 1 3° 2 4° 1 4° 2 5° 1 5° 2 CON UETS+CON DRYS+CON 154.5 155.1 154.5 155.6 156.4 154.8 156.4 155.3 154.8 156.3 0V(%): 252.0 244.5 254.4 246.8 255.0 248.2 251.6 245.1 253.6 246.3 254.7 247.7 249.0 241.4 250.3 243.4 254.0 246.8 246.6 239.8 11.87 Std: Remarks : NONE CMU3BD Crop Residue (Z): 1.67 Depth to layer B : 12.0 inch 0v 80 12.50 1.50 12.67 1.53 11.33 1.56 10.83 1.49 12.17 1.50 11.67 1.55 12.67 1.42 11.50 1.47 12.00 1.53 11.33 1.39 .63 BD(g/cm**3): 1.49 Std: 25 JULY 1989 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1° 1 1° 2 2° 1 2° 2 3° 1 3° 2 4° 1 4° 2 5° 1 5° 2 CON HETS*CON DRYS*CON 156.3 156.1 155.2 155.2 154.7 155.9 155.0 155.9 154.8 155.9 0v(X): 247.9 243.6 250.0 245.9 248.6 244.0 250.1 245.6 247.8 242.7 246.4 241.3 248.9 244.1 244.8 241.1 249.9 245.3 245.1 240.8 7.52 Std: Remarks : NONE CMHS RESIDUE READING : °1 Crop Residue (X): 7 Depth to layer 8 : 12.0 inch 0v 80 7.17 1.46 6.83 1.50 7.67 1.48 7.50 1.51 8.50 1.47 8.50 1.42 8.00 1.49 6.17 1.42 7.67 1.51 7.17 1.42 .73 80(g/cm**3): 1.47 Std: 6 JULY 1989 GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 1 580.00 610.00 470.00 2 640.00 598.00 520.00 Total Sample 7.62 BD(9/cm**3): 1.63 0v(X): CON NETS+CON DRYS+CON <2MM 13.90 903.80 868.80 -1.00 13.90 791.80 752.40 °1.00 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1° 1 CON HETS+CON DRYS+CON 156.3 251.6 247.0 0v 80 7.67 1.51 0v 7.00 .06 .04 80 1.71 1.54 139 APPENDIX 8 (cont'd) 1° 2 156.1 250.1 245.4 7.83 1.49 2° 1 155.2 248.2 243.5 7.83 1.47 2- 2 155.2 248.6 243.6 8.33 1.47 3- 1 154.7 248.3 243.9 7.33 1.49 3- 2 155.9 250.3 245.9 7.33 1.50 4° 1 155.0 247.8 243.7 6.83 1.48 4- 2 155.9 250.4 245.7 7.83 1.50 5- 1 154.8 248.6 243.9 7.83 1.48 5° 2 155.9 249.4 244.8 7.67 1.48 0v(X): 7.65 Std: .40 BO(g/cm**3): 1.49 Std: .01 Remarks : NONE CMNZBD 6 JULY 1989 RESIDUE READING : 0 Crop Residue (X): .00 Depth to layer B : 14.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 CON NETS+CON DRYS+CON <2MM 0v BD 1 540.00 595.00 562.00 13.90 828.00 794.70 -1.00 5.40 1.27 2 520.00 490.00 510.00 14.00 788.00 760.00 -1.00 5.83 1.55 Total Sample 0v(%): 5.62 BD(9/cm**3): 1.41 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON UETS+CON DRYS+CON 0v BD 1- 1 154.6 244.9 240.5 7.33 1.43 1- 2 154.5 241.7 237.9 6.33 1.39 2° 1 153.9 241.1 237.4 6.17 1.39 2° 2 153.9 236.9 233.6 5.50 1.33 3° 1 153.7 236.5 233.7 4.67 1.33 3° 2 154.5 239.8 236.5 5.50 1.37 4- 1 154.6 232.5 229.4 5.17 1.25 4- 2 153.7 226.8 223.4 5.67 1.16 5- 1 155.1 243.6 239.1 7.50 1.40 5- 2 154.4 243.5 240.1 5.67 1.43 0v(X): 5.95 Std: .90 80(g/cm**3): 1.35 Std: .09 Remarks : CRUST 1/4“ CDUSBD 10 JULY 1989 RESIDUE READING : °1 Crop Residue (X): 7 Depth to layer B : 11.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 CON HETS+CON DRYS+CON <2MM 0v 80 1 593.00 911.00 248.00 13.90 967.50 928.30 °1.00 6.93 1.62 2 646.00 692.00 550.00 13.90 1064.60 1019.70 °1.00 7.53 1.69 Total Sample 0v(X): 7.23 BO(9/cm**3): 1.65 140 APPENDIX 8 (cont'd) MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0V BD 1- 1 155.4 254.3 249.9 7.33 1.58 1- 2 156.4 257.2 252.5 7.83 1.60 2- 1 156.0 252.5 248.1 7.33 1.54 2- 2 155.2 251.2 247.1 6.83 1.53 3— 1 156.6 259.0 255.1 6.50 1.64 3- 2 156.8 254.9 251.1 6.33 1.57 4- 1 155.6 262.8 256.6 10.33 1.68 4- 2 156.9 255.1 249.8 8.83 1.55 S- 1 156.7 257.1 251.9 8.67 1.59 5- 2 155.1 254.2 248.8 9.00 1.56 0v(X): 7.90 Std: 1.28 BD(g/cm**3): 1.58 Std: .05 Remarks : NONE CDNZBD 10 JULY 1989 RESIDUE READING : °1 Crop Residue (x): 7 Depth to layer B : 12.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 CON HETS*CON DRYS+CON <2MM 0v BO 1 561.00 805.00 510.00 14.00 1082.00 1057.40 °1.00 3.26 1.38 2 620.00 945.00 650.00 27.90 1403.60 1335.00 °1.00 7.04 1.34 Total Sample 0v(X): 5.15 BD(9/cm**3): 1.36 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON UETS+CON DRYS+CON 0v 8D 1- 1 155.3 234.4 231.3 5.17 1.27 1- 2 154.8 240.0 238.0 3.33 1.39 2° 1 156.4 238.2 235.7 4.17 1.32 2- 2 156.2 248.0 245.7 3.83 1.49 3— 1 155.0 246.2 241.3 8.17 1.44 3- 2 156.3 246.3 242.7 6.00 1.44 4- 1 154.9 238.8 234.5 7.17 1.33 4- 2 154.6 236.1 231.5 7.67 1.28 5° 1 155.2 247.0 243.0 6.67 1.46 5° 2 154.7 249.3 244.7 7.67 1.50 0v(X): 5.98 Std: 1.76 80(g/cm**3): 1.39 Std: .09 Remarks : NONE CNN6BD 11 JULY 1989 RESIDUE READING : 49 Crop Residue (2): 81.67 Depth to layer B : 24.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 CON HETS+CON DRYS+CON <2MM 0v BD 1 598.00 725.00 572.00 13.80 1151.80 1122.50 °1.00 4.19 1.59 2 593.00 815.00 536.00 27.60 1253.50 1227.80 °1.00 3.39 1.58 APPENDIX 8 (cont'd) Total Sample 0v(X): 3.79 BD(g/cm**3): 1.58 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON UETS+CON DRYS+CON 0v 80 1° 1 157.0 241.6 240.4 2.00 1.39 1° 2 155.7 236.2 234.7 2.50 1.32 2- 1 155.7 237.8 236.5 2.17 1.35 2- 2 156.6 242.7 240.9 3.00 1.40 3- 1 °1.0 °1.0 °1.0 .00 .00 3° 2 °1.0 °1.0 °1.0 .00 .00 4° 1 155.6 230.4 229.9 .83 1.24 4- 2 °1.0 °1.0 °1.0 .00 .00 5° 1 155.4 246.3 244.9 2.33 1.49 5° 2 156.4 243.3 242.0 2.17 1.43 0v(X): 2.14 Std: .66 80(9/cm**3): 1.37 Std: 141 Remarks : SURFACE RESIDUE REMOVED FOR GROSSMAN METHOD CNN1BD RESIDUE READING : 50 Crop Residue (X): 83.33 Depth to layer B : 25.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: 11 JULY 1989 SET INIV FINALV1 FINALV2 CON HETS+CON DRYS+CON <2MM 0v 1 550.00 645.00 578.00 14.00 941.20 913.50 °1.00 4.12 2 668.00 725.00 590.00 13.90 1041.70 1026.10 °1.00 2.41 Total Sample 0v(X): 3.26 80(g/cmr*3): 1.45 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0v 80 1- 1 156.8 240.6 237.9 4.50 1.35 1- 2 155.5 238.8 236.7 3.50 1.35 2- 1 156.6 239.5 239.0 .83 1.37 2- 2 156.5 241.1 240.0 1.83 1.39 3- 1 155.4 238.6 237.5 1.83 1.37 3- 2 155.2 245.5 244.4 1.83 1.49 4- 1 156.4 243.6 243.0 1.00 1.44 4° 2 156.3 245.4 244.8 1.00 1.48 5- 1 155.4 230.9 229.9 1.67 1.24 5- 2 156.4 236.4 235.0 2.33 1.31 0v(X): 2.03 Std: 1.16 BD(9/cm**3): 1.38 Std: Remarks : RESIDUE REMOVED FROM SURFACE FOR GROSSMAN METHOD CMN3BD Crop Residue (X): 3.33 Depth to layer B : 12.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON CV 80 25 JULY 1989 .08 80 1.34 1.56 .07 APPENDIX 8 (cont'd) 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. ne-aae-ano-anJ-ane-a 155.3 154.8 156.4 156.2 155.0 °1.0 154.9 154.6 155.2 154.7 0v(X): 239.3 233.3 232.3 238.1 237.1 °1.0 234.5 229.2 236.2 237.8 5.85 E§§§§ J. Nwowooo-o game PMO Std: Remarks : SURFACE CRUST CDU3BD Crop Residue (X): Depth to layer B : 3.33 12.0 inch “NVO OOOWOEG—D-IUT OWOO OUIUIUIUI 04100040 .54 142 30(9/CM**3): 25 JULY 1989 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1. 1. 2. z. 3. 3. 4. 4. 5. 5. NdN-lN-‘N-PN-P CON HETS+CON DRYS+CON 155.1 156.0 155.5 155.8 154.9 155.1 154.6 155.1 156.1 155.2 0v(X): 248.3 249.6 249.4 248.5 246.1 242.1 243.9 248.4 247.1 248.8 10.13 242.4 243.6 243.1 242.0 239.9 235.8 238.0 242.8 241.2 242.6 Std: Remarks : SURFACE CRUST CNUSBD Crop Residue (X): Depth to layer 8 : 71.67 99.0 inch 0v 9.83 10.00 10.50 10.83 10.33 10.50 9.83 9.33 9.83 10.33 .44 BO .45 .46 .46 .44 .42 .34 .39 .46 .42 .46 dfiad‘ddd‘d BD(g/cm**3): 27 JULY 1989 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. COM UETS+CON DRYS+CON 155.1 155.1 154.4 153.9 153.8 154.3 154.5 155.2 155.2 155.2 0v(X): 246.1 248.4 249.0 244.6 244.6 245.3 240.8 245.7 247.0 243.2 7.60 241.1 243.8 244.9 240.3 240.7 241.4 235.3 240.4 242.3 238.9 Std: 0v .94 xn3~e~ SUINMUIU'Ig-IOU .a—a—a—a—a-a—a—add . U C I O ##0158‘ BD(9/cm**3): Remarks : EXPT. TERMINATED BECAUSE OF STORM 1.28 1.43 1.44 Std: Std: Std: .05 .04 .04 APPENDIX 8 (cont'd) CNN1BD Crop Residue (X): Depth to layer s : 75.00 25.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1. 1. 2. 2. 3. 3. k. 4. S. 5. N-‘N-‘N-DN-IN.‘ CON HETS+CON DRYS+CON 157.0 155.7 155.7 156.6 156.5 155.6 155.6 155.2 155.4 156.4 0V(X): Remarks : NO CORN PLANTS ON ONE SIDE 256.9 256.4 258.0 259.4 253.0 252.7 254.7 253.7 245.7 255.3 15.05 247.8 247.3 249.4 249.4 244.0 242.8 246.6 245.7 236.4 246.1 Std: 1. CDN68D Crop Residue (X): Depth to layer B : 3.33 14.0 inch 0v 15.17 15.17 14.33 16.67 15.00 16.50 13.50 13.33 15.50 15.33 10 ‘dddd‘d‘d‘ . . C I . . . . 143 27 JULY 1989 BD(g/cm**3): 1.49 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1. 1. 2. 2. 3. 3. ‘. ‘. s. 5. N-DN-PN-‘NdN-D CON‘ HETS+CON DRYS+CON 156.8 155.5 156.6 156.5 155.4 155.2 156.4 156.3 155.4 156.4 0V(X): Remarks : NONE Crop Residue (X): 237.0 231.9 243.7 237.8 244.3 238.8 242.1 236.5 242.5 236.8 240.6 235.0 242.6 237.2 239.7 234.2 237.1 232.3 241.5 237.1 8.92 Std: CDN6BD 1.67 13.0 inch Depth to layer B : 0v 8.50 9.83 9.17 9.33 9.50 9.33 9.00 9.17 8.00 7.33 .76 80 1.25 d is ‘V uhhuh'uu maomugufl ddddd‘dd . C 28 JULY 1989 BD(9/cm**3): 1.33 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. ~d~d~d~d~d CON UETS+CON DRYS+CON 155.4 156.4 156.0 155.2 156.6 156.8 155.6 156.9 156.7 155.1 256.4 257.2 253.5 254.7 253.9 255.5 251.2 253.7 257.9 255.6 249.5 250.2 247.1 247.8 247.4 249.1 244.8 247.4 250.8 248.9 0v 11.50 11.67 10.67 11.50 10.83 10.67 10.67 10.50 11.83 11.17 80 1.57 1.56 1.52 1.54 1.51 1.54 1.49 1.51 1.57 1.56 28 JULY 1989 Std: Std: .06 .04 13441 APPENDIX 8 (cont'd) 0v(X): 11.10 Std: .49 BD(g/cm**3): 1.54 Std: Remarks : NONE CMUZBD 3 AUG 1989 Crop Residue (X): 3.33 Depth to layer B : 13.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON UETS+CON DRYS+CON 0v 80 1° 1 157.0 252.7 246.2 10.83 1.49 1° 2 155.7 251.4 245.1 10.50 1.49 2- 1 155.7 250.3 243.2 11.83 1.46 2° 2 156.6 252.1 245.1 11.67 1.48 3° 1 156.5 252.2 245.0 12.00 1.48 3- 2 155.6 250.3 242.8 12.50 1.45 4- 1 155.6 251.2 244.6 11.00 1.48 4° 2 155.2 247.6 240.6 11.67 1.42 5° 1 155.4 251.7 244.9 11.33 1.49 5° 2 156.4 252.6 245.9 11.17 1.49 0v(X): 11.45 Std: .60 BD(9/cm**3): 1.47 Std: Remarks : NONE CMN1BD 31 JULY 1989 Crop Residue (X): .00 Depth to layer 8 : 13.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON NETS+CON DRYS+CON 0v 80 1° 1 157.0 245.3 244.1 2.00 1.45 1- 2 155.7 252.9 251.5 2.33 1.60 2° 1 155.7 248.4 246.8 2.67 1.52 2- 2 156.6 252.2 250.9 2.17 1.57 3° 1 156.5 240.8 239.1 2.83 1.38 3- 2 155.6 244.0 242.7 2.17 1.45 4° 1 155.6 249.9 247.9 3.33 1.54 4- 2 155.2 242.9 240.9 3.33 1.43 5— 1 155.4 247.0 245.1 3.17 1.50 5- 2 156.4 253.4 251.6 3.00 1.59 0v(X): 2.70 Std: .51 BD(g/cm**3): 1.50 Std: Remarks : SURFACE CRUST CMN4BD 31 JULY 1989 Crop Residue (X): 1.67 Depth to layer B : 14.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0v 80 1° 1 154.6 239.8 238.0 3.00 1.39 1° 2 154.5 242.2 240.7 2.50 1.44 2° 1 153.9 233.8 232.4 2.33 1.31 .03 .02 .07 APPENDIX 8 (cont'd) 2° 2 153.9 232.3 231.0 3° 1 153.7 245.6 243.9 3° 2 154.5 242.9 241.4 4° 1 154.6 236.1 234.6 4- 2 153.7 234.8 233.3 5- 1 155.1 235.4 233.6 5° 2 154.4 241.7 240.0 0v(X): 2.62 Std: .28 Remarks : SURFACE CRUST 1/4" Crop Residue (X): Depth to layer 8 : CNNSBD 73.33 99.0 inch dddddd s a e a uuubm auumog 1.43 145 BD(g/cm**3): 1.38 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0v 1- 1 155.1 254. 1° 2 156.0 257. 2- 1 155.5 249. 2° 2 155.8 257. 3- 1 154.9 250. 3° 2 155.1 248. 4° 1 154.6 253. 4- 2 155.1 248. 5- 1 156.1 251. 5° 2 155.2 246. 7 243.1 1 246.7 2 239.0 8 246.5 1 239.9 7 238.4 6 243.1 6 237.4 3 241.4 6 237.4 0v(X): 17.47 Std: 19.33 17.33 17.00 18.83 17.00 17.17 17.50 18.67 16.50 15.33 1.19 80 1.47 1.51 1.39 1.51 1.42 1.39 1.48 1.37 1.42 1.37 2 AUG 1989 BD(g/cm**3): 1.43 Remarks : 1.2" OF IRRIGATION ADDED THIS MORNING Crop Residue (X): Depth to layer B : CNH3BD 81.67 99.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETSPCON DRYS+CON 0v 1- 1 154.6 258. 1° 2 156.6 254. 2° 1 156.3 245. 2- 2 156.0 237. 3- 1 154.8 250. 3° 2 155.2 253. 4° 1 156.4 254. 4° 2 154.7 246. 5° 1 156.3 257. 5° 2 156.0 252. 0v(X): 15.25 7 249.7 2 244.2 1 236.6 3 228.0 4 241.3 1 243.5 8 246.5 2 237.9 9 248.5 2 242.2 Std: 15.00 16.67 14.17 15.50 15.17 16.00 13.83 13.83 15.67 16.67 1.06 ddddd-‘dddd assassssas 2 AUG 1989 BD(9/cm**3): 1.44 Remarks : 1.2" OF IRRIGATION ADDED THIS MORNING, WINDY Crop Residue (X): CDN1BD 5.00 2 AUG 1989 Std: Std: Std: .07 .05 .11 APPENDIX 8 (cont'd) Depth to layer B : 155.3 inch 146 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1° 1 155.3 251.3 1° 2 156.2 251.3 2° 1 155.4 243.7 2° 2 156.6 249.7 3° 1 155.3 241.5 3- 2 156.3 253.5 4° 1 155.3 248.3 4° 2 155.7 251.0 5° 1 156.3 249.4 5° 2 °1.0 °1.0 0v(X): 14.89 CON NETS+CON DRYS+CON 242.0 241.6 235.7 241.1 233.4 244.1 239.4 241.9 240.1 °1.0 Std: 0v 15.50 16.17 13.33 14.33 13.50 15.67 14.83 15.17 15.50 .00 .98 BD .44 .42 .34 .41 .30 .46 .40 .44 .40 .00 J—I-I-D—D—Ic-l-fi-D BD(g/cm**3): 1.40 Remarks : 1.2" OF IRRIGATION ADDED THIS MORNING, WINDY CMNSBD Crop Residue (X): 3.33 Depth to layer 8 : 13.0 inch 3 AUG 1989 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1- 1 155.3 234.0 1- 2 154.8 233.5 2- 1 156.4 237.8 2° 2 156.2 235.5 3- 1 155.0 240.0 3° 2 156.3 242.9 4- 1 154.9 237.7 4° 2 154.6 238.2 5° 1 155.2 240.2 5- 2 154.7 247.8 0v(X): 10.90 Remarks : NONE CON UETSPCON DRYS+CON 228.4 228.1 231.4 229.2 233.2 235.9 231.1 231.3 233.3 240.3 Std: 1 CDH1BD Crop Residue (X): Depth to layer 8 : .00 14.0 inch 0v 9.33 9.00 10.67 10.50 11.33 11.67 11.00 11.50 11.50 12.50 .07 80 1.22 1.22 1.25 1.22 1.30 1.33 1.27 1.28 1.30 1.43 BD(g/cm**3): 3 AUG 1989 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1° 1 154.5 259.9 1- 2 155.1 262.0 2° 1 154.5 263.4 2° 2 155.6 255.0 3- 1 156.4 261.7 3° 2 154.8 260.8 4— 1 156.4 261.5 4° 2 155.3 260.8 5- 1 154.8 262.6 5- 2 156.3 262.0 0v(X): 16.10 Remarks : NONE CON HETS+CON DRYS+CON 250.7 252.4 253.1 245.4 251.8 251.2 252.0 251.1 252.8 252.6 Std: 0v 15.33 16.00 17.17 16.00 16.50 16.00 15.83 16.17 16.33 15.67 .50 2883233238 dddddddddd 30(9/CM**3): 1.28 1.60 Std: Std: Std: .05 .06 .04 147 APPENDIX 8 (cont'd) PMUSBD 30 JUNE 1989 RESIDUE READING : °1 Crop Residue (X): 7 Depth to layer 8 : 11.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 CON NETS+CON DRYS+CON <2MM 0v BD 1 480.00 475.00 355.00 13.80 624.60 585.40 °1.00 11.20 1.63 2 430.00 420.00 482.00 13.80 844.50 773.60 °1.00 15.02 1.61 Total Sample 0v(X): 13.11 BD(9/cm**3): 1.62 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON NETS+CON DRYS+CON 0V BD 1- 1 157.0 260.3 252.7 12.67 1.59 1- 2 155.7 257.1 249.6 12.50 1.57 2° 1 155.7 257.6 249.4 13.67 1.56 2- 2 156.6 262.1 254.0 13.50 1.62 3- 1 156.5 258.0 250.3 12.83 1.56 3- 2 155.6 258.4 250.6 13.00 1.58 4- 1 155.6 259.2 251.4 13.00 1.60 4° 2 155.2 254.8 247.3 12.50 1.54 5- 1 155.4 257.0 249.3 12.83 1.57 5- 2 156.4 261.4 254.5 11.50 1.64 0v(X): 12.80 Std: .60 BD(g/cm**3): 1.58 Std: .03 Remarks : NONE PNN4BD 30 JUNE 1989 RESIDUE READING : °1 Crop Residue (X): 7 Depth to layer 8 : 12.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 CON HETS+CON DRYS+CON <2MM 0v BD 1 530.00 860.00 240.00 13.80 825.40 766.00 °1.00 10.42 1.32 2 585.00 780.00 280.00 13.90 690.50 635.10 °1.00 11.66 1.31 Total Sample 0v(X): 11.04 BO(9/cm**3): 1.31 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS*CON DRYS+CON 0v BD 1- 1 155.6 241.7 237.0 7.83 1.36 1° 2 155.1 237.5 232.2 8.83 1.28 2- 1 156.8 242.5 236.7 9.67 1.33 2° 2 155.1 239.3 233.8 9.17 1.31 3° 1 155.3 242.0 234.9 11.83 1.33 3° 2 155.2 237.4 232.0 9.00 1.28 4° 1 156.9 249.2 241.6 12.67 1.41 4- 2 156.9 247.0 239.2 13.00 1.37 5° 1 156.0 245.7 237.9 13.00 1.36 5° 2 155.7 236.0 228.5 12.50 1.21 0v(X): 10.75 Std: 2.03 80(g/cm**3): 1.33 Std: .06 APPENDIX 8 (cont'd) 148 Remarks : CENTER RIDGE REMOVED FOR GROSSMAN PPN4BD RESIDUE READING : °1 Crop Residue (X): 7 Depth to layer 8 : 12.0 inch GROSSMAN COMPLIANT CAVITY METHOD READING: CON UETS+CON DRYS+CON <2MM 0v SET INIV 1 Total Sample 0V(X): 15.83 FINALV1 FINALV2 520.00 612.00 375.00 2 580.00 590.00 500.00 BD(g/cmr*3): 1.56 MADERA METHOD READING AND INDIVIDUAL OUTPUT: CON HETS+CON DRYS+CON SET 1- 1 1° 2 2° 1 2° 2 3° 1 3° 2 4° 1 4° 2 5° 1 5° 2 154.5 155.1 154.5 155.6 156.4 154.8 156.4 155.3 154.8 156.3 0v(X): Remarks : NONE RESIDUE READING : °1 Crop Residue (X): 7 Depth to layer B : 257.6 249.5 259.2 250.8 257.0 248.7 252.8 244.2 260.4 251.3 259.3 250.1 260.0 250.7 262.1 252.6 260.4 250.7 261.0 253.0 14.70 Std: 1 PPN4BD 10.0 inch 0v 13.50 14.00 13.83 14.33 15.17 15.33 15.50 15.83 16.17 13.33 .02 5 JULY 1989 80(9/cm**3): 1.58 GROSSMAN COMPLIANT CAVITY METHOD READING: SET INIV FINALV1 FINALV2 1 610.00 628.00 705.00 2 480.00 605.00 550.00 0v(X): Total Sample 8.77 BD(9/cm**3): CON UETS+CON DRYS+CON <2MM 0v 13.80 1131.00 1058.60 °1.00 10. 13.80 1034.30 983.50 °1.00 7. 1.44 MADERA METHOD READING AND INDIVIDUAL OUTPUT: CON HETS+CON DRYS+CON SET 1° 1 1° 2 2° 1 2° 2 3° 1 3° 2 4° 1 4° 2 5° 1 5° 2 154.6 156.6 156.3 156.0 154.8 155.2 156.4 154.7 156.3 156.0 237.0 236.8 239.7 242.5 239.2 237.1 241.9 236.5 248.9 242.4 233.9 234.3 235.8 239.0 235.8 234.3 237.7 232.1 244.3 238.9 0v 5.17 4.17 9 U1 0 Pfififl??? 8338238 asakaaaah° déddddégdd 8 5 JULY 1989 13.90 824.20 758.50 °1.00 14.07 14.00 886.60 796.90 °1.00 17.59 Std: 01 53 80 1.59 1.54 .04 80 1.45 1.44 149 APPENDIX 8 (cont'd) OV(X): 5.98 Std: 1.15 BD(g/cm**3): 1.35 Std: Remarks : CENTER RIDGE REMOVED PPNZBD 19 JULY 1989 Crop Residue (X): .00 Depth to layer B : 10.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON UETS+CON DRYS+CON 0V BD 1- 1 157.0 238.9 232.4 10.83 1.26 1° 2 155.7 237.0 230.8 10.33 1.25 2- 1 155.7 238.7 232.8 9.83 1.29 2- 2 156.6 243.7 237.3 10.67 1.34 3° 1 156.5 243.3 236.3 11.67 1.33 3- 2 155.6 239.9 233.2 11.17 1.29 4- 1 155.6 239.4 232.3 11.83 1.28 4- 2 155.2 240.9 234.3 11.00 1.32 5- 1 155.4 238.4 231.8 11.00 1.27 5° 2 156.4 237.3 230.8 10.83 1.24 0v(X): 10.92 Std: .58 80(9/cm**3): 1.29 Std: Remarks : NO CURST ON SURFACE PPU6BD 14 JULY 1989 Crop Residue (X): .00 Depth to layer B : 10.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON NETS+CON DRYS+CON CV 80 1° 1 156.8 260.8 252.8 13.33 1.60 1- 2 155.5 260.3 252.6 12.83 1.62 2- 1 156.6 262.9 254.5 14.00 1.63 2- 2 156.5 261.5 253.5 13.33 1.62 3- 1 155.4 255.9 248.7 12.00 1.56 3- 2 155.2 262.0 253.3 14.50 1.64 4— 1 156.4 259.4 250.5 14.83 1.57 4- 2 156.3 257.0 247.9 15.17 1.53 5- 1 155.4 260.3 250.7 16.00 1.59 5- 2 156.4 255.8 246.4 15.67 1.50 0v(X): 14.17 Std: 1.29 80(9/cm**3): 1.58 Std: Remarks : NONE PPN1BD 26 JULY 1989 Crop Residue (X): 33.33 Depth to layer 8 : 13.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0v 80 1° 1 155.6 238.6 235.0 6.00 1.32 1° 2 155.1 237.9 234.5 5.67 1.32 .05 .03 .05 150 APPENDIX 8 (cont'd) 2° 1 156.8 240.2 236.4 6.33 1.33 2° 2 155.1 237.0 233.1 6.50 1.30 3° 1 155.3 241.2 236.7 7.50 1.36 3° 2 155.2 241.5 237.8 6.17 1.38 4° 1 156.9 246.2 242.4 6.33 1.42 4- 2 156.9 238.8 235.3 5.83 1.31 5- 1 156.0 237.4 233.2 7.00 1.29 5° 2 155.7 242.3 237.5 8.00 1.36 0v(X): 6.53 Std: .75 80(9/cm**3): 1.34 Std: .04 Remarks : Residue generated by this year's crop PMNSBD 26 JULY 1989 Crop Residue (X): 20.00 Depth to layer B : 13.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0v 8D 1° 1 154.6 243.1 240.6 4.17 1.43 1° 2 156.6 236.6 234.0 4.33 1.29 2° 1 156.3 238.3 235.3 5.00 1.32 2- 2 156.0 234.6 231.6 5.00 1.26 3° 1 154.8 237.4 233.6 6.33 1.31 3- 2 155.2 238.0 234.1 6.50 1.32 4- 1 156.4 239.9 236.2 6.17 1.33 4- 2 154.7 234.7 231.2 5.83 1.27 5° 1 156.3 239.3 234.7 7 67 1.31 5- 2 156.0 240.6 235.8 8 00 1.33 0v(X): 5.90 Std: 1.30 BD(g/cm**3): 1.32 Std: .05 Remarks : Residue generated by current crop pmu6bd 26 July 1989 Crop Residue (X): 56.67 Depth to layer s : 9.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON UETS+CON DRYS+CON 0V 80 1° 1 154.6 258.5 252.4 10.17 1.63 1° 2 154.5 258.1 251.7 10.67 1.62 2° 1 153.9 259.2 252.8 10.67 1.65 2° 2 153.9 257.2 250.8 10.67 1.62 3° 1 153.7 255.9 249.1 11.33 1.59 3- 2 154.9 257.9 250.7 12.00 1.60 4- 1 154.6 251.2 245.3 9.83 1.51 4° 2 153.7 255.2 247.4 13.00 1.56 5- 1 155.1 258.1 252.1 10.00 1.62 5° 2 154.4 255.3 249.3 10.00 1.58 0v(X): 10.83 Std: 1.01 BD(9/cm**3): 1.60 Std: .04 Remarks : none ppu1bd 26 July 1989 155]. APPENDIX 8 (cont'd) Crop Residue (X): 25.00 Depth to layer 8 : 9.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 0v BO 1- 1 155.3 246.7 243.1 6.00 1.46 1- 2 156.2 252.5 248.5 6.67 1.54 2° 1 155.4 247.7 244.5 5.33 1.49 2- 2 156.6 249.7 245.4 7.17 1.48 3° 1 155.3 257.4 253.3 6.83 1.63 3- 2 156.5 257.8 253.2 7.67 1.61 4° 1 155.3 253.2 249.2 6.67 1.56 4- 2 155.7 253.3 249.4 6.50 1.56 5- 1 156.3 259.5 254.5 8.33 1.64 5- 2 155.3 258.1 252.9 8.67 1.63 0v(X): 6.98 Std: 1.02 BD(9/cm**3): 1.56 Std: .07 Remarks : So compacted that He could not press cupholders into soil. PPUSBD 1 AUG 1989 Crop Residue (X): 10.00 Depth to layer 8 : 15.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON NETS+CON DRYS+CON 0v 80 1° 1 155.1 265.1 254.9 17.00 1.66 1- 2 155.1 264.6 254.5 16.83 1.66 2- 1 154.4 265.4 256.4 15.00 1.70 2- 2 153.9 262.0 251.5 17.50 1.63 3- 1 153.8 267.9 257.3 17.67 1.72 3- 2 154.3 266.2 255.9 17.17 1.69 4° 1 154.5 257.5 248.0 15.83 1.56 4° 2 155.2 260.5 250.5 16.67 1.59 5- 1 155.2 263.2 252.6 17.67 1.62 5- 2 155.3 261.3 250.2 18.50 1.58 0v(X): 16.98 Std: 1.00 BD(g/cm**3): 1.64 Std: .06 Remarks : NONE PPNSBD 1 AUG 1989 Crop Residue (X): 15.00 Depth to layer 8 : 11.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON UETS+CON DRYS+CON CV 80 1° 1 °1.0 °1.0 °1.0 .00 .00 1° 2 155.1 243.1 232.5 17.67 1.29 2° 1 156.8 °1.0 °1.0 .00 .00 2° 2 155.1 242.9 232.4 17.50 1.29 3° 1 155.3 241.0 231.7 15.50 1.27 3° 2 °1.0 °1.0 °1.0 .00 00 4° 1 156.9 239.1 230.8 13.83 1.23 4° 2 °1.0 °1.0 °1.0 .00 00 5° 1 °1.0 °1.0 °1.0 .00 00 5° 2 155.7 245.7 236.2 15.83 1.34 0v(X): 16.07 Std: 1.58 80(9/cm**3): 1.28 Std: .04 APPENDIX 8 (cont'd) 1552 Remarks : HALF OF MADERA SOIL SAMPLE BEEN OUT ACCIDENTLY PMNZBD Crop Residue (X): Depth to layer B : 6.67 14.0 inch MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON UETS+CON DRYS+CON 0v 1- 1 °1.0 °1.0 °1.0 .00 1° 2 155.1 237.8 230.1 12.83 2° 1 °1.0 °1.0 °1.0 .00 2° 2 155.6 242.4 233.8 14.33 3- 1 156.4 245.3 236.4 14.83 3- 2 °1.0 °1.0 °1.0 .00 4° 1 156.4 238.1 229.9 13.67 4° 2 °1.0 °1.0 °1.0 .00 5° 1 °1.0 °1.0 °1.0 .00 5° 2 156.3 247.7 238.4 15.50 0v(X): 14.23 Std: 1.03 Remarks : HALF OF MADERA SOIL PMU4BD Crop Residue (X): Depth to layer 8 : 5.00 13.0 inch 80 .00 1.25 .00 1.30 1.33 .00 1.23 .00 .00 1.37 1 AUG 1989 80(9/cm**3): 1.30 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1. 1. 2. 2. 3. 3. 4. 4. 5. 5. N-fiN-‘N-DN-DN-P CON HETS+CON DRYS+CON 156.3 156.1 155.2 155.2 154.7 155.9 °1.0 °1.0 154.8 155.9 0V(X): Remarks : NONE Crop Residue (X): 262.6 254.5 259.1 251.4 259.3 252.0 257.0 249.5 254.3 247.1 256.4 249.6 °1.0 °1.0 °1.0 °1.0 255.5 248.9 255.8 249.6 11.96 Std: 1 PMN3BD 6.67 13.0 inch Depth to layer 8 : 0v 13.50 12.83 12.17 12.50 12.00 11.33 .00 .00 11.00 10.33 .03 80 1.64 1.59 1.61 1.57 1.54 1.56 .00 .00 1.57 1.56 SAMPLES BEEN OUT ACCIDENTLY 1 AUG 1989 BO(g/cm**3): 1.58 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET UNN-D-D 1 dN-IN CON NETS*CON DRYS+CON 155.4 156.4 156.0 155.2 156.6 240.7 244.1 243.2 237.9 246.4 232.5 235.3 234.4 229.2 236.9 0v 13.67 14.67 14.67 14.50 15.83 80 1.29 1.32 1.31 1.23 1.34 7 AUG 1989 Std: Std: .06 .03 APPENDIX 8 (cont'd) 3° 2 156.8 242.3 233.8 4° 1 155.6 246.3 237.5 4° 2 156.9 246.7 238.1 5- 1 156.7 245.6 237.4 5- 2 155.1 241.4 233.8 0v(X): 14.28 Std: Remarks : NONE PMUZBD Crop Residue (X): 6.67 Depth to layer s : 12.0 inch 14.17 14.67 14.33 13.67 12.67 da—I—D—I-fi 3123358 153 BD(g/cm**3): 1.31 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON HETS+CON DRYS+CON 1° 1 156.8 261.5 251.8 1- 2 155.5 259.6 250.7 2- 1 156.6 258.3 249.1 2° 2 156.5 263.5 253.3 3- 1 155.4 257.5 248.7 3- 2 155.2 260.0 249.5 4- 1 156.4 262.4 253.3 4- 2 156.3 262.7 253.3 5— 1 155.4 265.2 255.1 5- 2 156.4 262.7 252.9 0v(X): 15.95 Std: Remarks : NONE PPNZDD Crop Residue (X): 16.67 Depth to layer 8 : 12.0 inch 0v 16.17 14.83 15.33 17.00 14.67 17.50 15.17 15.67 16.83 16.33 .97 80 1.58 .59 .54 .61 .56 .57 .62 .62 .66 .61 .l—I—I—Dd-I—D-J-D 7 AUG 1989 BD(9/cm**3): 1.60 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET CON UETS+CON DRYS+CON 1° 1 156.3 263. 1° 2 156.1 259. 2- 1 155.2 260. 2° 2 155.2 257. 3- 1 154.7 259. 3- 2 155.9 263. 4° 1 155.0 256. 4- 2 155.9 257. 5- 1 154.8 252. 5° 2 155.9 261. 0v(X): 12.23 Remarks : NONE Crop Residue (X): Depth to layer B : 9 255.3 3 251.9 9 253.2 9 249.9 6 251.9 8 256.0 2 250.1 9 250.9 4 246.0 6 254.9 Std: 1 PPN3BD 5.00 13.0 inch 0v 14.33 12.33 12.83 13.33 12.83 13.00 10.17 11.67 10.67 11.17 .30 mosssassg _a_a.a_a_a_a_a_a . U C UTUTO .o-a a a GUI U'IN 7 AUG 1989 80(g/cm**3): 1.61 7 AUG 1989 Std: Std: Std: .04 .03 .04 APPENDIX 8 (cont'd) 154 MADERA METHOD READING AND INDIVIDUAL OUTPUT: SET 1° 1 1° 2 2° 1 2° 2 3° 1 3° 2 4° 1 4° 2 5° 1 5° 2 CON NETS+CON DRYS+CON 154.6 237.2 154.5 237.7 153.9 241.1 153.9 247.5 153.7 243.8 °1.0 °1.0 154.6 245.2 153.7 244.0 155.1 247.1 154.4 245.1 0v(X): 14.52 Remarks : NONE 229.5 229.6 232.1 238.3 234.5 °1.0 236.4 235.4 238.2 236.3 Std: 12 13 15. 15 15 14 14 14 14 .86 0v .83 .50 00 .33 .50 .00 .67 .33 .83 .67 80 1.25 1.25 1.30 1.41 1.35 .00 1.36 1.36 1.38 1.37 80(g/cm**3): 1.34 Std: .06 APPENDIX 9 Field measured ponding time and water applied depth at ponding for sprinkling infiltrometer experiment 155 APPENDIX 9. Field measured ponding time and water applied depth at ponding for sprinkling infiltrometer experiment. PMUS 30 JUNE 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 1.2171 7.25 30.9137 .1471 3.7354 1 .9132 8.50 23.1942 .1294 3.2859 2 1.1775 8.50 29.9084 .1668 4.2370 3 1.3348 4.00 33.9045 .0890 2.2603 4 1.1202 11.50 28.4527 .2147 5.4534 5 2.4709 1.75 62.7609 .0721 1.8305 6 PMN4 30 JUNE 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# . 8 15.50 20.3139 . 5.2478 1 1.0584 13.25 26.8831 .2337 5.9367 2 1.0048 13.25 25.5231 .2219 5.6363 3 1.4324 5.00 36.3831 .1194 3.0319 4 3.6705 3.00 93.2318 .1835 4.6616 5 3.1647 1.50 80.3840 .0791 2.0096 6 PPH4 5 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(MMIhr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .7990 17.50 20.2950 .2330 5.9194 1 1.2032 7.25 30.5618 .1454 3.6929 2 1.0184 5.50 25.8661 .0933 2.3711 3 1.6185 5.25 41.1090 .1416 3.5970 4 1.1280 3.25 28.6517 .0611 1.5520 5 2.8075 1.50 71.3109 .0702 1.7828 6 PPN4IN 5 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 1.2032 11.50 30.5618 .2306 5.8577 1 1.3991 9.50 35.5370 .2215 5.6267 2 1.1996 10.50 30.4709 .2099 5.3324 3 1.4762 6.50 37.4948 .1599 4.0619 4 1.0938 10.75 27.7835 .1960 4.9779 5 2.3366 3.00 59.3500 .1168 2.9675 6 PMN1IN 13 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) cUM_AMT(mm) NOZZLE# .6870 18.50 17.4490 .2118 5.3801 1 .7938 13.00 20.1623 .1720 4.3685 2 .7438 10.25 18.8935 .1271 3.2276 3 1.6450 5.00 41.7837 .1371 3.4820 4 1.3966 3.75 35.4735 .0873 2.2171 5 3.4781 1.50 88.3428 .0870 2.2086 6 PPNZIN 14 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(nnD NOZZLE# 1.6215 5.17 41.1868 .1396 3.5466 1 1.7284 1.2972 1.8012 1.5096 2.7395 APPENDIX 9 (cont'd) 1556 RATE(in/hr) .8569 1.1809 1.6091 1.4453 2.7260 RATE(in/hr) .6247 .9816 .8996 1.9740 1.9281 3.8353 RATE(in/hr) 1.0046 1.9289 1.7133 3.2149 RATE(in/hr) .7190 .8532 RATE(in/hr) . 7 .6677 1.4555 1.3536 2.8201 4.17 43.9018 .1200 3.0487 3.83 32.9495 .0829 2.1051 2.83 45.7503 .0851 2.1604 5.50 38.3427 .1384 3.5148 1.17 69.5827 .0533 1.3530 PPU6IN 14 JULY 1989 PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) 30.67 16.1744 .3255 8.2669 8.33 21.7643 .1190 3.0228 4.00 29.9948 .0787 1.9997 3.50 40.8708 .0939 2.3841 4.83 36.7100 .1164 2.9572 1.33 69.2416 .0606 1.5387 ppn1in 26 July 1989 PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) 41.83 15.8669 .4355 11.0627 17.00 24.9325 .2781 7.0642 26.83 22.8511 .4023 10.2195 5.50 50.1405 .1810 4.5962 6.83 48.9744 .2196 5.5776 1.83 97.4158 .1172 2.9766 pmnSin 26 July 1989 PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) 21.17 25.5179 .3544 9.0022 8.00 48.9944 .2572 6.5326 8.50 43.5182 .2427 6.1651 3.00 81.6574 .1607 4.0829 NON°PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) 29.42 18.2624 .3525 8.9537 29.42 21.6714 .4183 10.6250 pmu6in 26 July 1989 PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) 20.33 23.1062 .3083 7.8304 14.00 16.9605 .1558 3.9574 4.83 36.9699 .1172 2.9781 5.50 34.3821 .1241 3.1517 2.17 71.6293 .1018 2.5866 NON-PONDED PRIMARY RATE(in/hr) RATE(in/hr) 1.0521 .8108 2.4064 TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) 58.67 14.0003 .5389 13.6891 ppu1in 26 July 1989 PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) 17.17 26.7232 .3010 7.6458 12.50 20.5934 .1689 4.2903 4.33 61.1236 .1738 4.4145 OWS‘WN NOZZLE# O‘UIJ-‘LNN-e NOZZLE# ombUN-D NOZZLE# O‘U‘bN NOZZLE# 1 3 NOZZLE# OmbuN NOZZLE# 1 NOZZLE# 2 3 4 157 APPENDIX 9 (cont'd) 1.7775 5.00 45.1482 .1481 3.7623 5 3.6849 2.17 93.5956 .1331 3.3798 6 NON-PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .6294 57.50 15.9868 .6032 15.3207 1 PPNSIN 1 AUG 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# NON-PONDED SECONDARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) .6517 7.50 16.5543 .0815 PMNZIN PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) .6939 21.02 17.6249 .2431 .6970 17.53 17.7046 .2037 .8154 13.50 20.7121 .1835 1.8019 3.65 45.7695 .1096 1.1496 7.60 29.1992 .1456 2.7305 1.82 69.3553 .0827 PMH4IN PONDED PRIMARY RATEgggéhr) TP(min) RATE(mm/hr) CUM_AMT(in) . 19.25 18.7841 .2373 1.5824 5.08 40.1920 .1341 1.1482 8.83 29.1633 .1690 2.5783 2.63 65.4896 .1132 NON-PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) .4745 8.67 12.0523 .0685 1.7409 1 .8831 10.50 22.4304 .1545 3.9253 2 .8356 6.67 21.2235 .0928 2.3582 3 2.0868 3.50 53.0057 .1217 3.0920 4 1.2062 5.00 30.6366 .1005 2.5531 5 2.6814 1.50 68.1065 .0670 1.7027 6 PPNSIN AUG 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .6363 12.67 16.1625 .1343 3.4121 1 1.0887 6.83 27.6522 .1240 3.1493 2 .9505 6.83 24.1417 .1082 2.7495 3 2.4440 3.00 62.0787 .1222 3.1039 4 1.5980 3.83 40.5899 .1021 2.5932 5 3.2901 1.33 83.5675 .0731 1.8571 6 CUM_AMT(mm) NOZZLE# 2.0693 AUG 1989 CUM_AMT(mm) NOZZLE# 6.1736 5.1737 4.6602 2.7843 3.6986 2.0999 O‘UIJ‘U‘N-i AUG 1989 CUM_AMT(mm) NOZZLE# 6.0266 2 3.4052 4 4.2935 5 2.8743 6 CUM AMT(mm) NOZZLE# .5774 56.33 14.6649 .5421 1377687 1 .7058 56.33 17.9285 .6627 16.8329 3 PMN3IN 7 AUG 1989 PONDED PRIMARY APPENDIX 9 (cont'd) 158 RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLEN .5089 22.00 12.9256 .1866 4.7394 1 .9099 12.20 23.1124 .1850 4.6995 2 .8502 11.00 21.5957 .1559 3.9592 3 1.7383 4.83 44.1518 .1400 3.5567 4 1.7672 4.83 44.8877 .1424 3.6160 5 2.9006 2.00 73.6758 .0967 2.4559 6 PMHZIN 7 AUG 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(flthr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .5582 23.75 14.1782 .2210 5.6122 1 .9380 7.50 23.8262 .1173 2.9783 2 .9991 5.17 25.3772 .0860 2.1853 3 1.2918 4.25 32.8108 .0915 2.3241 4 1.5687 2.92 39.8438 .0763 1.9369 5 2.4440 1.17 62.0787 .0475 1.2071 6 PPUZIN 7 AUG 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .4929 30.75 12.5207 .2526 6.4169 1 .7104 17.17 18.0451 .2033 5.1629 2 .8278 9.50 21.0267 .1311 3.3292 3 1.4698 4.00 37.3340 .0980 2.4889 4 1.5980 4.50 40.5899 .1199 3.0442 5 3.0551 1.75 77.5984 .0891 2.2633 6 PPN3IN 7 AUG 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .5098 43.00 12.9484 .3653 9.2797 1 .9125 12.75 23.1769 .1939 4.9251 2 .9605 8.17 24.3965 .1307 3.3206 3 1.7296 4.17 43.9326 .1201 3.0509 4 1.8988 2.83 48.2304 .0897 2.2775 5 3.4311 1.33 87.1489 .0762 1.9366 6 CMN3IN 25 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 1.0716 4.33 27.2191 .0774 1.9658 1 1.3016 8.17 33.0597 .1772 4.4998 2 1.0636 5.33 27.0145 .0945 2.4013 3 2.7655 2.17 70.2429 .0999 2.5365 4 1.8988 2.50 48.2304 .0791 2.0096 5 4.6531 1.33 118.1883 .1034 2.6264 6 CMN3IN 25 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .7435 10.67 18.8841 .1322 . 1 1.4582 5.17 37.0376 .1256 3.1893 2 1.1012 4.83 27.9695 .0887 2.2531 3 3.0833 2.00 78.3147 .1028 2.6105 4 2.6164 2.00 66.4560 .0872 2.2152 5 4.6061 1.33 116.9945 .1024 2.5999 6 CDH3IN 25 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLEN APPENDIX 9 (cont'd) 1559 1.0064 8.33 25.5618 .1398 3.5503 1 1.6744 3.83 42.5299 .1070 2.7172 2 1.0399 5.00 26.4133 .0867 2.2011 3 2.9963 2.00 76.1061 .0999 2.5369 4 2.3688 1.00 60.1686 .0395 1.0028 5 4.7001 1.17 119.3821 .0914 2.3213 6 CNNSIN 27 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 2.0798 2.50 52.8266 .0867 2.2011 2 2.1679 2.50 55.0650 .0903 2.2944 4 3.9951 1.67 101.4748 .1110 2.8187 6 NON-PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 1.2240 23.50 31.0902 .4794 12.1770 1 CNN1IN 27 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 1.7048 6.83 43.3032 .1942 4.9317 4 NON-PONDED PRIMARY RATE(in/hr) TP(min) RATE(tlln/hr) CUM_AMT(in) CUM_AMT(IIm) NOZZLE# 4.5886 19.67 116.5493 1.5040 38.2023 1 1.8559 44.17 47.1402 1.3662 34.7004 2 1.8558 31.00 47.1367 .9588 24.3540 3 1.7422 52.50 44.2510 1.5244 38.7196 5 3.4085 42.33 86.5755 2.4049 61.0839 6 CDN6IN 28 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .6517 7.33 16.5543 .0797 2.0233 1 1.3282 2.33 33.7351 .0517 1.3119 2 .8997 5.33 22.8531 .0800 2.0314 3 2.4744 1.17 62.8489 .0481 1.2221 4 1.9467 2.17 49.4473 .0703 1.7856 5 4.2301 .67 107.4439 .0470 1.1938 6 CDU6IN 28 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(IIIn/hr) CUM_AMT(in) CUM_AMT(ImI) NOZZLE# .9464 7.17 24.0383 .1130 2.8712 1 1.0545 7.33 26.7831 .1289 3.2735 2 .7410 8.17 18.8202 .1009 2.5616 3 2.2184 3.00 56.3484 .1109 2.8174 4 1.1205 4.67 28.4620 .0872 2.2137 5 3.1430 1.33 79.8311 .0698 1.7740 6 CMNZIN 3 AUG 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# . . 16.8840 .1016 2.5795 1 1.0916 4.92 27.7275 .0895 2.2721 2 1.4644 3.50 37.1970 .0854 2.1698 3 1.7830 3.00 45.2882 .0891 2.2644 4 2.4816 1.83 63.0338 .0758 1.9260 5 3.6765 .92 93.3833 .0562 1.4267 6 160 APPENDIX 9 (cont'd) CMN1IN 31 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .5724 22.33 14.5381 .2130 5.4114 1 .7130 8.50 18.1100 .1010 2.5656 2 .8376 7.67 21.2760 .1070 2.7186 3 2.0304 5.00 51.5731 .1692 4.2978 4 1.2287 6.50 31.2078 .1331 3.3808 5 .5099 2.00 12.9521 .0170 .4317 6 CMN4IN 31 JULY 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# . 16.50 17.9421 .1943 4.9341 1 1.1050 7.33 28.0670 .1351 3.4304 2 1.1040 7.50 28.0421 .1380 3.5053 3 2.6199 4.00 66.5459 .1747 4.4364 4 1.6257 4.83 41.2922 .1310 3.3263 5 4.8411 1.00 122.9636 .0807 2.0494 6 CNNSIN 2 AUG 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 3.9481 4.33 100.2810 .2851 7.2425 2 2.5102 5.67 63.7601 .2371 6.0218 3 2.7109 4.67 68.8565 .2108 5.3555 4 1.1689 15.83 29.6909 .3085 7.8351 5 4.4181 1.50 112.2192 .1105 2.8055 6 NON-PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 1.4782 46.17 37.5472 1.1374 28.8905 1 CNN3IN 2 AUG 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 1.5581 12.83 39.5752 .3333 8.4647 1 4.4584 6.67 113.2425 .4954 12.5825 6 NON-PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 3.5079 35.67 89.1015 2.0853 52.9659 2 1.7592 46.17 44.6843 1.3536 34.3821 3 1.9616 49.17 49.8248 1.6074 40.8287 4 1.5123 49.17 38.4127 1.2393 31.4771 5 CDN1IN 2 AUG 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .7296 9.50 18.5310 .1155 2.9341 1 1.2032 2.67 30.5618 .0535 1.3583 2 .6255 8.20 15.8867 .0855 2.1712 3 2.2184 2.58 56.3484 .0955 2.4261 4 2.1081 1.72 53.5458 .0603 1.5320 5 3.8804 .83 98.5619 .0539 1.3689 6 CNNSIN 3 AUG 1989 PONDED PRIMARY APPENDIX 9 (cont'd) 161 RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .6212 30.08 15.7781 .3115 . 1 1.0887 6.17 27.6522 .1119 2.8420 2 .6858 19.98 17.4185 .2284 5.8013 3 2.1022 2.25 53.3964 .0788 2.0024 4 2.2748 3.00 57.7809 .1137 2.8890 5 3.8071 .83 96.6995 .0529 1.3430 6 CDN1IN 3 AUG 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .7381 6.50 18.7474 .0800 2.0310 1 1.2944 4.88 32.8790 .1054 2.6760 2 .9772 5.37 24.8199 .0874 2.2200 3 2.1636 2.50 54.9549 .0901 2.2898 4 2.5192 1.33 63.9888 .0560 1.4220 5 4.7941 1.00 121.7698 .0799 2.0295 6 CMN6 26 June 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .4305 32.50 10.9358 .2332 5.9235 1 .9068 8.25 23.0337 .1247 3.1671 2 1.0340 6.25 26.2641 .1077 2.7358 3 1.6486 5.25 41.8756 .1443 3.6641 4 1.7234 5.25 43.7734 .1508 3.8302 5 4.6296 1.50 117.5914 .1157 2.9398 6 CDN4 28 JUNE 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLEN .6381 8.00 16.2070 .0851 2.1609 1 .9400 6.50 23.8764 .1018 2.5866 2 1.1414 6.00 28.9928 .1141 2.8993 3 1.2784 3.50 32.4719 .0746 1.8942 4 1.8487 2.75 46.9570 .0847 2.1522 5 2.7072 1.25 68.7641 .0564 1.4326 2 CDNZ 28 June 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(uthr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# .2995 14.75 7.6081 .0736 1.8703 1 .6963 6.75 17.6862 .0783 1.9897 2 .5216 7.25 13.2476 .0630 1.6007 3 1.3348 3.75 33.9045 .0834 2.1190 4 1.8048 3.50 45.8427 .1053 2.6742 5 3.1664 1.75 80.4258 .0924 2.3458 6 CMN6 26 June 1989 CNHZ 29 JUNE 1989 PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 1.3687 6.00 34.7641 .1369 3.4764 4 4.4745 2.50 113.6518 .1864 4.7355 5 NON-PONDED PRIMARY RATE(in/hr) TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# . 43.00 17.4909 .4935 12.5351 1 .9199 39.75 23.3659 .6094 15.4799 2 .8882 RATE(in/hr) 2.1432 4.2746 3.7959 RATE(in/hr) 1.1900 1.4637 RATE(in/hr) .7332 .7322 1.3732 .7520 1.6981 3.4311 RATE(in/hr) .7718 .9697 2.1996 2.0868 1.9427 4.7172 RATE(in/hr) .7438 1.0795 1.5040 2.3456 1.3944 4.0891 RATE(in/hr) .6306 1.1917 1.2943 2.3312 3.1466 2.3688 RATE(in/hr) 4.5485 162 APPENDIX 9 (cont'd) 14.50 22.5591 .2146 5.4518 3 CNN3 29 JUNE 1989 PONDED PRIMARY TP(min) RATE(mmlhr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 4.50 54.4382 .1607 4.0829 4 2.00 108.5749 .1425 3.6192 5 1.75 96.4153 .1107 2.8121 6 NON-PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLEN 18.50 27.8773 .3384 8.5955 21.25 30.2247 .4214 10.7046 2 28.00 37.1790 .6831 17.3502 3 CMNS 6 JULY 1989 PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 13.75 18.6236 680 2 8.25 18.5985 .1007 2.5573 2 4.00 34.8803 .0915 2.3254 3 9.25 19.1011 .1159 2.9448 4 7.50 43.1316 .2123 5.3915 5 1.75 87.1489 .1001 2.5418 6 CMNZ 6 JULY 1989 PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) N022LE# 9.25 19.6038 .1190 3.0223 1 9.08 24.6304 .1468 3.7288 2 4.00 55.8708 .1466 3.7247 3 2.50 53.0057 .0870 2.2086 4 3.25 49.3446 .1052 2.6728 5 1.25 119.8162 .0983 2.4962 6 CDUSIN 10 JULY 1989 PONDED PRIMARY TP(min) RAIEInthr) CUM-AMT(in) CUM_AMT(mm) NOZZLE# 11.25 18.8935 .1395 3.5425 1 7.00 27.4194 .1259 3.1989 2 3.25 38.2023 .0815 2.0693 3 2.25 59.5774 .0880 2.2342 4 4.75 35.4167 .1104 2.8038 5 1.00 103.8624 .0682 1.7310 6 CDNZIN 10 JULY 1989 PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 12.67 16.0165 3.3813 1 6.23 30.2680 .1238 3.1445 2 2.67 32.8741 .0575 1.4611 3 2.25 59.2135 .0874 2.2205 4 1.42 79.9232 .0743 1.8871 5 2.25 60.1686 .0888 2.2563 6 CNN6 11 JULY 1989 PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 2.33 115.5311 .1769 4.4929 6 163 APPENDIX 9 (cont'd) RATE(in/hr) 2.4709 RATE(in/hr) .6787 1.0076 .3802 1.8324 1.5322 CNU1 11 JULY 1989 PONDED PRIMARY TP(min) RATE(nm/hr) CUM_AMT( in) CUM_AMT(m) NOZZLE# 5.50 62.7609 .2265 5.7531 4 NON-PONDED PRIMARY TP(min) RATE(mm/hr) CUM_AMT(in) CUM_AMT(mm) NOZZLE# 48.75 17.2400 .5515 14.0075 1 51.50 25.5918 .8648 21.9663 2 22.50 9.6567 .1426 3.6213 3 37.50 46.5431 1.1453 29.0894 5 20.00 38.9186 .5107 12.9729 6 BIBLIOGRAPHY BIBLIOGRAPHY Adamowski, K., and A.F. 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