UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A comparison of techniques used in rainfall-runoff models : model efficiency Loague, Keith Michael 1982

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1982_A6_7 L63.pdf [ 19.33MB ]
[if-you-see-this-DO-NOT-CLICK]
Metadata
JSON: 1.0052442.json
JSON-LD: 1.0052442+ld.json
RDF/XML (Pretty): 1.0052442.xml
RDF/JSON: 1.0052442+rdf.json
Turtle: 1.0052442+rdf-turtle.txt
N-Triples: 1.0052442+rdf-ntriples.txt
Original Record: 1.0052442 +original-record.json
Full Text
1.0052442.txt
Citation
1.0052442.ris

Full Text

A COMPARISON OF TECHNIQUES USED IN RAINFALL-RUNOFF MODELS: MODEL EFFICIENCY by Keith Michael Loague B.Sc, The University of Michigan, 1978 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Geological Sciences) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November 1982 ©Keith Michael Loague, 1982 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Geological Sciences  The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date 25 November 1982 DE-6 (3/81) ABSTRACT A suite of three underlying rainfall-runoff modeling techniques is applied to two data sets and the results used to compare model efficiencies for selected events. Linear regression, unit hydrograph, and quasi-physically based models make up the modeling suite. The two data sets come from a 7.2 KM subwatershed (MCW) near Klingerstown, Pennsylvania and a 0.096 KM2 subwatershed (R-5) near Chickasha, Oklahoma.-Individual model efficiencies are determined on the basis of a sums of squares criterion. These efficiencies are surprisingly poor. Results indicate that the most informative independent linear regression variables for MCW and R-5 are volume of rainfall and average rainfall intensity respectively. There is a general improvement in correlation coefficients and regression model efficiencies for both MCW and R-5 with increases in the number of selected events. The unit hydrograph and quasi-physically based models exhibited predictive prowess only for the R-5 events. The unit hydrograph technique is found to be strongly dependent upon an accurate estimate of spatially-variable excess rainfall. The efficiency of the physically-based, deterministic, distributed model was found to deteriorate drastically with increases in basin size due to the lumping of spatially-variable soil hydraulic properties. i i i Based on this work a definitively superior rainfall-runoff modeling technique is not suggested. Limitations of each of the three models and the efficiency criterion used for their evaluation are discussed. This work provides the foundation for a subsequent investigation to be carried out by the author, to determine if space-time tradeoffs exist across data sets of various rainfall-runoff modeling techniques. Future research will focus on the concept of data-worth and the question of model choice. TABLE OF CONTENTS Page ABSTRACT iii LIST OF TABLES. vLIST OF ILLUSTRATIONS ix ACKNOWLEDGEMENTS . xii 1. INTRODUCTION 1 1.1 Terminology and Classification of Hydrologic Models ..2 1.2 Underlying Techniques used in Hydrologic Modeling ...10 1.2.1 Correlation Analysis 11 1.2.2 Partial System Synthesis with Linear Analysis ..12 1.2.3 System Synthesis 4 1.2.3.1 Physically-Based Models 11.2.3.2 Quasi-Physically-Based Models 15 1.3 Space-time Tradeoffs 17 1.4 Data-Worth and Model Choice 22 1.5 Thesis Objective 23 2. MODELS AND COMPARISON2 . 1 Regression 7 2.2 Unit Hydrograph 33 2.3 Quasi-Physically-Based 42.4 Model Efficiency 58 3. DATA SOURCES AND EVENT SELECTION 61 3.1 Mahantango Creek Subwatershed 4 3.2 R-5 Subwatershed 77 3.3 Event Selection 81 4. RESULTS AND DISCUSSION 5 4.1 Regression Models 86 4.2 Unit Hydrograph Model 102 4.3 Distributed Model 115. CONCLUSIONS AND FUTURE RESEARCH 125 REFERENCES • 132 APPENDIX A 146 APPENDIX B 1 50 APPENDIX C 17APPENDIX D 185 LIST OF TABLES Table Page 1 Major rainfall-runoff event simulation models (after Viessman et al., 1977) 19 2 Hydrologic processes and options used by major event simulation models (from Viessman et al., 1977) 20 3 Characterization of selected rainfall-runoff modeling techniques (after Freeze, 1982a) 21 4 Normal equations for the equality-constrained least squares technique used in the computer program UNIT (after Morel-Seytoux and Kimzey, 1980) 43 5 Input requirements for selected modeling techniques relative to the calibration process 60 6 Average soil depths within the Mahantango Creek Subwatershed (abstracted from Engman, 1974) 67 7 Soil characteristic parameters for the Mahantango Creek Subwatershed (after Engman and Rogowski, 1974a) .68 8 Antecedent soil water contents for the Mahantango Creek Subwatershed and the R-5 Subwatershed. 72 9 Characteristic parameters and depths for R-5 Subwatershed soils 80 10 Rainfall-runoff characteristics from the Mahantango Creek Subwatershed and the R-5 Subwatershed .....84 v i LIST OF TABLES—CONTINUED i Table Page 11 Correlation matrix for Mahantango Creek Subwatershed rainfall-runoff variables based on 15 selected events without base flow separation 88 12 Correlation matrix for Mahantango Creek Subwatershed rainfall-runoff variables based on 15 selected events with base flow separation 89 13 Correlation matrix for Mahantango Creek Subwatershed rainfall-runoff variables based on 21 selected events without base flow separation 90 14 Correlation matrix for Mahantango Creek Subwatershed rainfall-runoff variables based on 21 selected events with base flow separation 91 15 Summary of correlation matrix tables .' 92 16 Linear regression models and efficiencies for the Mahantango Creek Subwatershed 95 17 Correlation matrix for R-5 Subwatershed rainfall-runoff variables based on six selected events 97 18 Correlation matrix for R-5 Subwatershed rainfall-runoff variables based on nine selected events ..98 19 Linear regression models and efficiencies for the R-5 Subwatershed 100 vi i LIST OF TABLES—CONTINUED Table Page 20 Unit hydrograph model efficiencies for the Mahantango Creek Subwatershed and R-5 Subwatershed 105 21 Summary of the transformed Mahantango Creek Subwatershed ...115 22 Distributed model efficiencies for the Mahantango Creek Subwatershed and R-5 Subwatershed 117 23 Summary of the transformed R-5 Subwatershed 120 24 Effect of antecedent soil water content on simulated lateral inflow hydrograph volumes for selected Mahantango Creek Subwatershed events 122 vi i i LIST OF ILLUSTRATIONS Figure Page 1 Flow chart of hydrologic model classification (abstracted from Clarke, 1 973 ) 7 2 Flow chart illustrating the pot and pipeline structure of the Stanford Watershed Model IV (after Crawford and Linsley, 1966) 18 3 Possible methodology for selecting a rainfall-runoff modeling technique (after Dooge, 1978) 24 4 Flow chart of the operations involved in the unit hydrograph technique (from Amorocho and Hart, 1964) 36 5 Determination of a design storm hydrograph: (a) Excess rainfall, (b) unit hydrograph, and (c) surface runoff hydrograph (from Viessman et al., 1977). 37 6 Instantaneous unit hydrograph: (a) input function, (b) kernel function, and (c) output function (after Chow, 1964b) 39 7 Nash's model for routing instantaneous rainfall through a series of linear storage resevoirs (after Chow, 1964b) 41 8 <J> index method of calculating excess rainfall 45 9 Base flow separation technique (after Engman, 1974)...... 46 10 Systems representation of hydrologic cycle (from Viessman et al., 1977) 48 ix LIST OF ILLUSTRATIONS-_Continued Figure Page 11 Schematic diagram of a dynamic watershed (from Engman, 1974).... 49 12 Flow chart for distributed model code (after Engman, 1974) 51 13 Mahantango Creek Subwatershed (Gburek, personal communication, 1982) 65 14 Spatial variation of soil type and land slope within the Mahantango Subwatershed (Gburek, personal communication, 1982) ..66 15 Example soil water frequency distributions (after Engman and Rogowski, 1974a) 70 16 Soil moisture for 1971 within the Mahantango Creek Subwatershed (Henninger, 1972) 71 17 Depression storage as a function of land slope and use (after Hiemstra, 1968) 74 18 Open channel cross section 75 19 Base flow separation relationship for the Mahantango Creek Watershed (after Engman, 1974).. 76 20 R-5 Subwatershed (Gander, personal communication, 1981) . 78 x LIST OF ILLUSTRATIONS--Continued Figure page 21 Location of instrumentation and soil parameter measurements within the R-5 Subwatershed (Gander, personal communication, 1 981 ) 79 22 Averaged one-hour unit hydrograph for the Mahantango Creek Subwatershed (Component events 15, 24, 25, 32, 42, 47, and 49) 104 23 Linear * index relationship for the Mahantango Creek Subwatershed 107 24 Example unit hydrograph 108 25 Averaged one-hour unit hydrograph for the R-5 Subwatershed (Component events 1, 5, 10, 12, and 15) 109 26 Linear * index relationship for the R-5 Subwatershed 110 27 Watershed segments used to transform the Mahantango Creek Subwatershed into overland flow planes 114 28 Channel routing scenario for the Mahantango Creek Subwatershed 116 29 Watershed segments used to transform the R-5 Subwatershed into overland flow planes 119 x i ACKNOWLEDGEMENTS A number of people have been directly or indirectly involved in the realization of this thesis. Their interest, generosity and contributions are gratefully acknowledged. I express my very sincere thanks to Allan Freeze who initiated this research and employed me as a research assistant. Al's stimulating advise and enthusiasm throughout this project has been invaluable. I am grateful to the groups at the Northeast Wastershed , Research Center, University Park, Pennsylvania and the Southern Great Plains Research Watershed, Chickasha, Oklahoma for providing me with precious data sets. Specifically, appreciation is extended to William Gburek and Gene Gander of University Park and Chickasha respectively for their assistance. I am very thankful to Edwin Engman of the Beltsville Agricultural Research Center, Beltsville, Maryland for providing his partial area code. The esprit de corps of friends, Grant Garven and Jennifer Rulon, has also greatly facilitated this work. I appreciate the interest and helpful comments of committee members Jan de Vries, Mike Novak and Leslie Smith. Many thanks are extended to Gordon Hodge and Melanie Sullivan for drafting figures and tables. Support for this work came from a grant to Allan Freeze from the Natural Science and Engineering Research Council of Canada. Lastly, my most sincere thanks to my partner Emily, for her continued support. xi i 1 CHAPTER ONE INTRODUCTION / Dooge (1972) describes the research hydrologist as one who is bound to be prolific in the production of all kinds of models, but one who must recognize the hardships the applied hydrologist faces attempting to choose the correct one for a given situation. Dooge (1978) notes that within the last two decades there has been an immense growth in the modeling -literature dealing almost exclusively with description and recommendation, but hardly ever evaluation. This thesis and the research it represents is an attempt to evaluate, by comparison, the efficiencies of selected rainfall-runoff modeling techniques. A brief historical review of the development of hydrology and the types of models currently in use is presented in Linsley's (1981) overview of rainfall-runoff models. This work underlies a subsequent investigation to determine if space-time tradeoffs exist across the data sets of various rainfall-runoff modeling techniques. Building upon this foundation, future research will focus on the concept of data-worth and the question of model choice. Chapter One is introductory. It reviews the terminology and classification of hydrologic models; underlying modeling techniques in hydrology; and the concepts of space-time. 2 tradeoffs, data-worth and model choice as they are related to hydrologic modeling. At the end of this first chapter the general thesis objective is described. In Chapter Two, the three rainfall-runoff modeling techniques that are used in this study are fully described, and efficiency and comparison criteria are presented. Chapter Three describes the data sources and the methods used to select events from the available records. The simulations and their results are presented in Chapter Four. Conclusions and discussions of future research appear in Chapter Five. 1.1 Terminology and Classification of Hydrologic Models Woolhiser (1973) describes a hydrologic model as an abstraction that replaces the original hydrologic system with a similar but simpler structure. Each of these models reflects some but not all the properties of the prototype. A great number of hydrologic models currently exist. These models are the result of attempts by research hydrologists both to expand theoretical understanding of hydrologic phenomena and to provide engineers with the necessary tools for decisions concerning operation and design. As noted by Dooge (1978) the methods used in hydrologic research have not enjoyed a unified terminology in their 3 classification. As a result, much of todays jargon is undercut with a confusing array of shared or conflicting definitions. The purpose of this section is to review, not introduce, hydrologic model classifications and their terminology. The focus of this review is exclusively on mathematical models rather than models of the sand-box or resistance-capacitance type. Many authors have attempted to classify the continuum of methods and models applied in hydrology. The most widely quoted classification schemes are: Amorocho and Hart (1964), and Clarke (1973). Amorocho and Hart (1964) in their classic paper divided the modeling community into physical hydrology and systems investigation. Physical hydrology is directed towards a full understanding of mechanisms and interactions, while systems investigation deals with designing workable relationships between measurable parameters. Amorocho and Hart further characterize systems investigation as either parametric or stochastic. Following their definitions, parametric hydrology is the development of relationships among physical parameters involved in hydrologic events and the use of these relationships to generate synthetic sequences. Stochastic hydrology is the use of statistical characteristics of hydrologic variables to solve problems. This often involves the generation of sequences to which certain levels of probability can be attached. Kisiel (1967) states that parametric hydrology is concerned with 4 discrete events while stochastic hydrology is concerned with the time sequences of these descrete events. Dawdy and O'Donnell (1965) follow the delineations of Amorocho and Hart, labeling physical hydrology and system investigation as component and overall catchment modeling respectively. These two groups of models are obviously linked together, as the overall class gains additional information from the component class while the former provides feedback information to the latter. Kisiel (1967,1969) defines determinism as synonomous with causation and describes the stochastic approach as weaving uncertainty, by way of probability laws, into the fabric of the hydrodynamic and phenomenological relations of the system. Cornell (1964) describes a stochastic model as concerned not only with the central tendency values predicted by deterministic models, but also with the inherent and unexplained variation observed in physical phenomena. (Chow, 1964a) defines a model as deterministic if the chance of occurrence for the variable involved is ignored, and as stochastic or probabilistic if chance is taken into consideration and the concept of probability introduced. Rosenblueth and Weiner (1945) separate models into two classes: material and symbolic. According tc Woohiser (1973) a symbolic model is a mathematical description of an idealized situation that shares some of the structural properties of the 5 real system. Woolhiser classifies mathematical models as empirical or theoretical, lumped or distributed, and deterministic or stochastic. In Woolhiser's judgement, an empirical model is based upon fact, having no predictive prowess under changing conditions, while the theoretical model hinges upon explanation of observation. According to Woolhiser, a lumped model can be represented in general, by an ordinary differential equation or a series of linked ordinary differential equations. A distributed model alternatively includes spatial variations in inputs, parameters and dependent variables, and would consist of a partial differential equation or linked partial differential equatibns. Under Woolhiser's classification, a model is deterministic if, when the initial conditions, boundary conditions and inputs are specified, the output is known with certainty. Woolhiser defines stochastic models as describing processes governed by probability laws. Dooge (1968) defines a hydrologic system as a set of physical, chemical and/or biological processes acting upon input variables to convert them into output variables. According to Clarke (1973) a model is a simplified representation of a complex system. Clarke categorizes mathematical models into four major groups: Stochastic-conceptual, stochastic-empirical, deterministic-conceptual and deterministic-empirical. A model is regarded as stochastic if any of the variables in its mathematical expression are described by a probability 6 distribution. A model is termed deterministic if all the variables are believed to be free from random variations so that the model involves no distributions in probability. Models are called conceptual if their mathematical expressions are derived from consideration of the physical processes, and empirical if they are not. In Clarke's assessment, there are several sub-categorizations as well. A model is linear in the systems theory sense if the principle of superposition holds and linear in the statistical regression sense if linear in the parameters to be estimated. Clarke further identifies three sub-categories involving spatial variability of input variables. These are 1) lumped models, that do not account for spatial distribution, 2) probability-distributed models, that describe spatial variability without reference to geometrical configuration in the measurement network and 3) geometrically distributed models that express spatial variability in terms of orientation within the measurement network. Figure 1 shows Clarke's classification of hydrologic models, and references a few examples of each type. Machado-01ive (1975) distinguishes between statistical and stochastic models. A model is statistical if it includes the concept of probability, with hydrologic variables subject to random fluctuations that are assumed to be independent for different observations. Stochastic models incorporate the HYDROLOGIC MODELS PHYSICAL ANALOG Chow 1967 Diskin 1967 STOCHASTIC-CONCEPTUAL I Dawdy & O'Oonnell 1965 Freeze 1980 LINEAR IN THE SYSTEMS THEORY SENSE MATHEMATICAL MODELS STOCHASTIC-EMPIRICAL r~ Snyder 1955 DETERMINISTIC-CONCEPTUAL Wooding 1966 Eagleson 1970 Freeze 1971 NON-LINEAR IN THE SYSTEMS THEORY SENSE DETERMINISTIC-EMPIRICAL Amorocho & Ortob 1961 LINEAR IN THE STATISTICAL REGRESSION SENSE Same Sub-Classifications as Linear in the Systems Theory Sense LUMPED PROBABILITY DISTRIBUTED GEOMETRICALLY DISTRIBUTED Same Sub-Classifications as Linear in the Statistical Regression Sense Same Classification as Stochastic -Conceptual Figure 1. Flow chart of hydrologic model classification (abstracted from Clarke, 1973) 8 sequence with which hydrologic events occur within a time series and presume past events may influence future events. Dooge (1972), Quimpo (1973) and Laurenson (1974) each discuss the combination of deterministic and stochastic model components into a unified type of model, classified as hybrid by Kisiel (1969). Klemes (1978) however, cautions that what often happens with such combinations is that the determinist has just included an error term while the stochasticist was only noticing mathematically similar models. Klemes adds, that unification of stochastic and deterministic models amounts to a "Don Quixotian" task, as any model can be classified as either depending upon whether its variables and parameters contain an element of randomness. Outlining his own classification scheme, with the most decisive changes in terminology-interpretation seen yet, Klemes (1978) defines the term deterministic, as a one-to-one relationship dependent upon theory development, knowledge of initial conditions and accuracy of measurement. Klemes defines the term random, as a completely haphazard order, and finally, the term stochastic, as incorporating both an element of determinism and randomness. Klemes argues that with these definitions it follows that the two classifications, deterministic and random, are only special cases of the stochastic. Klemes further defines a probabilistic model as one that implies description and explanation, while a statistical 9 model only involves description. Finally, Klemes addresses the arbitrariness of hierarchy in model classification and concludes that the most fundamental level of classification should be the conceptual-empirical division (Clarke, 1973; Kisiel, 1969) that has also been labeled synthetic-analytic (O'Donnell, 1966), genetic-statistical (Kartvelishvili, 1967), conceptual-analytic (Wood, 1973), descriptive-prescriptive (Jackson,1975), physically based-operational (Klemes, 1974) and empirical-theoretical (Woolhiser, 1973). The final level of classification for hydrologic models to be presented here differentiates between generic and site-specific models. Generic models are used to further the understanding of hydrologic phenomena, while site-specific models are used for operation and prediction. What is evident for the foregoing classification schemes and their terminology, is that the range and scope of the various hydrologic models must be great to permit such diversity in model categorization. To insure continuity in terminology throughout the remainder of this thesis, Clarke's classification, which has been adopted by many authors and which is summarized in Figure 1, will be used exclusively. 10 1.2 Underlying Techniques used in Hydrologic Modeling Clarke (1973) described the general hydrologic model as: Vf(pt-l'pt-2'",*qt-l*qt-2»""'ara2»",)+et (1) where, P = input variables q = output variables a^ = system parameters I = residual error t f = functional form of the model Variables and parameters are characteristics of the system being modeled. Variables change with time; parameters remain constant. The function can be either conceptual or empirical. The input and output variables as well as the system parameters and residual error can be either stochastic or deterministic. The purpose of this section is to review different techniques^ used in hydrologic modeling, concentrating upon those which will be employed in this study. In assessing any model for its efficiency in a given situation, as compared to another model, it is important to first recognize the basic structure and operational technique of the individual model with regard to the type of available or economically-obtainable data. The connection between the model classification described in the previous section,' and the underlying modeling techniques discussed here, lies in the combinations of individual modeling 11 techniques, inherent in the various hydrologic models, which satisfy various class definitions. The underlying modeling techniques to be briefly described here are: Correlation analysis, partial system synthesis with linear analysis, and system synthesis. Other techniques used in various hydrologic modeling situations not pertinent to this research but to be included in future investigations include: Non-linear analysis (Amorocho, 1973), frequency analysis (Chow, 1964a), time-series analysis (Matalas, 1967; Kisiel, 1969), Monte Carlo simulation (Fiering and Jackson, 1971; Freeze, 1980) and Kriging (de Marsily, 1982). Delineation of modeling techniques in this manner is largely based upon the nomenclature of Amorocho and Hart (1964). 1.2.1 Correlation Analysis Correlation analysis explores different combinations of dependent variables to determine the combination that most closely approximates the output function in terms of the recorded input function. Along with other arbitrary parameters, the correlation-analysis technique describes the best linear prediction equation. Often hydrologic systems that are naturally non-linear can be transformed and explained by linear models. Yevdjevich (1964) discusses when and why data 12 transformations are necessary. Haan (1977) discusses many aspects of correlation analysis as related to its use in hydrologic modeling. Examples of correlation analysis are simple and multiple linear regression, multivariate statistical methods (Snyder, 1962; Wong, 1963; Wallis, 1965), and linear programing (Kolman and Beck, 1980). Diskin (1970) concludes that the regression equation can be interpreted in terms of a simple three-element conceptual model for annual rainfall-runoff relationships. However, many authors believe that the use of correlation analysis as a direct tool in hydrologic modeling leads to unwarranted generalizations (Haan, 1977). Amorocho and Hart (1964) note that a great deal of subjectivity underlies the process of selecting a best model and there is no assurance that the optimum model has been considered. Correlation analysis is used extensively in the estimation of model parameters for other techniques. Correlation analysis is a stochastic-empirical aproach in Clarke's classification scheme. 1.2.2 Partial System Synthesis with Linear Analysis Amorocho and Hart (1964) describe system analysis as a mathematical process used to define an input-output relationship, involving the use of measured input and output 13 data only, without any attempt to describe the internal mechanisms of the system in explicit form. System synthesis is defined by Amorocho and Hart as an attempt to describe the system operation of components whose presence is presumed to exist and whose functions are known and predictable. Analysis has the form of unique function while synthesis does not. The classical unit hydrograph (Sherman, 1932; Dooge, 1959) combines both synthesis and analysis as defined above into a technique that can be described as partial system synthesis with linear analysis. Rainfall excess and base flow separation functions combined with a linear convolution operation represent the unit hydrograph synthesis that is assumed equivalent to the operation of a watershed. Unit hydrograph theory can be summarized in six words: The system is linear and t ime-invar iant. The constrained linear system model proposed by Natale and Todini (1977) is another example of partial system synthesis with linear analysis. It relates effective precipitation to runoff for a time invariant linear system where constraints are placed on the parameters to be estimated. Partial system synthesis with linear analysis is either a deterministic-empirical or stochastic-empirical approach in Clarke's classification scheme, depending on whether there is a probability distribution associated with the parameters to be estimated. 14 1.2.3 System Synthesis Amorocho and Hart (1964) describe the process of system synthesis as beginning with the postulation of a more-or-less complex model, whose structure is based upon qualitative and semi-qualitative knowledge of phenomena involved in the hydrologic cycle. Depending upon the level of sophistication, systems synthesis can vary from a black-box model to a fully conceptual model. System synthesis can be subdivided into two levels of abstraction. These are physically-based models and quasi-physically-based models which are discussed below. Clarke's four major classification groups are represented by various combinations of the sytem-synthesis technique. 1 .2.3.1 Physically-Based Models In their blue print, Freeze and Harlan (1969a) assess the feasibility of developing a rigorous physically-based mathematical model of the complete hydrologic system. Freeze and Harlan describe a physically-based model of the time-dependent hydrologic processes as being represented by a set of partial differential equations interrelated by the concepts of continuity of mass and momentum. These equations along with the respective boundary conditions comprise the 15 boundary-value-problem that Freeze and Harlan call the hydrologic response model. In response models of this type, the movement of water through the hydrologic system is governed by the Saint Venant equations in the overland and channel flow phases and the Darcian equation of groundwater flow in the subsurface flow phase (Freeze and Harlan, 1969a; Freeze, 1974; Freeze, 1978). Stehale (1966) however, has argued that while the purpose of mechanics is to provide a complete description of systems occurring in nature, that in hydrology this has not been accomplished and may never be. To date, Stehale has been proven correct as no physically-based model of the type described above has ever proven successful in field applications on any reasonable scale (Woolhiser, 1973; Klemes, 1978). Klemes (1979) also discusses the reasons why a hydrologic model in the form of a component boundary value problem cannot be considered the ultimate model. 1 .2.3.2 Quasi-Physically-Based Models Physically-based models are usually made up of a set of coupled partial differential equations. Quasi-physically-based models on the other hand use solutions to these equations.as operating algorithims. Such a model is described by Engman 16 (1974). The mathematical function used to describe the soil infiltrability is Philip's (1969) two-parameter solution to Richard's general flow equation. The kinematic approximation to the complete flow equation is used for the overland-flow and channel-flow components and the Manning relationships are r assumed to hold (Brakensiek, 1966). The development of the kinematic form of the shallow-water equations is reviewed by Eagleson (1970). The kinematic approach does not have the same restrictive assumptions of linearity and time invariance seen in the unit hydrograph methods (Wooding, 1965; Kilber and Woolhiser, 1970). Quasi-physically-based models often have non-physically based components. Components are linked and keyed by some sort of trigger that may or may not have physical basis. In such models, mathematical approximations representing complex natural mechanisms convert precipitation into stream flow. The influence of these mathematical functions, defining the model algorithims, are dependent upon the magnitude of calibrated parameters within the equations. Once the model parameters have been calibrated, a fixed budgeting framework for prediction, exists. Uncertainties in this kind of synthesis are due to: Errors in recorded data, spatial distributions of parameters, imperfections in model structure and the non-uniqueness of the process. Freeze and Harlan (1969a) describe non-physically-based model components as storage elements and 17 transmission routes, connected in parallel and in series by a set of decision points. A pot and pipeline structure, illustrated in Figure 2, is a fitting description for the way these models represent the hydrologic cycle. Along with unit hydrographs, various combinations of reservoir routing, channel routing, infiltration, snowmelt and base flow component' techniques are used to explain complex natural mechanisms. Routing methods are reviewed by Chow (1959) and Henderson (1966). Table 1 lists a number of the digital system-synthesis event simulation models in use. Table 2 differentiates between the component techniques used in these models (Viessman et al., 1977). Table 3 lists the techniques described in section 1.2, as they are used, and classifies them according to input requirements, nature of variables, model structure, spatial and temporal response and use. 1.3 Space-time Tradeoffs Moss (1979) defines the space-time' tradeoff of hydrologic data collection as the ability to substitute spatial coverage for temporal extensions of records. Freeze (1982b) defines a time-space tradeoff as the relative increase in efficiency that can be achieved through a lengthening of records as opposed to 18 Figure 2. Flow chart illustrating the pot and pipeline structure of the Stanford Watershed Model IV (after Crawford and Lins ley, 1966) CODE NAME MODEL NAME HEC-1 HEC-1 Flood Hydrograph Package TR-20 Computer Program for Project Hydrology HYMO Hydrologic Model Computer Language SWMM Storm Water Management Model USGS USGS Rainfall - Runoff Model AGENCY/ORGANIZATION Army Corps of Engineers (1073) Soil Conservation Service (1074) Agricultural Research Service (Williams and Harm, 1073) Environmental Protection Agency (1071) Geological Survey (Carrigan. 1073) Table 1. Major rainfall-runoff event simulation models (after Viessman et al., 1977) 20 Model Code Names Modeled Components HEC-1 TR-20 USGS HYMO SWMM (Corps) (SCS) (USGS) (ARS) (EPA) Infiltration and Losses Holtan's equation Horton's equation Phillip's equation SCS curve number method Variable loss rate Standard capacity curves Unit Hydrograph Input Clark's Snyder's 2-parameter gamma response Dimensionless unit hydrograph River Routing Hydraulic Muskingum Tatum Straddle-stagger Modified Puis Working R&D Variable storage coefficient Convex method Translation only Reservoir Routing Storage-indication Base Flow Input Constant value Recession equation Snowmelt Routine X X X X X X X X X X Yes X X X X X X No X X X X X X No No No Table 2. Hydrologic processes and options used by major event simulation models (from Viessman et al., 1977) 1 MODELING TECHNIQUE INPUT REQUIREMENTS NATURE OF VARIABLES MODEL STRUCTURE SPATIAL RESPONSE TEMPORAL RESPONSE USE Streamflow Precipitation Watershed Parameters Stochastic Deterministic Empirical Conceptual Lumped Distributed Time -Invariant Time -Variant I - ? St •* m *i si5 Operational Forecast RAINFALL -RUNOFF MODEL8 Regression • • • • • • • UnH Hydrograph • • • • • • • • Quasi - Physically Baaed • • • • • • • • STREAMFLOW ROUTING Hydraulic Routing Using Open Channel Flow Equations • • • • • • Table 3. Characterization of selected rainfall-runoff modeling techniques (after Freeze, 1982a) 22 an increase in the density of measuring points. Most documented examples of the aforementioned tradeoff have been for a single precipitation data set using only one model. There is great promise for extending the space-time tradeoff idea across hydrologic data sets. This research underlies future work, by the author, which will address the possibility of improving hydrologic modeling efficiency by increasing geometrically distributed measurements of spatially-variable time-invariant watershed parameters on a one-time collection basis, and thereby, reducing the need for long continuous rainfall-runoff records. 1.4 Data-Worth and Model Choice The concept of data worth is married to cost-benefit analysis. Hence, increases in model efficiency due to improvements in the data aquisition network are subject to economical justification. Dooge (1972) states that the use of incorrect methods leads to either economic waste due to conservative factors of safety, or economic loss resulting from faulty predictions. Davis et al.(l979) define the value of additional data as the incremental increase in expected payoff or reduction in expected loss. 23 If time-space tradeoffs exists, the demands of increasing individual model efficiencies can be evaluated economically based upon the cost and delay of obtaining the required data. Depending upon the situation, certain modeling techniques and their corresponding data sets may be preferred. The worth of this data will be directly related to the size and cost of a project. Also, delays in a project to obtain additional data, for specific model efficiency requirements, will be characterized by a decreasing marginal utility. In this research,the stage is being set for an initial assessment of data-worth as indicated by the efficiencies of individual rainfa 11-runoff-modeling techniques as it relates to space-time tradeoffs. The data-worth concept as described here, along with adequate definition of the modeling problem, may become a basis for future model choice. A possible methodology for selection of a modeling technique that might be coupled with this type of data-worth assessment is shown in Figure 3. 1.5 Thesis Objective The correct choice of a hydrologic modeling technique is often less than obvious. Criteria are needed to facilitate such decisions. These criteria must be functions not only of the Define problem Choose class of model Select a particular model Calibrate the model for given data Evaluate model performance Use calibrated model for prediction Embed in general problem Figure 3. Possible methodology for selecting a rainfall-runoff modeling technique (after Dooge, 1978) 25 available models, but also the available data. Freeze (I982a,b) proposes that it may be possible to increase modeling efficiency by a tradeoff of longer rainfall and stream flow records against additional measurements of spatially variable-soils information. The testing of this hypothesis requires simulations across a suite of modeling approaches with a variety of data sets. The objective of the present research is to compare the efficiencies of various selected hydrologic modeling techniques on a limited suite of selected data sets. The scope of this work, in its initial phase as presented here, is limited to event-based rainfall-runoff modeling techniques. The selected techniques are linear and multiple regression, the unit hydrograph,and quasi-physically-based system synthesis. Selected rainfall-runoff events, at experimental subwatersheds in Oklahoma and Pennsylvania are used to determine individual model efficiencies. Comparison of model efficiencies for the aforementioned techniques may be useful in future assessment of space-time-tradeoff potential and to gain an initial indication of data worth. The two subwatersheds were chosen because each maintained instrumentation and measurement programs compatible with the data requirements of the three selected modeling techniques. If space-time tradeoffs across data sets have the potential to increase prediction efficiencies, then rainfall-runoff 26 modeling techniques and data collection networks can conceivably be selected for given design or operational specifications, based upon model efficiency and cost-benefit analysis. Such criteria would be useful to the applied hydrologist. 27 CHAPTER TWO MODELS AND COMPARISON In this chapter the three established underlying rainfall-runoff-rnodeling techniques employed in this study are fully described. The efficiency and comparison criterion used for model evaluation are presented. 2.1 Regress i on Models based on simple linear regression (SLR) with one independent variable, are commonly used in hydrology. A linear relationship of the form: Y=a+6X (2) is assumed between two variables X and Y, where X and Y are the independent and dependent variables respectively. A common example is for the independent variable to be precipitation and the dependent variable to be discharge. The regression line: Y=a+bX (3) approximates Equation 2, where a and b are estimates of a and 3 respectively. The coefficient b and constant a are 28 calculated from a set of data [X^, [Y ] with means X and Y as follows: b=£x.y./Ex? 11 1 (4) a=Y-bX ,_. (b) where, x . =X . -X 1 1  (6) yrVY (7This procedure of least squares is based upon minimizing the difference between the observed and predicted values: Z.e?=Z(Y.-Y.)2 1 1 1 (8) The deviation between an observed value Y and the value predicted Y from the regression model described by Equation 3, is represented by a residual error term. In order to determine if a regression line is the correct approach for a given set of data, some sort of evaluation is required. One approach is to determine how much of the variability in the dependent variable is explained by regression. The method commonly used is a ratio of the sum of squares due to regression and the sum of squares corrected for the mean, expressed as: 29 r2=E(Y.-Y)2/i:v? (9) The range of r2, which is known as the coefficient of determination, is between zero and one as hydrologic systems have positive correlation. When r2 is equal to one, the regression equation is providing perfect predictions and Ee =0. When r2 is equal to zero the regression line is explaining none s of the variation and E.e?=£y2. A SLR rainfall-runoff model could take any of the following forms: Va+bVPPT QpK=a+bPPT TQpK=a+bPPTD where, = predicted volume of runoff VppT = observed volume of rainfall QpK = predicted peak discharge (10) (11) (12) PPT = average observed rainfall intensity T * Q_.. = predicted time to peak discharge PPTp = observed duration of rainfall Multiple linear regression (MLR) rainfall-runoff models are possible with combinations of independent variables or when more than one rain gage is available. In MLR the dependent variable is a function of several independent variables and unknown 30 parameters expressed by: Y=B1X1+B2X2+-"+BpXp (13) where, 6 ,B2, • • •,Bp are the unknown parameters. The SLR model is a special case of the MLR model. In practice, there would be n observations of the dependent variable and n corresponding observations of each independent variable. Subsequently, there will be n equations and p unknown parameters, where n should be greater than or equal to the number of independent variables. In practice n should be at least three or four times as large as p. The matrices of these n equations are written: •~Yf Y2 — Y 8 n Xl,l Xl,2 '"' X1,P X2,l X2,2 '"• X2,P n, 1 Xn, 2 Xn, P Written in matrix notation: Y=8 X (14) Similar to the coefficient of determination seen in SLR, the multiple coefficient of determination is an evaluation of the usefulness of MLR for a given data set. Written in matrix notation, the multiple coefficient of determination is as 1 follows: 31 r 2=^TXTY-nY 2 / Y_TY-nY 2 (15) "X T T where, J3 ,_X ,Y are the transpose of JL>2L>X n is the size of the Y vector ~T x -1 T 1 =(X X) X Y The range of rf2 is from zero to one, the closer to one the better the fit. A correlation matrix should be computed before using the MLR technique to determine if a linear model can be used and what independent variables should be included. All the variables retained in a regression model should make a significant contribution. High correlation between two . variables does not always mean there is a cause-and-effect relationship though, as external forces can be involved. Regression coefficient inferences, extrapolation and confidence intervals for MLR, as well as SLR, are discussed by Hann (1977). Johnston (1963) discusses the underlying assumptions and technique of MLR analysis in detail. Multivariate regression analysis is used to predict more than one dependent quantity from the same set of independent variables. Wallis (1965) discusses six multivariate statistical methods used in hydrology including regression analysis. A MLR rainfall-runoff model has the following general form: Y=b1X1+b2X2+---+bMVa •32 where, Y = a predicted runoff variable Xi = an observed rainfall variable at gage i b± = calculated coefficients a = calculated constant A MLR rainfall-runoff model can have any of the general forms shown in Equations 10, 11, and 12 with more than one independent variable. In this study, the UBC Triangular Regression Package (TRP) is used for simple and multiple linear regression analysis. TRP calculated means, standard deviations, the correlation matrix of independent and dependent variable's, as well as the coefficients of determination, residuals, predicted values and confidence intervals for the desired regression equation. Illustrative examples from the implementation of the TRP algorithm are shown in the TRP description (Le and Tenisci, 1977). In a predictive mode SLR and MLR rainfall-runoff models require precipitation records in order to abstract various independent rainfall variables. The output produced from these models is in the form of runoff variables. 33 2.2 Unit Hydrograph The regression rainfall-runoff models just described only allow for the estimation of runoff variables such as volume and peak flow. Often a rainfall-runoff model is desired that predicts the form of the storm hydrograph. The unit hydrograph is such a model. Sherman (1932) defined the unit graph as follows: If a given one-day rainfall produces a one inch depth of runoff over the given drainage area, the hydrograph showing the rates at which runoff occurred can be considered a unit graph for that watershed. Sherman's unit graph is a dimensionless routing model that is roughly linear and of unit volume. The unit hydrograph theory having evolved from the unit graph method incorporates unit t ime. The unit hydrograph, despite being an approximate technique with many theoretical difficulties, has received considerable use by the hydrologic community, usually as a predictor of flood peaks. All unit hydrographs are based on the following two principles (Dooge, 1959): 1) Invariance-the hydrograph of surface runoff from a catchment due to a given pattern of rainfall excess is invariable. 2)Superposition-the hydrograph resulting from a given pattern of rainfall excess can be built by superimpositing the unit hydrographs due to the separate amounts of rainfall excess occurring in each period. This 34 includes the principle of proportionality, by which the ordinates of the hydrograph are proportional to the volume of rainfall excess. Dooge (1973) clearly states the implications of the linear assumptions in the unit hydrograph theory. Implicit to its linear assumption, the development of a unit hydrograph requires simultaneous data of excess rainfall and storm flow. Excess rainfall is defined here as total rainfall minus infiltration. Storm flow is defined as total runoff minus base flow. Base flow is generally accounted for by normal day-to-day groundwater contributions to stream flow. Excess rainfall and storm flow volumes for a selected event are equal. Various base flow separation techniques used to estimate storm flow volumes are discussed by Viessman et al. (1977) and Dunne and Leopold (1978). The Soil Conservation Service curve number methodology, with empirical ratings based on soils and vegetation (U.S. Soil Conservation Service, 1972), is one method of establishing excess rainfall values. Other methods include the antecendent precipitation index (Viessman et al., 1977),the <j> and the W indices (Schultz, 1976). Generally, the assumptions about uniform rainfall distribution are not met and variation in unit hydrograph ordinates for different storms should be expected. Averaging independently derived unit hydrographs is discussed by Linsley et al.d 975). Linsley et al.(1975), Viessman et al.d 977), and 35 Dunne and Leopold (1978) all show examples of unit hydrograph derivations. Figure 4 shows a flow chart of the basic operations involved in the unit hydrograph procedure. An illustration of matrix methods used to define the unit hydrograph is presented in Viessman et al.(l977). Calculation of a design storm hydrograph is graphically demonstrated for a three period storm in Figure 5. In matrix notation the storm hydrograph is given by: ^ (,7) where, Q_ = the existing storm hydrograph vector P = known excess rainfall matrix U = the unit hydrograph vector The reverse of the process shown in Figure 5 is the basis of the matrix method. Subject to the restrictions of matrix algebra the solution for the unit hydrograph matrix becomes: T -IT u=CP P) P o -~ (18) Reproduction of initial storm hydrographs based on matrix methods are generally not exact. Adjustments are usually made by reducing the square of the errors. Matrix methods are discussed by Snyder (1955), Newton and Vinyard (1967) and Morel-Seytoux (1982). The instantaneous unit hydrograph (IUH), traced to Clark (1945) is the hydrograph of one inch runoff spread uniformly ABBREVIATIONS R.E = RAINFALL EXCESS INF. t INFILTRATION SR « STORM RUNOFF BF. « BASE FLOW ANALYSIS TIME Figure 4. Flow chart of the operations involved in the unit hydrograph technique (from Amorocho and Hart, 1964) 37 Figure 5. Determination of a design storm hydrograph: (a) Excess rainfall, (b) unit hydrograph, and (c) surface runoff hydrograph (from Viessman et al., 1977) 38 over an area generated in an infinitesimal time period. Mathematically, the IUH is the kernal function in the convolution relationship for a lumped linear time invariant causal system. The convolution integral has the following form: to y(t)=/ X(X)h(t-A)dA 0 (19) where, y(t) = storm runoff hydrograph x(A) = excess rainfall hyetograph h(t~A) = unit hydrograph Figure 6 shows the input, output and kernal functions. Quimpo (1973) and Freeze (1982a) discuss the linkage of IUH and autoregressive stream flow models. The equation of continuity for any reservoir can be written as: p-q=ds/dt (20) where, p = inflow q = outflow s = outflow storage A linear reservoir is one in which the outflow is a linear function of the storage: q=ks (21 ) where k is a watershed parameter. Combining equations 20 and 21 leads to the differential equation: 39 X(A) EXCESS RAINFALL HYETOGRAPH - t h htoH i " INSTANTANEOUS UNIT HYDROGRAPH h(t -A) H Figure 6. Instantaneous unit hydrograph: (a) input function, (b) kernel function, and output function (after Chow, 1964b) 40 (dq/dt)+kq=kp (22) The solution to this equation for the initial condition q=0 at t=0 is: q(t)=/t ke"k(t_X)p(A)dA 0 (23) Equations 19 and 23 are equivalent when h(t)=(l/K)e"t/K (24) where K = 1/k. Using Equation 24 as the IUH and Equation 19 as a rainfall-runoff predictor is equivalent to considering a watershed as a single linear reservoir. A conceptual model of the IUH described by Nash (1959) is shown in Figure 7. "Nash proposed routing instantaneous rainfall through a series of successive linear reservoirs. For n linear resevoirs the IUH becomes: h(t)=(l/kr(n))(t/K)n"1e"t/K , x (25) where r (n) is the nth order gamma function. The approach here is linear as K is a constant that can be evaluated by the method of moments. The calculation of unit hydrographs for experimental subwatersheds in this study was carried out with the computer program UNIT, which uses a matrix method employing optimization techniques, authored by Morel-Seytoux and Kimzey (1980). From the theory of linear systems, the instantaneous storm flow rate Figure 7. Nash's model for routing instantaneous rainfall through a series of linear storage resevoirs (after Chow, 1964b) 42 at the end of period n is given by the discrete equivalent to Equation 19: n _ q(n)=Z 6(n-j+l)r(j) , v j-1 (26) where, ^(m) = nth ordinate of the unit hydrograph r(j) = mean excess rainfall rate during period j Following the development of Morel-Seytoux and Kimzey (1980), the normal equations used in the equality-constrained least square method of UNIT are summarized in Table 4. The resulting system of linear equations is solved by gaussion elimination. The first M solutions are the desired unit hydrograph. The UNIT code, or more specifically the technique it uses, is a practical choice for determining unit hydrographs in this study. Computer solution greatly reduces the computational time relative to hand calculation methods. The IUH method requires rainfall patterns to be known as continuous functions, which they rarely are. A listing of the UNIT code is given in Appendix A. Illustrative examples and hand computations verifying the UNIT program are found in the users manual (Morel-Seytoux and Kimzey, 1980). To employ UNIT, excess rainfall and storm flow must be determined for selected events. The $ index method of calculating excess rainfall is used in both experimental subwatersheds. The * index is defined as the amount of rainfall that is retained by the basin divided by the duration of the M+1 I a. .x. = b. i = 1,2,...,M + 1 j=l 1J J 1 where the a^ and b^ are given by the formulae: N as-i = I r(n-i+l)r(n-j+l) for i = 1,-2 M n=j and j = 1,2,... ,M but with j > i For j < i = a^. (symmetry) i = 1,2 M ai,M+l = \ 1 = 1.2,---.M aM+l,j = 1 j = 1,2M aM+l,M+1 = 0 N b = ^/7(n-l+l)q(n) i = 1.2.....M 1 n=l bM+l = 1 -The prime indicates that the indices corresponding to periods with missing runoff are skipped in the summation. These equations guarantee that the discrete kernels add up to one but do not guarantee nonnegativity for them. Table 4. Normal equations for the equality-constrained least squares technique used in the computer program UNIT (after Morel-Seytoux and Kimzey, 1980) 44 storm (Dunne and Leopold, 1978). The $ index provides a means of replacing the time varying infiltration function by an average value. When data are insufficient to derive an infiltration curve, the <J> index is often used. The <t> index method is illustrated in Figure 8. Storm flow is determined by separating base flow from the total observed hydrograph.. Only one of the experimental subwatersheds considered in this study experiences base flow separation. The criteria used for separation in this study is the simple but objective technique described by Engman (1974). The procedure is illustrated in Figure 9, and in effect shows that no surface runoff is contributing to the hydrograph after . the intersection of the base flow separation line and the hydrograph recession. The value of the slope a is chosen by analyzing several hydrographs from a study area with a subjective decision as to where the most rapid change in the recession curve occurs on the average. The o index determined from a single storm is not generally applicable to other storms and therefore not considered a basin constant in this study. The slope a used for base flow separation is considered a basin constant in this study serving as a lynchpin between storm flow and calculated excess rainfall. In its predictive mode the unit hydrograph requires mean values of excess rainfall for unit periods as input and produces output in the form of a storm flow hydrograph. HYETOGRAPH O < cr 5 10 -15 ~ 20 -25 -30 -35 TIME (hours) 2 _L 4 5 I I 6 INFILTRATION EXCESS RAINFALL (storm flow) ure 8. $ index method of calculating excess rainfa 46 Figure 9. Base flow separation technique (after Engman, 1974) 47 2.3 Quasi-Physically-Based Quasi-physically-based-rainfall-runoff models attempt to approximate the physical processes occurring within the hydrologic cycle illustrated in Figure 10. Many authors have attempted to describe the component mechanisms responsible for runoff. Rainfall-runoff processes are reviewed by Kirkby (1978) and Freeze (1974). A number of rainfall-runoff simulation models have been proposed to explain watershed physics. Common to all is the problem of accounting for natural watershed variability in terms of necessary input data as well as boundary and initial conditions. The model chosen for use in this study (Engman, 1974) is based on partial area concepts (Betson, 1964) and emphasizes transformation of a natural heterogeneous system into a corresponding distributed system compatible with computer simulation. Hereafter, Engman's quasi-physically-based rainfall runoff modeling technique will be referred to as a distributed model. Based on a dynamic watershed approach, illustrated in Figure 11, the distributed model may be divided into three parts (Engman and Rogowski, 1974a). The first part describes a physically based soil infiltrability calculation for developing the precipitation excess. The next two parts deal with kinematic routing phases: One for developing a lateral inflow System inflow System outflow 1'recipitation Kvnporalion I R;im Sleet ll:iil Snow Inlen cplion Depression storage Snow ;Ki'inntil.ition ami melt Wale laml surl 1 •t on I (Keilaiul How urlaee | Dneel nmoll Infiltration System oul flow __J Root /.OI1C storaee l-vapotranspiration I ( hannel flow I. Diversions System ontllow ( hannel secpar.i Imported (iioiindwater water inflow } -f System inllow System inflow —Intcrllnw A iV.Tul.ihnii —M I < iioiimtwatei storage J Kesc rvoir storage Water alloeatiims System outflow (iroumlwalcr I low System outflow Figure 10. Systems representation of hydrologic cycle (from Viessman et al., 1977) 00 BEPORI PRECIPITATION Figure 11. Schematic diagram of a dynamic watershed (from Engman, 1974) 50 hydrograph from the overland flow plane and one for routing the channel hydrograph. The model does not address possible origins of runoff other than those caused by the rainfall intensity exceeding the infiltration capacity. Application of the model is therefore limited to the prediction of the storm flow hydrograph from areas contributing overland flow without consideration of. subsurface storm flow to the stream, direct groundwater discharge to the stream, or the evapotranspirat ion component mechanisms. A flow chart of the simulation model is shown in Figure 12. The first computational step of the distributed model involves calculation of pertinent infiltration capacity and excess rainfall, as functions of time for the different soil series composing the watershed. The model simulates a two layer system. This step is based on Richard's (1931) one-dimensional infiltration equation for a unsaturated-saturated system: (3/3z){K(i|0 (Oi|i/3z) + l) }=C(^) 3^/9t where, t = time z = vertical distance from the soil surface downward ty = pressure head R(ty),C{ty) are unsaturated functional relationships for hydraulic conductivity and specific moisture respectively. Analytic and numeric solutions for one-dimensional infiltration boundary value problems are discussed by Philip (1957a,b,c,d,e, f Read in watershed \ ( geometry and W V depression storage J Read in break point precipitation data from raingage or simulated event Calculate precii for each soil ty chosen initial s citation excess 'pe for the oil moisture Subtract depression storage until all depressions are filled and assign a depth of water for routing to each soil zone Route overland flow to calculate lateral inflow hydrograph -includes infiltration where capacity is available Route lateral inflow hydrographs in proper downstream sequence Outflow hydrograph Figure 12. Flow chart for distributed model code (after Engman, 1974) 52 1958a,b) and Freeze (1969b) respectively. In the model, infiltration capacity is described by Philip's (1969) two-parameter infiltration equation: i=%St 2+A where, i = infiltration rate S = Sorptivity A is a constant that is approximated by 1/2 the saturated hydraulic conductivity Sorptivity values are computed from Parlange's (1972) approximation: S = {2/ (6-e0)Ddc1"2 where, 6 = volumetric soil water content 6i = soil water content of soil surface So = initial soil water content D = soil water diffusivity The soil water diffusivity is described by: D=K(6) (dij>/de) (28) l 60 (29) (30) where K is hydraulic conductivity. The unsaturated characteristic curves of hydraulic conductivity and soil water pressure head as a function of soil water content are computed using modified models proposed by Rogowski (1971, 1972a,c,d) and Parlange (1972). 53 The input required for the first step of the distributed model is: 1) antecendent soil moisture for each soil, 2) the degree of saturation for each soil, 3)hydraulic conductivity at air entry for each soil, 4) sorptivity values for each soil, 5) the initial infiltration rate for each soil. The input required to determine soil characteristic curves with the methods described by Rogowski (1971, 1972a,c,d) and Parlange (1972) is: 1) the porosity of each soil, 2) soil moisture at 1.5 MPa for each soil, 3) the air entry value for each soil, 4) the water entry value of each soil, and 5) the hydraulic conductivity of each soil at air entry. The second step of the distributed model routes excess surface water from contributing areas to the stream taking into account detention storage and reinfiltration. Flow of water over a surface or in a channel is described by two differential equations based on the following assumptions (Chow, 1959): 1) velocity at any section is uniform and unidirectional, 2) channel slope is small, 3) streamline curvatures are small, 4) energy losses are represented by the slope of the energy gradient times the length of the channel reach. The continuity equation, based on the conservation of mass, is expressed as: A(3V/3X)+V(3A/3X)+3A/3t=q The momentum equation, based on the concept that the sum of 54 forces acting on an element of water is equal, is expressed as: S.-S =(l/g){(3V/3t)+V(3V/3X) + (g/A)(3(Ay")/3X)+Vq/A} , % 0 t (32) where, A = cross sectional area of water V = average velocity X = horizontal distance y = depth of water to centroid of volume SQ = bed slope of channel Sf = friction slope t = time g = acceleration of gravity cf = source term Equations 31 and 32, which are known as the, Saint Venant or shallow water equations, mathematically describe the propogation of a wave and cannot be solved in closed form for practical situations. (Ligget and Woolhiser, 1967; Strelkoff, 1969, 1970). Kinematic approximations to the complete flow equations are used to simulate the overland flow hydrograph that results from rainfall excess. The kinematic equations take the form of first order differential equations, computationally much simpler than the complete hyperbolic shallow water equations. Kinematic routing has been analyzed by Kibler and Woolhiser (1970), Overton and Brakensiek (1970), and Smith and Woolhiser (1971). Kinematic flow occurs on a plane whenever a balance between 55 gravitational and frictional forces is achieved. Under these conditions Equation 32 reduces to S = S . S is defined by a M Off stage discharge relationship. In their kinematic forms the equations of motion and continuity are given respectively by: Q=Qn (33) (9Q/SX)+9y/at=q (34where, Q = discharge Q = normal discharge n y = depth of water q = source term = precipitation excess, P E Turbulent flow is assumed in the distributed model, therefore Equation 33 is written in form: Q-Cl.O/iOy1'66^ (35) where n is Manning's roughness coefficient. The continuity equation in finite difference form is: E (36) CAQ/AX)+Ay/At=P Rewriting equation 36 in terms of the change in water depth: Ay=(.(AQ/AX)-PE)At . {37) Equation 37 is solved numerically by explicit finite difference methods. For a discussion of the stability of the explicit 56 method, parameter fitting and component verification of the surface water routing algorithm the reader is directed to Engman (1974). The input requirements for the second step include: 1) a three-dimensional soil distribution of the watershed, 2) soil slopes, 3) depression storage, 4) Manning's n roughness values for overland flow, 5) average water surface widths, and 6) channel reach lengths. In the third and final step of the distributed model surface runoff hydrographs become lateral inflow for channel routing. A kinematic flood routing program developed by Brakensiek (1966a) is used to synthesize the channel hydrograph in any given reach of a stream. The method is identical to that employed in step two, except that flow in a rectangular open channel is considered rather than flow across a plane. The formulation of kinematic flood routing is composed of the continuity equation: (8Q/3X)+3A/8t=q (38) The source term q is now the lateral inflow to the stream determined as output from the step-two simulation of overland flow. The equation of motion is now in the form of a rating function: Q=Q(A) (39) 57 Utilizing an algorithm developed by Brakensiek (1966b) a rating function is developed for each channel cross section so that: AQ=f (AA) (40) Normal (turbulent ) flow is assumed so that: qn=(1.0/„>R°-6^ (41) where R is the hydraulic radius of the channel (area/wetted perimeter). Simultaneous solutions of Equation 40 and the finite difference approximation of Equation 38 requires an iterative procedure. The numerical technique used is the method of false position (Kunz, 1957). Brakensiek (1967) reviews the application of the kinematic technique in flood routing. As described by Engman (1974) Brakensiek1s (1966a) flood routing program takes the upstream inflow hydrograph for any given reach, adds the lateral inflow hydrograph for that reach, and routes the two together to form the outflow hydrograph from the reach. This calculated outflow hydrograph becomes the inflow hydrograph for the next reach. Tributaries are treated as lateral inflow hydrographs over a very short reach. Dummy sections are used above and below short tributary sections to smooth the averaging done in the numerical solution. The simulation philosophy of the distributed model proposed by Engman (1974), as described here, is that of a conceptually sound model that does not depend upon the calibration of 58 watershed parameters with historical records. The selection of watershed parameters should be made on the basis of simple field measurements and values available in the literature. The input required for the third step is: 1) channel reach lengths, 2) Manning's n roughness values for open channel flow, and 3) a' normal flow rating function. The inputs required for the program used to develop the channel rating functions (Brakensiek, 1966b) are: 1) channel bed slopes, 2) Manning's n roughness values for open channel flow, and 3) channel cross section geometry. Listings of the four codes that define the distributed rainfall-runoff technique are found in Appendix B. Each of these codes was verified with the example output contained in the source documentation. 2.4 Model Ef f ic iency The model-calibration process is made up of calibration, verification, and prediction time periods (Freeze, 1982b). In the calibration period, model parameters are estimated on the basis of available rainfall-runoff records. During the verification period, the calibrated model is applied to the available rainfall records and computed runoff values are compared with the observed records in order to assess the predictive efficiency of the model. If the efficiency is 59 adequate, the model can then be used for runoff prediction in the prediction period. The input data requirements for the techniques described in the previous section, relative to the calibration process, are summarized in Table 5. The verification procedure, proposed by Nash and Sutcliffe (1970), is used in this study to compare relative model efficiencies. The efficiency (analogous to the coefficient of determination) of a given modeling technique is defined by: ? ? ? 2 R =(F0-F )/F0 (42) where the residual variance F and initial variance F are 0 defined as follows: F2=X(q'-q)2 (43) 2 — 2 Fj=I(q-q)Z (44) where, q = observed runoff variable q' = computed runoff variable q = mean of observed runoff variables Based on this sum of squares criterion, maximum model efficiency 2 is achieved by maximizing R . The maximum value for model efficiency is one. This value would be reached only if the observed and computed runoff variables were identical. A negative efficiency infers that the model's predicted value is worse than simply using the observed mean. DISTRIBUTED MODEL* INPUT REQUIREMENT REGRESSION UNIT HYDROGRAPH 80IL CHARACTERISTICS OVERLAND FLOW ROUTING CHANNEL RATING FUNCTION OPEN CHANNEL ROUTING Rainfall CVP P Excess Rainfall CVP Runoff CV Baseflow CVP Stormflow CV Porosity P Soil Moisture 1.5 MPa P Antecedent Soil Moisture P Soil Moisture Frequency P Degree of Saturation P Pressure Air Entry P Pressure Water Entry P Hydraulic Conductivity, Air Entry P P Sorptivity P Initial Infiltration Rate P 3-D Soil Distribution P Depression Storage P Soil Slope P Manning n, Overland P Manning n, Channel • P P Average Water Surface Width P Channel Length P P Channel Bed Slope P Channel Geometry P Normal Flow Ratings P Tolerance Levels P P Time Step P P P 60 C - Calibration mode V - Verification mode P - Prediction mode • - Ungaged basin Table 5. Input requirements for selected modeling techniques relative to the calibration process / 61 CHAPTER THREE DATA SOURCES AND EVENT SELECTION In this chapter, the two experimental subwatersheds chosen for this study are described and the available data from each are discussed. The criteria used for selecting rainfall-runoff events are also presented. The selection of study areas for this research was restricted to North American experimental subwatersheds. It is felt by the author that the evaluation of rainfall-runoff modeling techniques must begin at the hillslope or subwatershed scale and progress to larger basin scales only after understanding the smaller scale. The experimental subwatershed data bases described here are used to compare the efficiencies of the selected modeling techniques described in Chapter Two. In order for an experimental subwatershed to be selected for this study, available records from the basin instrumentation program and data collection network had to be compatible with the input requirements of each underlying rainfall-runoff modeling technique being evaluated. Another limitation placed upon basin selection is that runoff not be generated from snowmelt. Scientists at three Canadian experimental subwatersheds and ten experimental subwatersheds located in the United States were contacted to find data sets, that included: 1 )' precipitation and 62 stream flow records inclusive enough to allow abstraction of selected rainfall-runoff events, 2) soil surveys, 3) sufficient soil moisture measurements to allow for the estimates of antecedent soil water conditions for each selected runoff event, and 4) measurements of spatially variable, physically based parameters, including the characteristic curves of hydraulic conductivity and moisture content as functions of pressure head. The experimental subwatersheds contacted range in area from 2 2 80,000 M to 10.4 KM . All thirteen subwatersheds have adequate rainfall-runoff data. Three otherwise acceptable data sets were eliminated becouse snowmelt was the principal source of runoff. The most restrictive data requirement, however turned out to be the measurement of spatially variable physical parameters, the lack of which eliminated seven more basins. One of the three selected data sets, from a 132,000 M2 subwatershed located in the Hubbard Brook Experimental Forest, New Hampshire, is not used in this study due to the necessity for considerable data reduction. This precious data set was obtained with the generous cooperation of the Northeastern Forest Experiment Station, Durham, N. H., (Federer, personal communication, 1982) and will certainly be included in future research. The first of two subwatersheds used in this study is within 2 the 420 KM Mahantango Creek Watershed located in east-central Pennsylvania. The Agricultural Research Service CARS) of the ) 63 .United States Department of Agricultural (USDA) has a number of Watershed Research Centers throughout the United States. The Mahantango Creek Watershed, described by Pionke and Weaver (1977), is the research watershed for the Northeast Watershed Research Center (NWRC) of the ARS. Data collection programs at NWRC, and within the ARS in general, have been designed to facilitate specific research projects within the general areas of rainfall-runoff relationships, hydrology-water quality interactions, and mathematical modeling of hydrologic processes (Engman et al., 1971; Engman et al., 1974; Rogowski et al., 1974; Henninger et al., 1976; Gburek, 1977). The subwatershed data set, from the Mahantango Creek Watershed, used in this study was obtained from NWRC, University Park, Pa. (Gburek, personal communication, 1982). The second subwatershed used in this study is within the ARS Southern Great Plains Research Watershed. A number of experimental watersheds are located near Chickasha, Oklahoma. The subwatershed chosen was recommended to the author, while inquiring about another facility, as meeting the data requirements of this study (Luxmoore, personal communication, 1981). The data set itself was obtained from the ARS at Chickasha (Gander, personal communication, 1981). The two experimental data sets used in this work are described in the following sections. 64 3.1 Mahantango Creek Subwatershed 2 The 7.2 KM Mahantango Creek Subwatershed (MCW) shown in Figure 13 is located in the ridge and valley region near Klingerstown, Pennsylvania. The characteristic physiographic features of this region are long mountain ridges of fairly uniform elevation cut at intervals by water gaps. The major land uses are permanent pasture and cultivated fields. Precipitation and stream flow records in break point form, covering the six year period 1971 through 1976, are used in this study. The locations of two rain gages and a dual notch weir with water level recorder, making up the continuous rainfall-runoff monitoring network, are shown in Figure 13. Carr (1973) describes the gages, the gage network and the data reduction procedure used. Texturally, the soils are classified as shaly silt loams. The spatial distribution of soil type and the variation in land slopes are shown in Figure 14. Average topsoil and subsoil depth are listed in Table 6. Moisture characteristic, hydraulic conductivity, and soil water diffusivity curves for the modeled soils shown in Figure 14 were constructed using input parameters similar to the averaged values shown in Table 7. These parameters were either abstracted or estimated from the available literature (Engman and Rogowski, 1974a). Engman and Rogowski (1974b) discuss the selection of soil moisture 65 Datum It ••• toval Figure 13. Mahantango Creek Subwatershed (Gburek, personal communication, 1982) Figure 14. Spatial variation of soil type and land slope within the Mahantango Subwatershed (Gburek, personal communication, 1982) SOIL NUMBER SOIL NAME DEPTH (m) TOPSOIL SUBSOIL 149 KKnesville .23 .46 145 Berks .23 .64 166 Calvin .20 .71 66 Leek Kill .20 .71 54 Hartleton .23 .76 71 Albrights .23 .52 69 Meckensville .23 .61 57 Alvira .23 .76 Table 6. Average soil depths within the Mahantango Creek Subwatershed (abstracted from Engman, 19 68 SOIL NUMBER SOIL NAME K.nlO4 (M/S) 01.5 (PERCENT BY VOLUME) 149 Klinesvlfle 3.0 47 38 11 145 Berks 3.0 47 38 11 166 Calvin 2.19 47 38 11 66 Leek Kid 2.19 37 30 12 54 Hartteton 1.6 42 34 12 71 Albrights .64 43 34 14 69 Meckensvllle .64 39 31 18 57 Alvira .64 38 30 15 Ke - Averaged values of hydraulic conductivity at air entry (T^ 0o - Total pore space Be - Soil water content at air entry 6A 5- Soilwater content at 1.5 MPa <Pe'- Estimated as 60 mm of water i Table 7. Soil characteristic parameters for the Mahantango Creek Subwatershed (after Engman and Rogowski, 1974a) 69 parameters. The locations of a very limited amount of soil moisture data obtained for this study are shown in Figure 13. These data were measured by the neutron scattering method over a five year period. However, records of soil moisture proved to be inadequate for affixing initial conditions for each selected rainfall-runoff event. In order to estimate antecedent soil water contents for topsoil and subsoil layers, soil water frequency distributions similar to the ones shown in Figure 15 were used. The general approach to the seasonal soil water frequency distribution is outlined by Rogowski (I972bc). The employed distributions were developed with Henninger's (1972) soil moisture data, gathered in 1971. These data are summarized in Figure 16. The general assumption made in using these distributions is that the same or very similar soil moisture conditions will apply in any given year. Except for two events, no measurement of antecedent soil moisture was available. Therefore, initial conditions for the respective soils were set at their 50% probability level. For the two events in which measurements of soil moisture roughly coincide with the start of rainfall, the frequency of measured soil moisture associated with the most obvious source area was used for all other soils to estimate initial conditions. The most obvious source area is taken as the soil with the lowest hydraulic conductivity: Alvira silt loam in Figure 14. Table 8 summarizes the antecedent soil •1.0 H H- 0-8 i Z LU Z 0.7 i o o LU .H < 0.5 O 0.4 H (0 LU > 0.3 H < Qj 0.2 H OC 0.1 H #57 #71 #66 #54 #145 #149 #166 JULY. "T—i 1 r 0.1 10 50 90 PROBABILITY (%) 99 99.9 Figure 15. Example soil water frequency distributions (after Engman and Rogowski, 1974a) HARTLETON KLINESVILLE LECK KILL , 1 1 1 1 -j June July August Sept. October Nov. MONTHS Soil moisture for 1971 within the Mahantango Creek Subwatershed (after Henninger, 1972) ANTECEDENT SOIL WATER CONTENT* 80IL NO. SOIL NAME SOIL LAYER MCW R-5 149 Itijnesville T S .225 .225 145 Berks T S .225 .225 166 Calvin T S .237 .237 66 Leek Hill T S .237 .237 54 Hartleton T S .229 .229 71 Albrights T S .258 .258 69 Meckensville T S .278 .278 57 Alvira T S .278 .278 1 Kingfisher T S .218 .245 2 Grant T S .218 .245 3 Renfrow T S .218 .245 T - Topsoil ) S - Subsoil • - Initial soil moisture m8 water/m3 soil Table 8. Antecedent soil water contents for the Mahantango Creek Subwatershed and the R-5 Subwatershed 73 water contents for MCW soils, at their 50% probability levels. Huggins and Monke (1966) and Hiemstra (1968) propose that depression storage (Viessman et al., 1977) is a watershed constant for a given pattern of land use. Figure 17 illustrates the estimation of depression storage as a function of land slope and use as described by Hiemstra (1968). The average total depression storage for MCW is taken as 4 mm of water (Engman and Rogowski, 1974a ) . Values of Manning's n of 0.35 and 0.05, for overland and channel flow respectively, are assumed (Engman, 1974). Engman determined the n value for the overland flow portion of the hydrograph by fitting Izzard's (1946) data for a sloping turf plane. The n value for channel flow was chosen by handbook procedures and verified with field measurements. Channel geometry was taken as prismatic triangular. Figure 18 shows the assumed channel cross section. The average water surface width is taken to be 3.0 M. Channel slopes were abstracted from topographic contour maps. The base flow separation slope a , shown on Figure 9, is taken as 1 . 28* 1 0~4 M 3/Sec 2, based on the 1 . 79* 1 0~5 M3/Sec 2-KM Z relationship illustrated in Figure 19, that was established by Engman (1974) for the Mahantango Creek Watershed. 74 Figure 17. Depression storage as a function of land slope and use (after Hiemstra, 1968) < 1 1 10 100 1000 X m MAHANTANGO CREEK BASIN AREAS (km2) Figure 19. Base flow separation relationship for the Mahantango Creek Watershed (after Engman, 1974) 77 3.2 R-5 Subwatershed 2 The 96,000 M R-5 subwatershed (R-5), shown in Figure 20, is located in rolling prairie grassland terrain in the Washita river valley, near Chickasha, Oklahoma. R-5 has been subjected to continuous well-managed grazing of beef cattle (Sharma et al., 1980). Precipitation and stream flow records in break point form covering the eight-year period 1967 through 1974, are used in this study. Locations of the continuous recording rain gage and weir used in this study are shown in Figure 21. Soil types and surface contours for R-5 are shown in Figure 20. Approximately 51% of the area is Renfrow silt loam, 43% Grant silt loam, and 6% Kingfisher silt loam (Sharma et al., 1980). Topsoil and subsoil depths are shown in Table 9. There is an overall gentle land slope of about 3%. Parameters used to construct soil characteristic curves are shown in Table 9. These data are taken from the reference soil parameters described by Luxmoore and Sharma (1980). Water retention and hydraulic conductivity data are discussed by Sharma and Luxmoore (1979) and Luxmoore and Sharma (1980). Based on standard statistical tests, no difference can be shown between the three soils (Sharma and Luxmoore, 1979). The locations of soil moisture data, for topsoil and subsoil layers, from neutron scattering measurements are shown LEGEND |H Grant silt loam | | Renfrow silt loam IH Kingfisher silt loam Scale: 1cm = 12m Area: 96.000m2 Contour interval: 4 ft. Datum Is eea level Figure 20. R-5 Subwatershed (Gander, personal communication, 1981) 79 SOIL SOIL NAME LAYER Ke*104 Oo #1.5 DEPTH NUMBER (M/S) (PERCENT BY VOLUME) (m) 1 Kingfisher Silt Loam T S 1.86 .31 44 44.3 39.6 39.9 9 14.8 .2 .8 2 Grant Silt Loam T S 1.88 .31 44 44.3 39.6 39.9 9 14.8 .2 1.30 3 Renfrow Silt Loam T S 1.86 .31 44 44.3 39.6 39.9 9 14.3 .2 1.30 T - Topsoil S - Subsoil Ke- Estimated as 1/2K saturated 0e - Estimated as 0.9f?0 (Rogowski, 1972b) Table 9. Characteristic parameters and depths for R-5 Subwatershed soils 81 in Figure 21. These data represent measurements taken at 34 sites over a four year period and averaged values from a separate four year period. Antecedent soil water contents for R-5 were estimated as the means of all measured values, taken from the two layers previously described, for the same six month period used in event selection. Assuming soil water content to be normally distributed (Rogowski, 1972b), this mean value is the same as the 50% frequency utilized at MCW. Table 8 summarizes the antecedent soil water contents used for R-5 soils. Depression storage for R-5 is estimated, from Figure 17, as 10 mm. Manning n Values are taken as 0.35 for overland flow (Engman, 1974) and 0.2 for channel flow (Luxmoore and Sharma, 1980). Channel geometry is taken as prismatic triangular. The average water surface width is assumed to be 1.5 M. The channel slope is constant at 2%. No base flow separation is considered as observed hydrographs exhibit a flashy response with little or no base flow (Luxmoore and Sharma, 1980). 3.3 Event Selection In this section the criteria used for selecting individual rainfall-runoff events from the MCW and R-5 data sets are discussed. These selected rainfall-runoff events are simulated 82 in Chapter Four, using the underlying modeling techniques described in Chapter Two. The observed events are used to compare the efficiencies of the individual models in Chapter Four. Events were selected on the following basis: 1) Only events that show an obvious cause-and-effect rainfall-runoff relationship were chosen. 2) Only storms of simple structure were considered. 3) Only events occurring in the six month period April through September were considered, to avoid runoff due to snowmelt. 4) The duration of an individual rainfall event was restricted to a maximum of ten hours. The duration of a runoff event was taken from the start of the rainfall event until runoff had subsided to the prestorm rate. Both base flow separation and/or another rainfall event occurring in the tail of the hydrograph shorten this period. 5) An attempt was made to select storms that maintained a uniform intensity throughout the period of rainfall. The assumption was made that rainfall was uniformly distributed over the entire subwatershed. Simple arithmetic averages were used when the rainfall record for an event was available from two gages. 6) Only precipitation and stream flow records showing error free data were considered in the selection of an event, with no attempt to adjust records based on available error codes. Nine events were selected from the R-5 data base. Twenty-one events, six of which have rainfall at two gages, were 83 selected from the MCW data base. The selected rainfall-runoff events and their characteristics are summarized in Table 10. EVENT NO. VPPT PPT PPTD VQ QPK V QPK* TQPK 1 2804. 11.43 2.58 429. .11 .51 2 6071. 7.37 8.65 1958. .58 1.56 3 4170. 7.37 5.83 1367. .48 5.19 4 7510. 18.29 4.28 1002. .26 1.65 R-5 5 7754. 32.26 2.51 408. .17 1.54 10 8778. 63.50 1.44 4378. 1.79 .51 12 3146. 17.02 1.92 1601. .51 2.03 14 4779 . 7.87 6.25 974. .22 2.95 15 2780. 2.79 10.16 626. .09 10.40 3 201865. 30.73 .91 6476. .78 2346. .77 1. 33 4 73405. 7.62 1.33 19465. .56 1631. .40 2.25 15 128460. 5.59 3.25 73895. 1.76 4519. 1.37 1.58 16 128460. 104.65 .17 17629. 1.08 • 1316. 1 .02 .92 17 146811. 35.05 .58 7034. .59 1597. .56 1.16 • •20 201865. 3.05 9.24 198326. 1.95 11799. 1.60 8.00 21 293622. 5.33 7.54 43580. 2.86 9520. 2.81 3.92 24 183514. 13.21 1.91 17479. 1.04 6082. 1.03 2.16 MCW 25 403730. 14.48 3.83 206484. 5.76 35859. 5.67 2.00 26 183514. 8. 38 3.00 93602. 1.66 37129. 1.56 1.24 32 • 238568. 10.41 3. 17 66527. 1.20 19427. 1.13 2.41 33 183514. 7.62 3. 33 8569. .46 2059. .44 . 4.17 • 42 128460. 3.56 5.08 80237. .49 4121. . 31 6.07 ••43 128460. 4.06 4.42 8290. . 17 752 . .13 3. 87 • •43b 110108. 2.82 5.50 63518. .29 3534. .22 6.11 ••44 73405. 3.30 3.17 9840. .17 94. .06 3.29 ••45 137635. 10.41 1.83 10676. .63 1395. .51 2.00 ••46 192689. 3.30 8.34 133564. .59 2344. .46 5.19 47 201865. 11.94 2.33 97750. 1.84 13154. 1.75 2.41 48 73405. 13.46 .75 6164. .52 997. .43 1.49 49 201865. 4.06 6.92 1 32825. 1.24 5676. 1.08 1.94 VpPT - Volume of rainfall, m3 QPK - Peak flow rate, m3/sec PPT - Average rainfall intensity, mm/hr TQPK - Time to peak flow, hrs PPTD - Duration of rainfall, hr * - With base flow separation Vr, - Volume of runoff, m3 - Rainfall records averaged from two rain gages Table 10. Rainfall-runoff characteristics from the Mahantango Creek Subwatershed and the R-5 Subwatershed 85 CHAPTER FOUR RESULTS AND DISCUSSION In this chapter site-specific rainfall-runoff events are simulated for the selected Mahantango Creek and Chickasha subwatersheds. The purpose of this chapter is the presentation and discussion of these results. The underlying rainfall-runoff modeling techniques described in Chapter Two and the MCW and R-5 data sets presented in Chapter Three make up the suite of models and sets of data used in this study. Predicted runoff variables are evaluated with the efficiency criterion described in Chapter Two. This criterion is used to standardize model evaluation across the suite of modeling techniques under comparison. Levels of efficiency acceptability are not established in the present study for decisions concerning model use. Instead, calculated efficiencies are used as an index for a more general qualitative model interpretation. Efficiencies of less than zero, do arise in this study, but their values are set equal to zero. The efficiency values are therefore restricted to the range zero to one. All simulations and most calculations in this work were done on the UBC AMDAHL V8-II computer operating under the Michigan Terminal System. 86 4.1 Regression Models Independent rainfall variables and dependent runoff variables, from MCW and R-5, used to construct simple-and multiple-linear-regression rainfall-runoff models, as described in Chapter Two, are shown in Table 10. The regression-analysis scenario used in this study involved the following three steps: 1) construct a number of rainfall-runoff models based on less than the total number of events available; 2) use these models to predict the remainder of the events; and 3) incorporate all available events into new regression models. The determination of the coefficients and constants in the first step constitutes the calibration phase of the model calibration process, as described in Chapter Two. The second step constitutes the verification phase, wherein the established regression models are used to predict the dependent runoff variables. In the third or predictive phase, not included in this study, the regression models are used to predict runoff variables outside the combined set used in the first two phases. By repeating the first phase of model calibration, after incorporating the additional events, subsequent improvements in the regression models can be identified. The evaluation of linear regression models in this work is presented in terms of the efficiencies calculated for predicted runoff variables in the verification phase of model calibration. 87 The natural rainfall-runoff process shows only positive correlation. Therefore, only rainfall-runoff variables showing positive correlation are considered in this work. No other significance testing of rainfall-runoff variables is used in this study. Correlation matrices for the six MCW linear regression variables (Table 10) are shown in Tables 11, 12,. 13, and 14. The correlation coefficients in Tables 11 and 13 are based upon the observed rainfall-runoff variables, while those in Tables 12 and 14 result from dependent-variable data reduction, in the form of base flow separation as described in Chapter Two. The correlation coefficients in Tables 11 and 12 are based upon variables from 15 selected events, while those in Tables 13 and 14 result from the variables of 21 MCW selected events. Table 15 differentiates between Tables 11, 12, 13, and 14. The heavy lined boxes in Tables 11, 12, 13, and 14 separate out the nine correlations that represent rainfall-runoff relationships. In Table 11 there are five positive correlations between rainfall-runoff variables: 1) Volume of rainfall and volume of runoff, 2) volume of rainfall and peak flow rate, 3) duration of rainfall and volume of runoff, 4) duration of rainfall and peak flow rate, and 5) duration of rainfall and time to peak flow. The closer these coefficients are to 1.0 the better the suggested rainfall-runoff relationship. Also in Table 11, there are four negative correlations between rainfall-runoff VPPT PPT PPTD VQ QPK TQPK VPPT 1.0 PPT -.1174 1.0 PPTD .2779 -.5730 1.0 VQ 1 .5585 -.2802 .5813 1.0 QpK .8723 -.0584 .2610 .7242 1.0 TQpK -.0764 -.4816 .8423 .3858 -.1250 1.0 Table 11. Correlation matrix for Mahantango Creek Subwatershed rainfall-runoff variables based on 15 selected events without base flow separation oo oo VRPT PPT PPTD VQ QPK TQPK VP T 1.0 PPT -.1174 1.0 PPTD .2779 -.5730 1.0 • VQ I .8610 -.1711 .2657 1.0 QPK .8944 -.0367 .2294 .8664 1.0 TQPK -.0764 -.4816 .8423 .0087 -.1533 1.0 Table 12. Correlation matrix for Mahantango Creek Subwatershed rainfall-runoff variables based on 15 selected events with base flow separation oo VPPT PPT PPTD VQ QPK TQPK VPPT 1.0 PPT -.0696 1.0 PPTD .3337 -.5153 1.0 VQ .6045 -.2658 .6525 1.0 QPK .8541 -.0069 .1961 .6577 1.0 TQPK -.0056 -.4419 .7702 .3840 -.1124 1.0 Table 13. Correlation matrix for Mahantango Creek Subwatershed rainfall-runoff variables based on 21 selected events without base flow separation o VPPT PPT PPTD VQ QPK TQpK VPPT 1.0 PPT -.0696 1.0 PPTD .3337 -.5153 1.0 VQ .8408 -.1 127 .1942 1.0 QPK .8712 .0146 .1668 .8778 1.0 TQPK -.0056 -.4419 .7702 .0109 -.1373 1.0 Table 14. Correlation matrix for Mahantango Creek Subwatershed rainfall-runoff variables based on 21 selected events with base flow separation VO TABLE SUBWATERSHED NUMBER OF SELECTED EVENTS BASE FLOW SEPARATION 11 MCW 15 NO 12 MCW 15 YES 13 MCW 21 NO 14 MCW 21 YES 17 R-5 6 NO 18 R-5 9 NO Table 15. Summary of correlation matrix tables 93 variables: 1) Volume of rainfall and time to peak flow, 2) average rainfall intensity and volume of runoff, 3) average rainfall intensity and peak flow rate, and 4) average rainfall intensity and time to peak flow. • The individual correlation coefficients in Tables 12, 13, and 14 show the same general positive and negative correlations described for Table 11. The negative correlations in Tables 11, 12, 13, and 14 include every rainfall-runoff variable combination of average rainfall intensity. This suggests that the average rainfall intensity is not a useful rainfall-runoff regression model variable for MCW with comparable events and sample sizes. Tables 12 and 14 (with data reduction) when compared with Tables 11 and 13 (no data reduction) show increases in two positive correlation coefficients. Both of these increased correlation coefficients have the volume of rainfall as a component variable. This suggests that using the volume of rainfall as an independent variable in a rainfall-runoff regression model for MCW will be more informative for storm flow predictions. Again comparing Tables 12 and 14 with Tables 11 and 13, there are decreases in two positive correlation coefficients with data reduction. Both of these decreased correlation coefficients have the duration of rainfall as a component variable. This suggests that using the duration of rainfall as an independent variable in a rainfall-runoff regression model for MCW will be more informative for total flow predictions. 94 The seven MCW linear regression models included in this study, with and without data reduction, and their respective verification efficiencies are summarized in Table 16. The heavy lined boxes in Table 16 separate out the model verification efficiencies. The verification efficiencies of models based on 15 events without data reduction range from 0.0 to 0.83. The verification efficiencies of models based on 15 events with data reduction range from 0.0 to 0.48. Table 16 also includes the coefficient of determination for each rainfall-runoff regression model. These regression model evaluations (calibration phase) are shown for both 15 event and 21 event models. The point should be made that even for calibrated data, model efficiencies will not be equal to one. A constant increase in the coefficient of determination is seen with data reduction, in all MCW models that include the rainfall volume as an independent variable. The coefficients of determination based on 21 events are greater than the coefficients of determination based on 15 events for runoff volume models, without data reduction, in every case suggesting stronger relationships for these models with increased sample sizes. In Table 16, model number one (without data reduction) has a. verification efficiency (0.48) that is greater than either of its coefficients of determination (0.31 and 0.37). Verification - efficiencies higher than the coefficients of determination are NO SEPARATION WITH BASEFLOW SEPARATION MODEL VPPT PPT PPTD QPK TQPK R* 'I r2 6 1 • • .31 .48 .37 .74 .48 .71 2 • • .34 .68 .43 .07 .0 .04 3 • • • .51 .83 .59 .74 .42 .72 4 • • .76 .48 .73 .80 .43 •76 5 • • .07 .0 .04 .05 .0 .03 6 • • • .76 .43 .74 .80 .48 .78 . 7 • • .71 .0 .59 .71 .0 .59 r2 - Regression (multiple) models based on events 3, 4, 15, 16, 17, 20, 21, 24, 25, 26, 32, 33, 42, 1,4 43, and 43b R 2 5 - Predicting events 44, 45, 46, 47, 48, and 49 with r^r4) regression (multiple) models r* - New regression (multiple) models based on all events R - Model efficiency r - Coefficient of determination Table 16. Linear regression models and efficiencies for the Mahantango Creek Subwatershed 96 also seen in the other two MCW runoff volume models (without data reduction) in Table 16. These higher verification efficiencies for models 1, 2, and 3 are explained by the observed volumes of runoff being, by chance, close to the fitted regression line. The correlation coefficient interpretations, relating to data reduction, for MCW are also illustrated in Table 16. With data reduction the coefficient of determination values are shown to increase for models including the volume of rainfall and decrease for models including the duration of rainfall. In general the predictive prowess of MCW regression models, that include the volume of rainfall as an independent variable, would appear to be fairly good within their calibrated ranges. This suggests that the volume of rainfall is the most useful independent variable for MCW rainfall-runoff regression models. It seems intuitive that there should be a strong correlation between rainfall-volumes and storm flow volumes. Dunne and Leopold (1978) describe the scatter that is usually found in regression models of this type as resulting from differences in rainfall intesity and duration as well as the antecedent moisture conditions of the basin from event to event. The correlation matrices for the R-5 linear regression variables (Table 10) are shown in Tables 17 and 18. The correlation coefficients in Table 17 are based upon variables from six selected events, while those in Table 18 result from VPPT PPT PPTD VQ QPK TQPK VPPT 1.0 PPT .7418 1.0 PPTD -.2614 -.7032 1.0 VQ .5223 .7162 -.1306 1.0 QPK .5364 .7861 -.2442 .991 1 1.0 TQPK -.3215 -.4690 .4566 -.1981 -.2103 1.0 e 17. Correlation matrix for R-5 Subwatershed rainfall-runoff variables based on six selected events VO VPPT PPT PPTD VQ QPK TQPK VPPT 1.0 PPT .7444 1.0 PPTD -.3363 -.6743 1.0 VQ I .5159 .7395 -.2828 1.0 QPK .6156 .8126 -.3741 .9897 1.0 TQPK -.5038 -.4973 .7336 -.3168 -.3520 1.0 Table 18. Correlation matrix for R-5 Subwatershed rainfall-runoff variables based on nine selected events ^3 CO 99 the variables of nine R-5 selected events. Table 15 differentiates between Tables 17 and 18. The heavy lined boxes in Tables 17 and 18 separate out the nine correlations that represent rainfall-runoff relationships. There are five positive and four negative correlations between rainfall-runoff variables shown in Tables 17 and 18. The positive correlations in Tables 17 and 18 are: 1) Volume of rainfall and volume of runoff, 2) volume of rainfall and peak flow rate, 3) average rainfall intensity and volume of. runoff, 4) average rainfall intensity and peak flow rate, and 5) duration of rainfall and time to peak flow. The negative correlations in Tables 17 and 18 are: 1) Volume of rainfall and time to peak flow, 2) average rainfall intensity and time to peak flow, 3) duration of rainfall and volume of runoff, and 4) duration of rainfall and peak flow rate. The negative correlations shown in Tables 17 and 18 suggest that the duration of rainfall is not a useful rainfall-runoff model variable for R-5. There is a general increase in positive correlation coefficients from Table 17 to Table 18 suggesting greater model efficiencies with increased sample sizes as would be expected. The seven R-5 linear regression models, included in this study, and their respective efficiencies are summarized in Table 19. The verification efficiencies of these models, based on six events, range from 0.14 to 0.99. The models that verify most efficiently all include the average rainfall intensity as an i MODEL VpRT PPT PPTD QPK TQPK i 1 • • .27 .14 .27 2 • • .51 .91 .55 3 • • • .51 .92 .55 4 • • .29 .52 .31 5 • • .62 .98 .66 6 • • • .62 .99 .67 7 • • .21 .37 .54 Regression (multiple) model based on events 1, 2, 3, 4, 5, and 10 Predicting events 12. 14, and 15 with r, regression (multiple) models New regression (multiple) models based on all events '1 -"i -Table 19. Linear regression models and efficiencies for the R-5 Subwatershed 101 independent variable. These same models also have the highest coefficients of determination, suggesting that the average rainfall intensity variable may provide the best regression analysis information for R-5. The seven MCW (with and without data reduction) and the seven R-5 linear regression models described thus far, represent only 33% of the rainfall-runoff linear regression relationships that could concievably be used as prediction models. The remainder were not analyzed because the correlation analysis on Tables 11, 12, 13, 14, 17, and 18 showed negative correlations. Verification efficiencies for R-5 regression models are in general much better than verification efficiencies for MCW regression models despite the smaller R-5 sample size. For MCW and R-5 the most informative independent regression variables would appear to be volume of rainfall and average rainfall intensity respectively. Correlation matrices for nine linear regression variables (two rain gages) are presented in Appendix C for MCW data. These matrices are based on the six selected events flagged in Table 10." Following the positive correlation standard for rainfall-runoff variables, 168 MCW linear regression models are established and presented in Appendix C. The 168 models represent 44% of those possible. Coefficients of determination for MLR models, with and without data reduction, are in general very high. The analysis of "these models is not taken any 102 further, as more events with records at two rain gages, are needed to advance it to a verification mode. The small sample sizes used in this study without question effects correlation coefficients and in turn must control, to some degree, the predictive efficiencies of rainfall-runoff regression models. In future work more rainfall-runoff events are necessary to uncover potential linear regression models and monitor the relative increase in model efficiencies for MCW and R-5. These additional events will require longer periods of record. There appears to be some promise for using MLR analysis where independent variables are abstracted from two rain-gage data sets. The standard test for the significance of a correlation coefficient, at a specific confidence level, could perhaps be used as a basis for setting standards of efficiency acceptability in future work. 4.2 Unit Hydrograph Model In this section one-hour duration unit hydrographs are determined for MCW and R-5, as described in Chapter Two, using observed hydrographs and hyetographs from a set of rainfall-runoff events. These models are then used to simulate selected rainfall-runoff events. $ index values are calculated for each of the MCW and R-5 selected events summarized in Table 103 10. The calibration phase for unit hydrograph model calibration in this study consisted of three parts: 1) Calculating $ index values for each selected event based on storm flow volumes, 2) averaging individually developed unit hydrographs, and 3) measuring the efficiency with which event storm flow hydrographs can be reconstructed with an average unit hydrograph model. In order to verify the form of a storm hydrograph predicted with the unit hydrograph model, excess precipitation must be determined for a rainfall event without knowledge of the storm runoff. In this study two methods used are: 1) a mean $ index, and 2) a least-squares $ index^excess-rainfall relationship. The predictive phase for unit hydrograph model calibration is not included in this study. The MCW one-hour unit hydrograph determined in this study is shown in Figure 22. It is averaged from one-hour unit hydrographs developed for each of seven separate events. The calibration efficiencies for three runoff variables, based on the MCW events showing excess rainfall are summarized in the top line of the upper table of Table 20. The efficiency of the MCW unit hydrograph for reconstructing storm flow volumes and peak storm flows both show very high values. Verification efficiencies for the MCW unit hydrograph model based on events showing excess rainfall are summarized in the heavy lined boxes of the upper table of Table 20. The mean MCW 30 H 0 12 3 4 5 6 7 8 TIME (hours) Figure 22. Averaged one-hour unit hydrograph for the Mahantango Creek Subwatershed (Component events 15, 24, 25, 32, 42, 47, and 49) MCW R2 NO. OF EVENTS QPK TQPK INDIVIDUALLY CALCULATED 191 1.0 .70 .0 LINEAR RELATIONSHIP 102 .0 .0 .0 AVERAGE RELATIONSHIP 102 .0 .0 .0 R-5 R2 NO. OF EVENTS QPK TQPK INDIVIDUALLY CALCULATED 9 .81 .23 .0 LINEAR RELATIONSHIP 83 .48 .19 .0 AVERAGE RELATIONSHIP 54 .28 .30 .0 1 - Events 3. 4, 15. 16, 17. 20, 21, 24, 25. 26. 32, 33, 42,43b. 45, 46. 47. 48. 49 2 - Events 3, 16. 17. 21. 25. 26. 32. 45, 47, 49 3 - Events 1. 2. 3. 5. 10, 12. 14, and 15 4 - Events 2, 4. 5, 10, and 12 Table 20. Unit hydrograph model efficiencies for the Mahantango Creek Subwate and R-5 Subwatershed 106 $ index, based on 21 events, is 13.0 mm/hour. The linear index relationship for MCW is shown in Figure 23. The MCW unit hydrograph model now shows absolutely no predictive abilities and dramatically illustrates the importance of knowing the excess rainfall distribution .before employing the model as a predictor. Example computer output from the implementation of the UNIT code for MCW event #25 is shown in Figure 24. This is one of the seven unit hydrographs used to get the MCW average unit hydrograph. The R-5 one-hour-duration unit hydrograph used in this study, is shown in Figure 25. It is averaged from one-hour unit hydrographs from five events*. The same calibration and verification scenario established for the MCW unit hydrograph model was used for the R-5 unit hydrograph model. The bottom table in Table 20 summarizes the calibration and verification efficiencies of the R-5 unit hydrograph model. Verification efficiencies are located in the heavy lined boxes. The mean R-5 $ index, based on nine events, is 21 mm/hour. The linear * index relationship for R-5 is shown in Figure 26. The R-5 unit hydrograph calibration efficiencies for storm flow volumes and peak storm flows are both lower than those described for MCW, although the former is still quite high. Verification efficiencies for the R-5 unit hydrograph model using the linear and average $ index relationships, show greater promise than in the MCW case. This is especially so 7.62 25.4 50.8 X TOTAL PRECIPITATION DEPTH (mm) Figure 23. Linear b index relationship for the Mahantango Creek Subwatershed o 108 UNIT HVDROGRAPH FDR MCW25-1HR PERIOD NUMBER OF LAST NON-ZERO EXCESS RAINFALL . PERIOD NUMBER OF LAST NON-ZERO RUNOFF . 5 MEMDRV TIME > 5 TIME PERIOD RAINFALL EXCESS 0 2COOO 0 0 0.0 0.0 0.0 0 02133 0 11172 0.0*905 0 02326 O 00947 DISCRETE KERNELS FOR UNIT HYDROGRAPH 0 091 BO 0 5*375 0.23040 O 10155 O 03250 I— CEo " Q or 1 4.0 TIME ~i— 5.0 I— E.O ~I— 1.0 0.0 •—I— 1 .0 2.0 I— 3.0 6 0 Figure 24. Example unit hydrograph i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—r 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 TIME (hours) Figure 25. Averaged one-hour unit hydrograph for the R-5 Subwatershed (Component events 1, 5, 10, 12, and 15) Ill when one considers the limited number of events included in the two $ index standards used to calculate excess rainfall. The fact that R-5 is a smaller and more homogeneous basin than MCW may account for the fact that the R-5 unit-hydrograph model appears to have greater predictive prowess than the MCW unit-hydrograph model. In these models, excess rainfall is a lumped input parameter, whereas in reality, it is strongly variable over space due to differences in infiltration capacities. Smaller basins are less effected than larger basins by this variability. Linsley et al. (1975) suggest that unit-hydrograph models are best suited to basins of limited spatial variability. Neither of the unit hydrograph models used in this study show any efficiency for reconstructing or predicting the time it takes for peak storm flows to occur. This may be the result of the way the models were constructed. The MCW and R-5 unit hydrographs are simple arithmetic averages of concurrent coordinates. Linsley et al. (1975) suggest that a more defensible procedure is to compute average peak flow and time to peak flow, then sketch the average unit hydrograph conforming to the general shape of the component graphs passing through the computed point. This recommendation will be tested in future work. The results' from MCW and R-5 unit-hydrograph models presented here illustrate that the technique may be dependent 112 upon the averaging criterion used, and is strongly dependent upon the calculation of excess rainfall. Attempts to increase the sensitivity of the unit-hydrograph technique by calculating shorter duration models were stymied as excess-rainfall distributions, determined by the $ index method, failed to correlate well with either MCW or R-5 storm flow hydrographs. The efficiency criterion adapted for this study is insufficient for evaluating the predicted form of the storm hydrograph simulated with the unit hydrograph technique. 4.3 Distributed Model Results from simulations of MCW and R-5 rainfall-runoff events, using the distributed model described in Chapter Two, are presented and discussed in this section. The input data required by the distributed model is described in Chapter Two, the available MCW and R-5 data used to fill these requirements is presented in Chapter Three. There is no calibration phase required for the distributed model used in this study. Verification efficiencies for storm hydrographs predicted with the distributed model are calculated for two types of rainfall-runoff events: 1) Events that produced excess rainfall (lateral inflow hydrographs), and 2) events that did not generate excess rainfall. The predictive phase of model 113 calibration is not addressed in this study for the distributed model. The watershed segments used to transform MCW into overland flow planes compatible with the distributed model are shown in Figure 27. The size and orientation of the overland flow planes are based upon the MCW contributing areas described by Engman (1974). Table 21 summarizes the transformed subwatershed. The 16 major segments and their subdivisions were abstracted from Figure 14 and topographic contour maps. The major watershed segment lengths define routing reaches of equal channel slope and hydraulic behavior. The subdivisions of the major watershed segments characterize averaged soil zone dimensions and slope. These soil zones identify the areas over which particular infiltration curves apply in the calculation of excess precipitation. The reaches and tributaries describing the channel routing scenario used for MCW are illustrated in Figure 28. The storm runoff volumes for each of the 21 selected MCW events were simulated in this study. The top table in Table 22 (Group A) shows that there is no predictive efficiency for the distributed model when all of these events are taken as a group. The dashes in Table 22 represent runoff variables not evaluated in the respective group of events. Inspection of individual simulations revealed that in more than one-half of all selected events no lateral inflow was being generated. This was due to 114 Figure 27. Watershed segments used to transform the Mahantango Creek Subwatershed into overland flow planes Ol -tk CO O CD 00 CD CO ro SUBBASIh I ro -» _* —A to -» to -» 4k CO to -* co ro -» ro -> co ro -» to -> SEGMENT r~ m -ti -i CO o m cn 4^ cn 4^ CD CD a> co •A 4k cn 4k cn 0> CO" CD 0> cn 4k 4k cn cn 4k cn cn 4k 0) cn 4k CD o> +k cn co CD CD CD 4k o> CD cn co —A CD 4k CD Ol CD 4k CD CD cn co -J 4k -» cn SOIL TYPE co -j cn _& _* cn 1» b -» cn cn cn ro to -A cn cn cn ro co cn -» to cn -* -* CO -* _» -vl cn cn cn cn cn bub cn -J cn oi cn cn CO -» -J Ol Ol 0 co ro 01 —J oi cn cn cn SOIL SLOPE _& co CO IO co to to -» cn -» 0) CT) CD cn CO ro co co •A •A o> ro ro o co -» 4k o _» 4k O cn 4k cn to -» 0) ->l CD CO to -» -» CO to to -si CD CO 4k -» to CO 4k CO CO to CD cn co cn -» co CO CD Ol -J WIDTH (m) _& co -t to -» ro -» ro -» ro -» co ro -» to -» ro -» co ro -» Co ro —* co ro -» to -» SEGMENT RIGHT SIDE cn O) W 0) 4k » 4k co cn CO 4k o> cn 0) 4k co cn CD CT) 4k 0") cn 0) cn 4k 0> 4k cn cn 4k 4k cn cn CD 4k CO cn cn 4k ~-l CD 4. CD CD Ol CO CD 4k CD CD cn co CD 4k -J CD cn -A CD -~1 CO —* SOIL TYPE RIGHT SIDE cn O O cn cn cn cn o -» cn -» cn cn -» to cn -» ro cn cn -* co -» -~i cn cn -* -» ro cn cn cn cn cn cn -» O -> cn cn cn O CO O Ul S Ol cn oi oi 0 -» o cn -» cn 01 Ol Ol o -» o cn -* cn cn cn oi -» O -k Ol Ol Ol SOIL SLOPE RIGHT SIDE _* cn to co O "s| cn co ro -» ro o O 4k cn ro -~l o CO co ro o> o o -4 4k 00 CD 4k _» CO cn -» to -» CO 4k ^1 co o co cn cn to CD CO CO CD 4k CO cn co CO -» ro ro cn co 0) cn -» 4k O >l 4k IO CO CO 4k -> S 4» cn co co co CO 4k CD CO WIDTH (m) RIGHT SIDE 1055 -vi ro cn ro cn co co cn to CO ro CO CO co CO ro to CO CO cn 4k CO 4k o CD CD 4k CO CO cn co 4k 4k co CO CO Ol CO CO REACH LENGTH (m) b cn b 4k b 4k b --4 b to b to b to b ro b ro b O) b to b CO b ro b to b CO —1 o REACH SLOPE Figure 28. Channel routing scenario for the Mahantango Creek Subwatershed MCW GROUP NO. OF EVENTS QPK TQPK A 271 .0 — — • B 82 .0 .0 .01 R-5 R2 GROUP NO. OF EVENTS VQ QPK TQPK A 9 .20 — — B 53 .56 .81 1.0 1-15 events with 1 raingage and 6 events with 2 raingages 2 - Events 3, 16, 17, 21, 24, 25, 26, and 45 3 - Events 3, 4, 5, 10, and 12 A - Including an events B - Including only events generating lateral inflow Table 22. Distributed model efficiencies for the Mahantango Creek Subwatershed and R-5 Subwatershed 118 the way break point precipitation was distributed over the duration of the selected event. When the rainfall intensity was averaged over the entire events in these cases, it remained lower than the infiltration capacity thus preventing surface runoff. The eight MCW events in which lateral inflow was generated are taken as a subgroup of the total events. The top table in Table 22 (Group B) summarizes the lack of predictive efficiency the distributed model has for this subgroup of events. These simulations draw attention to a specific limitation in the criterion being used to evaluate model efficiency in this study. Only groups of predicted runoff events can be evaluated, without any individual event evaluation. The evaluation of a given distributed model simulation is important for uncovering the type of events the model can or cannot handle efficiently. The watershed segments used to transform R-5 into the overland flow planes, shown in Figure 29, were abstracted from Figure 20. The entire subwatershed was taken as a contributing area. Table 23 summarizes the transformed subwatershed. The storm runoff volumes for each of the nine selected R-5 events were simulated in this study. The bottom table in Table 22 (Group A) shows the relatively low predictive efficiency for the distributed model when all of these events are taken as a group. The five R-5 events generating lateral inflow are taken as a subgroup of the total events. The bottom table in Table 22 S - Section L - Left subbasln segment R - Right subbasln segment Subbasln Figure 29. Watershed segments used to transform the Subwatershed into overland flow planes 120 LEFT SIDE RIGHT SIDE X ft-REACH LENG' (m) SUBBASIN SEGMENT SOIL TYPE WIDTH (m) SEGMENT SOIL TYPE WIDTH (m) REACH LENG' (m) 1 1 3 98 1 2 3 3 2 3 61 128 220 146 2 1 2 24 1 2 31 85 2 3 122 2 3 122 1 1 12 1 1 12 3 2 2 49 2 2 31 79 3 3 110 3 4 3 2 49 116 1 1 12 1 1 12 4 2 2 61 2 2 37 73 3 3 85 3 4 3 2 61 122 Table 23. Summary of the transformed R-5 Subwatershed 121 (Group B) summarizes the predictive efficiencies for this subgroup of events. Taken overall these values, used to verify the model, are quite high when compared with the MCW values. The antecedent soil water contents for the MCW and R-5 selected events would appear to be the parameter of greatest uncertainty. The sensitivity of the antecedent soil water contents was investigated for a suite of seven MCW events. Table 24 summarizes the results of this analysis. Soil moisture frequencies, discussed in Chapter Three, of 20% and 80% are used as indicative of dry and wet conditions respectively. The dashes in Table 24 represent initial soil water contents not considered for specific events. For each event simulation two values are presented in Table 24: 1) Calculated storm runoff volumes, and 2) percentages of measured storm runoff volumes. Although the distributed model is sensitive to antecedent soil water content, selected MCW events are still poorly predicted using the soil moisture frequency criteria as shown in Table 24. Using existing time series of soil moisture to produce initial moisture estimates, as a function of time of year, could be useful in future work. This author feels though, that improved estimates of antecedent soil water content, to be used as deterministic input parameters, will not necessarily increase the predictive efficiency of the distributed model due to the spatial variability of soil hydraulic properties. There are at least three reasons that could be advanced in explanation of the 122 SIMULATED RUNOFF VOLUMES (m3) (PERCENTAGE OF MEASURED VALUES*) EVENT NO. MEASURED RUNOFF VOLUME (m3) SOIL MOISTURE FREQUENCY 20% 50% 75% 80% 3 2346 462 19.7* 566 24.1* 800 34.1* 4 1631 8 0.5* 8 0.5* , 8 0.5* 15 4519 14 0.3* 14 0.3* 14 0.3* 16 1316 1568 119.0* 2127 162.0* 2242 170.0* 17 1597 573 35.9* 878 55.0* 20 11799 23 0.2* 23 0.2* 23 0.2* 25 35859 1239 3.5* 3278 9.1* 4028 11.2* Table 24. Effect of antecedent soil water content on simulated lateral inflow hydrograph volumes for selected Mahantango Creek Subwatershed events 123 poor predictive efficiencies of the distributed model. The next three paragraphs discuss each in turn. First, subsurface storm flow (Whipky, 1965), has been shown to be an important component of the rainfall-runoff relationship for R-5 events (Sharma and Luxmoore, 1979; Luxmoore, 1982). As described in Chapter Two, the distributed model does not consider the subsurface storm flow component, thereby helping to explain why the simulated R-5 runoff volumes are too low. Second, as previously described, the way in which a rainfall-intensity distribution is derived in the distributed model appears to be limited to high intensity storms of short duration. The efficiency of the distributed model is therefore strongly dependent upon the type of rainfall event being simulated. Third, when concurrent stream reaches or tributaries are substantially different in length (MCW), the channel flow routing component of the distributed model does not satisfy conservation of mass going from one section to the next. The finite difference approximation used by the distributed model simply averages the concurrent reach/tributary lengths. It is suggested here that the incorporation of a weighting function may be necessary. Of course if all reaches are of similar lengths (R-5), weighting functions are not necessary as conservation of mass is already achieved. If a very large number of watershed segments were used for a big basin, the 124 averaging and linear approximations made with the distributed model would be less subjective, but the amount of spatially variable input data required would be staggering. Based on the results presented here and those of Engman (1974), the modeling efficiency of the distributed model, . although promising for smaller basins, appears to degenerate with an increase in the number of overland flow planes necessary to simulate larger basins. It is felt by the author that uncalibrated, physically-based, deterministic, rainfall-runoff models will probably not provide satisfactory results for larger basins due to the spatial variability of the input data requirements. The efficiency of the distributed model may improve if a calibration phase is included. Parameters that might be calibrated against include the saturated hydraulic conductivity, depression storage and the roughness coefficients. As with the unit hydrograph technique, the efficiency criterion used in this study is not sufficient for analyzing the form of the storm flow hydrograph simulated by the distributed model. Illustrative examples, in the form of sample computer output, for each of the four codes (Appendix B) making up the distributed model are presented in Appendix D. The simulated event used for these examples is MCW #16. 125 CHAPTER FIVE CONCLUSIONS AND FUTURE RESEARCH The vitality of a false notion is often surprising. It is sometimes crushing to our faith in the survival of the fittest Chamberlin, 1884 In this study a suite of three underlying rainfall-runoff modeling techniques were applied to two data sets and the results were used to compare model efficiencies for selected events. Individual model efficiencies, based on a sum of squares criterion, were referenced to the three phases of model calibration. A toe hold for continuing research, this work establishes a framework for evaluating rainfall-runoff models. Future work will emphasize the quantitative investigation of space-time tradeoffs and data worth concepts. It will require an extension of the established data sets and a refined model efficiency criterion. The efficiencies of the three underlying rainfall-runoff modeling techniques used in this study were found to be surprisingly poor. The results lead to the following qualitative conclusions: a) The most informative independent variables for MCW and R-5 linear regression models appear to be volume of rainfall and average rainfall intensity respectively. There is a general 126 improvement'in correlation coefficients and regression-model efficiencies for both MCW and R-5 with increases in the number of selected events. The efficiencies are surprisingly high in some cases considering the small sample sizes. Positive and negative correlation coefficients for MCW and R-5 rainfall-runoff variables were presented in Tables 11, 12, 13, 14, 17, and 18. Efficiency values for MCW and R-5 regression models are shown in Tables 16 and 19. The effect of base flow separation on correlation coefficients and regression model efficiencies for MCW were summarized in Tables 11, 12, 13, 14, and 16. b) With respect to the unit hydrograph model only the R-5 analysis demonstrated any predictive prowess. The unit hydrograph technique was found to be strongly dependent upon an accurate estimate of spatially variable excess rainfall. The efficiencies for MCW and R-5 unit hydrograph models were presented in Table 20. c) The distributed modeling technique only exhibited predictive prowess for the R-5 events. It is believed by the author that the efficiency of the physically-based, deterministic, distributed-model deteriorates drastically with increases in basin size due to the lumping of spatially-variable soil hydraulic properties. The efficiencies with which the distributed model predicted selected MCW and R-5 rainfall-runoff events were summarized in Table 22. 127 d) The efficiencies determined for three rainfall-runoff modeling techniques used in this study do not uncover a definitively superior model. Limitations in each of the underlying modeling techniques were discussed in Chapter Four. Small sample sizes and spatial variability in input parameters were identified as the primary factors contributing to low predictive efficiencies. The regression model was found to be the only technique with any predict.ive efficiency for MCW. These regression model predictions are shrouded though by marginal calibration ranges and large confidence intervals. The unit hydrograph model and the distributed model were both found to be more efficient for the smaller R-5, but require improved estimates of spatially variable input parameters to reach acceptable levels. e) Rainfall-runoff regression model efficiencies can be improved by increasing the number of selected events upon which they are based. Spatial variability of soil hydraulic properties is the reason for low predictive efficiencies for the unit hydrograph model and the distributed model. For R-5, these variabilities are smaller and the efficiencies of both modeling techniques are greater. Deterministic representation of model input parameters would appear to be the major pitfall of the distributed model used in this study. ^. f) The efficiency criterion itself is inadequate for: 1) Evaluating the form of a simulated storm flow hydrograph instead 128 of selected runoff variables, 2) uncovering small sample biases, 3) evaluating a single event, and 4) establishing acceptable model standards. This study has set the stage for continuing research by the author. The following discussion of future research is centered in three areas: 1) Modeling techniques, 2) model evaluation, and 3) additional data. The spatial variability of input parameters is the Achilles' heel of the comprehensive, physically-based, rainfall-runoff model at any practical spatial grid scale. Future research will focus upon determining effective values for these parameters. This will include: 1) assessing the worth of additional data points in estimating effective values, and 2) analyzing the influence of uncertainties in the estimates of effective values on runoff predictions. Optimization techniques, such as linear programming may be useful for calculating parameters such as depression storage, while the infiltration parameter might best be handled as a stochastic var iable. The spatial variability of soil hydraulic properties has been addressed by a number of authors. Future assessment of the distributed rainfall-runoff modeling technique will include the evaluation of various component techniques that are being used to describe soil hydraulic properties. These may include: Kriging (de Marsily, 1982), scaling methods (Warrick et al., 1977) and statistical analysis (Russo and Bresler, 1980). 129 Future evaluation of the quasi-physically based modeling technique will not be restricted to the model used in this study. A model similar to the one used in this work is described by Smith and Woolhiser (1971). Two recent approaches used in the distributed modeling technique are found in Freeze (1980) and Moore and Clarke (1981). Various methods of calculating excess rainfall will be tested with the unit hydrograph technique. The linear-reservoir model, described in Chapter Two and the constrained linear system model (Natale and Todini, 1977) will also be added to the suite of underlying rainfall-runoff modeling techniques being evaluated. Regression analysis of rainfall-runoff variables will be facilitated in future work with increased sample sizes. The major focus of future research will be determining if space-time tradeoffs exist across the data sets of various rainfall-runoff modeling techniques. The criterion used to establish tradeoffs will be model efficiency. The standard a model must meet to be considered suitably efficient is the key question in model evaluation. Moore and Clarke (1981) describe the present state of rainfall-runoff modeling as extremely fragmented with a bewilderingly large array of models to choose from. With so many models a standardized evaluation is indeed an important problem. The model evaluation approach used in this study will continue to be employed in future research, but the simple 130 criterion used here must be supplemented with new criteria for improved assessments. Future work will incorporate a quantitative index, based on Pearson product-moment coefficients, for comparing the form of computed and measured hydrographs (McCuen and Snyder, 1975). Future research will also concentrate on evaluating model components as described by Nash and Sutcliffe (1970). Sensitivity analysis, in the form of Monte Carlo simulation, may be useful for evaluating model components. The future studies will employ data sets from three rather than two subwatersheds. In addition to R-5 and MCW, data from the Hubbard Brook Subwatershed, described in Chapter Three, will also be used. For the Pennsylvania watershed (MCW) a subwatershed known as Mr. Pauls' farm (Engman and Rogowski, 1974a) shown in Figure 13, will be emphasized in future investigation. The author hopes to visit each of the subwatersheds used in future study, in order to augment the respective data sets of soil hydraulic properties for specific needs. An extensive summary of published soil hydraulic properties is also now available to the author (Rawls, personal communication, 1981). In order to estimate antecedent soil moisture conditions in future work all available soil moisture records need to be plotted into time series and seasonal soil-water frequency distributions. Finally, rainfall-runoff records need to be put 131 into as complete a form as possible in order to increase the number of selected events and modeling options. 132 REFERENCES Amorocho, J., and G. T. Orlob, Non-linear analysis of hydrologic systems, Univ. of Calif. Contrib. 40, Water Resourc. Cent., Berkeley, California, 1961. Amorocho, J., and W. E. Hart, A critique of current methods in hydrologic systems investigation, Transact ions Amer ican  Geophysical Union, 45(2), 307-321, 1964. Amorocho, J., Nonlinear hydrologic analysis, Advances in  Hydroscience, 9, 203-251, 1973. Betson, R. P., What is watershed runoff?, Journal of Geophysical Research, 69(8), 1541-1552, 1964. Brakensiek, D. L., Storage routing without coefficients, ARS-41-122, Agricultural Research Service, USDA, Beltsville, Maryland, 1966a. Brakensiek, D. L., Reduction Of channel cross section coordinate data to hydraulic and geometric elements, Research Report  No. 384, Agricultural Research Service, USDA, Beltsville, Maryland, 1966b. Brakensiek, D. L., A technique for analysis of runoff hydrographs, Journal of Hydrology, 5, 21-32, 1967. Carr, J. C, A system for collection, preparation, translation, and computer reduction of digital hydrologic data, ARS-NE-18, Agricultural Research Service, USDA, Washington, D. C, 1973. Carrigan, P. H., Calibration of U.S. Geological Survey rainfall-runoff model for peak-flow synthesis-natural basins, U^ S^ Geological Survey Computer Report, Department of Commerce National Technical Information Service, 1973. Chow, V. T., Open Channel Hydraulics, McGraw-Hill, New York, 1959. 133 Chow, V. T., Statistical and probability analysis of hydrologic data; Part I, frequency analysis, in Handbook of Hydrology, edited by V. T. Chow, pp. 8.1-8.42, McGraw-Hill, New York, 1964a. Chow, V. T., Runoff, in Handbook of Hydrology, edited by V. T. Chow, pp. 14.1-14.54, McGraw-Hill, New York, 1964b. Chow, V. T., Laboratory study of watershed hydrology, in Proc.  Int. Hydrol. Symp., pp. 194-202, Fort Collins, Colorado, 1967. Clark, C. 0., Storage and the unit hydrograph, Trans. Amer. Soc.  Civ. Eng., 110, 1419-1446, 1945. Clarke, R. T., A review of some mathematical models used in hydrology, with observations on their calibration and'use, Journal o_f Hydrology, 19, 1-20, 1973. Cornell, C. A., Stochastic process models in structural engineering, Technical Report No. 24, Stanford University, Stanford, California, 1964. Crawford, N. H., and R. K. Linsley, Jr., Digital simulation in hydrology: Stanford Watershed Model IV, Tech. Rept. No. 39, Department of Civil Engineering, Stanford University, Stanford California, 1966. Diskin, M. H., A dispersion analogue model for watershed systems, Proc. Int. Hydrol. Symp., pp. 38-45, Fort Collins, Colorado, 1967. Diskin, M. H., Definition and uses of the linear regression model, Water Resources Research, 6(6), 1668-1673, 1970. Davis, D., L. Duckstein, and R. Krzysztofowicm, The worth of hydrologic data for non-optimal decision making, Water  Resources Research, J_5(6), 1733-1742, 1979. 134 Dawdy, D. R., and T. O'Donnell, Mathematical models of catchment behavior, J^ Hydraul. Div. Amer. Soc. of Civ. Enq., 9J_(HY4), 123-131, 1965. de Marsily, G., Krigin and the inverse problem, Hydrogeology Seminar, University of British Columbia, Vancouver, 1982. Dooge, C. I., A general theory of the unit hydrograph, Journal of Geophysical Research, 64(2), 241-256, 1959. Dooge, C. I., The hydrologic cycles as a closed system, Bull.  Int. Sci. Hydrol., 13(1), 58-68, 1968. Dooge, C. I., Mathematical models of hydrologic systems, International Symposium on Mathematical Modeling Techniques  in Water Resource Systems, Ottawa, _1_, pp. 171-189, Department of the Environment, 1972. Dooge, C. I., Linear theory of hydrologic systems, Techn ical  Bullet in No. 1468, Agricultural Research Service, USDA, Washington, D. C, 1973. Dooge, C. I., General report on model structure and classification, in Logistics and Benef its of using  Mathemat ical Model of Hydrologic and Water Resource  Systems, edited by A. J. Askew, F. Greco, and J. Kindler, pp. 1-21, Pergamon, New York, 1978. Dunne, T., and L. B. Leopold, Water in Environmental Planning, Freeman, San Francisco, 1978. Eagleson, P. S., R. Meija, and F. March, Computation of optimum realizable unit hydrograph, Water Resources Research, 2(4), 755-764, 1965. Eagleson, P. S., Dynamic Hydrology, McGraw Hill, New York, 1970. 135 Engman, E. T., W. T. Gburek, L. H. Parmele, and J. B. Urban, Scale problems in' interdisciplinary water resource investigation, Water Resources Bulletin, 7(3), 495-505, 1 971 . Engman, E. T., A partial area model for simulating surface runoff from small watersheds, Ph.D. thesis, Pennsylvania State University, University Park, 1974. Engman, E. T., and A. S. Rogowski, A partial area model for storm flow synthesis, Water Resources Research, 10(3), 464-472, 1974a. Engman, E. T., and A. S. Rogowski, Selection of soil moisture parameters for synthesizing storm hydrographs, reprint from Am. Soc. Civil Engrs. National Meeting of Water Resources Engineering, Los Angeles, 1974b. Engman, E. T., L. H. Parmele, and W. J. Gburek, Hydrologic impact of tropical storm Agnes, Jounal of Hydrology, 22, 179-193, 1974c. Fiering, M. B. and B. B. Jackson, Synthetic streamflow, Water  Resources Monograph j_, American Geophysical Union, Washington D. C., 1971 . Freeze, R. A. and R. L. Harlan, Blueprint for a physically-based, digitally-simulated hydrologic response model, Journal of Hydrology, 9, 237-258, 1969a. Freeze, R. A., The mechanism of natural groundwater recharge and discharge: One dimensional, vertical, unsteady unsaturated flow above a recharging or discharging groundwater flow system, Water Resources Research, 5, 153-171, 1969b. Freeze, R. A., Three-dimensional transient saturated-unssturstec flow in a grounwater basin, Water Resources Research, 2(2), 347-366, 1971. 136 Freeze, R. A., Streamflow generation, Reviews of Geophysics and  Space Physics, J_2(4), 627-647, 1974. Freeze, R.. A., Mathematical models of hillslope hydrology, in Hillslope hydrology, edited by M. J. Kirkby, pp. 177-225, Wiley-Interscience, New York, 1978. Freeze, R. A., A stochastic-conceptual analysis of rainfall-runoff processes on a hillslope, Water Resources  Research, j_6(2), 391-408, 1980. Freeze, R. A., Hydrological concepts in stochastic and deterministic rainfall-runoff models, in Recent Trends in  Hydrogeology edited by T. N. Narasimhan, pp. 63-80, • Geological Society of America, Boulder, Colo., 1982a. Freeze, R. A., The influence of hillslope hydrological processes on the stochastic properties of streamflow in Statistical  Analysis of Rainfall and Runoff, edited by V. P. Singh, pp. 155-172, Water Resources Publications, Littleton, Colo., 1982b. Gburek, W. J., The Mahantango Creek Watershed-general hydrology and research results, in Watershed Research in North  Amer ica, edited by D. L. Correll, Smithsonian Institution, Edgewater, Maryland, 1977. Haan, C. T., Statistical Methods in Hydrology, Iowa State University Press, Iowa, 1977. Henderson, F. M., Open Channel Flow, MacMillan, New York, 1962. Henninger, D. L., Surface soil moisture within a watershed-variations, factors influencing, and relationships to runoff, M.Sc. thesis, Pennsylvania State University, University Park, 1972. Henninger, D. L., G. W. Petersen, and E. T. Engman, Surface soil moisture within a watershed-variations, factors influencing, and relationships to surface runoff, Soil Sci. Soc. of Amer., 40, 773-776, 1976. 137 Hiemstra, L., Frequencies of runoff for small basins, Ph.D. thesis, Colorado State University, Fort Collins, 1968. Huggins, L. F., and E. J. Monke, The mathematical simulation of the hydrology of small watersheds, Technical Report No. j_, Purdue University Water Resource Center, Lafayette, Indiana, 1966. Izzard, C. F., Hydraulics of runoff from developed surfaces, Highway Research Board, 26, 129-150, 1946. Jackson, B. B., The use of streamflow models in planning, Water  Resources Research, JJ_(1), 54-63, 1975. Johnston, J., Econometric Methods, McGraw-Hill, New York, 1963. Kartvelishvili , N. A., "Teoriya veroyatnostnykh protsessov v gidrologii i regulirovanii rechnogo stoka." Gidrometeorologicheskoe Izdatel'stvo, Leningrad, 1967. Kibler, D. F. and D. A. Woolhiser, The kinematic cascade as a hydrologic model, Hydrology Paper 39, Colorado State University, Fort Collins, Colorado, 1970. Kirkby, M. J. (ED.), Hillslope Hydrology, Wiley-Interscience, New York, 1978. Kisiel, C. C, Transformation of deterministic and stochastic processes in hydrology, in Proceedings of International  Symposium on New Techniques in Hydrology, Fort Collins, Colorado, pp. 600-607, Water Resources Publications, Littleton, Colorado, 1967. Kisiel, C. C, Time series analysis of hydrologic data, Advances  in Hydroscience, 5, 1-119, 1969. Klemes, V., The Hurst phenomenon: A puzzle?, Water Resources  Research, J_0(4), 675-688, 1974. 138 Klemes, V., Physically-based stochastic hydrologic analysis, Advances in Hydroscience, 11, 285-356, 1978. Kolman, B. and R. E. Beck, Elementary Linear Programming with  Applications, Academic Press, New York, 1980. Kunz, K. S.,. Numerical Analysis, McGraw-Hill, New York, 1 957. Laurenson, E. M. , Modeling of stochastic-deterministic hydraulic systems, Water Resources Research, 10(5), 955-961, 1974. Le, C, and T. Tenisci, A General Computer Program for Regression Methods-TRP, University of British Columbia, Vancouver, 1977. Liggett, J. A., and D. A. Woolhiser, Difference solutions to the shallow-water equation, Jj_ Mech. Di v. Amer . Soc . Civ. Eng . , 93(EM3), 39-71, 1967. Linsley, R. K., Jr., M. A. Kohler, and J. L. H. Paulhus, Hydrology for Engineers, (2nd Ed.), McGraw-Hill, New York, 1 975. Linsley, R. K., Jr., Rainfall-runoff models-An overview, in Rainfall-Runoff Relationship, edited by V. P. Singh, pp. 3-22, Water Resources Publications, Littleton, Colorado, 1 982. Luxmoore, R. J., and M. L. Sharma, Runoff responses to soil heterogeneity: Experimental and simulation comparisons for two contrasting watersheds, Water Resources Research, 16(4), 675-684, 1980. Luxmoore, R. J., Simulated dynamics of variable contributing areas in relation to soil heterogenity, Water Resources  Research (in press), 1982. Machado-Olive, D., Probability-distributed parameters within conceptual catchment models, Ph.D. thesis, University of Lancaster, England, 1975. 139 Matalas, N. C, Time series analysis, Water Resources Research, 3(3), 817-829, 1967. McCuen, R. H., and W. M. Snyder, A proposed index for comparing hydrographs, Water Resources Research, 11(6), 1021-1024, 1975. Moore, R. J., and R. T. Clarke, A distribution function approach to rainfall-runoff modeling, Water Resources Research, 17(5), 1367-1382, 1981. Morel-Seytoux, H. J., and J. Kimzey, User's manual for UNIT: A fortran IV program to identify unit hydrograph ordinates using a constrained least-squares approach, HYDROWAR  Program Rep. CER8Q-81HJM-JK-FC16, Colorado State University, Fort Collins, 1980. Morel-Seytoux, H. J., Optimization methods in rainfall-runoff modeling, in Rainfall-Runoff Relationships, edited by V. P. Singh, pp. 487-507, Water Resource Publications, Littleton, Colorado, 1982. Moss, M. E., Some basic considerations in the design of hydrologic data networks, Water Resources Research, 15(6), 1797-1800, 1979. Nash, J. E., Systematic determination of unit hydrograph parameters, Journal of Geophysical Research, 64(1), 111-115, 1959. Nash, J. E., and J. V. Sutcliffe, River flow forecasting through conceptual models, Part 1, A discussion of principals, Journal of Hydrology, J_0, 282-290, 1970. Natale, L., and E. Todini, A constrained parameter estimation technique for linear models in hydrology, in Mathemat ical  Models for Surface Water Hydrology, edited by T. A. Ciriani, U. Maione and J. R. Wallis, pp. 109-148, Wiley, New York, 1977. 140 Newton, D. W., and J. W. Vineyard, Computer-determined unit hydrograph from floods, Hydraul. Div. Amer. Soc. Civ. Eng., 93(HY5), 219-236, 1967. O'Donnell, T., Methods of computation in hydrograph analysis and synthesis, in Recent Trends in Hydrograph Synthesis, 65-104, Committee for Hydrological Research TNO, The Hague, 1966. Overton, D. E., and D. L. Brakensiek, A kinematic model of surface runoff response, International Symposium on the Results of Research on Representive and Experimental Basins, Int. Ass. Sci. Hydrol. Brussels Publ. 96, 100-112, 1970. • Parlange, J. Y., Analytical theory of water-movement in soils, Joint IAHR and ISSS Symposium on Fundamentals of Transport  Phenomena in Porous Media, J_, pp. 222-236, Huddleston and Barney Ltd., Woodstock, Ont., 1972. Philip, J. R., The theory of infiltration: 1. The infiltration equation and its solution, Soil Science, 83, 345-357, 1957a. Philip, J. R., The theory of infiltration: 2. The profile at infinity, Soil Science 83, 435-448, 1957b. Philip, J. R., The theory of infiltration: 3. Moisture profiles and relation to experiment, Soil Science, 84, 163-178, 1957c. Philip, J. R., The theory of infiltration: 4. Sorptivity and algebraic infiltration equations, Soil Science, 84, 257-264, I957d. Philip, J. R., The theory of infiltration: 5. The influence of the initial soil moisture content, Soi1 Science, 84, 322-339, I957e. 141 Philip', J. R. , The theory of infiltration: 6. Effect of soil water depth over the soil, Soi1 Science, 85, 278-286, 1958a. Philip, J. R., The theory of infiltration: 7., Soil Science, 85, 333-337, 1958b. Philip, J. R., Theory of infiltration in Advances in  Hydroscience, 5, 215-296, 1969. Pionke, H. B., and R. N. Weaver, The Mahantango Creek Watershed-an interdisciplinary watershed research program in Pennsylvania, in Watershed Research in North Amer ica, edited by D. L. Correll, Smithsonian Institution, Edgewater, Maryland, 1977. Quimpo, R.G., Link between stochastic and parametric hydrology, J. Hydraul. Div. Amer. Soc. Civ. Eng., 99(HY3), 461-170, 1 973 . Rawitz, E., E. T. Engman, and G. D. Cline, Use of the mass balance method of examining the role of soils in controlling watershed performance, Water Resources  Research, 6(4), 1115-1123, 1970. Richards, L. A., Capillary conduction of liquids through porous mediums, Physics, j_, 318-333, 1931. Rogowski, A. S., Watershed physics: Model of soil moisture characteristics, Water Resources Research, 1_{6) , 1575-1582, 1 971 . Rogowski, A. S., Two-and three-point models of the soil moisture characteristic and hydraulic conductivity for field use, Joint IAHR and ISSS Symposium on Fundamentals of Transport  Phenomena in Porous Media, j_, pp. 124-136, Huddleston and Barney Ltd., Woodstock, Ont., 1972a. Rogowski, A. S., Watershed physics: Soil variability criteria, Water Resources Research, 8(4), 1015-1023, 1972b. 142 Rogowski, A. S., Variability of the soil water flow parameters and their effect on the computation of rainfall excess and runoff, in Proceedings of the International Symposium on  Uncertainties in Hydrologic and Water Resource Systems, j_, edited by C. C. Kisiel and L. Duckstein, pp. 359-377, Department of Hydrology and Water Resources, University of Arizona, Tucson, 1972c. Rogowski, A. S., Estimation of the soil moisture characteristic and hydraulic conductivity: Comparison of models, Soil  Science, JJ_4(6), 423-429, I972d. Rogowski, A. S., E. T. Engman, and E. L. Jacoby, Jr., Transient response to a layered sloping soil to natural rainfall in the presence of a shallow water table: Experimental results, ARS-NE-30, Agricultural Research Service, USDA, Hyattsville, Maryland, 1974. Rosenblueth, A. and N. Wiener, The role of models in science, Philosophy of Science, 7(4), 316-321, 1945. Russo, D., and E. Bresler, Field determinations of soil hydraulic properties for statistical analyses, Soil Sci.  Soc. Amer. Proc., 44(4), 687-702, 1980. Schultz, E. F., Problems in Applied Hydrology, Water Resource Publications, Littleton, Colorado, 1976. Sharma, M. L., R. J. Luxmoore, Soil spatial variability and its consequences on simulated water balance, Water Resources  Research, J_5(6), 1567-1573, 1979. Sharma, M. L., G. A. Gander, and C. G. Hunt, Spatial variability of infiltration in a watershed, Journal of Hydrology, 45,101-122, 1980. Sherman, L. K., Streamflow from rainfall by unit graph method, Engineering News Record, 108, 501-505, 1932. 143 Smith, R. E., and D. A. Woolhiser, Mathematical simulation of infiltrating watersheds, Hydrology Paper 47, Colorado State University, Fort Collins, 1971. Snyder, W. M. , Hydrographanalysis by the method of least squares, Hydraul. Div. Amer. Soc. Civ. Eng., 81, 793.1-793.25, 1955. Snyder, W. M., Some error properties of segmented hydrograph functions, Water Resources Research, 3(2), 359-374, 1962. Stehale, P., Quantum Mechanics, Holden-Day, San Francisco, 1966. Streikoff, T. , One-dimensional equations of open-channel flow, J. Hydraul. Div. Amer. Soc. Civ. Eng., 95(HY3), 861-876, 1969. Streikoff, T. , Numerical solution of Saint-Venant equations, J.  Hydraul. Div. Amer. Soc. Civ. Eng., 96(HY1), 223-252, 1 970. U. S. Army Corps of Engineers, HEC-1 Flood hydrograph package, Users and Programmers Manuals 723-X6-L2010, 1973. U. S. Environmental Protection Agency, SWMM, Volume No. J_, Water Resources Engineers and Metcalf and Eddy Inc., 1971. U. S. Soil Conservation Service, Computer program for project formulation hydrology, Tech. Release No. 20, 1973. U. S. Soil Conservation Service, National Engineering Handbook,  Section 4, Hydrology, Soil Conservation Service, USDA, Washington, D. C, 1972. Viessman, W., Jr., J. W. Rnapp, G. L. Lewis, and T. E. Harbaugh, Introduction to Hydrology, (2nd Ed.), Harper and Row, New York, 1977. 144 Wallis, J. R. , Multivariate statistical methods in hydrology-a comparison using data' of known function relationships, Water Resources Research, j_(4), 447-461, 1965. Warrick, A. W., G. J. Mullen, and D. R. Nielsen, Scaling field-measured soil hydraulic properties using a similar media concept, Water Resources Research, 13(2), 355-362, 1 977. Williams, J. R., and R. W. Hann, HYMO: Problem-Oriented Computer Language for Hydrologic Modeling, USDA, Agricultural Research Service, 1973. Wood, E. F., Digital catchment model based on subsurface flow, Ph.D. thesis, University of Canterbury, New Zealand, 1973. Wooding R. A., A hydraulic model for the catchment-stream 1: Kinematic wave theory, Journal of Hydrology, 3, 254-267, 1965. Wooding R. A., A hydrologic model for the catchment-stream problem 3: Comparison with runoff observations, Journal of  Hydrology, 4, 21-37, 1966. Woolhiser, D. A., Hydrologic and watershed modeling-state of the art, Trans. Amer. Soc. Eng., 16, 553-559, 1973. Wong, S. T., A multivariate statistical model for predicting mean annual flood in New England, Annals Ass. Amer.  Geographers, 53(3), 298-311, 1963. Yevdjevich, V. M. , Statistical and probability analysis of hydrologic data; Part II, Regression and correlation analysis, in Handbook of Hydrology, edited by V. T. Chow, pp. 8.43-8.67, McGraw-Hill, New York, 1964. Personal Communication, Federer, C. A., USDA-Forest Service, Durham, New Hampshire, 1981. 145 Personal Communication, Gander, G. A., USDA-Agricultural Research Service, Chickasa, Oklahoma, 1981. Personal Communication, Gburek, W. J., USDA-Agricultural Research Service, University Park, Pennsylvania, 1982. Personal Communication, Luxmoore, R. J., Oak Ridge National Laboratory, Oak Ridge, Tennessee, 1981. Personal Communication, Rawls, W. J., USDA-Agricultural Research Service, Beltsville, Md., 1981. 146 o APPENDIX A Unit hydrograph code UNIT 147 C This code computes the coefficients A(I,J) and B(I) for a C system of linear equations used for identifying. Unit C Hydrograph ordinates based on the method of least squares. C ie. sum over J( A(I,J) * X(I)) = B(I) C where , I and J = 1,2,....,M+1 C C Original code , Morel-Seytoux and Kimzey (1980). The code C as shown in this theis was adapted , by Loague (1982) , for C use at UBC. C C IMSL LIBRARY : subroutine LEQT1F C C XRAIN = array for excess rainfall input C XRUN = array for runoff input C **NOTE** for missing runoff data set XRUN(I)= -1. e C IRAIN = period number of last non-zero excess rainfall C IRUN = period of last non-zero runoff C X(J) = unit hydrograph ordinate J = 1,2,...,M C M = memory time of watershed C T1,...,T10 = title C DIMENSION B(700), A(700,700), XRAIN(700), XRUN(700), WKAREA(700), 1 Bl(700,1), X(700), Y(700) C read input data and information READ (5,160) IRAIN, IRUN, M, TI, T2, T3, T4, T5, T6, T7, T8, T9, 1T1 0 DO 1 0 J = 1 , I RUN XRAIN(J) = 0.0 XRUN(J) = 0.0 10 CONTINUE DO 30 I = 1, IRUN READ (5,20) XRAIN(I), XRUN(I) 2 0 FORMAT (FiO.2, 1X, F10.2) 30 CONTINUE MM = M + 1 N = IRUN C calculate coefficients A(I,J) = sum over N=J,J+i,..., C M(XRAIN(N-I+1)*XRAIN(N-J+1)) , where I and J = 1,2,...,M C and J > I C C initialize A-matrix DO 50 I = 1 , 20 DO 40 J = 1, 20 40 A(I,J) = 0. 50 CONTINUE IF (IRAIN .GE. N) GO TO 70 KI = IRAIN + 1 DO 60 I = KI, N 60 XRAIN(I) = 0. 70 DO 100 I = 1, M DO 90 J = I, M SUMIJ =0. DO 80 JJ = J, N XRU = XRUN(JJ) IF (XRU .EQ. - 1.) GO TO 8 0 II = JJ - I + 1 JJJ = JJ - J + 1 AIJ = XRAIN(II) * XRAIN(JJJ) SUMIJ = SUMIJ + AIJ . 80 CONTINUE 148 A (I,J) = SUMIJ C completed 1 loop of J, now increase J by 1 and repeat 90 CONTINUE C completed J loops for one I, now increase I by 1 and repeat 100 CONTINUE C completed A(I,J) matrix for J > I, now complete rest of matrix A (MM, MM) = 0. DO 110 I = 1 , M A(I,MM) = .5 A(MM,I) = 1 . 110 CONTINUE DO 130 I = 2, M 11=1-1 DO 120 J = 1, II 120 A(I,J) = A(J,I) 130 CONTINUE C calculate coefficient B(I) = sum over N = 1,1*1,...,N (XRAIN C (N-I+l)*XRUN(N)) , where I = l,2,...,M DO 150 I = 1 , M SUMRQ = 0. DO 14 0 K = I , N IF (XRUN(K) .EQ. - 1.) GO TO 140 RQ = XRAIN(K - I + 1) * XRUN(K) SUMRQ = SUMRQ + RQ 140 CONTINUE B(I) = SUMRQ C completed loop for B(I) with K = I ,N 150 CONTINUE B ( MM ) = 1 . C completed for all B(I) I = i,M C C print results WRITE (6,170) Tl, T2, T3, T4, T5, T6, T7, TE, TS, TlO, IRAIN, II RUN, M 160 FORMAT (315, A4, A4, A4, A4, A4, A4, A4, A4, A4, A4) 170 FORMAT ('1', 5X, A4, A4, A4, A4, A4, A4, A4, A4, A4, A4, /////, 1 5X, 'PERIOD NUMBER OF LAST NON-ZERO EXCESS RAINFALL = ', 2 115, //, EX, 'PERIOD NUMBER OF LAST NON-ZERO RUNOFF = ', 3 115, //, 5X, 'MEMORY TIME = ', 115, ////) WRITE (6,180) WRITE (6,190) (I ,XRAIN(I) ,XRUN(I ) ,1 = 1 ,I RUN) 180 FORMAT (5X, 'TIME PERIOD', 10X, 'RAINFALL EXCESS', 14X, 'RUNOFF', 1 /, 5X, ' ' , 1 OX, ' ' , 1 4X, 2 ' ' , ///) 190 FORMAT (8X, 115, 17X, FlO.5, 14X, F10.5) DO 200 1=1, MM 200 Bl(I,1) = B(I) CALL LEQT1F(A, 1, MM, 700, Bl, 0, WKAREA, IER) WRITE (6,220) WRITE (6,210) (I,B1(I,1),1=1,M) 210 FORMAT (1X, 16, 5X, 1F9.5) 220_FORMAT ('0', //, 1 OX, 'DISCRETE KERNELS FOR UNIT HYDROGRAPH' , //, 1 10X, ' , //, 5X, 'I', 2 ) C compute maximum discrete kernel AMAXB = 0. DO 230 I = 1 , M IF ( B 1 (I , 1 > .GT. AMAXB) AMAXB = B1(I,1 ) 230 CONTINUE C plot resulting discrete kernels 149 XMAX = FLOAT(M + 3) YMAX = AMAXB + (0.1*AMAXB) DO 240 I = 1, M X(I) = I Y(I) = B1(I , 1 ) 24 0 CONTINUE CALL ALSI2E(8.0, 5.0) CALL ALAXIS('TIME', 4, 'UNIT ORDINATE', 13) CALL ALSCAL(0.0, XMAX, 0.0, YMAX) CALL ALGRAF(X, Y, M, -3) CALL PLOTND STOP END 150 APPENDIX B Distributed model component codes: B.1 Code used to determine soil characteristic curves. B.2 Code used to synthesize storm hydrographs from partial source areas. B.3 Code used to calculate normal discharge rating functions. B.4 Code used for open channel flow routing. appendix b.1 151 C The first part of the code performs computations of soil C hydraulic conductivity and difussivity as a function of C water content and/or pressure. The second part of the code C utilizes Parlanges' approximation to Philip's equations to C compute absorption rate, cumulative soil absorption, C infiltration rates and depth of the wetting front penetration. C C Orginal code, Rogowski (197 1 > . The code as shown in C this thesis was adapted, by Loague (1982), for use at UBC. C C ID = sample identification C I END = termination card (80 columns punched with 9's) C NC = number of incremented pore classes chosen for C calculating data (NC is limited to 99, dimensions C can be changed) C N = number of pore classes between THETA1 and THETAE C M = N+1 C THETAE = water content at air entry pressure, (CM**3/CM**3) C CONE = experimentally obtained or estimated conductivity C (CM/DAY) C TF = field temperature in degrees centigrade C TM = tempeature at matching in degrees centigrade C PSI 1 = initial pressure (CM of water), absolute value C PSIE = absolute value of air entry pressure, (CM) C PSI2 = water entry pressure =(1/2) PSIE C PSI15 = absolute value of 15-bar pressure, (CM) C THET15 = moisture content at 15-bar C STDINC = standard water content increment for calculated C values (CM**3/CM**3) C TINC = incremented THETA (CM**3/CM**3) C PSI = incremented PSI for respective TINC (CM OF WATER) C PCH = intermediate sum of products of coefficients and C heads in conductivity equation C SPCH = final sum of products C TAU = conversion factor that takes into account temperature C and gravity influences C = (325.4*TF+9671.7)/(325.4*TM+9671.7) C A = the exponent alpha in the PSI,THETA function C B = the exponent beta in the PSI, THETA function C PRESSURE = matric suction (CM of water), absolute value C THETA = water content (CM**3/CM**3) C upper limit = higher moisture, lower absolute pressure C CCAL = relative permability, of resistivity ratio(W/WE) C CMAT = matched conductivity (CM/DAY), called 'CONDUCTIVITY' C DPSI = is the partial of PRESSURE (PSI) with respect to . C THETA at a given value of THETA, (CM) C DIF = the diffusivity given as the product of K(THETA) and C the partial of PRESSURE (PSI) with respect to THETA at C a given value of THETA, (CM**2/DAY) C SORP = sorptivity (CM/HRS**0.5) C FS = sorptivity (FT/HRS**0.5) C PROS = initial inf. cap. after one sec. (CM/HRS) C Fl = initial inf. cap. after one sec. (FT/HRS) C ETA = THETA/THETA2 C KE = conductivity in FT/HRS C PHI = solution of one dimensional absorption equation C SS = sorptivity ,Phi 1ip,1969,Advances in Hydroscience C 5(237),CM/SEC**0.5 C S = sorptivity,CM/DAY**0.5 C SINC = normalized value of STDINC 152 C CONE = conductivity at air entry = 1/2 Ksat C HETA(I) = normalized value of* THETA(I) C IDATE = date on which event occured C TSRT = starting time (HRS) C TEND = ending time (HRS) C MSOL = soil identification number C NM = denates initial soil water class in the C moisture characterist C NT = number of intervals a given time period C of rain is divided into C DIMENSION ID(10), TINC(99), PSI(99), SPCH(99), CCAL(99), CMAT(99), 1 DPS1(99), DIF(99), TIN(99), C(99), THETA(99), CP(99), 2 D(99), F(99), G(99), H(99), PHI(99), SUM1(99), SUM2(99), 3 S(99), T(99), TIME(99), CABS(99), ABSRT(99), VO(99), 4 Z(99,99), SUM4(99,99), HETA(99), CPP(99), SUM11(99), 5 SORP(99), PROS(99), ETA(99), HDF(99), FS(99) , F1(99) C read input parameters and variables 10 READ (5,20) IDI, ID2, ID3, ID4, ID5, ID6, ID7, ID8, ID9, ID10, 11 END 20 FORMAT (10A4, 30X, 12) IF (I END - 99) 30, 680, 30 30 READ (5,40) NC, THET15, THETAE,' THETA2, PSI 15, PSI 1 , PSIE, PSI2, 1 CONE, TF, TM 40 FORMAT (13, 3(1X,F6.0), 2(1X,F7.0), 2(1X,F5.0), 2X, F8.0, 1 2(1X,F4.0)) C calculate exponent alpha A = (THET15 - TKETAE) / AL0G(PSI15.- PSIE + 1) C calculate exponent beta B = (THETA2 - THETAE) / ALOG(PSIE - PSI2 + 1) C calculate initil moisture content corresponding to PSI1 THETA1 = (ALOG(PSIl - PSIE + 1)) * A + THETAE C calculate conversion factor TAU = (325.4*TF + 9671.7) / (325.4*TM + 9671.7) C calculate increment size RNC = NC STDINC = (THETA2 - THETA1) / RNC C initialize TINC array TINC(1) = THETA1 TIN(1) = THETA1 NCP1 = NC + 2 DO 50 I = 2, NCP1 50 TIN(I) = TIN(I - 1) + STDINC C calculate midpoint values of each increment for TINC DO 60 I = 2, NCP1 60 TINC(I) = (TIN(I) + TIN(I - 1)) * 0.5 C calculate adjusted PSI(I) values at midpoint of each C increment N = ((THETAE - THETA1)/STDINC) + 0.5 DO 110 IIIII = 1, NCP1 C (11111 ) = TINC(IIIII) - THETAE IF (Cdllll ) ) 70, 70, 90 7 0 CONTINUE DO 80 I = 1, N PSI(I) = PSIE - 1 + EXP((TINC(I) - THETAE)/A) C calculate partial of PRESSURE with respect to THETA DPSI(I) = (l./A) * EXP((TINC(I) - THETAE)/A) DPSI(I) = ABS(DPSI(I)) 80 CONTINUE GO TO 110 153 90 CONTINUE M = N + 1 DO 100 I = M, NCP1 PSI(I) = PSIE + 1 - EXP((TINC(I) - THETAE)/B) C calculate partial of PRESSURE with respect to THETA DPSI(I) = (1./B) * EXP((TINC(I) - THETAE)/B) 100 CONTINUE 1 10 CONTINUE C calculate product of coefficient and 'HEAD' terms for C each pore class NCI = NC + 1 KL = NC1 DO 130 J = 1, NC1 NL = NCP1 - J PCH = 0.0 DO 120 I = J, NC1 PCH = PCH + (2*1 + 1 - 2*J) * (1./PSI(NL)) ** 2 120 NL = NL - 1 SPCH(KL) = PCH C calculate W for a given water content and pressure CCAL(KL) = SPCH(KL) 130 KL = KL - 1 DO 140 I = 1, NCI C calculate relative conductivity CCAL(I) = CCAL(l) / CCAL(NCI) * ((THETAE/TINC(I ) ) * * 2 ) * 2 C calculate matched conductivity at each water content CMAT(I) = TAU * CONE * CCAL(I ) C calculate diffusivity DIF(I) = CKAT(I) * DPS!(I) DIF(I) = ABS(DIF(I)) 140 CONTINUE WRITE (6,150) IDI, ID2, ID3, ID4, ID5, ID6, ID7, ID8, ID9, ID1 0 150 FORMAT ('1', 20X, 10A4i WRITE (6,160) 160 FORMAT ('0', ' NC THET15 THETAE THETA2 PPSI15 PSI 1 PSIE PSI2 1 CONE TF TM ' ) WRITE (6,170) 170 FORMAT (' ', ' (CM3/CM3) (CM OF WATER) (CM 1/DAY) DEG.C '/) WRITE (6,180) NC, THET15, THETAE, THETA2, PSI15, PSI1, PSIE, PSI2, 1 CONE, TF, TM 180 FORMAT (' ', 13, 3(1X,F6.4), 2(1X,F7.1), 2(1X,F5.1), 1X, F8.4, 1 2(1X,F4.1)) WRITE (6,190) 190 FORMAT CO', ' CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFF 1USSIVITY DPSI/DTHETA') . WRITE (6,200) 200 FORMAT (' ', ' (CM) (CM3/CM3) (CM/DAY) (CM 12/DAY '/) DO 220 I = 1, NCI WRITE (6,210) I, PSI(I), TINC(I), CCAL(l), CMAT(I), DIF(I), 1 DPSI(I) 210 FORMAT (' ', 13, 2X, F9.1, IX, F6.4, 2X, 1PE9.2, 4X, 1PE9.2, 6X, 1 1PE9.2, 6X, 1PE9.2) 220 CONTINUE C computation of sorptivity as a function of THETA/THETAE C Parlange, Guelph.Symp equation 10 WRITE (6,230) 230 FORMAT ('1', ' SORPTIVITY AS A FUNCTION OF WATER CONTENT '//) FE = CONE / (24.0*2.54*12.0) 154 i 240 1 250 1 260 270 280 290 300 310 320 330 340 350 360 370 380 390 WRITE (6,240) THETAE, ID1, ID2, ID3, ID4 IDI0, FE FORMAT CO', ' THETAE = ', F6.4, 5X, 10A4, 1PE13.4, //) WRITE (6,250) FORMAT C ', ' CLASS INITIAL FLUX (CM./HRS) 0.5) Fl(FT/HRS) FS(FT/HRS**.5) THETA/THETA2 DO 260 I = 1, NC1 ETA(I) = TIN(I) / THETA2 CONTINUE NM = 1 MN = NM + 1 DO 280 I = NM, NC1 HDF(I) = DIF(1) / 24.0 DO 2 90 I = MN, NCI CPP(I) = (TINC(I) - TINC(NM)) * HDF(I) * STDINC SUM 11(NM) = 0.0 DO 300 I = MN, NC1 SUM11(I) = SUM11(I - 1) + CPP(I) SORP(NM) =• (2.0*SUM11(NCI)) ** 0.5 FS(NM) = SORP(NM) / (2.54*12.0) PROS(NM) = (0.5*SORP(NM)/(1.0/60.0)) + (CONE/24.0) F1(NM) = PROS(NM) NM = NM + 1 IF (NM - NC1) 270, SORP(NC1) = 0.0 DO 330 I = 1, NC1 WRITE (6,320) I, FORMAT (' ', 2X, I 6X, 0PE6.4 CONTINUE computation of PHI 111(2)134,1971 READ (5,340) NM, FORMAT (213, MN = NM + 1 HETA(NM) = 0 IF (NC - MN) ID5, ID6, ID7, ID8, ID9, A 4, ' KE(FT/HRS) = ' , SORPTIVITY(CM/HRS * * THETA MID.INT.', //) / (2.54*12.0) 310, 310 PROS(I), SORP(I) 13, 10X, 1PES.2, , 9X, F6.4) Fl (I ), FS(I ) , ETA(I ), TINC(I ) 15X, E9.2, 10X, 2(3X,E9.2), AND sorptivity from Parlange Soil Science 2F5, .0 10, NT, 2, TSTRT, 16, 3X, TEND, 13) I DATE, MSOL 1 0 , and 350 STDINC normalize THETA DO 360 I = MN, NC1 HETA(I) = (TINC(MN - 1) -SINC = STDINC / (THETA2 -DO 370 I = MN, NC1 CP(I) = SINC * (DIF(I)) TINC( I ) ) • TI NC(MN -/ (TIN C(MN 1 ) ) 1) - THETA2! D(I ) = CONTINUE SUM 1 (NM) SUM2(NM) DO 380 I SUM1(I) SUM2(I) CONTINUE compute (HETA(I)) * (CP(I)) = 0.0 = 0.0 = MN, NCI = SUM1(I -= SUM2(I -first term 1 ) 1 ) CP (I ) D(I ) Of * * equatlon E = (2.0*SUM2(NC1)) ** 0.5 compute second term of equation DO 3 90 I = MN, NC1 F(I) = (HETA(I)) * SUM 1(NCI) G(I) = CP(I) / F(I) CONTINUE H(NCP1) = 0.0 1 4 (Parlange,71) 14 (Parlange,71 MNN = NCP1 - MN DO 400 L = 1, MNN I = NCP1 - L H(I) = H(I + 1) + G(I) 400 CONTINUE C compute PHI as a product of the first and second terms C of equation 14 DO 410 I = MN, NC1 PHI(I ) = H(I) * E 410 CONTINUE C integrate PHI to obtain sorptivity S on per day basis S(NM) = 0.0 DO 420 I = MN, NC 1 420 S(I) = S(I - 1) + (STDINC*PHI(I)) C compute sorptivity of per second basis SS = S(NC1 ) / 293.9388 SSS = S(NC1) * 10.0 / 24.0 ** 0.5 WRITE (6,430) 430 FORMAT ('1', WRITE (6,440) 4 40 FORMAT (' 1 /)" DO 4 60 I = MN 4 50 FORMAT (' 4 60 CONTINUE WRITE (6,470) 4 70 FORMAT ('0', VALUES OF PHI AND SORPTIVITY ', //) PSI(CM) THETA(CM3/CM3) THETA* PHI NC 1 WRITE (6,450) I, PSI(I), TINC(I), HETA(I), PHI(I) 13, 2X, F9.1, 5X, F6.4, 7X, F6.4, 7X, 1PE9.2) S(NC1), SS, SSS SORPTIVITY(CM/DAY**0.5) = ', 1PE9.2, 1 ' (CM/SEC**0.5)= ', 1PE9.2, 2 ' (MM/HRS**0.5)=', 1PE9.2, //) WRITE (6,480) A, 3, SINC, STDINC 480 FORMAT (4(4X,F7.4)) C computation of infiltration capacity C using values of sorptivity SS(CM/HRS**0.5),and conductivity C at air entry, cone,and Philip's equation. TINT = (TEND - TSTRT) / 50.0 TIME(1) = 0.0 C sorptivity in CM/HRS**0.5 and hydraulic conductivity C in CM/HRS SS = S(NC1) / 24.0 ** 0.5 CONE = CONE / 24.0 DO 490 K = 2, 51 TIME(K) = TIME(K - 1) + TINT T(K) = (TIME(K)) ** 0.5 VO(K) = (0.5*SS/T(K)) + CONE 4 90 CONTINUE C Parlange considers this VO negative and less than C cone,(Guelph,Symp.) WRITE (6,500) 500 FORMAT ( ' 1 ' , ' INFILTRATION CAPACITY (CM/HRS) '//) WRITE (6,510) 510 FORMAT (' ', ' K TIME(HRS) INF.CAPP.(CM/HRS) '//) DO 530 K = 2, 51 L = K - 1 WRITE (6,520) L, TIME(K), VO(K) 520 FORMAT (' ', 13, 2(6X,1PE9.2)) 530 CONTINUE WRITE (6,540) IDATE, TSTRT, TEND, TINC(NM) 540 FORMAT CO', ' DATE ', 16, 'START TIME(HRS)=', F6.2, 1 'END TIME(HRS) = ' , F6.2, 'THETA INITIAL(CM**3/CM**3) = ' 156 2 F6.4) C computation of moisture profiles, Parlange EQ.24 DO 590 K = 2, 11 MN = NM + 1 DO 570 I = NM, NC Z(I,K) = (DIF(I)*STDINC) / ((CMAT(NC1)*TINC(I)) - CMAT(I)) IF (Z(I,K)) 550, 560, 560 550 Z(I,K) = (DIF(I)*STDINC) / ((CMAT(NCl)) - CMAT(I)) 560 CONTINUE 570 CONTINUE TINT = (TEND - TSTRT) / 10.0 TIME(1) = 0.0 TIME(K) = TIME(K - 1) + TINT Z(NC1,K) = CONE * (TIME(K)) SUM4(NCP1,K) = 0.0 NMM = NCP1 - NM DO 58 0 I = 1, NMM NL. = NCP1 - 'I 580 SUM4(NL,K) = SUM4(NL + 1,K) + Z(NL,K) 590 CONTINUE WRITE (6,600) 600 FORMAT (T, ' MOISTURE PROFILES , Z(CM) '//) WRITE (6,610) 610 FORMAT ('0', ' I THETA* K=1 K=2 K=3 K=4 1 K=5 THETA(CM**3/CM**3) '//) DO 630 I = NM, NC1 WRITE (6,620) I, HETA(I), (SUM4(I,K),K=2,6), TINC(I) 620 FORMAT (' ', 13, 2X, F6.4, 5(2X,1PE9.2), 5X, 0PF6.4) 630 CONTINUE WRITE (6,640) 64 0 FORMAT ('0', ' MOISTURE ROFILES CONTINUED ,Z(CM) '//) WRITE (6,650) ' 650 FORMAT ('0', ' I THETA* K=6 K=7 K=8 K=9 1 K=10 THETA(CM**3/CM**3) '//) WRITE (6,660) I, HETA(I), CSUM4(I,K),K=7,11), TINC(I) 660 FORMAT C ', 13, 2X, F6.4, 5(2X,1PE9.2), 5X, 0PF6.4) 67 0 CONTINUE GO TO 10 680 STOP END APPENDIX B.2 157 C This code is for the synthesis of storm hydrographs from C partial areas C C Orginal code ,Engman (1974). The code as shown in C this thesis was adapted, by Loague (1982), for use at UBC. C C MHR = hours from raingage chart C MIN = minutes from raingage chart C PACCUM = accumulated precip in inches from raingage chart C W = channel width in feet C SECLEN = delta x, incremental length of flow plane for routing C SECLEN2 = delta x for overland flow routing if changed C RCHLEN = length of main channel reach between xsects in feet C SLOPLl(),SLOPR() = average slope values for overland flow C plane in each soil zone from SCS maps C DEPL(),DEPR() = total depth of depression storage C for that soil zone in feet C WDTH() = perpendicular distance from stream to soil boundary C w = actual width of channel water surface in feet C XLLL = length of flow plane (maximum possible) C NEND = number of increments available for routing C ie. number of increments XLLL can be devided into C XEND = number of overland flow routing sections C XR(),XL() = the dimension of the soil zones on either C side of the channel measured in feet from the C channel to the farthest edge (should be even C multiples of SECLEN) C TIMINC = computational time interval in seconds C XMANNN = mannings "N" for overland flow C SLPRNT = 0.0 infiltration and soils information not printed C DPPRNT = 0.0 the depths are not printed C PRPRN'T = 0.0 the values of PRE() are not printed C XPUNCH =0.0 QI cards are not punched C SOILNH = soil identification number C SOILDP = depth of top soil layer in feet C SOLDP2 = depth of second soil layer in feet C THETA2 = soil water content C THETAE = soil water content at air entry C DEGSAT = degree of saturation , THETA2/THETA(saturation) C FRQDEG = frequency of soil moisture from a probability C distribution C FS = sorptivity in ft/sec**.5 C FK = conductivity at air entry in ft/sec C Fl = initial infiltration value in ft/sec C NTINT = length of array (ie. 1.5 times the length of C the storm so the hydrograph will have a full C recession and not be cut short) C * note * NTINT will always be 40 for short storms C PREX = the precipitation excess after depression storage C is subtracted C PRCP = rainfall intensity in inches/hour C DUR = duration of rainfall DIMENSION MHR(50), MIN(50), PACCUM(50), PTOT(50), ITTOT(50) DIMENSION THETA2(10), THETAE(10), DEGSAT(10), FRQDEG(10) DIMENSION XL(10), XR(10), PINF(500), WFRNT(500) DIMENSION PEX(10,500), QLLL(500), QLLR(500), QL(500), PREX(10,500) DIMENSION XLLL(500), XLLR(500) DIMENSION FS(10), FK(10), F1(10), THETAI(10) DIMENSION LI STL(10), LISTR(10) 158 10 20 30 40 50 60 70 80 DIMENSION SOILDPO0), THETI2O0), THET22(10), THETE2 (10), 1 DEGST2(10), FRQDG2(10), FS2O0), FK2(10), F12(10), 2 SOLDP2(10) DIMENSION SLOPLO0), SLOPRO0), DEPL(lO), DEPR(lO) INTEGER SOILN(IO), SOIL2(10) COMMON PRE(500,500), FLO(500,500), DPTK(500,500), V01(10,500) 1 FTLONG(500), P(500), SLOP(500) LOGICAL*1 DATE(70) LOGICAL*1 GAGE(70) LOGICAL*1 SECTON(70) FORMAT (70A1) (212, F14.7, 11) (8F10.0) (13 ( ' 1 (' ( ' FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT '//> 90 100 FORMAT FORMAT 1 110 FORMAT ION AND 2 120 FORMAT FORMAT FORMAT FORMAT FORMAT FORMAT ( ' 08X ' FK ( ' ( ' 08X ( ' 1 EXCESS //) 2X, 7F10.0, F4.0, 11) 45X, '<<< SOIL PARAMETERS >>: IX, 13, 8(2X,F12.5)///) 1X, 13, 6X, 13, 5(2X,F12.5)) 'SOIL*', 06X, 'THETA21, 08X, 'DEGSAT', 08X, 'FRQDEG', 07X, (FT/HR)', 0 5X, 'F1(FT/HR)'/) 'SECONDS PER TIMI NT = ', F5.0////) 'SOIL*', 03X, 'TIMI NT' , 06X, 'VOl(FT)', 08X, PEX(FT)', 07X, 'PINF(FT)', 7X, 'WFINC(FT)'/) 5X, ' DIVISION OF TOTAL PRECIPITATION INTO INF1LTRATI COMPONENTS USING SOIL PARAMETERS AND RAINGAGE DATA'/ 'THETAE', 08X, 'THETAI 'FS(FT/HR)', 05X, 1 P(F1 1 30 140 1 50 1 60 1 70 (' ', 10X, 'DATE OF EVENT: ', 70A1//////) (' ', 'ORIGINAL RAINFALL DATA FROM ', 70A1//) (' ', 30X, 'TIME', 06X, 'INCHES'/) (' ', 30X, 212, IX, F10.2) ('I', 'CALCULATION OF LATERAL INFLOW HYDROGRAPHS' (' ', 'TC? LAYER SOIL DEPTH=', F5.3, 5X, 'SECOND LAYER SOIL DEPTH=', F7.3) initialize ail arrays used in' the precip breakdown DO 180 J = 1, 500 180 1 90 200 210 220 SLOP (J ', DO 200 = 0.0 J = 1 , 500 1 , 500 = 0.0 = 0.0 = 0.0 230 DO 190 K = DPTH(K,J) FLO(K,J) PRE(K,J) CONTINUE CONTINUE DO 220 J = 1 , DO 210 K = PREX(K,J) PEX(K,J) CONTINUE CONTINUE DO 230 J = 1 , XLLL(J) = 0 PINF(J) = .0 XLLR(J) = 0 FTLONG(J) = P(J) = 0.0 QLLR(J) = 0.0 QLLL(J) = 0.0 QL(J) = 0.0 CONTINUE DO 240 J = 1, 50 500 1 , 10 = 0.0 = 0.0 500 0 0 0 0.0 159 MIN(J) = 0.0 MHR(J) = 0 MIN(J) = 0 PACCUM(J) = 0.0 PTOT(J) = 0.0 ITTOT(J) =0.0 240 CONTINUE C read the event date and raingage used READ (5,10) DATE READ (5,10) GAGE C read breakpoint raingage data; after last card, insert a card , C of all 1's I = 1 250 READ (5,20) MHR(I), MIN(I), PACCUM(I), NSTOP IF (NSTOP .NE. 0) GO TO 260 1 = 1 + 1 GO TO 250 260 NPINTS = I-- 2 C read time interval of calculations in seconds READ (5,30) TIMINC, SECLEN, TOLR, XEND, SLPRNT, DPPRNT, PRPRNT, 1XPUNCH NEND = XEND INCTIM = TIMINC XEND3 = XEND DELTX = SECLEN C. convert breakpoint data to precip depth vector NTSUM = 0 DO 260 1=1, NPINTS PTOT(I) = (PACCUM ( I •+ 1) - PACCUM(U) / 12. INCHR = MHR(I + 1) - MHR(I) INCMIN = MIN(I + 1) - MIN(I) IF (INCMIN .GE. 0) GO TO 27 0 INCMIN = INCMIN + 60 INCHR = INCHR - 1 270 ITTOT(I) = (INCHR*3600) * (INCMIN*60) + NTSUM 280 NTSUM = ITTOT(I) PSUM = 0.0 PCUM = 0.0 NSECSS = 0 ITIME = 0 ITSUM = 0 1 = 1 290 NSECSS = NSECSS + INCTIM ITIME = ITIME + 1 IF (NSECSS .GE. ITTOT(NPINTS)) GO TO 320 300 IF (NSECSS .LE. ITTOT(I)) GO TO 310 ITSUM = ITTOT(I) PSUM = PTOT(I) 1 = 1 + 1 GO TO 300 310 SECS = NSECSS TTOT = ITTOT(I) TSUM = ITSUM P(ITIME) = ((SECS - TSUM)/(TTOT - TSUM)) * (PTOT(I) - PSUM) + 1PSUM - PCUM PCUM = PCUM + P(ITIME) GO TO 290 320 P(ITIME) = PTOT(NPINTS) - PCUM C write heading,date,gage,and orginal precip data WRITE (6,110) 160 WRITE (6, 120) DATE, .WRITE (6, 130) GAGE WRITE (6,90) TIMINC WRITE (6,140) NPREC = NPINTS + 1 DO 330 K = 1, NPREC 330 WRITE (6,150) MHR(K), MIN(K), PACCUM(K) C read soil input data C C top soil layer C after last card insert card with all 3's I = 1 340 READ (5,40) SOILN(I), THETA2(I), THETAE(I), DEGSAT(I), FRQDEG(I), 1FS(I), FK(I), F1(I), SOILDP(I), MSTOP IF (MSTOP .GT. 2) GO TO 350 1 = 1 + 1 GO TO 340 350 I = 1 . 360 CONTINUE C second soil layer read in data C after last card insert card with all 6's READ (5,40) SOIL2U), THET22(I), THETE2 (I ) , DEGST2(I), FRQDG2 (I ) , 1FS2(I), FK2(I), F12(I), SOLDP2U), MSTOP IF (MSTOP .GT. 5) GO TO 370 1 = 1 + 1 GO TO 360 370 1=1-1 C calculate soil-time array of VOl, excess, and infiltration C print initial soil parameters and calculated output NTI NT = 1.5 * I TIME + 1 IF (NTI NT .LT. 40) NTI NT =40 DO 500 NSOIL = 1, I IF (FS(NSOIL)) 360, 380, 400 380 DO 390 INP = 1, NT I NT 390 PEX(NSOIL,INP) = P(INP) GO TO 440 400 CONTINUE THETAI (NSOIL) = DEGSAT(NSOI L) * THETA2(NSOIL) V01(NSOIL,l) = Fl(NSOIL) * TIMINC / 3600. PEX(NSOIL,l) = P(l) - VOl(NSOIL,1) IF (PEX(NSOIL,1) .GT. 0.0) PINF(1)V= VOl(NSOIL,1) IF (PEX(NSOIL,1) .LE. 0.0) PINF(1) = P(1) WETFRT = PINF(1) / (THETAE(NSOIL) - THETAI(NSOIL)) WFRNT(1) = WETFRT DO 410 INP = 2, NT I NT RLTIME = INP * TIMINC / 3600. VOl(NSOIL,INP) = ((0.5*FS(NSOIL)/RLTIME**0.5) + FK(NSOIL)) * 1 TIMINC / 3600. PEX(NSOIL,INP) = P(INP) - VOl(NSOIL,INP) IF (PEX(NSOIL,INP) .GT. 0.0) PINF(INP) = VO1(NSOIL,INP) IF (PEX(NSOIL,INP) .LE. 0.0) PINF(INP) = P(INP) WETFRT = WETFRT + PINF(INP) / (THETAE(NSOIL) - THETAI(NSOIL)) WFRNT(INP) = WETFRT IINP = INP C checking to see if wetting front has proceeded below C the top soil. if it has go to second layer which now C controls VOl IF (WETFRT .GT. SOI LDP(NSOIL)) GO TO 420 410 CONTINUE 420 XWET = 1.0 161 THETI2(NS0IL) = DEGST2(NS0IL) * THET22(NSOIL) DO 430 INP = IINP, NTINT RLTIME = INP * TIMINC / 3600. VOl(NSOIL,INP) = ((0.5*FS2(NSOIL)/RLTIME**0.5) + FK2(NSOIL)) * 1 TIMINC / 3600. PEX(NSOIL,INP) = P(INP) - VOl(NSOIL,INP) IF (PEX(NSOIL,INP) .GT. 0.0) PINF(INP) = VOl(NSOIL,INP) IF (PEX(NSOIL,INP) .LE. 0.0) PINF(INP) = P(INP) WETFRT = WETFRT + PINF(INP) / (THETAE(NSOIL) - THETAI(NSOIL)) WFRNT(INP) = WETFRT 4 30 CONTINUE • IF (SLPRNT .LE. 0.0) GO TO 490 440 CONTINUE IF (FS(NSOIL)) 450, 450, 470 450 WRITE (6,460) 460 FORMAT (' ', 'LATERAL INFLOW FROM IMPERVIOUS AREA ,.PEX=PRECI P' ) GO TO 470 470 CONTINUE write orginal soils data •WRITE (6,50) WRITE (6,80) WRITE (6,60) SOILN(NSOIL), THETA2(NSOIL), THETAE(NSOIL), 1 THETAI(NSOIL), DEGSAT(NSOIL), FRQDEG(NSOIL), FS(NSOIL), 2 FK(NSOIL), Fl(NSOIL) WRITE (6,60) SOIL2(NSOIL), THET22(NSOIL), THETE2(NSOIL), 1 THETI2(NSOIL), DEGST2(NSOIL), FRQDG2(NSOIL), FS2(NS01L), 2 FK2(NSOIL), F12(NSOIL) WRITE (6,170.) SOILDP(NSOIL) , SOLDP2 (NSOI L ) write out infi1tration,precipitation excess and depth of the wetting front. WRITE (6,100) DO 480 INP = 1, NTINT 480 WRITE (6,70) SOILN(NSOIL), INP, VO1(NSOIL,INP), P(INP), 1 PEX(NSOIL,INP), PINF(INP), WFRNT(INP) 4 90 CONTINUE 50 0 CONTINUE NNSOIL = I 510 CONTINUE set arrays to zero DO 520 1=1, 500 DO 520 J = 1, 500 PRE(I,J) = 0.0 520 CONTINUE DO 530 L = 1, 10 XL(L) = 0.0 XR(L) = 0.0 SLOPL(L) =0.0 SLOPR(L) =0.0 DEPL(L) = 0.0 DEPR(L) = 0.0 LI STL(L) = 0 530 LISTR(L) = 0 I = NNSOIL read in watershed geometry READ (5,540) SECTON, IZSTOP 540 FORMAT (70A1, 9X, II) IF (IZSTOP - 9) 550, 1040, 550 550 READ (5,560) (LISTL(L),L=1,10), (LISTR(L),L=1,10), LISTNL, LISTNR 560 FORMAT (1012, 1012, 12, 12) READ (5,570) (XL(L),L=1,LISTNL), (XR(L),L=1,LISTNR) 570 FORMAT (16F5.0) READ (5,570) (SLOPL(L),L=1,LISTNL), (SLOPR(L),L=1,LISTNR) READ (5,570) (DEPL(L),L=1,LISTNL), (DEPR(L),L=1,LISTNR) READ (5,30) RCHLEN, W, XMANNN, SECLN2, XEND2 IF (SECLN2 .GT. 0.0) GO TO 580 XEND = XEND3 NEND = XEND SECLEN = DELTX GO TO 590 580 SECLEN = SECLN2 XEND = XEND2 NEND = XEND 590 CONTINUE C subtracting detention storage only when infiltration C is exceeded L = 1 600 LIST = L NSOIL = LI STL(L) DETENT = DEPL(LIST) DO 630 INP = 1, NTINT DELDEP = 0.1 * DEPL(LI ST) IF (PEX(NSOIL,INP) .LE. 0.0) GO TO 620 IF (DETENT .LE. 0.0) GO TO 620 IF (DELDEP .LE. PEX(NSOIL,INP)) GO TO 610 DETENT = DETENT - PEX(NSOIL,INP) PREX(NSOIL,INP) = 0.0 GO TO 630 610 PREX(NSOIL,INP) '= PEX(NSOIL,INP) - DELDEP DETENT = DETENT - DELDEP GO TO 630 620 PREX(NSOIL,INP) = PEX(NSOIL,INP) 6 30 CONTINUE L = L + 1 IF (L .LE. LISTNL) GO TO 600 XN2 = XEND LN2 = NEND C distributing SLOPE and PREX to each routing segment C in the flow plane DO 660 LIST = 1, LISTNL DO 650 I TINT = 1 , NTINT XN1 = XN2 - XL(LI ST) / SECLEN LN1 = XN1 JOK = LISTL(LIST) DO 640 L = LN1, LN2 SLOP(L) = SLOPL(LI ST) 640 PRE(L,ITINT) = PREX(JOK,ITINT) 650 CONTINUE LN2 = LN1 - 1 660 CONTINUE CALL SUROUT(TIMINC, NEND, SECLEN, XMANNN, I TIME, TOLR) DO 67 0 I TINT = 1, NTINT XLLL(ITINT) = FTLONGfI TINT) 670 QLLL(ITINT) = FLO(NEND,ITINT) 680 CONTINUE C exact duplicate of left side calculations C right side partial area DO 700 J = 1, 500 DO 690 K = 1, 500 PRE(K,J) =0.0 690 CONTINUE 700 CONTINUE DO 710 K = 1, 500 710 SLOP(K) = 0.0 L = 1 720 LIST = L NSOIL = LISTR(L) DETENT = DEPR(LIST) DO 750 INP = 1, NTINT DELDEP = 0.1 * DEPR(LIST) IF (PEX(NSOIL,INP) .LE. 0.0) GO TO 740 IF (DETENT .LE. 0.0) GO TO 740 IF (DELDEP .LE. PEX(NSOIL,INP)) GO TO 730 DETENT = DETENT - PEX(NSOIL,INP) PREX(NSOIL,INP) = 0.0 GO TO 750 730 PREX(NSOIL,INP) = PEX(NSOIL,INP) - DELDEP DETENT = DETENT - DELDEP GO TO 7 50 740 PREX(NSOIL,INP) = PEX(NSOIL,INP) 750 CONTINUE L = L + 1 IF (L .LE. LISTNR) GO TO 720 XN2 = XEND LN2 = NEND DO 780 LIST = 1, LISTNR DO 77 0 I TINT = 1 , NTINT XN1 = XN2 - XR(LIST) / SECLEN LN1 = XN 1 JOK = LISTR(LIST) DO 760 L = LN1, LN2 SLOP(L) = SLOPR(LIST) 760 PRE(L,ITINT) = PREX(JOK,ITINT) 770 CONTINUE LN2 = LN1 - 1 780 CONTINUE CALL SUROUT(TIMINC, NEND, SECLEN, XMANNN, I TIME, TOLR) DO 790 I TINT = 1 , NTINT XLLR(ITINT) = FTLONG(ITINT) 790 QLLR(ITINT) = FLO(NEND,ITINT) C total lateral inflow C sums left + right sides + channel precipitation 800 CONTINUE DO 810 INQQ = 1, NTINT QL(INQQ) = QLLL(INQQ) + QLLR(INQQ) + W * P(INQQ) / 3600 810 CONTINUE QLT = 0.0 C volume of precip excess DO 820 ITQL = 1, NTINT QLT = QLT + QL(ITQL) * TIMINC 820 CONTINUE C total volume of runoff from reach QLTT = QLT * RCHLEN C format for output C print out and punched Card output WRITE (6,160) WRITE (6,10) SECTON WRITE (6,830) (DEPL(L),L=1,LISTNL) 830 FORMAT (' ', 'LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE' 1 10(F6.4,3X)) WRITE (6,840) (DEPR(L),L=1,LISTNR) 164 840 FORMAT (' ', 'RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE', 5X, 1 10(F6.4,3X)) WRITE (6,850) (SLOPL(L),L=1,LISTNL) 850 FORMAT (' ', 'LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE', 5X, 1 10(F6.4,3X)) WRITE (6,860) (SLOPR(L),L=1,LISTNR) 860 FORMAT (' ', 'RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE', 5X, 1 10(F6.4,3X)) WRITE (6,870) (XL(L),L=1.LISTNL) 870 FORMAT (' ', 'LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM', 5X, 1 10(F6.1,3X)) WRITE (6,880) (XR(L),L=1,LISTNR) 880 FORMAT (' ', 'RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM', 5X, 1 10(F6.1,3X)) WRITE (6,890) RCHLEN, W, XMANNN, SECLEN 890 FORMAT (' ', 'REACH LENGTH=', 5X, F7.2, 5X, 'STREAM WIDTH=', 5X, 1 F5.2, 5X, 'MANNINGS N=', 5X, F8.6, 5X, 'DELTAX=', F7.2) WRITE (6,900) QLT 900 FORMAT (' ', 'VOLUME OF PRECIPITATION EXCESS=', F20.10, 5X, 1 'CU FT') WRITE (6,910) QLTT 910 FORMAT (' ', 'TOTAL RUNOFF VOLUME FROM REACH=', F20.10) WRITE (6,920) 920 FORMAT ('-', 30X, 'PRECIP EXCESS VALUES FOR EACH DELT') WRITE (6,930) 930 FORMAT (' ', ' QL CFS/FT PRECIP DEPTH LEFT SIDE 1QL WIDTH OF CONTRIB AREA RIGHT SIDE QL WIDTH OF RIGHT SIDE') DO 940 I = 1, NTINT 94 0 WRITE (6,950) QL(I), P(I), QLLL(I ), XLLL(I ), QLLR(I ), XLLR(I) 950 FORMAT (' ', 6(F14.7,5X)) IF (XPUNCH .LE. 0.0) GO TO 990 DO 960 1=1, NTINT 960 PUNCH 970, QL(I) 970 FORMAT (20X, F12.7, 48X) DUMMY = 1111111. PUNCH 980, DUMMY ' 98 0 FORMAT (F10.0) 990 CONTINUE DO 1010 I = 1, NTINT WRITE (8,1000) QL(I) 1000 FORMAT (' ', 19X, F12.7, 48X) 1010 CONTINUE DUMMY = 1111111. WRITE (8,1020) DUMMY 1020 FORMAT (' ', F10.0) 1030 CONTINUE DPCT = 0.0 GO TO 510 1040 STOP END SUBROUTINE SUROUT(TIMINC, NEND, SECLEN, XMANNN, I TIME, TOLR) C subroutine routes depth of precip excess over partial C area length usings simple kinematic formulation COMMON PRE(500,500), FLO(500,500), DPTH(500,500), VO1(l0,500), 1 FTLONG(500), P(500), SLOP(500) DUR = I TIME TINT = TIMINC / 60. NTINT = 1.5 * ITIME IF (NTINT .LT. 40) NTINT = 40 NSECS = TIMINC * I TIME 165 NTPL1 = NTINT + 1 NTIMEP = NSECS / TIMJNC INTER = NTIMEP + 1 NTPLS = NTINT + 1 DO 10 I TINT = 1, NTINT 10 FTLONG(I TINT) = 0.0 DO 30 I TINT = 1 NTPLS DO 20 I SECT = 1, NEND 2 0 DPTH(I SECT,ITINT) = 0.0 30 CONTINUE DO 50 I TINT = 1, NTINT DO 4 0 I SECT = 1 , NEND 40 FLO(ISECT,ITINT) = 0.0 50 CONTINUE C set initial depth = precipitation excess DO 60 ISECT = 1, NEND 60 DPTH(I SECT,1) = PRE(I SECT,1 ) DO 210 ITINT = 1, NTINT C calculates flow rate from manning's equation NTT = 0 DO 80 ISECT = 1, NEND IF (DPTH(I SECT,I TINT) .LE. 0.0) GO TO 70 FLO(I SECT,ITINT) = 1.486 * (DPTH(I SECT,ITINT)* * 1.67) * (SLOP( 1 ISECT)**0.5) / XMANNN GO TO 80 7 0 FLO(I SECT,I TINT) = 0.0 8 0 CONTINUE ITPL1 = ITINT + 1 DO 200 ISECT = 2, NEND I SMI 1 = I SECT - 1 QIN = FLO(I SMI 1 ,I TINT) QOUT = FLO(I SECT,I TINT) C routing with continuity equation IF (PRE(ISECT,ITPL1) .LT. 0.0) GO TO 90 PRP = PRE(ISECT,ITPL1) GO TO 100 90 PRP = 0.0 100 YDELT = ((QIN - QOUT)*60.*TINT/SECLEN) + PRP C calculating new depth DPTH(ISECT,ITPL1) = DPTH(I SECT,ITINT) + YDELT A IF (PRE(ISECT,ITPL1) .GT. 0.0) GO TO 120 DIF = PRE(I SECT,ITPL1 ) + DPTH(I SECT,ITPL1 ) C PRE is subtracted if PRE is negative C this amount to be re-infi1trated for this DELTAX IF (DIF .LT. 0.0) GO TO 110 PRE'(ISECT,ITPL1 ) = 0.0 DPTH(I SECT,ITPL1 ) = DIF GO TO 120 110 PRE(ISECT,ITPL1) = DIF DPTH(ISECT,ITPL1) = 0.0 120 CONTINUE IF (DPTH(I SECT,ITPL1)) 130, 1 40, 140 130 DPTH(I SECT,ITPL1 ) = 0.0 140 IF (DPTH(I SMI 1,ITPL1 )) 150, 160, 160 150 DPTH(I SMI 1,ITPL1) = 0.0 160 CONTINUE C check to see if DEPTH is not too large A = (DPTH(I SECT,ITPL1) - DPTH(I SECT,ITINT) + DPTH(I SMI 1 ,1TPL1) 1 -DPTH(I SMI 1,ITINT)) * 0.5 / TIMINC B = ( 1 .486*(SLOP(ISECT)**.5)/XMANNN) * (DPTH(I SECT,ITPL1)**1. r 166 1 33 - DPTH(ISMI1,ITPL1)**1.33) C = (PRE(ISECT,ITPL1) + PRE(I SECT,ITINT)) / 2. FH = A + B - C IF (FH .LT. TOLR) GO TO 180 DFH = 0.5 / TIMINC + ( 1 .486*5.*(SLOP(I SECT)**.5)/XMANNN* 3.) * 1 DPTH(I SECT,ITPL1) ** 0.67 DPTH(I SECT,ITPL1) = DPTH(I SECT,ITPL1) - FH / DFH IF (DPTH(I SECT,ITPL1)) 1 70, 160, 1 60 170 DPTH(I SECT,ITPL1) = 0.0 GO TO 160 180 CONTINUE IF (NTT .GT. 0) GO TO 200 IF (DPTH(I SECT,ITPL1) .GT. 0.0) GO TO 190 GO TO 200 190 FTLONG(1TPL1) = (NEND - I SECT) * SECLEN NTT = 1 200 CONTINUE 210 CONTINUE RETURN END APPENDIX B.3 167 C C C C C C C C c c c c c c c c c c c c c c c c 10 20 30 40 50 60 70 80 90 100 1 10 1 20 This code performs data reduction for channel hydraulic studies. The orginal code ,Brakensiel (1966), was modified Engman (1974). The code as shown in this thesis was adapted , by Loague (1982), for use at UBC. by SLOPC = bed slope of channel SLOPR = ground slope in direction of flow ,right bank SLOPL = ground slope in direction of flow ,left bank ZU1 = distance below zmax (zmax is maximum depth) DELN = divisor for calculation an elevation increment XR = channel manning's N divided by right bank N XL = channel manning's N divided by left bank N ZZ = card punch trigger (if .GT. 1.0 punching cards) XID1 = watershed location XID2 = identification of section KODE = digit having value of 1 for last card KODEi = digit having value of 1 for left bank coordinate = digit having value of 2 for right bank coordinate YCOR(I) = horizontal distance of each survey point (referenced to an orgin at centerline of channel) ZCOR(I) = vertical elevation of each survey point DIMENSION DIMENSION DIMENSION DIMENSION DIMENSION DIMENSION DIMENSION DIMENSION DIMENSION XINT(C,D,E YCOR(500), YCORld), AREA( 500,1), ZCOR( 500), ZCORl(l) WP( 500,1), XLA(1), XLWPd), XCA(l), XCWPd), XRA ( 1 ) XRWRd), AHZd), WPHZd), AMODd), WPMOD ( 1 ) , TW(l) RH(1), RVR(1), RVC(1), RVL(1), RMOD(1) XKNVR(1), XKNVC(l), XKNVL(1), XKNVT(I) XQNMOd), XQNVT(I), XHYD ( 1 ) XQNHZ(1), XQNVR(1), XQNVC(1), XQNVL(1) YCOR3 (500), ZCOR3(500), XRWPd) DEPTH(1 ) F,G) = C + ((G - E)/(F XKNHZ(1 ) XKNMO(1) E) ) (D • * (D -E) / C) 2. (C D) ) XAREA(A,B,C,D,E) = (2.*A - B - C) XWP(A,B,C,D) = SQRT((A - B)*(A - B) + (C - D)' XKN(A,B) = 1.486 * (A**0.67) * B XQN(A,B,C) = XKN(A,B) * SQRT(C) LL = 1 IC1 = 0 LS = 0 IC = 0 I = 0 READ (5,30,END=630) SLOPC, SLOPR, SLOPL, ZU1, DELN, XR, XL, ZZ FORMAT (8F8.4) READ IN SECTION DATA CARDS AND SET INDEXS FOR LEFT,RIGHT BANKS, channel bottom and max left Y-CORRDINATE 1 = 1 + 1 READ (5,50) XID1, XID2, KODE, KODE1, YCOR(I), ZCOR(I) FORMAT (2A4, 212, 2F8.2) IF (YCOR(I)) 90, 60, 70 LS = LS + 1 GO TO 90 GO TO (80, 90), LS YCOR(I) = -YCOR(I) IF (YCOR(I)) 100, 110, 120 YCOR2 = YCOR(I) GO TO 120 I LOW = I IF (KODE1 - 1) 150, 130, 140 168 130 I LOB = I GO TO 150 140 I ROB = I 150 IF (KODE) 40, 40, 160 160 NO = I C Y-CORRDINATE referenced to left most point of section N01 = NO - 1 YCOR3(1) = YCOR(1) ZCOR3(1) = ZCOR(1) N02 = 1 DO 190 I = 1, N01 J = I + 1 YCOR3(J) = YCOR(J) ZCOR3(J) = ZCOR(J) IF (YCOR(J)) 170, 180, 170 170 N02 = N02 + 1 GO TO 190 180 I ZERO = N02 + 1 190 CONTINUE I ZER01 = I ZERO - 1 DO 200 K = 1, IZER01 J = 1ZERO - K YCOR(K) = YCOR3(J) 200 ZCOR(K) = ZCOR3(J) K = I ZERO DO 210 L = K, N01 M = L + 1 YCOR(L) = YCOR(M) 210 ZCOR(L) = ZCOR(M) I LOW = I ZER01 I LOB = I ZERO - I LOB I ROB = I ROB - 1 NO = NOI • DO 220 I = 1, NO 220 YCOR(I) = YCOR(I) - YCOR2 C Y-CORRDINATES of out.-of-bank points,elev differnce in section,and C elev computation points YL = YCOR(ILOB) YR = YCOR(IROB) IF (ZCOR(ILOB) - ZCOR(IROB)) 230, 230, 240 230 ZL = ZCOR(ILOB) GO TO 250 240 ZL = ZCOR(IROB) 250 IF (ZCORd) - ZCOR(NO)) 260, 260, 270 260 ZMAX = ZCOR(1) GO TO 280 270 ZMAX = ZCOR(NO) 280 ZLOW = ZCOR(ILOW) ZU = ZMAX - ZU1 DELZ1 = (ZMAX - ZLOW) / DELN DELZ = DELZ1 290 GO TO ( 300, 10) , LL 300 I = 1 IC1 = 0 ZCOR1(I) = ZLOW + DELZ IF (ZCORl(I) - ZMAX) 310, 320, 320 310 DELZ = DELZ + DELZ1 GO TO 330 320 ZCOR1(I) = ZMAX LL = 2 169 C initialize for section computations 330 K = 1 XRA(K) =0.0 XRWP(K) = 0.0 XCA(K) = 0.0 XCWP(K) = 0.0 XLA(K) =0.0 XLWP(K) = 0.0 TW(K) = 0.0 TW1 = 0.0 TW2 = 0.0 TW3 = 0.0 TW4 = 0.0 C section computations for area,wetted perimeter,and top width N2 = NO N22 = N2 - 1 DO 48 0 J = 1, N22 IF (ZCOR.(J) - ZCORI(K)) 340, 350, 360 340 IF (ZCOR(J + 1) - ZCOR1(K)) 370, 370, 380. 350 IF (ZCOR(J + 1) - ZCORI(K)) 370, 400, 400 360 IF (ZCOR(J + 1) - ZCOR1(K)) 390, 400, 400 370 AREA(J,K) = XAREA(ZCOR1(K),ZCOR(J),ZCOR(J + 1),YC0R(J + 1),YC0R( 1 J) ) WP(J.K) = XWP(YCOR(J + 1),YCOR(J),ZCOR(J + 1),ZC0R(J)) TW1 = YCOR(J + 1) - YCOR(J) GO TO 4 10 360 YCORl(K) = XINT(YCOR(J),YCOR(J + 1),ZCOR(J),ZCOR(J + l),ZCOR1(K) 1 ) AREA(J,K) = XAREA(ZCOR1(K),ZCORl(K),ZCOR(J),YCOR1(K),YCOR(J)) WP(J,K) = XWP(YCOR1(K),YCOR(J),ZCOR1(K),ZCOR(J)) TW2 = YCOR1(K) - YCOR(J) GO TO 4 10 390 YCORl(K) = XI NT(YCOR(J),YCOR(J + 1 ),ZCOR(J),ZCOR(J + l),ZCORl(K) 1 ) AREA(J,K) = XAREA(ZCOR1(K),ZCOR1(K),ZCOR(J + l),YCOR(J + 1), 1 YCORl(K)) WP(J,K) = XWP(YCOR(J * 1),YCOR1(K),ZCOR1(K),ZCOR(J + 1)) TW3 = YCOR(J + 1) - YCORl(K) GO TO 4 10 400 AREA(J , K ) = 0.0 WP(J,K) = 0.0 TW4 = 0.0 410 IF (YCOR(J) - YL) 420, 440, 440 420 IF (YCOR(J + 1) - YL) 430, 430, 440 4 30 XLA(K) = XLA(K) + AREA(J,K) XLWP(K) = XLWP(K) + WP(J,K) GO TO 470 440 IF (YCOR(J + 1) - YR) 450, 450, 460 4 50 XCA(K) = XCA(K) + AREA(J,K) XCWP(K) = XCWP(K) + WP(J,K) GO TO 470 460 XRA(K) = XRA(K) + AREA(J,K) XRWP(K) = XRWP(K) + WP(J,K) 4 70 CONTINUE TW(K) = TW(K) + TW1 + TW2 + TW3 + TW4 TW1 = 0.0 TW2 = 0.0 TW3 =0.0 TW4 = 0.0 480 CONTINUE 170 C section computations for total area.hydraulic radius,CVY*N,Q*N, C and hydraulic depths AHZ(K) = XLA(K) + XCA(K) + XRA(K) WPHZ(K) = XLWP(K) + XCWP(K) + XRWP(K) IF (ZCORl(K) - ZU) 490, 510, 510 490 IF (ZCORI(K) - ZL) 510, 510, 500 500 D = ZU - ZL D1 = ZCOR1(K) - ZL AD = AHZ(K) - XCA(K) WPD = WPHZ(K) - XCWP(K) AMOD(K) = XCA(K) + (Dl/D) * AD WPMOD(K) = XCWP(K) + (Dl/D) * (WPD) GO TO 520 510 AMOD(K) = AHZ(K) WPMOD(K) = WPHZ(K) 520 CONTINUE RH(K) = AHZ(K) / WPHZ(K) IF (XRWP(K)) 530, 530, 540 530 RVR(K) = 0.0 GO TO 550 54 0 RVR(K) = XRA(K) / XRWP(K) 550 IF (XLWP(K)) 560, 560, 570 560 RVL(K) = 0.0 GO TO 58 0 570 RVL(K) = XLA(K) / XLWP(K) 58 0 RVC(K) = XCA(K) / XCWP(K) RMOD(K) = AMOD(K) / WPMOD(K) XKNHZ(K) = XKN(RH(K) ,AH Z(K) ) XKNVR(K) = XKN(RVR(K),XRA(K)) XKNVC(K) = XKN(RVC(K) , XCA(K)) XKNVL(K) = XKN(RVL(K),XLA(K)) XKNVT(K) = XR * XKNVR(K) + XKNVC(K) + XL * XKNVL(K) XKNKO(K) = XKN(RMOD(K),AMOD(K)) XQNHZ(K) = XQN(RH(K),AHZ(K),SLOPC) XQNVR(K) = XQN(RVR(K),XRA(K),SLOPR) XQNVC(K) = XQN(RVC(K),XCA(K),SLOPC) XQNVL(K) = XQN(RVL(K),XLA(K),SLOPL) XQNVT(K) = XR * XQNVR(K) + XQNVC(K) + XL * XQNVL(K) XQNMO(K) = XQN(RMOD(K),AMOD(K),SLOPC) DEPTH (K) = ZCORI'(K) - ZLOW 590 XHYD(K) = AHZ(K) / TW(K) IC = IC + 1 IC1 = IC1 + 1 IF (ZZ .LE. 1.0) GO TO 610 PUNCH 600, AHZ(I), XQNHZ(I) 600 FORMAT (20X, 2F10.5, 50X) 610 WRITE (6,620) ZCOR1(I), DEPTH(I), AHZ(I), XQNHZ(I), WPHZ(I), 1TW(I), XID1, XID2, IC1, IC 620 FORMAT (' ', F9.4, 5F10.5, 2X, A4, 2X, A4, 2X, 13, 13) GO TO 290 630 STOP END APPENDIX B.4 171 C This code performs storage flood routing without coefficients C C The orginal code .Brakensiek (1966), was modified by C Engman (1974). The code as shown in this thesis C was adapted , by Loague (1982), for use at UBC. C C C - lower bound for wanted table C D = upper bound for wanted table C E = lower bound for argument table C F = upper bound for argument table C G = argument C DELT = time increment used in routing computations C (constant) in seconds C DELT1 = same as DELT , saved for initialization C DELA = area increment in rating table , used to C establish an upper of lower bound C DELA = same as DELA , saved for initialization C TOLR = tolerance , iteration cutoff C N1 = number of inflow hydrograph entries C N2 = number of tabulated rating function entries C N5 = 0 read all lateral inflow cards C = 1 no input-lateral inflows all zero C =2 laterla inflows all equal to one value (read) C ZZ = card punch trigger (if .GT. 1.0 punching cards) C DIMENSION AREA1(2000), DISCH1(2000), Q1(2000), A1(2000), 1 AREA2(2000) DIMENSION DISCH2(2000), Q2(2000), A2(2000), QL1(2000), QL2(2000) DIMENSION QN1(2000), QN2(2000) COMMON AREA 1 , NI, I, J, K, M, XI, DELT, DELT1 COMMON N2, X4, X2, DELA, DELA 1 , ANEW", TOLR, X3 : COMMON Al, DELX, QL1, QL2 COMMON QN1, QN2 10 FORMAT (F5.0, F8.4) 20 FORMAT (20X, F12.7, 48X) 30 FORMAT (F5.3) 40 FORMAT (20X, 2F10.5, 40X) 50 FORMAT (20X, F12.7, 48X) 60 FORMAT (4F5.0, F7.0, 313, F5.0) XINT(C,D,E,F,G) = C + ((G - E)/(F - E)) * (D - C) READ (5,60) DELT, DELT1, DELA, DELA1, TOLR, NI, N2, N5, ZZ C read first section rating and inflow DO 7 0 I = 1, N1 70 READ (5,50) Q1(I) DO 80 I = 1, N2 80 READ (5,40) AREA 1(I), QN1(I) IF (N5 - 1) 90, 140, 160 90 DO 130 I = 1, N1 READ (5,20) QL1(I) IF (QL1(I) - 100.) 120, 100, 100 100 IKE = I DO 110 IMP = IKE, N1 110 QL1(IMP) = 0.0 GO TO 180 120 CONTINUE 130 CONTINUE GO TO 180 140 DO 150 I = 1, N1 150 QL1(I) = 0.0 GO TO 180 160 READ (5,20) QL1(1) N7 = N1 - 1 DO 170 I = 2, N7 17 0 QL1(I) = QL1(1) QL1(N 1 ) = 0 . 0 C calculate first section areas 180 READ (5,30) XN1 WRITE (6,1,90) XN1 190 FORMAT ('1', 15X, 'XN1=', F8.4) DO 200 I = 1, N2 2 00 DISCH1(I) = QN1(I) / XN1 210 DO 220 I = 1, NI CALL TBLLP(DISCH1, Ql) 220 A1(I) = XI NT(AREA 1 (K),AREA 1 (J) ,DISCH1 (K),DISCH1 (J),Q1(I )) C read second section rating and lateral inflow LL 1 = 0 ' LL2 = 0 Nil = NI 230 M = NI 240 1=1 DELT = DELT1 N 1 = N 1 1 J 1 = N1 + 1 IF (M - NI) 270, 270, 250 250 DO 260 J = J1 , M 260 QL2(J) = 0.0 270 CONTINUE DO 280 I = 1, N2 280 READ (5,40,END=670) AREA2(I), QN2(I) IF (N5 - 1) 310, 360, 290 290 READ (5,20) QL2(1) N7 = Ni - 1 DO 300 I = 2, N7 300 QL2(I) = QL2(1) QL2(N1) = 0.0 GO TO 380 310 DO 350 I = 1, N1 READ (5,20) QL2(I) IF (QL2(I) - 100.) 340, 320, 320 320 IPE = I DO 330 IMP = IPE, NI 330 QL2(IMP) = 0.0 GO TO 380 340 CONTINUE 3 50 CONTINUE GO TO 380 360 DO 370' I = 1 , NI 370 QL2(I) = 0.0 C read second section initial value ane delx 380 I = 1 . READ (5,10) DELX, Q2(I) READ (5,30) XN2 DO 390 I = 1, N2 390 DISCH2(I) = QN2(I) / XN2 I = 1 CALL TBLLP(DISCH2, Q2) A2(I) = XI NT(AREA2(K),AREA2(J),DISCH2(K),DISCH2(J),Q2(I)) J = 1 N1 = M C routing during inflow 173 400 ALPHA = (A1(I) + A2(I)) / 2. I = J + 1 BETA = (DELT/DELX) * Q1(I) + (-AI(I) + (DELT)*(QL1(I) + QL2(I))) / 1 2. XI = ALPHA + BETA IF (XI - TOLR) 410, 410, 430 410 Q2(I) = Q2(1) A2(I) = A2(1) DELT = DELT + DELT1 I = I - J J = J + 1 IF (J - N1) 400, 420, 420 420 I = J GO TO 470 430 CALL SOLVE(DISCHl, DISCH2, QI, Q2, AREA2, A2) IF (Q2(I) - Q2(1) - TOLR) 440, 440, 450 440 Q2(I) = Q2(1) A2(I) = A2(1) 450 CONTINUE DELT = DELT1 IF (I - N1) 460, 470, 470 460 J = I GO TO 400 C routing after inflow 470 N3 = 0 480 J = I N3 = N3 + 1 IF (J - 199S) 510, 490, 490 490 WRITE (6,500) 500 FORMAT (' LATERAL INFLOW TOO LARGE,SUBSCRIPT I > 2000') 510 ALPHA =(A1(Nl)+A2(I))/2. I = J + 1 BETA = (DELT/DELX) * Q1(N1) + (-Al(Nl) + DELT*(QL1(N1) + QL2(N1))) 1/2. XI = ALPHA + BETA IF (XI - TOLR) 520, 520, 530 520 Q2(I) = QI(NI) A2(I) = Al(N1) GO TO 550 530 CALL SOLVE(DISCH1,DISCH2, Q1, Q2, AREA2, A2) IF (Q2(I) - Q1(N1) - TOLR) 520, 520, 540 540 GO TO 480 550 M = M + N3 12 = NI + 1 DO 560 I = 12, M QL1(I) = 0.0 QL2(I) = 0.0 A 1 (I ) = Al (N1 ) 560 QI(I) = QI(N1) LL1 = LL1 + 1 .LL2 = LL1 + 1 C print out and interchange IF (LL1 .GT. 1) GO TO 580 WRITE (6,570) TOLR, XN2, DELT1, DELA, DELX 570 FORMAT (' ', 15X, 'TOLR=' , F8.7, 5X, 'XN2=', F8.4, 5X, 'DELT=' , 1 F10.5, 5X, 'DELA=' , F10.5, 5X, 'DELX=' , F8.0, 5X///) GO TO 600 580 WRITE (6,590) TOLR, XN2, DELT1, DELA, DELX 590 FORMAT ('1', 15X, 'TOLR=' , F8.7, 5X, 'XN2=', F8.4, 5X, 'DELT=' , 1 F10.5, 5X, 'DELA-' ,' Fl 0.5, 5X, 'DELX=' , F8.0, 5X///) 174 600 WRITE (6,610) LL1, LL2 610 FORMAT (20X, 'IN SECTION NO =', 13, 14X, ' OUT SECTION NO =', 13) WRITE (6,620) 620 FORMAT (24X, ' IN AREA', 6X, ' IN DISCH', 10X, ' OUT AREA', 5X,_ 1 ' OUT DISCH', 10X, 'TOTAL TIME , SECONDS') 630 FORMAT (20X, 2F13.5, 5X, 2F13.5, 15X, F10.0) DO 650 I = 1, M CUMT = DELT1 * FLOAT(I) - DELT1 WRITE (6, 630) A1(I), Q1(I), A2(I), Q2(I) , CUMT 640 QL1(I) = QL2(I) , A 1 (I) = A2(I) 650 QI(I) = ,Q2(I) C interchange rating tables DO 660 I = 1, N2 AREA 1(I) = AREA2(I) 660 DISCH1(I) = DISCH2(I) GO TO 240 670 CONTINUE DO 690 I = 1, M WRITE (8,680) Q1(I) 680 FORMAT (' ', 19X, FlO.5, 50X) 690 CONTINUE DO 710 I = 1, M IF (ZZ .LE. 1.0) GO TO 7 20 PUNCH 700, Q1(I) 700 FORMAT (20X, F10.5, 50X) 710 CONTINUE 720 STOP END SUBROUTINE SOLVE(DISCH1, DISCH2, QI, Q2, AREA2, A2) . DIMENSION AREA1(2000), DI SCH 1(2000), QU 2000), A1(2000), 1 AREA2(2000) DIMENSION DISCH2(2000) , Q2(2000), A2(2000), QL1(2000), QL212000 ) DIMENSION QN1(2000), QN2(2000) COMMON AREA 1 , N1 , I , J, K, M, XI, DELT, DELT1 COMMON N2, X4, X2, DELA, DELA1, ANEW, TOLR, X3 COMMON Al, DELX, QL1, QL2 COMMON QN1, QN2 XINT(C,D,E,F,G) = C + ((G - E)/(F - E)) * (D - C) AU = 0. FAU = 0. AL = 0. FAL = 0. DELA = DELA1 10 A2(I) = A2(I - 1) 20 CALL TBLLP(AREA2, A2) Q2(I) = XI NT(DISCH2(K) ,DISCH2(J),AREA2(K) ,AREA2(J) ,A2(I ) ) X2 = (DELT/DELX) * Q2(I) + (A2(I)) / 2. X2 = X2 - XI IF (X2) 70, 130, 30 30 DELA = DELA1 AU = A2(I) FAU = X2 IF (AL) 110, 40, 110 40 A2(I) = A2(I) - DELA 50 IF (A2(I)) 60, 60, 20 60 DELA = DELA * .5 A2(I ) = A2(l) + DELA GO TO 50 7 0 DELA = DELA1 175 AL = A2(I ) FAL = -X2 IF (AU) 110, 80, 110 80 A2(I) = A2(I) + DELA 90 IF (A2(I) - AREA2(N2) ) 20, 20, 100 100 DELA = DELA * .5 A2(I) = A2(I) - DELA GO TO 90 110 ANEW = AU - (FAU/(FAU + FAL)) * (AU - AL) X3 = ANEW - A2(I) X3 = ABS(X3) IF (X3 - TOLR) 130, 130, 120 120 A2(I ) = ANEW GO TO 20 130 A2(I ) = ANEW CALL TBLLP(AREA2, A2 ) Q2(I) = XI NT(DISCH2(K),DISCH2(J),AREA2(K),AREA2(J),A2(I)) RETURN END SUBROUTINE TBLLP(A, B) C A=argument table C B=argument DIMENSION A(2000), B(2000) DIMENSION AREA1(2000), DI SCH 1 ( 2000 ) , Q1.(2000), Al(2000), 1 AREA2(2000) DIMENSION DISCH2(2000), Q2(2000), A2(2000), QLK2000), QL2(2000) DIMENSION QN1(2000), QN2(2000) COMMON AREA 1 , N1, I, J, K, M, XI, DELT, DELT1 COMMON N2, X4 , X2, DELA, DELA1, ANEW, TOLR, X3 COMMON Al, DELX, QL1, QL2 COMMON QN1, QN2 X4 = B(I) IF (X4) 20, 10, 20 10 J = 2 K = J - 1 RETURN 20 DO 40 J = 2, N2 IF (A(J) - X4) 40, 30, 30 30 K = J - 1 RETURN 4 0 CONTINUE WRITE (6,50) 50 FORMAT (' WHOOPS!') RETURN END APPENDIX C Results from rainfall-runoff regression analysis of six Mahantango Creek Subwatershed events (two rain gages): C.1 Correlation matrices of nine Mahantango Creek Subwatershed regression variables, with and without data reduction. C.2 Summary of 168 Mahantango Creek Subwatershed linear regression models and their respective verification efficiencies. APPENDIX Cl Without base flow separation VPPT YPPT ppT(B) PPT,U PPTf," PPT(DE) QpK TQPK VPPT 1.0 w <E)  VPPT .0708 1.0 PPT(B) .0138 .1626 1.0 PPT(E) .1614 .2876 .0705 1.0 PPTlDB) .7364 .6124 -.5026 -.4022 1.0 PPT(DE) .7066 .6401 -.5051 -.4517 .0427 1.0 VQ .3768 .3283 -.3876 -.4180 .7467 .8553 1.0 QPK .8863 .0434 .1466 .2760 .4641 .5023 .0792 1.0 TQPK .1071 .0160 -.7734 -.7753 .6855 .6764 .6902 -.0818 1.0 With base flow separation VPPT VPPT ppT(B) PPT(B) PPT(oB) PPT(DE) VQ QpK TQPK VPPT 1.0 w <E> VPPT .9708 1.0 PPT(B) .0138 .1626 1.0 WT(E) .1614 .2876 .9795 1.0 PPJ(D B) .7364 .6124 -.5926 -.4922 1.0 PPTCDE) .7066 .6491 -.5051 -.4517 .9427 1.0 .8270 .8793 -.0616 .0576 .5639 .6121 1.0 .8864 .9388 .1347 .2687 .4667 .4966 .9507 1.0 .1071 .0160 -.7734 -.7753 .6855 .6764 .1992 -.0750 1.0 APPENDIX C.2 VPPT W (E) VPPT ppTCB) PPTtk) PPTDB> PPTDE) QPK TQPK 'I • • • • • .88 .93 • • • • .76 .80 • • • • .84 .80 • • • • .84 .73 • • • • .78 .85 • • • .18 .79 • • • .62 .69 • • • .60 .84 • • • .77 .68 • • • .82 .78 • • • .76 .38 • • .68 .14 • • .77 .11 • • .32 .66 • • .38 .73 180 Oi. CM CD CD as CS o n 09 o CO a CO OS OS o 01 OS o o o o as o OS CM CD q o CO o CD CO o o o o o CM as OS a O t-a O >° i° Q. Q. • • • • • • • • !Q r-a. a. • • • • • • • • • i r— 0. a. • • D >-QL a. • • • • • • • • • Ul a. a, > • • • • • • • • • • • • CD — h-a. >°-• • CM CM k-o CO CO o 00 IO CO eo 00 CO CO CM 00 CM CO CO 00 q CO 00 CO CO -00 CO CO CM «-CD CM CO o CO IO CD CO CO CO CO CN 00 CM CO o CD CO CO CD CO CO o CO co 09 Q. o t-Q. o >° So 1-0. CL • • • • • • • ta \-0. Q. • • • • • • • • <*• I J 0. Q. • • • • • • • 1 0 r-Q. a. • • • • • • • +s — a. a. • • * a o. >°-182 o o • CM 01 CO o 0 CO CM »- • • o o • CM • • o o> T-09 o a> in O 0. O >° =p 0. • • • • • • w O H OL Q. • • • • • UJ 1 • • • • • c 0 I-Q. QL • • • • • • • UJ -K 0. a > • • • • • CD a. 1 183 W (B) VPPT VPPT PPT(B) PPtlt) PPTDB) PPTDE) QPK TQPK 2 R 1 'I • • • .82 .82 • • • .73 .73 • • • .73 .73 • • • .77 .77 • • • .48 .48 • • .01 .01 • • .0 .0 • • .47 .47 • • .46 .46 r - Coefficient of extermination r1 - Regression (multiple) models lor •vents 20, 43,43b. 44, 4ft, and 4« with no baaeflow separation r2 - Regression (multiple) models for events 20, 43. 43b, 44, 46, and 46 with baaeflow aeparatlon Bf - Rain gages 185 APPENDIX D Example implementation of the distributed model: D.1 Computer generated soil characteristic curved for the Mahantango Creek Subwatershed. D.2 Computer generated lateral inflow hydrographs for D.3 Computer generated normal discharge rating function for a 1:1.5 prismatic triangular open channel of 2% slope. D. 4 Computer generated open channel flow routin.g for Mahantango Creek Subwatershed selected event #16. APPENDIX D.l #2 BERKS (145) SILT LOAM NC THET15 T.HETAE THETA2 PPSI15 PSI1 PSIE PSI2 CONE TF (CM3/CM3) (CM OF WATER) (CM/DAY) DEG.C 48 0.1100 0,3800 0.4700 15306.0 15306.0 6.0 3.0 108.0000 20.0 20.0 CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFFUSSIVITY DPSI/DTHETA (CM) (CM3/CM3) (CM/DAY) (CM2/DAY .1 15306. 0 0. 1 100 1 . 03E-08 1 . 11E-06 6 . 09E-01 5 . 46E+05 2 13389 . 4 0. 1 1 38 4 . 16E-08 4 . 49E-06 2 . 14E+00 4 . 78E+05 3 10246. 3 0 12 13 9 . 47E-08 1 . 02E-05 3 . 74E+00 3 . 65E+05 4 784 1 . 4 0 . 1288 1 . 81E-07 1 . 96E-05 5 . 47E+00 2 . 80E+05 5 6001 . 1 0. 1363 3 . 18E-07 3 . 43E-05 7 . 34E.+ 00 2 . 14E+05 6 4593 . 1 0. 1438 5 . 32E-07 5 . 75E-05 9 41E+00 1 . 64E+05 7 3515 . 7 0. t5 13 8 . 67E-07 9 . 37E-05 1 . 17E+01 1 . 25E+05 8 2691 . 2 0. 1587 1 . 39E-06 1 . 50E-04 1 . 44E+01 9 . 59E+04 9 2060. 4 0. 1662 2 . 22E-06 2 . 39E-04 1 . 76E+01 7 . 34E+04 10 1577 . 8 0. 1737 3 . 5 1E-06 3 . 80E-04 2 13E+01 5 . 61E+04 1 1 1208 . 4 0. 18 12 5 . 56E-06 6 . 01E-04 2 . 58E+01 4 . 29E+04 12 925 . 8 0. 1887 8 . 80E-06 9 . 50E-04 3 . 12E+01 3 . 29E+04 13 709 . 6 0. 1962 1 . 39E-05 1 . 50E-03 3 . 78E+01 2 . 51E+04 14 544 . 1 0. 2037 2 . 21E-05 2 . 38E-03 4 . 59E->01 1 . 92E+04 15 4 17. 5 0. 2 112 3 . 50E-05 3 . 78E-03 5 . 57E+01 1 . 47E+04 16 320. 7 0. 2 187 5 . 56E-05 6 01E-03 6 . 77E+01 1 . 13E+04 1 7 246 . 5 0. 2262 8 84E-05 9 . 55E-03 8 . 23E+01 8 . 62E+03 18 189 . 8 0. 2337 1 41E-04 1 . 52E-02 1 . 00E+02 6 . 60E+03 19 146 . 4 0. 24 12 2 .24E-04 2 42E-02 1 . 22E+02 5 . 05E+C3 20 113. 2 0. 2487' 3 56E-04 3 .84E-02 1 . 48E+02 3 . 86E+03 2 1 B7 . 8 0 . 2562 5 .64E-04 6 .10E-02 1 . 80E+02 2 95E+03 22 68 , 4 0. 2637 8 .94E-04 9 .65E-02 2 18E+02 2 . . 26E + 03 23 53 . 5 0. 27 12 .1 .41E-03 1 .52E-01 2 64E+02 1 73E+03 24 42 . 1 0. 2787 2 .22E-03 2 .39E-01 3 .17E+02 1 . 32E + 03 25 33 . 4 0. 2862 3 .46E-03 3 .73E-01 3 .78E+02 1 .01E+03 26 26 . 7 0. 2937 5 .35E-03 5 .78E-01 4 . 48E+02 7 . 75E+02 27 2 1 6 0. 3012 8 .19E-03 8 .85E-01 5 .25E+02 5 .93E+02 28 17 . 7 0. 3087 1 .24E-02 1 .34E+00 6 .07E+02 4 .54E+02 29 14 . 7 0. 3 162 1 .85E-02 1 .99E+00 6 .93E+02 3 .47E+02 30 12 . 4 0. 3237 2 .71E-02 2 .92E+00 7 .77E+02 2 .66E+02 31 10 . 7 0. 3312 3 .89E-02 4 .20E+00 8 .55E+02 2 .03E+02 32 9 . 4 0. 3387 5 .49E-02 5 .92E+00 9 .22E+02 1 .56E+02 33 8 . 3 0. 3462 7 .57E-02 8 .17E+00 9 .73E+02 1 .19E+02 34 7 . 6 0 . 3537 1 .02E-01 1 .10E+01 1 .OOE+03 9 .11E+01 35 7 .0 0. . 3612 1 .35E-01 1 .46E+01 1 .02E+03 6 .97E+01 36 6 . 5 0. . 3687 1 .75E-01 1 .89E+01 1 .01E+03 5 .33E+01 37 6 . 1 0 . 3762 2 .22E-01 2 .39E+01 3 .48E+02 1 .45E+01 38 5 .9 0. .3837 2 .76E-01 2 .98E+01 4 .86E+02 1 .63E+01 39 5 . 8 0 .3912 3 .37E-01 3 .64E+01 6 .66E+02 1 .83E+01 40 5 . 7 0. . 3987 4 .04E-01 4 .37E+01 8 .98E+02 2 .06E+01 4 1 5 . 5 0 .4062 4 .78E-01 5 .16E+01 1 .19E+03 2' '. 3 1 E +01 42 5 . 3 0 .4137 5 .58E-01 6 .02E+01 1 .56E+03 2 .59E+01 43 5 . 1 0 .4212 6 .44E-01 6 .95E+01 2 .02E+03 2 .91E+01 44 4 .9 0 .4287 7 .36E-01 7 .95E+01 2 .60E+03 3 . 26E+01 45 4 .6 0 . 4362 8 .36E-01 9 .02E+01 3 .31E+03 3 .66E+01 46 4 . 3 0 .4437 9 .43E-01 1 .02E+02 4 .19E+03 4 . 1 1E+01 47 4 .0 0 .4512 1 .06E+00 1 . 14E+02 5 .28E+03 4 .62E+01 48 3 .6 0 .4587 1 . 19E+00 1 .28E+02 6 .64E+03 5 .18E+01 49 3 . 2 0 . 4662 1 . 33E+00 1 .43E+02 8 .34E+03 5 .82E+01 THETAE = 0.3800 Ii2 KIRKS (14b) SI I. I LOAM CLASS INITIAL F LUX ( CM/HRS I ' SORP T I V I I Y ( CM/HRS ' ' 0 . '."> ) 1 9 58E+01 3 04 E ' ()D 2 9 53E+0I 3 03 fc OO 3 9 4 2E '01 2 99 E OO 4 9 30E tOI 2 95 E oo 5 9 18Ft01 2 91E 00 6 9 07E+01 2 87E 100 7 8 95E+01 2 83E • OO 8 8 83E+01 2 79E >00 9 8 70E*01 2 75E OO 10 8 58E+OI 2 7 IF '00 1 1 8 45E+01 2 67E 'OO 12 8 32E+01 2 62F 00 13 8 19E *01 2 58E • oo 14 8 ORE tQ1 2 54E '00 15 7 92E'01 2 4 9 F • OO 16 7 79E+01 2 45E 00 17 7 65E+01 2 40E •OO 18 7 50E+01 2 35 E OO 19 7 36E'01 2 30E • 00 20 7 2 1E + 01 2 25E • no 2 1 7 06E +01 2 20E • 00 22 6 9 IE «01 2 15E '00 23 6 75E+01 2 10E • 00 24 6 59E+01 2 05 E • 00 25 6 43E+01 1 99 E • 00 26 6 2GE KM 1 9 IE 00 27 6 09E»01 1 HHF • OO 28 5 92E+01 1 82F • Ot) 29 5 75E »G1 1 77F (10 30 5 57EiQI 1 7 1 F oo 3 1 5 39E +01 1 6b F 'OO 32 5 2UE H)1 1 581 l oo 33 5 0 1 F. • 0 1 1 521 t 1 «) 34 4 82F'Ol 1 4(.l. Mill 35 4 03E<01 1 3'M > oo 36 4 43F*01 1 3 31' I ( lO 37 4 22FMM 1 261 1 oo 38 4 OIOOI 1 I9L 'OO 39 3 7HF K) 1 1 1 1 F M">0 40 :> 55F'01 1 03F ' IJO 4 1 3 30E ' O 1 9 5 (.)f • 111 4 2 3 04 F • 0 1 8 b'.M -O 1 43 2 761 KM / ('.;)( I) 1 4 4 2 4GF •(.) 1 /Ol (> 1 4 b 2 1 IF till 5 65 f" O 1 Kt(FI/HRS) = 1 4764E-01 F1IM/HRS) FS( F T/HRS • ' 5 ) THETA/THETA2 THE T A MIDI NT . 3 14F *00 9 99E -02 0 2340 O 1 100 3 13F'OO 9 93E -02 0 2500 0 1 138 3 09F'00 9 ROE 02 0 2660 0 12 13 3 05E+00 9 6RE -02 0 28 19 0 1288 3 OIE'OO 9 55E 02 0 2979 0 1363 2 97E+00 9 42E -02 0 3138 0 1438 2 94E'00 9 29E -02 0 3298 0 1513 2 90F <-00 9 16E -02 0 3457 0 1587 2 86E'OO 9 02E -02 0 3617 0 1662 2 8 IE *00 . 8 89 F -02 0 3777 0 1737 2 77E+00 8 7 5F. -02 0 3936 O 18 12 2 73E+00 8 6 1E -02 0 4096 O 1887 2 69E *00 8 47E -02 O 4255 o 1962 2 64F tOO 8 32E -02 0 44 15 0 2037 2 GOEKJO 8 17E -02 0 4574 o 2 112 2 55F *00 8 02E -02 0 4734 o 2 187 2 51F +00 7 87E -02 0 4894 0 2262 2 46F tOO 7 7 IE -02 O 5053 0 2337 2 41E tOO 7 56E -02 0 52 13 0 24 12 2 37F tOO 7 39E -02 0 5372 0 2487 2 32t tOO 7 23E 02 0 5532 0 2562 2 2 7 E t OO 7 06E -02 0 569 1 0 2637 2 21E * OO 6 89E -02 0 5851 0 27 12 2 16EtOO 6 72E -02 0 601 1 0 2787 2 1 IE tOO 6 '54E -02 0 6 170 0 2862 2 05EtOO 6 36E 02 0 6330 0 2937 2 OOF tOO 6 17F -02 o 64 89 0 3012 1 9 IEtOO 5 9RE -02 0 6649 0 3087 1 89ftOO 5 79E 02 o 6809 0 3162 1 R3F.tOO 5 60E -02 o 6968 0 3237 1 7 7 E•OO 5 40E -02 0 7 128 0 3312 1 7 IEtOO 5 20E -02 0 7287 0 3387 1 64E tOO 4 99E -02 0 7447 0 3462 1 58E tOO 4 78E -02 0 7606 0 3537 1 52FtOO 4 57E -02 0 7766 o 36 12 1 45FtOO 4 35E -02 0 7926 0 3687 1 39EtOO 4 13E -02 0 8085 0 3762 t 32F.tOO 3 89E -02 0 8245 0 3837 1 2 4 E'OO 3 G5E -02 o 8404 o 3912 1 16E tOO 3 39E -02 0 8564 0 3987 1 ORE *00 3 12E •02 0 8723 0 4062 ;i 96E-01 2 83E -02 0 8883 o 4137 9 05E-01 2 52E -02 0 9043 0 42 12 R 07E-01 2 20E -02 0 9202 0 4287 7 03E 01 1 85E -02 0 9362 0 4362 188 *4 LECK KILL (66) SILT LOAM NC THET15 THETAE THETA2 PPSI15 PSI1 PSIE PSI2 CONE TF TM (CM3/CM3) (CM OF WATER) (CM/DAY) DEG.C 48 0.1200 0.3000 0.3700 15306.0 15306.0 6.0 3.0 79.0000 20.0 20.0 CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFFUSSIVITY DPSI/DTHETA (CM) (CM3/CM3) (CM/DAY) (CM2/DAY 1 15305 . 9 0 . 1200 4 . 68E-09 3 .70E-07 3 .03E-01 8 .19E+05 2 13315 .0 0 . 1226 1 .94E-08 1 .53E-06 1 .09E+00 7 .13E+05 3 10076 . 4 0 . 1278 4 .65E-08 3 .68E-06 1 .98E+00 5 .39E+05 4 7625 . 9 0 . 1330 9 .36E-08 7 .39E-06 3 .02E+00 4 .08E+05 5 577 1 .6 0 . 1382 1 .73E-07 1 .36E-05 4 .21E+00 3 .09E+05 6 4368 . 5 0 . 1434 3 .03E-07 2 .40E-05 5 .60E+00 2 .34E+05 7 3306 . 8 0 . 1486 5 .19E-07 4 .10E-05 7 . 24E + 00 1 .77E+05 8 2503 . 4 0 . 1539 8 .72E-07 6 .89E-05 9 . 21E + 00 1 .34E+05 9 1895 . 5 0 . 159 1 1 .45E-06 1 .15E-04 1 . 16E + 01 1 .01E+C5 10 1435 . 5 0 . 1643 2 .4 1E-06 1 .90E-04 1 . 46E + 01 7 .66E+04 1 1 1087 . 5 0 . 1695 3 .97E-06 • 3 .14E-04 1 .82E+01 5 .79E+04 12 824 . 1 0. . 1747 6 .55E-06 5 .18E-04 2 .27E+01 4 .38E+04 13 624 . 8 0 . 1799 1 .08E-05 8 .53E-04 2 .83E+01 3 .32E+04 14 474 .0 0 .185 1 1 .78E-05 1 .41E-03 3 .53E+01 2 .51E+04 15 359 . 9 0. 1903 2 .93E-05 2 .32E-03 4 .40E+01 1 .90E+04 16 273 . 5 0 1955 4 .84E-05 3 .82E-03 5 .49E+01 1 .44E+04 17 208 . 2 0. 2007 7 .97E-05 6 .29E-03 6 .85E+01 1 .09E+04 18 158 , 7 0. 2059 1 .31E-04 1 .04E-02 8 .53E+01 8 .23E+03 19 12 1 . 3 0 2 111 2 .16E-04 1 .70E-02 1 .06E+02 6 .23E+03 20 93 . 0 0 . 2 164 3 .54E-04 2 .80E-02 1 .32E+02 4 .71E+03 2 1 7 1 . 6 0. 22 16 5 .79E-04 4 .57E-02 1 .63E+02 3 . 57E+03 22 55 . 4 0. 2268 9 .43E-04 7 .45E-02 2 .01E+02 2 . 70E+03 23 43 . 1 0. 2320 1 .53E-03 1 .21E-01 2 .46E+02 2 .04E+03 24 33 . 9 0. 2372 2 .46E-03 1 .94E-01 3 .00E+02 1 .54E+03 25 26 . 8 0. 2424 3 .91E-03 3 .09E-01 3 .61E+02 1 .17E+03 26 2 1 . 5 0. 2476 6 .16E-03 4 .87E-01 4 .31E+02 8 .85E+02 27 17 . 5 0. 2528 9 .56E-03 7 .55E-01- 5 . 06E + 02 6 .69E+02 28 14 . 5 0. 2580 1 .46E-02 1 .15E+00 5 . 84E + 02 5 .06E+02 29 12 . 2 0. 2632 2 .19E-02 1 .73E+00 6 62E+02 3 .83E+02 30 10 . 4 0. 2684 3 .21E-02 2 .53E+00 7 .34E+02 2 .90E+02 31 9 . 1 0'. 2736. 4 .60E-02 3 .63E+00 7 .97E+02 2 .19E+02 32 8 . 1 0. 2789 6 .44E-02 5 .09E + 00 ' 8 44E+02 1 .66E+02 33 7 . 3 0. 284 1 8 .80E-02 6 .95E+00 8 .74E+02 1 .26E+02 34 6 8 0. 2893 1 .18E-01 9 .29E+00 8 .83E+02 9 .51E+01 35 6 . 3 0. 2945 1 .53E-01 1 . . 2 1E + 01 8 .72E+02 7 .19E+01 36 6 .0 0. 2997 1 .96E-01 1 . .55E+01 3 05E+02 1 .97E+01 37 5 . 9 0. 3049 2 .45E-01 1 . .94E+01 4 . .23E+02 2 .18E+01 38 5 8 0. 3101 3 01E-01 2 . 38E+01 5 . 75E+02 2 42E+01 39 5 . .6 0. 3153 3 .62E-01 2 . 86E+01 7 67E+02 2 .68E+01 40 5 . 5 0. 3205 4 •29E-01 3 . . 39E+01 1 . 01E+03 2 97E+01 4 1 5. . 3 0. 3257 5 02E-01 3 . 97E+01 1 . . 31E+03 3 .30E+01 42 5 . 2 0. 3309 5 81E-01 4 . . 59E+01 1 . 68E+03 3 .G5E+01 43 5 . .0 0. 336 1 6 66E-01 5 . .26E+01 2 . .13E+03 4 .05E+01 44 4 . . 7 0. 3414 7 .56E-01 5 . . gsE'+oi 2 . 68E+03 4 .49E+01 45 4 . 5 0. 3466 8 . .54E-01 6. 75E+01 3 . .36E+03 4 .98E+01 46 4 . . 2 0. 3518 9 .59E-01 7 , 57E+01 4 . .18E+03 5 .52E+01 47 3. 9 0. 3570 1 07E+00 8 . 47E+01 5 . .19E+03 6 . 12E + 01 48 3 . 6 0. 3622 1 . .20E+00 9 . 45E+01 6 . 41E+03 6 . 79E + 01 49 3 . 2 0. 3674 1 . .33E+00 1 . 05E+02 7 . .93E+03 7 .52E+01 CJ x. ai cn -J cc IO C - M CJ i- Ln cn -J co to to O - ro oo x. £ 'J uj uiUirji>i>i»ots>i<5iui*.uio-iDOicni.rooO>oia mmrrmmmmmmrrrrmrrmmrrmrnmrnmrnrnrr, n rr + +. + + 4.*4.* + r+- + f + + + + * + + + + + i*X ooooooooocoococoooooooccoo t>iffl-ui.m'>iiiOMui.w<!ia-routui'ai^Boo-routij^ cxo — ooomrocrco-J — ' » O " " 31 O i m m rr. rr m m ri +.»•* + + •+• + + •**-+'+•*• + cooooocooooooocooo .CCJICJVCXI-O-OCOCECOCO — — -*-»-» — — — - - u u ro w ro oooiNitfltnOcn — ffi — tDCOC • 'o ro u-imO-Oi.^-JU'COu'Ou^y 'O co u t ^ ui L" jijic^3i<-J<co3)ia]CDCocoOO X'jcJix-i-JO-OCrj-^C'J T ci ffl c. n c o o o o m rr, rr rr m rr m m m m rr O O O C^ O Z- O C O O C C C- ~ C O C O O O O C O n —< r— X ro —• m > m Z . II O > I- CJ C -n o on o- r- o O CD C X «. •—-o o n ' \ ~r — X3 LE * 30 r-r— < — ro ro Ci •5) o c -< —-! -r -r (—i * r — ', "~ — 7Z c > — — ro ro fO ro ro NJ ro COCOOOC - --o >Z ro o- —i O co ui ul i.CJlfflJl^CCXCCLC----'--*--'-1-'-'"'"'"'"'"'"'-"'''"'"--"*-£ * £ m m £ 8 m m m S m rr rr, m rr rr, m rr rr m m rr m rr. m m rr. m rr m m rr rr rr ^. .+ .; icoooooocoocgog -^-^.ouurouuucouuuuutti-tiiit.Jiuioiui arm tnioi^o5ioieio<T>_mcn<ri<Jiai ro'cJl^CC-UUlfflCOC-CJJC.Ul^CO^ sssssssssssssssssssss^ OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO SgsS5Sss=issS§sasSss§= CO CD ooooooooooooooooooooooooooooooooooooooooooooo > o 68T \ 190 <»5 HARTLETON (54) SILT LOAM NC THE T15 THETAE THETA2 PPSI15 PSI1 PSIE PSI2 CONE TF TM (CM3/CM3) (CM OF WATER) (CM/DAY) DEG.C 48 0.1200 0.3400 0.4200 15306.0 15306.0 6.0 3.0 58.0000 20.0 20.0 CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFFUSSIVITY DPSI/DTHETA (CM) (CM3/CM3) (CM/DAY) (CM2/DAY 1 15306 . 0 0 . 1200 6 .39E-09 3 .71E-07 2 .48E-01 6 .70E+05 2 1 3348 . 7 0 .1231 2 .62E-08 1 .52E-06 8 .88E-01 5 . 84E + 05 3 10153 . 3 0 . 1294 6 .17E-08 3 .58E-06 1 .59E+00 4 .44E+05 4 7723 . 1 0 . 1356 1 .22E-07 7 .06E-06 2 .39E+00 3 .38E+05 5 5874 . 9 0 .14 19 2 .20E-07 1 .28E-05 t 3 .28E+00 2 .57E+05 6 4469 . 2 0 .148 1 3 .80E-07 2 .20E-05 ' 4 .30E+00 1 .96E+05 7 3400 . 2 0 . 1544 6 .37E-07 3 .69E-05 5 .49E+00 1 .49E+05 8 2587 . 1 0 . 1606 1 .05E-06 . 6 .09E-05 6 .89E+00 1 .13E+05 9 1968 . 8 0 . 1669 1 .72E-06 9 .96E-05 8 .56E+00 8 .60E+04 •10 1498 . 5 0 .1731 2 .79E-06 1 .62E-04 1 .06E+01 6 . 54E + 04 1 1 1 140 . 9 0 . 1794 4 .53E-06 2 .63E-04 1 .31E+01 4 .97E+04 12 868 . 9 0 . 1856 7 .34E-06 4 . 26E-04 1 .61E+01 3 .78E+04 13 662 .0 0 .19 19 1 .19E-05 6 .90E-04 1 .98E+01 2 .88E+04 14 504 . 7 0 . 198 1 1 .93E-05 1 .12E-03 2 . 45E + 01 2 .19E+04 15 385 .0 0 . 2044 3 .13E-05 1 .81E-03 3 .02E+01 1 .66E+04 16 294 .0 0 . 2 106 5 .07E-05 2 .94E-03 3 .72E+01 1 .27E+04 1 7 224 . 8 0 . 2 169 8 .23E-05 4 .77E-03 4 .59E+01 9 .63E+03 18 172 . 2 0 . 223 1 1 .33E-04 7 .74E-03 5 .67E+01 7 .32E+03 19 132 . 1 0 . 2294 2 .16E-04 1 .25E-02 6 .99E+01 C .57E+03 20 101 . 7 0 . 2356 3 .50E-04 2 .03E-02 8 .60E+01 4 .23E+03 2 1 78 . 5 0 .24 19 5 .65E-04 3 .28E-02 1 .06E+02 3 .22E+03 22 60 . 9 0 . 248 1 9 .10E-04 5 .28E-02 1 .29E+02 2 . 45E+03 23 47 . 5 0 . 2544 1 .46E-03 8 45E-02 1 .57E+02 1 . 86E + 03 24 37 . 3 0. . 2606 2 .32E-03 1 .35E-01 1 .91E+02 1 . 42E + 03 25 29 6 0. 2669 3 66E-03 2 .13E-01 2 .29E+02 1 . .08E+03 26 23 . 7 0. 2731 5 .73E-03 3 .32E-01 2 .72E+02 8 . 19E+02 27 19 . 2 0. 2794 8 .84E-03 5 . .13E-01 3 .20E+02 . 6. 23E+02 28 15 . 8 0. 2856 1 .35E-02 7 . 80E-01 3 .70E+02 4 . 74E+02 29 13 . 2 0. 29 19 2 . .01E-02 1 . 17E+00 4 .21E+02 3 . 60E+02 30 1 1 . . 3 0. 2981 2 . .95E-02 1 . 71E+00 4 , .70E+02 2 . 74E+02 3 1 9 . 8 0. 3044 4 . 24E-02 2 . 46E+00 5 . .13E+02 2 . 09E+02 32 8 . 6 0. 3106 5 . 96E-02 3 . 46E+00 5 . 48E+02 1 . 59E+02 33 7 . 8 0. 3169 8 . 19E-02 4 . 75E+00 5. 73E+02 1 . 21E+02 34 7 . 1 0. 3231 1 . 10E-01 6 . 38E+00 5 . 85E+02 9 . 17E+01 35 6 . 6 0. 3294 1 . 44E-01 8 . 38E+00 5 . 84E+02 6 . 98E+01 36 6 . 1 0. 3356 1 . 86E-01 1 . 08E+01 1 . 73E+02 1 . 61E+01 37 6 . 0 0. 34 19 2 . 34E-01 1 . 36E+01 2 . 43E+02 1 . 79E+01 38 5 . 8 0. 3481 2 . 89E-01 1 . 68E+01 3 . 35E+02 1 . 99E+01 39 5 . 7 0. 3544 3 . 51E-01 2 . 03E+01 4 . 52E+02 2 . 22E+01 40 5 . 6 0. 3606 4 . 18E-01 2 . 43E+01- 6 . 01E+02 2 . 48E+01 4 1 5 . 4 0. 3669 4 . 92E-01 2 . 85E+01 7 . 87E+02 2 . 76E+01 42 5 . 2 0. 3731 5 . 71E-01 3. 31E+01 1 . 02E+03 3 . 08E+01 43 5. 0 0. 3794 6 . 56E-01 3 . 80E+01 1 . 30E+03 3. 43E+01 44 4 . 8 0. 3856 7 . 47E-01 4 . 33E+01 1 . 66E+03 3 . 82E+01 45 4 . 5 0. 3919 8 . 46E-01 4 . 90E+01 2 . 09E+03 4 . 26E+01 46 4 . 3 0. 3981 9. 51E-01 5 . 52E+01 2 . 62E+03 4 . 74E+01 47 3 . 9 0. 4044 1 . 07E+00 6 . 18E+01 3 . 27E+03 5 . 29E+01 48 3 . 6 0. 4 106 1 . 19E+00 6 . 91E+01 4 . 07E+03 5 . 89E+01 49 3 . 2 0. 4 169 1 . 33E+00 7 . 72E+01 5 . 07E+03 6 . 57E+01 191 O — Tcco) — Ticcn — 91c 01 •• T 10 o — t » rji - ^caci — ^IOCIO — rrioo">"-'rioo)"-'Tioo)"-'Tcooi Ococnin — corroioncnin — co-TOioocnin — co^Oiococnin — o^Oioo cNCNCNCO'TTiniotor^ocooioiO — r<Nn^T^lnB^o^^orJ1(7)0'-•-(N(^ln^J'IlnlIlUl^^•o(Il "'"""'"'"'''''nnnniNnNnnnicNNNnriinnnnnnnnonnnnnno ooooooooooooooooooooooooooooooooooooooooooooo ID in CN — O o CO 10 in m CN O 01 CO r- to in ci CN — o CT) co m r> .- O 01 co r- in *T Cl CN ,_ 0) CO co in in O LO O LO O in cn 01 0) T 01 T CO n co to CO n CO Cl CO CN r- CN r- CN CN r- 10 CO 10 CO o in O in c CO O n ID r~ CO o *~ to T ID r~ 01 O CN r> in 10 CO 01 CN *r cn r- co O co CO r- 0) o CN co LO CO CO m CN CN n o n r> c-> co *T in in in in in in in u> LO CO 10 10 CO r~ r- r- r- CO CO CO CO co co co 0) 01 01 o O O O o O O O o o o o o O O O O O O O O O o o O O O O O O O O O O O O O O O o O O O O O CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN O O O O G o O o O O O O O o O O O o O o O cu LU LU UJ UJ UJ UJ UJ UJ UJ UJ UJ LU UJ Lu LU UJ UJ LU Lu UJ LU CN cc C CN n LO 10 cc O ~- CN co CO T T ~- T ro ro CN in to CN — O 0) i 00 r- ID cn Cl CN *~ O 01 CO to 10 10 10 10 10 CO CO in m in LO in in in LO in in in T T CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN c o o C o o O O o O O o C O Q p O O o o o 0 o LU UJ UJ UJ UJ UJ UJ LU UJ LU UJ UJ LU UJ UJ UJ UJ UJ UJ UJ UJ UJ '— 01 00 O r? CN 0) r- T — r~ T O — LO O <N LP LP Cl — co CN o 01 r~ to LO CN O CO LT n CN c X LD rr CN T rt T T co ro co co Cl co co CN CN c\ CN CN CN — —• — O o O C O O O o O C O O O o O O o o o O O 0 O c O o o o O O o o o O O o o o o Q 0 + » * •r •*• * » * * •*• + + + 4- * -» 4. UJ U_ UJ UJ UJ -J UJ UJ UJ U-' UJ UJ UJ u- UJ LU LU LU UJ UJ CN o r- CN o !-- LP CN c- — cc LO CN 01 CO n ,^ O O C cn at Cl •31 CO x. X r- '•0 to to LO LO IT. CN CN O 0 O 0 0 O O O 0 O O 0 O c O 0 0 O O c 0 c C 0 O O O O O 0 O c O O O •* — •* •* + •*• 4- * 1 1 • 1 1 UJ UJ UJ u-- UJ UJ LU UJ UJ UJ LL,' 'jJ UJ UJ UJ UJ UJ UJ UJ :aJ n O J) ui CN X T '«£ CN to CN LP C »- Q CN *T n CN CN CN — 0 n J) n T r; '- — oooocoooo ooooocooo ^*^**»** + UUjUU'ULJUJtUU oir^incNOr^LOrNO oioioioioicococox •0 o c ceo c c c o x to Co O r-r-r-iotOtOcOLOLOLOT O O O C O O ^ — *r rr rt n n O C C C C O C r- 71 01 c CN x <N O. - - - O 01 LO — r» r~ CN OlWOlcOCOr-r-lC'JJ OOOOOOOOOOOOOOOOOOOOOO COO C OOOOOOOCOOOOO O C- c~ ^ " G + + + + + + + + + + + + + + + + + + + + + UJUJLUUJLUmuJUJUJluLUUJLuLUlUUJlxJWWUJUJLUUJUJUJL^ OtooiCN^rtooi^nintoccO^CNcorTLOcocO'^cototOin*TcocN-- crcc-opco'-cc'or, cc~^^-*,-.^ -CN — 000)cor~r-cOLOTCOncN — OOioor-toji'dncN — ocj!flo^ir)innroi>inr^'ji!»^!;; lOicifltsinLTinininininininifiifiiri^'r'j'i'r^^'r'i'jpincir, nnnnr<Mr<nci«r(----rc^ln^tqls^offlOrc^l^7lnlC^oolO-cNn7lDcB^co^O'c\nTl^lt^ccalO••c^n'tl.•! ^rrr^^^^^^^NMn(NCNnncNnnnnrinnnnnn,7rr,:ii:^ 192 *7 ALBRIGHTS (71) SILT LOAM NC THET15 THETAE THETA2 PPSI15 PSI1 PSIE PSI2 CONE TF TM (CM3/CM3) (CM OF WATER) (CM/DAY) DEG.C 48 0.1400 0.3400 0.4300 15306.0 15306.0 6.0 3.0 23.0000 20.0 20.0 CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFFUSSIVITY DPSI/DTHETA 1 2 3 4 5 6 7 8 9 10 1 1 1 2 13 14 15 16 17 18 19 20 2 1 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4 1 42 43 44 45 46 47 48 49 (CM) 15306.0 13233 . 6 9892 . 8 7395 . 7 5529 . 2 4134 . 1 309 1 . 4 2311.9 1729 . 3 1293 . 9 96S 725 543 407 305 229 . 8 173.0 1 30 95 75 57 44 34 26 2 1 17 14 11.8 10. 1 8 . 8 9 1 6 1 0 9 8 6 5 3 2 0 8 6 4 1 (CM3/CM3) 1400 1430 149 1 155 1 16 1-1 1672 1732 1793 1853 0. 1914 0.1974 O.2034 0.2095 0.2155 0. 2216 0. 2276 0. 2336 O.2397 0.2457 0.2518 0.2578 O.2639 0.2699 0.2759 0 . 2820 0. 2880 . 294 1 3001 306 1 3122 3 182 3243 3303 3364 3424 3484 3545 3605 3666 3726 3786 3847 3907 3968 4028 4089 8 0.4149 5 0.4209 2 0.4270 13 ) (CM/DAY ) (CM2/DAY 3.84E-09 8.84E-08 6.52E-02 7.37E+05 1.60E-08 3.67E-07 2.34E-01 6.37E+05 3.87E-08 8.90E-07 4.24E-01 4.76E+05 7.88E-08 1.81E-06 6.45E-01 3.56E+05 1.48E-07 3.39E-06 9.03E-01 2.66E+05 2.64E-07 6.07E-06 1.2 1E+00 1 .99E + 05 4.60E-07 1.06E-05 1.57E+00 \,49E+05 7.90E-07 1.82E-05 2.02E+00 l'. 1 1E + 05 1.34E-06 3.09E-05 2.57E+00 8.31E+04 2.28E-06 5.24E-05 3.25E+00 6.21 E + 04 3.85E-06 8.85E-05 4.11E+00 4.64E+04 6.50E-06 1.49E-04 5.19E+00 3.47E+04 1.10E-05 2.52E-04 6.54E+00 2.59E+04 1.85E-05 4.26E-04 8.25E+00 1.94E+04 3.12E-05 7.19E-04 1.04E+01 1.45E+04 5.27E-05 1.21E-03 1.31 E + 01 1.08E+04 8.89E-05 2.04E-03 1.65E+01 8.09E+03 1.50E-04 3.44E-03 2.08E+01 6.05E+03 2.51E-04 5.78E-03 2.62E+01 4.52E+03 4 , 2 1 E-04 9.69E-03 3 27E+01 3.38E+03 7.03E-04 1.62E-02 4.08E+01 2.53E+03 1.16E-03 2.68E-02 5.06E+01 1.89E+03 1.91E-03 4.40E-02 6.22E+01 1.41E+03 3.12E-03 7.17E-02 7.56E+01 1.06E+03 5.01E-03 1.15E-01 9.08E+01 7.89E+02 7.92E-03 1.82E-01 1.07E+02 5.89E+02 1.23E-02 2.83E-01 1.25E+02 4.41E+02 1.87E-02 4.30E-01 1.42E+02 3.29E+02 2.78E-02 6.39E-01 1.57E+02 2.46E+02 4.03E-02 9.26E-01 1.70E+02 1.84E+02 5.68E-02 1.31E+00 1.80E+02 1.38E+02 7.82E-02 1.80E+00 1.85E+02 •1 .03E+02 1.05E-01 2.41E+00 1.85E+02 7 .68E + 01 1.37E-01 3.16E+00 4.60E+01 - 1 .46E+01 1.76E-01 4.05E+00 6.47E+01 1.60E+01 2.20E-01 5.06E+00 8.88E+01 1.75E+01 2.69E-01 6.20E+00 1.19E+02 1.93E+01 3.24E-01 7.45E+00 1.57E+02 2.11E+01 3.83E-01 8.81E+00 2.04E+02 2.32E+01 4.47E-01 • . 1.03E+01 2.62E+02 2.55E+01 5.15E-01 1.19E+01 3.31E+02 2.79E+01 5.89E-01 1.35E+01 4.15E+02 3.07E+01 6.67E-01 1.53E+01 5.16E+02 3.36E+01 7.50E-01 1.72E+01 6.37E+02 3.69E+01 8.39E-01 1.93E+01 7.82E+02 4.05E+01 9.34E-01 2.15E+01 9.55E+02 4.45E+01 1.04E+00 2.38E+01 1.16E+03 4.88E+01 1.15E+00 2.64E+01 1.41E+03 5.36E+01 1.27E+00 2.92E+01 1.72E+03 5.88E+01 THETAE = 0.3400 "7 CLASS INITIAL FLUX(CM/HRS) 1 3 54E»0 1 2 3 52E*01 3 3 18E+01 4 3 44E+01 5 3 39E*01 6 3 35E+01 7 3 30E*01 8 3 26E+01 9 3 21E+01 IO 3 17E+01 1 1 3 12E+01 12 3 07E+01 13 3 02E+01 14 2 97E+01 15 2 92E+01 16 2' 87E+01 17 2 82E+01 18 2 76E+01 19 2 7 1E+01 20 2 65E+01 2 1 2 60E+01 22 2 54E+01 23 2 48E+01 24 2 42E+01 25 2 36E+01 26 2 30E «01 27 2 23E+01 28 2 17E+01 29 2 10E+01 30 2 04E+01 3 1 1 97E+01 32 1 90E+01 33 1 83E »01 34 1 76E *01 35 1 69E »01 36 1 .6-1001 37 1 .53E»01 38 1 •» -1E • 0 1 39 1 . JGE-K) 1 40 1 . 26E+01 4 1 1 . 1 7 O 0 1 42 1 . 0CiO01 4 3 9 .57E*00 44 8 . 4 31: K.K.) 4 5 7 . 2JOOO ALHKlCMrS (7 1) SILI LOAM SORPTI VIT Y(CM/HRj••0.5) 1 1'JEUJO 1 ME-tOO 1 13E tOO 1 1 1E 100 1 10E t()(j 1 08E+00 1 07E tOO 1 05Et00 1 04 Ft 00 1 02E+0G 1 01E*00 9 9 1F-01 9 7GE-01 9 5HE 01 9 4 11: 0 1 9 24E-0 1 9 07E-01 8 89E-01 8 7 1 E 01 8 52E-01 8 33E-01 8 ME -01 7 95E-01 7 75E-01 7 54 E Ol 7 34E-01 7 13E-01 6 9 1E-01 6 C.9E-01 6 47E-01 6 25E-U1 6 02 E- 01 5 79E- 01 5 55F. -0 1 5 30E 0 1 5 OlL- 01 4 77E-01 4 I9F -Ol 4 I'OL - 0 1 3 H9E-01 3 571 - 0 1 3 ?3E-01 2 . 87E-01 2 .49E-U1 2 .09E -o 1 KLM FT/MRS) = 3 FKFI/HHS) FS( FT/HRS' *. 5 ) 16E tOO 3 77E -02 KiE-tOO 3 75E -02 ME tOO 3 70E -02 13E+00 3 65E -02 1 I E 100 3 6 IE -02 101tOO 3 56E -02 08EtOO 3 5 1E -02 07 F * 00 3 46E -02 05E+00 3 4 IE -02 OIF tOO 3 36E -02 02f. tOO 3 3 1E -02 01E t OO 3 25E -02 9 IE-01 3 20E -02 75E 01 3 ME -02 5HE-01 3 09E -02 11F.-01 3 03E -02 2 IE -O 1 2 97E -02 9 06E-01 2 92E -02 8 8RE-01 2 86E -02 8 70E-01 2 80E -02 8 52E-01 2 73E -02 8 33E-01 2 67E -02 8 14 F - 01 2 6 IE -02 7 94E-01 2 5 IE -02 7 7 4 F - 0 1 2 48E -02 7 54E-01 2 4 IF. -02 7 33E-01 2 34 E -02 7 12E-01 2 2 7E -02 6 90E-01 2 20E -02 6 69E-01 2 12E -02 6 46E-01 2 05E -02 6 24E-01 1 97E -02 6 OIF.-01 1 90E -02 5 77E-01 1 82E -02 53E-01 1 74E -02 5 2HE-01 1 6SE -02 5 01E-01 1 57E -02 4 74E-01 1 47E -02 4 .45E 01 1 . 3BE -02 4 ME -Ol 1 . 28E -02 3 . B3I -01 1 . 1 7E -02 ;i . 491- -Ol 1 . OGE -02 j . ME -01 9 . 4 2E -03 2 77E-01 8 . 1 7 E -03 o 37E-01 6 . 86E -03 1441E-02 T HE TA/THE TA 2 THETA MID. INT. 0. 3256 0. MOO 0. 3396 0. 14 30 0. 3537 0. 149 1 0. 3677 0. 1551 o. 38 18 0. 161 1 0. 3958 0. 1672 0. 4099 0. 1732 0. 4239 0. 1793 0 4380 0. 1853 o 4520 0. 19 14 0 4661 0. 1974 0 4801 0. 2034 0 4942 0. 2095 0 5082 0. 2 155 o 5223 0. 22 16 o 5363 0. 2276 0 5504 0. 2336 0 5644 0 2397 0 5785 0. 2457 0 5925 0. 2518 0 6066 0 2578 0 6206 o 2639 0 6347 0 2699 0 6487 0 2759 0 6628 0 2820 o 6768 0 2880 o 6909 0 294 1 0 7049 0 3001 0 7 190 o 306 1 0 7330 0 3122 o 747 1 0 3182 o 76 1 1 0 3243 0 7752 0 3303 0 7892 0 3364 0 8033 0 3424 0 8 173 0 3484 0 8314 0 3545 o 8454 o 3605 0 8595 0 3666 0 8735 0 3726 0 8876 0 3786 0 9016 0 3847 0 . 9 157 0 3907 0 .9297 0 3968 0 . 9438 o .4028 194 »8 MECKENSVILLE (G9 ) SILT LOAM NC THET15 THETAE THETA2 (CM3/CM3 ) PPSI15.PSI1 PSIE PSI2 CONE TE (CM OF WATER) (CM/DAY) DEG.C TM 48 0.1800 0.3100 0.3900 15306.0 15306.0 6.0 3.0 23.0000 20.0 20.0 CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFFUSSIVITY DPSI/DTHETA 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 1 7 18 19 20 2 1 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4 1 42 43 44 45 46 47 48 49 (CM) 15305 13015 94 12 6807 4923 356 1 2576 1864 1 349 977 707 5 1 3 372 270 197 143 105 77 57 43 32 24 19 15 12 10 8 7 7 6 . 6 5 . 5 . 5 . 5 . 5 . 5 . 5 . 5 . 5 . 4 . 4 . 4 . 4 . 4 . 3 . 3 . 3 . 3 . (CM3/CM3) .90.1800 .8 0.1822 .4 0.1866 .10.19C9 .2 0.1953 0. 1997 0 . 204 1 0. 2084 O. 2 128 0.2 172 22 16 2259 2303 2347 239 1 243J 2J78 2522 2566 2609 0 . 2653 0 . 2697 0.274 1 2784 2828 2872 29 16 2959 1 0.3003 5 0.304 7 309 1 3 1 34 3178 3222 3266 3 309 3353 3397 3441 3484 3528 3572 36 16 3659 3703 3747 3791 3834 3878 !3 (CM/DAY ) (CM2/DAY 1 .45E-09 3 .33E-08 3 .78E-02 1 .13E+06 6 .20E-09 1 .43E-07 1 .37E-01 9 . 64E+05 1 .59E-08 3 .66E-07 2 .55E-01 6 .97E*05 3 .46E-08 7 .97E-07 4 .02E-01 5 .04E+05 6 .98E-08 1 .61E-06 5 .85E-01 3 .65E+05 1 .35E-07 3 .11E-06 8 .19E-01 2 .64E+05 2 .55E-07 5 .87E-06 1 .12E+00 1 .91E+05 4 .76E-07 1 .10E-05 1 . 51E+00 1 .38E+05 8 .83E-07 2 .03E-05 2 .02E+00 9 .96E+04 1 .63E-06 3 .75E-05 2 . 70E+00 7 . 20E-"-04 3 .OOE-06 6 .89E-05 3 . 59E + 00 5 .21E*04 5 .51E-06 1 .27E-04 4 . 77E->00 3 .77E+04 1 .01E-05 2 .33E-04 6 . 33E+00 2 .72E+04 1 .85E-05 4 .26E-04 8 . 39E + 00 1 .97E+04 3 .39E-05 7 .80E-04 1 . 1 1E+01 1 .42E+04 6 .19E-05 1 .42E-03 1 .47E+01 1 .03E+04 1 .13E-0J 2 .59E-03 1 . 93E+01 7 .44E+03 2 .C4E-C4 4 .70E-03 2 . 53E+01 5 . 38E + 03 3 .6BE-04 8 .46E-03 3 . 29E + 01 3 .89E+03 6 .57E-04 1 .51E-02 4 . 25E + 01 2 .81E*03 1 .16E-03 2 .67E-02 5 . 43E + 01 2 .03E+03 2 .02E-03 4 .64E-02 6 . 83E+01 1 .47E+03 3 .45E-03 7 .94E-02 8 .44E*01 1 .06E+03 5 .77E-03 'l .33E-01 1 .02E+02 7 .69E+02 9 .41E-03 2 .16E-01 1 .20E+02 5 .56E+02 1 .49E-02 3 .43E-01 1 .38E+02 4 .02E+02 2 .29E-02 5 . 26E-01 1 .53E+02 2 .91E+02 3 40E-02 7 .82E-01 1 , 64E+02 2 . 10E+02 4 . 89E-02 1 , 13E+00 1 . 71E+02 1 . 52E+02 6 . 82E-02 1 . 57E+00 1 . 72E+02 1 . 10E*02 9 . 22E-02 2 . 12E+00 3 . 62E+01 1 . 70E+01 1 . 21E-01 2 . 79E+00 5 . 13E+01 1 . 84E+01 1 . 55E-01 3 . 56E+00 7 . 07E+01 1 . 98E+01 1 . 93E-01 4 . 44E+00 9 . 50E+01 2 . 14E+01 2 . 35E-01 5 . 4 1E + 00 1 . 25E+02 2 . 31E+01 2 . 82E-01 6 . 47E+00 1 . 61E+02 2 . 49E+01 3 . 32E-01 7 . 63E+00 2 . 05E+02 2 . 69E+01 3 . 86E-01 8 . 88E+00 2 . 57E+02 2 . 90E+01 4 . 44E-01 1 . 02E+01 3 . 19E+02 3 . 13E+01 5 . 06E-01 1 . 16E+01 3 . 93E+02 3 . 37E+01 5 . 72E-01 1 . 32E+01 4 . 79E+02 3 . 64E+01 6 . 42E-01 1 . 48E+01 5 . 80E+02 3 . 93E+01 7 . 16E-01 1 . 65E+01 6 . 98E+02 4 . 23E+01 7 . 95E-01 1 . 83E+01 8 . 35E+02 4 . 57E+01 8 . 79E-01 2 . 02E+01 9 . 96E+02 4 . 93E+01 9. 68E-01 2 . 23E+01 1 . 18E+03 5 . 32E+01 1 . 06E+00 2 . 45E+01 1 . 40E+03 5 . 73E+01 1 . 17E+00 2 . 68E+01 1 . G6E+03 6 . 19E+01 1 . 28E+00 2 . 94E+01 1 . 96E+03 G . 67E+01 THETAE = 0.3100 #8 CLASS INITIAL FLUX(CM/HRS) 1 2 86E+01 2 2 84E+01 3 2 81E+01 4 2 77E+01 5 2 74E+01 6 2 70E+01 7 2 67E+01 8 2 63E+01 9 2 59E+01 10 2 56E+01 1 1 2 52E+01 12 2 48E+01 13 2 44E+01 14 2 .'40E+01 15 2 36E+01 16 2 32E+01 17 2 28E+01 18 2 24E+01 19 2 19E+01 20 2 15E+01 2 1 2 10E+01 22 2 06E+01 23 2 01E+01 24 1 96E+01 25 1 9 1E+01 26 1 87E+01 27 1 82E +01 28 1 76E +01 29 1 7 1E+01 30 1 G6E+01 3 1 1 6 1E+01 32 1 55E+01 33 1 49E+01 34 1 43E+01 35 1 37E+01 36 1 . 3 1E + 01 37 1 .24E+01 38 1 . 17E+01 39 1 . 10E+01 40 1 02E+01 4 1 9 .44E+00 42 8 .6 IE+ 00 43 7 .74E+00 44 6 .83E+00 45 5 .87E+00 MECKENSVILLE (69) S1LI LOAM SORPT[VI1Y(CM/HRS•'O.5) 9 2 IE •01 9 15E -01 9 04E -0 1 8 93E -01 8 8 1E •O 1 8 69E -01 8 57E -01 8 4 5E -O 1 8 33E -Ol 8 2 1E -01 8 08 E O 1 7 95 E -01 7 82E -O 1 7 69E 01 7 55E •oi 7 42E •01 7 28E -01 7 13E -01 6 99E -01 6 84E -01 6 69E -01 6 54E -Ol 6 38E -01 6 22E -01 6 061 -0 1 5 90E -01 5 73E •0 1 5 56F. -0 1 5 39E -C) 1 5 2 1E -01 5 04E -(.11 4 B5E -01 4 66E -01 4 46E -01 4 25E -oi 4 04 E -0 1 3 82E -01 3 59E -oi 3 . 34E -01 3 09E -01 2 . 83E -01 2 55E -oi 2 . 26E -01 1 . 96E -01 1 . 64E -01 KEIFT/HRS) = 3 F 1 (F 1/HRS) FS(FT/HRS*' . 5 ) 9 . 38E 01 3 02E -02 9 33E 01 3 00 E 02 9 2 IE 01 2 97 E 02 9 10E -01 2 93E 02 8 99E -01 2 89E 02 8 87 F -01 2 85E 02 8 75F -01 2 8 1E -02 8 63E 01 2 77E 02 8 5 IE -01 2 73E -02 8 39 E -01 2 69 E -02 a 27E -01 2 65E -02 8 14E -01 2 6 1E -02 8 01E 01 2 57 E 02 7 88E -01 2 52E -02 7 75E 01 2 48E -02 7 61E -01 2 43E -02 7 4RE -01 2 39E -02 7 34E -01 2 34E -02 7 19E -01 2 29E -02 7 05 E -01 2 24E -02 6 90E -01 2 20E -02 6 75E -01 2 15E -02 6 60E -01 2 09 E -02 6 44E -01 2 04 E -02 6 28E -01 1 99E -02 6 12E -01 1 94E -02 5 96 E -01 1 88E -02 5 79E -01 1 83€ -02 5 62E -01 1 77E -02 5 45E -01 1 7 1E -02 5 27E -01 1 65E -02 5 09 E -01 1 59E -02 4 90E -01 1 53E -02 4 70E -01 1 46E -02 4 50E -01 1 . 40E -02 4 29E -oi 1 33E -02 4 07E -01 1 . 25E -02 3 84E -01 1 .18E-02 3 6 1E -01 1 . 10E -02 3 36E -01 1 .01E -02 3 . 10E -01 9 . 28E -03 2 . 83E -01 8 . 37E -03 2 .54E -01 7 42E -03 2 24E -01 6 . 42E -03 1 93E -01 5 . 37E -03 1441E-02 THETA/THETA2 THETA MID.INT. 0. 46 15 O. 1800 0. 4728 0. 1822 0. 4840 0. 1866 0. 4952 O. 1909 0. 5064 O. 1953 0. 5176 O. 1997 0. 5288 0. 204 1 0 5401 0. 2084 0 5513 0. 2 128 0 5625 0. 2 172 0 5737 0. 22 16 0 5849 0. 2259 0 5962 0. 2303 0 6074 0. 2347 0 6 186 0 2391 o 6298 O 2434 0 64 10 0 2478 0 6522 0 2522 0 6635 0 2566 0 6747 0 2609 0 6859 0 2653 0 697 1 O 2697 0 7083 0 274 1 0 7 196 0 2784 0 7308 0 2828 0 7420 0 2872 0 7532 0 2916 0 7644 0 2959 0 7756 o 3003 0 7869 0 304 7 0 7981 0 309 1« 0 8093 o 3134 0 8205 0 3178 0 83 17 0 3222 0 8429 0 3266 0 8542 o 3309 0 8654 0 3353 0 8766 0 3397 0 .8878 0 344 1 0 .8990 0 . 3484 0 .9103 0 . 3528 0 .9215 o . 3572 0 .9327 0 .3616 0 . 9439 0 . 3659 0 .9551 0 .3703 VO Ln *9 ALVIRA (57) SILT LOAM NC THET15 THETAE THETA2 PPSI15 PSI1 PSIE PSI2 CONE TF TM (CM3/CM3) (CM OF WATER) (CM/DAY) DEG.C 48 0.1500 0.3000 0.3800 15306.0 15306.0 6.0 3.0 23.0000 20.0 20.0 CLASS PRESSURE THETA PERMEABILITY CONDUCTIVITY DIFFUSSIVITY DPSI/DTHETA (CM) (CM3/CM3) (CM/DAY) (CM2/DAY 1 15306. 0 0. 1500 2 . 22E-09 5 . 11E-08 5 . 02E-02 9 .83E+05 2 13123. 4 0. 1524 9 . 38E-09 2 . 16E-07 1 . 82E-01 8 . 43E + 05 3 9647 . 8 0. 1572 2 . 35E-08 5 . 40E-07 3 34E-01 6 .19E+05 4 7093 . 0 0. 16 20 4 . 95E-08 1 . 14E-06 5 . 19E-01 4 .55E+05 5 52 15 . 1 0. 1668 9 . 65E-08 2 . 22E-06 7 , 43E-01 3 .35E+05 6 3834 , 8 0. 17 16 1 . 80E-07 4 . 14E-06 1 . 02E+00 2 .46E+05 7 2820. 1 0. 1764 3 . 27E-07 7 . 52E-06 1 . 36E+00 1 .8 1E+05 8 2074 . 3 0. 18 11 5 . 86E-07 1 . 35E-05 1 . 79E+00 1 .33E+05 9 1526 . 0 0. 1859 1 . 04E-06 2 . 40E-05 2 34E+00 9 . 77E + 04 10 1123. 1 0. 1907 1 . 85E-06 4 . 25E-05 3 . 05E+00 7 .18E+04 1 1 826 . 8 0. 1955 3 . 26E-06 7 . 50E-05 3 96E+00 5 .28E+04 12 609 . 1 0. 2003 5 . 76E-06 1 . 32E-04 5 14E+00 3 .88E+04 13 . 449 . 0 c. 205 1 1 . 01E-05 2 . 33E-04 6 66E+00 2 .85E+04 14' 33 1 . 4 0. 2099 1 . 79E-05 4 . 11E-04 8 . 62E+00 2 .10E+04 15 244 , 9 0. 2 147 3 . 14E-05 7 . 23E-04 1 11E+01 1 54E+04 16 18 1. 4 0 . 2 195 5 . 53E-05 1 . 27E-03 1 .44E+01 1 .13E+04 17 134 , 6 0. 2243 Q 70E-05 2 . 23E-03 1 86E+01 8 33E+03 18 100 3 0. 229 1 1 .70E-04 3 . 90E-03 2 . 39E + 01 6 12E+03 19 75 0 0 . 2339 2 96E-04 6 . 80E-03 3 .06E+01 4 .50E+03 20 56 . 5 0. 2386 5 12E-04 1 .18E-02 3 90E+01 3 . 31E + 03 2 1 42 . 8 0. 2434 8 . 82E-04 2 . 03E-02 4 . 93E + 01 2 . 43E + 03 22 32 . . 8 0. 2482 1 , 50E-03 3 . .46E-02 6 . 17E+01 1 .79E+03 23 25 . 4 0. 2530 2 .53E-03 5 .81E-02 7 .64E+01 1 .31E+03 24 20 .0 0. 2578 4 .19E-03 9 63E-02 9 .30E+01 9 . 66E + 02 25 16 .0 0. 2626 6 81E-03 1 .57E-01 1 .11E+C2 7 .10E+02 26 13 . 1 0. 2674 1 08E-02 2 . 49E-01 1 .30E+02 5 . 22E + 02 27 1 1 .0 0. 2722 1 68E-02 3 . 86E-01 1 .48E+02 ' 3. .83E+02 28 9 . 4 0. 2770 2 .53E-02 5 . 83E-01 1 .64E+02 2 .82E+02 29 8 . 2 0. 2818 3 .72E-02 8 . 55E-01 1 .77E+02 2 .07E+02 30 7 . 4 0. 2866 5 .29E-02 1 .22E+00 1 .85E+02 1 .52E+02 31 6 . 7 0. 2914 7 .32E-02 1 .68E+00 1 .88E+02 1 .12E+02 32 6 . 1 0. 2961 9 .87E-02 2 .27E+00 3 .68E+01 1 .62E+01 33 6 .0 0. 3009 1 .30E-01 2 .98E+00 5 .25E+01 1 .76E+01 34 . 5 . 9 0. 3057 1 .66E-01 3 .8 1E+00 7 .30E+01 1 .91E+01 35 5 . 8 0. 3105 2 07E-01 4 .75E+00 9 .89E+01 2 .08E+01 36 5 . 7 0. 3153 2 .52E-01 5 .80E+00 " 1 . 31E+02 2 .26E+01 37 5 . 6 0. 3201 3 02E-01 6 .95E+00 1 .71E+02 2 .45E+01 38 5 . 5 0. 3249 3 .56E-01 8 .20E+00 2 .19E+02 2 .67E+01 39 5 . 3 0. 3297 4 .15E-01 9 .54E+00 2 .76E+02 2 .90E+01 40 5 . 2 0. 3345 4 .77E-01 1 .10E+01 3 .46E+02 3 .15E+01 4 1 5 .0 0. 3393 5 .44E-01 1 .25E+01 4 .28E+02 3 .42E+01 42 4 . 9 0. 344 1 6 .14E-01 1 .41E+01 5 .26E+02 3 .72E+01 43 4 . 7 0. 3489 6 .90E-01 1 .59E+01 6 .41E+02 4 .04E+01 44 4 . 5 0. 3536 7 .70E-01 1 .77E+01 7 .77E+02 4 .39E+01 45 4 .2 0. . 3584 8 .55E-01 1 .97E+01 9 .38E+02 4 . 77E + 01 46 4 .0 o. . 3632 9 .46E-01 2 . 17E+01 1 .13E+03 5 .18E+01 47 3 .7 0, 3680 1 .04E+00 2 .40E+01 1 .35E+03 5 .63E+01 48 3 . 5 0. . 3728 1 .15E+00 2 .64E+01 1 .62E+03 6 .12E+01 49 3 . 2 0. . 3776 1 .26E+00 2 .90E+01 1 .93E+03 6 .65E+01 THETAE = 0.3000 #9 ALVIRA (57) SILT LOAM KF. ( F F/HRS ) 3 . 144 IE-02 CLASS INITIAL FLUX(CM/HRS) SORPTI V ITY(CM/MRS 4*0.5) FKFT/HRS) F S(F T/MRS'* .5 ) THE TA/THETA2 THETA MIDI NT 1 3 05E+01 9 84E-01 1 OOF•OO 3 23E-02 0 3947 0 1500 2 3 03E+01 9 78E-0I 9 94L -O 1 3 2 IE-02 0 4073 0 1524 3 2 99E+01 9 66E-01 9 82F-01 3 17E-02 0 4 200 0 1572 4 2 96E+01 9 51E-01 9 70F-oi 3 13E-02 0 4326 0 1620 5 2 92E+01 9 41E-01 9 58E-01 3 09E-02 0 4452 0 1668 6 2 88E+01 9 29E-01 9 I'.'.F -O 1 3 05F. -02 0 4578 O 17 16 7 2 84E+01 9 16F-01 9 33E-01 3 OOF -02 0 4704 0 1764 8 2 80E+01 9 03E-01 9 20F-Ol ? 96E 02 0 4830 0 18 11 9 2 77E+01 8 90E-01 9 07F-01 2 92E-02 0 4956 0 1859 10 2 73E+01 8 7GF-01 fl 9 IE-01 2 8RE-C2 0 5082 0 1907 1 1 2 6RE+01 8 63E-01 R 8 IF-Ol 7 R3E-02 o 5208 0 1955 12 2 64E+01 8 49E-01 8 G7E-01 2 79E-02 0 5334 0 2003 13 2 60E+01 8 35E-01 8 5 IE -Ol 2 74E-02 o 546 1 0 205 1 14 2 56E+01 8 21E-01 8 40F-01 2 69E-02 0 5587 0 2099 15 2 52E+01 8 07E-01 8 25F-01 2 G5E-02 0 57 13 0 2 147 16 2 47E+01 7 92E-01 8 1 1E-01 2 60E-02 0 5839 0 2 195 17 2 43E+01 7 77E-01 7 96F. -Ol 2 55E-02 0 5965 0 2243 18 2 38E+01 7 62E-01 7 R 1 E - 0 1 2 50E-02 0 609 1 0 2291 19 2 34E+01 7 47E-01 7 66F-01 2 4 5E-02 0 62 17 0 2339 20 2 29E+01 7 31E-01 7 5 IF. Ol 1 40E-02 0 6343 0 2386 2 1 2 24E+01 7 15E-01 7 35E-01 2 34E 02 0 6469 0 2434 22 2 19E+01 6 98F-01 7 19E-01 2 29E-02 0 6595 0 2482 23 2 14E+01 6 82E-01 7 02E-01 2 24E-02 0 672 1 0 2530 24 2 09E+01 6 65E-01 6 B6E-01 2 18E-02 0 6848 0 2578 25 2 04E+01 6 47E-01 6 69E-01 2 12E-02 0 6974 o 2626 26 1 99E+01 6 30E-01 6 51E-01 2 07E-02 0 7 100 0 2674 27 1 93E+01 6 12E01 6 3 IE-01 2 OIE-02 0 7226 0 2722 28 1 88E*01 5 94E01 G 16E-01 1 95E-02 0 7352 0 2770 29 1 82E+01 5 75E-01 5 9RE-01 1 R9E-02 0 7478 0 2818 30 1 77E+01 5 57E-01 5 79E-01 1 R3E-02 0 7604 0 2866 3 1 1 71E+01 5 38E-01 5 6 IE-01 1 76E-02 0 7 7 30 0 2914 32 1 65E+01 5 18E-01 5 4 lE-OI 1 70E-02 0 7856 0 2961 33 1 59E+01 4 98E-01 5 22E-01 1 63E-02 0 7982 0 3009 34 1 53E+01 4 77F-01 5 01E-01 1 57E-02 0 8 109 0 3057 35 1 46E+01 4 55E-01 4 80E-01 1 49E-02 0 8235 0 3105 36 1 39E+01 4 33E-01 4 57E-01 1 4?E-0'2 0 8361 0 3153 37 1 32E+01 4 3 09E-01 4 34E-01 1 34E-02 0 8487 0 3201 38 1 25E+01 85E-01 4 10E-01 1 26E-02 0 8613 0 3249 39 1 17E+01 3 59F-01 3 85E-Ol 1 18E-02 0 8739 0 3297 40 1 09E+01 3 32F-U1 3 59E-01 1 09E-02 0 8865 0 3345 4 f 1 OIE'01 3 04 E-0 1 3 3 IE-01 9 9RE-03 0 899 1 0 3393 42 9 20E+0O 2 75E-01 3 02E-O1 9 02E-03 0 9117 0 344 1 4 3 8 28E+00 2 44F-0 1 2 72E-01 8 OOE-03 0 924 3 0 3489 44 7 30E-»00 2 11E-01 2 40E-Ol G 94E-03 0 9369 0 3536 45 6 27E+00 1 77E-01 2 06E-01 5 8 IE-03 0 9496 0 3584 APPENDIX D.2 198 DATE OF EVENT: ORIGINAL RAINFALL DATA FROM SECONDS PER TIMINT = 120. 21 JULY 72 2.77 SQUARE MILE MAHANTANGO SUB-WATERSHED TIME INCHES 1750 1755 18 0 3 . 20 3.40 3.90 SOIL/C 145 THETA2 O. 26300 THFTAE 0. 37600 THETAI O. 149 1? DECSA I O . 56 700 F RUDEG O.7 5000 FSIFT/HR) FMFT/HR) FKFT/HR) 0.06940 0.14720 2.O90OO 145 O. 26300 0. 37GOO O. 14912 0. 56700 O. 7 5000 O . 06940 O. 14720 2 . 33000 TOP LAYER SOIL DEPTH=0.750 SOIL* TIMINT VOKFT) SECOND LAYER P(FT) SOIL D E P T H = PEX(FT ) 1 . 500 PINF(FT) WFINC(FT) 145 1 0. 06967 0. 00667 -0. 06300 0. 00667 0. 02938 145 2 0. 00939 0. 00667 -o. 002 7 2 O. O06G7 0. 05877 145 3 0. 00856 0. 01 167 0. 003 10 0. 00856 0. 09652 145 4 0. 00807 0. 01667 0. 00859 0. 00807 0. 132 1 1 145 5 0. 007 7 4 O 01667 0 00893 0. 007 7 4 0. 16622 145 6 0. 0074 9 0 0 -o. 007 4 9 0. 0 0. 16622 145 7 0. 007 30 0 0 -o. 007 30 0. 0 0. 16622 145 8 0. 007 15 0 0 -0. 0O7 15 0. 0 0. 16622 145 9 o. 00702 0 0 -0. 00702 O. 0 0. 16G22 145 10 0. 00691 0 0 -o. 0069 1 0. 0 0. 16622 145 1 1 0. 00682 0 0 -0. 0068 2 0. 0 0. 16622 145 12 0. 00674 0 0 -0. 0067 4 0. 0 0. 16622 145 13 0. 00666 0 0 -0. 00666 0. 0 0. 16622 145 14 0. 00660 O 0 -o. 0O66O O. O 0 16622 145 15 0. 00654 0 0 -o. 006 54 0. .0 0. 16622 145 16 0. .00649 0 0 -o. 0064 9 0. .0 0. 16622 145 17 0. 0064 4 0 0 -0. 0064 4 0. o 0. 16622 145 18 0 00640 0 0 -0 006 4 O 0. .0 0. 16622 145 19 0 00636 0 0 -0. 006 36 0 .0 0 16622 145 20 0. .00632 0 .0 -0. .00632 0. .0 0 16622 145 2 1 o .00629 0 .0 -o 00629 o o 0. 16622 145 22 0 .00626 0 .0 -0 00626 0 o 0 16622 145 23 0 .00623 0 .0 -o .00623 0 .0 0 16622 145 24 0 .00620 0 .0 -0 00620 0 .0 0 16622 145 25 0 .00617 0 .0 -o .00617 o .0 o 16622 145 26 0 .00615 0 .0 -0 .00615 0 .0 0 . 16622 145 27 0 .006 13 0 .0 -0 .00613 0 .0 0 16622 145 28 0 .00610 0 .0 -o .006 10 0 .0 0 . 16622 145 29 0 .00608 0 .0 -o .00608 0 .0 0 .16622 145 30 0 .00606 o .0 -0 .00606 0 .0 0 16622 145 31 0 .00604 0 .0 -0 .00604 0 .0 0 . 16622 145 32 0 .00603 0 .0 -0 .00603 0 .0 0 . 16622 145 33 0 .00601 0 .0 -0 .00601 0 .0 0 .16622 145 34 0 .00599 0 .0 -0 .00599 0 .0 0 . 16622 145 35 0 .00598 0 .0 -0 .00598 0 0 0 . 16622 VO VO <rir--CDTioOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 0*-cNCNnronc7Con(^nroronnnnnnron ooooooooooooooooooooooooooooooooooo t» CO O f- CN C - ec cn >j CP in TT TJ rr O O O O O ooooooooooooooooooooooooooooooooooo ooooooooooooooooooooooooooooooooooo CNOO — "-OOCOOOOOOOCOOOOCOCOOOOOOOOOOOO ooooooooocooooooooooooooooooooooooo ooooooocoooooooooooooooooooooooocoo r~ r-- r-- r--CO CD cp CD CD ID CD — CD CD O O — — — ooooooooooooooooooooooooooooooooooo ooooooooooooooooooooooooooooooooooo ^co0^c^O-Tco^DLnMcJl^BTlf^oto^JlnnnOC!co^lXllnTtnr^Ol-0 *---coirTTrocN*-ooojCOCT)a>cocooDcor^r^r~r^r^r^cDcco rNin^TTTTfTfTT^Tinnnnnnnnoonnnnonn co co co n n n co co COOOOOOCOOOOQOOOOOOOOOOOOOOOOOOOOOOO ooooooooooooooooooooooooooooooooooo ooooooooooooooooooooooooooooooooooo ^c\nT^Lnll^^slO)0'"«nTtln^l^^oO)0'wnTlLnlJ5^coalO'•cNnTJln T-^T-T-T-T-T-T-T-^CNCNCSCNCNCNCNCNCNCNnnnCOCOCO CDlj?CD<j3CDCD(jOCDCDlj?(jPCDCDCDlDCjOircDCO CDCj?CPCDCDCDCDCDCDCPCC(j7cpcjOCDCDCDCj?CDCDtj7a^ -^Msnnnnnnnnnnnnnnnnnnnnnr, nnnnnnnnn CNO'T^aOOOCDCCCCCOCD(2tXCCK'XCCCOCCCOCOCDeDCDCCCQCOCO(DCO[CCCCCOa^ — cc. — rTr^r~r^r^r^r^r~r^t^r^r~>r^r^r~r^r^r^r^r^r^r~r~r~r^r-r^i^r~r^r^ ° ° ~~ " " ' " " " ' . " *~ "~ "". ~ ooocooooooooooooooooooooooooooocooo I- Cl CN — 0) is 01 T — cc C- IT. in IT. TT ccoooooooooooooooooooooooooooocoooo oocoocoooooooooocooooooocoocooooooo ci ci IT r-•rr CN CN TT r-_ CO CN CC' — cc in CN O co CO TT CN — 01 cc Ll T CN — C 01 CO n CN in r- IT IT. "J n n CN CN — — - o c O O cn 01' 01 01- Cl cc CO CO X X X cc X r~ r~ b c  — TT TT TT T TT -7 T? TT TT T? TT •» T CO n r> n o r> r> n n ci r, ci Cl n n n «- G o o c C O c o o o o o o c o  O O O O O O O C c O D r-, o O C O O O b o O O o o o O o o o o c c o o o O C O O O O C O O O o o ocoooooooooooocoooooooooooooooocoo r» r- r» r» r-cp cp co CD CD CD CD — CD CD Sooooooooooooooooooooooooooooooooco 00000000000000000000000000000000000 0 r> CN O TT CN CN TT r- CO CN CO TT — eo in CN 0 on ID TT CN — 0) co CD in TT CN O 0) 0 0 0) TT — CO t- CD in TT C1 D CN CN - O 0 O 0 0) 01 CD 01 0) CO CO co CO CO X X X r~ r~ TT in in in TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT TT ci CO r> n ci r> r> n O n rs r> r> TT O OOO 0 O O 0 0 0 O O O 000 0 0 0 O O O O O O O O O O O O O O Q O O OOO 0 O O 0 0 0 O O O 000 0 0 0 O O O O O O O O O O O O O O O 00000000000000000000000000000000000 "-cNr>TTinij5r~xa>O"-c>ir5Tjinij5t^x0jO'-cNC0TT)ni^ TTTTTTTTTTTTTTTTTfTT'TTTTTfTITTTTTfTTTl'TTTTTfTTTTTTTTTTTTTTTTTTTTTTTTT inuiininininininininuiininininininiAininu^ SOIL* THETA2 THETAE , THETAI DEGSAT FROOEG FSIFT/HR) FK(F T/HR) F1 ( F T/HR) 7 1 0.29400 0.34200 0.20374 O.G9300 0.75000 0.03250 0.05900 O.97700 7 1 0. 29400 O. 34 200 0. 20374 0.69300 O. 75000 O.02370 0.03 130 O. 74200 TOP LAYER SOIL 0EPTH=0.75O SOIL* TIMINT VOKFT) SECOND LAYER SOIL OFPTH= P(FT) PEX(F r ) 1 . 670 PINFIFT) WFINC(FT) 7 1 1 0 .03257 0 .00667 -0 .02590 0 .00667 0. 04822 7 1 2 0 .00406 0 .00667 0 .00260 o .00406 0. 077G2 7 1 3 0 .00368 0 .01167 0 .007 99 O .00368 0. 10423 71 4 0 .00345 0 .01667 0 .01322 0 .00315 o. 1 29 18 7 1 5 0 .00329 0 .01667 0 .01337 O .00329 o. 1 5 30 1 7 1 6 0 .00318 0 .0 -o .00318 0 0 0. 15301 71 7 0 .00309 0 0 -0 .OO309 0 0 0 15301 71 8 0 .00302 0 .0 -0 .00302 0 .0 o. 15301 71 9 0 .00296 0 .0 -o .002 96 O O 0. 15301 7 1 10 0 .00290 0 0 -0 .00290 o O 0 15301 71 1 1 0 .00286 0 .0 -o .002A6 0 .0 0. 15301 7 1 12 0 .00282 0 .0 -o .002n2 o .0 0. 1530 1 71 13 0 .00279 0 .0 -0 .00279 0. 0 0. 15301 71 14 0 .00276 0 .0 -0 .00276 o 0 0. 15301 7 1 15 0 .00273 0 0 -0 0027 3 0. .0 0. 15301 71 16 0 .00271 0 .0 -0 .002 71 0 0 0. 15301 7 1 17 0 .00269 0 .0 -o .002G9 0 O o. 15301 7 1 18 0 .00267 O 0 -0. 00267 0 0 0 15301 7 1 19 0 .00265 0 0 -0. .00265 0. 0 o. 15301 7 1 20 0 00263 0 0 -o 00263 0 0 o. 15301 7 1 2 1 0 0026 1 0 0 -0 .007G1 o. 0 0. 15301 7 1 22 0 00260 0 0 -0. .00260 0 0 0. 15301 7 1 23 0 .00259 0 0 -0 00259 0. 0 o. 15301 7 1 24 0 00257 0. 0 -0. 002T.7 o. 0 o. 15301 7 1 25 0. 00256 0. 0 -o. 00256 0 . 0 0. 15301 7 1 26 0. 00255 0 0 •0 00255 0 . 0 0. 1530 1 7 1 27 0 00254 0 0 -o 00254 0. 0 0. 15301 7 1 28 0. 00253 0. 0 -o. 00253 0. 0 0 15301 7 1 29 0. 00252 0. 0 -0. 00252 0. 0 0 15301 7 1 30 ' 0. 00251 0 0 -0. 0025 1 0. 0 0 15301 71 31 0. O0250 0. 0 -0 00250 0 0 0. 15301 7 1 32 0. 00249 0. 0 -0 . 00249 o. 0 0. 15301 7 1 33 0. 00248 o. 0 -o. O02JH o. 0 0 15301 7 1 34 0 00248 0. o - 0 . .00248 0. 0 0. 1530 1 7 1 35 0 0024 7 0 0 -0 . 002 4 7 0. 0 0 1530 1 O r-O SOIL* THETA2 THETAE THE TAI DFGSAI FRODF.C, FS(FT/HR) FK(FT/HR) F1(FT/HR) 69 0.33700 O.3150O 0.29016 0.86100 0.75000 0.01790 0.05900 0.53900 69 O. 33700 0. 31500 0. 29016 0. 86 100 O. 7 5000 0.01280 0.03130 0. 4 1400 TOP LAYER SOIL DEPTH=0.750 SOIL* TIMINT VOKFT) SECOND LAYER SOIL DEPTH-P(FT) PEX(FT) 2 . OOO PINF(F T ) WFINC(FT ) 69 1 0 .01797 0 .00667 -0. 01 130 0 . 00667 0. 26835 69 2 0 .00312 0 .00667 0 00354 0 003 12 0. 39402 69 3 0 .00291 0 .01167 0 00876 0 00291 0. 51116 69 4 0 .00278 0 .01667 0 01388 0 .00278 0. 6232 1 69 5 0 .00270 O .01667 0 .01397 O 00270 0. 73 179 69 6 0 .00263 0 .0 -0. 00263 0 .0 0. 73179 69 7 0 .00258 0 .0 -o 00258 0 .0 0. 73 179 69 8 0 .00254 O .0 o 00254 0 0 0. 73 179 69 9 0 .00251 O .0 -0. 0025 1 0 O 0. 73 179 69 10 0 .00248 O .0 -0. 00248 O 0 0. 73 179 69 1 1 0 .00246 0 .0 -o 0024 6 o .0 0. 73 179 69 12 0 .00244 O .0 -o .00244 0 0 0. 73 179 69 13 0 .00242 O .0 -0 00242 0 .0 0. 73 179 69 14 0 .00240 O O -0. .00240 0 0 0. 73 179 69 15 - 0 .00239 0 0 -0. 00239 0 0 0. 73 179 69 16 0 .00238 O O -0 00238 0 0 o. 73 179 69 17 0 .00236 0 .0 -0. 002 36 0 0 0. 73 179 69 18 0 .002 35 0 0 -0 00235 0. 0 0. 73 179 69 19 0 00234 0 .0 -o. 00234 0 0 0. 73 179 69 20 0 .00233 0 0 -o 00233 0 0 0. 73179 69 21 0 .002 32 0 0 -o. 00232 0 .0 0. 73 179 69 22 0 .00232 0 O -o. 00232 0 0 0. 73 179 69 23 0 .00231 0 .0 -0. 002 31 0 0 0. 73 179 69 24 0. .00230 0 0 -0 00230 0 0 0. 73 179 69 25 0 .00229 0 0 -0 00229 0 0 0. 73 179 69 26 0 .00229 0 0 -0 00229 0 0 0. 73 179 69 27 0 .00228 0 .0 -0. 00228 0 0 0. 73 179 69 28 0 .00228 o 0 -0. 00228 0 .0 0. 73 179 69 29 0 O0227 o .0 -0 00227 0 .0 0. 73179 69 30 0 .00226 o .0 -o 00226 0 0 0. 73 179 69 31 0 .00226 0 .0 -0 00226 0 0 0. 73179 69 32 0 .00226 0 .0 -0. 00226 0 0 0. 73 179 69 33 0 .002 25 o .0 -0. 00225 0 0 0. 73179 69 34 0 O02 25 o .0 -0 00225 0 0 0. 73179 69 35 0 .00224 0 .0 -0. 00224 0 0 0. 73179 NJ O LO SOIL* THETA2 THETAE THE TAI DEGSAT FRODEG FS(FT/HR) FMFT/HR) FKFT/HR) 57 0.28700 0.30400 0.21812 0.76000 0.75000 0.02570 O 05890 0.77100 57 0.28700 0.30400 0.21812 0 76000 0.75000 0.01870 0.03130 0.59200 TOP LAYER SOIL DEPTH=0.750 SECOND LAYER SOIL DEPTH= 2.500 SOIL* TIMINT V01(FT) P(FT) PEX(FT) PINF(FT) WFINC(FT) 57 1 0 .02570 0 .00667 -0 .01903 0 .00667 0 .07763 57 2 0 .00362 0 .00667 0 . 00304 0 00362 0 . 1 138 1 57 3 0 .00332 0 .01167 0 .008 35 0 .00332 o , 15844 57 4 0 .00314 0 .01667 o .0135 3 o .003 14 0 19496 57 5 0 .00301 0 .01667 0 013G5 0 .00301 0 2 3004 57 6 0 .00292 0 . 6 -0 .00292 0 .0 o 2 3004 57 7 0 .00285 0 .0 -o .00285 0 .0 0 2 3004 57 8 0 .00279 0 0. -o .00279 0 . 0 0 2 3004 57 9 0 .00275 0 .0 -0. 002 75 o .0 0 23004 57 10 0 .00271 0 .0 -0. .002 7 1 o 0 o 23004 57 1 1 0 .00267 0 .0 -0 .00267 0 o 0 2 3004 57 12 0 .00264 0 .0 -0. 00264 0 0 0. 2 3004 57 13 0 0026 1 0 .0 -0. 0026 1 0 0 0. 2 3004 57 14 0 00259 0 O -0. 00259 0 .0 0. 2 3004 57 15 0 00257 0 O -o 00257 0 0 0. 23004 57 16 0. .00255 0 .0 -o 00255 0 0 0. 23004 57 17 O 00253 0 .0 -0. 00253 0 o 0 23004 57 18 O. .00252 0 0 -0. 00252 0 0 0. 23004 57 19 0. 00250 0 0 -0. 00250 0 0 0 23004 57 20 0. 00249 0 0 -o 002 4 9 o 0 o 2 3004 57 21 0 00248 0 0 -0 0024 8 0. 0 0. 23004 57 22 O 00246 O 0 -o 0024 6 0 0 o 23004 57 23 0. 00245 0 0 -0 0024 5 0 0 0. 23004 57 24 0. 00244 0 0 -o. 00244 0 0 0. 23004 57 25 0 00243 0 0 -0. 00243 0. 0 0. 23004 57 26 0. 00242 0 0 -0. 00242 0. 0 0. 2 3004 57 27 0. 0024 1 0. 0 -o. 002 4 1 0 0 0. 23004 57 28 0. 0024 1 0 0 -0 0024 1 0 0 0. 23004 57 29 0. 00240 0. 0 -0. 00240 0. 0 0. 2 3004 57 30 0. 00239 0 0 -0. 00239 0. 0 0. 2 3004 57 3 1 0 00238 0 0 -o 00238 0 0 0. 2 3004 57 32 0. 00238 o 0 -o. 00238 0 0 0. 2 3004 57 33 0 00237 0 0 -o. 00237 0 0 0. 2 3004 57 34 0 00237 0 0 -0. 00237 0 0 0. 23004 57 35 0 00236 0 0 -0. 00236 0 0 0. 2 3004 f ho o CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 1 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0 0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.0550 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 220.0 1100.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 140.0 1300.0 REACH LENGTH= 1750.OO STREAM WIDTH= 10.00 MANNINGS N= 0.350000 DE LTAX = 20.00 VOLUME OF PRECIPITATION EXCESS= 2.3111543655 CU FT TOTAL RUNOFF VOLUME FROM REACH^ 4044.52001953 13 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT SIDE 0 .0000185 0 .0066667 0 .0 0 .0 0 .0 0 .0 O .OOOO185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0 .0003071 0 .0116667 0 .0000394 1 100 .OOOOOOO 0 .0002353 1300 .OOOOOOO 0 .0019133 0 .0166667 0 .00057 20 1 100 .OOOOOOO o .0012949 1300 .OOOOOOO o .0046056 0 .0166667 o .0015763 1 100 .OOOOOOO o 0029829 1300 .OOOOOOO 0 .0030786 0 .0 0 .00059 12 1 100 .OOOOOOO o 0024874 1300 .OOOOOOO 0 .0020887 0 .0 0 .00004 7 7 1 100 OOOOOOO o .0020410 ' 1300 .OOOOOOO 0 .OO16400 0. .0 0 .0 1080. OOOOOOO o .0016400 1280 .OOOOOOO 0 .0012818 0. .0 0 .0 1060. OOOOOOO 0 0012818 1260. .OOOOOOO 0 .0009651 0. .0 0 .0 1040. .OOOOOOO 0. 0009651 1240 .OOOOOOO 0 .0007058 0. .0 0 .0 1020. OOOOOOO 0 0007058 1220. . OOOOOOO 0 .0005586 0. 0 0 .0 1000. OOOOOOO 0 0005586 1200. . OOOOOOO 0 .0005656 0. 0 0 .0 980. OOOOOOO 0 0005656 1 180. OOOOOOO 0 .0005399 0. O 0 .0 940. OOOOOOO 0. 0005399 1 140. .OOOOOOO 0 .0004394 o. 0 0 .0 920. OOOOOOO 0. 0004394 1 120. . OOOOOOO 0 .00O3021 0. 0 0 .0 900. OOOOOOO 0. 0003021 1 100. .OOOOOOO 0 .0001677 0. 0 0 .0 880. OOOOOOO 0. 0001677 1080. .OOOOOOO 0 .0000611 0. 0 0. .0 840. OOOOOOO 0. 000061 1 1040. . OOOOOOO 0 .0000024 0. 0 0. .0 0. 0 0 0000024 80. .OOOOOOO 0. 0 0. 0 0. 0 0. 0 0. 0 0. .0 N3 O Ln INFLOW HYDROGRAPHS CALCULATION OF LATERAL SECTION 2 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.2000 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.0550 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 100.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 140 0 REACH LENGTH= 1290.00 STREAM WIDTH= 10.00 VOLUME OF PRECIPITATION EXCESS^ 4.6148881912 TOTAL RUNOFF VOLUME FROM REACH= 5953.2031250000 0.0125 0.0125 O.3750 0.1150 180.0 260.0 MANNINGS N CU FT 0.0125 0.0125 0.0550 0.0550 940.0 1360.0 0.350000 DELTAX= 20. OO OL CFS/FT 0.0000185 0.0000185 .0008053 .004 1353 .0093574 .0079914 .0067818 .0056747 0.0013448 0.0009992 0.0006796 O.0004050 0.0001926 0.0000534 O.O O. O. O. O. O. O. PRECIP PRECIP DEPTH 0.0066667 0066667 0116667 0166667 0166667 O O 0 0 O O 0 0 0 O EXCESS VALUES FOR LEFT SIDE OL 0.0 0.0 0.0005376 0.0027940 0.0063281 0.0055040 0.0047408 0.0040348 0.0000630 0.0000341 0.0000062 0.0 0.0 0.0 0.0 EACH DELT WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT SIDE 0 .0 0 .0 0 .0 0 .0 0 .0 0 .0 940 .0000000 0 .0002353 1360 .OOOOOOO 940 .0000000 0 .0012949 1360 .OOOOOOO 940 0000000 0 .0029829 1360 .OOOOOOO 940 .ooooooo 0 .0024874 1360 .OOOOOOO 940. 0000000 0 .0020410 1360. .OOOOOOO 920. ooooooo 0. 0016400 1340. .OOOOOOO 900. ooooooo o. 0012818 1320. OOOOOOO 880. ooooooo 0. 0009651 1300. OOOOOOO 840. ooooooo 0. 0006734 1260. OOOOOOO 0. 0 0. 0004050 80. OOOOOOO 0. 0 0. 0001926 60. OOOOOOO 0. 0 0. 0000534 20. OOOOOOO 0. 0 0. 0 0. 0 NJ O CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 3 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.3750 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.0550 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 140.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 140.0 REACH LENGTH= 1130.00 STREAM WIDTH= 10.00 VOLUME OF PRECIPITATION EXCESS^ TOTAL RUNOFF VOLUME FROM REACH= 2 .8512601852 322 1 .9238281250 0.0125 0.0125 0.1150 0.1150 980.0 260.0 MANNINGS CU FT 0.0125 0.0550 1320. N = 0.350000 DELTAX= 20.00 OL CFS/FT 0.0000185 .0000185 .0003855 .0025444 .0062 1 13 0.0039540 0.0025722 0.0021158 0.0017742 .OO14606 .0011294 .0007709 .0004668 0.0002397 0.0000888 O.0000098 0.0 0. 0. O. 0. O. O. O. O. PRECIP EXCESS VALUES FOR EACH DELT SIDE OL WIDTH OF CONTRIB AREA O.O 0.0 980.OOOOOOO 980.0000000 980.OOOOOOO PRECIP DEPTH 0.0066667 0.0066667 0.0116667 0.0166667 0.0166667 0 0 0 0 0 0 O 0 O 0 0 0 LEFT 0.0 O 0 O O 0 0 0000711 0010329 0028465 0010676 0000861 O 0 O 0 O 0 O O 0 0 980.OOOOOOO 960.OOOOOOO 940.0000000 920.0000000 880.0000000 860.OOOOOOO .0 .0 .0 .0 0. O. O. 0. O . O 0.0 RIGHT 0.0 0 O O O 0 O 0 O 0 0 O 0 o o o 0 SIDE OL O 0002819 0014652 0033185 0028863 002486 1 0021158 0017742 0014606 OOI1294 0007709 0004668 0002397 0000888 00O0098 O WIDTH OF RIGHT SIDE 0.0 O.O 1320.0000000 1320.0000000 1320.0000000 1320.0000000 1320.0000000 1300.OOOOOOO 1280.0000000 1260.0000000 1220.0000000 100.OOOOOOO 80.OOOOOOO 60.OOOOOOO 20.OOOOOOO 0.0 0.0 o CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 4 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM REACH LENGTH= 1170.00 STREAM WIDTH* VOLUME OF PRECIPITATION EXCESS^ TOTAL RUNOFF VOLUME FROM REACH= 0.0125 0.0125 0.0550 0.0550 100.0 100.0 10.00 4.2111063004 4926.9921875000 0.0125 0.0125 O.3750 0.3750 220.0 180.0 MANNINGS CU FT 0.0125 0.0125 0.0550 0.0550 900.0 740.0 N = O.350000 DELTAX= 20.00 PRECIP EXCESS VALUES FOR EACH DELT . CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIFJ AREA RIGHT SIDE OL WIDTH OF RIGI 0 .0000185 0 .0066667 0 .0 0 .0 0 . 0 o .0 0 .0000185 0 .0066667 0 .0 0 .0 0 .0 O .0 O .0005962 0 .0116667 0 .0002819 900 .OOOOOOO 0 .00028 19 740 .OOOOOOO 0 .0029767 0 .0166667 0 .0014652 900 .OOOOOOO 0 .0014652 740 .ooooooo 0 .0066833 0 .0166667 0 .0033185 900 .OOOOOOO 0 .0033185 740 .ooooooo 0 .0057727 O 0 0 .0028863 900 .OOOOOOO 0 .0028863 740 .ooooooo 0 .0049722 0 .0 0. 0024861 900 .OOOOOOO 0 .0024861 740 .ooooooo 0 .0042317 0. .0 0 002 1158 880 ooooooo 0 0021158 720 .ooooooo 0 .0033824 0. 0 0 0016912 860. ooooooo 0 0016912 700 .ooooooo 0. .0025036 0. 0 0. 0012518 840. ooooooo. 0. 0012518 680. ooooooo 0. .0018534 0. 0 0. 0009267 800. ooooooo 0. 0009267 640. ooooooo 0. .0011660 0. 0 0. 0005830 60. ooooooo 0. 0005830 60. ooooooo 0. 0006190 0. 0 0. 0003092 40. ooooooo 0. 0003099 40. ooooooo 0. 0002511 0. 0 0. 000125 1 20. ooooooo 0. 0001260 20. ooooooo 0. 0000473 0. 0 0. 00002 34 0. 0 0. 0000239 0. 0 0. O 0. 0 0. 0 0. 0 0. 0 0. o o 00 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 5 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.0550 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 1220.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 300.0 520.0 REACH LENGTH= 2130.00 STREAM WIDTH= 10.00 MANNINGS N= 0.35OO0O DELTAX= 20.00 VOLUME OF PRECIPITATION EXCESS^ 3.4995746613 CU FT TOTAL RUNOFF VOLUME FROM REACH= 7454.0937500000 OL CFS/FT 0.0000185 0.0000185 O.0005405 0.0029334 O.0067417 0.0053478 0.0041594' 0.0031252 0.0022451 0.0015246 0.0009793 0.0006569 0.0004433 0.0002662 O.OOO1282 0.0000345 0.0 PRECIP PRECIP DEPTH 0.0066667 0.0066667 0.0116667 O.0166667 0.0166667 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 EXCESS VALUES FOR LEFT SIDE OL 0.0 0.0 0.00025 13 0.001513 1 0.0035563 0.0026755 0.001913 1 0.0012670 0.0007 391 0.0003360 0.00007 37 0.0 0.0 0.0 O.O 0.0 0.0 EACH DELT WIDTH OF O 0 CONTRIB AREA O 0 12 20.0000000 12 20.0000000 ' 12 20.OOOOOOO 1220.0000000 1200.0000000 1180.OOOOOOO 1 160.OOOOOOO 1120.OOOOOOO 1 10O.OOOOOOO 0.0 0.0 0.0 0.0 0.0 0.0 RIGHT SIDE OL 0.0 O.O 0.0002568 0.0013740 0.0031391 0.0026723 0.0022463 0.0018582 0.0015060 0.0011887 0.0009056 0.0006569 0.0004433 O.0002662 0.0001282 0.000034 5 0.0 WIDTH OF RIGHT SIDE 0.0 0.0 520.0000000 520.0000000 520.0000000 520.0000000 500.OOOOOOO 480.0000000 440.OOOOOOO 4 20.0000000 300.OOOOOOO 300.OOOOOOO 280.0000000 260.0000000 220.0000000 180.OOOOOOO 0.0 NJ O VO CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 6 "LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 100.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 100.0 REACH LENGTH= 1340.00 STREAM WIDTH* 10.00 VOLUME OF PRECIPITATION EXCESS* 5.2303237915 TOTAL RUNOFF VOLUME FROM REACH* 7008.6328 125000 0.0125 0.012' 0.3750 0.1150 220.0 1260.0 MANNINGS CU FT 0.0125 560.0 0.0125 0.1150 0.1150 860.0 O.350000 DELTAX* • 20.00 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT 0 ,0000185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0. ,0000185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0 ,0008477 0 .0116667 0 .0004077 860 .OOOOOOO 0 .0004077 1260 .OOOOOOO 0. .0042836 0. .0166667 0 .0021187 860 .OOOOOOO 0 0021187 1260 .OOOOOOO 0 .0096434 O .0166667 0 .0047985 860 .OOOOOOO 0 0047985 1260 .OOOOOOO 0. .0083473 0 .0 0 .0041736 860 .OOOOOOO 0 0041736 1260. .OOOOOOO 0. .007 1898 0 .0 0. .0035949 840 .ooooooo 0 0035949 1240. .OOOOOOO 0. .0061190 O .0 0 .0030595 820 .ooooooo 0 0030595 1220. .OOOOOOO 0. .0035175 0 .0 0 .0015988 800 .ooooooo 0 .0019 187 1 180 .OOOOOOO 0 .0017627 0 .0 0 .0008016 760 .ooooooo 0. 0009610 1 160. OOOOOOO O. .0011186 0. .0 0. .0004886 740. .ooooooo 0. 0006300 100. .OOOOOOO 0 .0005359 0. O 0. .0001920 40. .ooooooo 0 0003439 80. .OOOOOOO 0. .0001665 0. .0 0 0000322 0. 0 0 0001343 60. OOOOOOO 0. .0000170 0 .0 0. 0 0. .0 0. 0000170 20. OOOOOOO 0. .0 0 .0 0. 0 0. .0 0. 0 0 0 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 7 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM REACH LENGTH= 1800.00 STREAM WIDTHS VOLUME OF PRECIPITATION EXCESS= TOTAL RUNOFF VOLUME FROM REACH= 0.0125 0.0125 0.0125 0.2000 0. 1 150 O. 1 150 180.0 340.0 4 20.0 10.00 MANNINGS 3.9879989624 CU FT 7178.3945312500 N = O. 350000 DELTAX= 20.00 OL CFS/FT PRECIP PRECIP DEPTH EXCESS VALUES FOR LEFT SIDE OL EACH DELT WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT SIDE 0 OOOO185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0. .0000185 0 .0066667 0 .0 0 .0 0 .0 0 .O 0. .0005615 0 .0116667 0 .0004897 340 .OOOOOOO 0 .O000394 420 .OOOOOOO 0. .0032384 0 .0166667 0 .0026201 340 .OOOOOOO 0 .0005720 420 .OOOOOOO 0. .0076086 0 .0166667 0 .0059860 340 OOOOOOO 0 .0015763 420 .OOOOOOO 0. .0056870 0 .0 0 .0050958 340 .OOOOOOO 0 .0005912 400 .OOOOOOO 0. .0043313 0 .0 0 .0042836 320 .OOOOOOO 0 .00004 7 7 380 .OOOOOOO 0. .0035435 0 .0 0 0035435 300 .OOOOOOO 0 O 0 .0 0. .0028719 0 .0 0. 0028719 260 .OOOOOOO 0 .0 0 .0 0. .0022667 0. .0 0. 0022667 240. OOOOOOO 0 0 0 .0 0 .0017269 0. .0 0. .0017269 180. OOOOOOO 0 .0 0 .0 o. .0012527 0. .0 0. 0012527 120. .OOOOOOO 0 0 0. o 0. .0001078 0. .0 0. 0001078 0. 0 0 0 0 .0 0. .0 0. 0 0. 0 0. 0 o. 0 0. .0 CALCULATION OF LATERAL INFLOW HYOROGRAPHS SECTION 8 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.3750 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 340.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 180.O REACH LENGTH* 960•OO STREAM WIDTH* 10.00 VOLUME OF PRECIPITATION EXCESS* TOTAL RUNOFF VOLUME FROM REACH* 3 . 37 10384369 3236.1967773438 0.0125 O.2000 1 120.0 MANNINGS CU FT O.350000 DELTAX* 20.00 PRECIP EXCESS VALUES FOR EACH DELT . CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT 0.0000185 0 .0066667 0 .0 0 .0 O.O 0 .0 0.OOOO185 0 .0066667 0 .0 O .0 0.0 0 .0 0.0006130 0 .0116667 0 .0003737 1 120 .ooooooo 0.0002069 180 .OOOOOOO 0.0038079 0 .0166667 0 .0024210 1 120 .ooooooo 0.0013407 . 180 .OOOOOOO 0.0090562 0 0166667 0 .0057987 1120 .ooooooo 0.0032112 180. .OOOOOOO 0.0064231 0 .0 0 004 1339 1 100. OOOOOOO 0.0022892 180, .OOOOOOO 0.0042516 0 .0 0 0027363 1060. OOOOOOO 0.0015153 160. .OOOOOOO 0.0024888 0 0 0 0016018 240. ooooooo 0.0008870 140. OOOOOOO 0.0011466 0. 0 0. 0007379 220. ooooooo 0.0004086 100. OOOOOOO 0.0002G78 0. 0 0. 0001723 200. ooooooo 0.0000954 80. OOOOOOO 0.0 0. 0 0. 0 0. 0 0.0 0. 0 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 9 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.2000 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 720.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 260.0 REACH LENGTH= 1090.00 STREAM WIDTH= 10.00 VOLUME OF PRECIPITATION EXCESS^ TOTAL RUNOFF VOLUME FROM REACH= 1.66129016RR 1810.0061523438 0.0125 0.0125 0. 1 150 0. 1 150 460.0 MANNINGS CU FT 960. N = 0.350000 DELTAX= 20.00 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE QL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT 0. .0000185 0 .0066667 0. .0 0 .0 0 .0 0 .0 0. .0000185 0. .0066667 0 .0 0 O 0 .0 0 .0 0 .0002913 0. .0116667 0 00020G9 720 .OOOOOOO 0 .0000519 960 .OOOOOOO 0. .00214 13 0 .0166667 0. .0013407 720 .OOOOOOO 0 000754 3 960 .OOOOOOO 0. ,0053363 0, .0166667 0 0032112 720 OOOOOOO 0 0020788 960 .OOOOOOO 0. .0030689 0. .0 0 0022892 720. OOOOOOO 0 0007797 960 .OOOOOOO 0. 0015782 0. .0 0. 0015153 700 OOOOOOO 0. 0000629 940 .OOOOOOO 0. .0008870 0. .0 0. 0008870 680. OOOOOOO 0 0 920. OOOOOOO 0. .0004086 0. 0 0. 0004086 640. OOOOOOO 0. 0 900 OOOOOOO 0. .0000954 0. 0 0. 0000954 620 OOOOOOO 0. 0 860. .OOOOOOO 0. 0 0. 0 0. 0 0. 0 0. 0 840. OOOOOOO CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 10 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.017.5 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.3750 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 380.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 300.0 1360.0 REACH LENGTH* 960.00 STREAM WIDTH* 10.00 MANNINGS N= 0.350OO0 DELTAX* 20.00 VOLUME OF PRECIPITATION EXCESS* 2.1109523773 CU FT TOTAL RUNOFF VOLUME FROM REACH* 2026.514 1601563 OL CFS/FT PRECIP DEPTH 0 .0000185 0 .0066667 0 .0000185 0 .0066667 0 .0003548 0 .0116667 0 .0025923 O .0166667 0 .0064491 0 .0166667 o .0037431 0 .0 0 .0019992 0 .0 o. .0012670 0 .0 0 .0007 391 0. 0 0. .0003360 0. 0 0. 0000737 0. 0 0. 0 0. 0 XCESS VALUES FOR EACH DELT LEFT SIDE QL WIDTH OF CONTRIB AREA 0 .0 0 .0 0 .0 0 .0 0 .0002513 380 .OOOOOOO 0 .001513 1 380 .OOOOOOO 0 .0035563 380 .OOOOOOO 0 .0026755 380 .OOOOOOO 0. 0019131 360 OOOOOOO 0. 0012670 340. ooooooo 0. 0007391 320. ooooooo 0. 0003360 280. ooooooo 0. 00007 37 260. ooooooo o. 0 0. 0 RIGHT SIDE OL WIDTH OF RIGHT SIDE 0 .0 0 .0 0 .0 0 0 0 .0000711 1360 .ooooooo 0 .0010329 1360 .ooooooo 0 .0028465 1360 .ooooooo o .0010676 1360 .ooooooo 0. 000086 1 1340. .ooooooo 0. 0 1320. ooooooo 0. 0 1300. ooooooo 0. 0 1260. ooooooo 0 . 0 1240. ooooooo 0. o 0. 0 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 11 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 120.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 1600.0 REACH LENGTH= 420.00 STREAM WIDTH= 10.00 MANNINGS N= 0.350000 DELTAX= 20.00 VOLUME OF PRECIPITATION EXCESS= 4.1731872559 CU FT TOTAL RUNOFF VOLUME FROM REACH= 1752.7 385253906 PRECIP EXCESS VALUES FOR FACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT SIDE o .0000185 0 .0066667 0 .0 0 .0 0 0 0 .0 O .OOO0185 0 .0066667 0 .0 0 .0 0 .0 0 .0 o .0006913 0 .0116667 0 .0004077 120 .OOOOOOO 0 .00025 13 1600 .OOOOOOO o, .0036781 0 .0166667 0 .0021187 120 .OOOOOOO 0 .OO15131 1600 .OOOOOOO o. .0084011 0 .0166667 0 .0047985 120 .OOOOOOO 0 0035563 1600 .OOOOOOO o. .0068491 0 .0 0 .00417 36 120 .OOOOOOO 0. 0026755 1600. .OOOOOOO 0. 0O55080 0 .0 0 0035949 120 .OOOOOOO 0. 0019131 1580. .OOOOOOO 0. .0043265 0 .0 0 .0030595 100. .OOOOOOO 0 0012670 1560. OOOOOOO o. .0033046 0. .0 0 0025656 80 OOOOOOO 0. 0007 391 1540. OOOOOOO 0. .0014180 0 .0 0 0010820 60. .OOOOOOO 0. 0003360 1500. OOOOOOO o. .0004582 o. .0 0. .0003845 40. OOOOOOO 0. 0000737 1480. OOOOOOO 0. .0001028 0. .0 0 0001028 20. OOOOOOO 0. 0 0. 0 0. OOOOO18 0. 0 0 OOOOO18 0. 0 0. 0 0. 0 o. o 0. .0 0. 0 0. 0 0. 0 0. .0 ho Ul CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 12 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.2000 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.2000 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 1O6O.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 680.0 REACH LENGTH= 1170.00 STREAM WIDTH= 10.00 VOLUME OF PRECIPITATION EXCESS= TOTAL RUNOFF VOLUME FROM REACH= 0.9140815735 1069.4753417969 0.0125 0. 1 150 1180.0 MANNINGS CU FT N^ O.350000 DELTAX= 20.OO OL CFS/FT 0.0000185 0.0000185 O.OOO1363 O.OO15550 0.0042039 O.OO15594 0.0001258 0.0 PRECIP EXCESS VALUES FOR EACH DELT PRECIP DEPTH 0.00666G7 0.0066667 0.0116667 0.0166667 0.0166667 O.O 0.0 O.O LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL 0.0 0.0 0000519 0007543 0020788 0007797 0000629 0 0.0 0.0 1060.0000000 1060.0000000 1060.0000000 1040.0000000 1000.OOOOOOO 0.0 o 0 0000519 000754 3 0020788 0007 797 0000629 O WIDTH OF RIGHT SIDE 0.0 0.0 1180.OOOOOOO 1180.OOOOOOO 1180.0000000 1180.OOOOOOO 1 180.0000000 1 160.0000000 i—1 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 13 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.2000 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.2000 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 640.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 680.0 REACH LENGTH* 2680.00 STREAM WIDTH* 10:00 VOLUME OF PRECIPITATION EXCESS* TOTAL RUNOFF VOLUME FROM REACH* 0.9140815735 2449.7385253906 0.0125 O. 1 150 1880.0 MANNINGS CU FT 0 . 3500OO DELTAX= 20.00 PRECIP EXCESS VALUES FOR EACH DFLT OL CFS/FT 0.0000185 0.0000185 0.0001363 0.0015550 0.0042039 0.0015594 0.0001258 0.0 PRECIP DEPTH 0.0066667 0.0066667 0.0116667 0.0166667 0.0166667 0.0 0.0 0.0 LEFT SIDE OL WIDTH OF CONTRIB AREA 0 0 0000519 000754 3 0020788 0007797 0000629 0 0.0 0.0 640 OOOOOOO 640.OOOOOOO 640.0000000 620.0000000 580.0000000 0.0 RIGHT SIDE OL 0.00005 19 0.0007543 .0020788 .0007797 .0000629 .0 O. O. 0. O. WIDTH OF RIGHT SIDE 0.0 0.0 1880.0000000 1880.0000000 1880.0000000 1880.0000000 1860.0000000 1840.0000000 N5 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 14 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.0550 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 0.0550 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 380.0 840.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 340.0 720.0 REACH LENGTH* 2380.00 STREAM WIDTH* 10.00 MANNINGS N= 0.350000 DELTAX* 20.00 VOLUME OF PRECIPITATION EXCESS* 2.7123842239 CU FT TOTAL RUNOFF VOLUME FROM REACH* G455.4726562500 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH ' . LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT 0 .OOOO185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0 .0000185 0 .0066667 0 .0 0 .0 0 .0 0 .0 0 .0003537 0 .0116667 0 .0002819 840 .OOOOOOO o .0000394 720 .OOOOOOO 0 .0020835 0 0166667 0 .0014652 840 .OOOOOOO 0 .0005720 720 .OOOOOOO 0 .00494 1 1 0 .0166667 0 .0033185 840 .OOOOOOO 0 .0015763 720 .OOOOOOO 0 .0034776 0. .0 0. 0028863 840 .OOOOOOO o .0005912 720 .OOOOOOO 0 .0025338 0 0 0. 0024861 820 .ooooooo 0 .00004 7 7 720 .OOOOOOO 0 .0021158 0 .0 0. 0021158 800 .ooooooo o .0 720 .ooooooo 0 .0017742 0. .0 0. 0017742 780 .ooooooo 0 .0 700 .ooooooo 0 OOI4606 0. 0 0. 0014606 740 .ooooooo 0 .0 680 .ooooooo 0, .0011746 0. 0 0. 0011746 720 .ooooooo 0 .0 680. .ooooooo 0. .0009162 0. 0 0. 0009 162 380 ooooooo 0 .0 "660 .ooooooo 0. .0006859 0. 0 0. 0006859 380. .ooooooo 0 0 640. .ooooooo 0. .0004844 0. 0 0. 0004844 360 ooooooo 0 0 620. ooooooo 0. .0003130 O. 0 0. 0003 130 340 ooooooo 0. 0 600 ooooooo 0. .0001737 0. 0 0. 0001737 300 ooooooo 0. 0 580. ooooooo 0. .0000698 0. 0 0. 0000698 280. ooooooo o. 0 540. ooooooo 0. .0000082 0. 0 0. 0000082 240. ooooooo 0. o 500. ooooooo 0. O 0. 0 0. 0 . 0. 0 0. 0 0. 0 CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 15 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.0550 0.0550 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 760.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 260.0 1000.0 REACH LENGTH= 2380.00 STREAM WIDTH= 10.00 MANNINGS N= 0.350000 DELTAX= 20.00 VOLUME OF PRECIPITATION EXCESS^ 2.0400657654 CU FT TOTAL RUNOFF VOLUME FROM REACH= 4855.3554687500 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT 0. .0000185 0 .0066667 0 .0 0 .0 0 0 0. .0 0 .0000185 0 0066667 0 .0 0 0 0. 0 0. .0 o .0003824 0 .0116667 0 .0002069 760 .OOOOOOO 0 0001431 1000. .OOOOOOO 0. 002314 1 0 .0166667 0 .0013407 760 OOOOOOO 0. 0009272 10OO. OOOOOOO o. 0054782 0 0166667 0 .0032112 760 OOOOOOO o 0022208 1000. OOOOOOO 0. .0038724 0 0 0 .0022892 760 .OOOOOOO 0. 0015831 1000. .OOOOOOO 0. 0025632 0 0 0 .0015 153 740 OOOOOOO o 0010479 1000. OOOOOOO 0. .0015004 0 0 0 .0008870 720 .OOOOOOO 0. 0006134 980. OOOOOOO 0. 00069 1 3 0 .0 0 .0004086 680 .OOOOOOO 0 0002826 960. OOOOOOO 0. .0001614 0. .0 0 .0000954 660 .OOOOOOO 0 0000660 940 . OOOOOOO o. 0 0. 0 0 .0 0 .0 0. 0 900. .OOOOOOO CALCULATION OF LATERAL INFLOW HYDROGRAPHS SECTION 16 LEFT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 RIGHT DEPRESSION STORAGE FOR EACH SOIL ZONE 0.0125 LEFT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.3750 RIGHT SIDE AVERAGE SLOPE FOR EACH SOIL ZONE 0.1150 LEFT SIDE DISTANCE OF SOIL ZONE FROM STREAM 600.0 RIGHT SIDE DISTANCE OF SOIL ZONE FROM STREAM 500.0 REACH LENGTH= 3460.00 STREAM WIDTH= 10.00 MANNINGS N= 0.350000 DELTAX= 20.00 VOLUME OF PRECIPITATION EXCESS= 3.3710384369 CU FT TOTAL RUNOFF VOLUME FROM REACH= 11663.7929687500 PRECIP EXCESS VALUES FOR EACH DELT OL CFS/FT PRECIP DEPTH LEFT SIDE OL WIDTH OF CONTRIB AREA RIGHT SIDE OL WIDTH OF RIGHT SIDE o OOOO185 0 .0066667 0 .0 0 .0 0 .0 0 .0 o OOOO185 0 .0066667 0 .0 0 .0 0 o 0 .0 o .0006130 0 .0116667 0 .0003737 600 .OOOOOOO 0 .0002069 500 .OOOOOOO 0. .0038079 0 .0166667 0 .0024210 600 .OOOOOOO 0 .0013407 500 .OOOOOOO 0. .0090562 0 .0166667 0 .0057987 600 .OOOOOOO 0 .0032112 500 .OOOOOOO o. .0064231 0 .0 0 .0041339 580 .OOOOOOO 0. 0022892 500 .OOOOOOO 0. .0042516 0 .0 0. 0027363 540 .OOOOOOO 0 0015153 480 .OOOOOOO o. .0024888 0 0 0 0016018 500 OOOOOOO 0. 0008870 460 .OOOOOOO 0. 0011466 0 .0 0. 0007379 480 OOOOOOO 0. 0004086 4 20 .OOOOOOO 0. 0002678 0. .0 0. 0001723 460. .OOOOOOO 0. 0000954 400. ,OOOOOOO 0. 0 0 0 0. 0 0. 0 0. 0 0. .0 NJ NJ O 221 APPENDIX D.3 a b C d e f 0 .0835 0 .08350 0 .00996 0 .00022 0 .29121 0 . 23857 0 . 1670 0 .16700 0 .03984 0 .00139 0 .58244 0 .477 16 0 . 2505 0 .25050 0 .08964 0 .00410 0 . 87364 0 .7157 1 0 . 3340 0 .33400 0 . 15937 0 .0088 3 1 . 16487 0 .95430 0 4 175 0 .41750 0 .24901 0 .01603 1 .45607 1 .19286 0 . 5010 0 .50100 0 .35858 0 .02608 1 .74729 1 .43144 0 . 5845 0 .58450 0 .48806 0 .03936' 2 .03849 1 .67000 0 . 6680 0 .66800 0 .63747 0 .05622 2 . 32972 1 .90858 0 .75 15 0 .75150 0 .80742 0 .07669 2 .6415 1 2 . 17 168 0 .8350 0 .83500 1 .00037 0 .10149 2 .96609 2 .4 5000 0 .9185 0 .91850 1 .21657 0 .13126 3 .29067 2 .72832 1 . 0020 1 .00200 1 .45600 0 . 16636 3 .6 1527 3 .00667 1 . 0855 1 .08550 1 .71868 0 .20717 3 .93985 3 .28499 1 . 1690 1 .16900 2 .00460 0 .25404 4 . 26446 3 . 55334 1 . 2525 1 .25250 2 .31375 0 .30732 4 .58904 3 .84 166 1 . 3360 1 .33600 2 .64584 0 .36798 4 . 89924 4 .10286 1 . 4 195 1 .4 1950 2 .99839 0 .43626 5 .19044 4 .34 142 1 . 5030 1 .50300 3 .37086 0 .5 1143 5 .48 167 4 .58000 1 . 5865 1 . 58650 3 76325 0 . 59373 5 .77287 4 .81856 1 . 6700 1 .67000 4 . 17556 0 . 68340 6 .06410 5 .05714 1 . 7535 1 . 75350 4 .60779 0 .78067 6 .35530 5 29570 1 . 8370 1 .83700 5 .05994 0 . 88576 6 . 64652 5 53429 1 . 9205 1 .92050 5 .53201 0 99892 6 . 93772 5 . 77284 2 004 0 2 .00400 6 .02400 1 12037 7 .22895 6 01143 2 .0875 2 08750 6 .53592 1 .25033 7 .52015 6 . 24998 2 .17 10 2 . 17 100 7 .06775 1 .38901 7 . 8 1 138 6 . .48857 2 .2545 2 . 25450 7 . 6 195 1 1 . 53665 8 .10258 6 . 727 13 2 . 3380 2 . 33800 8 . 19 118 1 , . 69344 8 .39380 6 9657 1 2 .4215 2 42 150 8 78278 1 , 8596 1 8 .68500 7 , . 20427 2 . 5050 2 . 50500 9 . 39430 2 . 03537 8 . 97623 7 . 44286 2 5885 2 . 58850 10. 02573 ' 2 . 22093 9 . 26743 7 , 68 1 4 1 2 .6720 2 . 67200 10. 67709 2 . 4 1648 9 55866 7 . 92000 2 7555 2 . 75550 1 1 . 34910 2 . 61858 9 . 87204 8 . 18498 2 . 8390 2 . 83900 12 . 044 17 2 82986 10. 19664 8 . 46333 2 . 9225 2 . 92250 12 . 76248 3 . 05253 10. 52122 8 . 74 165 3 . 0060 3 . 00600 13. 50402 3 . 28686 10. 84580 9 . 01997 3 . 0895 3 . 08950 14 . 2688 1 3 . 53309 11. 17040 9 . 29832 3 . 1730 3 . 17 300 15 . 05684 3 . 79 147 11. 49498 9 . 57664 3 . 2565 3 . 25650 15 . 86812 4 . 06225 11. 81959 9 . 85500 3 . 3400 3 . 34000 16 . 70222 4 . 34934 12 . 12818 10. 1 1427 3 . 4235 3 . 42350 17 . 55672 4 . 65271 12 . 4 194 1 10. 35286 3 . 5070 3 . 50700 18 . 43112 4 . 96836 12 . 7 1061 10. 59142 3 . 5905 3 . 59050 19 . 32549 5 . 29649 13 . 00183 10. 83000 3 . 6740 3 . 67400 20. 23975 5 . 63725 13 . 29303 1 1 . 06856 3 . 7575 3 . 75750 2 1 . 17392 5 . 99083 13 . 58426 1 1 . 307 14 3 . 84 10 3 . 84 100 22 . 12802 6 . 35743 13 . 87546 1 1 . 54570 3 . 9245 3 . 92450 '23 . 10207 6 . 73722 14 . 16669 1 1 . 78429 4 . 0080 4 . 00800 24 . 09599 7 . 1301 1 14 . 45862 12 . 02373 4 . 0915 4 . 09150 25 . 1 1029 7 . 53440 14 . 75744 12 . 27147 4 . 1750 4 . 17500 26 . 14532 7 . 95264 15 . 05625 12 . 51921 4 . 2585 4 . 25850 27 . 20102 8 . 38497 15 . 35508 12 . 76697 4 . 3420 4 . 34200 28 . 27740 8 . 83162 15 . 65390 13 . 0147 1 4 . 4255 4 . 42550 29 . 37448 9 . 29275 15 . 95273 13 . 26247 4 . 5090 4 . 50900 30. 49223 9 . 76855 16 . 25154 13 . 51021 4 . 5925 4 . 59249 31 . 63068 10. 25920 16 . 55037 13 . 75797 4 . 6760 4 . 67599 32 . 78979 10. 76489 16 . 84917 14 . 00569 4 . 7595 4 . 75949 33. 97002 1 1 . 28077 17 . 15988 14 . 26761 4 . 8430 4 . 84299 35 . 17253 1 1 . 81048 17 . 47537 14 . 53523 4 . 9265 4 . 92649 36 . 39743 12 . 35632 17 . 79089 14 . 80287 5 . 0100 5 . 00999 37 . 64464 12 . 91845 18 . 10640 15 . 07050 222 5 .0935 5 .09349 38 .91418 5 . 1770 5 .17699 40 .20607 5 . 2605 5 .26049 4 1 .52034 5 . 3440 ' 5 .34399 42 . 85660 5 . 4275 5 .42749 44 .21303 5 .5110 5 .51099 45 .58940 5 . 5945 5 . 59449 46 .98572 5 . 6780 5 .67799 48 .40195 5 . 76 15 5 .76 149 49 .83806 5 . 8450 5 .84499 51 .294 10 5 . 9285 5 .92849 52 .77011 6 .0120 6 .01199 54 .26599 e .0955 6 .09549 55 . 78 178 6 . 1790 6 .17899 57 .31754 6 . 2625 6 .26249 58 .8732 1 e . 3460 6 .34599 60 .44879 G .4295 6 .42949 62 .04428 6 . 5 130 6 .51299 63 .65970 6 . 5965 6 .59649 65 .29507 6 . 6800 6 .67999 66 .95030 6 . 7635 6 . 76349 68 .62645 6 . 8470 6 .84699 70 .32573 6 . 9305 6 .93049 72 .04829 7 .0140 7 .01399 73 .79405 7 .0975 7 .09749 75 .56303 7 .18 10 7 .18099 77 . 35530 7 2645 7 .26449 79 :17082 7 . 3480 7 .34799 8 1 .00899 7 .43 15 7 .43 149 82 .86737 7 .5150 7 .51499 84 .74570 7 . 5985 7 .59849 86 .64398 7 .6820 7 .68199 88 562 15 7 . 7655 7 . 76549 90. .50021 7 . 8490 7 .84899 92 . . 45822 7 . 9325 7 . 93249 94 .43619 e .0160 8 .01599 96 43404 e .0995 8 .09949 98 . 45172 8 . 1830 8 .18299 100. 48947 8 2665 8 26649 102 . 54700 8 3500 8 . 34999 104 . 62466 8 . 4335 8 . .43349 106 . 72200 8 . 5170 • 8 . 51699 108 . 83945 8 . 6005 8 . 60049 1 10. 97665 8 . 6840 8 . 68399 113. 13397 8 . 7675 8 . 76749 115. 31209 8 . 85 10 8 . 85099 117. 51358 8 . 9345 8 . 93449 119. 738 1 1 9 . 0180 9 . 01799 121 . 98613 9 . 1015 9 . 10149 124 . 257 16 9 . 1850 9 . 18499 126 . 55159 9 . 2685 9. 26849 128 . 86909 9 . 3520 9 . 35199 131 . 2094 1 9 . 4355 9 . 43549 133 . 56967 9 . 5190 9 . 51899 135 . 95003 9 . 6025 9 . 60249 138 . 35013 9. 6860 9 . 68599 140. 77037 9. 7695 9 . 76949 143 . 21028 9 . 8530 9 . 85299 145 . 67036 9 . 9365 9 . 93649 148 . 15013 10. 0200 10. 01999 150. 65005 13 .49707 18 .42 19 1 15 .33813 14 .09241 18 . 73740 15 .60574 14 .70467 19 .05290 15 . 87337 15 .34060 19 .3556 1 16 . 12569 15 .99913 19 .64684 16 .36427 16 .67435 19 .93803 16 .60283 17 .36639 20 . 22925 16 . 84 142 18 .07545 20 .52045 17 .07997 18 .80159 20 .81 168 17 .31856 19 .54504 2 1 .10287 17 . 557 1 1 20 .30600 2 1 .394 10 17 .79570 2 1 .08453 2 1 .68529 18 .03424 2 1 .88080 2 1 .97650 18 .27283 22 .69502 22 .26772 18 .51138 23 . 52733 22 .55893 18 . 74997 24 . 37784 22 .85013 18 .98853 25 . 24670 23 .14136 19 . 227 1 1 26 . 134 12 23 .43256 19 .46567 27 .04022 23 . 72379 19 .70425 27 .965 1 3 24 .01498 19 .9428 1 28 .88951 24 .33157 20 .21164 29 .82800 24 .65616 20 .48996 30 . 787 14 24 .98073 20 .76828 3 1 .76706 25 .30533 2 1 .04663 32 .76794 25 .62991 2 1 .32495 33 .79007 25 .95451 2 1 .60330 34 .83359 26 .27908 2 1 .88 162 35 .91554 26 . 58450 22 .13712 37 .03075 26 . 87570 22 .37567 38 .16650 27 .16693 22 .61426 39 32301 27 . 458 1 1 22 8528 1 40 .50031 27 .74934 23 . 09 140 4 1 69858 28 . 04054 23 . 32996 42 9 1792 28 33 177 23 . 56854 44 . 15862 28 . 62297 23 . 807 10 45 . .42067 28 . 914 18 24 , 04568 46 . . 70419 29 . 20538 24 . 28424 48 . 00951 29 . 49660 24 . 52283 49 . 33655. 29 . 7878 1 24 . 76 1 38 50. 68567 30. 07903 24 . 99997 52 . 05676 30. 37022 25 . 23853 53 . 45016 30. 66 145 25 . 477 1 1 54 . 86589 30. 95265 25 . 7 1567 56 . 30424 31 . 24388 25 . 95425 57. 73293 3 1 . 56204 26 . 22495 59 . 17831 3 1 . 88663 26 . 50330 60. 64801 32 . 2 112 1 26 . 78162 62 . 14261 32 . 53580 27 . 05995 63 . 66185 32 . 86040 27 . 33829 •65 . 20627 33 . 18497 27 . 61661 66 . 7757 1 33 . 50957 27 . 89496 68 . 39833 33 . 81337 28 . 14853 70. 06175 34 . 10458 28 . 38708 71 . 74939 34 . 39580 28 . 62567 73. 46107 34 . 68700 28 . 86423 75. 19739 34 . 97820 29 . 10281 76 . 95795 35 . 26942 29 . 34137 78 . 743-32 35 . 56062 29 . 57996 80. 55324 35. 85185 29 . 81851 82 . 38828 36 . 14 305 30. 057 10 10. 1035 10.1870 10.2705 10.3540 10.4375 10.5210 10.6045 10.6880 10.7715 10 . 8550 10.9385 1 1 .0220 1 1 . 1055 11.1890 1 1.2725 11.3560 11.4395 1 1 . 5230 11.6065 11.6900 11.7735 11.8570 11 9405 12.0240 12.1075 12.1910 12.2745 12.3580 12.44 15 12.5250 12.6085 12.6920 12.7755 12.8590 12.9425 13.0260 13.1095 13.19 30 13.2765 13.3600 13.4435 13 . 5270 13.6105 13 .6940 13 . 7775 13.8610 13.9445 14.0280 14.1115 14.1950 14.2785 14.3620 14.4455 14.5290 14.6125 14.6960 14.7795 14.8630 14.9465 15.0300 10.10349 10.18699 10.27049 10.35399 10.43749 10.52099 10.60449 10.68799 10.77149 10.85499 10.93849 11.02199 11.10549 11.18899 11.27249 11.35599 11.43949 11.52299 11.60549 11.68999 11.77349 11.85699 11.94049 12.02399 12.10749 12.19099 12.27449 12.35799 12 .44 149 12.52499 12.60849 12.69199 12.77549 12.85899 12.94249 13.02599 13.10949 13.19299 13.27649 13.35999 13.44349 13.52699 13.61049 13.69398 13.77748 13.86098 13.94448 14.02798 14. 11 148 14.19498 14.27848 14.36198 14.44548 14.52898 14 .61248 14.69598 14 . 77948 14.86298 14.94648 15.02998 153.16966 155.70943 158.26888 160.84846 163.44775 166.06721 168.70634 17 1. 36563 174.0458 1 176.74945 179.47609 182.22618 184.99930 187.79593 190.61551 193.4578 1 196.31999 199.20238 202.10442 205.02660 207.96846 210.93053 2 13.91223 2 16.91408 2 19.93562 222.9774C 226.03877 229.12030 232.22 15 1 235.34300 238.48405 241.64526 244.8275 1 248.03334 251.26207 254.51427 257.78906 261.08765 264.40918 267.75342 271.11743 274.50171 277 . 90576. 281.32959 284.77344 288.23706 291.72095 295.22534 298.74854 302.29248 305.85547 309.43896 313.04224 316.66553 320.30859 323.97168 327.65576 331 .36353 335.09448 338 .84839 84.24808 86.13332 88.04356 89.97939 91.94057 93.92764 95.94028 97.97905 99.99544 102.03175 104.09601 106.18860 108.30954 110.45930 1 12. 63742 114. 88608 117.182 17 119.50606 12 1.857 16 124.2361 1 126.64270 129.07738 13 1.53972 134.03058 136.5494 1 139.09597 14 1.67259 144.27728 146.91025 149.57257 152.26369 154.98398 157.66539 160.37 128 163.10846 165.87732 168.67723 17 1.50981 174.37421 177.32918 180.33717 183.37622 186.44565 189.54576 192.67664 195.83870 199.03201 202.25725 205.51256 208.80020 2 12.11862 215.46930 218.85155 222.26593 225.7 1220 229.19063 232.60960 236.05896 239.54309 243.06177 36.43427 36.72546 37.01668 37.30789 37.59909 37.89032 38.18152 38.47275 38.79253 39. 1 17 1 1 39 . 44 170 39 . 76627 40.09087 40.41545 40.74005 41.04224 41.33347 41.62466 41 .91588 42.20708 42.49831 42.78951 43.08073 43.37 192 43.66315 43 . 95435 44 . 24556 44 . 53677 44.82799 45.11920 45.41042 45 . 70163 46.02301 46.34760 46.672 15 46.99675 47.32133 47.64594 47.97052 48.27112 48 . 56235 48.85355 49. 14478 49.43597 49.72720 50.01840 50.30963 50.60083 50.89204 5 1 . 18326 5 1 . 47446 5 1 . 76567 52.05688 52.34808 52.63931 52.93051 53 . 25348 53.57808 53.90265 54.22723 30.29565 30.53424 30.77280 31.01138 31.24995 31.48853 31.72710 31.96567 32.23828 32.51660 32.79495 33.07327 33.35162 33.62994 33.90826 34.15994 34.39853 34.63708 34.87567 35.11423 35.3528 1 35.59137 35.82996 36.06851 36.307 10 36.54565 36.78424 37.02280 37.26138 37.49994 37.73853 37.97708 38.25162 38.52994 38.80826 39.08661 39.36493 39.64328 39.92160 40.17137 40.40994 40.64851 40.88708 4 1 . 12566 4 1 .36423 4 1 .60280 41.84137 42.07996 42.31851 42 . 557 10 42.79565 43.03424 43.27280 43.51138 43.74994 43.98853 44.26492 44 . 54327 44.82159 45.09993 15 . 1 135 15 .11348 342 .62573 246 .61557 54 .55182 45 . 37827 15 . 1970 15 .19698 346 .42676 250 .20500 54 .87640 45 .65659 15 . 2805 15 .28048 350 .25049 253 '. 82886 55 .20102 45 .93494 15 . 3640 15 .36398 354 .09619 257 .5664 1 55 .50002 46 . 18280 15 . 4475 15 .44748 357 .96240 26 1 .36206 55 .79121 46 .42 136 15 . 53 10 15 .53098 361 .84863 265 .19 116 56 .08244 46 .65994 15 .6 145 15 .61448 365 .75464. 269 .05396 56 .37363 46 .89850 15 . 6980 15 .69798 369 .68042 272 .94995 56 .66486 47 .13708 15 78 15 15 . 78 148 373 .62622 276 88013 56 .95605 47 .37564 15 . 8650 15 .86498 377 , 59180 280 . 84399 57 . 24728 47 .61423 15 . 9485 15 .94848 38 1 . 57764 284 , .84229 57 . 53848 47 , .85278 16 . 0320 16 .03198 385 . 58301 288 . 87402 57 , .82970 48 09 1 37 16 . 1 155 16 .11548 389 . 60864 292 . •94 1 16 58 . . 12090 48 32993 16 . 1990 16 . 19897 393 . 65356 297 . 04 126 58 . 4 1 209 48 . 56848 16 . 2825 16 . 28247 397 . 7 1875 301 . 17676 58 . 70328 48 . 80704 16 . 3660 16 . 36597 401 . 80396 305 . 34668 58 . 99449 49 . 04562 16 . 4495 16 . 44946 405 . 909 18 309 . 55151 59 . 28569 49 . 284 18 16 . 5330 16 . 53296 4 10. 034 18 313. 79077 59 . 57690 49 . 52274 16 . 6 165 16 . 6 1646 4 14. 17896 318 . 06494 59 . 868 10 49 . 76129 16 . 7000 16 . 69995 4 18. 34375 322 . 37476 60. 15929 49 . 99985 16 . 7000 16 . 70000 4 18. 34668 322 . 37744 60. 15945 50. 00000 a Water Surface Elevation b Water Depth c Area of Section d Normal Discharge e Wetted Perimeter f Top Width of Water Surface XNI= O.O5O0 TRIBUTARY A ™ T T 0 L R = . OOOO010 XN2 = 0.0500 DE L T = 120 OOOOO DE L A = 10.00000 DELX= 2390. APPENDIX D.4 IN SECTION NO = 1 OUT SECT I ON NO IN AREA IN DISCH OUT AREA OUT OISCH TOTAL TIME 0 .0 0.0 0 .0 0 0 0 0 .0 0.0 0 00-12 1 0 00227 120 0 .0 0.0 0 . oon i •) 0 005 1 3 240 0 .0 0.0 0 .08836 0 .11506 360 0 .0 0.0 0 .52 15 1 1 2 17 2 3 480 0 .0 0.0 1 .39103 4 . 43395 • ' 600 0 .0 0.0 1 72748 5 90.4 4 6 720 0 0 0.0 1 . 7 4 276 5 973^4 840 0 .0 0.0 1 . 57720 5 23466 960 o .0 O.O 1 . 32530 4 16066 1080 o .0 0.0 1 .05482 3 07925 1200 0 .0 0.0 0 . 82809 2 24890 1320 0 .0 0.0 0 66 12 1 1 67086 1440 0 0 0.0 0 . 53472 1 25964 1560 0 0 0 0 o 4 3 7 7 7 O 96546 1680 0 0 0.0 0 36237 0 75087 1800 0 .0 0.0 0 303 1 1 o 59013 1920 0 0 O.O 0 2557 1 0 47204 2040 o 0 0 0 0 2 175H o 37966 2 160 0 0 0 o 0 1BG4 3 0 3 1026 2280 0 .0 0.0 0 16097 0 25354 2400 0 0 0.0 0 13974 0 2 1 134 2520 0 .0 0.0 0 12 199 0 17675 2640 0 0 0.0 0 107 15 0 14783 2760 o .0 0.0 0 09457 0 12528 2880 0 0 0.0 0 OR37 7 0 1075 1 3000 0 0 0.0 0 07 4 5 1 0 09226 3120 0 0 0.0 0 06G56 0 07917 3240 o 0 0.0 0 059 7 4 0 06794 3360 0. .0 0.0 0 05380 0 05915 3480 0 0 0.0 0 04855 0 0522 1 3600 0 0 0.0 0 04393 0 04609 3720 0 0 0 0 0 03984 0 04068 3840 o 0 O.O 0 .0362 4 0 03591 3960 0 0 0.0 0 03305 0 03 170 4080 0 0 0.0 0 0302 4 o 02798 4 200 0 0 0.0 0 02776 0 02470 4320 0. 0 0.0 o .02557 0 02 180 4440 0 0 0 0 0. 02359 0 01980 4560 0. 0 0.0 0 02 177 0. 01808 4680 0 .0 0.0 0 0201 1 0 01650 4800 0 0 0.0 0. .01860 0 0 1506 4920 o. o O.O 0 O 1 7 2 2 0 01375 5040 0. 0 0.0 0 01596 0 01256 5 160 SECONDS NJ NJ Ln XNI= 0.0500 TRIBUTARY B TOLR=.0000010 XN2 = 0.0500 DE L T = 120 00000 DE LA = 10.00000 DELX = 3460. IN SECTION NO OUT SECTION NO = IN AREA IN DISCH OUT AREA 0U1 DISCH TOTAL TIME 0 0 0 .0 • 0 0 0 0 0 0 0 0 0 0 004 26 0 00256 120 0 .0 0 .0 0 .000 29 0 .00588 240 0 .0 0 .0 0 139 1 1 0 . 2 3501 360 0 .0 0 .0 0 .06791 2 .66855 480 0 .0 0 .0 2 3523 1 9 .93426 600 0 .0 0 .0 2 95526 13 53142 7 20 0 0 0 0 3 01222 13 B8944 B40 0 .0 0 0 2 .75582 12 . 30760 - 960 0 .0 0 .0 2 3 44BO 9 .89285 1080 0 .0 0 0 1 . B925B 7 .4459B 1200 0 .0 0 0 1 .50950 5 5228 1 1320 0 .0 0 0 1 22023 4 17019 1440 0 .0 0 0 0 . 9979R 3 .20417 1560 0 .0 0 0 0 82475 2 49745 1680 0 0 0 0 0 6RR 1 2 1 .96976 IBOO 0 .0 0 0 0 .57932 1 .56843 1920 0 .0 0 0 0 4 9 19 3 1 .259R8 2040 0 .0 0 0 0 4 2095 1 .02 339 2 160 0 .0 0 0 0 362G5 O .R4040 2280 0 .0 0 0 0 3 1457 0 . 693 15 2400 0 0 0 0 0 . 27436 0 57974 2520 0. 0 0 0 0 . 24066 0 48585 2640 0 0 0 0 0 2 12 15 0 .41097 2760 0 0 0. 0 0 1R7B4 0 35045 2880 0. 0 0. 0 0 16 7 12 0 298B4 3000 0. 0 0. 0 0 14928 0 257 14 3120 0 0 0. 0 0 13378 0 22340 3240 0. 0 0. 0 0 12032 0 19409 3360 0. 0 0. 0 0 10R62 0 16862 3480 0. 0 0 0 0 09R4 1 O 14727 3600 0. 0 0 0 0 OR 9 35 0 13056 3720 0. 0 0 0 0 OR 1 32 0 1 1574 3840 0. 0 0 0 0 .07421 O 1026 1 3960 0. 0 0 0 0. 06790 0 09097 4080 0. 0 0. 0 0 OC2 30 0 08064 • 4200 0. 0 0. 0 0 05734 0. 07 149 4320 0. 0 0. 0 0 052R6 0 06467 4440 0. 0 0 0 0 04879 0 05864 4560 0 0 0. 0 0. 045 10 0. 053 18 4680 0. 0 0. 0 0 04 176 0. 04822 4800 0 0 0. 0 0. 03R72 0 04373 4920 0. 0 0. 0 0 03597 0. 03966 5040 0. 0 0. 0 0. 033 18 0 03596 5160 SECONDS K3 XN1= 0.0500 TRIBUTARY C T0LR=.0000010 XN2 = 0.0500 DEl_T = 120 00000 DELA = 10.00000 DELX= 2 130. IN SECTION NO IN AREA 0.0 0.0 O 0 0.0 O.O 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 0 0.0 0 0 0.0 0.0 0.0 0.0 O.O 0.0 0.0 0.0 0.0 0.0 . 0.0 O.O 0.0 0.0 0 0 0.0 0.0 0.0 0.0 0.0 0.0 O.O 0.0 IN DISCH 0.0 0. o. o. o. 0. o. o. o. 0. 0. o. o. o. o. o. 0. 0. o 0 o o o. o 0 0 o 0 o 0 o o 0 o o 0 o o 0 o o 0 0.0 0.0 OUT SECTION NO OUT AREA O.O 0 00«17 t o oon 15 0. 1 2083 0 . 66 1f>7 1 71O80 2.7003R 2.33831 2 26385 2.07050 1.8 1913 1 .553G7 1.31110 1.09998 0.91-172 O.7 52 36 0.61316 0 50O65 O 4 t350 O.34490 0 29040 O 24656 0.21095 0 18170 0.15766 0 13747 O 12O50 0.10624 0 094 10 0 08363 0.07462 0.06686 0.OGO17 0 054 3 1 0.04918 O . 04.160 0.04054 0 03G95 0.03376 O 03091 O.0284 4 0.0262? 0 02422 O.02239 OUT DISCH 0.0 O 00200 0 004 50 O. 15 115 1 44825 5.04797 7 04662 7.63535 7.31753 6.49802 5.475G5 4.4445 1 3 55204 2.81791 2 2 1119 1.71399 1 30892 O.99844 O 77349 O.60884 O.48367 O 38908 O.31603 0 25962 O. 2 1333 O. 17924 O.15059 0. 12652 0.10782 0.09286 O 07998 O 06889 0 05933 O.05173 0.04585 0.04063 0.03601 0.03191 '0.02828 0.02506 0.02221 0.01968 0.01774 0.01623 TOTAL TIME . 0. 120. 240. 360. 480. 600. 720 . 840. 960 . 10BO. 1200. 1320. 1440 . 1560. 1680. 1800. 1920. 2040. 2 160. 2280. 2400. 2520. 2640. 2760. 2880. 3000. 3120. 3240. 3360. 3480. 3600. 3720. 3840. 3960. 4080. 4200. 4320. 4440. 4560. 4680 . 4 800. 4920. 5040. 5160. SECONDS Ni ls? XNi* O.O500 TRIBUTARY D TOLR= .0000010 XN2= 0 0500 OEI.T = 120. 0O000 D F L A = 10 OOOOO DE LX = 2380. IN SECTION NO = OUT SEC1 I ON NO = IN AREA IN DISCH OUT AREA OUT DISCH TOTAL TIME 0 0 0 0 0.0 0 .0 0 0 .0 0.0 0.004 21 0 .002 2 7 120 O .0 0.0 0 ..00H1:) 0 .005 1 2 240 0 .0 0.0 O.OB24 1 0 .10526 360 0 .0 0.0 0 . 4 7 4 1 r, 1 073B8 480 0 .0 0.0 1.26552 3 9 1 208 600 0 .0 0.0 1 57378 5 2 1978 720 0 .0 0.0 1 .63058 5 . 467 16 840 0 .0 0.0 1.60034 5 . 33546 960 0 .0 0.0 1 .52237 4 .99585 1080 0 .0 0.0 1 .4 1552 4 .53580 1200 0 .0 0.0 1 .29 188 4 .02166 1320 0 0 0.0 1 . 15977 3 .49063 1440 0 .0 0.0 1.02512 2 .96774 1560 0 .0 0.0 0 B9205 2 .47244 1680 0 .0 0.0 0.7637 1 2 Ol 762 1800 0 .0 0.0 O.64309 1 .60956 1920 0 .0 0.0 0.53328 1 .25504 2040 0 .0 0.0 0 43787 0 96575 2 160 0 .0 0.0 0 36220 0 .75040 2280 0 0 0.0 O.302 7 7 0 58929 2400 0 0 0.0 0 25528 0 47097 2520 0 .0 0.0 0 2 17 10 0 .37B59 2640 0 0 0.0 0 18593 0 .30915 2760 0 .0 0.0 0 1604 7 0 25244 2880 0 .0 0.0 0.13926 0 .21039 3000 0 0 0.0 O. 12 152 0 175B4 3120 0 0 0.0 0.106 70 0 14696 3240 0 0 0.0 0.09414 0 12458 3360 0. 0 0 0 0.OB337 0 10684 3480 0. 0' 0.0 0.07413 0 .09163 3600 0. 0 0.0 0.06620 0 .07858 3720 0. 0 0.0 0.0594 1 0 .06739 3840 0. 0 0.0 0.05348 0 05873 3960 0. 0 0.0 0 04826 0 05 182 4080 0. 0 0.0 0 04 365 0 04572 4200 0. 0 0.0 0.03958 0 .04034 4320 0. 0 0.0 0 03599 0 .03559 4440 0. 0 0 0 0.03283 0 03 140 4560 0. 0 0.0 0.03003 0 .02770 4680 0. 0 0.0 0 02757 0 .02444 4800 0. 0 0.0 0.02539 0 02 156 4920 0. 0 0.0 0.02341 0 01964 5040 0. 0 0.0 0.02161 0 01792 5160 SECONDS NJ 00 XIMI= . 0.0500 TRIBUTARY E TOLR-.0000100 XN2 = 0.0500 DEL T = 1?0 OOOOO DE I A = 10.00000 DE L X = 1750. IN SECTION NO Oil T SFCTION ND = IN AREA IN DISCH Our AREA OUT DISCH TOTAL TIME 0 .0 o .0 o 0 0 0 0 0 .0 0 .0 0 .0030 7 0 .00340 120 0 .0 o .0 0 .007JJ 0 00708 240 0 .0 0 .0 0 06 J66 O 12015 3GO 0 .0 0 .0 0 36 153 1 1B358 480 0 .0 0 .0 0 9 1 3R9 4 032 15 600 0 .0 0 .0 1 .01636 4 .64032 720 0 .0 0 .0 0 94 1 RR 4 19R30 840 0 .0 o . 0 o R39G5 3 6 1518 960 0 .0 0 0 0 732GO 3 .02372 1080 0 .0 0 .0 0 62G90 2 .4 5960 1200 0 .0 0 .0 0 527B9 t .95709 1320 0 .0 o 0 0 . 4 4 6 7 R 1 5G903 1440 0 .0 0 .0 0 39R33 1 .34 305 1560 0 .0 0 .0 o .3640R 1 19162 1680 0 .0 0 0 0 3274G 1 .03595 1800 0 .0 0 0 o 2829 1 O 85348 1920 0 .0 o 0 0 .2 3304 0 657 1 1 2040 0 .0 0 .0 0 1H237 0 . 4 7640 2 160 0 .0 0 0 0 .137R8 0 .32860 22BO 0 .0 0 0 0 10620 0 .23099 2400 0 .0 0 0 0 083 12 0 .16833 2520 0 .0 0 0 0 066 1 2 0 12396 2640 0 .0 0 0 o 05342 0 .09261 2760 0 .0 0 0 0 04 355 0 07 198 2880 0 0 o. 0 0 0358 7 o .05595 3000 0 0 0 0 0 0299 1 0 0 1349 3120 0 0 0. 0 0 02527 0 03380 3240 0 0 0 0 0 02 1 43 0 02804 3360 0 0 0. 0 0 01R2J o 02326 3480 0. 0 o. 0 o. 0 1559 0 01929 3600 0 0 o. o 0 013 IO 0 . 0 1600 3720 0 0 0. 0 0 01 15R 0 01328 3840 0 0 0 0 0. 01006 0 01 101 3960 0. 0 0. o 0 OORfl 1 0. 009 1 3 4080 0. 0 0. 0 o 007 7 7 0 007 58 4 200 0. 0 o. 0 0 0069 1 o. 00629 4320 0. 0 0. 0 o. OOG 1 9 o. 00529 4440 0. 0 o. o 0 005 5-1 0. 00J73 4560 0. 0 0. o 0 . 00-19G 0 OOJ2 3 4680 0. 0 0. 0 0. OO 14 1 0. 0037 9 4 800 0. 0 0 0 0 0039 7 0. 00339 4920 o. 0 0 0 0 0035 5 0. 00304 5040 0. 0 0. o 0 003 18 0 . 002 7 2 5 160 SECONDS VD TOLR= .0000100 XN2 = O 0500 DF L T - 1 20 . OOOOO DF I. A - 10.OOOOO DE I X = 1290 IN SECTION NO 0U1 SECTIDN NO IN AREA IN DISCH OUT ARFA OUT DISCH TOTAL TIME 0 0 O 0 O.O 0 . 0 0 0. 00397 0. 00340 0.00101 0. 0004 8 120 0. 00744 0 0O70R O.O03O3 0 OO 1 4 4 240 0 06466 O. 12015 0 OR 4 7 1 0 09 369 360 0. 36 153 1 . 18358 0 53 188 1 08302 480 0. 91389 4 . 032 15 1 568 18 4 49923 600 1 01636 4 . 64032 2.28178 7 39407 720 0 94 188 4 . 19830 2.5802 4 8 7 158R 840 O 83965 3 . 6 1548 2 597 I'l 8 79 187 960 0 7 3260 3 02372 2 . 2397.1 7 2 1460 1080 0 62690 2 . 4 5960 1.93403 5 93 7 80 1200 0 52789 1 . 95709 1 .66089 4 8509 7 1320 "0 .44678 1 56903 1.41746 3 93502 1440 0 39833 1 . 34305 1.21142 3 19994 1560 0 .36 408 1 . 1946 2 1 04 7 4 7 2 64265 16BO 0 .32746 1 . 03595 0 91686 2 2 18 18 1BOO 0 28291 O. 85348 0 806 7 9 1 87938 1920 0 23304 O 657 1 1 O. 7056 3 1 57 707 2040 0 18237 0. 47640 0 61025 1 30084 2 160 0 13788 0 32860 O 5 2053 1 05 1 50 2280 0 . 10620 O. 2 3099 0.4 3903 0 83938 2400 0 083 12 O. 16833 O . 36 9 36 O 66686 • 2520 0 .06612 O. 1239G O . 3 1 108 0 52 860 2640 o 05342 O 0926 1 O 26 2:iO 0 4 2 304 2760 0 04 355 O 07 198 0.2 2 260 0 33848 2880 0 03587 O. 05595 0. 18956 0 27477 3000 0 .02991 O. 04 349 O. 16228 0 222 17 3 120 0 02527 O 03380 0 13929 0 1823 1 3240 0 .02143 O O2 804 O 1203/ 0 15037 3360 0 01B24 O 02326 O 104RO 0 12409 3480 o 01559 O. 01929 0.OH 163 0 10430 3600 0 .01340 0 01600 0.08039 0 .08823 3720 0 .01158 0 01328 0 07081 0 07454 3840 0 01006 0 01101 0 06267 0 06 290 3960 0 .00881 0 009 1 3 O 05571 0 .05329 4080 0 .00777 0. 00758 0.04 955 0 04627 4 200 0 0069 1 0 006 29 O.04 4 1 7 0 04 008 4320 0 006 19 0 00529 0.03938 0 03168 4440 0 00554 0 004 7 3 0 03532 0 03005 4560 0 00496 0 004 2 3 0 031R3 0 .02608 4680 0 00444 0 0037 9 O 02884 0 .02 26 7 4 800 0 00397 0 00339 0.02627 0 0 1974 4920 0 00355 0 00304 O 02 3<iR 0 01754 5040 o 003 18 0 002 7 2 0.02 19.' 0 .Ol584 5 160 0 00285 0 0024 3 0 02004 0 0 1 4 30 5280 SECONDS ho O TOLR = OOOO100 XN2 = O.0500 IN SECTION NO = 3 IN AREA IN DISCH 0. 0 0. 0 O. 00101 0. 0004 8 0. 00303 0. 00144 0. 0842 1 0. 09369 0. 53188 1 08302 1 5G8 18 4 . 49923 2 . 28 178 7 . 39407 2 58024 8 : 7 1588 2 . 597 19 8 . 79 187 2 . 23973 7 . 2 1460 1 . 93403 5 . 93780 1 . 66089 4 85097 1 4 1746 3 . 93502 1 . 21 142 3 19994 1 . 04747 2 . 64265 O. 91686 2 . 2 18 18 O 80679 1 . 8793B 0 70563 1 . 57707 0 6 1025 1 . 30084 0 .52053 1 . 05 150 o 43903 0. 83938 0 36936 0. 66686 O .31108 0. 52860 0 .26230 0. 42304 o . 22260 0 33848 o . 18956 0 27477 0 . 16228 0. 222 17 O . 13929 0 1823 1 0 .12037 0 . 15037 o .10480 0 .12409 0 .09163 0 .104 30 0 .08039 0 .08823 0 .0708 1 0 07454 o .06267 0 06290 0 .05571 0 .05329 0 .04955 0 .04627 0 044 12 0 .04008 0 .03938 0 .03468 0 .03532 0 03005 0 .03183 0 .02G0R 0 .02884 0 022G7 0 .02627 0 .01974 o .02398 0 .01754 0 .02192 0 .01584 0 .02004 0 01430 D E I. T = ISO 00(100 DEI. A- 10.000O0 DEl.X = 1130. OUT SECT ION NO = 4 OUT AREA OUT DISCH TOTAL TIME , SECONDS 0.0 0 . 0 0 0.003 2 7 0 00 1 7 4 120 0 00551 0 . 002 1 1 240. 0 07 35 4 0 . 0G407 360 . 0 48936 0 79 146 480. 1 .52493 3 54047 600 . 2 . 4 24 66 G . 54 7 12 720. 3 13253 9 . 7627H 840 3.5G932 1 1 . 057 12 960. 3 52487 10. R69 1 7 1080. 3 . 28G73 9 RR8 1 3 1200. 2 973RR fl G32 1 1 1320. 2 63757 7 . 32927 1440. 2.303 79 6 1 1397 1560. 1 .992 70 5 0149 1 1680. 1.72704 4 15759 1800. 1.4 9807 3 45773 1920 . 1.3154G 2 9 13 12 2040. 1 1G 17 4 2 . 47372 2 160. 1 027G7 2 105 16 2280. 0.90778 1 787G0 2400. 0.79791 1 5 12 18 2520. 0.G9R5G 1 27077 2640. 0 6 1115 1 OG4 25 2760 0 53393 0 RR901 2880 . 0.4G7 17 0 74468 3000 0.40935 0 .62281 3120. O.3594 9 0 52534 3240 0.3164 7 0 .44199 3360 0 77885 0 .37453 3480 0.2466G 0 3 1786 3600 O 21911 0 2 7090 3720 O. 19503 0 23299 3840 0 17 40G 0 19998 3960 0 155B7 0 .17174 4080 0 14002 0 .14989 4 200 0 126 18 0 13080 4320 0. 1 1405 0 1 1409 4440 0.10339 0 09938 4560 0 09379 0 08769 4680 0.OH512 0 07757 4800 0.0/734 0 .06850 4920 0.07019 0 0605 1 5040 0.0G455 0 .05357 5 160 0.0593G 0 04752 5280 TOLR =.OOOO100 XN2 = 0.0500 IN SECTION NO = 4 IN AREA IN DI SCH 0. 0 0. 0 0. 00327 0. 00124 0. 00554 0. 002 1 1 0. 07354 0. 06407 0. 4B936 0. 79146 1 . 52493 3 54047 2 . 42466 6 . 547 12 3 . 13253 9. 26278 3 56932 1 1 . 057 12 3 52487 10 86917 3 2B673 9 . 8BB 13 . 2 973B8 8 632 1 1 2 63752 7 32927 2 30379 6 1 1392 1 99270 5 0449 1 1 72204 4 15759 1 49807 3 45773 1 31546 2 91312 1 16 174 2 47372 1 02767 2 105 16 0 90778 1 78760 0 7979 1 1 5 12 18 0 69856 1 27077 0 61115 1 06425 0 53393 0 88901 0 467 17 0 74468 0 40935 0 6228 1 0 35949 O 52534 0 31647 0 44 199 0 27885 0 37453 0 24666 0 3 1786 0 219 11 0 27090 0 19503 0 23299 0 17 406 0 19998 0 15587 0 17 17 4 0 14002 0 14989 0 12618 0 .130BO 0 1 1405 0 .11409 0 .10339 0 .09938 0 .09379 0 .08769 0 .085 12 0 .07757 0 .07 7 34 0 .06B50 0 .07049 0 .06051 0 .06455 0 .05357 0 .05936 0 04752 DELT- 120.00000 OE L A - 10 OOOOO DELX = OUT SECT ION NO = 5 OUT AREA OUT DISCH TOTAL TIME . SECONDS 0.0 0.0 0. O.OO132 0 00050 120. 0.00363 0.00138 240. 0.05732 0.045 13 360. 0.3588 7 0.524 13 4BO. 1.11582 2 34520 60O. 1 8 13 26 4 4 5 106 720. 2.50640 6 8463 3 840. 3 16935 9 409 16 960. 3.68966 11.56597 1080. 3 B8658 1? 408 12 1200. 3.831 75 12.16952 1320. 3 G0495 11 207 7 7 1440. 3 29 110 9 90605 1560. 2.94 709 B.525G3 16BO. 2.60700 7.21458 1800. 2 29-1 17 6.08041 1920. 2.O204 2 5. 13785 2040 1.78632 4.36 4 39 2 160 1 586B5 3 73 1 16 2280 1 41552 3.20728 2400 1 .267 15 2.77108 2520 1.13506 2.39904 2640 1.01555 2.07 2 99 2760 0.908 2 2 1 .7B869 2880 0 B1088 1.54468 3000 O 72353 1.3304 7 3 120 0 64618 1 . 14 550 3240 0.577 31 0 98745 3360 0.5 17 19 0.85102 3480 0 46314 0.73682 3600 0.41595 0 63672 3720 O.3742 1 0 55386 3840 0.33727 0.48229 3960 0 30458 0 . 4 1982 4080 0 2 7 554 0 36870 4 200 0 -24986 0. 32348 4320 O. 22720 0.28364 4440 0.20669 O.25135 4560 0. 1885 7 0.22283 4680 0. 17260 0 19768 4 800 0 . 158-15 0. 1754 1 4920 0. 1454.) 0 157 3 5 5040 0 13347 0 14086 5 160 0.1225" O 12585 5280 TOLR*.OO0O100 XN2* 0.0500 DELM 120 OOOO DELA- 10.00000 DELX* IN SECTION NO = 5 OUT SECTION IN AREA IN 1 DISCH OUT ARE 0. 0 0. 0 O 0 0. 00132 0. 00050 0. OO 1 3 2 0. 00363 0. OO 138 0. 003 15 0. 05732 0. 045 13 0. 057 15 0. 35887 0. 524 13 0 35837 1. 1 1582 2 . 34520 1 . 1 14 76 1. 81326 4 . 45 106 1 R1234 2 . 50640 6 . 84633 2 . 50549 3. 16935 9 . 409 16 3 . 16849 3 . 68966 1 1 . 56597 3 68903 3 8865B 12 . 408 12 3 . 88649 3 83 175 12 . 16952 3 R3 706 3 . 60495 1 1 . 20777 3 6055 3 3 29 1 10 9 90605 3 79 18 1 2 . 94709 8 52563 2 . 94785 2 60700 7 . 2 1458 2 . 607 7 8 2 . 294 17 6 . 0804 1 2 . 2949? 2 . 02042 5 . 13785 2 . 0? 1 10 1 78632 4 . 36439 1 . 78693 1 . 58685 3 . 73116 1 . 58 7 39 1 4 1552 3 . 20728 1 4 1 COO 1 . 267 15 2 . 77 10B 1 . 767 57 1 .13506 2 39904 1 . 1 354 5 1 .01555 2 07299 1 . 0159? 0 .90822 1 78869 0 9085 7 0 .81088 1 5446H O. 8 1 1 70 0 . 72353 1 .33047 O 7 7 3B3 0 . 646 18 1 .14 550 0 64645 0 .57731 0 .98745 0 57756 0 .517 19 0 .85102 0 .51741 0 . 46344 0 . 73682 0 46365 0 . 4 1595 0 . 63672 0 .41614 0 .3742 1 0 .55386 0 . 37439 0 .33727 0 .48229 0 3 37-13 0 .30458 0 .4 1982 0 .304 7 3 0 .27554 0 .36870 0 .7 7 56B 0 .24986 0 .32348 0 .7 4998 0 . 22720 0 .28364 0 .7773? 0 .20669 0 .25135 0 .706BO 0 . 18857 0 .22283 0 . 1BH67 0 .17260 0 . 19768 0 . 17 269 0 .15845 0 .17541 0 . 15B53 0 . 14543 0 .15735 0 . 14551 0 . 13347 0 .14086 0 13354 0 .12259 0 .12585 0 .17265 6 OUT DISCH TOTAL TIME . SECONDS .0.0 0. 0.OOO50 120. 0.0013 1 240. 0 0-1493 360. 0.57308 480. 2 3 17 2 2 600. 4.-148 11 6 8-1 300 720. 840. 9 405/4 960. 1 1 56330 1080 . 1 2'. 407 7 2 1 200 . 12 1709 1 1320. 11.21073 \ 1440. 9 90B97 1560. B 57867 1680. 7 7 17-13 1800. 6 08 301 1920. 5 14013 2040. 4 . 36634 2 160. 3 .73782 2280. 3 70870 2400. 7 . 7773? 2520. 2.40013 2640. 2 07399 2760. 1.7B958 2B80. 1 54550 3000. 1 33 170 3 120. 1 . 146 15 3240. 0.9BB03 3360 0.85152 3480 0 73727 3600 0.6371 1 3720 0 55420 3840 0 48 259 3960 0 42010 4080 O.36894 4 200 0.32370 4320 0 28382 4440 0 25 152 4560 0.22298 4680 0 197B2 4 800 0 17553 4920 0 15746 5040 0.14096. 5160 0.12594 5280 TOLR=.0000100 XN2 = 0.0500 IN SECTION NO = G IN AREA IN DISCH 0. 0 0. 0 0. 00132 O. 00050 0. 00345 0. 0013 1 0. 057 15 0. 04493 0. 35832 0. 52308 1 . 1 1476 2 . 34222 1 . 8 1234 4 . 448 1 1 2 50549 6 . 84 300 3 . 16849 9 . 40574 3 . 68903 1 1 . 56330 3 . 88649 12 . 40772 3. 83206 12 . 17091 3 60553 1 1 . 2 1023 3 . 29 18 1 9 . 90897 2 . 94785 8 52862 2 . 60778 7 . 2 1743 2 29492 6 . 08301 2 02 1 IO 5 14013 1 78693 4 36634 1 58739 3 73282 1 .41600 3 20870 1 . 26757 2 77232 1 13545 2 40013 1 .01592 2 07399 0 .90857 1 78958 0 .81 120 1 54550 0 . 723B3 1 33 120 0 .64645 1 . 14615 0 .57756 0 98803 0 .5 174 1 0 .85 152 0 .46365 0 .73727 0 .41614 O .6371 1 0 .37439 0 .55420 0 .33743 O .48259 0 .304 7 3 0 .420IO 0 . 27568 0 .36894 0 . 24998 0 .32370 0 .22732 0 .28382 0 .20680 O .25152 0 . 18867 O .22298 0 17269 0 .19782 0 .15853 0 .17553 0 . 14 55 1 0 .15746 0 .13354 0 .14096 0 .12265 0 .12594 Dl'Ll^ 120.000O0 DE L A = 10.00000 DE L X = 0U1 SECTION NO = 7 OUT AREA OUT DISCH TOTAL TIME . SECONDS 0.0 0. 0 0. 0.0O389 0 . 0014B 120. 0.007 93 0. 00348 240. O 118 19 0. 1 1979 360. 0 687 18 1 . 24 354 480. 1.93688 4 8578 1 GOO. 2 80286 7 . 96488 720 . 3 47363 IO. 65497 840 4.036 2 5 13 059 3 7 960. 4.43015 14 . 80848 1080. 4.504 60 15 . 14 140 1200, 4.33748 14 . 39408 1320. 4.0199 7 12 . 98852 1440 3 63169 1 1 . 32086 1560 3.2256 1 9 . 63734 1680 2 832 15 8 . 07748 1800 2 4 774 2 6 . 74025 1920 2 16H29 5 64 178 2040 1.906 2 5 4 . 755 15 2 160 1 .685 1 a 4 . 03899 2280 1 4 9622 3 4 5 204 2400 1 .334 18 2 968 15 2520 1.19230 2 55929 2640 1.0652 2 2 20482 2760 0 94930 1 897 17 2880 0.84728 1 63595 3000 0 7 556 3 1 407 24 3 1 20 0 673 18 1 2 1008 3240 0.60158 1 04252 3360 0.538 10 O . 89846 3480 0 48284 0 .77771 3600 0 43267 O .67196 3720 0 38988 0 .58422 3840 0 35094 0 .508 7 7 3960 O 3 1 7 1 5 0 .44 330 4080 0.28735 0 .38950 4 200 0.26033 0 .34 192 4320 0 2 3650 0 .29997 4440 0.21 589 0 26583 4560 0 19673 0 .2 3566 4680 0 . 17983 0 .20906 4 800 O 16486 0 18549 4920 0.15202 0 . 16644 5040 0. 1 3950 0 . 149 18 5 160 0 128 IO 0 13346 5280 TOLR=.0000100 XN2 = 0.0500 IN SECTION NO = 7 IN AREA IN 1 DISCH 0. 0 0. 0 0. 00389 O. 00148 0. 00793 0. 00348 0. 118 19 0. 1 1979 0. 687 18 1 . 24354 1 . 93688 4 . 8578 1 2 . 80286 7 . 96488 3 . 47363 10. 65497 4 . 03625 13 . 05937 4 . 43015 14 . 80848 4 . 50460 15 . 14440 4 . 33748 14 . 39408 4 . 01997 12 . 98852 3 . 63169 1 1 . 32086 3 . 2256 1 9 . 63734 2 . 832 15 8 . 07748 2 . 47742 6 . 74025 2 . 16829 5 . 64 17B 1 . 90625 4 . 755 15 1 . 68518 4 . 03899 1 49622 3 . 45204 1 . 334 18 2 . 968 15 1 19230 2 . 55929 1 06522 2 . 20482 0 94930 1 . 897 17 0 . 84728 1 63595 0 . 75563 1 40724 0 .673 18 1 .21008 0 .60158 1 .04252 0 .538 10 0 .89846 0 .48284 0 .7777 1 0 .43267 0 .67196 0 .38988 0 .58422 0 .35094 0 .50877 0 .31715 0 .4 4 330 0 .28735 0 .38950 0 .26033 0 .34192 0 .23650 0 .29997 0 .21589 0 .26583 0 . 19673 0 .2 3566 0 .17983 0 .20906 0 .16486 0 .18549 O 15202 0 .16644 0 .13950 0 .14918 0 . 128 10 0 .13346 DELT- 120.OOOOO DELA- 10.00000 DELX= OUT SEClION NO = 8 OUT AREA OUT DISCH TOTAL TIME . SECONDS 0.0 O.O 0 0.00637 0 00244 120. 0.01112 0.00564 240 . 0 17039 0. 19420 360. 0.97 370 1 96 192 480 . 2.648O0 7 36957 600. 3 66940 1 1 .48031 720 . 4.35378 14 . 46697 840 . 4 846 13 16 7137 1 960. 5.13096 18 05464 1080. 5.094 3 1 17 88206 1200. 4 82565 16 6 18 15 1320. 4.42100 14.76755 1440. 3.96132 12 73334 1560 . 3.49587 IO.74656 1680. 3.0508 ? 8 93797 1800. 2.65536 7 . 3978.) 1920 . 2 31234 6 14 37 1 2040. 2.02231 5 144 19 2 160 . 1.7804O 4 34534 2280. 1 57528 3.6955 1 2400. 1.40083 3.16409 2520. 1.249 19 2 7 1852 2640. 1 1 1244 2.3357 3 2760 0 . 98987. 2.00483 2880. 0 88338 1 7 264 3 3000 O.706IO 1.48332 3 120. O.69993 1.2 7 404 3240 0.6 2560 1 09704 3360 0 55880 0.94543 3480 0 50203 0.81817 3600 0.44921 0.70684 3720 0.405 29 O.6 1425 3840 0.36446 0.53497 3960 0.32913 0 4665 1 4080 0.29903 0 41007 4 200 0.2 7069 0 36016 4320 0 24568 0.31613 4440 0 22498 0 28014 4560 0.204 7 9 0 24836 4680 0.18697 0.22031 4800 0 17 119 0 19546 4920 0.15846 O. 1754 2 5040 0.14 547 0.15740 5 160 0.13356 O 14098 5280 LO TOLR =.OOOO100 XN2 = 0.0500 IN SECTION NO = 8 IN AREA IN I DISCH 0. 0 0. 0 0. 00637 0. 0024 4 0. 01112 0. 0056 1 0. 17039 0. 19420 0. 97370 1 . 96 192 2 64800 7 . 36957 3 . 66940 1 1 . 4803 1 4 . 35378 14 . 46697 4 . 846 13 16 . 7 137 1 5 . 13096 18 . 05464 5 . 094 31 17 . 88206 <J 82565 16 . 6 18 15 4 . 42 lOO 14 76755 3. 96132 12 . 73334 3 49587 IO. 74656 3 . 05082 8 . 93797 2 65536 7 39783 2 . 3 1234 6 . 1437 1 2 . 02231 5. 144 19 1 78040 4 . 34534 1 57528 3 6955 1 1 . 40083 3 16409 1 24919 2 7 1852 1 .11244 2 . 33573 0 .98987 2 00483 0 .88338 1 .72643 o .78640 1 48332 0 .69993 1 .27404 0 .62560 1 .09704 0 .55880 0 .94543 0 .50203 O .8 1817 0 . 4492 1 0 .70684 0 .40529 0 .61425 0 . 36446 0 .53497 0 .32913 0 .46651 0 .29903 o .41007 0 .27069 o .36016 0 .24568 0 .31613 0 .22498 0 2 8014 0 .20479 0 . 24H36 0 .18697 0 .2 2031 0 .17 119 0 19546 0 . 15846 o . 17542 0 .14547 o . 15740 0 .13356 0 .14098 DELT" 120.00000 DE L A = 1O.0OO00 DELX = 1340. OUT SECT ION NO - 9 OUT AREA OUT DISCH TOTAL TIME . SECONDS 0.0 0. 0 0. 0.0 0 . 0 120. 0.0 0. 0 240. 0.15O09 0 . 164 GO 360. 0.17634 0 . 2035G 480 . O.73567 1 . 35950 600 . 1.91512 4 . 78489 720. 3 07008 9 01454 840. 3.99706 12 88885 960. 4.5R745 15 . 52472 1080. 4 95397 17 . 22 1 39 1200. 5.11393 17 . 97444 1320. 5 05674 17 70522 1440 . 4 83385 16 . 65590 1560. 4 5095R 15 . 16726 1680. 4.13753 13 . 50007 18O0. 3 74475 1 1 . 79889 1920. 3 36189 10. 1965 1 2040. 3.00503 8 . 75595 2 160. 2.68193 7 50000 2280. 2 39546 6' 44024 2400. 2 14 234 5 55136 2520. 1.92060 4 80324 2640. 1 72775 4 17595 2760. 1 557 39 3 64042 2880. 1 40446 3 . 17478 3000. 1 26954 2 778 12 3 120. 1.14R0? 2 43532 3240. 1.03724 2 13057 3360. 0 93R65 1 86890 3480. 0.B4R43 1 . 63882 3600. 0 7696R 1 .44141 3720 0 . 6967(1 1 26650 3840 O. 63363 1 1 155 1 3960 0 576 14 0 984RO 4080 0.524 35 0 . 8G776 4 200 O 17926 0 7 7018 4320 0 4 38 3H 0 . 68400 4440 0 400H? 0 . 6054 2 4560 0.3GR33 0 , 54248 4680 0.3 3872 0 .485 10 4800 0.3 1193 0 .43319 4920 O 28G56 0 388 1 1 5040 0.26 503 o .35019 5 160 0 2-! 559 0 .31597 5280 XN1= 0.0500 T0LR=.0000010 XN2 = 0.0500 IN SECTION NO = 1 IN AREA IN 1 O .0 0.0 0 .0 0 0 0 .0 0.0 0 .0 0.0 0 .0 0.0 0 .0 O.O 0 .0 0.0 0 .0 O.O 0 .0 0.0 0 .0 0.0 0 0 0.0 0 .0 0.0 0 .0 0 0 0 .0 0.0 0 .0 O.O 0 .0 O.O 0 .0 0.0 0 .0 0.0 0 0 0.0 0 .0 O 0 0 0 0.0 0 0 0.0 0 .0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0 0 0.0 0. 0 0.0 0 0 0.0 0 0 0 0 0 o 0.0 0 0 0.0 0 0 0.0 0. 0 O.O 0 0 0 0 0 0 0.0 0 0 0.0 0. 0 0.0 0. 0 0.0 0. 0 O 0 0. 0 0.0 0. 0 0.0 0. 0 0.0 TRIBUTARY F DELT* 170 00000 DELA* 10.00000 OUT SECT ION NO * 2 OUT AREA OUT DISCH 0 .0 0 .0 0 .001OB 0 .002 71 0 .007 7.1 0 .00585 0 . 1 1565 0 20139 0 . 63468 1 .93635 1 .59399 6 .50O69 1 .88059 8 .08706 1 85B5 1 7 . 9G 1 70 1 .7374 1 7 28679 1 .57 407 6 .39446 1 .397B1 5 43953 1 .20683 4 .50323 1 .02372 3 .62B22 0 .73563 2 3547 1 0 53 157 1 .53042 0 .39455 1 .02762 0 2996 1 0 .71207 o 232 1 1 0 50627 0 18276 o .37012 0 146 IB 0 . 27432 0 1 1844 0 . 20807 0 09726 0 . 158B7 0 OB057 0 . 125 14 0. 06743 0 .09857 0 05708 0 07764 0 04857 0 063B2 0 04 157 0 0525 1 0 035B 1 0 .04321 0. 03 107 0 03556 o. 027 16 0 02926 0 02389 0 02459 0 07 105 o 0? 130 0 0 1859 0 01844 0 . 01646 0 01597 0 01461 0 01383 0. 0 1 30? 0 01 198 0 01163 0 01037 0 01O-14 0 00898 0 . O0940 0 007 7 8 0 008 50 0 0067 3 0. 007 7 3 0 0058 3 0 00705 0 00505 0 . OOG 1 7 o 004 3 7 0. 00594 0 00395 DELX* 1800. TOTAL TIME . SECONDS O. 120. 240. 360. 480. 600. 720. 840. 960. 1080. 1200. 1320 1440. 1560. 1680. 1800. 1920 . 2040. 2 160. 2280. 2400. 2520. 2640. 2760. 2880. 3000. 3 120. 3240. 3360. 3480. 3600. 3720. 3840. 3960. 4080. 4200. 4320. 4440. 4560. 4680. 4 800 . 4920. 5040. 5 160. XN1 = 0.0500 T0LR=.0000100 XN2 = 0.0500 MAIN CHANNEL DELT = 120 OOOOO D F. L A = 10.00000 DELX = 2680 IN SECTION NO = 1 OUT SECTION NO = 2 IN AREA IN DISCH our ARFA OUT DISCH TOTAL TIME 0. 0 0. 0 0. o 0. 0 O. 0 0 0. 0 0. 00-1 1 8 0 . 0029 1 120. 0 0 0. 0 0 00803 0. 00655 240. 0. 0 0. 0 0. 036.16 0. 04775 360. 0. o 0. 0 0 3309 1 0. R7937 480 0. 0 0. 0 0 99902 3 . 799 IB 600. 0. 0 0. 0 1 023 1 7 3 . 9 16 14 720. 0. 0 o. 0 0 799:19 2 . B3609 840. 0 0 0 0 0 6 1835 2 . 02 153 960. 0. 0 o. 0 0. 4B670 1 . 47016 1080. 0. o o. 0 0. 3 a no 7 1 . 09O15 1200. 0 0 o o 0 3 1537 O. 8 2 305 1320. 0. o o o 0. 2 58 59 O 63405 1440. 0. o 0 0 0. 2 14.13 0. •19309 1560. 0 0 0 0 0. 17 949 o 390 1 2 1680. 0 o 0 0 0. 15 169 0 3 104B 1800. o 0 0 o o 1 2 9 10 0 . 25224 1920. 0 0 0 0 0 1 1075 0 20493 2040 0 0 0 0 0. 09568 o 1682 1 2 160 0 .0 0 0 o 08 3(19 0 . 14069 22RO 0 0 0 0 0 07 2 55 o 1 176 7 2400 0 0 0 0 0 06 3 7 3 0 09842 2520 0 .0 0 0 0 056 35 0 08 250 2640. 0 0 0 o 0. 04 996 0 07 134 2760. 0 0 0 0 0 04 4 4 3 o 06 169 2B80 0 0 o .0 0 03966 o 05334 3000 0 o 0 0 o 0355 3 0 04612 3 120 0 .0 0 0 0 ,03195 0 039RB 3240 0 .0 0 0 0 028B7 0 03448 3360 0 0 0 .0 0 02620 0 .02982 3480 0 0 0 .0 0 02 38 3 o 02639 3600 0 .0 0 .0 0 .0217 1 0 02373 3720 0 .0 0 .0 0 .01980 0 .02133 3840 0 o 0 .0 o .0IBOB 0 019 17 3960 0 o 0 0 0 O 1 6 5 4 0 .01723 4080 0 .0 o .0 0 015 1 5 o 01549 4 200 0 .0 o .0 o 0 1390 0 01392 4320 0 .0 0 .0 0 0 12 78 o .01252 4440 0 o 0 .0 o .01178 0 .01125 4560 0 .0 0 .0 0 O 108 7 0 01011 4680 0 0 0 .0 0 .01006 o .00909 4800 0 .0 0 .0 o .009 3 2 0 .008 1 7 4920 0 o 0 .0 o .0O86 7 0 .007 35 5040 0 0 o .0 0 .00807 0 .00660 5160 TOLR=.0000100 XN2 = 0.0500 IN SECT ION NO = 2 IN AREA IN DISCH 0. 0 0. 0 0. 004 18 0. 00291 O. 00803 0. 00655 0. 03646 0 04775 0. 3309 1 0. 87937 0. 99962 3 . 799 18 1 . 023 17 3 . 91614 0. 79939 2 . 83609 0. 61835 2 . 02 153 0. 48670 1 . 47016 0. 38907 1 . 09015 0. 3 1537 0. 82305 • 0. 25859 0. 63405 o. 2 1443 0. 49309 o. 17949 0. 39012 0. 15169 0 3 1048 0. 12910 o. 25224 0. 1 1075 o. 20493 0. 09568 o. 1682 1 0 08309 0. 14069 0. 07255 o. 1 1767 0. 06373 0. 09842 0. 05635 0. 08250 0. 04996 0. 07 134 0. .04443 o 06 169 0. .03966 o. 05334 0 .03553 o. 046 12 0 .03195 o. 03988 0 .02887 0. 03448 0 02620 0. 02982 0 02383 0 02639 0 .02171 0 02373 0 01980 0 02133 0 0 1 BOB o 01917 0 .01654 0 01723 0 .01515 0 01549 0 .01390 0 01392 0 .01278 0 01252 0 .01178 0 .01125 0 .01087 0 .01011 0 .01006 0 .00909 0 .00932 0 .00817 0 .00867 0 O0735 0 .00807 0 .00660 0 .00754 0 .00594 DELT= 120.00000 DEL*"- 10 OOOOO D E L X = 1 170 our sFcnoN NO = 3 our AREA OUT DISCH TOTAL TIME 0.0 0 0 O 0.00080 0. 00030 120 0.00253 0. 00096 240 0.01492 0. 0082 1 360 0.21863 O . 270 15 480 0.94912 1 . 89668 600 1.43405 3 26 175 720 1.53633 3 5755B 840 1 .45 191 3 . 3 1559 960 1.29807 2 86 198 1080 1.13007 2 . 3B507 1200 0.97 14 1 1 95584 1320 0.83103 1 59520 1440 0.71003 1 . 29820 1560 O 60811 1 057 34 16BO 0 52254 O 863 16 1800 0.45108 0. 7 1076 1920 O.39 1 13 0 58664 2040 0 34049 o 48852 2 160 O 298 15 0 408 5 1 2280 O.26206 0. 34497 2400 0.23138 o 29095 2520 0.20476 0 24831 2640 0. 182 15 0 2 127 1 2760 0.16290 0 18242 2880 0. 146 14 0. 15B34 3000 0. 13 14 2 0 13803 3 1 20 0.11851 0 12023 3240 0. 1072 1 0 10465 3360 0 09719 0 .09166 3480 0.0BB29 0 OB 128 3600 0 OBOlfl 0 072 1 7 3720 0 0736 1 0 064 15 3840 O.06 7 55 0 .05708 3960 0.06220 0 0508 3 40B0 0.057 17 0 .04 531 4 200 0.05314 0 .041 14 4320 0.049 15 0 .03742 4440 0.04519 0 .03102 4560 0.04213 0 .03089 46BO 0.03906 0 .02803 4 800 0 036 2 5 0 .02542 4920 0.03 369 0 02304 5040 0 03136 0 .02007 5 160 0 02923 0 .01889 5280 TOLR=.0000100 XN2 = O.0500 IN SECTION NO - 3 IN AREA IN I DISCH O. 0 0. 0 0. 00080 0 00030 0. 00253 0. 00096 O. 01492 0. 00821 0. 2 1863 0. 27015 0. 94912 1. 89668 1 . 43405 3 . 26 175 1 . 53633 3 57558 1 . 45191 3 . 3 1559 1 . 29807 2 . 86 198 1 . 13007 2 38507 0. 97 14 1 1 . 95584 0. 83 103 1 . 59520 0. 7 1003 1 . 29820 0. 608 1 1 1 . 05734 0 52254 0. 863 16 o 45 108 O. 7 1G76 0. 39 1 13 0. 58664 0. 34049 o. 48852 0. .29815 o. 4085 1 0 26206 0. 34 497 0 23138 0 29095 0 . 20476 0. 2483 1 0 . 182 15 o. 2 127 1 0 .16290 o 18242 0 146 14 o 15834 0 . 13 142 o 13803 0 . 1 1851 0 12023 0 .107 21 o .10465 0 .09719 0 .09166 0 .08829 0 .08128 0 .08048 o .07 2 1 7 0 .0736 1 o .06415 0 .06755 o 05708 0 .06220 0 .O5083 0 .05747 0 04 53 1 o .053 14 0 .04 1 14 0 049 15 0 03742 0 .04549 0 .03402 0 .04213 o .03089 0 .03906 0 .02803 0 .03625 0 02542 0 .03369 0 .02 304 0 03 136 0 .02087 DEL T ='1 20 .00000 DEI. A = 10.00000 DELX = (JUT SECT I ON NO - 4 OUT AREA OUT DISCH TOTAL TIME 0 O 0 0 0. 0 000RO O.0OO30 120. 0 002 36 0 00090 240. 0,014/R 0.OOR 1 1 360. O.21R03 O 269 19 480 . 0 94761 1 89767 600. 1 43293 3 2584 7 720. 1 53607 3.57478 840. 1 .45? 14 3.3 1679 960. 1.29R50 2.R6376 1080. 1 13057 7 38646 1200. 0 97190 1 .957 16 1320. 0.8 3 150 1 59637 1440. 0.71046 1 799? 1 1560. O.60H4R 1 05R19 1680 . 0.52286 O.B63R7 1800 0 45136 O. > 1136 1920. 0 39 1 39 0 587 14 2040. O.3407O 0.4 8R94 2 160. 0 2MH35 0.40BH6 2280. 0.26773 0 34577 2400. 0.23 15? 0 29 12 1 2520. 0.204 90 0.24853 2640. 0 18727 0 2 1290 2760 O 16301 0 18258 2880 0. 14674 0. 15847 3000 0 13 15 1 O 138 16 3 120 0 1 1R59 0 17034 3240 0.10727 0.10474 3360 O.09776 0.0917 4 3480 0.08R36 O OS 136 3600 0.08054 0 07223 3720 0.07366 0.064 20 3840 0 067 59 0.057 13 3960 0.06224 0.0508 8 4080 0.057 5 1 0.04535 4 200 0.0531H 0.04117 4320 0 04918 0.03746 44 40 0 04 55? 0.03405 4560 0.04?16 0.03092 4680 0.03909 0.0?806 4 800 O.03678 0.02544 4920 0.0337 1 0.02306 5040 0 03138 0 02088 5 160 TOLR* OOOO100 XN2 = 0.0000 DELT = 120.00000 nn A= 10.00000 DELX* IN SECTION NO OUT SECTION NO IN AREA IN DISCH OUT ARE A our DISCH TOTAL TIME 0 0 0. 0 0 .0 0 0 0 0 00080 0 00030 0 .003 7 4 0 OO 1 4 2 120 O 00236 0 00090 0 .007 7 7 0 00338 240 0 O 1-178 0 008 1 1 0 07038 0 06038 360 O 2 1803 0 269 19 0 .49507 O 803-19 480 0 9-176 1 1 . 89267 1 6225 1 3 84096 600 1 43293 3 25847 2 23200 5 8637R 720 1 53607 3 57478 2 359 17 6 30738 840 1 452 14 3 . 3 1629 2 766 7 2 5 9R476 960 1 . . 29850 2 86326 2 08746 5 36257 1080 1 .13057 2 . 38646 1 87665 4 65594 1200 O 97 190 1 95716 1 66 360 3 96954 1320 '0 83 150 1 59637 1 46085 3 343 1 1 1440 0 7 1046 1 2992 1 1 27 167 2 7 84 37 1560 0 60848 1 058 19 1 09809 2 29556 1680 0 52286 0 86307 0 940-16 1 87370 1ROO 0 45136 0 7 1 136 0 79984 1 51702 1920 0 39 139 0 587 14 0 6 7 5 12 1 2 154 3 2040 0 34070 0. . 48894 0 5707 1 0 97247 2 160 0 29835 0. 40886 0 486 IO O 78459 2280 0 26223 0 34527 0 4 1 768 O 64035 2400 0 23 152 0 29 12 1 0 36038 0. 52706 2520 0 . 20490 0. 24853 0 3 1448 0 4 3812 2640 0 18227 0 2 1290 0 2 7 4 99 0 36773 2760 0 16301 0 18258 0 24 16-1 0 30902 2880 0 14624 0 15847 0 2 14 6 3 0. 26385 3000 0 13 15 1 0; .13816 0 1907 4 0 2 7674 3 120 0 1 1859 0 12034 0 17024 0 19396 3240 0. 10727 0 10474 0 15254 0 167 15 3360 0 09726 0 09 174 0 1366 7 0 14527 3480 0 08836 0. 08 136 0 1 2 36 1 0 12776 360O 0 08054 0 07 223 0 1 1275 0 1 1 160 3720 0 07366 0 06420 0 IO? 36 0. 09797 3840 0 067 59 0 057 13 0 097B2 0 08656 3960 0 06224 0 05088 0 Ofl-149 0 07685 4080 0 0575 1 0 04535 0 07 7 14 0 06876 4 200 0 053 18 0 04117 0 07 124 0 06 138 4320 0 049 18 0 03746 •0 0660? 0 . 05579 4440 0 04 552 0 03405 0. 06 1 30 0 04978 4560 0 04216 0 .03092 0. 05703 0 O4 4R0 4680 0 03909 0 02806 0 052 75 0 0403 1 4 800 0 036 28 0 02514 0. 0-1789 0 036 25 4920 0 0337 1 0 023O6 0 .04 429 0 03290 5040 0 03138 0 02088 0 04 103 0. 02987 5 160 0 02925 0 0189 1 0 038O6 0 027 10 5280 SECONDS T0LR=.0000100 XN2- 0.0500 DELT = 120.00000 DF.LA- 10.00000 DELX = 1 IN SECTION NO = OUT SECTION NO IN AREA IN DISCH OUT AREA OUT DISCH TOTAL TIME 0.0 0.0 0.0 0.0 0 0.00374 0.00142 . 0.00649 0.0025 1 120 0.00777 0.00338 O . 0 114 3 0.00585 240 0.07038 0.06038 0. 1 1275 0. 1 1229 360 0.49507 0 80349 0.72588 1.33608 480 1.62251 3.84096 2.20971 5.7 8609 600 2.23200 5.86378 2.93262 8.46809 720 2.359 17 6.30738 3.07644 9.03980 840 2.26672 5.98476 2.97920 8.65327 960 2.08746 5.36257 2.776 12 7.86208 1080 1.87665 4.65594 2.528 10 6 . 92575 1200 1.66360 3 96954 2 26603 5 . 98234 1320 1.46085 3 343 t1 2.00625 5.09035 1440 1 .27167 2.78437 1 7570C) 4.2 7006 1560 1.09809 2.29556 1 .52206 3 53347 1680 0.94046 1.87370 1.30558 2.88407 1800 0.79984 1 .5.1702 1.10797 2.3232 1 1920 0.67542 1 .2 1543 0.92935 1.8442 1 2040. 0.57071 0.97247 0.77507 1 45642 2 160. 0.486 10 O.78459 0.65252 1 . 16066 22BO. 0.41768 0 64035 0 55450 0.93569 2400. 0.36038 0 52706 0 4 7591 0.7631 1 2520. 0 31448 0.4 38 12 0.41 176 O.62788 2640. 0.27499 0.36773 0.35812 0 52269 2760. 0.24164 0.30902 0.3 13 15 0.43556 2880. 0.21463 0.26385 0 27589 0.36931 3000. 0.19074 0.22624 0.24469 0.31439 3120. 0.17024 0.19396 0 24 704 0.26764 3240. 0.15254 0. 167 15 0 19289 0.22961 3360. 0.13667 0.14527 0.17334 0.19884 34B0. 0.12361 0. 12726 0.15692 0.17320 3600. 0. 1 1225 0.11 160 0.14083 O 15101 3720. 0.10236 0.09797 0.1268 7 0. 13176 3840. 0.09282 OOB656 O 11545 0 11601 3960. 0.08449 0.07685 0.10589 O.10283 4080. 0.07714 0.06826 0.09679 O.09119 4 200. 0.07124 0.06138 0.08858 O.OB 16 1 4320. 0.06602 0.05529 0.08 132 O 073 14 4440. 0.06130 0.0497B 0.07479 0.06553 4560. 0 05703 0.04480 0.06894 0.05869 4680. 0.05225 0 0403 1 0.06369 0.05257 4800 . 0.04789 0.03625 0.05898 0.04707 4920. 0.04 4 29 0.03290 0 05488 0.04276 5040. 0.04103 0.02987 O 05069 0.03886 5160. 0.03806 0.02710 O 04687 0.03530 5280. SECONDS ho TOLR=.0000100 XN2 = 0.0500 IN SECTION NO = G IN AREA IN DISCH 0. 0 0. 0 0. 00649 0. 0025 1 0. 01143 O. 00585 0. 1 1275 0. 1 1229 0. 7258R 1 . 33608 2 . 2097 1 5. 78609 2 . 93262 8 46809 3 . 07644 9 03980 2 . 97920 8 65327 2 77612 7 . 86208 2 52810 6. 92575 2 . 26603 5. 98234 2 . 00625 5 . 09035 1 . 75700 4 . 2 7006 1 52266 3 . 53347 1 30558 2 88407 1 10797 . 2 . 3232 1 0 92935 1 . 8442 1 0. 77567 1 . 45642 0. 65252 1 . 16066 0 55450 0. 93569 0 .47591 0. 763 1 1 0. .41 176 0 62788 0 .358 12 0 52269 0 .31315 0. 43556 0 .27589 0. 3693 1 0 .24469 0 3 1439 0 .21704 0 26764 0 .19289 0 2296 1 0 .17334 0 19884 0 .15692 O 17320 0 .14083 0 15 101 0 .12687 0 13176 0 .11545 0 .11601 0 .10589 0 10283 0 .09679 0 .09119 0 08858 0 .08 161 0 OS 132 0 .07314 0 .07479 0 06553 0 .06894 0 .05869 0 .06369 0 .05257 0 .05898 0 .04707 0 .054 88 0 .04276 0 .05069 0 .03886 0 .04687 0 .03530 DE L T = 120.OOOOO DE L A = 10.00000 DELX = 420. OUT SECTION NO = 7 OUT AREA OUT DISCH TOTAL TIME . SECONDS 0.0 0. 0 0. 0 o 0. 0 120. 0 0 0. 0 240. 0 1 1970 0. 12 187 360. 0 38402 0. 57288 480. 1 40297 3 . 17039 600. 2 48 1 25 6 75427 720 . 3 05258 8 . 94494 840. 3 19004 9 . 49 14 1 960. 3.08874 9 OR872 1080. 2 83735 8 09749 1200. 2.556 31 7 02901 1320. 2 28364 6 . 0437 1 1440. 2 02619 5 157 17 1560. 1 786 1 1 4 . 36370 1680. 1 56232 3 . 65559 1800. 1 35553 3 0309 1 1920. 1 . 1666 2 2 . 48739 2040. O 99664 2 0228 1 2 160. 0 84766 1 . 63689 2280. O 7 2 207 1 32699 2400. 0 6 1874 1 . 08 148 2520. 0 53382 0 88876 2640. 0 . 464 19 0 7384 1 2760 O 40609 0 6 1593 2880 O 35698 0 52048 3000 0 3 1590 0 44088 3120 0.28065 o 3777 1 3240 0.25051 0 32463 3360 0.22425 0 .2 7 900 3480 0 20 107 0 24 250 3600 0.18202 0 . 2 1251 3720 0 16508 0 . 18583 3840 0.14 960 0 16309 3960 0 13568 0 . 14391 4080 0.12392 0 . 12769 4 200 0 11378 0 . 1 1372 4320 0 10488 0 10144 4440 0 096 7 6 0 09 1 15 4560 0 089 14 0 08227 4680 0 08211 0 .07 406 4 800 0 07 568 0 .06656 4920 0.06998 0 0599 1 5040 0 06528 0 .05442 5 160 O.06101 0 .04945 5280 TOLR=.0000100 XN2 = 0.0500 IN SECTION NO = 7 IN AREA IN DISCH O 0 0. 0 0. 0 0. 0 0. 0 0. 0 0. 1 1970 0. 12 187 0. 38402 • 0. 57288 t. 40297 3 17039 2 48 125 6 75427 3 05258 8 94494 3. 19004 9 49 14 1 3 08874 9 . 08872 2 R3735 8 09749 2 . 5563 1 7 . 02901 2 . 28364 6 . 0437 1 2 . 02619 5 . 157 17 1 7861 1 4 . 36370 1 . 56232 3 . 65559 1 . 35553 3 0309 1 1 . 16662 2 . 48739 0 99664 2 0228 1 0. 84766 1 . 63689 0. 72207 1 . 32699 0 61874 1 OB 148 0. 53382 0. 88876 0. 464 19 0 73B4 1 0 40609 0 6 1593 0 35698 0 52048 0. 31590 0 44088 0 28065 0 3777 1 0 2505 1 o: : 32463 0. 22425 0 27900 0 20107 0 24250 o. 18202 o 2 1251 0 16508 0 18583 0. 14960 0. 16309 0 13568 0 1439 1 0 12392 0 12769 0 1 1378 0 1 1 37 2 0. 10488 0 10144 0. 09676 0 09 1 1 5 0 089 14 0 08227 0 (182 1 1 0 07 406 0 07568 0 06656 0 06998 0 0599 1 0 06528 0 05442 0 06 101 0 04 94 5 DELT = 120.00000 DELA- 10.00000 DELX = 1. OUT SECT ION NO = 8 our ARFA our DISCH TOTAL TIME O.O 0 . 0 O 0.0 0 0 120 0.0 0 0 240 0.11923 0 12 122 360 0 38382 0 57249 480 1 40150 3 16607 600 2 47972 6 .74868 720 3 05206 8 94 289 840 3.1902B 9 49239 960 3 08937 9 09 1 2 1 1080 2 B3808 8 .10029 1200 2.55701 7 03 158 1320 2.28431 6 04603 1440 2 02683 5 . 15932 1560 1 .78673 4 36570 16B0 1 .56292 3 .65746 1BOO 1 356 1 1 3 03262 1920 1.16 7 18 2 ,4BB96 2040 0 997 1 7 2 .02423 2 160 0 848 16 1 638 13 2280 0 7 2 251 1 32804 2400 0.6 19 12 1 08234 2520 0.534 13 0 . 8B946 2640 O.46447 0 7 3899 2 760 O 4063? 0 6 1642 28BO 0.357 19 0 .52089 3 OOO 0.31607 0 .44 122 3 120 0.?8082 0 .37800 3240 0 2 5065 0 32488 3360 O 22439 0 .27922 3480 0.20119 0 .24269 3600 0 1 82 1 2 0 .2 1 267 3720 0.16517 0 .18598 3840 0 14969 b .16322 3960 0 13576 0 .14402 40BO 0 12399 0 . 12779 4 200 0.11 385 0 . 1 1380 4320 0.10493 0 .10151 4440 0 096B1 0 09 1 22 4560 0 O8920 0 .08233 4680 0 08 ? 16 0 074 1 2 4 BOO 0 07573 0 .06662 4920 0 07002 0 ,05996 5040 0.06 5 31 0 .05446 5160 0 . 06 104 0 .04948 5280 TOLR=.0000100 XN2 = 0.0500 DF I. I= 120.00000 DELA = 10.00000 DELX = IN SECTION NO = fl OUT SECTION IN AREA IN DISCH OUT ARE 0. 0 0. 0 0 0 0. 0 0. 0 0.00796 O. 0 0. 0 0.0064 7 O. 1 1923 0. 12 122 0.15983 O 38382 0 57249 0 65972 1 . 40150 3 . 16607 2.09052 2 . 47972 6 . 74868 3 23884 3 . 0520G 8 . 94289 3.77463 3 . 19028 9 . 49239 3 81782 3 . 08937 9 . 09 1 2 1 3 59669 2 . 83808 8 . 10029 3.226H7 2 . 55701 7 . 03 158 2 . 85329 2 . 2843 1 6 . 04603 2.5 1669 2 . 02683 5 . 15932 2 2 1175 1 . 78673 4 . 36570 1 93 17? 1 . 56292 3 65746 1 68390 1 . 356 1 1 3 . 03262 1 .4564 3 1 . 167 18 2 . 48896 1.7520? 0. 997 17 2 . 07423 1 06975 0. 848 16 1 . 638 13 0 9 1055 o. 72251 1 32804 0 77546 0 61912 1 . 08234 O 664 3 3 0 .53413 0 88946 0.57 340 0 . 46447 0 73R99 O.499H1 0 .40632 0 6 1642 O 43678 0 .357 19 0 .52089 0 385 1 5 0 .31607 0 44 122 0.3 4007 0 .28082 O .37 800 O 303 4 7 0 .25065 0 .32488 0 2 7010 0 .22439 0 27977 (). 24 16 4 0 .20119 0 . 24269 0.2 1790 0 . 182 12 0 2 1267 0.19080 0 .16517 0 18598 0. 1 78 18 0 .14969 0 . 16327 0. 1627.0 0 .13576 O .1140? 0. 1 17 35 o .12399 0 .17779 0 13 4 2 1 0 .11385 O .11380 O. 17 287 0 .10493 0 .1015 1 O.11789 0 .09681 0 .09 172 0.10470 0 .08920 0 08733 0 O97O0 0 .08216 0 .07 412 0.089 7 8 0 .07573 0 .0666 2 0 . (18773 0 07002 0 05996 O.07 590 0 .06531 0 054 46 0 0707 3 0 06 104 0 .04948 0 00 599 OUT DISCH TOTAL TIME . SECONDS 0.0 0. 0.00 1 1 7 170. 0.00750 240 . 0 17758 360. 1 . 17787 480 5.37782 600. 9.69 162 720. 11.97573 840. 1?.10894 960. 11.17787 lOBO. 9.64 750 1200. 8 15875 1320. 6.BS400 1440. 5 7 9 14 8 1560. 4.85058 1680 . 4.03487 1800. 3 3 79 50 1920. 7.7760? 2040. 7.21 '.'.53 2 160. 1 .79454 2280. 1 . 45589 2400 . 1 18890 2520. 0 97857 2640. 0 8 1350 2760 . 0 67956 2880. 0.5 7 506 3 OOO . O 4877 1 3 120. 0 4 1788 3240. 0.35912 3360. 0.3090? 3480 . 0.76899 3600. 0.73588 37 20. 0.70646 3840 . 0 18 13 1 3960 0.15999 4080 0 14 189 4 200 0. 17674 4320 O. 1 1 249 4440 0.10119 4560 0.09143 4680 0.08 24 3 4800 0.07 4 70 4920 0.06688 5040 0.0607 8 5 160 0.05575 5280 TOLR^.0000)00 XN2- 0.0500 IN SECTION NO = 9 IN AREA IN DISCH 0. 0 0. 0 0. 00296 0 001 12 0. 0064 7 0. 00250 O. 15983 0 . 17758 0. 65972 1 . 17787 2 09052 5 . 37282 3 . 23R84 9 . 69 162 3 . 77463 1 1 . 92523 3 . 8 17B2 12 . 10894 3 . 59669 1 1 . 17287 3 . 22687 9. 64250 2 85329 8 . 15875 2 . 5 1669 6 . 88400 2 . 21 125 5 . 79 148 1 . 93472 4 . 85058 1 . 68390 4 . 03487 1 . 45643 3 . 32950 1 . 25202 2 . 72662 1 . 06925 2 2 1553 O 9 1055 1 . 79454 O. 77546 1 . 45589 0. 66433 1 . 18890 o 57340 - 0. 97857 0 .49981 0 8 1350 0 .43628 0 67956 0 .38515 0 57506 0 .34007 0 4877 1 0 .30347 0 . 4 1788 0 .27010 0 .35912 0 .24164 0 .30902 o .21790 0 26899 0 .19686 0 .23588 0 .17818 0 .20646 0 .16220 o .18131 0 14735 0 .15999 0 . 13421 0 .14189 0 . 12287 o .12624 0 .11289 0 .11249 0 .10470 0 .10119 o .09700 0 .09143 0 .08928 0 .08243 0 .08223 0 .07420 0 .07596 o .06688 0 .0707 3 0 .06078 0 .06599 0 .05525 D E L T = 120. OOOOO DELA- 10.00000 DELX = OUT AREA OUT DISCH TOTAL TIME 0.0 0 0 0. 0.00585 0.002 2? 1 20 . 0.01014 0.004 98 240. 0 195 16 0 23366 360. 0.90531 1.78141 480. 2 70179 7.57633 600. 3.93847 12.63388 720 . 4 . 45237 14.9078 1 840. 4.41177 14 726.16 960. 4.08133 13.25550 1080. 3.5997 2 1 1 . 18567 1200. 3.13854 9.28668 1320. 2 7 3981 7 72249 1440. 2.39103 6 42403 1560. 2.07946 5.33576 1680. 1 80128 4.41250 1800. 1.55288 3.62654 1920. 1 33291 2 96440 2040 . 1.13788 2.40693 2 160. 0.96959 1.95103 2280. 0.82649 1 .5R382 2400. 0.70892 1.29553 2520. 0.6 1268 1 067 7 3 2640. 0.53351 0.88805 2760. 0.46625 0 74275 2880. 0 4 1241 O.62925 3000. 0.36408 0.53423 3120. 0.32462 0 . 45778 3240. 0.28955 0.39337 3360. 0 25858 0 33884 3480. 0.23385 0.29530 3600. 0.2116? O.25910 3720. 0. 19 t 20 0 22697 3840 0.17 369 0.19940 3960 0. 1588 1 O 17597 4080 0.14444 0.15599 4 200 0.13190 0 13869 4320 0.1?0B6 0 12348 4440 0.1119 3 0.11116 4560 0.10423 0 . 10054 4680 O.096 4 1 0.09075 4800 0.088 7 4 0 08180 4920 0.08189 0.07381 5040 O.0"6 15 0.06 7 1 1 5 160 0.07093 0.06102 5280 , SECONDS TOLR*.0000100 XN2* 0.0500 Df. LI- 120.00000 DTLA- 10.00000 DELX* 960. IN SECTION NO 10 OUT SECTION NO 1 1 IN AREA IN DISCH OUT ARE A OUT DISCH TOTAL TIME 0. 0 O.O 0 0 0 0 0 0. 00585 0.00222 0 0 0 0 120 0. 01014 0.OO49B O.0557 3 O. 04355 240 0. 19546 0.23366 0. 1854 3 0. 2 1 7H8 360 0 9053 1 1.78141 0 494 33 0. 80 195 4 80 2 . 70179 7.57633 O . 7 1 4 1 2 1 . 307 97 600 3 93847 12.63388 1 7854 4 4 36 154 720 4 . 45237 14.90781 2.9837? 8 . 6697 3 840 4 . 4 1177 14 72626 3 793 17 12 00364 960 4 . 08 133 13.25550 4.17089 13 . 4 7 766 1080 3 . 59972 1 1 . 18567 4.08734 13 . 78 168 1200 3 . 13854 9.28668 3 82986 12 16 132 1320 2 . 7398 1 7.72249 3 4841 1 10 6997? 1440 2 . 39103 6.42403 3.17800 9 . 74.178 1560 2 . 07946 5.33576 7.797 3 7 7 . 974 5G 1680 1'. 80128 4.41250 2.48377 6 76 166 1800 1 . 55288 3.62654 7.70017 5 75270 1920 1 . 3329 1 2.96440 1.94725 4 87580 2040 1 . 13788 2.40693 1.7O901 4 . 1 1 759 2 160 0. 96959 1.95103 1 .499H5 3 . 46322 2280 0. 82649 1.58382 1 31768 2 . 90493 2400 0. 70892 1.29553 1 . 1464? 2 . 4 308 4 2520 0. 6 1268 1.06773 1.00099 2 . 03437 2640 0. 53351 0.88805 0 8755 1 1 70669 2760 0. . 46625 0.74275 0 7687 1 1 43897 2880 0 4 124 1 0.62925 0.67579 1 2 1630 3000 0 36408 O 53423 0 59868 1 . 03590 3 120 0 32462 0 45778 0 53 16.1 0 883BO 3240 0 . 28955 0.39337 0 47484 0 76085 3360 0 25858 0.33884 0 4 7603 0 65797 3480 0 23385 0.29530 0.38773 .o 5694 1 3600 0 2 1162 0.25910 0 34 4 95 0 497 1 7 3720 0 .19120 0.22697 0.3 13 19 0 43564 3840 0 .17369 0.19940 0 78 145 O . 384 40 3960 0 . 1588 1 0. 17597 0 2580 1 0 33889 4080 0 .14444 0.15599 0 . 73683 0 30055 4 20O 0 .13190 0.13869 0.21711 0 . 26776 4320 0 .12086 0. 12348 0. 199 15 0 .7 394 7 4440 0 .11193 O. 11116 0. 18 7 5 4 o ? 1333 4560 0 .10423 0.10054 0 16783 ~ o 19017 4680 0 .09641 O.0907 5 0.1555? 0 . 17 177 4 800 0 .08874 0.08 180 0 14-159 0 . 156 20 4920 0 08 189 0.07381 0 13-130 0 .14 209 5040 0 076 15 0.06711 0. 17470 0 . 17876 5 160 0 .07093 0 06 102 0 11598 • 0 1 1674 5280 SECONDS NJ TOLR=.0000100 XN2- 0.0500 DFLT = 120 onooo IN SECTION NO * IN AREA 0.0 0.0 0.05573 0. 185 13 0.49433 0.71412 1.78544 2.98322 3.79317 4.12089 4.08734 3.82986 3.4844 1 3.12800 2 79237 2 . 48327 2.20012 1 94225 1 .7096 1 1.49985 1.31268 1.14642 1.00099 . 0.87551 0.76871 0.67579 0.59868 0.53164 0. 47484 0.42603 0.38223 0.34495 0.31319 0. 28445 0. 25861 O. 23683 0.21711 0. 199 15 0.18254 O.16783 O.15552 O.14459 O.13436 O.12470 0 1 1598 IN DISCH 0.0 0.0 0.04355 0.21788 O.80195 1.30797 4 36154 8 . 66923 12.00364 13.42766 13.28168 12.16132 10.69922 9 . 24478 7.92456 6.76166 5 . 75270 4 .87580 4.11759 3.46322 2 . 90493 2.43084 2.03437 1 . 70669 1.43897 1.21630 1.03596 O.88380 0.76085 0.65797 0.5694 1 0.497 17 O.43564 O.38440 0.33889 O.30055 0.26776 0.23947 0.21333 O.19017 O.17 127 0 15620 O.14 209 0. 12876 O. 1 1674 OUT SECTION NO OUT AREA 0 0 0.004IO 0.00254 0.21026 0 78368 1 30607 1 .2 2 166 1.50684 2.23874 3.01782 3.56526 3.82622 3.84001 3 68742 3 44643 3.17108 2 89 183 2.62234 2.36673 2 . 12784 1 90704 1 . 705 10 1 . 52134 1 . 35536 1.20664 1.07 57 2 O.95807 0.855 16 O 764H0 0 68554 O.6 1730 O 556H6 O 50364 0 45753 0.41771 0.38052 O 34830 0 32012 0 . 29498 0.2718? 0.2504 0 0.?3158 O.?149 1 0 19993 0 18 6 13 DEI A* 10.00000 DE L X = 1090 12 OUT DISCH TOTAL TIME . SECONDS 0.0 0. 0.00156 120 . 0.0009 7 240. 0.25697 360. 1 4 7650 480. 2.88550 600. 2 64 M6 720 . 3 . 48474 840. 5.88727 960. 8.80678 1080. 11.03994 1200. 12. 14548 1320. 12.20549 - 14 40. 1 1 .55650 1560. 10.54339 1680. 9.41604 1800. 8.3069 2 1920. 7.27092 2040. 6.33505 2 160. 5.50084 2280. 4.75779 2400. 4.10307 2520 3.52940 2640. 3.0304 2 2760. 2.59943 2880. 2.23293 3000 1 .92045 3 120 1.65569 3240 1 429 18 3360 1 .23962 3480 1.07821 3600 O.94103 3720 0.82156 3840 0.72436 3960 0.63937 4080 0.56609 4 200 0.50366 4320 0.44906 4440 0.40293 4560 0. 362 15 4680 0 . 3?444 4800 0.29131 4920 0 . 26428 5040 0.24070 5160 0.21898 5280 TOLR=.0000100 XN2* 0 0500 DELI = 120.0OO00 IN SECTION NO = IN AREA 0.0 0.00410 0.00254 0.2102G 0.78368 1.30G07 1 .22166 1 .50684 2 . 23874 3.01782 . 3.56526 3.82622 3.84001 3.68742 3 .44643 3 . 17108 2.89183 2.62234 2.36673 2.12784 1.90704 1.70510 1 .52134 1 .35536 1 .20664 1 .07572 0.95807 0. 855 16 O. 76480 0.68554 0.61730 O. 55686 0.50364 O.45753 0.4 172 1 O. 38052 O. 34830 0. 32012 O. 29498 O 27182 0 25040 O 23158 0 2 149 1 0 19993 0 186 13 IN DISCH 0 0 0.00156 0.00097 O. 25697 1 . 47650 2 . R8550 2.64146 3.48474 5.88727 8.80678 1 1 .03994 12.14548 12.20549 1 1 . 55650 10.54339 9.41604 8.30692 7 27092 6.33505 5.5008 4 4.75779 4.10307 3.52940 3.0304 2 2 . 59943 2.23293 1.92045 1.65569 1.42918 1.23962 1.07821 0.94103 0.82156 0.72436 0.63937 0 56609 0.50366 O.41906 0 40293 0.362 15 0.32444 0.2913 1 0 26428 0.24070 O.21898 OUT SEC1ION NO OUT AREA 0 0 0.00403 0.00260 0.20922 O. 782 19 1 30548 1 22246 1 .506 3 1 2 237 1 1 3.01623 3.56 4 1 8 3.82572 3 . 83998 3 . 68772 3.44G92 3 . 17166 2.89244 2.62293 2.36731 2 1284 1 1.907 59 1 70562 1 . 52184 1 .35583 1 .20708 1 .076 1 1 O. 95044 O.85550 O . 765 10 0 68582 0.6 1755 O 55708 0 50385 0 . 4577 1 0.41737 O.380GS O 34844 O 32024 0.795 10 O 77193 O . 75050 0.7 3 16 7 0 7 1499 O 7OOOI 0.186 70 DELA- 10.00000 DE L X = 1 13 OUT DISCH TOTAL TIME . SECONDS 0.0 O. 0.00153 120. 0.00099 240. 0.75534 360. 1 .47777 480 . 2.88378 600. 2.64369 720. 3 . 48312 840. 5 88159 960. 8.80046 1080. 1 1 .03540 1200. 12. 14329 1320. 12.20535 1440. 1 1 .55777 1560. 10.54539 1680 . 9 . 4 1833 1800. 8.30925 1920. 7 . 273 16 2040. 6.33718 2 160. 5.5O203 2280. 4.75963 2400. 4 10475 2520. 3.53093 2640. 3.03181 2760. 2.60066 2880. 2.23402 3000. 1 .92 143 3120. 1 .65655 3240. 1 .42994 3360 1.24028 3480 1.07878 3600 0.94154 3720 0.82201 3840 0.72474 3960 0.63971 4080 0 56639 4200 0.50393 4320 0 44929 4440 0.40314 4560 0.36235 4680 0 374G7 4800 0.79147 4920 0. 76442 5040 0.24083 5 160 0.21910 5280 TOLR =.0000100 XN2 = 0.0500 DELT- 120.OOOOO DELA- 10 OOOOO DE L X = IN SECTION NO = 13 OUT SECTION NO = 14 IN AREA IN DISCH OUT ARFA OUT DISCH TOTAL TIME 0 .0 0.0 0 0 0 .0 0 0 .00403 0.00153 0 006 86 0 OO? 7 7 120 0 00260 0.00099 0 00850 0 .00387 240 0 . 20922 0.25534 0.27674 0 3 IOH 1 360 0 .78219 1.47277 1.27714 2 .8004 5 480 1 . 30548 2.88378 2 77102 7 . 84248 600 1 . 22246 2.64369 3 16908 9 408O8 720 1 .50631 3.48312 3.41772 10 4 2559 840 2 .2371 1 5.88159 3.79958 12 0307 2 "960 3 .01623 8.8004 6 4 . 19164 13 74 199 1080 3 . 564 18 11.03540 4 41822 14 755 14 1200 3 82572 12.14329 4 45139 14 90343 1 320 3 . 83998 12.20535 4.31411 14 29095 1440 3 68772 1 1 .55777 4 0597 3 13 16 155 1560 3 44692 10.54539 3.744 17 1 1 79643 1680 3 17 166 9.41833 3 4 1?R8i 10 4057 3 1800 2 89244 8.30925 3.0905 7 9 09597 1920 2 62293 7.273 16 2.7874 1 7 . 90549 2040 2 36731 6.337 18 2.507 71 6 85 111 2 160 2 1284 1 5.50283 2.24 960 5 92509 2280 1 90759 4.75963 2.01155 5 108 12 2400 1 70562 4.10475 1 79626 4 39636 2520 1 52 184 3.53093 1 60123 3 77543 2640 1 35583 3.03 181 1 .4 2621 3 2387 1 2760 1 20708 2 6O066 1 26922 2 777 16 2880 1 . 076 1 1 2.23402 1 . 12989 2 38457 3000 0 95844 1.92 143 1 007 26 2 05 100 3 120 0. 85550 1.65655 0 90041 1 , 76912 3240 0. 765 10 1.42994 0.80413 1 . 52776 3360 0. 68582 1.24028 0 72135 1 32527 3480 0 61755 1 07878 0.64931 1 . 15300 3600 0. 55708 0.94154 0.58607 1 , 0O733 3720 0. 50385 0.82201 0.530I1 0 88033 3840 0 4577 1 0 .72474 O 48223 0 77644 3960 0. 4 1737 0.6397 1 0 43911 0. 68554 4080 0. 38068 0.56639 0.40165 0. 60702 4 200 0. 34844 0.50393 0 36 703 0 53995 4320 0. 32024 O.44929 O.33705 0. 48 187 4440 0. 295 10 0.40314 0 3 1 166 0. 43267 4560 0. 27 193 .0.36235 0 287 14 0. 389 13 4680 0. 25050 0.32462 0.264 30 0 34892 4800 0. 23 167 0.29147 0 244 18 0 3 1349 4920 0. 2 1499 O.26442 0 22765 0. 28439 5040 0. 2000 1 0.24083 0 2 115 1 0 25894 5160 0. 18620 0 2 19 10 0 19664 0 23552 5280 SECONDS Ln O TOLR=.0000100 XN2 = 0.0500 DE L T = 120.00000 DE IA = 10.00000 DE L X = IN SECTION NO = 14 OUT SECTION NO 15 IN AREA IN DISCH OUT AREA OUT DISCH TOTAL TIME 0. 0 0.0 0.0 0 . 0 0 0. 00686 0.00277 0.00866 0 00398 120 0. 00850 0.00387 0 01273 0 . 006 ; 3 240 0. 27674 0.37081 0.339O9 0 . •1858 1 360 1 . 277 14 2.8004 5 1.71185 4 1248 1 4 80 2 77 102 7.84248 3.97525 12 79394 600 3 . 16908 9.40808 4 72780 16 . 16896 720 3 4 1772 10.42559 4.985 15 1 7 368 16 840 3 79958 12.03072 5.15806 18 187 19 960 4 19164 13.74199 5.26358 18 686 33 1080 4 4 1822 14.75514 5.22024 18 4 7 736 1200 4 45139 14.90343 5.04829 17 . 66542 - 1320 4 3 144 1 14.29095 4 77329 16 37776 1440 4 .05973 13.16155 4 4 2069 14 7 66 16 1560 3 744 17 11.79643 4.03366 1 3 04 808 1680 3 4 1288 10.40573 3.64890 1 1 . 39360 1800 3 09057 9.09597 3 28549 9 88 304 1920 2 7874 1 7.90549 2.95023 a 53809 2040 2 5077 1 6.85111 2 64687 7 . 36523 2 160 2 24960 5.92509 2.37013 6 34752 2280 2 . .01155 5 . 10812 2.115 18 5 4 5675 2400 1 . 79626 4.39636 1 .88624 4 68808 2520 1 .60123 3 . 77543 1.67929 4 02003 2640 1 .42621 3.2387 1 1 .494 16 3 44569 2760 1 26922 2.777 16 1.32927 2 95372 2880 1 . 12989 2.38457 1.1R369 2 53517 3000 1 00726 2.05100 1 05609 - 2 1806 1 3120 0. 9004 1 1 .769 12 0 94319 1 . 88 174 3240 O 804 13 1 52776 0 843 17 1 62562 3360 0 72135 1.32527 0.75691 1 4 1028 3480 0 6493 1 1.15300 0 68037 1 22725 3600 0 58607 1.00733 O 6 1507 1 07315 3720 0 . 53011 0.88033 0.55582 0 93868 3840 0 . 48223 0.77644 0.5067 6 o 82815 3960 o .4391 1 0.68554 0.46086 0 73 140 4080 0 .40165 0.60702 0.421 14 o 64 766 4 200 0 36703 0.53995 0.38563 o 57599 4320 0 . 33705 0.48187 0 35387 0 5 1446 4440 0 .31166 0.43267 0.3 7690 0 4677 1 4560 0 .287 14 0.389 13 0.302 36 0 4 1593 4680 0 .26430 0.34B92 0.778 1 1 0 .37372 4 800 0 .244 18 0.3 1349 0 25670 0 33553 4920 0 22765 0.28439 0 2 3900 0 .30436 5040 o .21151 0.25894 0.22301 o .27705 5 160 0 . 19664 0.23552 0.20708 0 .25196 5280 SECONDS NJ Ln TOLR=.0000100 XN2 = 0.0500 DELT- 120.00000 DELA- 10.00000 0ELX = 960. IN SECTION NO = 15 OUT SECTION NO - 16 IN AREA IN DISCH OUT ARIA OUT DISCH TOTAL TIME 0. 0 0.0 O.O 0 0 0. 0. 00866 0.00398 O 0 O 0 120. 0. 01273 0.00673 0.0 0 . 0 240. 0. 33909 0.4858 1 0 . 1 368 3 0. 14549 360 . 1 . 7 1 185 4. 1248 1 0. 194 2 6 0. 23 178 480. 3 . 97525 12.79394 1 .4 1480 3 . 205 1 7 600. 4 . 72780 16.16896 3. 146 10 9 3 1670 720. 4 . 98515 17.36816 4.24540 13 98235 840 . 5 . 15806 18. 182 19 4.79608 16 . 4824 1 960. 5. 26358 18.68633 5 06-14 1 1 7 . 74 132 10BO 5 . 22024 18.47736 5. 18 36 1 18 . 302 4 7 1200. 5 . 04829 17 66542 5 18944 18 32993 1320 4 . 77329 16.37776 5 09 157 17 . 86920 1440 4 . 4 2069 14 766 16 4 8 9 7 19 16 . 95409 1560 4 . 03366 13.04808 4 62359 15 . 6906 1 16BO 3. 64890 11.39360 4.30006 14 . 22676 1800 3 . 28549 9.88304 3.956 3 2 12 . 7 1 159 1920 2 . 95023 8.53809 3 6 1429 1 1 24727 2040 2 . 64687 7.36523 3 2868? 9 . 8885 1 2 160 2 37013 6.34752 2 98318 8 66907 2280 2 11518 5.45675 2.70507 7 . 58896 2400 1 88624 4 68808 2 44 794 6 63235 2520 1 . 67929 4 02003 2.21167 5 79294 2640 1 494 16 3 .44569 1 . 9950-1 5 05275 2760 1 . . 32927 2.95372 1.79792 4 40172 2880 1 18369 2.53517 1 6 1943 3 83 149 3000 1 .05609 2. 1806 1 1 45833 3 33537 3 120 0 . 94349 1 . 88 174 1 3 14 10 2 909 1 1 3240 0 843 17 1 62562 1 . 18 565 2 . 54067 3360 0 7569 1 1.41028 1 0/006 2 2 1768 3480 0 68037 1 .22725 0 96723 1 94475 3600 0 6 1507 1 . O / 3 15 0 . 8 7 466 1 7045B 3720 0 .55582 O 93868 0 79338 1 5008 2 3840 0 50676 0 828 15 0.719 36 1 32049 3960 0 .46086 0.73140 0.65591 1 . 16877 4080 0 .42114 ' 0.64766 0.59860 1 .03577 4 200 0 .38563 0.57599 0.54792 ,0 .92076 4320 0 .35387 0 51446 0 503 16 'o .82055 4 4 40 0 .32690 0.4622 1 0 . 462 15 0 7 34 1 1 4560 0 .30236 0 41593 0 . 426 13 0 . 658 18 4680 0 . 278 1 1 0.37322 0.395 1 1 O .594 35 4800 0 .25670 0.33553 0 36594 0 . 53783 4920 0 .2 3900 O.304 36 0.33854 0 48476 .5040 0 .22301 0.27705 0.31433 0 . 43784 5 160 0 20708 0.25196 0 29327 0 . 39993 5280 TOLR =.0000100 XN2 = OOOOO DE L T = 120 OOOOO DELA = IO.OOOOO DELX' 1 IN SECTION NO = 16 OUT SECTION NO = 17 IN AREA IN DISCH OUT AREA OUT DISCH TOTAL TIME 0 .0 0.0 0.0 0 .0 0 0 .0 0.0 0 0 0 .0 120 0 .0 0.0 0.0 O .0 240 0 . 136B3 0. 14549 0. 13623 0 . 14466 360 0 . 19426 0.23 178 0. 195 14 0 . 233 16 480 1 . 4 1480 3.20517 1.41288 3 .19952 600 3 . 146 10 9.3 1670 3 14327 9 .30549 720 4 . 24540 13.98235 4.24382 13 . 97529 840 4 .79608 16.4824 1 4.79535 16 47905 960 5 .06441 17.74 132 5.06405 1 7 .73964 1080 5 .18361 18.30247 5 18342 18 .30159 1200 5 .18944 18.32993 5. 1894 3 18 32986 1320 5 09157 17 .86920 5.09175 1 7 .87003 1440 4 89719 16.95409 4 89753 16 95570 1560 4 62359 15.69061 4 62 409 15 69289 1680 4 30006 14.22676 4 30066 14 22945 1800 3 95632 12.71159 3.95698 12 7 14 4 5 1920 3 61429 11.24727 3.61496 1 1 25012 2040 3 28682 9.88851 3.28749 9 89 124 2 160 2 . 983 18 8.66907 2 98381 8 67 160 2280 2 . 70507 7.58896 2.70568 7 59128 2400 2 . 44794 6.63235 2 4 4 853 6 63449 2520 2 2 1 167 5.79294 2 2 1223 5 79490 2640 1 99504 5.05275 1 99557 5 05456 2760 1 79792 4.40172 1 . 79843 4 40336 2B80 1 . 6 1943 3.83 149 1 61991 3 83297 3000 1 . 45833 3.33537 1.45877 3 3367 1 3120 1 314 10 2.90911 13 145 1 2 . 9 103 1 3240 1 . 18565 2.54067 1 18604 2 54 174 3360 1 . 07006 ' 2.21768 1.0704 3 2 2 1865 3480 0. 96723 1.94475 O 96755 1 . 9456 1 3600 0. 87466 1.70458 0 87497 1 70535 3720 0. 79338 1.5008 2 O.79365 1 50150 3840 0. 7 1936 1.32049 0 7 196 1 1 . 32 1 10 3960 0. 6559 1 1 . 16877 0 656 13 1 . 169 30 4080 0 59860 1.03577 O 5988 1 1 . 03625 4 200 0. 54792 0.92076 0.548 1 1 0. 92 118 4320 0. 503 16 0.82055 0 50333 0 82092 4440 0. 462 15 0.73411 0 40231 0. 73445 4 560 0. 426 13 0.65818 0.42627 0 658 18 4680 0. 395 1 1 0.59435 0 39524 0 59460 4800 0. 36594 0.53783 0.366O0 O. 5 3808 4920 0 33854 0.48476 0.33866 0 . 48498 5040 0 3 1433 0.43784 0 3 14 4 3 0. 4 3804 5 160 0. 29327 0.39993 0 29337 0 '40010 5280 . SECONDS LO T 0 L R r.OOOO10O XN2= 0.0500 IN SFCTION NO = 17 IN AREA IN DISCH 0 0 o 0 0 0 0 0 0 O O 0 0 13623 0 14 466 0 195 14 0 233 16 1 4 1288 3 19952 3 14327 9 30549 4 24382 13 97529 4 79535 16 47905 5 06405 17 73964 5 18342 18 30159 5 18943 18 32986 5 09 175 17 87003 4 89753 16 95570 4 62409 15 69289 4 30066 14 22945 3 95698 12 7 1445 3 6 1496 1 1 25012 3 28749 9 89 124 2 9838 1 8 67 160 2 70568 7 59128 2 44853 6 63449 2 2 1223 5 79490 1 99557 5 05456 1 79843 4 40336 1 6 1991 3 83297 1 45877 3 3367 1 1 31451 2 9 103 1 1 18604 2 54 174 1 07043 2 2 1865 0 96755 1 94 56 1 0 87497 1 70535 0 79365 1 50150 0 7 196 1 1 32 1 10 0 65613 1 16930 0 5988 1 1 03625 0 548 1 1 0 92 118 0 50333 O 82092 0 46231 0 7 34.15 0 42627 0 65848 0 39524 0 59460 0 36606 0 53808 0 33866 0 .18498 0 3 14 4 3 0 4 380 1 0 29337 0 40010 DELT" 120 OOOPO DTLA- 10.00000 DE1.X= 1. OUT SECTION NO - 18 OUT AREA OUT DISCH TOTAL TIME 0 O O 0 O 0 0 0 0 120 O O 0 0 2 40 0.19091 0 2 265 1 360 0 25604 0 3 3 4 3 7 480 1 . 6 3 1 4 3 3 8684 3 600 3.717 IO 1 1 6R201 720 5.21907 18 47 169 840 6 12452 22 9 1737 960 6.63031 25 49876 10BO 6.90167 26 9 1064 1200 6 97876 27 3 1673 1320 6 866 15 26 7235 1 1440 6 58898 25 2856 1 1560 6 t967? 23 27930 1680 5.7 3608 20 98276 1800 5.24928 18 6 1736 1920 4 76 763 16 35 179 2040 4 31028 1 4 27248 2 160 3 89037 1? 4246 1 2280 3 51185 IO 8 14 13 2400 3 1702 3 9 4 1266 2520 2.86370 8 19879 2640 2 58788 7 14458 2760 2 3 3580 6 27544 2880 2 105 7 1 5 4 7 706 3000 1 89791 4 77730 3 120 1 713 26 4 17934 3240 1.54694 3 60825 3360 1 39746 3 15420 3480 1 2654 2 2 76600 3600 1.14 503 2 42694 3720 1 03911 2 13553 3840 0 9-1267 1 87957 3960 0 . 85780 1 6623 1 4080 0 . 78 1 26 1 4 704 4 4 200 O.7 1 36? 1 30676 4320 O 65364 1 16335 4440 0 . 5993! 1 1 03755 4560 O.55 702 0 93006 4680 O 5 1 11 8 0 83745 4 800 0 4 7 701 0 75496 4920 0 . 4 36 15 0 67930 5040 0.404 8 7 0 6 1337 5 160 0.37650 0 55829 5280 Ln TOLR =.0000100 XN2 = 0.0500 DE L T = 120 OOOOO DELA- 10.OOOOO DELX = IN SECTION NO = 18 OUT SECTION NO" 19 IN AREA IN DISCH 0U1 AREA OUT DISCH TOTAL TIME 0. 0 0.0 0 0 0. 0 0. 0. 0 0.0 0.0 0. 0 120. 0. 0 0.0 0.0 0. 0 240. 0. 19091 0. 22651 0.24118 0. 3082 1 360. 0. 25604 0 . 33437 0.31314 0 43554 480. 1 63143 3 . 86843 1.83968 4 53606 600. 3. 7 17 10 11.68201 4.26179 14 05564 720. 5 2 1907 18.47169 6.13393 22 . 96487 840. 6 . 12452 22.91737 7 36240 29 . 35287 960. 6 . 63031 25.49876 8.08020 33 . 25601 1080. G . 90167 26.9 1064 8 48583 35 5 1849 1200. 6. 97876 27.31673 8 62549 36 30301 1320. 6 8G6 15 26.72351 8 . 49632 35 577 12 1440. 6 58898 25.28561 8 . 14537 33 6 16 18 1560. 6 19622 23.27930 7.64401 30 86664 1680. 5 .73608 20.98276 7 05857 27 737 14 1800. 5 24928 18.61736 6.44083 2 4 . 52 1 39 1920. 4 76763 16.35 179 5 83167 2 1 45457 2040. 4 . 31028 14.27248 5.25703 18 65475 2 160. 3. .89037 12.42461 4.72989 16 17856 2280. 3 5 1 185 10.81413 4.25780 14 03779 2400. 3 17023 9.4126G 3 83680 12 19152 2520. 2 B6370 8.19879 3.46102 10 60325 2640. 2 58788 7.14458 3.12557 9 23510 2760. 2 . 33580 G.22544 2 8 2 4 4 6 8 04795 2880 . 2 1052 1 5.42 206 2 55154 7 01 155 3000. 1 89794 4.72730 2.30503 6 1 1825 3120. 1 7 1326 4.12934 2.OH 33? 5 34869 3240. 1 54694 3.60825 1.88?36 4 67506 3360. 1 39746 3.154 20 1 70104 4 09002 3480. 1 26542 2.76600 1 53992 3 58662 3600. 1 . 14503 2.42694 1.39561 3 . 14875 3720 1 039 1 1 2. 13553 1.26670 2 76975 3840. 0 94267 1.87957 1.14 905 2 4382 1 3960. 0 .85780 1.66231 1.04663 2 15549 4080 0 .78126 1.47044 0 952 17 1 90478 4200 0. .71362 1.30676 0.86984 1 69248 4320 0 65364 1.16335 0 7 9541 1 5059 1 4440 0 59939 1.03755 0 72784 1 . 34077 4560 0 55202 0.93006 0 66970 1 .20174 4680-0 51118 0.83745 0 . 6 1826 1 .08039 4 800 0 47204 0.75496 0.5704 6 0 .97191 4920 0 436 15 0.67930 0 527 18 0 87369 5040 0 40487 O.61337 0.4 8807 O .78875 5 160 0 37650 0.55829 0 45382 0 .7 1654 5280 NJ Ln Ln = .0000100 XN2 = 0.0500 DE L T = 120.O0O00 IN SECTION NO = 19 OUT SECTION NO IN AREA IN 1 DISCH OUI ARE O. 0 0. 0 0 0 O 0 0 0 0 o O. 0 0. 0 0. 0 0. 24 1 18 0 3082 1 0. 24080 0. 3 13 14 0. 43554 0 3 128.2 1 . 83968 4 . 53606 1 83572 4 . 26179 14 . 05564 4 . 25727 6 . 13393 22 . 96487 6 . 1 308 4 7 . 36240 29 . 35287 7 . 36050 8 . 08020 33 . 25601 8 . 079 10 8 48583 35 . 5 1849 8 48522 8 62549 36 . 30301 8 62528 8 . 49632 35 . 577 12 8 4965? 8 . 14537 33 6 1618 8 . 1 4 590 7 . 64401 30. 86664 7 644 78 7 . 05857 27 737 14 7 . 05949 6 . 44083 24 . 52 139 6 44 18? 5. 83167 2 1 45457 5 . 83?70 5. 25703 18 . 65475 5 . 25R03 4 72989 16 17856 4 7 308 5 4 25780 14 03779 4 25868 3 83680 12 19 152 3 8376 1 3 .46102 10 60325 3 46 178 3 12557 9 23510 3 1262 7 2 .82446 8 .04795 2 B25 12 2 .55154 7 .01 155 2 552 16 2 .30503 6 . 1 1825 2 3056 2 2 .08332 5 .34869 2 08387 1 .88236 4 .67506 1 88286 1 70104 4 .09002 1 .70151 1 . 53992 3 .58662 1 54036 1 .39561 3 . 14875 1 .39602 1 . 26670 2 76975 1 .267(16 1 .14905 2 .43821 1 1 .194(1 1 .04663 2 .1554 9 1 .04 695 O .952 17 1 .904 7 8 O 95216 0 .86984 1 .69248 O .87011 0 .79541 1 .50591 o .79566 0 .72784 1 .34077 0 .72807 0 .66970 1 20174 0 66990 0 . 6 1826 1 .08039 0 .61845 0 .57046 0 .97 19 1 0 .57064 0 .527 18 O .87 369 o .527 34 0 .48807 0 .78875 0 488? 3 0 .45382 0 .71654 0 . 45395 [1ELA= 10.00000 D E L X = = 20 OUT DISCH TOTAL TIME . SECONDS O.O O . O 0 1 20 . 0.0 240 . O.307 54 360 . 0.43 192 480. 4 52332 600. 14.0354 2 720 . 2?.94926 840. 29.3 1264 960 . 33 25000 1080 . 35.51509 1200. 36 30185 1320. 35.57822 1440. 33 61909 1560. 30.870BO 1680 . 2 7.7 4 200 1800. 24.52654 1920 . 21.4 5966 2040. 18.65955 2 160. 16 18295 2280. 14.0417 3 2400. 12.19502 2520. 10 60638 2640. 9 23790 2760. 8.05045 2880. 7.01382 3000. 6.12030 3 120. 5.35054 3240. 4.67673 3360 4 09153 3480 3 58797 3600 3.14995 3720 2.7 708 3 3840 2.4 39 19 3960 2 15634 4080 1.9055 7 4 200 1 .69316 4320 1.50653 4440 1.34133 4560 1.202 2 3 4680 1.08OR2 4800 0.9723 1 4920 0.87 405 5040 0.78908 5 160 0.71682 5280 TOLR- OOOO100 XN2 = O 0500 DFL T- 120.OOOOO nri.A= 10.00000 DEI.X = 1. IN SECT IN 0 O 0 O O 1 4 6 7 8 8 . 8 8 8 7 7 6 5 5 4 4 3 3 3. 2 . 2 2 2 . 0. 0. o. 0 o. 0. 0. 0. o. 0. I ON NO AREA .0 .0 .0 .24080 .31282 .83572 .25727 .13084 .3G050 .07910 .48522 .62528 .49652 .14590 .64478 .05949 .44182 . 83270 .25803 .7 3085 .25868 .83761 . 46 178 . 12627 825 12 552 16 30562 08387 88286 70151 54036 39602 26706 14940 04695 95246 8701 1 79566 72007 66990 6 184 5 57064 52734 48823 45395 20 IN DISCH 0.0 0 0 0.0 0 . 30754 O. 43492 4 . 52332 14.03542 22.94926 29.34264 33.25000 35.51509 36.30185 35.57822 33.61909 30.87080 27.74200 24.52654 21.45966 18.65955 16.18295 14.04173 12.19502 10.60638 9.23790 8 .0504 5 7.01382 6 . 1 2030 5.35054 4 . 67673 4.09153 3.58797 3.14995 2 77083 2.43919 2.15634 1.90557 1 .693 16 1.50653 1.34 133 1 20223 1.08082 O.97 23 1 0.8 7 405 O 78908 O.7 1682 SFCTI ON NO = 2 1 OUT AREA OUT DISCH TOTAL TIME O.O 0.0 0 . 0 00353 0.00134 120. 0.OO700 0 00286 240 . O.29672 0 40599 360 . 0.75296 1.40086 480. 2 74930 7 75898 600 . 5 . 1.1 187 1B.05893 720. 6 90249 26.914 9 3 840. 8 029 16 32.97620 960 B 64984 36 44162 1080. B.964 36 38.231B4 1200 9.02071 38.55263 1320. 8 B17 10 37 39368 1440. 8.35722 34.79987 1560. 7.7B553 31.64049 1680. 7 15799 28.26088 1BOO. G 5 1 187 24 B87B3 1920. 5 8B503 2 17 1794 2040. 5 2974 1 (fl B4944 2 160. 4 76 169 16 32454 2280. 4 28283 14 14972 2400. 3 85667 12 27798 2520. 3 47780 10.672O9 2640. 3 13937 9.28998 2760. 2.83587 8.09179 28BO. 2.56150 7 04B01 3000. 2 3 1375 6.14B61 3120 2.09O8 7 5 37399 3240 1 88866 4.696 19 3360 1.70653 4.10768 3480 1.54 4 79 3.60161 3600 1.4 0O05 3. 16 ISO 3720 1.2 7056 2 78 1 12 3840 1 15260 2.448 16 3960 1 04988 2 164 11 40BO 0.95502 1 91234 4200 0.87245 1.69904 4320 0 797 70 15 1165 4440 O.72994 1 . 34579 4560 0.67151 1.20608 4680 0 6 199? 1.OB416 4 800 0.57193 0 97524 4920 0 52846 0 87659 504 0 O 48932 0.79138 5 160 0 4 54 95 0. 7 1892 5280 SECONDS Ln -^1 TOLR=.0000100 XN2 = 0.0500 DE L T = 120 OOOOO DEI.A= 10 OOOOO DE L X = IN SECTION NO 2 1 OUT SECTION NO = 22 IN AREA IN DISCH OUT AREA OUT DISCH TOTAL TIME 0. 0 0. 0 0.0 0. 0 0 0. 00353 0. 00134 O 00669 0. 00265 120 0. 00700 0. 00286 0.01120 0. 00570 240 0. 29G72 0. 40599 0.34850 0 50404 360 0. 75296 1 . 40086 1.12250 2 . 36388 480 2 . 74930 7 . 75898 3.55365 10 99086 600 5 13187 18 . 05893 5.95888 22 08249 720 6 . 90249 26 . 9 1493 7.64674 30 . 88 1 35 840 8 02916 32 . 97620 8.67954 36 . 6 1066 960 8 . 64984 36 . 44 162 9.20812 39 63403 1080 8 96436 38 . 23 184 9.43507 40. 94933 1200 9 0207 1 38 . 55263 9.4lOOl 40. 80409 1320 8 817 10 37 . 39368 9.13491 39 20976 1440 8 35722 34 . 79987 8.56869 35 98 148 1560 7 . 78553 3 1 . 64049 7.92603 32 . 41075 1680 7 . 15799 28 . 26088 7.25585 28 7801 1 1800 6. 51 187 24 . 88783 6.58196 25 24936 1920 5. 88503 2 1 . 7 1794 5 93738 2 1 97636 2040 5. 2974 1 18 84944 5.33681 19 . 03944 2 160 4 76 169 16 . 32454 4.79255 16 466 19 2280 4 . 28283 14 . 14972 4 30699 14 . 25778 2400 3 . 85667 12 27798 3 .87575 12 36098 2520 3 47780 10. 67209 3.49380 10. 73782 2640 3 13937 9 28998 3.152 18 9 34 2 10 2760 2 83587 8 09 179 2.84663 8 133 15 2880 2 56 150 7 . 04801 2.57084 7 08220 3000 2 31375 6 1486 1 2.32188 6 17694 3 120 2 09087 5 37399 2 09787 5 397 46 3240 1 88866 4 69619 1 89447 4 7 1566 3360 1 .70653 4 10768 1.7 1155 4 . 12383 3480 1 . 54479 3 . .60161 1 54922 3 6 1525 3600 1 .40005 3 . 16180 1 40408 3 17366 3720 1 . 27056 2 78 1 12 1.27407 2 79 142 3840 1 . 15260 2 448 16 1 . 1558 1 2 . 457 12 3960 1 .04988 2 164 1 1 1.05280 2 .17188 4080 O .95502 1 .91234 0.95757 1 .91913 4 200 0 .87245 1 .69904 0 87480 1 .70491 4320 0 . 79770 1 5 1 165 0 79974 1 5 1676 4440 0 .72994 1 . 34579 0 73 180 1 35024 4560 O 67 15 1 1 20608 0 673 12 1 20993 4680 0 .61992 1 .08416 0 62 140 1 .0875 1 4800 0 57 193 0 .97524 0 57322 0 97816 4920 0 .52846 0 .87659 0.52958 0 879 14 5040 0 48932 0 .79138 0. 1901 1 0 . 79368 5160 0 45495 0 .71892 0.4 5595 0 72 103 5280 SECONDS NJ Ln 00 

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
United States 11 0
China 10 36
Japan 9 0
Russia 3 0
Italy 2 0
Republic of Korea 1 0
Canada 1 0
City Views Downloads
Unknown 12 0
Tokyo 5 0
Beijing 3 0
Ashburn 3 0
Carson City 3 0
Shenzhen 2 36
Dongguan 2 0
Saint Petersburg 1 0
Calgary 1 0
Boardman 1 0
Guangzhou 1 0
Nanchang 1 0
Sunnyvale 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0052442/manifest

Comment

Related Items