application of non-point source response functions to general
TRANSCRIPT
Application of Non-Point Source Response Functions to General Urban Land Uses
Washington, D.C. 20052
APPLICATION OF NON-POINT SOURCE RESPONSE FUNCTIONS TO GENERAL URBAN LAND USES
FINAL REPORT
DISTRICT.-OF COLUMBIA WATER RESOURCES RESEARCH CENTER Agreement No. 4.042.060 ANNUAL COOPERATIVE PROGRAM OFFICE OF WATER RESEARCH AND TECHNOLOGY U.S. DEPARTMENT OF THE INTERIOR
Authored by:
Dr. G. Kenneth Young, Principal Investigator Dr. Eddie Neal,
Research Associate
DEPARTMENT OF CIVIL ENGINEERING THE CATHOLIC UNIVERSITY OF AMERICA
"The research on which this report is based was financed in part by the United States Department of the Interior, Geological Survey, through the D.C. Water Resources Research Center."
"The Contents of the publication do not necessarily reflect the views and policies of the United States Department of the Interior, nor does mention of trade names or commercial products constitute their endorsement by the United States Government."
June 30, 1986
A microcomputer based daily accounting model of runoff and pollutant emission from
urban catchments has been developed. The model has been calibrated and verified by
application to District of Columbia area watershed data. The results from the investigation
indicate that the model is accurate and reliable. The model is easily implemented on a
microcomputer and thus avoids the extensive time and costs associated with modeling urban
water quality on mainframe computers, using existing complex simulation models. The model
can be used to generate pollutant emission frequency functions for small urban watersheds that
possess a range of different rainfall inputs and cultural factors.
The developed simulation model was utilized in a Monte Carlo context to generate a
large data base of non-point source emissions and associated urban land use attributes. Least
squares regression was applied to the data base to develop emission functions of land use and
other physical independent variables. The resultant transfer function between rainfall watershed
parameters and runoff and pollutant emissions is used without recourse to additional
mathematical modeling.
ABSTRACT
ACKNOWLEDGEMENTS
The author wishes to acknowledge the contributions of other individuals
to this study. Ms. Kathy Saunders served as research assistant to the-1 and
contributed significantly to the collection and analysis of field d;1 Mr. Maurice
Benjamin and Mr. Glenn Tucker assisted respectively with the development of
the computer program and with the graphical presentation of data. Ms. Julie A.
Cirillo of the U.S. Department of Transportation kindly arranged for the author
to spend several quiet days at the Turner-Fair Research Station during a critical
stage of the investigation in the summer 1985. The overhead funding provided
by GKY & Associates, Inc. and The Scientex Corporation is gratefully
acknowledged.
The field data used in the study were graciously provided by the Water
Monitoring Laboratory (OWML) from its Metropolitan Washington County
Governments (MWCOG) NPS data file. Dr. Tom Grizzard and Dr. Barry Wit
OWML were very cooperative.
The research reported in this paper was partially funded by the Water
Resources Research Center of the District of Columbia through the am Pi the
Annual Cooperative Program of the Office of Water Research and Technical
U.S. Department of Interior. The assistance and encouragement of Dr. H. Watt,
Director of the Center, is gratefully acknowledged. The support and
encouragement of Dr. Timothy Kao, Chairman of the Civil Engineer.
Department, The Catholic University of America and the assistance Dr. J.
Casarella and Dr. Ramesh Vaishnav as readers are gratefully acknowledged. Ms.
Jacqueline Jones painstakingly word processed the document under great time pressure.
Her performance and commitment were essential to the project’s completion.
TABLE OF CONTENTS
Title Page
1. INTRODUCTION . . . . . . . . . . . . . ... . . . . . ……………………….. 1
1.1 General . . . . . . . . . . . . . . . . …………………………………….. 1 1.2 Problem Definition . . . . . . . . . . . . . . …………………………… 3 1.3 Technical Context . . . . . . . . . . . . . . . …………………………... 4 1.4 Method . . . . . . . . . . . . . . . . . . . ………………………………… 4 1.5 Validation . ... . . . . . . . . . . . . . . ………………………………… 5 1.6- Planning Method . . . . . . . . . . . . . . . …………………………… 8 1.7 Summary and Overview . . . . . . . . . . . . ………………………… 13
2. LITERATURE REVIEW . . . . . . . . . . . . . . . . . ……………………. 15
3. MODEL DEVELOPMENT . . . . . . . . . . . . . . . . . …………………. 19
3.1 Objective . . . . . . . . . . . . . ………………………………………. 19 3.2 General Logic of the Model . . . . . . . . . ………………………… 19 3.3 Model Building and Verification . . . . . . . . …………………….. 22 3.4 Model Variables and Parameters . . . . . . . . …………………….. 24 3.5 Model Components . . ………………………………………….. 26 3.6 Evapotranspiration, Infiltration and Percolation . ………………. 28 3.7 Pollutant Loading . . . . . . . . . . . . . . . …………………………… 32 3.8 Pollutant Emission . . . . . . . . . . . . . . …………………………… 33 3.9 Computational Form . . . . . . . . . . ………………………………. 35 3.10 Summary of Principal Assumptions . . . . . . . . ………………… 36
4. MODEL APPLICATION AND EVALUATION . . . . . . . . . . …….. 38
4.1 Approach . . . . . . . . . . . . . . . . . . . ……………………………… 38
4.2 Application to Field Data . . . . . . . . . . . ………………………… 38 Field Data Selection . . . . . . . . . . . . ………………………………….. 38 Description of Data Sites . . . . . . ……………………………………... 39 Data Selection, Preparation and Analysis . . . ………………………... 42
4.3 Model Calibration and Verification . . . . . . ……………………. 43 Calibration Procedure . . . . . . . . . . . . . ……………………………….. 43 Calibration Results . . . . . . . . . . . . . . ………………………………… 45 Verification Procedure . . . . . . . . . . . . ……………………………….. 59 Verification Results . . . . . . . . . . . . . …………………………………. 59
Summary . . . . . . . . . . . . . . . . . . . . …………………………………... 71
4.4 Parameter Sensitivity Analysis . . . . . . . ………………………............. . . . . .71
Analysis Procedure . . . . . . . . . . . ………………………………….... . . . . . . 71
Sensitivity Analysis Results . . . . . . . . . . ……………………………….. . . . 72
5.
DEVELOPMENT OF SYSTEM TRANSFER FUNCTION . . . . . . . . …… . 5.1 Objective . . . . . . . . . . . . . . . . . . . . . ……………………………………. 5.2 Approach . . . . . . . . . . . . . ……………………………………………... . 5.3 Selection and Pre-Processing of Representative
Rainfall Data . . . . . . . . ……………………………………………
73 73
73 75
5.4 Specification of Parameter Sampling Distributions . . …………………. 78
5.5 Generation of System Response Using Monte Carlo Experiments . . . . . . . . . . . . . ………………………………………
84
5.6 Transfer Function Generation . . . . . . . . . . . ……………………………. 88
5.7 Transfer Function Validation . . . . . . . . . . . . …………………………… 93
6. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . . 95
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . …………………………………… 95 6.2 Conclusions . . . . . . . . . . . . . . . . ………………………………………... 966.3 Recommendations Toward Future Research . . . . . . . ………………….. 98
7. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . ……………………………….. 99
8. APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . ………………………………. 101
TABLE OF CONTENTS (CONT’D)
Title
TABLE 1.
LIST OF TABLES
VALIDATION RESULTS FOR CONCEPTUAL SIMULATION MODEL . .………………………………………………………………
Page 7
TABLE la. TYPICAL IMPERVIOUSNESS FRACTIONS AS FOUND IN CIVILENGINEERING PRACTICE . . . . . . . . . . . . ……………………… 13
TABLE 2. FIELD DATA SITE CHARACTERISTICS . . . . . . . . . . . …………… 41
TABLE 3. MEANS AND STANDARD DEVIATIONS . . . . . …………………..
44
TABLE 4. INITIAL ESTIMATES OF PARAMETER VALUES (Burke Pond Site) . . . . . . . . . . . . . . . . . …………………………… 46
TABLE 5. OPTIMUM PARAMETER VALUES (Burke Pond Site) . . . . . . ……… 47
TABLE 6. COMPARISON OF ACTUAL AND PREDICTED MOMENTS
(Burke Pond Site) . . . . . . . . . . . . . . . . ……………………………..
53
TABLE 7. OPTIMUM PARAMETER VALUES (Stedwick Inlet Site) . . . . . 60
TABLE 8. COMPARISON OF ACTUAL AND PREDICTED MOMENTS (Stedwick Inlet Site) . . . . . . . . . . . . . . . . 65
TABLE 9. OPTIMUM PARAMETER SENSITIVITY ANALYSIS . . . . . . . . . 72
TABLE 10. SUMMARY OF STATISTICS FOR TWENTY DATA SITES USED FOR RAINFALL INPUT TO MONTE CARLO SIMULATIONS . . . 77
TABLE 11. RELATIVE FREQUENCY OF OCCURENCE OF THE TWENTY RAINFALL DATA SITES IN THE MONTE CARLO SIMULATION 85
TABLE 12. RANGE OF PARAMETERS FROM MONTE CARLO SIMULATION . . . .
86
TABLE 13. SUMMARY OF STATISTICS FROM MONTE CARLO SIMULATIONS . . ……………………………………………………... 87
TABLE 14. F-STATISTIC VALUES FOR PHOSOPHORUS TRANSFER FUNCTION . . . . . . . . . . . . . . . . . . . . . . …………………………... 90
TABLE 15. REGRESSION COEFFICIENTS FOR F-STATISTIC VALUES . . . . . 91
TABLE 16. COMPARISON OF RUNOFF AND POLLUTANT EMISSION PREDICTIONS . . . . . . . . . . . . . . . . . . . . …………………………. 93
LIST OF FIGURES
Title Page
FIGURE 1. MODEL ELEMENTS LOGIC FLOW CHART . . . . . . . . . …………. 20
FIGURE 2. INFILTRATION-SOIL MOISTURE RELATIONSHIP . . . . . …….. 29
FIGURE 3. MAXIMUM ONSET INFILTRATION-RAINFALL RELATIONSHIP 29
FIGURE 4. INFILTRATION-RAINFALL RELATIONSHIP (Burke Pond Site) . . . . . . . . . . . . . . . ……………………………… 30
FIGURE 5. INFILTRATION-RAINFALL RELATIONSHIP (Stedwick Inlet Site) . . . . . . . . . . . . . ……………………………… 31
FIGURE 6. BURKE POND INFILTRATION SITE . . . . . . . . . . ………………… 40
FIGURE 7. COMPARISON OF ACTUAL AND PREDICTED RUNOFF TIME SERIES (Burke Pond Site) . . . . . . . . . . . …………………………. 48
FIGURE 8. COMPARISON OF ACTUAL AND PREDICTED COD TIME SERIES (Burke Pond Site) . . . . . . . . . . . …………………………. 49
FIGURE 9. COMPARISON OF ACTUAL AND PREDICTED TP TIME SERIES (Burke Pond Site) . . . . . . . . . . . …………………………. 50
FIGURE 10. COMPARISON OF ACTUAL AND PREDICTED TN VALUES (Burke Pond Site) . . . . . . . . . . . . . ..………………………………. 51
FIGURE 11. COMPARISON OF ACTUAL AND PREDICTED RUNOFF FREQUENCY FUNCTIONS (Burke Pond Site) . . . . . . . . . . ……… 54
FIGURE 12. COMPARISON OF ACTUAL AND PREDICTED COD FREQUENCY FUNCTIONS (Burke Pond Site) . . . . . . . . . . ………. 55
FIGURE 13. COMPARISON OF ACTUAL AND PREDICTED TP FREQUENCY FUNCTIONS (Burke Pond Site) . . . . . . . . ………… 56
FIGURE 14. COMPARISON OF ACTUAL AND PREDICTED TN FREQUENCY FUNCTIONS (Burke Pond Site) . . . . . . . . . . ……… 57
FIGURE 15. COMPARISON OF ACTUAL AND PREDICTED RUNOFF TIME SERIES (Stedwick Inlet Site) . . . . . . . . . …………………………. 61
FIGURE 16. COMPARISON OF ACTUAL AND PREDICTED COD TIME SERIES (Stedwick Inlet Site) . . . . . . . . . …………………………. 62
LIST OF FIGURES (CONT’D)
FIGURE 17. FIGURE 18.
COMPARISON OF ACTUAL AND PREDICTED TP TIME SERIES (Stedwick Inlet Site) …………………………………………………...63
COMPARISON OF ACTUAL AND PREDICTED TN TIME
SERIES (Stedwick Inlet Site) . . . . . . . . . ……………………………………64
FIGURE 19. COMPARISON OF ACTUAL AND PREDICTED RUNOFF FREQUENCY FUNCTIONS (Stedwick Inlet Site) . . . . . . . . ………………………………….67
FIGURE 20. COMPARISON OF ACTUAL AND PREDICTED COD FREQUENCY FUNCTIONS (Stedwick Inlet Site) . . . . . .. . …………………………………..68
FIGURE 21. COMPARISON OF ACTUAL AND PREDICTED TP FREQUENCY FUNCTIONS (Stedwick Inlet Site) . . . . . . . …………………….. …………69
FIGURE 22. COMPARISON OF ACTUAL AND PREDICTED TN FREQUENCY FUNCTIONS (Stedwick Inlet Site) . . . . . ... . ………………………………….70
FIGURE 23. TRANSFER FUNCTION MODELING SCHEME . . . . ………. . . . ………….74
1. INTRODUCTION 1.1 General
The primary objective of this research is to develop a microprocessor based simulation tool for
predicting the mean and standard deviation of nonpoint source emissions in urban and suburban drainage
systems.
To accomplish the objective of the research it is necessary to derive analytical transfer functions to
map input rainfall and system parameters directly into runoff and pollutant concentration levels without
recourse to simulation. The developed procedure can be used to assess the risk of urban water pollution from
nonpoint sources.
Research over the past decade has resulted in the development of complex models of runoff, sediment
erosion and chemical migration into water systems. Such models have been shown, upon calibration and
verification, to yield measures of pollution concentrations that are statistically identical to corresponding
measures obtained directly from instrumented watersheds. The models have been used to predict time series
outflows of pollutants such as pesticide, nitrogen and phosphorus to surface waters and to determine chemical
residues in the soil.
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1.2 Problem Definition
Sensitivity analyses of the developed models have identified the major parameters that
affect the predicted results. Sediment transport is a function of water flow in a system simulation.
Also, chemical simulations are driven by the hydrologic and sediment sections of the model, as
movements of chemicals are determined by water flow and sediment transport. Initial
investigations indicated that the sensitivity results and findings of previous investigations, using the
complex simulations, could be employed to develop a conceptually simpler analysis that depends
on a smaller number of parameters and that can be implemented in a microprocessor simulation.
The microprocessor based simulation may then be readily used to develop statistical measures of
the time-varying concentration of contaminants. Calculations may then be made to determine
pollution measures such as frequency of occurrence and durations of specified concentrations and
concentration level distributions.
The developed microprocessor based runoff and pollutant level prediction tool may be
applied to obtain rapid calculations of runoff and pollution levels under a wide range of parameter
variations and input rainfall distributions. The results from these parametric analyses will be used
to formulate an analytical transfer function to directly connect the input rainfall and parameter
values directly to the output runoff and pollution concentration processes without recourse to the
time domain simulations.
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1.2 Problem Definition
Nonpoint source pollution is an area of increasing concern to urban and suburban
environments such as Washington, D.C. Surface waters in such areas are degraded by pollutants,
particularly sediment, siltration and nutrients from surrounding lands. In surface waters, urban
runoff is the primary nonpoint source causing impacts on 972,000 lake acres, 8,000 river miles
and 1,000 square miles of estuaries (ASIWPCA (1985) Previous investigations have employed
mathematical models to simulate the process of water transport and sediment erosion through
which pollutants are introduced into the environment. Such simultations have been shown to yield
a high degree of accuracy when calibrated and compared to measurements made from test
watersheds. Previous model investigations have been performed in complex, large scale computer
simulations, resulting in time consuming and expensive simulation assessments. Urban planners
require practical tools to assess the risk of nonpoint pollution in urban environments; such tools
must be reliable, easily accessible, convenient to use and cost effective.
The approach of this investigation entails the adaptation and simplification of existing
rainfall, runoff, soil moisture and sedimentation models in a microprocessor based simulation. In
this study, the approach leads to an analytical formulation of a system transfer function between
system inputs and outputs that renders the simulation process unnecessary in practical
applications. The research results provide a management tool for evaluating the probability that
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4
specified level of pollution will occur, given information on the extent of rainfall and the physical
description of the exposed area. The developed tool can be used in the assessment of pollution
exposure and in the evaluation of the risk of nonpoint source pollution. 1.3 Technical Context
The research develops and tests a continuous simulation model of nonpoint source pollution
emissions. The model is applicable to the prediction of daily time increment emissions on small urban
or suburban watersheds. The model incorporates soil moisture accounting, soil loss computations for
pervious areas and pollutant accumulation and wash-off computations for impervious areas. The
model parameters form a small and manageable set. To the extent practical, members of the parameter
set are selected using physical characteristics of the watershed. The remaining small subset are
calibration parameters. The model is used to study the transformation of rainfall distributions to
pollutant distributions using the method of derived distributions. The derived distributions are to be
determined using time series simulations. 1.4 Method
The variables and logic of previously developed complex models of the physical processes
(Crawford (1971)) are analyzed by examining sensitivity results. Those variables and model
assumptions that are found, based on sensitivity analysis, to have little or no bearing on results are
eliminated. Simplifications are sought that are conceptually correct and which capture as much of the
output response as
i
possible. These simplifications are integrated into a mathematical model that will fit on microcomputers and
that generate output time series quickly. The simplified model is checked against field data, calibrated and
verified.
Upon verification, the developed model is used to perform a comprehensive parametric analysis using
a characteristic set of measured rainfall inputs and randomly sampled physical parameter values. The results
of the parametric analysis are used to formulate an analytical transfer function to map rainfall inputs and
system parameters directly into runoff and pollution level distributions without recourse to the simulation
procedure
1.5 Validation
Extensive simulation with the conceptual model tested the validity of its formulation. Runoff and
pollution level trends were tested against trends in the rainfall and catchment parameter values. The observed
trends matched engineering experience as well as results from previous investigations. Therefore, the
essential formulations in the model are presumed to be valid.
The next two paragraphs discuss first the fit of the conceptual model to actual data. Second, the
discussion is of the fit of the transfer function (derived by Monte Carlo simulation followed by statistical
regression) to the actual data.
The developed simulation model was calibrated and verified by application to two experimental data
sites in the metropolitan
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Washington, D.C area. Both sites were small-watersheds of less than 30 acres. The Burke Pond Site
(18.3 acres) in Northern Virginia was used to calibrate the model. The Stedwick Inlet Site (27.4 acres)
in Gaithersburg, Maryland was used to verify the model. Means and standard deviations of the runoff
and pollutants (Chemical Oxygen Demand (COO), Phosphorus (TP) and Nitrogen (TN)) were
compared between the actual (measured) and predicted (simulation model) values at each site.
Excellent agreement was obtained between each set of the mean values and good agreement was
obtained between each set of standard deviations as shown in Table 1.
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TABLE 1. VALIDATION RESULTS FOR CONCEPTUAL SIMULATION MODEL
OUTPUT* CALIBRATION SITE** VERIFICATION SITE" measured predicted measured predicted
Runoff (in.)X 0.267 0.267 0.098 0.099
SX 0.305 0.313 0.132 0.167 COD (lbs)
X 43..663 44.070 40.262 40.460SX 34.477 38.367 34.354 50.561
Phosphorus (lbs)X 0.372 0.371 0.302 0.313
SX 0.465 0.309 0.273 0.388 Nitrogen (lbs)
X 3.056 3.046 2.539 2.567SX 2.539 2.445 2.224 3.099
* Output per rain event or per wet day. Sample size was 54 rain days over a one-
year period.
* All differences for means and standard deviations are insignificant at the 0.05
level.
* All differences for means and standard deviations are insignificant at the 0.10 level.
The derived transfer function was validated based on its application to runoff and the
pollutant phosphorus at the Burke Pond calibration site. A single chemical was selected to
validate the transfer function due to the large computational effort required to derive the transfer
function for a given pollutant. Phosphorus was selected as the pollutant of interest due to its
significance to the environment as a major pollutant whose trend is increasing (EPA (1984)).
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The results showed that for the Burke Pond site, the transfer function predicted mean runoff
of 0.304 in. with a predicted standard deviation of 0.376 in. It predicted a mean phosphorus
emission of 0.270 lbs. with a standard deviation of 0.349 lbs. Comparing these numbers with those
predicted by the conceptual model of 0.313 in., 0.371 in., 0.372 lbs. and 0.309 lbs. respectively, it
is seen that the transfer function provides reasonably accurate predictions (within 25% accuracy) of
the simulation model results. However, as a predictor of the measured field data, the transfer
function is generally less accurate than the conceptual model (see Table 16).
1.6 Planning Method
The utility of the transfer function method may be demonstrated by application to an urban
planning context as follows:
A. The overall predictive equations for phosphorus emission(Y3), and its standard
deviations, Y4, are
Where the variables are defined by Y1 – Mean Runoff Y2- Runoff Standard Deviation Y1, Y2 – Mean Value of Y1, Y2 on an annual basis X1 – Mean Rainfall X2- Standard Deviation Rainfall X3 –Deep Percolation X4 –Root Zone Depth X5- Porosity X6- Maximum Infiltration X7- Impervious Fraction of Catchment Area X8- Evapotranspiration Factor X9-Washoff Coefficient X10- Pollutant Dissipation Coefficient X11- Active Layer Thickness X12- Catchment Slope X13 – Soil Loss Coefficient X14- Large Storm Infiltration Curve Intercept X15- Large Storm Infiltration Curve Slope The coefficients are to be determined from the regression analysis results given in Table 14
9
B. Determine values of those variables that can be readily obtained from environmental or public or
public entities. Generally these variables and their likely sources are:
1. Slope (topographic maps)
2. Land use (zoning permits)
3. Perviousness as function of land use (see Table 1a)
4. Average rainfall ( analysis of National Weather Service Data)
5. S.D. Rainfall (analysis of National Weather Service Data)
6. Drainage area (the maximum size area for this methodology is probably less than 1,000
acres. This is arrived at by noting that the test data were for small drainage areas)
7. Number of rain days (analysis of National Weather Service Data)
C. Set the remaining variables to their mean (default) levels as defined in Table 14. Using
the independent variables as defined above, we have
The units for these mean- values are provided in Table 12.
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D. Using the overall prediction equation with the default values prescribed in ( C) above and the coefficients as
given in Table 14 , calculate
1.Y1 = mean runoff per storm (in.) = 0.320 + 0.843784 (X1 – 0.414) + 0.021546 (X2 – 0.510) + 0.188090 ( X7 – 0.510) 2. Y2 = runoff standard deviation (in.) = 0.422 – 0.799001 (X1 – 0.414) – 0.737617 ( X2 – 0.510) - 0.034581 (X7 – 0.099
3. Y3 = mean phosphorus emission per storm (in.) = 0.255 + 0.079.15 (X2- 0.510) – 0.85650 ( X7- 0.510 4. Y4 = phosphorus standard deviation (lbs.) = 0.360 + 1.181080 ( Y3 – 0.255) 0.348021 ( X2 - 0.510) + 0.251481 (X7- 0.510) – 0.340322 (X12 – 0.099
The annual emission rate for the land use saturation would be
E= Mean emission per storm X number of days of rain Area For example, consider an undeveloped area near Annapolis, Maryland. Assume an area
of 100 acres. The major parameters affecting the transfer function prediction that may be readily
determined are the following:
Number of rain days Mean rainfall (X1) Standard Deviation of rainfall (X2) Land Use Impervious fraction (X7) Catchment Slope(X12)
The mean and standard deviation of rainfall for the Annapolis may be determined from the National
Weather Service records as 0.522 and 0.562 respectively. Intended land use for the selected area may be
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determined from zoning application. Table 1a provides typical values of the imperviousness
fraction as a function of land use. Assuming a relatively undeveloped wooded area, the
imperviousness fraction is 0.2. Assume that the mean slope of the area may be determined from
topographical maps as 0.15. Then the mean runoff and phosphorus emission levels may be
computed as
Y1 = mean runoff
= 0.354 inches/acres
Y2= standard deviation runoff
= 0.309 inches/acres, and
The annual phosphorus rate would then be
Y3 x number of days of rain =0.312 x 106 = 33.07 lbs./acre/year
The total amount generated from the 100 acre site would be 3307 lbs. per year.
Furthermore, the standard deviation of the estimated emission is computed as 0.350 lbs/acre per
year.
This calculation is seen to be consistent by comparing it to figures shown in the
“Maryland Air and Water Quality Atlas, 1982” which shows that the Annapolis, Maryland area
generate phosphorus levels in the range of 0.2-0.6 lbs./acre/storm.
12
Land Use Imperviousness
Meadow 0.2 Woods 0.2 Pasture 0.3 Crops 0.3 Residential 0.4 Urban 0.7 Pavement 0.9
13
TABLE la. TYPICAL IMPERVIOUSNESS FRACTIONS AS FOUND IN CIVIL ENGINEERING PRACTICE
The objective of this dissertation is to detail the derivation, validation and application of a
new and practical method for estimate frequency functions for nonpoint source risk evaluation. The
dissertation is divided into six chapters. The first chapter gives an introduction to an overview of
the research project. The second chapter is a review of literature pertinent to the background and
focus of the dissertation. The third chapter details the derivation of the conceptual model and
summarizes the principal assumptions involved in this development. The fourth chapter documents
application of the model to two selected small catchments in the metropolitan Washington, D.C.
area. Calibration and verification results are provided. The fifth chapter discusses the synthesis of
the system transfer function based on the application of Monte Carlo experiments using the model
developed in Chapter 3. In the sixth Chapter conclusions are drawn and recommendations are made
toward future research. References are listed
1.7 Summary and Overview
in Chapter 7. The Appendices list the computer code for the conceptual model, the data
sets used to calibrate and verify the model and the database generated to synthesize the
transfer functions.
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2. Literature Review
Stormwater from urban areas is a serious source of water pollution. Urban runoff quality
has been a recurring topic of investigation over the past century. The pollution generated as the
results of a rainfall event can exceed that of raw sanitary sewage. The Metropolitan Washington
Council of Governments Water Resources Planning Board has found that nonpoint pollution is a
serious surface water quality problem for the Washington area, and planning tools for local
nonpoint pollution management programs are needed( Danner 1982)). The Environmental
Protection Agency ( 1984) has estimated that $106 billion for stormwatch pollution control in the
United States will be required by the year 2000.
Engineers have been concerned over the years with the problem of estimating urban
stormwater runoff. For the most part of last century engineers used ad hoc rules to assess runoff.
A typical rule of thumb is that about half of rainfall would appear as runoff from urban surfaces.
Later, empirical formulas became the principal mechanism determining quantities of urban
runoff. Some 100 empirical formulas have been published by Chow (1962). Probably the most
prominent empirical formula is the Rational Formula ( known as the Lloyd- Davies method in
the United Kingdom). The Rational Formula employs the relation Q= CIA, where Q is the peak
discharge, C is a runoff coefficient, I is the rainfall rate in inches per hour for a selection duration
equal to the time of concentration for the drainage area, and
15
is the geographical drawing area. The hydrograph, a graph of discharge versus time for a storm
event, extended the rational method from peak flow to flow per unit precipitation.
Hydrograph motivated methods, since their early introduction, have formed the basis for
much of the later developments in the estimation of runoff. Tholin and Keifer (1959) developed
the Chicago Hydrograph. This graphical method was later computerized by Keifer (1970)
Eagleson (1962) developed the unit hydrograph concept for the analysis of sewered drainage
areas in an urban catchment.
The search for improved methods of predicting urban water quality combined with the
increasing availability of digital computers, led to the introduction of simulation models. These
mathematical models attempt to represent or simulate the performance of complex hydrologic
systems on a computer. Such models may be either conceptual in that they are designed to
simulate actual hydrologic events and their structure and parameters are based on physical,
chemical or biological processes, or they may be stochastic in that they seek to reproduce the
statistical behavior of a hydrologic time series without regard to an actual event. Most hydrologic
models for engineering applications fall within the conceptual category (Linsley, Kohler, and
Paulhus (1982)). Many conceptual models have been reported in the literature. Watkins (1962)
reported the development of an urban catchment model called the British Road Research
laboratory Model ( RRLM). Dawdy (1965) developed a rainfall- runoff event simulation for the
U.S. Geological Survey.
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Later, this model (Dawdy, Lichty and Bergman (1970)) was adapted to urban catchments. Eagleson
(1970) and his collaborators at MIT developed t complex MIT model. Most of these earlier models
were developed for rural settings, later adapted to urban catchments and generally do not include a
water quality component.
Several comprehensive simulation models have been developed which apply to an urban catchment
and also include a water quality component Crawford (1971) reported the development of the Hydro
Comp Simulation Program (HSP), as an extension of the Stanford Watershed Model. An urban
component has since been added. The U.S. Environmental Protection Agency ( 1971) sponsored the
development of the Storm Water Management Model (SWMM) m a huge ( 14,000 cards) Program
which has been defined several versions. The University of Cincinnati (1970) developed an urban
runoff model ( UCURM) which has been widely used ( Danner (1982)). Finally, the U.S. Army Corps
of Engineers (1974) developed the Storage Treatment, Overflow and Runoff Model (STORM).
A major need in the field of urban planning and applied hydrology is to modify and adapt existing
simulation models to the assessment urban water quality in a timely and cost effective manner. Work
by Dr. G. Kenneth Young and his collaborators at The Catholic University of America over the past
ten years has demonstrated significant progress in the simplification of complex simulation models
and their adaption as practical water quality assessment tools through the use of systems analyses
guided by data by data from model verification and calibration studies.
18
See e.g. Young and Danner (1982), Michael et al. (1982), Danner, et al. (1974). This
work has resulted in the introduction of conceptually and computationally simpler
simulation tools for studying water quality in an urban environment.
This research effort represents a consolidation and extension of the efforts by Dr. G.
K. Young and his associates to develop conceptually simple and yet accurate tools for the
study and assessment of urban water quality.
3. MODEL DEVELOPMENT
3.1 Objective
The objective of the model is to provide a conceptually valid a computationally simple
method to simulate storm runoff and pollution emission from an urban catchment. The model
concept is developed fro the well documented principles of runoff, evapotranspiration, soil
moisture, and sedimentation; combined with pollutant-soil mixing and transport processes.
Model simplifications are obtained by exploiting recently developed calibration and testing
results relating catchment model sensitivity to specific model parameters. Analysis of these
results allow the determination of a small number of key parameters that can be combined in a
catchment behavior model which is computationally efficient and yet achieves the prediction
accuracy of complex models.
The model is to be used as an intermediate analysis tool to generalize input/output
frequency function relationships. Given an input precipitation frequency function in the form
of a time series, model will compute the output frequency functions for runoff volumes and
pollutant concentrations. Analysis of the output time series will yield runoff and pollution level
exceedance probabilities, in the form of cumulative frequency functions or frequency density
functions.
3.2 General Logic of the Model
The general logic of the model is shown in Figure 1. The model structure is defined by
two input processes consisting of rainfall and dustfall time series, two output processes
consisting of runoff and
19
pollution emission time series, and analysis algorithms that transform the input into output.
The rainfall and urban pollutant functions are initially accumulated onto an urban
catchment surface consisting of pervious and impervious areas. For ease of discussion and
without loss of generality, we assume that there are two continuous and disjoint areas
representing the pervious and impervious portions of the catchment.
During periods between storms, the surface accumulation is reduced by the physical
processes of evapotranspiration and pollutant decay. During a storm, similar but distinct
processes are applied within the pervious and impervious areas. On the pervious area, the
pollutant is mixed with the rainfall and is partially or totally removed with the discharge,
depending upon the extent of rainfall, geometry of the catchment, and physical properties of the
soil and vegetal cover.
Rainfall accumulated on the pervious area is either discharged directly along with the
pollutant or it infiltrates the soil surface and enters the vegetation root zone. There, pollutant
mixing occurs in a thin active layer, whose thickness is determined by the chemical and soil
properties. Portions of the precipitation and pollutant may then be discharged, washed off or
retained, depending upon the extent of rainfall, soil moisture, vegetal cover and catchment slope.
Some portion of the volume in the root zone may also be lost due to deep percolation as the root
zone becomes saturated.
21
22
The total runoff and pollutant emission are obtained by summing the amounts from the pervious
and impervious areas.
3.3 Model Building and Verification
The following model building sequence is followed:
1. Generate a conceptual model logic. The conceptual model is based on known physical
relationships, whose parameters can be estimated to the maximum extent practicable, from
site-specific attributes.
2. Fit as many of the parameters of the conceptual model as possible using a priori logic
and site specific data.
3. Utilize statistical measures for the parameters that remain, such as ordinary least
squares (OLS); constrain the OLS as necessary to known dimensions and conditions
(for example, force the intercept to zero if a zero intercept is called for).
4. Apply the model using given input files to generate a model output time series.
5. Compare the model output time series to the known site measurements and
quantitatively evaluate "goodness of fit," using the K-S statistic (Massey (1951)).
6. Calibrate the model's coefficients to achieve a better fit to the known site’s data. Conduct
the calibration by adjusting those coefficients having the greatest uncertainty associated with
them.
7. Guide the calibration with knowledge of parameter sensitivity gained throughout
the model building activity or gained by formal sensitivity studies.
The model building sequence as it progresses will evaluate the sensitivity of
the various parameters and assumptions that comprises logic. Parameters and
assumptions that are insensitive are candidate for sound default values or "hard
coded" logic sequences that do not permit change by the analyst. Conversely,
sensitive parameters and assumptions are subject to calibration and need careful
estimation. Logic and equations may also be found to be of greater or lesser
importance and this information may be used in model specification.
Available watershed site data will be split prior to model building. Part of
the data will be used for model building. The remaining data will be used for
verification.
For the data site applicable to this task, the model(s) will be "set up" and
run for time series simulation and event prediction as the known measured output
data did not exist. Site-specific information will be used to estimate the parameters
and default values will be selected as necessary.
The predictions will then be compared to the actual measured data in the
project data sets. The standard errors of estimate will be calculated. If necessary,
additional calibration will be conducted.
23
3.4 Model Variables and Parameters
The runoff/pollution concentration model may be envisioned as an approximately linear
dynamical system with pairwise function of time. Output consists of the two time varying runoff
and pollution concentration functions. The system is characterized by a number of parameters
that apply within the system analysis to transfer the input process into output processes.
The system components are defined as follows.
Input
Parameter Definition
X1(t) – Rainfall time series (inches/day)
X2 (t) – Pollution loading time series (lbs./acre/day)
Output
Y1 (t)- Runoff time series (inches/day)
Y2(t)- Pollution emission time series (lbs./acre/day
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Variables Parameter Definition Units
C P1 -Fraction of Catchment that is impervious
0<P<1
Imax P2 Maximum Infiltration
Inches/
day
Vmax P3 Root zone saturation volume
Inches
Por P4 Porosity 0<P<1
D P5 Root zone depth Inches
P Active mixing
layer depth
inches
Intermediate Function Variables Used In Calculations
Vp (t) – Pervious area root zone volume
I(t) – Infiltration
LI(t) – Impervious area component of pollutant loading
Lp(t) – Pervious area component of runoff
QI(t)- Impervious area component of runoff
Qp(t)- Pervious area component to runoff
W I(t) – Impervious area components of pollutant emission
Wp(t)- Pervious area components of pollutant emission
25
Kw
P7 - Runoff Coefficients (inches/day)
Kp P8 - Pervious surface pollution removal rate
Day-1
KI P9 -Impervious surface pollution removal rate
Day-1
A P10 -Fraction of pollutant that is soluble
0<P<1
Kd P11 -Pollutant decay rate Time -1
S P12 -Land slope
- ft/ft
PK P13 -Soil type/ use factor
-
P P14 -Deep percolation
Inches/day
E P15 -Evapotranspiration
Inches/day
A P16 -Catchment area
Acre
V d P17 -Root Depth Volume
inches
Model Components
QI(t) = CR(t) (3.1)
In the pervious area, the runoff process may be described in terms of the rainfall,
infiltration, evapotranspiration and percolation processes. During dry periods, the volume
of water in the root zone is
where C is the fraction of A that is impervious.
26
Catchment Description. The catchment consists of a typical urban or suburban watershed
with surface and subsurface drainage components. The entire catchment, A, consisting of
a surface area and subsurface volume is divided into a net impervious component, I, and a
net pervious component, P. The impervious surface area represents paved areas such as
streets and sidewalks as well as roofs. The pervious surface area consists of unpaved soil
surface, which may contain some degree of vegetation.
Rainfall. Rainfall is assumed to be applied uniformly to the catchment for a period of
time, T. For the purpose of the model, rainfall data is provided as input. We let X(t)
denote the amount of rainfall at time T. We wish to consider a daily time increment
model. Therefore, the period of uniform rain, T, will be some time less than 24 hours and
X(t) will denote the 24 hour rainfall value, where T denotes the particular day under
consideration.
Runoff. All rainfall onto the impervious area is assumed to be converted to runoff.
Therefore, if qI(t) represents the impervious area runoff, then
Depleted by the processes of evapotranspiration and deep percolation. The water volume balance at any time
may be expressed as
dVp =I(t) – P(t)- E(t) dt and the condition of no surface runoff during dry periods may be expressed as q(t)= 0 if R(t)=0 During wet periods, the water balance is given by
dVp = I(t) –P(t) dt I(t), the infiltration volume, which represents the volume of water added from the surface to root zone storage is
assumed to decrease linearly from a maximum value at the onset of a storm to zero when the root zone becomes
fully saturated. Therefore, I(t) is represented
I(t)= Imax (t) – Imax (to) V p (to)) Vmax- Vp (to)
Where Imax (to) is the maximum value of infiltration experienced at to, the time of storm initiation, V(to) is the
root zone volume at the onset of the storm, and Vmax is the saturation volume of the root zone defined by
Vmax= Porosity x Root Depth Volume =Por. Vd .
The amount of pervious surface runoff is then computed as the difference between pervious surface rainfall and
the increment to root zone storage. That is,
Qp (t)= (1-C) R(t)- dVp (t). dt
27
The total runoff is then given by
Q(t) = QI (t) + Qp (t) (3.8)
3.6 Evapotranspiration, Infiltration and Percolation
The assumed infiltration versus soil moisture relationship is shown in Figure 2. Maximum
infiltration is seen to occur at the time of storm initiation and the infiltration rate decreases linearly
to zero at the maximum allowable soil moisture condition, defined by the product of soil porosity
and root zone depth. Figure 3 indicates the assumed relationship between maximum onset
infiltration rate and rainfall. We assume that the maximum infiltration rate is constant for small
storms, but increases linearly with rainfall amount after some threshold rainfall intensity is
achieved. Hence, the rainfall infiltration curve is a function of the three parameters A, B, and C
representing the small storm constant value, the slope of the large storm linear curve and its:
intercept. The three parameter set reduces to two parameters for the special case, A = C.
The assumed analytical relationship between maximum infiltration and rainfall for large
storms is derived from trends indicated by empirical field data. Figures 4 and 5 show plots of
rainfall versus infiltration, calculated as rainfall minus runoff, for daily records at rainfall and runoff
for two field data sites measured by the Occoquan Water Monitoring Laboratory for the 1983. The
two sites possessed similar rainfall experience. However, the linear form of the infiltration's large
rainfall relationship is evident from both sites.
28
32
Evaporation, infiltration and percolation are all processes that occur in the pervious
area. Percolation represents the movement of water from the upper zone (root zone)
adjoining the surface to a lower zone which connects to ground water. Percolation is
assumed to be constant in the model.
Evapotranspiration is assumed to be subject to seasonal fluctuations. That is
evapotranspiration is taken as a constant value, which changes monthly. Evapotranspiration
is assumed to occur only during dry days.
Infiltration or movement of water through the soil surface into the soil, is defined as
a linear function of soil moisture for a given rain level. It assumes its maximum value when
the pre-storm soil moisture is zero and it decreases linearly to zero with increasing soil
moisture to a fully saturated upper zone. The maximum infiltration is a site specific input,
whereas a minimum value of zero is reached when the soil moisture reaches the saturation
or maximum moisture volume stage. Maximum soil moisture is defined by the condition
Vmax = Por • V where Por is the porosity of the soil and V is the volume of the root depth
zone.
3.7 Pollution Loading
Pollution loading consists of the traffic debris and dust accumulation onto the
pervious and impervious surfaces of the catchment. The pollution is assumed to build up
during the periods between storms with a fraction of the build-up being lost each day
through dissipation
to the street or soil surface and the atmosphere in accordance with a first order loss mechanism.
That is, the daily loss is directly proportional to the total accumulation.
Let L p (t), L I (t) be loading functions that represent the application of pollution to the
pervious and impervious surfaces respectively. Let W P(t) be the accumulated pollution levels the
respective surface. Then at any time, the accumulated pollutants loading is
dW = L P (t)
dt
dW = L I (t) dt
3.8 Pollutants Emission
The pollution that accumulates on the impervious and pervious surfaces during the dry
periods between storms is partially or totally removed during a storm. The amount of pollutants
removed is a function of the amounts accumulated through the loading functions, the rainfall
intensity and duration and the physical properties of the impervious and pervious components of
the catchment.
On the impervious area, we assume that the pollutant emitted during a storm is
proportional to the product of the accumulated pollution and the rainfall intensity. That is, at any
time instance we have
dW = K. W I dt
33
We assume further that K= K W R such that
dW/dt = - KW. R. W
where KW is the runoff coefficient.
Further, during the dry periods, assume that some of the pollutant is dissipated by biotic on
physical mechanisms including chemical exchanges between the pollutant ad the atmosphere.
This loss is assumed to be proportional to the amount of pollution present, and it is modeled by
dW = -K 2 W I + LI(t) dt
On the pervious surface, the pollutant that is accumulated during dry periods is assumed
to be partitioned into a soluble part, W S(t) , which is dissolved into the rainfall and washed off
during a storm, as runoff and a sorbed part, Wb(t), which becomes part of the sediment which is
then removed or retained as part of sediment processes. Let α denote the fraction of the pollutant
that is soluble. Then in 1-α= 1- Wb (t) / Wp (t) of the pervious surface area, the pollutant will be
mixed in a thin layer of soil near the surface and then washed off with the removed sediment. Let
ℓ denote the depth of the active layer and let ℓ’ denote the amount of ℓ that is removed by
sediment processes at time t. Then at any time during the storm, the amount of pollutant washed
away is given by
(1 - α). Wp (t). ℓ’ (t)
34
and the remaining pollutant is given by
(1-ℓ’) (1-α) WP (t) This remaining mount is then subject to further partitioning in time until either the storm ends or the
entire pollutant is removed. During non-raining periods, the pollution is assumed to dissipate according to
the relationship
dW = - KP WP + LP(t) dt
where KP, KI are pollution dissipation constants. 3.9 Computational Form
A discrete form of the mathematical model is required in order to specify a daily digital
simulation. The discrete form is obtained by evaluating the continuous form developed above at discrete
time steps and approximating the differential operators by finite difference equations. The discrete time
steps selected are equally spaced and separated by the time steps selected are equally spaced and
separated by the time step, Δ t. Unless otherwise specified, we take Δ t as unity such that end time step
represents a unit increase in the time variable. By applying this approach to the model developed above
we obtain digital algorithms.
For any function of time, f(t), let
f I = f( i. Δ t), i= 0,1,2…N.
Then in this notation, we obtain the following algorithms:
35
Impervious Area Runoff
qIi =Ci Ri
Pervious Area Runoff
Dry period water balance: Vi+1= vI -Pi -Ei (3.19)
Wet period water balance: Vi +1 = Vi - Pi + Ii (3.20)
Infiltration: I= Imax - Imax ( V- Vo) (3.21) Vmax - Vo
Runoff: qPi = (1-C) Ri (Vi +1 - Vi) (3.22)
Pollution Concentration Impervious Surface: WIi = WIi-1 - K1 WI i-1 + LIi (dry period) (3.23) WIi= WIi-1 - K2Ri-1 WIi-1 +LIi
= WIi-1 (1-K2Ri-1) (wet period) (3.24) Pervious Surface: WPi +1 = WPi-K1WPi-1+ LPi (dry period) (3.25) WSi =WPi (3.26) WB I (1-α) WPI ℓ (wet period) ℓ (3.27) WP i+1 = (1 -ℓ (1-α) WP (3.28) ℓ ℓ’ I =C . PK. S .Ri . (1-α) (3.29)
3.10 Summary of Principal Assumptions The primary assumptions used in the development of the runoff pollutant concentration model are
following :
36
(1) The model operates with a daily time increment and a rainfall input that is averaged over each day (2) The pollutant loading forcing function is constant over the 2-hour time period for both the pervious
and impervious areas.
(3) The average daily rainfall for the catchment removes 90% of the accumulated impervious area
pollutants in a 24-hour time period.
(4) Evapotranspiration rates change slowly throughout the seasons and are assumed constant during a
given mouth.
(5) Deep percolation is constant
(6) The soil is fully saturated at the beginning of the study period (late winter/ early spring).
(7) Soil loss increases linearly with rainfall. The rate of increase is a function of catchment slope and
soil condition. This loss is forced to be proportioned to the product of rainfall, slope and soil condition.
The formulation is the same as the Universal Soil Loss Equation (USLE).
(8) An average rain (rainy day) washes off one-half of the active layer on the pervious area.
(9) Daily infiltration is directly proportional to daily rainfall and inversely proportional to soil moisture
(10) Infiltration rate is a function of soil moisture and rainfall intensity.
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4. Model Application and Evaluation
4.1 Approach
The approach to model application and evaluation entails three essential steps: (1) appropriate field
data for at least two sites must be identified whose characteristics can be quantified in a form suitable for
application to the simulation model; (2) the simulation model is then calibrated to one of the field sites by
adjustment of the model input parameters to attain close agreement between the simulation predictions with
the measured emission levels for that site and ; (3) data from the second site is then used to verify the
prediction accuracy of the simulation tool by applying the model to the data for that site. The results obtained
from the calibration and verification processes along with the results of related parameter sensitivity analysis
may be used to judge the validity of the developed model and to determine it’s range of applicability.
4.2 Application to field Data
Field Data Selection
Field data were needed to validate and evaluate the nonpoint source prediction model developed in this
project. Typical urban watershed were sought, with special interest toward data for the Washington D.C.
Metropolitan Area. Fortunately, some local data were identified. During the years 1979-1982, the Northern
Virginia Planning District Commission (NVPDC) and the Virginia Polytechnic Institute (VPI)
38
collaborated in a field data collection effort of over 600 station storms under the auspices of the EPA
Nationwide Urban Runoff Program (NURP). Available data from these urban watershed studies were selected
as the field data for use in the assessment of the model.
The MWCOG study included the collection of data on precipitation, runoff and pollutant
concentrations at twelve monitoring sites, six which were pond facilities (retention or detention) requiring
inflow and outflow monitoring. Two sites were selected for analysis from this set of twelve sires, Burke Pond
Site located in Burke, VA and Stedwick Inlet, located in Montgomery Village near Gaithersburg, Maryland.
Description of Data Sites
The Burke Pond site consists of a medium density single family residential development as shown in
Figure 6. The Stedwick site was a similar watershed that consisted of higher density townhouse/garden
apartments. The principal characteristics of the two sites are shown in Table 2. The two sites have comparable
slopes and impervious ground cover. The Stedwick site is 50% larger than Burke Pond although both qualify
as small watersheds Stedwick is also ore developed, consisting of mostly residential properties containing
significantly less curb and gutter area than the Burke Site.
39
TABLE 2. FIELD DATA SITE CHARACTERISTICS
The two sites differed primarily with respect to soil condition. The Burke Pond Site is
characterized as SCS hydrologic soil group C. This group of soils is characterized by slow
infiltration rates when thoroughly wetted and a slow rate of water transmission. Thus, the Burke
Site may be considered to have high runoff potential. The Stedwick Site is characterized as
hydrologic group B, whose soils have moderate infiltration rates when thoroughly wetted and a
moderate rate of water transmission. Therefore, the Stedwick Site may be considered to have
moderately low runoff potential.
41
Characteristics
Burke Pond Stedwick
Inlet
Watershed Area (Acres) 18.3 27.4
Average Density (du/Acre) 3.0 6.1
Percent Impervious (%) 32.7 33.8
Percent Effective Impervious (%) 25.1 25.1
Representative Slope (%) 4.5 4.7
Streets With Curb and Gutter (%) 100.0 79.7
Data Selection, Preparation and Analysis
The MWCOG study collected data on rainfall, runoff and chemical concentrations. State-of-
the-art measurement techniques were employed to measure baseflow , runoff, wetfall, dryfall and
high volume particulates. Rainfall and pollutant loading levels were selected as the input or loading
functions of interest. The pollutants, Chemical Oxygen Demand (COD), nitrogen (TN) and
phosphorus (TP) were selected as th contaminants of interest for use in assessing the simulation
model.
The field data had been recorded in units of cubic feet per second (cfs) for flow and
milligrams per liter (mg/L) for concentration. To obtain the units of inches (flow) and pound (loads)
required in the simulation model, the following conversion factors were used:
Loads (lbs)= Flow (cfs) x Concentration (mg/L) X sec x .0000624 Rain or Runoff (inches)= Flow (cfs) x sec x 1728 Sq. mi x (5280)2 x 14
Missing runoff data values were estimated by regressing inches of runoff against inches of
rain and antecedent dry period (days). The 1981 calendar year was taken as the time period of
interest as the data were fairly complete for that period.
Analysis of the data entailed the derivation of statistical measures (1st and 2nd moments) to
characterize the measure time histories are assumed to represent realization of stationary processes.
As such, it is expected that the first and second moments should suffice for their characterization.
42
Also, the physical parameters of the test site were measured or computed in order to provide a basis for a
comparison of the field data with the results of the simulation model. Table 3 shows the means and
standard deviations of the 1981 data from the Burke Pond and Stedwick sites. Rainfall is essentially
constant for the two sites due to their close proximity. The runoff values, however, vary substantially.
The runoff volume for the moderate infiltration capacity Stedwick Site is only 1/3 of the runoff volume
the Burke Pond site which has a different infiltration rate. The pollutant washed off is comparable
between the sites on an absolute basis. This is attributable to the larger Stedwick catchment size
combined with the larger runoff potential of the Burke Pond site.
3 Model Calibration and Verification
Calibration Procedure
The simulation model described in Chapter 3 was calibrated and verified with respect to the field data
for the Burke Pond site. This entailed the initial selection of model parameters based on the site specific
data and then refinement of the parameter values based on a calibration process intended to produce
unbiased, minimum variance estimates of the output moments. Formally, the computational procedure is
as follows.
(1). Select parameters based on physical dimensions
(2). Apply the model and conduct sensitivity analysis of bias
(3). Adjust bias to zero by modifying the sensitive parameters.
43
TABLE 3. MEANS AND STANDARD DEVIATIONS
44
Variable Burke Pond Site Stedwick Inlet Site
Rain (In.) X '0.448 0.443 SX 0.488 0.468
Ra.in._> 0.05 (In.) X 0.589 0.569SX 0.483 0.461
Runoff (lbs.) 0.267 0.098
SX 0.305 0.132 COD (lbs.)
X 43.663 40.262SX 24.477 34.354
TP (lbs.) X 0.372 0.302SX 0.465 0.273
TN (lbs.) X 3.056 2.539SX 2.539 2.224
(4) Apply the model and conduct sensitivity analysis of the standard error of estimate.
(5) Iterate on 2, 3, 4, and 5 to get bias and standard error simultaneously adjusted.
Bias and standard error are defined in the statistical sense. For any variable, Y with
mean u = EY, let Yc be an estimate of Y. Then,
Bias (Yc )= E -u (4.3)
Standard Error (Yc ) = (E(Yc - Y)2) 1/2 (4. 4)
The Burke Pond site was selected to calibrate the simulation mode Table 4 shows the
initial estimate of the parameter values for this si based on physical dimensions and
engineering analysis.
Calibration Results
Application of the calibration procedure resulted in the identification of model
parameters having minimum bias and standard errors of estimate when applied in the model
simulation to the Burke Pond data. Table 5 shows these optimum values of the model
parameter obtained by application of the calibration procedure outlined above is noted that
the slope and evapotranspiration parameters were fixed the geographic and environmental
conditions of the site and hence the parameters were not subjected to calibration.
Figures 7, 8, 9, and 10 show the comparison of Burke Pond field measurements
(actual) and simulation prediction (predicted) results based on the 1981 year data and using
the optimum parameter values shown in Table 5. Qualitatively, the results show excellent
agreement between
45
46
Parameters Value Units
Maximum Infiltration (Imax) 0.033 Inches/day Percolation 0.067 Inches/day Root Zone Depth 18.0 Inches Porosity 0.4 Inches Slope 0.045 Soil Loss Coefficient 58.6 Active Layer Thickness 5.4 x10-6 Inches Washoff Coefficient 5.1 Heavy Rain Infiltration -0.30 Inches
Intercept Heavy Rain Infiltration Slope 0.73 ft/ft Partition Coefficient
COD 0.20 - TP 0.20 - TN 0.80 -
Pollutant Dissipation Coefficient
COD 0.10 1/day TP 0.20 1/day
TN 0.20 1/day
Monthly Evapotranspiration
E(1) E(2) E(3) 0.02 0.03 0.05 Inches/day
E(4) E(5) E(6) 0.09 0.19 0.25 E(7) E(8) E(9) 0.2 0.18 0.12 E(10) E(11) E(12) 0.08 0.05 0.02
TABLE 4. INITIAL ESTIMATES OF PARAMETER VALUES (BURKE POND SITE)
47
TABLE 5. OPTIMUM PARAMETER VALUES (BURKE POND SITE)
Parameters Value Units
Maximum Infil trat ion (Imax) 0.275 Inches/dalPercolation* 0.067 Inches/dalRoot Zone Depth* 18.0 Inches Porosity* 0.4 Inches Slope* 0.045 Soil Loss Coefficient* 58.6 Active Layer Thickness 1.08 x10- 5 Inches Washoff Coefficient 1.25 Heavy Rain Infi l trat ion -0.30 Inches
Intercept Heavy Rain Infi l trat ion Slope 0.73 f t / ft Part i t ion Coefficient
COD 0.10 - TP 0.60 - TN 0.40 -
Pollutant Dissipation Coefficient
COD 0.008 1/day TP 0.057 1/day TN 0.033 1/day
Monthly Evapotranspiration*
E(1) E(2) E(3) 0.02 0.03 0.05 Inches/dayE(4) E(5) E(6) 0.09 0.19 0.25 E(7) E(8) E(9) 0.2 0.18 0.12
E(10) E(11) E(12) 0.08 0.05 0.02
52
the predicted and actual runoff results. The accuracy of predicted pollution concentrations is
less; however, the agreement is still quite good.
Table 6 shows a comparison of actual and predicted means and standard deviations
for the Burke Pond site. This data provides a quantitative analysis of the qualitative results
shown in Figures 7-10. The mean values are in agreement, indicating that the predicted
values are unbiased. The standard deviations are also in close agreement, indicating the
simulation model preserves the field data structure through low order moments.
Frequency functions consisting of sample cumulative distribution functions were
computed for the actual and predicted Burke Pond site data. Nonparametric tests of
significance were performed, to determine whether the simulation results could be deemed
statistically equivalent to the actual data. Figures 11-14 show a comparison of the simulation
and actual frequency functions for the Burke Pond site. It is seen that the distributions
compare well throughout, but that the comparison is better for large values of the variables
and worst for small values. This is especially true for the pollution concentration quantities.
It was desirable to apply statistical tests of significance to the differences between the
actual and predicted results. The Kolmogorov Smirnoff test was selected. This is a
nonparametric test that provides a robust test statistic which is fairly insensitive to the form
of underlying distribution of the data variables. At the 0.05 significance
TABLE 6. COMPARISON OF ACTUAL AND PREDICTED MOMENTS (BURKE POND SITE)
VARIABLE ACTUAL PREDICTED*
Rain (In.) X 0.448SX 0.488
Rain > 0.05 (In.) X 0.589SX 0.483
Runoff (lbs.) X 0.267 0.267 SX 0.305 0.313
COD (lbs.) X 43.663 44.070 SX 34.477 38.367
TP (lbs.) X 0.372 0.371 SX 0.465 0.309
TN (lbs.) X 3.056 3.046 SX 2.539 2.445
*Unbiased Minimum Variance Estimates.
53
level, the test statistic may be computed as
KS = 1.3581 N -1/2 (4.5)
where KS is the absolute value of the maximum difference between the actual and predicted
frequencies in the cumulative distributions and where N is the sample size, which is assumed to be
large (Massey (1950). For the Burke site data, N=54 such that the critical value of the test statistic at
the 95% significance level is
KS = 1.3581 x (54)-1/2 = 0.186
Based on a comparison of all the maximum differences in actual versus predicted
cumulative distribution frequencies using this test statistic, it was found that none of the simulation
time series was significantly different from the actual data. Differences in means and standard
deviation were also subjected to statistical significance tests. The standard deviations were tested,
using a variance ratio test (Hogg and Craig)) under the null hypothesis that the predicted and actual
time series were samples from a normal distribution with equal means and equal variances. This test
revealed that all of the differences in variances were insignificant at the 0.10 significance level.
Differences in means were then tested using the Student’s t-Test (Hogg and Craig (1969)), under the
null hypothesis of equal means. This test also found that the differences in means were insignificant
at the 0.05 significance level. This demonstrates that the calibration of the simulation of Burke Pond
site was successful based on the above statistical testing.
58
The verification procedure is designed to confirm that the simulation model that has been developed and
calibrated based on applications to a single data site may be shown to successfully predicted the behavior
of a second independent data site. Formally, the verification procedure is to: (1) Adjust the calibrated parameters to a second watershed.
(2) Run the model and compare the results based on standard error analysis.
The Stedwick Inlet site was used to verify the developed simulation tool, using the procedure detailed in
Section 5.1. That is, first optimum parameter values were determined through analysis of physic site data.
Then a bias analysis was performed to test the adequacy of the selected parameters. The optimum
parameter values are shown in Table 7. The determined parameters were then used as input to the
simulation and simulation output processes were computed.
Verification Results
Figure 15-18 show a comparison of the actual and predicted time series for runoff, COD, TP and TN at
the Stedwick Inlet site. Table 8 shows a comparison of first and second order moments between the actual
and predicted results. Very good statement is shown for runoff and reasonably good agreement is shown
for the pollutants COD, TP and TN. The mean values are unbiased, as expected. The model seems to
work for estimating expected pollutant emissions. The predicted standard
Verification Procedure
59
Parameters
Values Units
Maximum Infiltration (Imax) 0.62 Inches/day Percolation* 0.10 Inches/day
Root Zone Depth* 18.0 Inches Porosity* 0.45 Inches
Slope* 0.047 Soil loss Coefficient* 58.6
Active Layer Thickness 5.4x10-5 Inches Washoff Coefficient 1.25
Heavy Rain Infiltration Intercept -0.025 Inches Heavy Rain Infiltration Slope 0.75 In/in
Partition Coefficient COD 0.10 - TP 0.60 - TN 0.40 -
Pollutant Dissipation Coefficient COD 0.016 1/day
TP 0.097 1/day TN 0.061 1/day
Monthly Evapotranspiration* E(1),E(2),E(3), 0.02, 0.03, 0.05 Inches/day E(4),E(5),E(6), 0.09, 0.19, 0.25 E(7),E(8),E(9) 0.2, 0.18, 0.12
E(10),E(11),E(12) 0.08, 0.05, 0.02 *Values not optimized.
60
TABLE 7. OPTIMUM PARAMETER VALUES
(STEDWICK INLET SITE)
deviations differ more from the actuals than the means. It is usually less difficult to estimate
means than standard deviations and this research is no exception.
Frequency functions were computed for the actual and predicted Stedwick Inlet data.
Figure 19-22 shows a comparison of the actual and predicted cumulative functions. Statistical
comparisons were made , using the Kolmogorov- Smirnoff (K/S) test statistical discussed in
Section 4.3.
As one would expect, the agreement between the simulation and actual data is not as
good for the Stedwick site as for the Burke Pond site used to calibrate the model. However,
application of the K/S test statistic indicated that runoff was insignificantly different between
the actual and predicted values at the 95% significance level. Runoff processes are less
difficult to describe than more complex water quality processes and therefore, predictions
should be better. Analysis indicated, that the simulation consistently under predicted small
values of the pollution emissions. This prediction error trend was found to occur whenever
the model predicted no runoff from the pervious area based on the large infiltration
characteristics of the Stedwick sites. When the lowest 10% of the pollution emission data was
eliminated (very low rains) and the K/S significance test again performed, it was found that the
difference between the actual and predicted COP, TP, and TN values were all insignificant at
the 95% significance level.
66
TABLE 8. COMPARISON OF ACTUAL AND PREDICTED MOMENTS (STEDWICK INLET SITE)
Rain (In.)
Variable Actual Predicted*
*Unbiased Mimimum Variance Estimates.
X SX
Rain > 0.05 X (In.) SX
0.443 0.468
0.569 0.461
Runoff (lbs X 0.098 0.099 SX 0.132 0.167
COD (lbs.) X 40.262 40.460 SX 34.354 50.561
TP (lbs.) X 0.302 0.313 SX 0.273 0.388
TN (lbs.) X 2.539 2.567 SX 2.224 3.099
Summary
Calibration and verification analysis of the developed daily accounting model indicates
that the model is an accurate tool for predicting runoff and pollutant emission frequency
functions from urban watersheds. Applications of the model to two small watersheds having
vastly different runoff and pollution emission characteristics indicated that consistently good
prediction accuracy is achieved for both sets of input conditions. Errors were observed between
the simulation and actual data at the site used for model verification for small values of the
pollutant emissions. However, small pollutant levels are usually not of critical importance in an
urban water quality assessment. Further, it is suspected that this prediction anomaly is related to
the unusual runoff characteristics of the Stedwick Inlet site used in the verification and not
principally due to the model structure.
3.3 Parameter Sensitivity Analysis
Analysis Procedure
The sensitivity of the developed point source model to changes in the values of the
parameters may be assessed by computing changes in the model standard error relative to a site
with available measured emission values. To apply this approach, Stedwick Inlet measured data
was used as a baseline. Each parameter was varied independently by + 25 percent from its
baseline value, the simulation was performed and the standard error or estimate computed.
71
Sensitivity Analysis Results
Table 9 shows the percentage change in standard error resulting from + 25% change in each
parameter for each of the three chemicals COD, TP and TN. Not unexpectedly, the results show that the
parameter sensitivity is related to type of pollutant. For COD, which has a large sorbed component, the
most sensitive parameters are soil loss coefficient and active layer thickness. The highly soluble
pollutants TP, and TN, on the other hand , are more sensitive to the dissipation and washoff coefficients
TABLE 9.OPTIMUM PARAMETER SENSITIVITY ANALYSIS
Base Value Effect of Change in Parameter On Standard Error
72
COD Partition Coeff. Dissipation Coeff. Washoff Coeff.
+25% Change 0.1 +1.25% 0.02 -4.81% 2.5 +1.0%
-25%Change-2.5% +5.6% -0.2%
Soil Loss Coeff. 59 +15.1% -14.2% Active Layer Thickness 0.54 x 10-5 -12.0% +19.7%
TP
Partition Coeff. 0.8 +0:5% -2.1% Dissipation Coeff. 0.09 -3.8% +7.1%Washoff Coeff. 2.5 +10.5% -5.6%Soil Coeff. 59 +0.2% -0.4% Active Layer Thickness 0.54 x 10-5 -0.5% +0.2%
TN
Partition Coeff. 0.8 +8.5% -8.8% Dissipation Coeff. 0.058 -7.5% +10.8%Washoff Coeff. 2.5 +1.8% -1.9%Soil Loss Coeff. 59 +1.6% -1.5% Active Layer Thickness 0.54 x 10-5 -1.1% +2.1%
5.1 Objective
The objective of this chapter is to develop system transfer functions to map input rainfall
distributions into output runoff and water quality distributions into output runoff and water quality
distributions such that operational predictions of runoff and water quality measures may be made
without recourse to simulation methods. The developed transfer functions will contain as parameters
characteristics of the catchment for which a prediction is desired.
5.2 Approach
The approach to transfer function development entails application of a Monte Carlo sampling
scheme to selected rainfall time series catchment physical parameters to generate input to the
nonpoint source prediction model developed in Chapter 3. The model is then applied to the sequence
of generated inputs to produce a corresponding sequence of output runoff and pollution emission time
series. The statistical moments from this input and output data are then used in a generalized
regression model to derive the transfer function. The regression model contains properties of the
simulation model and therefore properties of the catchments as parameters. Thus, given the transfer
function we may input first and second rainfall moments and a small number of catchment
parameters to generate moments of output for the runoff and pollution emission variables.
Figure 23 shows the relationship among the mathematical model, the Monte Carlo sampling
scheme and the transfer function model development.
73
The order of steps in the process may be summarized as follows:
1. Select a set of N rainfall time histories as representative rainfall data
2. Specify sampling distributions for the occurrence of the rainfall time histories in the simulation
3. Specify sampling distributions for all of the parameters of the nonpoint source simulation model
4. Select random samples from the rainfall and parameter distributions as input to the simulation
5. Perform the simulation for each input data set and record the output statistical moments for runoff and
pollution emission
6. Perform regression analysis on the output runoff and pollution emission, statistical moments and input
rainfall moments to derive the transfer functions
7. Apply the transfer function to estimate output moments for given rainfall and catchment and
parameter variables and compare the prediction with that from the simulation model.
The remainder of this chapter details the application of this procedure
5.3 Selection and Pre- Processing of Representative Rainfall Data
Representative rainfall data was obtained from the national climatic data center in Ashville, N.C. Data
consisting of daily rainfall accumulation for the 1983 calendar year was obtained for twenty cities East of the
Mississippi River to the maximum extent possible,
75
each city was taken as the Capitol of a state contained in this geographic region. A complete
listing of the data is provided in Appendix C. The raw data was coded and pre- schooled to
obtain rainfall frequency and low order moments. The mean and standard deviation of rainfall
for each site is shown in Table 10. Mean rainfall per daily rainfall event ranged from 0.273
inches from Charleston, S.C. to 0.704 inches for Montgomery, AL. Daily rainfall frequency
ranged from a low of 94 rain days for Atlantic City, NJ to a high of 123 rain days for Boston,
MA.
76
TABLE 10. SUMMARY OF STATISTICS FOR TWENTY DATA SITES USED FOR RAINFALL INPUT TO MONTE CARLO SIMULATIONS
Site Number Site Location Number of Rain Days
Mean Rainfall Moments Standard Deviations
1 Albany, NY 131 .350 .425 2 Annapolis, MD 106 .522 .562 3 Atlanta, GA 112 .460 .629 4 Augusta, ME 130 .417 .545 5 Boston, MA 133 .392 .500 6 Charleston, SC 108 .273 .321 7 Columbia, SC 98 .462 .559 8 Columbus, GA 132 .318 .396 9 Concord, MA 131 .367 .436 10 Frankfort, KY 99 .359 .427 11 Harrisburg, PA 127 .382 .476 12 Hartford, CN 129 .435 .494 13 Montgomery, AL 107 .704 .731 14 Montpelier, VT 131 .342 .343 15 Nashville, TN 118 .438 .568 16 Providence, RI 129 .514 .698 17 Raleigh, NC 118 .401 .504 18 Richmond, VA 116 .438 .672 19 Tallahassee, FL 126 .535 .639 20 Atlantic City, NJ 94 .401 .428
77
5.4 Specification of Parameter Sampling Distributions
For the purpose of performing Monte Carlo simulations using the conceptual model
developed in Section 3 with the 20 eastern city daily rainfall histories as input, it was desired to treat
the model parameters as random samples from probability distribution. The idea is to introduce
uncertainty into the simulation model by specifying the parameters by probability distribution
functions rather than from point estimates and then from point estimates and then to perform Monte
Carlo simulations, choosing parameter values randomly from the distributions. This procedure is
related to the regionalized sensitivity analysis (RSA) method used by Hornberger and Cosby (1985)
for estimating the parameters environmental models. The uniform distribution was selected for use
with each model parameter. This distribution function is easily specified by the minimum and
maximum values throughout the parameter values throughout the parameter range with equal
likelihood.
Limiting parameter values were determined based on known physical properties of the
parameters and reported measurements. Whenever exact information on parameter ranges could not
be obtained, estimated values were employed. The range of rainfall means (X and standard
deviations (X was provided by the measured values for the twenty eastern city sites. These ranges
are broad enough to bound the mean and standard deviations rainfall values for the two data sites
used to calibrate and verify the developed conceptual model in Section 4. The rainfall limits
78
79
are also believed to characterize point rainfall throughout the eastern United States.
Deep percolation (X3) was assumed to average 2 inches per month for a typical catchment. This rate
results in a mean percolation rate of 0.067 in/day. The range of percolation values was specified by
taking-:a minimum value as 0.03 in/day and a corresponding maximum of 0.10 in/day. Root zone depth
(X4) is the depth of the upper zone Soil moisture storage. Published results have recommended values
between 5 and 20 inches. A value of 18 inches has been found to optimize the simulation of raw data
(Young, et al. (1981)). The minimum value for the simultation was taken as 6 inches and the maximum
value was taken as 36".
The porosity of typical soils is known to assume average values ranging from 0.05 for dense
limestone and shale to 0.35 for sand to 0.4.5 for Clay (Linsley (1982)). The minimum value for its
distribution was taken, as 0.10 and the maximum value as 0.60.
Maximum infiltration occurs at the beginning of a storm when the soil contains the least
moisture. Since infiltration may be computed>as the difference between precipitation and runoff,
maximum infiltration for a given level of precipitation accurs when the least amount of runoff occurs.
Analysis of the data from the Burke Pond and Stedwick Inlet sites demonstrated that for rainfall
events averaging less than l inch, infiltration ranged from 0 to 0.5 inches. For rainfall events
significantly larger than 1 inch, maximum infiltration increased
linearly with rainfall. Based on this observed trend the limiting values of maximum infiltration
were taken as 0.15 and 0.50.
The impervious fraction of as urban catchment generally may account up to 50% of the
catchment area. Typical fractions are on the order of 1/4 to1/3. However, as it was desired, to
cover the widest range of possibilities in the sampling distribution the impervious percentage
was assumed to range from a minimum of 5% to a maximum of 95% of the catchment area,
The American Society of Civil Engineers (ASCE) has reported a monthly
evapotranspiration values for a number of cities in the United States. The values used in the
development of the nonpoint source simulation in Section 3 were obtained by averaging the
reported values for two cities east of the Mississippi, namely Coshocton, Ohio and Seabrook,
New Jersey. Analysis of the ASCE data indicated a range of peak evapotranspiration from 0.15
inches/day to 0.45 inches/day with an average of approximately 0.25 inches/day. The
observation led to a selection of a curve shift factor, f, to be applied to the monthly
evapotranspiration curve having a minimum value of 0.5 and a maximum of 1.5. This
resulted in a random selection of evapotranspiration values ranging from 50 to 150% of the
ASCE reported values for a given month.
Data from the Burke Pond and Stedwick Inlet Sites used to calibrate and verify the
(inches/day)-1 for each site. Since then two sites possessed significantly different runoff
characteristics.
80
it would appear that the washoff coefficient does not depend significantly upon other parameters
and therefore, may be considered as a statistically independent variable, that varies of a reasonably
small range. A range was therefore, selected based on a variation of ± 0.50 (inches/day)-1 from the
computed optimum value of 1.25 (inches/day)-1.
The pollution dissipation coefficient depends upon the particular chemical being modeled.
Pollution emission data from the Burke Pond Site resulted in a dissipation coefficient for
Phosophorus of 0.057 (day)_I. It was assumed that this value is typical and that a coefficient range
from 0.05 day-1 to 0.07 day-1 was reasonable for use in the Monte Carlo runs.
The Universal Soil Loss Equation (Wischmeier (1965) may be usedto calculate the soil
loss per rainfall event, which may be expressed in units of inches loss per acre, from the soil active
layer. The USLE relationship takes the form
USLE (lbs/acre) = KPSR (5 .1)
where,
K in a constant, P is a practice factor, S is the land slope,
and R is the average rainfall per rain event. We define the product of constants K and P to
form the soil loss coefficient, KP. Then using the dry density value of 120 lbs/ft3 and
43,560 ft 3/acre, we obtain the equivalent active layer thickness soil loss in inches as
USLE (inches/acre) = USLE (lbs/acre) 1 (5.2) 435,600
81
Therefore, a soil loss of 1 lb./acre is equivalent to a loss of 2.3 x 10-6 in./acre.
If we then assume that the average rainfall event washes off 1/2 the active layer, the active
layer thickness may be readily determined as twice the equivalent thickness of soil loss resulting
from an average rain, i.e. ℓ= 2 x USLE ( R). Because each of the three factors in the soil loss
formulation may vary as much as an order of magnitude, active layer thickness may vary on the
order of 103. A fit of the USLE relationship to the Burke Pond data produced a value of ℓ= 5.4x 10-
5 Hence, in the Monte Carlo simulation, the parameter range was varied from a minimum of 10-6 to
a maximum of 10-4.
Catchment slope was assumed to vary from a minimum of 0.005 to a maximum of 0.200.
This range is thought to be representative of the realistic range of stores for typical urban and
suburban areas east of the Mississippi River.
The soil loss coefficient ids defined by the product KP, as defined above. It’s distribution
was specified by choosing a minimum of 30 and a maximum of 90. his results in a mean of 60,
which is close to the value of 59 computed for the Burke Pond site by fitting the annual soil loss of
1134 lbs. to the USLE relationship using the measured slope of 0.045 and measured annual rainfall
of 31.3 inches.
The large storm infiltration curve was computed as -0.30 and -0.025 respectively for the
Burke Pond and Stedwick Inlet data site. It was assumed that the Burke Pond site was more typical
of eastern
82
urban areas in terms of its infiltration behavior, a range of intercepts was selected around a
mean value of -0.250. The minimum value was taken as -0.50 and the maximum value as
zero.
Limits on the large storm infiltration curve slope were obtained by assuming a
variation around the values determined for the Burke Pond and Stedwick Inlet Sites. Plots of
the linear relationship between infiltration and rainfall for the Burke Pond Stedwick Inlet
sites are shown in Figures 4 and 5. A minimum value for the simulation was taken as 0.70
and a maximum of 0.80.
83
5.5 Generation of System Response Using Monte Carlo Experiments
It was desired to generate a data base for use in deriving the transfer function between
rainfall events and runoff and pollution emission events. This was accomplished by
employing the Monte Carlo simulation scheme shows in Figure 23. Random samples of
rainfall (from the twenty city sample) and parameter values (from the specified probability
distributions for the 15 model parameters) were used as input to the conceptual model
developed in Section 3 and model outputs were computed for runoff and the pollutant
phosophorus. The model outputs consisted of time histories, which were converted to sample
moments (means and standard deviations).
A sample size of 248 was used. The size of the resulting data base exceeded that
required as a minimum sample size (for instance, 58 samples would have been required to
assure 95% likelihood that each rainfall sample would have been selected at least once, using
a random sampling procedure). However, it was decided to create as large a sample as could
be stored on the microcomputer's floppy disc such that the more stable estimates of the
parameter values might be achieved.
The creation of such a large sample required a large amount of microcomputer time
since each simulation run including computation of statistics requires approximately 10
minutes CPU in the microcomputer.
Table 11 shows the frequency of occurrence of each of the twenty rainfall sites in the
simulation, based on random selection of site number from a uniform distribution on the
interval [1, 20].
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TABLE 11. RELATIVE FREQUENCY OF OCCURRENCE
OF THE TWENTY RAINFALL DATA SITES IN THE MONTE CARLO SIMULATION
Site Frequency 1 21 2 12 3 11 4 12 5 16 6 13 7 10 8 14 9 11 10 10 11 10 12 15 13 8 14 11 15 12 16 12 17 15 18 17 19 9 20 9
Total 248
Table 12 shows the definition and range of the catchment parameters resulting from the Monte
Carlo simulation. Table 13 shows a summary of model parameter , rainfall and pollutant emission
statistics, from the simulation. The complete set of time history data generated as input to and output from
the simulation is shown in appendix D.
85
TABLE 12. RANGE OF PARAMETERS FROM MONTE CARLO SIMULATION
Variable Label Units Mean Value Minimum
Value Maximum Value
Y1 Mean Runoff Inches 0.320 0.135 0.677 Y2 Standard Deviation
Runoff Inches 0.422 0.179 0.712
Y3 Mean Phosphorus Emission
Pounds 0.255 0.081 0.521
Y4 Standard Deviation Phosphorus Emission
Pounds 0.360 0.075 1.989
X1 Mean Rainfall Inches 0.414 0.273 0.704 X2 Standard Deviation
Rainfall Inches 0.510 0.321 0.731
X3 Deep Percolation Inches/Day 0.066 0.031 0.100 X4 Root Zone Depth Inches 22.730 8.000 37.000 X5 Porosity Dimensionless 0.343 0.107 0.599 X6 Maximum Infiltration Inches/Day 0.304 0.152 0.448 X7 Impervious Fraction of
Catchmet Area Dimensionless 0.510 0.055 0.945
X8 Evapotranspiration Factor
Dimensionless 0.994 0.504 1.492
X9 Washoff Coefficient Inches/Day -1 1.130 0.502 1.747 X10 Pollutant Dissipiation
Coefficient Day-1 0.060 0.050 0.070
X11 Active Layer Thickness Inches 1.84x 10-5 1.01x10-6 9.58x10-5
X12 Catchment Slope Dimensionless 0.099 0.006 0.200 X13 Soil Loss Coefficient (Lbs/acre)
(in/yr)-1 60.104 30.122 89.762
X14 LargeStorm Infiltration Curve Intercept
Inches -0.305 -0.457 -0.145
X15 Large Storm Infiltration Curve Slope
Dimensionless 0.750 0.700 0.800
86
TABLE 13. SUMMARY OF STATISTICS FROM MONTE CARLO SIMULATION
87
Variable Label Standard Deviation
Standard Error
Coefficient of variation
Skewness Kurtosis
Y1 Mean Runoff 0.087 0.006 27.171 0.664 1.100 Y2 Standard Deviation
Runoff 0.108 0.007 25.544 0.420 0.299
Y3 Mean Phosphorus Emission
0.079 0.005 30.870 0.148 0.532
Y4 Standard Deviation Phosphorus Emission
0.170 0.011 47.084 4.121 34.655
X1 Mean Rainfall 0.082 0.005 19.785 1.106 2.587 X2 Standard Deviation
Rainfall 0.110 0.007 21.615 0.228 -0.782
X3 Deep Percolation 0.021 0.001 31.581 0.022 -1.271
X4 Root Zone Depth 8.533 0.542 37.541 -0.041 -0.146 X5 Porosity 0.140 0.009 40.870 0.185 -1.141 X6 Maximum Infiltration 0.081 0.005 26.757 -0.235 -0.935 X7 Impervious Fraction of
Catchment area 0.261 0.017 51.254 -0.011 -1.127
X8 Evapotranspiration Factor 0.275 0.017 27.672 0.082 -1.198 X9 Washoff Coefficient 0.356 0.023 31.549 -0.036 -1.151 X10 Pollutant Dissipiation
Coefficient 0.006 0.000 9.250 0.068 -1.223
X11 Active Layer Thickness 0.000 0.000 128.551 1.709 1.996 X12 Catchment Slope 0.054 0.003 54.760 0.074 -1.095 X13 Soil Loss Coeffcient 17.794 1.141 29.888 0.018 -1.237 X14 Large Storm Infiltration
Curve Intercept 0.083 0.005 -27.198 0.190 -0.931
X15 Large Storm Infiltration Curve Slope
0.030 0.002 4.037 0.10 -1.250
This is the form of general linear model used in Regression Analysis and related least squares
analysis. It is written here in the centered form with respect to mean values without loss of generality
and in order to facilitate the interpretation of results from the analysis.
88
5.6 Transfer Function Generation
The approach to transfer function generation entails deriving relationships between the
means and standard deviations of runoff and pollution emission variables considered as dependent
variables and the Urban Catchment parameters considered as independent variables. We assume that
the relationships between the dependent and independent variables are linear.
Let Y1, Y2, Y3, Y4, X1, ... X15 be defined as in Table 12. Let Y, X denote the mean values
of Y,X. Then we specify the linear models of interest as
The inclusion of dependent variables on the right-hand side of the equations is
intended to model the physical situations where the standard deviation of runoff or
pollution emission may depend upon the mean runoff or pollution emission may depend
upon the mean runoff or pollution level and the pollution emission level may depend
also upon runoff mean and standard deviation.
The 248 observations derived from the conceptual model in Section 5.4 were
used to estimate the coefficients in Equations (5.3) through (5.6) through a stepwise
regression procedure. A generalized least squares regression procedure was also fit to
the data but its use was rejected in favor of the stepwise approach, which produced a
higher quality of fit.
Table 14 shows the coefficients for the four transfer function equations. Table 15
shows their relative significance as revealed by the F-Statistic. An overall quality of fit for
each equation is provided through the R2 value, which indicates the percentage of sums of
squares variation in the dependent variable that is explained or predicted by the
independent variables. The results indicate that excellent statistical fit is obtained for the
mean and standard deviation of runoff. The quality of fit is less for phosphorus emission
mean and standard deviation but remains good.
The significance level of the stepwise regression procedure was set to enter or
keep a variable in the model only if the variable's significance level exceeded 0.15.
Therefore, independent variables
89
TABLE 14. REGRESSION COEFFICIENTS FOR PHOSPHORUS TRANSFER FUNCTION
Independent Dependent Variables Variables Y1 Y2 Y3 Y4 Y5
Y1 -- 1.099578 -- -- 0
Y2 -- -- -- -- 0.422
Y3 -- -- -- 1.181080 0.256
Y4 -- -- -- -- 0.360
X1 0.843784 -0.799001 -- -- 0.411
X2 0.021546 -0.737617 0.079015 0.348021 0.510
X3 -0.360631 -0.142233 -- 0.806674 0.066
X4 0.000279 -- -- -- 22.730
X5 0.030124 0.010982 -- -- 0.343
X6 -0.212894 0.145150 0.071026
X7 0.188090 -0.034581 -0.085650 0.251481 0.51
X8 -0.009376 -- -- -- 0.994
X9 -0.003676 -- 0.069462 0.136510 1.13
X10 -- -- 1.255273 -- 0.06
X11 67.033363 90.522240 -1692.977154 -- 1.84 x 10-5
X12 -- -- 0.513074 -0.340322 0.09
X13 0.00007970 -- 0.000367 -- 60.10
X14 -0.173968 -- -- -- -0.30
X15 -0.062632 -0.065406 -- -0.458229 0.75
R2 0.986 0.985 0.637 0.549 -
NOTE: See Table 12 for variable definitions table.
90
Independent Dependent Variables Variables
Y1 -- (203) -- --
Y3 -- -- --
(101)
Y4 -- -- -- --
X1 (2679) (135) -- --
X2 (3) (2260) (8) (27)
X3 (121) (8) -- (5)
X4 (12) -- -- --
X5 (38) (3) -- --
X6 (8) (173) (4) --
X7 (5061) (5) (52) (70)
X8 (14) -- -- --
X9 (4) -- (964) (38)
X10 -- -- (5) --
X11 (5) (6) (169) --
X12 -- -- (80) (2)
X13 (4) -- (4) --
X14 (5) -- -- --
X15 (8) (5) -- (4)
R2 0.986 0.985 0.637 0.549
NOTE: See Tab le 12 fo r va r i ab le de f in i t ions t ab le .
TABLE 15. F-STATISTIC VALUES FOR PHOSPHORUS TRANSFER
91
92
having little or no predictive value to the dependent variables do not appear in the Table.
Several observations may be discerned from studs of the stepwise regression results:
The Standard Deviation of Runoff is a function of the mean level of runoff.
o The Standard Deviation of Phosphorus emission is a function of the mean phosphorus
emission.
o The most significant predictors of mean runoff are rainfall-, impervious fraction of the
Catchment and Deep Percolation. o The most significant predictors of the runoff
standard are the rainfall standard deviation, maximum infiltration and mean rainfall.
o The most significant predictors of mean phosophorus emission are active layer
thickness, catchment slope, washoff coefficient and impervious fraction.
o The most significant predictors of phosophorus emission standard deviation are mean
phosophorus emission, impervious fraction and washoff coefficient.
o The least significant parameters to the overall prediction process are evapotranspiration,
pollution dissipation and catchment slope.
5.7 Transfer Function Validation
The value of the transfer function is derived from its usefulness in estimating runoff
and pollutant emission values without recourse to computer simulation. Should the transfer
function provide reliable estimates of the physical quantities obtained from simulation,
considerable savings in making applications would accrue. To test the validity of the.
derived transfer functions in predicting the results of the simulation, a comparison was
made between the actual measured data, simulation predicted data and transfer function
predicted data for the Burke Pond data site. This data site was used to calibrate the
conceptual model and thus its data is in close agreement with the model simulation.
Data from the Burke Pond Site was input to the transfer function equations and
predicted values were computed. The results are shown in' Table 16.
TABLE 16. COMPARISON OF RUNOFF AND POLLUTANT EMISSION PREDICTIONS
Quantity Burke Pond Conceptual Measured_ DataModel Prediction
Transfer Function Prediction
Mean Runoff 0.267 0.267 0.304
Standard Deviation Runoff 0.305 0.313 0.376
Mean Phosphorus Emission 0.372 0.371 0.270
Standard Deviation Phosophorus Emission 0.465 0.309 0.349
93
The results of the validation comparison reveal that the transfer function method
produces reasonably accurate estimates compared to those provided by the conceptual model.
The prediction accuracy defined as the percentage of the conceptual model values predicted by
the transfer function equation; is 86.2% for mean runoff, 80% for runoff standard deviation,
14% for mean phosphorus emission and 113% for the standard deviation of phosphorus
emission.
94
6. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
6.1 Summary
This investigation produced a microprocessor based conceptual hydrologic model which predicts
runoff and pollution concentration levels from urban nonpoint sources. The model was based on daily
accounting of runoff and pollutant emissions from urban catchments. The model incorporates soil
moisture accounting, soil loss computation for pervious areas, and pollutant accumulation and wash-off
computations for impervious areas. The model uses the following parameters:
95
X1 - Mean Rainfall X2 - Standard Deviation Rainfall X3 - Deep Percolation X4 - Root Zone Depth X5 - Porosity X6 - Maximum Infiltration X7 - Impervious Fraction of Catchment Area X8 - Evapotranspiration Factor X9 - Washoff Coefficient X10 - Pollutant Dissipation Coefficient X11 - Active Layer Thickness X12 Catchment Slope X13 - Soil Loss Coefficient X14 - Large Storm Infiltration Curve Intercept X15 - Large Storm Infiltration Curve Slope
The model was developed in the Basic Language for execution on an IBM Personal
Computer having 256 Kilobytes of memory. The model may be readily adapted to other
computer hardware, including 16-bit microcomputers.
The developed model was calibrated and verified by application to measured field data
from two small urban catchments in the metropolitan Washington, D.C. area. The model was
shown to reproduce the time
history and first and second moments of runoff with excellent agreement and to
reproduce the time history's moments of the chemicals, C.O.D., Phosophorus and
Nitrogen with good agreement.
The developed model was used to perform a comprehensive parametric analysis
using a characteristic set of measured rainfall inputs and randomly sampled catchment
parameter values. The results of the analysis were used to formulate and derive an
analytical transfer function to convolve rainfall inputs and physical system parameters
directly into runoff and pollution level distributions without recourse to continuous
simulation processes. The transfer functions were validated by applying them to predict
runoff and phosophorus emission for a small urban catchment having known
(measured) runoff and pollution emission values. The transfer function method
provided reasonable accuracy in predicting means and standard deviation as runoff
obtained from the time domain conceptual model.
6.2 Conclusions
This research project has led to the following conclusions:
1. A daily accounting model of urban runoff and pollutant concentrations
was developed as a tool for urban water planning and analysis.
2. The model is feasible on a 16-bit microcomputer, having 256 Kilobytes
of memory.
96
3. Impervious area rational design methods and pervious area soil moisture
accounting methods can be integrated into one accurate and simple model
system.
4. The model can be used to generate emission frequency functions for small
urban watersheds for different rainfall inputs and cultural factors.
5. Sensitivity analysis indicates the following ranking of most sensitive
parameters:
highly sorbed pollutants
Soil loss coefficient Active layer thickness
highly soluble pollutants
Dissipation coefficient Washoff coefficient
6. Comprehensive parametric analysis conducted on the microcomputer based
conceptual model allow the development of practical, accurate transfer functions
which convolve input rainfall and catchment parameters into output runoff and
pollution concentration frequency functions directly and without recourse to
continuous simulations.
97
The following areas of future research are recommended as a means of refining the urban
nonpoint source water quality prediction tool developed in this investigation.
1. The model should be applied to additional watersheds of varying size and
geometry to further assess it’s accuracy.
2. The dustball accumulation model should be enhanced through further
evaluation against measurements and possible analytical development if warranted
3. Transfer functions should be derived for other pollutants including chemical
oxygen demand and nitrogen.
4. The computer programs developed in this study should be fully documented
for use by urban planners in their water quality assessment efforts.
98
RECOMMENDATIONS TOWARD FUTURE RESEARCH
7. REFERENCES
American Society of Civil Engineers, Consumptive Use of Water and Irrigation Water Requirements, Technical Report of the Irrigation and Drainage Division, 1975.
Association of State and Interstate Water Pollution Control Administrators (ASIWPCA), America's Clean Water: The States Nonpoint Source Assessment in 1985, September 1985.
Chow, V.T. "Hydrologic Determination of Waterways Areas for the Design of Drainage Structures In Small Drainage Basin," University of I11i.noi,s, Eng. Expt. Sta. Bulletin 462. 1962.
Corps of Engineers (U.S. Army). Urban Storm Water Runoff: STORM User's Manual, Hydrologic Engineering Center, Davis, CA. 1976.
Crawford, N.H. "Studies in the Application of Digital Simulation to Urban Hydrology." Hydrocomp International, Inc. Palo Alto, CA. 1971.
Danner, David L., et al. "Characteristic Urban Hydrograph Model." Paper under the direction of Dr. G.K. Young, The Catholic University of America, December 1974.
Danner, David L. "Planning Criteria for Urban Water Pollution Control,"Ph.D. Dissertation, The Catholic University of America. 1982.
Dawdy, D.R., R.W. Lichty, and J.M. Bergman. "A Rainfall Runoff Model for Estimation of Flood Peaks for Small Drainage Basins," Progress Report, U.S. Geological Survey Open File Report. 1970.
99
Environmental Protection Agency, Report to Congress: Nonpoint Source Pollution in the U.S., January 1984.
Eagleson, P.S. "Unit Hydrograph Characteristics for Sewered Areas," Proc. ASCE, J. Hydraulics Division, Vol. 88, No. HY2, Paper 30697, pp. 1-25. March 1962.
Eagleson, P.S., F.E. Perkins and B.M. Harley. "A Modular Distributed Model of Catchment Dynamics," Report No. 133, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Dept. of Civil Engineering, School of Engineering, MIT. 1970.
Dawdy, D.R. and T. O'Donnell, "Mathematical Models of Catchment Behavior," PASCE, J. Hydraulics Div., HY4, pp. 123-137.
100
Environmental Protection Agency. "Storm Water Management Model," Vols. 1-4 (Report prepared by Metcalf and Eddy, Inc., University of Florida, and Water Resources Engineers, Inc.), Report 110224DOC, 1971.
Hogg, R.V. and A.T. Craig, Introduction to Mathematical Statistics, Second Edition, The MacMillan Company, New York, 1969
Hornberger, G.M. and B.J. Cosby. Selection of Parameter Values in Environmental Models Using Sparce Data: A cast Study, “ Applied Mathematics and Computation , Volume 17, Number 4 November, 1985.
Linsley, R.K., Max A. Kohler and Joseph L.H. Paulhus, Hydrology For Engineers, 3rd Edition, McGraw- Hill Book Company, 1983
Massey, F.J., “The Kologorov- Smirnov Test for Goodness of Fit,” Jour Amer. Stat. Assn., Vol. 46, pp.68-78, 1951.
Micheal Andreas, et al. “ Factors Influencing Pesticide Migration Into The Environment, Systems Design Course Project, Under the direction of Dr. G.K. Young, The Catholic University of America, Spring 1982.
Tholin, A.L. and C.T. Keifer. : Hydrology of Urban Runoff.” ASCE, J. San. Engr. Division, 85, No. SA2: 47-106. 1959
University of Cincinnati, Department of Civil Engineering. “Urban Runoff Characteristics, Water Pollution Control Res. Ser. No. 11024 DQV UESPA, October 1970
Watkins, L.H.” The design of Urban Sewer Systems,” Road Research Technical Paper No. 55, Department of Scientific and Industrial Research, London England. 1962
Wischeir, W.H., and D.D. Smith. Predicting Rainfall Erosion Losses East of the Rocky Mountains, Agricultural Handbook 282, U.S. Department of Agriculture
Young, G.K. and D.L. Danner. Urban Planning Criteria for Non-popint Source Water Pollution Control,” Disrtrict of Columbia Water Resources Research Center Report No. 35, March 31, 1982
Young, G.K. and L.A. Mulkey, Accuract=y of Pesticide Transport Models, Final Report from GKY and Associates, Inc. to EPA Environmental Resaerch Laboratory, Athens, Georgia, December 1982
A. CONCEPTUAL MODEL COMPUTER PROGRAM LISTING
B .MEASURED AND PREDICTED PROBABILITY DENSITY FUNCTIONS
C. FIELD DATA
D. DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER
E. DATA GENERATED FROM MONTE CARLO EXPERIMENTS
101
8. APPENDICES
APPENDIX A
COMPUTER PROGRAM LISTING
APPENDIX B
MEASURED AND PREDICTED PROBABILITY
DENSITY FUNCTIONS
116
APPENDIX C
FIELD DATA
125
DAY RAINFALL(IN.) RUNOFF(IN.) COMBS) TN(LBS) TP(LBS)37 0.005 0.00 0.00 0.00 0.0039 0.290 0.19 30.20 1.80 0.2542 0.620 0.47 58.10 4.80 0.4451 0.540 0.35 59.91 2.88 1.4354 1.300 1.14 94.84 10.91 0.5259 0.005 0.00 0.00 0.00 0.0064 0.460 0.34 45.45 2.94 0.2070 0.005 0.00 0.00 0.00 0.0072 0.005 0.00 0.00 0.00 0.0073 0.005 0.00 0.00 0.00 0.0075 0.150 0.10 14.90 1.02 0.2980 0.020 0.00 0.00 0.00 0.0086 0.005 0.00 0.00 0.00 0.0089 0.900 0.53 83.71 7.86 0.9491 0.450 0.40 41.57 6.16 0.2095 0.430 0.12 87.74 1.49 0.1199 0.250 0.08 15.21 '1.43 0.14
102 0.710 0.63 78.56 9.22 0.73104 0.090 0.15 8.63 1.10 0.18107 0.180 0.19 17.72 1.13 0.05110 0.060 0.01 11.90 0.26 0.12113 0.300 0.17 8.81 1.46 0.06116 0.340 0.26 36.50 2.46 0.29121 0.730 0.56 67.15 5.77 O.S1126 0.010 0.00 0.00 0.00 0.00131 1.090 1.01 125.41 10.45 0.51135 0.620 0.48 58.85 4.67 0.44139 0.470 0.30 37.39 1.79 0.12146 0.410 0.50 69.93 3.70 0.24150 0.100 0.03 9.07 0.55 0.01153 0.830 0.54 74.80 3.46 0.25157 0.020 0.06 1.21 0.23 0.02161 0.660 0.56 61.93 5.02 1.28164 0.560 0.30 30.51 2.06 0.17170 0.260 0.06 14.83 1.25 0.09171 0.150 0.12 26.68 1.47 0.12176 0.650 8.44 36.60 3.77 0.42182 0.540 0.25 36.32 2.17 0.23
FIELD DATA FOR BURKE POND SITE, 1981
FIELD DATA FOR STEDWICK INLET SITE, 1981
N V
DAY RAINFALL (IN.) RUNOFF (IN.) COD (LBS) TN(LOS) TP(LBS) 184 0.140 0.02 3.62 0.19 0.01 185 2.650 1.45 36.58 5.82 0.46 194 0.570 0.22 34.23 2.07 0.21 201 0.680 0.28 55.75 2.89 0.22 206 1.440 0.71 68.32 4.32 0.39 209 0.600 0.31 31.30 1.20 0.42 215 0.340 0.14 28.31 1.65 0.14 218 0.200 0.29 31.31 2.14 0.10 224 1.090 0.40 58.62 3.31 0.46 227 0.500 0.38 38.61 3.53 0.43 236 0.005 0.00 0.00 0.00 0.00 242 0.1350 0.96 159.09 4.94 0.79 247 0.005 0.00 0.00 0.00 0.00 251 0.280 0.02 3.13 0.21 0.02 258 1.810 0.74 106.90 7.76 1.05 260 0.300 0.13 43.52 1.51 0.08 265 0.360 0.09 13.21 1.00 0.07 270 0.280 0.16 21.37 1.63 0.11 274 0.500 0.20 33.64 1.87 0.19 279 0.590 0.29 39.20 2.34 0.26 291 0.150 0.03 6.19 0.96 0.04 296 0.850 0.51 99.74 3.85 2.84 299 1.480 0.79 122.58 5.04 0.56 310 0.270 0.03 20.44 1.19 0.07 319 0.005 0.00 0.00 0.00 0.00 321 0.010 0.00 0.00 0.00 0.00 324 0.005 0.00 0.00 0.00 0.00 328 0.010 0.00 0.00 0.00 0.00 335 0.580 0.13 20.23 0.96 0.21 338 0.060 0.04 20.91 1.12 0.07 341 0.005 0.00 0.00 0.00 0.00 342 0.005 0.00 0.00 0.00 0.00 344 0.005 0.00 0.00 0.00 0.00
31.345 18.66 2441.23 165.00 20.08
FIELD DATA FOR STEDWICK INLET SITE, 1981
128
DAY RAINFALL (IN.) RUNOFF(IN.) COD(LBS.) TN (LBS.) TP (LBS.) 37 0.005 0.00 0.00 0.00 0.00 39 0.300 0.07 30.18 1.61 0.39 42 0.620 0.20 55.11 3.55 0.34 51 0.930 0.32 129.08 5.62 0.93 54 0.600 0.30 103.14 3.02 0.31 59 0.005 0.00 0.00 0.00 0.00 64 0.370 0.10 29.53 1.82 0.20 70 0.005 0.00 0.00 0.00 0.00 72 0.005 0.00 0.00 0.00 0.00 73 0.005 0.00 0.00 0.00 0.00 75 0.290 0.02 2.34 0.58 0.07 80 0.020 0.00 0.00 0.00 0.00 86 0.005 0.00 0.00 0.00 0.49 89 0.900 0.29 78.26 5.06 0.11 91 0.330 0.04 15.83 0.50 0.17 95 0.280 0.04 18.82 0.92 0.04 99 0.280 0.04 14.70 0.44 0.49 102 0.910 0.29 78.29 5.05 0.12 104 0.400 0.09 22.76 1.18 0.08 107 0.080 0.02 8.84 0.52 0.08 110 0.060 0.02 8.79 0.53 0.31 113 0.530 0.17 47.40 3.05 0.26 118 0.490 0.14 39.81 2.50 0.58 121 1.530 0.42 84.23 6.45 0.00 126 0.010 0.00 0.00 0.00 0.21 131 0.680 0.10 29.64 1.79 0.34 135 0.620 0.19 52.61 3.36 0.08 139 0.490 0.08 14.15 0.69 0.21 148 0.460 0.10 29.77 1.74 0.59 150 0.630
0.37 85.10 8.58 0.21
153 0.410 0.21 29.10 3.84 0.47 154 0.810 0.28 75.53 4.95 0.43 155 0.220 0.19 62.18 2.88 0.43 157 0.220 0.19 47.06 4.98 0.28 161 0.620 0.22 64.33 5.53 0.36 164 0.500 0.16 44.82 2.88 0.29 170 0.260 0.00 0.00 0.00 0.00 171 0.150 0.05 17.61 1.19 0.18 176 0.330 0.00 0.00 0.00 0.00 182 0.310 0.00 0.00 0.00 0.00 184 0.140 0.03
18.95 .052 0.06
FIELD DATA FOR STEDWICK INLET SITE, 1981
DAY RAINFALL (IN.) RUNOFF (IN.) COD (LBS.) TN (LBS.) TP (LBS.) 185 1.460 0.35 39.95 2.04 0.50 194 0.570 0.00 0.00 0.00 0.00 201 0.960 0.09 19.74 0.18 0.20 206 0.220 0.03 20.91 1.31 0.14 209 1.720 0.44 152.25 9.84 1.55 215 0.340 0.00 0.00 0.00 0.00 218 0.200 0.01 2.26 0.12 0.02 224 1.480 0.08 11.04 1.67 0.18 227 0.380 0.02 2.39 0.17 0.03 236 0.005 0.00 0.00 0.00 0.00 242 1.000 0.13 27.78 1.63 0.28 247 0.005 0.00 0.00 0.00 0.00 251 0.080 0.00 0.000 0.00 0.00 258 1.460 0.23 30.81 2.40 0.48 260 0.160 0.01 1.87 0.29 0.01 265 0.180 0.00 0.00 0.00 0.00 270 0.030 0.00 0.00 0.00 0.00 274 0.440 0.04 20.60 1.05 0.23 279 0.590 0.06 16.32 1.05 0.16
291 0.450 0.00 0.00 0.00 0.00 296 0.580 0.06 9.63 0.70 0.10 299 2.340 0.62 95.14 4.10 0.77 310 0.270 0.00 0.00 0.00 0.00 319 0.005 0.00 0.00 0.00 0.00 321 0.010 0.00 0.00 0.00 0.00 324 0.005 0.00 0.00 0.00 0.00 328 0.010 0.00 0.00 0.00 0.00 335 0.620 0.07 23.10 1.59 0.28 338 0.060 0.00 0.00 0.00 0.00 341 0.010 0.00 0.00 0.00 0.00 342 0.005 0.00 0.00 0.00 0.00 344 0.005 0.00 0.00 0.00 0.00
========= ========== ========== ========= ========= 31.460 6.98 1811.75 114.47 13.61
129
APPENDIX D
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
130
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER
ALBANY, NEW YORK
DAY RAINFALL (IN).
DAY RAINFALL (IN).
DAY RAINFALL(IN) DAY RAINFALL (IN)
3 0.01 100 0.89 155 0.53 287 0.11 10 0.14 101 0.02 157 0.53 296 0.70 11 0.71 105 0.02 167 0.03 297 0.06 15 0.78 106 1.76 168 0.02 302 0.02 16 0.58 107 0.04 169 0.01 307 0.16 23 1.27 109 1.65 176 0.02 310 0.11 30 0.24 110 0.17 179 0.79 314 0.36 33 0.21 111 0.05 183 0.08 315 0.24 34 0.55 114 0.65 185 0.05 316 0.01 37 0.01 115 0.74 190 0.16 319 0.23 38 0.97 116 0.05 202 0.89 320 0.56 39 0.21 117 0.03 205 0.09 324 0.72 43 0.05 119 0.07 2-6 0.04 327 0.01 48 0.03 120 0.82 210 0.03 328 0.41 61 0.21 121 0.22 213 0.27 329 1.23 63 0.09 122 0.81 214 0.02 332 0.55 66 0.30 123 0.53 216 0.02 332 0.13 67 0.50 124 0.02 223 1.76 334 0.01 68 0.06 125 0.01 224 0.26 336 0.03 69 0.17 128 0.56 230 0.84 337 0.05 70 0.24 129 0.11 234 0.03 338 0.54 71 1.16 135 0.41 242 0.12 340 0.84 72 0.02 136 0.06 243 0.09 341 0.04 77 0.26 139 0.12 253 0.05 346 0.56 78 0.74 140 0.12 255 0.01 347 1.87 79 0.12 142 1.34 259 0.02 348 0.11 80 0.78 143 1.43 262 0.11 349 0.01 86 0.47 146 0.48 264 1.88 352 0.05 87 0.21 147 0.48 265 0.01 353 0.01 91 0.43 149 0.14 274 0.06 356 0.48 94 0.05 150 0.13 277 0.23 358 0.02 97 0.31 151 0.29 278 0.50 362 0.05 98 0.20 154 0.02 285 0.50 . .
131
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
ANNAPOLIS, MARYLAND
DAY RAINFALL (IN.
DAY RAINFALL (IN.)
DAY RAINFALL (IN.)
DAY RAINFALL (IN.)
2 0.01 101 0.67 180 0.34 298 0.96 5 0.37 105 1.02 185 2.25 299 0.08 6 0.15 106 1.12 186 0.17
307 0.03
10 0.42 108 0.03 200 0.07 308 0.22 11 0.12 114 1.26 202 0.01 310 0.06 15 0.07 115 0.35 205 0.13 314 0.98 23 0.40 116 0.05 213 0.13 315 0.06 30 0.02 124 0.16 218 0.09 319 0.58 33 0.96 129 0.03 224 0.54 320 0.05 34 0.02 135 0.21 225 0.09 325 1.24 54 0.52 136 1.37 235 0.17 328 0.36 60 0.62 137 0.09 240 0.15 329 0.35 61 0.35 139 0.04 242 0.04 332 0.18 66 0.40 140 0.08 256 0.78 333 0.03 67 0.72 141 1.10 257 0.02 338 1.03 68 0.07 142 0.28 264 0.22 340 0.33 69 0.02 143 0.11 265 0.59 341 0.11 77 0.80 144 0.35 273 0.65 344 0.04 78 1.37 146 0.34 274 0.06 346 2.05 80 1.08 147 0.71 275 0.07 347 2.25 86 2.06 149 0.53 285 0.75 348 0.06 87 0.68 150 0.29 286 0.96 356 1.56 93 0.86 155 0.49 292 0.20 362 0.85 96 0.06 156 0.25 293 0.33 . . 97 0.07 158 1.06 294 0.35 . . 98 0.25 170 0.39 295 2.08 . . 99 0.74 171 2.02 297 0.51 . . 102 1.94 172 0.59 298 0.96 . .
132
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
ATLANTA, GEORGIA
DAY RAINFALL (IN.)
DAY RAINFALL (IN.)
DAY RAINFALL (IN.)
DAY RAINFALL(IN.)
1 0.57 76 0.16 157 0.29 277 0.21 2 1.46 77 0.01 158 0.27 278 0.11 3 0.03 79 1.39 168 0.02 284 0.23 10 0.11 83 1.71 169 0.01 285 0.06 20 0.31 85 0.98 170 0.37 286 0.76 21 0.31 86 0.08 173 0.26 295 0.07 22 0.01 89 0.16 182 0.64 296 0.53 26 0.01 92 0.51 186 0.02 308 0.25 27 0.23 95 0.22 198 0.08 313 0.08 29 0.05 96 0.13 212 1.11 318 0.94 32 1.12 97 0.03 213 2.71 319 1.08 33 0.78 98 2.78 216 0.34 324 1.54 36 0.32 99 0.10 218 0.01 327 1.37 37 0.30 104 0.14 219 0.02 328 0.87 40 0.05 105 0.13 224 0.16 331 0.17 41 0.09 108 0.44 237 0.22 332 1.16 42 0.01 112 0.01 243 0.04 337 3.10 44 0.19 113 0.29 244 0.03 338 0.02 45 0.18 114 0.01 245 2.11 339 0.31 47 0.11 123 0.15 246 0.62 340 0.96 48 0.01 128 0.06 248 1.11 345 1.79 53 1.26 136 0.50 249 0.48 346 0.02 55 0.27 139 0.43 251 0.02 348 0.01 58 0.30 142 0.01 255 0.34 355 0.05 60 0.02 146 0.02 256 0.56 356 1.15 64 1.86 149 0.25 257 0.03 . . 65 0.04 152 0.08 262 0.29 . . 66 0.01 155 0.13 263 1.49 . . 75 0.04 156 0.09 264 0.03 . .
133
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
ATLANTIC CITY, NEW JERSEY
DAY RAINFALL (IN.)
DAY RAINFALL (IN.)
DAY RAINFALL (IN.)
DAY RAINFALL (IN.)
5 0.29 128 0.05 205 0.02 307 0.07 6 0.10 135 0.65 213 0.11 308 0.24 10 1.00 136 0.82 219 0.02 314 1.17 15 0.43 139 0.03 223 1.20 215 0.09 22 0.05 140 0.19 224 0.27 316 0.09 23 0.45 141 0.85 230 0.02 318 0.20 30 0.14 142 0.96 234 0.01 319 2.40 33 0.05 144 0.08 240 0.02 320 0.32 34 0.22 146 0.14 241 1.19 324 0.07 37 0.55 147 00.25 243 0.01 325 0.63 38 0.42 149 0.10 255 0.15 328 0.75 42 1.20 150 0.32 256 0.26 329 0.62 48 0.14 151 0.52 257 0.07 332 0.05 54 0.74 152 0.16 264 1.00 337 0.03 60 1.06 154 0.23 265 0.20 338 1.10 61 0.03 155 0.02 273 0.54 340 0.39 66 0.37 159 0.16 274 0.99 346 0.32 67 0.62 170 0.96 275 0.06 347 0.68 109 0.35 171 0.22 285 0.83 348 0.01 110 0.20 172 0.58 286 0.05 349 0.12 113 0.05 179 0.63 292 0.18 356 1.65 114 0.94 180 0.05 296 0.80 358 0.04 115 0.01 183 0.32 297 0.54 362 0.72 124 0.25 202 0.17 298 0.03 . .
134
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
AUGUSTA, MAINE
DAY RAINFALL (IN.)
DAY RAINFALL (IN.)
DAY RAINFALL (IN.)
DAY RAINFALL (IN.)
6 0.31 101 1.47 158 0.12 279 0.01 7 0.02 104 0.01 164 0.20 285 0.20 11 0.64 105 0.02 165 0.05 286 2.05 13 0.06 106 0.16 176 0.01 287 0.03 15 0.05 107 0.77 178 0.06 296 0.09 16 0.24 108 0.01 183 0.56 297 0.41 23 0.28 110 0.12 186 0.60 302 0.02 24 0.06 111 0.11 187 0.38 307 0.17 26 0.01 112 0.05 194 0.75 308 1.03 31 0.26 114 3.41 196 0.15 309 1.63 34 1.09 115 1.62 201 0.04 310 0.01 35 0.06 116 0.01 202 0.56 315 1.37 38 0.34 117 0.01 203 0.63 316 0.13 39 0.17 120 0.25 205 0.06 320 0.97 43 0.44 121 0.02 208 0.18 321 0.03 48 0.34 122 0.56 211 0.02 325 0.56 49 0.15 123 0.18 213 0.07 328 0.54 54 0.08 124 0.35 214 0.65 329 2.18 61 0.75 125 0.07 219 0.05 332 0.03 69 0.26 129 0.25 220 0.29 333 0.33 70 0.01 131 0.18 221 0.03 338 0.20 71 0.18 133 0.22 223 0.74 339 0.13 74 0.08 135 0.22 224 1.11 340 1.25 75 0.01 136 0.05 234 0.03 341 0.71 78 1.73 140 0.52 242 0.06 346 0.42 79 0.07 143 0.64 243 0.62 347 1.95 80 0.96 144 0.14 254 0.25 348 0.39 81 0.44 147 1.14 260 0.18 350 0.05 87 0.39 148 0.17 265 1.37 356 0.71 93 0.46 149 0.18 274 0.01 358 0.04 94 0.21 150 1.45 275 0.02 362 1.12 98 0.07 151 0.06 277 0.04 . . 100 0.27 155 0.49 278 0.19 . .
135
136
BOSTON, MASSACHUSETTS
DAY RAINFALL (IN.) DAY RAINFALL
(IN.) DAY RAINFALL (IN.) DAY RAINFALL
(IN.) 6 0.50 94 0.01 177 0.04 292 0.24
11 0.70 96 0.48 178 0.01 296 0.54 15 0.44 100 2.08 179 0.36 297 0.82 16 0.16 101 0.24 183 0.16 307 0.10 23 1.14 106 0.30 186 0.08 308 0.67 30 0.21 107 0.29 187 0.04 309 0.43 31 0.42 109 0.49 190 0.09 314 1.26 34 0.49 110 0.03 199 0.04 315 0.04 37 0.08 114 1.95 202 0.25 316 0.03 38 1.45 115 0.01 203 0.04 318 0.03 39 0.03 116 0.05 205 0.27 319 0.18 42 0.20 117 0.01 206 0.09 320 1.69 43 1.04 118 0.02 211 0.01 325 0.46 48 1.59 122 0.01 213 0.20 328 0.36 54 0.10 123 0.18 214 0.02 329 2.76 56 0.02 124 0.12 216 0.09 332 0.53 60 0.49 125 0.07 223 0.59 333 0.35 61 2.24 126 0.01 224 1.06 336 0.01 62 0.05 129 0.03 230 0.26 337 0.06 66 0.21 131 0.06 239 0.09 338 0.94 67 0.50 133 0.07 240 0.05 340 0.4S 68 0.65 135 0.13 241 0.22 341 0.15 69 1.57 136 0.53 242 0.04 344 0.05 70 0.46 137 0.03 243 0.66 346 0.41 71 1.12 140 0.12 25S 0.08 347 1.20 72 0.02 141 0.03 260 0.29 348 0.30 75 0.04 143 0.32 265 0.69 349 0.07 78 0.68 144 0.10 274 0.14 353 0.02 79 0.04 147 0.31 275 0.33 356 0.77 80 0.77 149 0.01 278 0.01 358 0.03 81 0.14 150 0.81 285 0.65 362 0.48 86 0.06 153 0.02 286 0.97 87 0.64 155 0.50 287 0.01 93 0.90 176 0.14 291 0.03
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
137
DAILY RAINFALL RECORDS FOR TWENTY CITIES
EAST OF THE MISSISSIPPI RIVER, 1983
CHARLESTON, SOUTH CAROLINA
DAY RAINFALL (IN.) DAY RAINFALL
(IN.) DAY RAINFALL (IN.) DAY RAINFALL
(IN.) 9 0.01 79 0.14 128 0.38 205 0.29 10 0.25 80 0.08 134 0.07 206 0.01 11 0.10 81 0.11 135 0.60 213 0.58
14 0.01 85 0.01 136 1.00 217 0.04 15 0.23 86 0.69 139 0.37 221 0.02 17 0.11 87 0.02 141 0.55 223 0.76 21 0.09 88 0.02 142 0.71 230 0.12 22 0.21 89 0.03 143 0.01 234 0.99 23 0.07 90 0.13 146 0.01 336 0.06 30 0.16 92 0.05 148 0.19 337 0.31 32 0.01 93 0.05 148 0.49 338 0.17 33 0.84 97 0.16 152 0.02 340 0.57 34 0.05 98 0.18 154 1.04 342 0.05 37 0.09 99 0.23 155 0.05 343 0.13 38 0.10 100 0.16 157 0.02 345 0.18 41 0.24 101 0.02 179 0.81 346 0.18 42 1.04 104 0.15 180 0.24 347 0.05 43 0.01 105 0.61 181 0.33 348 0.05 54 0.30 107 0.02 184 0.14 349 0.04 56 0.04 113 0.80 185 0.47 353 0.01 65 0.09 114 0.69 186 0.02 354 0.02 67 0.86 118 0.05 191 0.01 355 0.27 68 0.05 119 0.79 198 1.57 356 0.37 69 0.02 121 0.02 199 0.13 357 0.07 70 0.39 122 0.24 201 0.02 361 0.02 77 0.38 123 1.05 203 0.55 362 0.63 78 0.13 124 0.29 204 0.98 363 0.01
138
COLUMBIA, SOUTH CAROLINA
DAY RAINFALL (IN.) DAY RAINFALL
(IN.) DAY RAINFALL (IN.) DAY RAINFALL
(IN.) 1 0.10 76 2.95 157 0.67 286 0.08 2 0.92 77 0.01 158 0.78 296 1.52 9 0.24 79 0.23 166 0.21 308 0.03
21 1.50 80 0.25 181 0.77 311 0.05 22 0.25 83 0.53 184 0.12 313 0.05 23 0.07 86 0.43 185 0.30 318 0.34 27 0.45 89 0.01 186 0.01 319 1.15 28 0.01 90 0.64 195 0.07 324 0.66 30 0.02 92 0.29 198 0.15 328 1.04 33 0.90 96 0.39 199 0.03 329 0.01 36 0.04 97 0.52 206 0.05 332 0.30 37 0.40 98 2.35 214 1.09 337 1.40 41 0.56 99 0.73 218 1.68 338 0.61 42 0.06 104 0.16 236 0.40 340 1.80 44 0.73 105 0.34 243 0.19 345 1.55 45 0.73 108 0.15 244 0.49 348 0.01 47 0.05 113 0.65 245 0.61 349 0.01 53 0.92 114 0.10 246 0.01 352 0.09 54 0.07 122 0.45 256 1.56 355 0.46 59 0.92 128 0.14 257 0.15 356 0.15 60 0.31 134 0.04 263 0.27 361 0.02 65 1.90 136 0.05 264 0.16 362 0.40 66 0.04 139 0.02 278 0.45 363 0.08 70 0.01 152 0.06 281 0.10 75 0.04 156 0.36 282 0.07
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
DAY RAINFALL (IN.) DAY RAINFALL
(IN.) DAY RAINFALL (IN.) DAY RAINFALL
(IN.) 10 0.24 94 0.01 179 0.52 296 0.17 11 0.04 96 0.07 181 1.09 297 0.10 14 0.05 97 0.22 182 1.13 298 0.01 16 0.04 98 0.65 185 0.51 305 0.14 21 0.03 99 0.54 198 1.59 306 1.02 22 0.42 101 0.06 199 0.34 307 0.09 23 0.08 103 0.36 201 0.08 314 1.03 29 0.02 104 0.53 203 0.11 315 0.25 30 0.28 107 0.03 212 0.04 319 0.36 32 0.01 108 0.01 213 0.46 323 0.01 33 0.41 113 0.08 216 0.10 324 0.19 34 0.07 114 0.62 223 0.17 327 0.47 35 0.01 119 0.02 229 0.03 328 0.03 37 0.10 120 2.03 230 0.07 331 0.83 38 0.03 121 1.45 233 0.02 332 0.38 42 0.09 122 0.63 234 0.01 336 0.30 55 0.02 123 0.53 239 0.04 337 0.16 65 0.16 124 0.01 240 0.91 338 0.75 67 0.03 127 0.05 243 0.40 340 0.26 68 0.01 128 1.07 250 0.01 341 0.03 69 0.12 134 0.95 254 0.20 342 0.11 70 0.16 135 0.50 255 0.07 343 0.08 76 0.01 139 0.42 259 0.52 345 0.31 77 0.15 142 0.87 203 0.31 346 0.04
78 0.18 145 0.10 264 0.80 348 0.04 79 0.07 148 0.01 277 0.46 350 0.01 80 0.01 149 0.44 278 0.28 355 0.27 81 0.01 154 0.43 284 0.03 356 0.25 86 0.67 157 0.06 285 0.01 361 0.02 87 0.10 166 0.01 286 0.62 362 0.54 88 0.01 167 0.01 291 0.60 - - 91 0.03 168 0.40 293 0.77 - - 92 0.78 169 0.19 294 0.01 - - 93 0.14 170 1.88 295 1.39 - -
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
COLUMBUS, GEORGIA
DAY RAINFALL (IN.) DAY RAINFALL
(IN.) DAY RAINFALL(IN.) DAY RAINFALL
(IN.) 5 0.06 86 0.21 147 0.31 275 0.52 6 0.25 87 0.52 149 0.12 277 0.02 7 0.01 93 1.02 150 1.20 278 0.06 10 0.07 94 0.02 151 0.02 285 1.05 11 1.98 97 0.01 155 0.59 286 0.10 15 0.10 98 0.18 157 0.08 288 0.03 16 0.13 100 1.28 158 0.01 296 0.42 23 0.99 101 0.31 164 1.24 297 0.31 24 0.04 106 0.17 176 0.52 307 0.11 30 0.10 107 0.33 177 0.01 308 1.52 31 0.19 109 0.20 178 0.01 309 0.24 33 0.08 110 0.15 179 0.06 314 0.24 34 0.82 111 0.01 186 1.42 315 0.58 38 0.35 114 1.55 192 0.02 316 0.07 39 0.03 115 0.23 193 0.03 319 0.03 43 0.19 116 0.17 202 0.34 320 1.36 48 0.65 120 0.25 203 0.03 325 0.45 54 0.05 121 0.74 205 0.22 328 0.53 60 0.01 122 0.63 206 0.01 329 1.48 61 1.37 123 0.01 213 0.14 332 0.32 66 0.14 124 0.12 214 0.01 333 0.43 67 0.14 128 0.10 217 0.03 336 0.02 68 0.39 129 0.23 218 0.34 337 0.05 69 0.98 131 0.17 223 0.38 338 0.40 70 0.08 133 0.04 224 0.07 339 0.02 71 1.10 134 0.02 234 0.17 340 0.58 74 0.14 135 0.30 239 0.21 341 0.17 75 0.03 136 0.18 242 0.18 346 0.26 77 0.01 137 0.03 243 0.54 347 1.26 78 1.46 139 0.01 260 0.15 348 0.64 79 0.07 140 0.08 264 0.10 356 1.12 80 0.37 143 0.87 265 0.96 362 0.83 81 0.05 146 0.01 274 0.77 - -
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
CONCORD, MASSACHUSETTS
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
FRANKFORT, KENTUCKY
141
DAY RAINFALL (IN.) DAY RAINFALL
( IN.) DAY RAINFALL(IN.) DAY RAINFALL
(IN.) 11 0.02 100 0.15 170 0.57 297 0.15 22 0.76 101 0.12 179 0.03 298 0.21 23 0.17 103 0.03 180 0.19 307 0.33 24 0.05 104 0.28 185 0.25 315 0.37 30 0.16 105 0.36 186 0.54 316 0.03 33 0.50 114 0.83 218 0.05 319 0.31 34 0.08 119 0.70 224 0.05 320 0.21 35 0.05 120 0.86 234 0.20 321 0.04 37 0.15 121 1.10 235 0.29 323 0.04 42 0.32 122 1.98 240 0.18 324 0.11 65 0.19 123 1.80 241 0.07 325 0.08 67 0.23 124 0.26 255 0.20 327 0.16 70 0.03 128 0.57 256 0.10 329 0.56 77 0.14 133 0.10 260 0.06 332 1.25 80 0.50 135 0.93 264 0.65 337 0.23 86 0.17 139 1.05 266 0.02 338 0.93 87 0.05 140 0.33 278 0.20 340 0.31 90 0.12 141 0.07 286 2.05 344 0.21 92 0.04 142 0.68 287 0.12 346 0.60 93 0.17 143 0.12 291 0.08 347 0.04 94 0.03 149 0.09 292 0.06 348 0.05 96 0.02 150 0.56 293 0.04 356 0.71 97 0.05 154 0.10 294 0.80 362 0.46 98 1.46 155 1.24 295 0.02 363 0.16 99 0.23 168 0.17 296 0.98 - -
142
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
HARRISBURG, PENNSYLVANIA
DAY RAINFALL (IN.) DAY RAINFALL
(IN.) DAY RAINFALL (IN.) DAY RAINFALL
(IN.) 5 0.03 100 1.05 172 0.01 297 0.07
10 0.78 101 0.06 179 0.44 298 0.08 14 0.08 105 2.17 180 0.01 299 0.02 15 0.32 106 0.01 198 0.03 307 0.10 16 0.02 109 0.06 201 0.50 309 0.04 22 0.05 110 0.04 202 0.02 314 1.10 23 0.70 113 0.26 204 0.36 315 0.63 30 0.28 114 1.74 20S 0.02 316 0.01 33 0.96 115 0.04 211 0.04 319 0.86 34 0.04 118 0.11 212 0.30 320 0.02 37 0.24 121 0.03 217 0.12 321 0.01 38 0.06 122 0.11 223 0.20 323 0.04 39 0.01 123 0.43 225 0.02" 324 0.64 42 2.00 124 0.02 230 0.38 325 0.02 43 0.05 128 0.42 234 0.22 327 0.01 60 0.10 134 0.09 239 1.03 328 0.58 65 0.36 135 0.43 240 0.03 329 0.31 67 0.74 136 0.81 241 0.08 332 0.88 66 0.04 139 0.32 243 0.12 333 0.04 69 0.24 140 0.01 255 0.22 336 0.12 70 0.02 141 0.32 256 0.02 338 0.73 77 1.07 142 1.42 264 0.94 340 0.74 78 0.26 146 0.56 273 0.22 346 0.66 80 1.07 148 0.02 274 0.04 347 2.73 86 0.94 149 0.37 278 0.01 349 0.10 87 0.02 154 0.42 284 0.06 355 0.04 92 0.49 155 0.42 28S 0.66 356 1.20 93 0.37 158 6.05 266 0.69 357 0.12 96 0.01 168 0.74 291 0.91 356 0.05 97 0.27 169 0.11 292 0.30 361 0.03 96 0.78 170 0.12 295 0.10 362 0.66 99 0.50 171 0.49 296 1.20 - -
DAY RAINFALL (IN.) DAY RAINFALL
(IN.) DAY RAINFALL (IN.) DAY RAINFALL
(IN.) 5 0.26 67 0.67 152 0.06 2.01 6 0.44 93 1.17 154 0.02 286 0.12
10 0.65 97 0.01 155 0.76 287 0.02 11 1.13 98 0.43 157 0.01 291 0.25 15 0.65 100 2.47 170 0.01 92 0.17 16 0.18 101 0.02 178 0.16 296 0.50 23 1.08 106 1.74 179 1.59 297 0.80 24 0.01 107 0.23 186 0.70 299 0.03 30 0.23 108 0.03 187 0.02 307 0.01 31 0.05 109 2.23 190 0.02 308 0.01 33 0.25 110 0.06 205 0.21 314 1.20 34 1.15 114 1.37 207 0.12 315 0.23 38 1.05 115 0.05 213 0.26 319 0.40 42 0.50 120 0.09 216 0.43 320 1.43 43 0.53 122 0.04 217 0.07 325 0.26 48 0.30 123 0.01 218 0.01 328 0.42 54 0.05 124 0.16 223 0.66 329 1.29 60 0.28 126 0.17 224 0.33 332 0.62
61 0.26 129 0.13 230 0.52 333 0.22 63 0.09 135 0.42 235 0.02 337 0.05 64 0.11 136 0.53 240 0.16 338 0.76 66 0.17 137 0.01 t41 0.16 340 1.10 67 0.69 139 0.02 242 0.02 344 0.01 68 0.30 140 0.08 243 0.04 346 0.81 69 0.35 141 0.06 255 0.33 347 1.15 70 0.33 142 0.16 259 0.03 348 0.12 71 0.23 143 0.77 260 0.42 353 0.02 77 0.16 144 0.1t 264 0.78 356 0.95 78 1.48 146 0.26 265 0.39 358 0.10 79 0.13 147 0.68 273 0.15 362 0.90 80 0.80 149 0.03 274 0.83 - - 81 0.01 150 1.10 275 -0.69 - - 86 0.78 151 0.05 276 0.10 - -
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
HARTFORD, CONNECTICUT
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
MONTGOMERY, ALABAMA
DAY RAINFALL (IN.) DAY RAINFALL
(IN.) DAY RAINFALL (IN.) DAY RAINFALL
(IN.) 1 1.58 89 0.29 178 0.06 281 0.03 2 1.68 92 0.75 179 1.85 283 0.02
10 0.25 95 0.88 180 0.44 284 0.04 19 0.02 96 0.39 184 0.05 285 2.02 20 1.42 97 2.11 186 0.05 286 0.12 21 0.08 96 3.83 188 0.08 295 0.63 26 0.60 99 0.35 199 1.13 296 0.67 27 0.16 104 1.30 207 0.46 306 0.05 29 0.33 108 0.13 212 0.59 318 1.27 32 3.37 112 0.78 21f 0.25 319 0.59 36 0.60 113 1.28 215 0.39 324 1.71 37 0.21 123 0.14 217 1.68 327 1.50 41 0.82 128 0.63 218 0.01 328 1.26 44 0.37 131 0.17 223 0.01 331 0.87 47 0.21 135 0.20 237 1.15 337 1.48 48 0.04 136 1.20 240 0.74 339 0.42 53 0.70 139 0.88 244 0.01 340 0.61 55 0.10 i55 0.07 24S 0.01 345 1.25 59 1.06 158 0.28 246 0.18 347 0.01 60 0.02 167 0.26 248 0.55 351 0.01 64 2.37 168 0.4S 249 0.45 352 0.01 7S 0.41 169 1.71 254 0.67 355 0.09 76 0.54 170 0.15 25S 0.72 356 0.42 79 1.50 171 0.88 256 2.30 361 0.94 82 0.49 172 0.03 263 0.71 362 1.65 63 1.22 174 0.22 264 0.19 363 0.53 85 2.12 177 0.06 278 0.05 - -
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI
MONTPELIER, VERMONT
DAY RAINFALL (IN.) DAY RAINFALL
(IN.) DAY RAINFALL(IN.).
DAY
RAINFALL (IN.)
7 0.02 102 0.05 177 0.15 281 0.04 11 0.92 106 0.44 178 0.24 285 0.43 15 0.68 107 0.28 186 0.24 296 0.33 16 0.68 109 0.26 187 0.23 297 0.14 17 0.02 110 0.08 190 0.24 299 0.05 23 1.08 111 0.02 202 0.88 307 0.21 24 0.02 114 0.68 203 0.02 308 1.60 30 0.03 115 0.41 205 0.70 309 0.36 34 0.88 116 0.15 212 1.32 311 0.02 35 0.02 117 0.07 213 0.52 314 0.02 38 0.02 120 0.42 214 0.02 315 0.63 39 0.13 121 0.03 217 0.31 316 0.09 40 0.03 122 0.97 218 0.05 319 0.08 48 0.04 123 1.00 219 0.05 320 0.78 54 0.07 124 1.10 220 1.18 321 0.03 61 O.t3 128 0.30 223 0.90 325 0.44 66 0.36 129 0.60 224 0.62 328 0.05 67 0.04 130 0.05 230 0.75 329 0.42 68 0.10 135 0.45 232 0.80 333 0.55 69 0.23 140 0.18 234 0.26 334 0.03 71 0.60 143 0.11 239 1.43 335 0.02 72 0.03 144 0.18 241 0.03 338 0.42 78 0.29 146 0.11 242 0.12 340 0.25 79 0.04 147 0.76 243 0.15 341 0.71 80 0.26 149 0.22 253 0.18 344 0.02 81 0.03 150 0.46 254 0.02 346 0.08 87 0.32 151 0.22 260 0.25 347 1.13 93 0.53 155 0.22 264 0.65 348 0.49 95 0.03 157 0.59 265 0.47 356 0.51 97 0.06 158 0.07 27S 0.01 358 0.02 98 0.02 168 0.43 277 0.25 359 0.01 100 0.70 169 0.34 278 0.49 362 0.79 101 0.28 176 0.28 279 0.13
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
NASHVILLE, TENNESSEE
DAY RAINFALL (IN.) DAY RAINFALL
( IN.) DAY RAINFALL ( IN.) DAY RAINFALL
( IN.) 2 0.03 92 0.85 149 0.33 296 0.14 8 0.21 94 0.06 154 1.65 299 0.02 9 0.67 95 2.06 155 0.05 306 0.02
11 0.07 97 0.31 166 0.33 307 1.13 20 0.25 98 0.65 167 0.37 308 0.34 21 1.07 99 0.02 168 0.33 314 0.16 22 0.07 103 0.05 173 0.03 315 0.01 23 0.01 104 0.30 174 0.25 318 0.57 29 0.18 106 0.02 178 0.31 319 0.10 32 1.02 108 0.26 181 0.61 320 0.03 33 0.23 111 0.16 182 0.11 323 0.12 36 0.19 113 1.20 186 0.01 324 0.95 37 0.12 114 0.01 198 0.27 327 1.68 40 0.01 118 0.02 199 0.37 331 1.87 41 0.91 119 0.04 204 0.95 336 1.75 42 0.06 120 0.23 223 0.57 337 1.70 53 0.33 122 0.02 228 0.05 339 0.07 55 0.03 123 1.76 235 0.51 340 0.05 59 0.03 127 0.06 240 0.23 343 0.12 64 2.25 131 0.02 246 0.08 345 1.95 65 0.03 132 0.11 248 0.02 346 0.09 67 0.01 135 1.50 263 0.20 348 0.27 68 0.06 136 0.04 264 0.15 353 0.05 73 0.01 138 2.07 277 0.21 354 0.01 76 0.14 139 1.72 278 0.24 355 0.42 77 0.26 140 0.95 285 0.85 356 0.16 79 0.38 141 1.85 286 0.50 361 0.35 85 0.27 142 0.14 291 0.04 362 0.76 89 0.03 143 0.06 294 0.02 91 0.52 148 0.40 295 0.75
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
PROVIDENCE, RHODE ISLAND
DAY RAINFALL (IN.) DAY
RAINFALL
(IN.) DAY RAINFALL
(IN.)
DAY
RAINFALL
(IN.)
1 0.03 87 0.57 166 0.07 291 0.25 6 0.43 93 0.85 176 0.09 292 0.42
10 0.17 97 0.03 177 0.05 296 0.4311 0.63 98 1.17 178 0.17 297 1.07l5 0.87 99 0.10 179 0.68 298 0.0116 0.05 100 4.30 186 0.38 307 0.0523 1.56 101 0.13 187 0.25 308 0.5524 0.03 106 0.61 188 0:'01 314 1.8030 0.19 107 0.35 193 0.17 315 0.2331 0.14 109 2.36 196 0.03 316 0.0333 0.01 110 0.06 201 0.02 319 0.1734 0.70 114 2.73 202 0.73 320 2.4838 1.07 115 0.01 205 0.55 321 0.0142 1.15 116 0.02 213 0.19 325 0.62 43 0.83 124 0.20 214 0.08 328 0.7048 1.75 128 0.06 216 0.68 329 3.5254 0.25 129 0.03 221 0.07 332 0.2656 0.05 131 0.08 223 0.70 333 0.4960 0.45 133 0.07 224 0.50 337 0.1261 0.85 134 0.01 230 0.33 338 0.9462 0.01 135 0.33 239 0.02 340 0.9066 0.42 136 0.76 241 0.03 341 0.0367 1.08 140 0.18 243 0.11 344 0.0268 0.09 141 0.03 255 0.29 346 0.7669 0.18 142 0.03 257 0.01 347 1.3470 0.52 143 0.25 260 0.28 348 0.3571 0.59 147 0.36 261 0.08 349 0.1977 0.56 149 0.07 265 0.82 356 1.9778 1.29 150 1.95 273 0.15 358 0.0579 0.01 151 0.26 274 0.14 362 1.0480 1.59 152 0.03 275 0.88 - -8l 0.01 153 0.02 285 1.17 - -86 0.32 154 0.80 286 0.13 - -
147
148
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
RALEIGH, NORTH CAROLINA
DAY RAINFALL (IN.) DAY RAINFALL
(IN.) DAY RAINFALL (IN.) DAY RAINFALL
(IN.) 2 0.20 77 3.17 150 0.01 282 0.04 3 0.23 80 0.27 152 0.08 284 0.19 4 0.01 83 0.73 157 0.14 285 0.04 5 0.37 86 0.27 158 0.71 286 0.63 9 0.01 89 0.10 159 0.65 293 0.03
10 0.02 90 0.29 165 0.37 294 0.48 12 0.02 92 0.18 170 P.07 296 1.76 21 0.16 95 0.02 171 0102 297 0.01 22 0.67 96 0.02 172 0.80 307 0.01 27 0.09 97 0.04 180 0.25 308 0.10 28 0.01 98 0.20 186 0.25 313 0.09 33 1.44 99 0.11 203 0.58 314 0.29 37 0.94 100 0.04 204 0.15 319 1.50 41 0.76 105 2.22 205 0.02 324 0.41 42 0.60 108 0.23 206 0.06 328 0.52 45 1.04 113 0.28 212 0.04 329 0.90 53 0.05 114 0.20 214 0.15 332 0.04 54 0.55 123 0.39 218 0.02 337 0.57 55 0.28 124 0.06 220 0.06 338 0.52 56 0.12 128 0.01 223 0.09 340 2.12 57 0.01 133 0.02 224 0.29 346 1.07 59 0.21 134 0.79 235 0.90 349 0.04 60 0.65 136 0.48 236 0.30 352 0.24 65 1.26 140 1.16 245 0.01 353 0.05 66 0.23 141 0.73 255 0.01 355 0.27 67 0.03 142 0.59 256 0.34 356 0.35 68 0.01 143 0.74 257 0.60 362 1.19 69 0.01 146 0.38 264 0.64 363 0.23 70 0.07 147 0.52 273 0.65 - - 76 0.69 149 0.01 278 0.41 - -
149
DAY RAINFALL
(IN.) DAY RAINFALL(IN.) DAY RAINFALL
(IN.) DAY RAINFALL (IN.)
2 0.03 60 0.01 159 0.15 285 0.10 3 0.11 64 0.62 170 0.10 286 1.26 5 0.35 65 4.70 171 2.96 293 0.53
10 0.23 66 1.06 172 0.20 294 0.08 15 0.12 74 0.23 179 0.03 295 0.11 22 0.50 75 0.56 180 0.20 296 1.43 23 0.24 92 0.20 200 0.35 297 0.06 24 0.01 93 0.15 202 0.05 298 0.11 33 0.71 96 0.20 203 0.02 308 0.01 37 0.53 97 0.26 204 0.07 314 1.64 38 0.02 99 0.26 205 0.02 319 1.02 41 0.40 100 0.62 213 0.05 324 0.81 42 1.49 105 2.51 217 0.12 328 0.51 45 0.31 107 0.01 218 0.02 329 1.61 48 0.06 113 0.42 221 0.34 332 0.03 54 0.30 114 0.58 223 0.05 336 0.01 56 0.13 123 0.27 224 0.02 337 0.19 60 0.85 124 0.23 230 0.17 138 0.82 65 0.20 136 0.32 234 0.10 340 0.49 66 0.04 139 0.02 243 0.10 344 0.02 67 0.22 140 0.45 247 0.03 346 1.21 68 0.10 141 0.03 255 0.10 347 0.09 69 0.11 142 0.83 256 0.34 349 0.03 76 0.04 146 0.26 257 0.31 355 0.05 77 1.00 150 0.04 264 0.92 356 0.80 78 0.01 15l 0.05 266 0.02 362 0.79 80 2.40 152 0.59 272 0.03 - - 86 0.92 155 0.08 273 1.30 - - 87 0.01 157 0.04 278 0.01 - - 90 0.14 158 1.11 284 0.33 - -
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER. 1981
RICHMOND. VIRGINIA
150
DAILY RAINFALL RECORDS FOR TWENTY CITIES EAST OF THE MISSISSIPPI RIVER, 1983
TALLAHASSEE, FLORIDA
DAY RAINFALL (IN.) DAY RAINFALL
(IN.) DAY RAINFALL (IN.) DAY RAINFALL
(IN.) 1 0.38 100 1.99 174 1.25 246 0.10 2 0.38 101 0.05 175 0.31 248 0.25
20 1.33 106 0.03 176 0.03 254 0.12 21 0.78 107 0.09 177 0.03 255 1.60 22 0.14 76 1.68 178 0.02 256 1.06 26 0.08 77 0.09 179 0.89 262 0.07 27 0.67 79 1.31 180 0,34 264 0.18 29 0.02 83 0.37 181 0.02 277 0.29 30 0.11 86 1.89 183 0.01 279 0.29 31 1.13 89 0.34 184 0.41 281 0.05 32 0.67 90 0.18 185 0.11 284 0.15 37 0.75 93 0.23 187 0.23 286 0.45 41 0.04 97 1.45 196 0.75 290 0.07 44 2.54 98 1.18 201 0.19 309 0.08 45 0.17 99 1.62 204 0.02 311 0.15 47 0.09 104 0.44 206 0.01 312 0.04 48 0.24 105 0.78 207 0.04 319 0.01 53 0.32 108 0.12 210 0.08 324 2.46 58 0.03 112 0.05 211 0.23 328 2.52 59 0.78 113 1.75 212 0.27 332 1.16 69 0.39 123 0.35 213 0.18 338 0.25 70 0.20 132 0.14 215 0.05 340 0.53 71 0.25 136 2.53 217 0.08 345 2.00 77 0.95 143 0.27 219 0.20 348 0.08 78 0.14 151 0.06 220 0.12 349 0.03 80 0.41 155 0.92 221 0.54 351 0.85 86 1.39 157 2.17 223 0.55 352 0.85 90 0.04 158 1.14 224 0.06 356 0.08 92 0.07 164 0.01 226 0.08 362 1.03 93 1.38 171 0.01 239 0.16 363 1.08 97 0.16 172 1.49 242 0.43 - - 98 0.37 173 0.76 244 0.98 - -
APPENDIX E
DATA GENERATED FROM MONTE CARLO EXPERIMENTS
OUTPUT FROM MONTE CARLO SIMULATION
OBS Yl Y2 Y3 Y4 X1 X2 X3 X4 X5 X61 0.299 0.382 0.218 0.306 0.350 0.425 0.080 32:000 0.471 0.3842 0.198 0.281 0.336 0.301 0.318 0.396 0.044 29.000 0.511 0.2413 0.294 0.404 0.280 0.336 0.438 0.568 0.094 31.000 0.107 0.2204 0.190 0.242 0.162 0.123 0.342 0.343 0.057 19.000 0.166 0.2385 0.383 0.491 0.198 0.309 0.392 0.500 0.057 13.000 0.221 0.2866 0.175 0.299 0.521 0.392 0.382 0.476 0.098 10.00.0 0.430 0.4327 0.279 0.346 0.149 0.202 0.350 0.425 0.060 13.000 0.577 0.2188 0.297 0.371 0.261 0.402 0.318 0.396 0.049 35.000 0.570 0.1599 0.350 0.453 0.144 0.211 0.382 0.476 0.050 36.000 0.442 0.24810 0.326 0.389 0.234 0.253 0.435 0.494 0.067 11.000 0.352 0.25211 0.333 0.407 0.300 0.548 0.350 0.425 0.049 25.000 0.581 0.31312 0.390 0.465 0.235 0.297 0.435 0.494 0.034 30.000 0.540 0.34713 0.412 0.465 0.358 0.617 0.522 0.562 0.076 16.000 0.260 0.34614 0.426 0.619 0.311 0.308 0.514 0.698 0.038 9.000 0.400 0.37715 0.306 0.381 0.163 0.252 0.350 0.425 0.080 14.000 0.244 0.28116 0.387 0.449 0.276 0.325 0.435 0.494 0.100 11.000 0.199 0.27617 0.178 0.252 0.332 0.389 0.273 0.321 0.082 22.000 0.299 0.35318 0.343 0.430 0.373 0.407 0.462 0.559 0.098 12.000 0.202 0.27919 0.261 0.331 0.264 0.255 0.392 0.500 0.100 16.000 0.190 0.19720 0.340 0.420 0.175 0.254 0.435 0.494 0.054 16.000 0.174 0.32121 0.200 0.266 0.189 0.243 0.273 0.321 0.085 31.000 0.184 0.34622 0.372 0.448 0.265 0.447 0.435 0.494 0.056 28.000 0.380 0.33623 0.412 0.645 0.288 0.715 0.438 0.672 0.056 11.000 0.546 0.43524 0.378 0.480 0.258 0.517 0.401 0.504 0.054 22.000 0.588 0.258
OBS X7 X8 X9 X10 X11 X12 X13 X14 X151 0.694 1.447 1.236 0.057 6.152E-06 0.045 89.440 -0.368 0.7152 0.108 0.727 0.644 0.064 5.709E-06 0.160 86.581 -0.249 0.7973 0.373 0.989 1.190 0.067 9.825E-06 0.102 52.289 -0.212 0.7584 0.131 0.786 1.140 0.056 5.677E-05 0.133 43.988 -0.248 0.7495 0.945 0.918 1.573 0.068 6.305E-05 0.176 74.099 -0.277 0.7446 0.106 1.436 1.381 0.062 2.437E-06 0.200 50.043 -0.423 0.7447 0.526 0.640 1.019 0.065 1.877E-05 0.029 74.243 -0.224 0.7758 0.847 1.002 1.252 0.065 5.217E-06 0.122 84.120 -0.160 0.7869 0.831 0.562 0.661 0.059 2.995E-05 0.010 32.097 -0.253 0.75310 0.470 1.130 0.635 0.068 6.430E-06 0.053 65.595 -0.252 0.77811 0.877 1.089 1.631 0.055 2.956E-06 0.075 47.036 -0.313 0.78412 0.691 0.988 0.663 0.053 5.270E-06 0.145 33.843 -0.350 0.72213 0.578 0.628 1.312 0.056 2.085E-06 0.182 38.436 -0.358 0.76814 0.526 1.060 1.219 0.064 3.316E-06 0.159 88.237 -0.381 0.72215 0.750 0.585 0.837 0.064 1.213E-05 0.093 45.670 -0.279 0.71016 0.790 0.754 0.934 0.065 1.850E-06 0.053 88.155 -0.267 0.78217 0.409 1.367 1.339 0.062 6.727E-06 0.156 48.114 -0.368 0.71318 0.499 1.476 0.944 0.057 1.057E-06 0.176 72.969 -0.292 0.70419 0.371 1.380 1.451 0.055 4.104E-05 0.132 85.143 -0.205 0.78020 0.467 0.631 1.129 0.065 7.137E-05 0.093 82.057 -0.325 0.79121 6.551 1.024 1.056 0.064 3.1811-05 0.174 76.132 -0.132 0.71322 0.611 0.626 1.373 0.052 ~:581E-04 0.152 34.791 -0.34§ 0.74791 0.865 0.722 1.285 0.054 '1:6181:-66 6.045 60.456 -0:426 6:717
153
OUTPUT FROM MONTE CARLO SIMULATION
OBS Y1 Y2 Y3 Y4 X1 X2 X3 X4 X5 X625 0.215 0.318 0.293 0.300 0.318 0.396 0.033 21.000 0.540 0.39826 0.212 0.265 0.343 0.380 0.342 0.343 0.067 34.000 0.561 0.32227 0.364 0.479 0.226 0.330 0.417 0.545 0.036 35.000 0.434 0.17028 0.348 0.415 0.274 0.322 0.435 0.494 0.047 37.000 0.567 0.16129 0.486 0.662 0.184 0.253 0.514 0.698 0.084 28.000 0.493 0.28630 0.279 0.332 0.322 0.331 0.401 0.428 0.081 32.000 0.370 0.31131 0.361 0.458 0.256 0.358 0.382 0.476 0.057 36.000 0.482 0.37932 0.276 0.455 0.168 0.158 0.460 0.629 0.050 8.000 0.236 0.40633 0.432 0.616 0.157 0.258 0.514 0.698 0.045 12:000 0.167 0,38334 0.337 0.424 0.162 0.218 0.435 0.494 0.044 15.000 0.431 0.37935 0.324 0.395 0,230 0.461 0.350 0.425 0.067 21.000 0.313 0.23436 0.299 0.393 0,343 0.386 0.438 0.568 0.082 32.000 0.220 0.16637 0.598 0.635 0.169 0.237 0.704 0.731 0.074 8.000 0.186 0.16638 0.391 0.624 0.193 0.386 0.438 0.672 0.044 35.000 0.369 0.30139 0.355 0.393 0.353 0.632 0.401 0.428 0.084 28.000 0.553 0.41340 0.250 0.360 0.129 0.153 0.382 0.476 0.090 28.000 0.144 0.41841 0.219 0.314 0.338 0.443 0.359 0.427 0.048 25.000 0.177 0.30942 0.232 0.283 0.317 0.346 0.350 0.425 0.099 16.000 0.310 0.15243 0.677 0.712 0.219 0.365 0.704 0.731 0.054 34.000 0.326 0.38944 0.316 0.497 0.286 0.358 0.438 0.672 0.091 33,000 0.133 0.33645 0.378 0.502 0.315 0.572 0.438 0.568 0.054 30.000 0.265 0.28746 0.255 0.330 0.231 0.349 0.318 0.396 0.086 24.000 0.379 0.30647 0.314 0.412 0.168 0.241 0.392 0.500 0.066 17.000 0.258 0.23748 0.327 0.402 0.280 0.493 0.350 0.425 0.033 23.000 0.312 0.296
OBS X7 X8 X9 X10 X11 X12 X13 X14 X1525 0.329 0.864 0.773 0.066 6.972E-06 0.092 77.490 -0.407 0.79326 0.193 0.762 1.569 0.053 2.533E-06 0.137 48.703 -0.315 0.77627 0.657 0.862 0.652 0.065 2.629E-06 0.077 46.609 -0.169 0.74628 0.360 0.715 1.287 0.053 1.410E-05 0.173 68.630 -0.169 0.75629 0.866 1.122 0.804 0.053 2.240E-05 0.152 67.188 -0.299 0.77930 0.365 1.134 0.595 0.065 1.906E-06 0.180 69.704 -0.320 0.71631 0.871 1.050 1.113 0.054 4.978E-05 0.080 58.602 -0.397 0.79432 0.124 1.423 0.626 0.051 7.223E-05 0.116 31.301 -0.402 0.76133 0.589 1.053 1.462 0.051 3.334E-05 0.014 60.225 -0.369 0.79434 0.454 0.990 1.263 0.054 8.863E-05 0.134 52.796 -0.378 0.79435 0.834 0.536 1.732 0.066 7.769E-06 0.105 51.434 -0.224 0.78436 0.368 1.241 1.138 0.057 4.066E-06 0.190 53.563 -0.169 0.71637 0.622 0.906 0.558 0.063 7.274E-05 0.115 71.603 -0.165 0.76538 0.684 0.582 1.385 0.064 8.054E-05 0.047 72.977 -0.305 0.73239 0.768 0.570 1.571 0.065 3.160E-06 0.198 40.107 -0.429 0.74240 0.416 1.420 0.635 0.058 7.954E-05 0.053 30.414 -0.399 0.74541 0.290 0.933 0.905 0.056 7.355E-06 0.116 56.320 -0.297 0.71642 0.380 1.160 1.273 0.061 4.523E-06 0.164 85.248 -0.152 0.75743 0.901 1.401 0.943 0.058 1.059E-05 0.020 39.619 -0.399 0.79244 0.492 1.209 0.681 0.057 1.710E-06 0.143 36.855 -0.344 0.77245 0.718 1.382 1.567 0.054 1.090E-05 0.064 89.377 -0.286 0.77246 0.668 0.973 1.241 0.069 4.965E-06 0.143 44.609 -0.302 0.79347 0.557 1.281 1.409 0.067 7 .255E-06 0.009 64.971 -0.247 0.76048 0.823 0.858 1.587 0.060 1.278E-06 0.121 87.886 -0.282 0.724
OBS Y1 Y2 Y3 Y4 X1 X2 X3 X4 X5 X649 0.301 0.392 0.176 0.211 0.382 0.476 0.041 31.000 0.573 0.17550 0.486 0.523 0.246 0.663 0.522 0.562 0.092 36.000 0.199 0.24051 0.324 0.400 0.141 0.206 0.350 0.425 0.067 15.000 0.474 0.33352 0.457 0.511 0.304 0.541 0.522 0.562 0.073 8.000 0.306 0.37253 0.258 0.384 0.364 0.427 0.417 0.545 0.095 34.000 0.228 0.34854 0.257 0.370 0.315 0.393 0.367 0.436 0.065 32.000 0.398 0.32755 0.325 0.424 0.304 0.329 0.462 0.559 0.074 34.000 0.599 0.15256 0.236 0.321 0.284 0.358 0.359 0.427 0.088 23.000 0.240 0.33957 0.465 0.566 0.209 0.514 0.535 0.639 0.094 19.000 0.354 0.28158 0.167 0.247 0.292 0.277 0.342 0.343 0.093 17.000 0.598 0.34359 0.237 0.296 0.293 0.358 0.273 0.321 0.035 23.000 0.257 0.36860 0.197 0.290 0.156 0.209 0.367 0.436 0.097 17.000 0.239 0.27361 0.229 0.301 0.317 0.267 0.401 0.428 0.056 21.000 0.576 0.34962 0.429 0.485 0.137 0.184 0.522 0.562 0.052 30.000 0.426 0.36363 0.352 0.456 0.264 0.345 0.392 0.500 0.037 18.000 0.574 0.15764 0.341 0.383 0.335 0.386 0.522 0.562 0.047 28.000 0.427 0.24765 0.356 0.436 0.209 0.217 0.435 0.494 0.068 19.000 0.519 0.32766 0.414 0.639 0.171 0.414 0.438 0.672 0,031 17.000 0.507 0.16167 0.222 0.284 0.235 0.303 0.318 0.396 0.098 28.000 0.175 0.19368 0.444 0.620 0.242 0.369 0.514 0.698 0.095 32.000 0.431 0.33969 0.235 0.317 0.164 0.266 0.350 0.425 0.077 20.000 0.308 0.29070 0.193 0.266 0.345 0.386 0.273 0.321 0.047 17.000 0.465 0.41471 0.229 0.278 0.468 0.441 0.401 0.428 ,0.095 29.000 0.184 0.25272 0.503 0.687 0.213 0.391 0.514 0.698 0.049 8.000 0.374 0.321
OBS X7 X8 X9 X10 X11 X12 X13 X14 X1549 0.332 0.504 1.604 0.062 7.487E-06 0.009 65.774 -0.179 0.75950 0.873 1.271 1.601 0.053 3.368E-06 0.033 86.060 -0.237 0.76651 0.860 1.458 0.783 0.060 6.664E-06 0.019 71.163 -0.336 0.77152 0.733 0.617 1.166 0.052 1.050E-06 0.034 78.506 -0.358 0.72453 0.256 0.549 1.330 0.065 7.537E-06 0.193 60.511 -0.335 0.70054 0.319 1.304 1.415 0.059 4.466E-06 0.079 44.600 -0.340 0.70055 0.236 1.183 0.627 0.060 1.251E-05 0.099 73.195 -0.145 0.74956 0.446 0.737 0.981 0.058 2.996E-06 0.126 83.717 -0.334 0.79857 0.715 0.767 1.057 0.068 3.516E-05 0.082 88.588 -0.292 0.72258 0.131 1.323 0.997 0.052 3.660E-05 0.132 55.231 -0.330 0.72159 0.709 0.706 1.253 0.053 1.934E-06 0.101 86.066 -0.368 0.72160 0.189 1.468 1.344 0.063 9.399E-05 0.056 58.517 -0.283 0.77161 0.134 1.408 1.098 0.057 2.404E-05 0.113 45.005 -0.344 0.74962 0.535 0.577 0.657 0.055 5.861E-05 0.048 72.951 -0.355 0.75363 0.706 1.277 1.725 0.063 7.797E-06 0.076 64.778 -0.153 0.70964 0.186 1.058 1.318 0.052 1.025E-05 0.068 77.907 -0.235 0.76865 0.539 0.721 0.515 0.056 7.619E-06 0.141 64.761 -0.334 0.70666 0.856 1.317 0.709 0.055 5.801E-05 0.071 52.761 -0.164 0.72167 0.450 1.146 1.103 0.057 2.590E-05 0.071 84.329 -0.193 0.74168 0.661 0.759 1.214 0.070 1.228E-06 0.015 36.887 -0.355 0.71569 0.354 0.957 0.871 0.070 3.539E-06 0.019 42.857 -0.282 0.71670 6.418 0.792 1.466 0.057 1.122E-06 0.053 69.661 -0.416 0.75171 0.167 0.562 6.952 0.058 9.243E-06 0.136 34.720 -0.253 0.740
154
OUTPUT FROM MONTE CARLO SIMULATION
OUTPUT FROM MONTE CARLO SIMULATION
OBS YI Y2 Y3 Y4 X1 X2 X3 X4 X5 X673 0.392 0.463 0.261 0.335 0.435 0.494 0.032 31.000 0.569 0.31374 0.329 0.412 0.180 0.188 0.435 0.494 0.048 37.000 0.425 0.29575 0.246 0.404 0.375 0.407 0.392 0.500 0.047 30.000 0.227 0.40876 0.281 0.390 0.304 0.277 0.392 0.500 0.065 22.000 0.383 0.27077 0.353 0.423 0.173 0.265 0.367 0.436 0.089 31.000 0.425 0.17178 0.332 0.402 0.215 0.417 0.350 0.425 0.050 25.000 0.513 0.18079 0.239 0.347 0.178 0.207 0.359 0.427 0.039 8.000 0.429 0.43780 0.341 0.409 0.217 0.299 0.359 0.427 0.093 22.000 0.581 0.26081 0.324 0.543 0.133 0.226 0.438 0.672 0.057 2i .000 0.503 0.24082 0.388 0.512 0.201 0.445 0.535 0.639 0.072 17.000 0.353 0.44483 0.295 0.346 0.346 0.503 0.401 0.428 0.091 30.000 0.414 0.41484 0.256 0.398 0.399 0.358 0.438 0.568 0.079 16.000 0.595 0.36685 0.442 0.607 0.256 0.941 0.460 0.629 0.091 24.000 0.428 0.29386 0.169 0.245 0.416 0.363 0.318 0.396 0.061 22.000 0.571 0.26187 0.343 0.559 0.285 0.377 0.438 0.672 0.079 14.000 0.309 0.41388 0.259 0.405 0.175 0.144 0.392 0.500 0.040 11.000 0.548 0.36489 0.211 0.323 0.246 0.318 0.359 0.427 0.072 33.0010 0.323 0.40790 0.361 0.544 0.194 0.168 0.514 0.698 07035 17.000 0.291 0.30891 0.322 0.390 0.111 0.167 0.359 0.427 0.090 27.000 0.236 0.20992 0.138 0.226 0.316 0.257 0.273 0.321 0.065 15.000 0.566 0.32893 0.320 0.475 0.347 0.534 0.460 0.629 0.084 30.000 0.314 0.35594 0.233 0.291 0.106 0.182 0.273 0.321 0.080 9.000 0.139 0.35895 0.282 0.344 0.264 0.431 0.350 0.425 0.073 17.000 0.323 0.17996 0.393 0.461 0.335 0.418 0.522 0.562 0.031 35.000 0.275 0.333
OBS X7 I X8 X9 X10 X11 X12 X13 X14 X1573 0.704 1.367 1.229 0.064 7.617E-06 0.185 54.293 -0.301 0.71074 0.346 1.252 0.739 0.065 1.342E-05 0.043 78.651 -0.283 0.76875 ' 0.082 0.777 1.583 0.051 1.601E-06 0.124 65.951 -0.412 0.73276 0.350 1.492 0.777 0.052 2.341E-06 0.105 73.617 -0.268 0.75377 0.915 1.199 0.649 0.063 2.403E-06 0.104 54.069 -0.174 0.70678 0.866 0.947 1.342 0.065 3.135E-05 0.091 34.730 -0.182 0.79579 0.419 1.039 0.810 0.062 2.977E-05 0.084 58.022 -0.457 0.74180 0.912 1.024 1.068 0.066 3.724E-06 0.152 61.366 -0.257 0.79681 0.310 0.704 0.696 0.052 3.514E-05 0.020 57.185 -0.230 0.73582 0.403 1.128 1.087 0.060 4.528E-05 0.050 72.900 -0.438 0.75983 0.504 0.599 1.443 0.056 4.563E-06 0.065 30.933 -0.426 0.79384 0.154 0.666 1.282 0.070 6.510E-06 0.133 48.706 -0.356 0.78885 0.916 1.131 1.682 0.057 7.529E-06 0.176 78.641 -0.299 0.71886 0.081 1.045 1.536 0.058 1.278E-06 0.164 88.159 -0.264 0.78587 0.56£ 0.707 1.297 0.058 1.823E-06 0.115 59.683 -0.410 0.71388 0.100 0.669 1.732 0.067 3.956E-05 0.099 50.635 -0.350 0.75489 0.258 0.732 1.419 0.062 7.478E-06 0.035 73.436 -0.415 0.78190 0.126 0.946 0.502 0.062 2.229E-05 0.091 35.508 -0.308 0.79791 0.818 0.613 0.683 0.052 6.002E-06 0.089 39.274 -0.201 0.72692 0.074 1.282 1.479 0.064 2.642E-05 0.097 82.154 -0.323 0.71893 0.359 0.755 1.470 0.052 1.088E-06 0.038 56.571 -0.349 0.75094 0.762 1.083 0.797 0.057 7.600E-05 0.075 49.947 -0.354 0.72195 0.597 0.566 1.164 0.064 5.150E-06 0.034 44.704 -0.170 0.75696 0.303 0.756 0.838 0.064 6.131E-06 0.178 38.263 -0.323 0.707
OUTPUT FROM MONTE CARLO SIMULATION
OBS Yl Y2 Y3 Y4 X1 X2 X3 X4 X5 X697 0.291 0.368 0.169 0.283 0.367 0.436 0.077 23.000 0.527 0.21496 0.300 0.393 0.335 0.464 0.417 0.545 0.075 37.000 0.239 0.18799 0.234 0.384 0.362 0.355 0.401 0.504 0.045 21.000 0.193 0.395100 0.298 0.357 0.329 0.463 0.535 0.639 0.094 19.000 0.298 0.155101 0.232 0.358 0.139 0.149 0.382 0.476 0.067 18.000 0.586 0.357102 0.297 0.406 0.199 0.240 0.438 0.568 0.037 16.000 0.216 0.170103 0.264 0.345 0.246 0.387 0.350 0.425 0.093 18.000 0.472 0.335104 0.289 0.352 0.276 0.288 0.350 0.425 0.064 34.000 0.261 0.168105 0.208 0.256 0.155 0.169 0.342 0.343 0.073 24.000 0.116 0.261106 0.283 0.419 0.324 0.440 0.417 0.545 0.054 16.000 0.196 0.382107 0.228 0.303 0.399 0.474 0.401 0.428 0.096 13.000 0.284 0.371108 0.481 0.585 0.255 0.293 0.704 0.731 0.096 28.000 0.289 0.447109 0.281 0.402 0.308 0.310 0.417 0.545 0.041 19.000 0.242 0.300110 0.347 0.509 0.360 0.347 0.514 0.698 0.072 13.000 0.304 0.297111 0.270 0.361 0.347 0.363 0.401 0.504 0.069 15.000 0.256 0.281112 0.240 0.307 0.195 0.217 0.350 0.425 0.070 37.000 0.507 0.167113 0.284 0.389 0.329 0.282 0.392 0.500 0.059 8.000 0.590 0.249114 0.495 0.677 0.130 0.199 0.514 0.698 0.040 15.000 0.164 0.292115 0.402 0.546 0.280 0.422 0.535 0.639 0.031 32.000 0.511 0.438116 0.231 0.307 0.309 0.401 0.318 0.396 0.072 11.000 0.540 0.304117 0.405 0.553 0.195 0.375 0.460 0.629 0.075 31.000 0.284 0.183118 0.286 0.373 0.260 0.551 0.318 0.396 0.045 30.000 0.401 0.440119 0.357 0.428 0.185 0.325 0.367 0.436 0.070 11.000 0.174 0.317120 0.308 0.388 0.203 0.299 0.350 0.425 0.049 16.000 0.513 0.332OBS X7 X8 X9 X10 X11 X12 X13 X14 X1597 0.546 1.452 0.897 0.052 7.343E-06 0.036 43.046 -0.222 0.74898 0.414 0.705 1.484 0.068 1.601E-06 0.166 86.476 -0.187 0.78099 0.123 0.818 0.552 0.059 3.642E-06 0.196 30.974 -0.396 0.729100 0.111 1.339 1.369 0.053 1.564E-06 0.193 53.962 -0.160 0.744101 0.143 1.071 1.263 0.067 7.260E-05 0.080 47.861 -0.360 0.702102 0.208 1.063 1.625 0.061 6.595E-06 0.022 40.095 -0.162 0.702103 0.522 0.617 1.661 0.061 6.713E-06 0.037 73.084 -0.343 0.770104 0.622 1.283 0.886 0.056 1.387E-06 0.193 84.250 -0.169 0.756105 0.275 0.863 1.630 0.063 3.327E-OS 0.023 86.016 -0.265 0.736106 0.369 1.406 1.534 0.061 1.678E-06 0.081 45.803 -0.373 0.709107 0.218 1.214 1.052 0.056 1.020E-06 0.191 66.034 -0.353 0.703106 0.263 0.838 0.951 0.058 1.351E-05 0.031 84.129 -0.455 0.766109 0.268 1.078 1.060 0.063 2.234E-06 0.108 52.511 -0.297 0.774110 0.221 0.985 1.521 0.052 8.349E-06 0.197 58.602 -0.297 0.729111 0.338 0.859 1.538 0.068 4.038E-06 0.122 84.823 -0.282 0.754112 0.158 1.253 0.627 0.064 4.575E-OS 0.146 68.597 -0.165 0.700113 0.345 0.965 1.117 0.054 6.953E-06 0.190 82.345 -0.238 0.744114 0.890 1.048 0.651 0.059 2.567E-05 0.030 33.490 -0.304 0.784115 0.205 0.802 0.931 0.064 1.318E-05 0.074 84.453 -0.442 0.747116 0.532 0.778 1.476 0.059 1.703E-06 0.196 52.655 -0.316 0.783117 0.733 0.776 0.863 0.060 36172E-05 0.122 70.520 4.189 0.768118 0.800 0.847 14734 0.068 1.552E-06 0.017 45.466 -0.454 0.701119 0.945 1.293 1.293 0:067 1.120E-06 0.093 19.922 -0.315 0.709120 0.789 1.310 0.068 2.202E-05 0.035 51.303 -0.331 0.140
156
OBS Y1 Y2 Y3 Y4 X1 X2 X3 X4 X5 X6121 0.416 0.566 0.200 0.356 0.460 0.629 0.036 35.000 0.449 0.177122 0.308 0.509 0.081 0.134 0.438 0.672 0.034 34.000 0.141 0.217123 0.180 0.246 0.095 0.075 0.342 0.343 0.063 18.000 0.372 0.295124 0.377 0.486 0.203 0.339 0.392 0.500 0.090 29.000 0.550 0.327125 0.280 0.357 0.125 0.171 0.359 0.427 0.100 26.000 0.210 0.306126 0.246 0.354 0.362 0.302 0.382 0.476 0.095 3.000 0.508 0.297127 0.334 0.554 0.220 0.310 0.438 0.672 0.097 3.000 0.228 0.444128 0.314 0.442 0.220 0.430 0.417 0.545 0.071 2.9.000 0.276 0.363129 0.370 0.467 0.244 0.408 0.462 0.559 0.073 13:000 0.192 0.345130 0.423 0.481 0.199 0.385 0.435 0.494 0.036 Y3.'000 0.127 0.157131 0.247 0.298 0.322 0.420 0.273 0.321 0.049 32.000 0.367 0.241132 0.358 0.499 0.359 0.985 0.460 0.629 0.081 22.000 0.321 0.215133 0.335 0.412 0.294 0.563 0.350 0.425 0.045 34.'000 0.520 0.369134 0.204 0.264 0.340 0.326 0.392 0.500 0.084 32.000 0.124, 0.170135 0.446 0.613 0.169 0.422 0.460 0.629 0.079 23.000 0.416 0.361136 0.335 0.426 0.135 0.157 0.462 0.559 0.066 17.000 0.303 0.258137 0.403 0.625 0.202 0.456 0.438 0.672 0.031 34.000 0.320 0.153138 0.336 0.548 0.213 0.426 0.438 0.672 0„046 12.000 0.124 0.412139 0.241 0.263 0.202 0.209 0.342 0.343 0.062 13.000 0.498 0.278140 0.347 0.399 0.368 0.426 0.522 0.562 0.044 20.000 0.351 0:268141 0.278 0.364 0.281 0.411 0.350 0.425 0.050 23.000 0.216 0.372142 0.332 0.408 0.171 0.201 0.435 0.494 0.080 18.000 0.251 0.356143 0.263 0.389 0.332 0.402 0.417 0.545 0.086 10.000 0.239 0.368144 0.568 0.643 0.300 0.505 0.704 0.731 0.034 10.000 0.588 0.319OBS X7 X8 X9 X10 X11 X12 X13 X14 X15121 0.757 0.759 0.610 0.066 6.706E-06 0.147 32.034 -0.166 0.772122 0.176 0.632 1.335 0.063 5.727E-05 0.013 49.536 -0.215 0.705123 0.083 0.582 1.440 0.062 7.853E-05 0.040 86.231 -0.288 0.762124 ' 0.916 1.159 1.692 0.056 3.131E-05 0.102 79.541 -0.324 0.796125 0.640 1.166 0.670 0.058 2.078E-05 0.121 41.888 -0.317 0.782126 0.144 0.652 1.015 0.069 4.156E-06 0.066 60.694 -0.283 0.719127 0.543 0.918 0.681 0.056 1.435E-05 0.152 58.380 -0.441 0.734128 0.477 0.515 1.686 0.067 1.547E-05 0.056 32.369 -0.378 0.776129 0.609 1.245 1.357 0.059 2.984E-05 0.090 55.082 -0.348 0.722130 0.929 1.157 1.087 0.052 1.864E-05 0.030 33.941 -0.162 0.771131 0.752 0.552 1.330 0.052 2.160E-06 0.089 71.369 -0.231 0.748132 0.517 0.982 1.602 0.068 8.400E-06 0.140 44.786 -0.210 0.705133 0.888 1.247 1.732 0.056 6.280E-05 0.105 86.616 -0.368 0.717134 0.055 1.397 0.613 0.057 1.634E-06 0.149 44.279 -0.162 0.783135 0.933 0.734 1.198 0.055 8.474E-05 0.096 80.198 -0.361 0.730136 0.360 0.809 0.504 0.062 1.585E-05 0.014 71.794 -0.264 0.708137 0.802 1.422 0.859 0.053 6.126E-06 0.019 31.489 -0.157 0.792138 0.446 0.623 1.156 0.068 8.854E-05 0.082 46.706 -0.433 0.783139 0.412 0.714 0.599 0.052 2.740E-06 0.026 39.866 -0.291 0.705140 0.233 1.246 1.203 0.056 3.288E-06 0.115 68.391 -0.268 0.710141 0.577 1.019 1.549 0.055 8.758E-06 0.075 84.703 -0.380 0.772142 0.532 1.084 0.528 0.070 9.376E-06 0.072 56.223 -0.373 0.793143 0.313 0.742 1.094 0.066 2.310E-06 0.123 85.374 -0.375 0.797144 0.360 0.544 1.514 0.053 2.370E-05 0.103 49.578 -0.331 0.735
OBS YI Y2 Y3 Y4 X1 X2 X3 X4 X5 X6145 0.322 0.435 0.338 0.414 0.438 0.568 0.049 8.000 0.333 0.201146 0.246 0.289 0.161 0.295 0.342 0.343 0.064 30.000 0.130 0.383147 0.499 0.606 0.313 1.989 0.535 0.639 0.099 21.000 0.263 0.406149 0.286 . 0.420 0.293 0.374 0.460 0.629 0.051 23.000 0.141 0.186149 0.328 0.443 0.181 0.235 0.392 0.500 0.046 25.000 0.296 0.316150 0.311 0.390 0.122 0.191 0.367 0.436 0.085 24,.000 0.387 0.262151 0.402 0.432 0.316 0.638 0.522 0.562 0.049 24.000 0.196 0.166152 0.441 0.545 0.213 0.441 0.535 0.639 0.045 8.000 0.133 0.245153 0.320 0.495 0.195 0.383 0.438 0.672 0.057 23.000 0.230 0.190154 0.208 0.309 0.317 0.402 0.350 0.425 0.090 8.000 0.146 0.369155 0.253 0.311 0.211 0.238 0.401 0.428 0.092 27.000 0.163 0.323156 0.380 0.489 0.191 0.289 0.392 0.500 0.031 31.000 0.191 0.270157 0.266 0.361 0.311 0.307 0.401 0.504 0.032 9.000 0.261 0.200158 0.328 0.510 0.143 0.268 0.438 0.672 0.097 20.000 0.533 0.180159 0.323 0.444 0.317 0.420 0.401 0.504 0.037 36.000 0.289 0.353160 0.223 0.280 0.299 0.388 0.273 0.321 0.098 10.000 0.438 0.336161 0.410 0.521 0.265 0.380 0.462 0.559 0.056 21.000 0.513 0.419162 0.286 0.369 0.245 0.318 0.350 0.425 0.054 36.000 0.172 0.370163 0.313 0.423 0.343 0.402 0.401 0.504 0.040 29.000 0.198 0.331164 0.166 0.223 0.387 0.328 0.318 0.396 0.054 13.000 0.500 0.218165 0.299 0.316 0.205 0.225 0.342 0.343 0.079 36.000 0.111 0.324166 0.411 0.642 0.270 0.462 0.438 0.672 0.047 35.000 0.188 0.414167 0.207 0.274 0.143 0.230 0.273 0.321 0.050 15.000 0.516 0.331168 0.337 0.494 0.339 0.343 0.514 0.698 0.055 17.000 0.502 0.292
OBS X7 X8 X9 X10 X11 X12 X13 X14 X15145 0.436 1.290 1.616 0.067 5.803E-06 0.128 81.256 -0.202 0.783146 0.532 1.031 1.543 0.069 6.136E-05 0.168 87.830 -0.366 0.740147 0.862 1.068 1.747 0.063 1.604E-06 0.046 51.723 -0.424 0.732148 0.066 0.952 1.747 0.059 1.878E-06 0.027 30.355 -0.178 0.710149 0.606 1.483 1.371 0.055 5.635E-06 0.031 36.149 -0.317 0.749150 0.675 0.713 0.761 0.069 7.848E-06 0.028 36.527 -0.265 0.748151 0.484 0.942 1.621 0.067 2.904E-06 0.039 73.911 -0.174 0.735152 0.475 0.720 0.967 0.060 5.171E-OS 0.130 85.722 -0.242 0.759153 0.412 0.849 1.128 0.062 2.536E-05 0.028 84.382 -0.198 0.795154 0.283 1.380 0.997 0.055 6.203E-06 0.093 37.314 -0.386 0.743155 0.304 0.613 1.026 0.064 4.333E-05 0.150 46.939 -0.308 0.730156 0.914 1.099 0.734 0.059 1.565E-06 0.070 50.678 -0.256 0.706157 0.077 0.638 1.198 0.055 1.673E-05 0.167 60.955 -0.209 0.746158 0.483 1.283 1.311 0.053 9.584E-05 0.020 45.190 -0.175 0.750159 0.547 1.332 1.527 0.059 1.685E-06 0.037 45.806 -0.348 0.743160 0.707 1.338 1.362 0.062 1.646E-06 0.093 60.225 -0.327 0.777161 0.728 1.100 0.645 0.058 5.114E-06 0.108 40.868 -0.436 0.727162 0.600 0.671 0.768 0.068 9.151E-06 0.052 75.157 -0.377 0.792163 0.537 1.349 0.935 0.056 5.400E-06 0.141 85.514 -0.322 0.799164 0.079 0.687 0.663 0.054 1.902E-06 0.051 69.361 -0.213 0.798165 0.789 1.485 1.030 0.056 2.291E-06 0.094 39.120 -0.339 0.763166 0.858 0.794 0.929 0.064 1.708E-06 0.045 82.213 -0.420 0.796167 0.500 0.914 0.813 0.061 4.510E-05 0.119 61.061 -0.343 0.722168 0.154 1.397 1.449 0.060 7.643E-06 0.188 33.087 -0.290 0.792
OUTPUT FROM MONTE CARLO SIMULATION
OUTPUT FROM MONTE CARLO SIMULATION
OBS Y1 Y2 Y3 Y4 X1 X2 X3 X4 X5 X6145 0.322 0.435 0.338 0.414 0.438 0.568 0.049 8.000 0.333 0.201146 0.246 0.289 0.181 0.295 0.342 0.343 0.064 30.000 0.130 0.383147 0.499 0.606 0.313 1.989 0.535 0.639 0.099 21.000 0.263 0.406148 0.286 0.420 0.293 0.374 0.460 0.629 0.051 23.000 0.141 0.186149 0.328 0.443 0.181 0.235 0.392 0.500 0.046 25.000 0.296 0.316150 0.311 0.390 0.122 0.191 0.367 0.436 0.085 24.000 0.387 0.262151 0.402 0.432 0.316 0.638 0.522 0.562 0.049 24.000 0.196 0.166152 0.441 0.545 0.213 0.441 0.535 0.639 0.045 8.000 0.133 0.245153 0.320 0.495 0.195 0.383 0.438 0.672 0.057 23.000 0.230 0.190154 0.208 0.309 0.317 0.402 0.350 0.425 0.090 8.000 0.146 0.369155 0.253 0.311 0.211 0.238 0.401 0.428 0.092 27.000 0.163 0.323156 0.380 0.489 0.191 0.289 0.392 0.500 0.031 31.000 0.191 0.270157 0.266 0.361 0.311 0.307 0.401 0.504 0.032 9.000 0.261 0.200158 0.328 0.510 0.143 0.268 0.438 0.672 0.097 20.000 0.533 0.180159 0.323 0.444 0.317 0.420 0.401 0.504 0.037 36.000 0.289 0.353160 0.223 0.280 0.299 0.388 0.273 0.321 0.098 10.000 0.438 0.336161 0.410 0.521 0.265 0.380 0.462 0.559 0.056 21.000 0.513 0.419162 0.286 0.369 0.245 0.318 0.350 0.425 0.054 36.000 0.172 0.370163 0.313 0.423 0.343 0.402 0.401 0.504 0.040 29.000 0.198 0.331164 0.166 0.223 0.387 0.328 0.318 0.396 0.054 13.000 0.500 0.218165 0.299 0.316 0.205 0.225 0.342 0.343 0.079 36.000 0.111 0.324166 0.411 0.642 0.270 0.462 0.438 0.672 0.047 35.000 0.188 0.414167 0.207 0.274 0.143 0.230 0.273 0.321 0.050 15.000 0.516 0.331168 0.337 0.494 0.339 0.343 0.514 0.698 0.055 17.000 0.502 0.292OBS X7 X8 X9 X10 X11 X12 X13 X14 X15145 0.436 1.290 1.616 0.067 5.803E-06 0.128 81.256 -0.202 0.783146 0.532 1.031 1.543 0.069 6.136E-05 0.168 87.830 -0.366 0.740147 0.862 1.068 1.747 0.063 1.604E-06 0.046 51.723 -0.424 0.732148 0.066 0.952 1.747 0.059 1.878E-06 0.027 30.355 -0.178 0.710149 0.606 1.483 1.371 0.055 5.635E-06 0.031 36.149 -0.317 0.749150 0.675 0.713 0.761 0.069 7.848E-06 0.028 36.527 -0.265 0.748151 0.484 0.942 1.621 0.067 2.904E-06 0.039 73.911 -0.174 0.735152 0.475 0.720 0.967 0.060 5.171E-05 0.130 85.722 -0.242 0.759153 0.412 0.849 1.128 0.062 2.536E-05 0.028 84.382 -0.198 0.793154 0.283 1.380 0.997 0.055 6.203E-06 0.093 37.314 -0.386 0.743155 0.304 0.613 1.026 0.064 4.333E-05 0.150 46.939 -0.308 0..730156 0.914 1.099 0.734 0.059 1.565E-06 0.070 50.678 -0.256 0.706157 0.077 0.638 1.198 0.055 1.673E-05 0.167 60.955 -0.209 0.746158 0.483 1.283 1.311 0..053 9.584E-05 0.020 45.190 -0.175 0.750159 0.547 1.332 1.527 0.059 1.685E-06 0.037 45.806 -0.348 0.743160 0.707 1.338 1.362 0.062 1.646E-06 0.093 60.225 -0.327 0.777161 0.728 1.100 0.645 0.058 5.114E-06 0.108 40.868 -0.436 0.727162 0.600 0.671 0.768 0.058 9.151E-06 0.052 75.157 -0.377 0.792163 0.537 1.349 0.935 0.056 5.400E-06 0.141 85.514 -0.322 0.799164 0.079 0.687 0.663 0.054 1.902E-06 0.051 69.361 -0.213 0.798165 0.789 1.485 1.030 0.056 2.291E-06 0.094 39.120 -0.339 0.763166 0.858 0.794 0.929 0.064 1.708E-06 0.045 82.213 -0.420 0.796167 0.500 0.914 0.813 0.061 4.510E-05 0.119 61.061 -0.343 0.722168 0.154 1.397 1.449 0.060 7.643E-06 0.188 33.087 -0.290 0.792
158
OUTPUT FROM MONTE CARLO SIMULATION
OBS Y1 Y2 Y3 Y4 X1 X2 X3 X4 X5 X6 169 0.400 0.445 0.331 0.532 0.522 0.562 0.046 31.000 0.180 0.288 170 0.338 0.414 0.232 0.272 0.435 0.494 0.096 24.000 0.207 0.387 171 0.284 0.370 0.189 0.307 0.359 0.427 0.084 30.000 0.368 0.429 172 0.538 0.627 0.336 0.412 0.704 0.731 0.049 30.000 0.569 0.332 173 0.427 0.660 0.147 0.383 0.438 0.672 0.046 15.000 0.345 0.388 174 0.298 0.378 0.170 0.279 0.318 0.396 0.076 10.000 0.354 0.363 175 0.202 0.265 0.313 0.359 0.342 0.343 0.089 21.000 0.378 0.400 176 0.220 0.284 0.195 0.273 0.273 0.321 0.054 29.000 0.326 0.414 177 0.308 0.426 0.242 0.484 0.392 0.500 0.096 24.000 0.232 0.398 178 0.180 0.261 0.350 0.501 0.342 0.343 0.075 32.000 0.253 0.419 179 0.288 0.366 0.217 0.386 0.350 0.425 0.084 27.000 0.172 0.317 180 0.309 0.350 0.195 0.259 0.401 0.428 0.0882 22.000 0.398 0.312 181 0.237 0.329 0.243 0.285 0.318 0.396 0.073 36.000 0.465 0.393 182 0.331 0.432 0.332 0.343 0.382 0.476 0.042 35.000 0.529 0.328 183 0.227 0.325 0.227 0.219 0.401 0.504 0.084 25.000 0.375 0.258 184 0.282 0.489 0.305 0.330 0.438 0.672 0.097 16.000 0.410 0.401 185 0.458 0.582 0.347 0.390 0.704 0.731 0.066 28.000 0.169 0.448 186 0.201 0.247 0.274 0.274 0.273 0.321 0.063 29.000 0.308 0.165 187 0.216 0.277 0.231 0.268 0.273 0.321 0.038 22.000 0.111 0.296 188 00.135 0.179 0.294 0.261 0.273 0.321 0.099 19.000 0.487 0.156 189 0.295 0.412 0.128 0.154 0.417 0.545 0.091 9.000 0.469 0.338 190 0.369 0.477 0.229 0.333 0.392 0.500 0.086 20.000 0.214 0.307 191 0.449 0.621 0.184 0.272 0.514 0.698 0.034 26.000 0.506 0.207 192 0.226 0.332 0.134 0.095 0.382 0.476 0.042 8.000 0.254 0.253 OBS X7 X8 X9 X10 X11 X12 X 13 X14 X15 169 0.485 1.043 1.416 0.054 4.758E-06 0.173 70.712 -0.287 0.780 170 0.583 0.903 0.857 0.066 1.970E-06 0.046 81.359 -0.379 0/787 171 0.661 1.277 1.473 0.059 3.105E-05 0.020 47.448 -0.429 0.738 172 0.259 0.717 1.534 0.065 3.375E-06 0.163 86.403 -0.345 0.785 173 0.942 1.023 0.867 0.058 1.448E-06 0.006 30.645 -0.392 0.702 174 0.899 1.247 0.864 0.059 4.440E-05 0.105 87.595 -0.378 0.789 175 0.344 0.688 0.729 0.054 5.571E-06 0.088 59.676 -0.396 0.772 176 0.618 0.898 1.229 0.053 5.179E-05 0.024 64.309 -0.433 0.702 177 0.584 0.677 0.943 0.052 2.042E-05 0.030 53.917 -0.403 0.753 178 0.232 1.076 1.263 0.070 6.185E-06 0.074 55.920 -0.428 0.727 179 0.676 1.396 1.392 0.053 8.237E-05 0.177 52.742 -0.329 0.749 180 0.556 1.188 0.847 0.051 8.734E-06 00.17 41.649 -0.323 0.768 181 0.536 1.253 0.708 0.060 4.221E-06 0.099 35.528 -0.404 0.761 182 0.606 0.641 1.116 0.061 1.684E-06 0.199 61.336 -0.312 0.727 183 0.080 0.653 1.275 0.058 3.174E-05 0.141 41.649 -0.247 0.793 184 0.297 0.839 0.701 0.063 5.120E-06 0.188 33.890 -0.415 0.708 185 0.123 1.002 1.724 0.069 4.044E-06 0.066 50.480 -0.442 0.748 186 0.446 1.191 0.736 0.059 2.834E-06 0.137 58.841 -0.157 0.713 187 0.582 0.707 0.690 0.057 1.008E-06 0.028 41.396 -0.291 0.729 188 0.068 1.101 1.103 0.053 3.298E-05 0.197 55.565 -0.151 0.747 189 0.471 1.174 0.555 0.064 5.679E-05 0.177 53.772 -0.341 0.740 190 0.879 0.976 1.686 .068 9.320E-05 0.132 63.437 -0.322 0.711 191 0.606 0.809 1.200 0.053 8.346E-05 0.081 66.982 -0.214 0.784 192 0.093 1.223 1.116 0.068 7.384E-05 0.093 61.831 -0.242 0.709
159
OUTPUT FROM MONTE CARLO SIMULATION
OBS Y1 Y2 Y3 Y4 X1 X2 X3 X4 X5 X6193 0.298 0.378 0.189 0.324 0.318 0.396 0.096 16.000 0.490 0.438194 0.259 0.345 0.148 0.118 0.382 0.476 0.058 16.000 0.373 0.288195 0.236 0.337 0.194 0.213 0.367 0.436 0.088 14.000 0.185 0.365196 0.348 0.453 0.364 0.392 0.438 0.568 0.084 20.000 0.336 0.166197 0.408 0.498 0.286 0.566 0.462 0.559 0.099 25.000 0.357 0.223198 0.322 0.396 0.191 0.350 0.359 0.427 0.068 25.000 0.409 0.302199 0.258 0.327 0.339 0.317 0.435 0.494 0.079 24.000 0.273 0.245200 0.379 0.489 0.196 0.301 0.392 0.500 0.031 34.000 0.357 0.270201 0.239 0.354 0.288 0.306 0.367 0.436 0.047 15.000 0.196 0.368202 0.419 0.519 0.230 0.330 0.462 0.559 0.062 23.000 0.447 0.305203 0.168 0.238 0.371 0.325 0.318 0.396 0.094 33.000 0.394 0.224204 0.291 0.419 0.245 0.236 0.392 0.500 0.041 27.000 0.444 0.341205 0.274 0.367 0.358 0.436 0.401 0.504 0.098 23.000 0.131 0.348206 0.333 0.423 0.319 0.416 0.462 0.559 0.058 19.000 0.113 0.312207 0.331 0.490 0.162 0.672 0.460 0.629 0.080 19.000 0.174 0.375208 0.339 0.410 0.181 0.328 0.350 0.425 0.062 35.000 0.221 0.153209 0.363 0.462 0.331 0.528 0.401 0.504 0.059 27.000 0.287 0.238210 0.413 0.546 0.266 0.453 0.438 0.568 0.073 20.000 0.532 0.398211 0.370 0.510 0.348 0.486 0.460 0.629 0.055 20.000 0.237 0.173212 0.239 0.364 0.381 0.506 0.401 0.504 0.041 8.000 0.312 0.381213 0.337 0.427 0.247 0.451 0.435 0.494 0.087 33.000 0.289 0.413214 0.366 0.504 0.359 0.531 0.438 0.568 0.056 33.000 0.327 0.337215 0.368 0.437 0.123 0.228 0.435 0.494 0.036 12.000 0.209 0.294216 0.259 0.387 0.302 0.273 0.438 0.672 0.066 11.000 0.344 0.200
OBS X7 X8 X9 X10 X11 X12 X13 X14 X15193 0.904 1.019 1.261 0.068 3.696E-06 0.089 60.403 -0.448 0.763194 0.327 1.247 0.527 0.054 1.894E-05 0.038 30.122 -0.220 0.745195 0.378 1.209 0.618 0.052 5.694E-05 0.156 73.409 -0.380 0.781196 0.597 1.455 1.052 0.051 1.817E-06 0.120 67.686 -0.171 0.721197 0.747 0.786 1.656 0.068 3.525E-05 0.046 85.374 -0.212 0.741198 0.817 1.253 1.323 0.061 7.525E-06 0.099 33.897 -0.311 0.741199 0.124 1.157 0.506 0.058 1.012E-06 0.105 75/675 -0.251 0.746200 0.905 1.048 1.223 0.068 1.554E-05 0.130 88.130 -0.275 0.707201 0.225 0.727 0.802 0.067 1.558E-05 0.096 83.685 -0.375 0.799202 0.774 1.245 0.635 0.055 1.848E-05 0.169 89.762 -0.294 0.723203 0.066 0.902 1.176 0.057 1.484E-05 0.172 88.781 -0.225 0.703204 0.341 1.250 0.692 0.065 1.461E-05 0.174 78.165 -0.352 0.791205 0.464 1.090 1.512 0.052 1.009E-06 0.095 70.336 -0.331 0.762206 0.422 1.471 1.277 0.060 8.866E-06 0.101 32.716 -0.310 0.716207 0.432 0.696 1.692 0.054 5.666E-05 0.017 67.727 -0.382 0.778208 0.932 1.314 1.022 0.065 4.771E-06 0.104 52.790 -0.154 0.800209 0.787 1.126 1.598 0.067 3.031E-06 0.090 60.327 -0.232 0.755210 0.887 1.184 1.061 0.062 2.629E-06 0.139 57.761 -0.416 0.746211 0.545 0.787 1.114 0.054 1.784E-06 0.077 87.512 -0.170 0.796212 0.202 1.487 1.275 0.054 1.713E-06 0.165 87.004 -0.369 0.757213 0.521 1.085 1.373 0.057 1.334E-05 0.130 68.658 -0.419 0.704214 0.593 0.631 1.549 0.065 1.524E-06 0.137 59.895 -0.352 0.737215 0.631 1.426 1.007 0.061 1.463E-05 0.011 43.138 -0.301 0.782216 0.176 1.021 0.514 0.057 2.137E-06 0.015 75.808 -0.208 0.788
160
OUTPUT FROM MONTE CARLO SIMULATION
OBS Y1 Y2 Y3 Y4 X1 X2 X3 X4 X5 X6217 0.314 0.391 0.207 0.292 0.359 0.427 0.061 21.000 0.263 0.349218 0.603 0.633 0.290 0.339 0.704 0.731 0.093 37.000 0.126 0.205219 0.423 0.551 0.339 0.687 0.438 0.568 0.041 34.000 0.215 0.212220 0.224 0.336 0.209 0.238 0.367 0.436 0.084 24.000 0.440 0.286221 0.326 0.334 0.182 0.244 0.342 0.343 0.067 26.000 0.333 0.419222 0.252 0.297 0.162 0.157 0.342 0.343 0.062 37.000 0.552 0.378223 0.348 0.453 0.294 0.358 0.401 0.504 0.088 32.000 0.380 0.303224 0.400 0.591 0.312 0.376 0.514 0.698 0.043 22.000 0.226 0.413225 0.197 0.314 0.164 0.195 0.359 0.427 0.053 27.000 0.123 0.400226 0.316 0.398 0.388 0.463 0.522 0.562 0.050 13.000 0.230 0.329227 0.337 0.397 0.232 0.399 0.52 0.562 0.053 15.000 0.328 0.342228 0.320 0.485 0.316 0.504 0.460 0.629 0.031 15.000 0.328 0.357229 0.468 0.516 0.217 0.373 0.522 0.562 0.037 31.000 0.260 0.365230 0.382 0.515 0.180 0.222 0.417 0.545 0.075 31.000 0.285 0.433231 0.367 0.582 0.352 0.639 0.438 0.672 0.095 20.000 0.185 0.403232 0.477 0.653 0.286 0.400 0.514 0.698 0.063 8.000 0.369 0.192233 0.386 0.491 0.348 0.516 0.401 0.504 0.036 16.000 0.369 0.391234 0.229 0.308 0.313 0.350 0.417 0.545 0.085 9.000 0.343 0.167235 0.348 0.445 0.194 0.259 0.462 0.559 0.090 24.000 0.576 0.262236 0.404 0.505 0.305 0.651 0.535 0.639 0.090 10.000 0.475 0.293237 0.391 0.492 0.252 0.371 0.401 0.504 0.068 18.000 0.573 0.251238 0.259 0.306 0.099 0.178 0.273 0.321 0.097 15.000 0.529 0.204239 0.353 0.484 0.372 0.818 0.438 0.568 0.057 34.000 0.125 0.293240 0.286 0.425 0.340 0.448 0.401 0.504 0.057 28.000 0.271 0.435
OBS X7 X8 X9 X10 X11 X12 X13 X14 X15217 0.791 1.217 1.149 0.068 2.720E-06 0.069 50.328 -0.345 0.733218 0.666 1.064 0.554 0.054 5.459E-06 0.144 54.19 -0.208 0.715219 0.915 0.863 1.682 0.061 9.893E-06 0.064 69.603 -0.206 0.760220 0.179 1.166 1.551 0.059 2.931E-05 0.092 34.202 -0.298 0.719221 0.920 0.772 1.239 0.063 8.130E-06 0.150 80.338 -0.433 0.766222 0.430 0.732 0.888 0.055 3.822E-06 0.013 55.433 -0.370 0.704223 0.722 1.348 0.952 0.058 1.743E-06 0.089 61.909 -0.316 0.756224 0.435 1.170 0.948 0.065 1.397E-06 0.057 37.186 -0.414 0.773225 0.235 0.999 0.705 0.069 1.126E-05 0.033 53.689 -0.386 0.730226 0.111 0.886 1.614 0.052 1.654E-06 0.182 78.837 -0.318 0.729227 0.276 1.131 1.630 0.059 2.532E-05 0.135 35.054 -0.331 0.794228 0.271 1.285 1.519 0.060 7.318E-06 0.152 39.760 -0.373 0.776229 0.760 1.150 1.110 0.050 2.287E-05 0.156 45.379 -0.370 0.750230 0.833 0.775 0.545 0.051 1.398E-06 0.117 79.331 -0.433 0.716231 0.703 1.461 1.527 0.067 9.583E-06 0.055 64.038 -0.390 0.700232 0.811 0.761 1.075 0.068 1.332E-06 0.036 56.924 -0.191 0.753233 0.921 1.473 1.516 0.051 2.152E-06 0.178 70.408 -0.391 0.749234 0.122 0.649 1.742 0.056 7.309E-06 0.060 71.914 -0.168 0.789235 0.428 0.590 0.957 0.067 2.989E-05 0.093 43.863 -0.255 0.799236 0.480 0.846 1.179 0.056 2.666E-06 0.148 43.677 -0.289 0.729237 0.941 1.219 0.985 0.058 2.967E-06 0.147 83.778 -0.239 0.7534238 0.902 0.759 0.519 0.052 7.4665E-06 0.061 71.588 -0.205 0.774239 0.576 0.766 1.482 0.065 2.430E-05 0.103 49.528 -0.294 0.716240 0.403 0.792 0.894 0.068 1.854E-06 0.147 75.021 -0.449 0.729
161
OUTPUT FROM MONTE CARLO SIMULATION
OBS Y1 Y2 Y3 Y4 X1 X2 X3 X4 X5 X6 241 0.213 0.327 0.422 0.330 0.367 0.436 0.079 16.000 0.499 0.322 242 0.346 0.453 0.243 0.314 0.401 0.504 0.058 25.000 0.467 0.320 243 0.356 0.454 0.264 0.337 0.462 0.559 0.083 29.000 0.459 0.272 244 0.397 0.532 0.187 0.256 0.438 0.568 0.052 10.000 0.382 0.394 245 0.355 0.532 0.318 0.445 0.438 0.672 0.089 18.000 0.271 0.378 246 0.329 0.366 0.210 0.262 0.401 0.428 0.056 18.000 0.282 0.290 247 0.257 0.355 0.194 0.249 0.367 0.436 0.042 16.000 0.200 0.274 248 0.323 0.424 0.349 0.565 0.535 0.639 0.092 24.000 0.433 0.244 OBS X7 X8 X9 X10 X11 X12 X13 X14 X15 241 0.147
0.638 1.081 0.054 1.897E-06 0.113 40.488 -0.320 0.788
242 0.699 1.354 0.937 0.065 4.713E-06 0.168 33.351 -0.329 0.795 243 0.471 1.240 0.915 0.066 1.629E-05 0.134 36.032 -0.269 0.775 244 0.805 0.849 0.532 0.068 1.417E-06 0.081 45.954 -0.378 0.777 245 0.563 0.980 0.866 0.066 1.777E-06 0.124 75.537 -0.359 0.778 246 0.637 0.684 0.810 0.060 5.815E-06 0.039 32.204 -0.289 0.778 247 0.339 1.262 0.817 0.055 2.844E-05 0.040 78.377 -0.287 0.702 248 0.110 1.266 1.655 0.063 3.763E-06 0.195 31.477 -0.243 0.700
162