UNCERTAINTY ANALYSIS FOR WATERSHED MANAGEMENT1
Carl W. Chen*, Systech Engineering, Inc.
Robert A. Goldstein, Electric Power Research Institute
Joel Herr, Laura Ziemelis, Systech Engineering, Inc.
Larry Olmsted, Duke Energy Co.
*Systech Engineering, Inc., 3180 Crow Canyon Pl., Suite 260, San Ramon, CA 94583
The Watershed Analysis Risk Management Framework is being applied to the Catawba River
Basin of North and South Carolina. To reach consensus on a watershed management plan,
stakeholders need to know the cost, effectiveness and chance of failure of various management
alternatives. This information, supplied by hydrologic and water quality models and cost
analyses, contains uncertainty. The sources of uncertainty include: nonpoint source loads (e.g.
urbanization, fertilizer application, etc.), point source loads, watershed characteristics, rate
coefficients, and meteorology. The first two sources of uncertainty contribute to the controllable
risk and the remaining three contribute to the uncontrollable risk. Through calibrations, we
attempt to minimize the effect of uncertainties in watershed characteristics and rate parameters.
The uncertainty of meteorology, which controls nonpoint loads and receiving water hydrology, is
addressed by running the model for several years. The analysis then proceeds to the risk of
management decisions regarding point source loads and nonpoint practices, the variabilities of
which are stratified sampled for multiple simulations. The statistical spread of water quality
responses is used to determine the probability of success or failure to meet a specified water
Watershed Model, Uncertainty, Control Options, Failure Risk.
The goal of watershed management is to develop and implement a plan that will improve water
quality of a river basin. The methodology usually involves the use of a watershed model to
predict water quality improvements expected of a plan that may include the control of point and
nonpoint pollution, and atmospheric deposition. The stakeholders, who are making decision on a
multi-million dollar plan, need to know not only how the plan may help meet the water quality
objective but also the risk of failure.
The Watershed Analysis Risk Management Frame (WARMF) model is being applied to the
Catawba River Basin, which extends from North Carolina to South Carolina, for a total drainage
area of 1.23 million hectares and a total length of 360 kilometers, including 11 reservoirs (Figure
1). The model simulates runoff and nonpoint source load from tributary land, accepts point source
load, and calculates hydrology and water quality of river and lake. It can predict water quality
conditions under various management scenarios.
The model contains thousands of variables. There are uncertainties in each of these variables,
which can lead to uncertainty in water quality predictions. With so many parameters involved, it is
not practical to perform a complete uncertainty analysis of the model. This paper focuses on a
sub-set of uncertainty analysis, evaluating the risk of failure for a control option. For that
In Proceedings from WEF Conference: Watershed Management: Moving From Theory to
Implementation, Denver, CO, May 3-6, 1998.
purpose, the WARMF model was used to calculate the statistical spread of water quality
responses due to the uncertainties of controlled variables. The methodology is demonstrated
with an example.
WARMF contains two modules: a consensus module that provides a road map of the consensus
building process (Chen et al. 1997a) and an engineering module that performs scientific
simulations of hydrology and water quality (Chen, et al. 1997b). The engineering module is the
tool used for uncertainty analysis (Chen, et al. 1996). In the engineering module, the watershed
is represented by a network of subcatchments, river segments, and reservoir layers.
Meteorology, atmospheric deposition, and fertilizer data are imposed on subcatchments to
simulate runoff and nonpoint source load from land. Point source loads are discharged into river
segments or reservoirs. The flow and pollutants, from both point and nonpoint discharges are
routed through the hydrologic network to predict water quality at various points of the river basin.
Clearly, the engineering module requires the input data of watershed characteristics (e.g. area,
ground slope, land use, etc.), model coefficients (e.g. infiltration rate, soil erosion index, decay
rate etc.), and meteorology (e.g. precipitation, temperature, wind speed, humidity, etc.). None of
these variables are to be controlled by a watershed management plan. Their uncertainties are to
be minimized by various means. For example, the digital elevation map data of US Geological
Survey is used to assign watershed characteristics. The uncertainties of model coefficients are
reduced by calibration. Meteorology has spatial and temporal uncertainties. The spatial
uncertainties are minimized by using multiple stations for distributed assignment to adjacent
subcatchments. Uncertainty due to orographic effect is minimized in hydrologic calibration. The
time series of meteorological data is input for real time simulations. A multiple year simulation is
made to cover the condition for wet and dry years.
After the model is shown to simulate the observed time series of hydrology and water quality at
multiple points in the river basin, the parameter values of the uncontrolled variables are said to be
quality assured. These values are not varied in the subsequent uncertainty analysis.
For the sample problem, a management plan will be formulated to reduce the eutrophication
problem in Lake Rhodhiss, the second of the eleven chained reservoirs (see Figure 1). Under the
base condition, the simulated maximum weekly average chlorophyll-a concentration was 33 ug/l,
which turned water green. It is desired to lower the algal density to non-nuisance level.
The variables subject to management control include point source load, nonpoint source load,
and atmospheric deposition. The ranges of their variabilities are estimated from data. For each
variable, five values are selected for the low, high, medium, and quarter points. A table for all
possible combinations of values for the control variables is prepared.
A hypothetical plan is formulated to cut the nutrient loading from point and nonpoint sources and
atmospheric deposition. Table 1 presents the multipliers used to calculate the reduced
concentrations of nutrients (phosphorus, nitrate, and ammonia) from the base condition. The
planned reduction for point source discharge is 0.5 (i.e. 50%). The expected variations can range
from 0.35 to 0.65. The planned reduction of fertilizer application is 0.5 and the expected range is
0.2 to 0.8, suggesting a higher variability for nonpoint source control. The planned reduction of
atmospheric deposition is 1.0 (i.e. zero or no change), assuming that regional air emissions are
beyond local control. However, the variability can go from 0.5 to 1.5, due to the highly variable
The combinations of the values in Table 1 are used in the model simulations. Each combination
of values are fed to the model for one scenario of simulation. For three control variables, there
are 125 possible combinations and 125 simulations. The outputs are analyzed for the statistical
spread of water quality responses. These statistical spreads provide information about the
chance of failure to meet a certain water quality objective.
Comparisons were made between simulated and observed data for flow and water quality at
various points of the river basin. Figures 2 to 5 show some selected results. The model was
reasonably calibrated and the uncertainties of uncontrolled variables were minimized.
Figure 6 presents a range of time series responses of chlorophyll-a concentration in Lake
Rhodhiss under the hypothetical management plan. The statistical spread is created by 125
simulations. The top line represents the 95 percentile, meaning that the chlorophyll-a
concentrations have a 95% probability of staying below the line. The bottom line represents the
value for 5% probability.
Figure 6 suggests that algal density is lowered by the hypothetical management plan. But the
magnitude of reduction is a function of season and year due to other environmental factors. In
1993, a major storm occurred in the spring. The entire summer was relatively dry, which led to a
warm surface water, low suspended sediment, and higher algal density. In 1994, a major storm
occurred in the summer, which led to a cooler surface temperature, higher suspended sediment,
and lower algal density. The effect of loading change on algal response appears to be larger in
the summer of 1993 than in the summer of 1994.
Figure 7 presents the frequency distribution of chlorophyll-a during the week of
maximum bloom in 1993 and 1994. Implementing the planned strategy (i.e. 50%
reduction of point source and fertilizer application, and no reduction of atmospheric
deposition), there is a 70% probability that the maximum weekly chlorophyll-a
concentration in 1993 may be reduced to 20 ug/l. In the other words, there is a 30%
probability of failing to meet the 20 ug/l chlorophyll-a objective. However, the
management plan will keep the maximum chlorophyll-a below 20 ug/l in 1994 with a
100% probability. This is not a big accomplishment, because the maximum weekly
chlorophyll-a is already below 20 ug/l without the plan.
A watershed is a complex system that requires a multi-parameter model to simulate its hydrologic
and water quality behaviors. A complete uncertainty analysis of the model is not only impractical,
but also undesirable. Too many numbers may be generated to confuse rather than enlighten the
decision makers. This paper presents a method to minimize the uncertainty of uncontrolled
variables and to focus the analysis on the sub-set of control variables. The output is the
probability of failure to achieve the water quality objective for a management plan, which may
involve a large expenditure of public and private funds.
The method presented in this paper is based on the classical frequencist’s view of probability
(Yoe 1996a and Yoe 1996b). It requires multiple simulations to generate the statistical spread of
water quality responses. For a multi-parameter watershed model, this is tedious and time
consuming. This paper outlines a method that is reasonable in term of the number of simulations
required. The method is derived from Jacknife technique of stratified sampling for joint
occurrences (Efron 1982, Efron and Gong 1983). The frequency distribution plot shown in Figure
11 is not smooth because only five values per variable is used. A higher number of values can
smooth out the curve, but the number of simulations would increase exponentially.
The alternate method is based on subjective/ personal/ Bayesian view of probability (Yoe 1996).
The method will rely on expert opinions. Experts are assembled in a workshop. These experts
will evaluate various scientific facts including similar case studies and then provide a direct
estimate of uncertainty. However, it is not known whether such experts can be found. The
estimates of experts cannot be objectively analyzed.
The sample problem is used only to demonstrate the methodology. The evaluated management
plan is strictly hypothetical, even though the data is real. The analysis suggests that the growth
of algae is not a function of nutrient load alone. To simulate algal growth, the model accounts for
the flushing effect of storms, the temperature effect on species of algae, and the shading effect of
total suspended sediment. For that reason, it will be necessary to run the model for an extended
period of time, say 10 years, to account for wet and dry years. Such simulations would be
possible when more meteorological data is input to the model.
The following conclusions are made:
• There is a wide range of uncertainty analyses that can be performed with a
watershed model. The sub-set of analysis relevant to decision makers is
the risk of failure to achieve the water quality objective.
• The procedure described in this paper can be used to calculate the risk of
failure for a management plan that may cost a large sum of money.
• High quality data can be used to reduce the uncertainties of uncontrolled
variables. Model calibration is a tool for the quality assurance of data to
ensure that they are internally consistent.
Funding for this project was provided by the Duke Energy Company and the Electric Power
Research Institute, under the Tailor Collaboration Program.
Chen, C.W., J. Herr, R. A. Goldstein, F.J. Sagona, K.E. Rylant, and G.E. Hauser (1996),
“Watershed Risk Analysis Model for TVA’s Holdston River Basin”, Water, Air and Soil Pollution
Vol. 90, pp. 65-70.
Chen, C.W., J. Herr, L. Ziemelis, M.C. Griggs, L. Olmsted, R.A. Goldstein (1997a) “Consensus
Module to Guide Watershed Management Decisions for Catawba River Basin”, the
Environmental Professional, Vol. 19, pp. 75-79.
Chen, C.W., L. Ziemelis, J. Herr, L., Olmsted, and R.A. Goldstein (1997b) “A Picture Book of
Watershed Analysis Risk Management Framework as Applied to Catawba River Basin”, Paper
presented at Workshop on Decision Support System for the Management of Neuse River
Eutrophication, North Carolina State University, North Carolina.
Efron, B. (1982) “The Jacknife, the Bootstrap, and Other Resampling Plans”, Society of Industrial
and Applied Mathematics, Philadelphia, Pensylvania.
Efron, B. and G. Gong (1983) “A Leisure Look at the Bootstrap, the Jacknife, and Cross-
Validation”, American Statisticians, Vol. 37, No.1, pp 36-48.
Yoe, Charles E. (1996a) “An Introduction to Risk and Uncertainty in the Evaluation of
Environmental Investments”, US Army Corps of Engineers, Institute for Water Resources,
Alexandria, Virginia, IWR Report 96-R-9.
Yoe, Charles E. (1996b) “Incorporating Risk and Uncertainty into Environmental Evaluation: an
Annotated Bibliography”, US Army Corps of Engineers, Institute for Water Resources,
Alexandria, Virginia, IWR Report 96-R-9.
Figure 1. Map of Catawba River Basin
Figure 2. Simulated and observed flow of Catawba River at Calvin
Figure 3. Simulated and Observed Lake Surface Temperature of Lake Rhodhiss
Figure 4. Simulated and Observed Total Nitrogen in Surface of Lake Rhodhiss
Figure 5. Simulated and Observed Chlorophyll-a in Surface of Lake Rhodhiss
9/1/92 12/10/92 3/20/93 6/28/93 10/6/93 1/14/94 4/24/94 8/2/94
Figure 6. Responses of Chlorophyll-a in Lake Rhodhiss to the hypothetical management plan
7/20 - 7/26/94 6/22 - 6/28/93
Percent Less Than
12 14 16 18 20 22 24
Weekly Average Chlorophyll-a, ug/l
Figure 7. Frequency Distribution of Chlorophyll-a During the Week of Maximum Bloom.
Table 1 Multipliers to Reduce Point and Nonpoint Load of Nutrients
Point source discharge 0.35 0.45 0.5 0.55 0.65
Fertilizer application 0.20 0.4 0.5 0.6 0.8
Atmospheric deposition 0.5 0.8 1.0 1.2 1.5