USE OF FIRST-ORDER UNCERTAINTY ANALYSIS TO OPTIMIZE SUCCESSFUL STREAM WATER QUALITY SIMULATION1

ABSTRACT: A first-order uncertainty technique is developed to quantify the relationship between field data collection and a modeling exercise involving both calibration and subsequent verification. A simple statistic (LTOTAL) is used to quantify the total likelihood (probability) of successfully calibrating and verifying the model. Results from the first-order technique are compared with those from a traditional Monte Carlo simulation approach using a simple Streeter-Phelps dissolved oxygen model. The largest single difference is caused by the filtering or removal of unrealistic outcomes within the Monte Carlo framework. The amount of bias inherent in the first-order approach is also a function of the magnitude of input variability and sampling location. The minimum bias of the first-order technique is approximately 20 percent for a case involving relatively large uncertainties. However the bias is well behaved (consistent) so as to allow for correct decision making regarding the relative efficacy of various sampling strategies. The utility of the first-order technique is demonstrated by linking data collection costs with modeling performance. For a simple and inexpensive project, a wise and informed selection resulted in an LTOTAL value of 86 percent, while an uninformed selection could result in an LTOTAL value of only 55 percent.     

A Sensitivity and Error Analysis Framework for Lake Eutrophication Modeling1

ABSTRACT: A framework for sensitivity and error analysis in mathematical modeling is described and demonstrated. The Lake Eutrophication Analysis Procedure (LEAP) consists of a series of linked models which predict lake water quality conditions as a function of watershed land use, hydrolgic variables, and morphometric variables. Specification of input variables as distributions (means and standard errors) and use of first-order error analysis techniques permits estimation of output variable means, standard errors, and confidence ranges. Predicted distributions compare favorably with those estimated using Monte-Carlo simulation. The framework is demonstrated by applying it to data from Lake Morey, Vermont. While possible biases exist in the models calibrated for this application, prediction variances, attributed chiefly to model error, are comparable to the observed year-to-year variance in water quality, as measured by spring phosphorus concentration, hypolimnetic oxygen depletion rate, summer chlorophyll-a, and summer transparency in this lake. Use of the framework provides insight into important controlling factors and relationships and identifies the major sources of uncertainty in a given model application.     

Applications of Explicitly Incorporated/Post‐Processing Measurement Uncertainty in Watershed Modeling

In the field of watershed modeling, the impact of measurement uncertainty (MU) on calibration results indicates the potential issue of inaccurate model predictions. It is important to note that MU refers to the uncertainty in measured data such as flow and nutrient values that are used to evaluate model outputs. The calculation of error statistics assuming measured data are deterministic may not be appropriate as has been frequently stated in literature. Although MU can affect model calibration results, it is rarely incorporated in modeling practice. MU can be incorporated in two schemes: explicitly incorporated (MU‐EI) during model calibration and post‐processed (MU‐PP) after calibration is completed. In this study, both schemes are implemented in a case study of the Arroyo Colorado Watershed, Texas. Unexpectedly, no substantial differences were observed between each scheme for flow predictions. Although MU did not cause dramatic differences in most sediment and NH₄‐N predictions, error statistics were affected in cases with MU greater than 50%, especially for sediment and NH₄‐N. Therefore, it is concluded that MU may not exert a significant impact on model predictions until certain threshold is reached. This study demonstrates that high levels of uncertainty in measured calibration/validation data significantly affect parameter estimation, especially in the auto‐calibration process.     

SUBWATERSHED SPATIAL ANALYSIS TOOL: DISCRETIZATION OF A DISTRIBUTED HYDROLOGIC MODEL BY STATISTICAL CRITERIA1

ABSTRACT: Complex hydrologic models, designed for simulating larger watersheds, require a huge amount of input data. Most of these models use spatially distributed data as inputs. Spatial data can be aggregated or disaggregated for use as input to a model, which can impact model outputs. Although, it is efficient to minimize data redundancy by aggregating the spatial data, upscaling reduces the detail/resolution of input information and increases model uncertainty. On the other hand, a large number of model inputs with high degrees of disaggregation take more computer time and space to process. Hence, a balance between striving for a maximum level of aggregation and a minimum level of information loss has to be achieved. This study presents a definition of an appropriate level of discretization, derived by establishing a relationship between a model's efficiency and the number of subwater‐sheds modeled. An entropy based statistical approach/tool called Subwatershed Spatial Analysis Tool (SUSAT) was developed to find an objective choice of an appropriate level of discretization. The new approach/tool was applied to three watersheds, each representing different hydrologic conditions, using a hydrologic model. Coefficients of efficiency and entropy estimated at different levels of discretization were used to validate the success of the new approach.     

MACROSCALE HYDROLOGIC MODELING FOR REGIONAL CLIMATE ASSESSMENT STUDIES IN THE SOUTHEASTERN UMTED STATES1

ABSTRACT: A macroscale hydrologic model is developed for regional climate assessment studies under way in the southeastern United States. The hydrologic modeling strategy is developed to optimize spatial representation of basin characteristics while maximizing computational efficiency. The model employs the “grouped response unit” methodology, which follows the natural drainage pattern of the area. First order streams are delineated and their surface characteristics are tested so that areas with statistically similar characteristics can be combined into larger computational zones for modeling purposes. Hydrologic response units (HRU) are identified within the modeling units and a simple three‐layer water balance model, Soil and Water Assessment Tool (SWAT), is executed for each HRU. The runoff values are then convoluted using a triangular unit hydrograph and routed by Muskingum‐Cunge method. The methodology is shown to produce accurate results relative to other studies, when compared to observations. The model is used to evaluate the potential error in hydrologic assessments when using GCM predictions as climatic input in a rainfall‐runoff dominated environment. In such areas, the results from this study, although limited in temporal and spatial scope, appear to imply that use of GCM climate predictions in short term quantitative analyses studies in rainfall‐runoff dominated environments should proceed with caution.     

Prediction and uncertainty source analysis of the spatial and temporal disturbance from off-road vehicular traffic in a complex ecosystem

Vehicle use during military training activities results in soil disturbance and vegetation loss. The capacity of lands to sustain training is a function of the sensitivity of lands to vehicle use and the pattern of land use. The sensitivity of land to vehicle use has been extensively studied. Less well understood are the spatial patterns of vehicle disturbance. Since disturbance from off-road vehicular traffic moving through complex landscapes varies spatially, a spatially explicit nonlinear regression model (disturbance model) was used to predict the pattern of vehicle disturbance across a training facility. An uncertainty analysis of the model predictions assessed the spatial distribution of prediction uncertainty and the contribution of different error sources to that uncertainty.For the most part, this analysis showed that mapping and modeling process errors contributed more than 95% of the total uncertainty of predicted disturbance, while satellite imagery error contributed less than 5% of the uncertainty. When the total uncertainty was larger than a threshold, modeling error contributed 60% to 90% of the prediction uncertainty. Otherwise, mapping error contributed about 10% to 50% of the total uncertainty. These uncertainty sources were further partitioned spatially based on other sources of uncertainties associated with vehicle moment, landscape characterization, satellite imagery, etc.     

A SYSTEMATIC ANALYSIS OF THE CONSTRAINTS TO URBAN STREAM ENHANCEMENTS1

ABSTRACT: The environment surrounding urban streams imposes constraints upon stream enhancement projects. Constraints include bridges, culverts, highways, sewer and water lines, lack of easements, and other floodplain structures. The consequences of failure of these infrastructure constraints can be significant and should be considered in the design process. Fault tree analysis provides a systematic technique for analyzing the interactions of events that could lead to infrastructure failure. A case study of a stream in Pittsburgh, Pennsylvania, shows that fault tree analysis can effectively model the interactions between the stream system and the infrastructure constraints and predict the most likely modes of failure. In addition, the relative success of alternative designs and failure mitigation techniques can be assessed using this analysis tool, lending insight into the urban stream enhancement design process. The method could also provide justification in the design permitting process and input for risk assessment.     

AN INTERACTWE MODELING ENVIRONMENT FOR NON-POINT SOURCE POLLUTION CONTROL1

ABSTRACT: Non-point source pollution cuntinues to be an important environmental and water quality management problem. For the moat part, analysis of non-point source pollution in watersheds has depended on the use of distributed models to identify potential problem areas and to assess the effectiveness of alternative management practices. To effectively use these models for watershed water quality management, users depend on integrated geographic information systems (GIS)-based interfaces for input/output data management. However, existing interfaces are ad-hoc and the utility of GIS is limited to organization of input data and display of output data. A highly interactive water quality modeling interface that utilizes the functional components and analytical capability of GIS is highly desirable. This paper describes the tight coupling of the Agricultural Non-point Source (AGNPS) water quality model and ARC/INFO GIS software to provide an interactive hybrid modeling environment for evaluation of non-point source pollution in a watershed. The modeling environment is designed to generate AGNPS input parameters from user-specified GIS coverages, create AGNPS input data files, control AGNPS model simulations, and extract and organize AGNPS model output data for display. An example application involving the estimation of pesticide loading in a southern Iowa agricultural watershed demonstrates the capability of the modeling environment. Compared with traditional methods of watershed water quality modeling using the AGNPS model or other ad-hoc interfaces between a distributed model and GIS, the interactive modeling environment system is efficient and significantly reduces the task of watershed analysis using tightly coupled GIS databases and distributed models.     

AN ILLUSTRATION OF MODEL STRUCTURE IDENTIFICATION1

ABSTRACT: The purpose of this article is to discuss the importance of uncertainty analysis in water quality modeling, with an emphasis on the identification of the correct model specification. A wetland phosphorus retention model is used as an example to illustrate the procedure of using a filtering technique for model structure identification. Model structure identification is typically done through model parameter estimation. However, due to many sources of error in both model parameterization and observed variables and data, error-in-variable is often a problem. Therefore, it is not appropriate to use the least squares method for parameter estimation. Two alternative methods for parameter estimation are presented. The first method is the maximum likelihood estimator, which assumes independence of the observed response variable values. In anticipating the possible violation of the independence assumption, a second method, which coupled a maximum likelihood estimator and Kalman filter model, was presented. Furthermore, a Monte Carlo simulation algorithm is presented as a preliminary method for judging whether the model structure is appropriate or not.     

A FRAMEWORK FOR PHOSPHORUS TRANSPORT MODELING IN THE LAKE OKEECHOBEE WATERSHED1

ABSTRACT: A modeling framework was developed to determine phosphorus loadings to Lake Okeechobee from watersheds located north of the lake. This framework consists of the land-based model CREAMS-WT, the in-stream transport model QUAL2E, and an interface procedure to format the land-based model output for use by the in-stream model. QUAL2E hydraulics and water quality routines were modified to account for flow routing and phosphorus retention in both wetlands and stream channels. Phosphorus loadings obtained from previous applications of CREAMS-WT were used by QUAL2E, and calibration and verification showed that QUAL2E accurately simulated seasonal and annual phosphorus loadings from a watershed. Sensitivity and uncertainty analyses indicated that the accuracy of monthly loadings can be improved by using better estimates of in-stream phosphorus decay rates, ground water phosphorus concentrations, and runoff phosphorus concentrations as input to QUAL2E.     

Privacy-preserving aggregation in life cycle assessment

Life cycle assessment (LCA) is the standard technique used to make a quantitative evaluation about the ecological sustainability of a product or service. The life cycle inventory (LCI) data sets that provide input to LCA computations can express essential information about the operation of a process or production step. As a consequence, LCI data are often regarded as confidential and are typically concealed through aggregation with other data sets. Despite the importance of privacy protection in publishing LCA studies, the community lacks a formal framework for managing private data, and no techniques exist for performing aggregation of LCI data sets that preserve the privacy of input data. However, emerging computational techniques known as “secure multiparty computation” enable data contributors to jointly compute numerical results without enabling any party to determine another party’s private data. In the proposed approach, parties who agree on a shared computation model, but do not trust one another and also do not trust a common third party, can collaboratively compute a weighted average of an LCA metric without sharing their private data with any other party. First, we formulate the LCA aggregation problem as an inner product over a foreground inventory model. Then, we show how LCA aggregations can be computed as the ratio of two secure sums. The protocol is useful when preparing LCA studies involving mutually competitive firms.     

METHODOLOGIES FOR CALIBRATION AND PREDICTIVE ANALYSIS OF A WATERSHED MODEL1

ABSTRACT: The use of a fitted parameter watershed model to address water quantity and quality management issues requires that it be calibrated under a wide range of hydrologic conditions. However, rarely does model calibration result in a unique parameter set. Parameter nonuniqueness can lead to predictive nonuniqueness. The extent of model predictive uncertainty should be investigated if management decisions are to be based on model projections. Using models built for four neighboring watersheds in the Neuse River Basin of North Carolina, the application of the automated parameter optimization software PEST in conjunction with the Hydrologic Simulation Program Fortran (HSPF) is demonstrated. Parameter nonuniqueness is illustrated, and a method is presented for calculating many different sets of parameters, all of which acceptably calibrate a watershed model. A regularization methodology is discussed in which models for similar watersheds can be calibrated simultaneously. Using this method, parameter differences between watershed models can be minimized while maintaining fit between model outputs and field observations. In recognition of the fact that parameter nonuniqueness and predictive uncertainty are inherent to the modeling process, PEST's nonlinear predictive analysis functionality is then used to explore the extent of model predictive uncertainty.     

THE USE OF A SIMPLE MODEL AND UNCERTAINTY ANALYSIS IN LAKE MANAGEMENT1

ABSTRACT: A simple, black-box lake model was developed for phosphorus, using nonlinear regression analysis on a data base of north temperate lakes. The uncertainty associated with the model was then combined with the parameter uncertainty and the independent variable uncertainty to provide an estimate of the confidence limits associated with a predicted value. The prediction uncertainty is often neglected, yet it is an important measure of the usefulness of a model. Prediction uncertainty reflects the modeler's confidence in the model, and it should be used by a decision maker as a weight indicating the value of the model prediction. A procedure is outlined that combined lake modeling and uncertainty analysis for use in lake quality assessment and lake management. An example is provided illustrating the use of this procedure in nutrient budget sampling design, data analysis, and the evaluation of lake management strategies for a 208 program in New Hampshire.     

SWMHMS - SMALL WATERSHED MONTHLY HYDROLOGIC MODELING SYSTEM1

ABSTRACT: SWMHMS is a conceptual computer modeling program developed to simulate monthly runoff from a small nonurban watershed. The input needed to run model simulations include daily precipitation, monthly data for evapotranspiration determination (average temperature, crop consumptive coefficients, and percent daylight hours), and six watershed parameter values. Evapotranspiration was calculated with the Blaney-Criddle equation while surface runoff was determined using the Soil Conservation Service curve number procedure. For watershed parameter evaluation, SWMHMS provides options for both optimization and sensitivity analysis. Observed runoff data are required along with the model input previously mentioned in order to conduct parameter optimization. SWMEIMS was tested with data from six watersheds located in different regions of the United States. Model accuracy was generally found to be very good except on watersheds having substantial snowfall accumulation. In having only six watershed parameters, SWMHMS is less complex to use than many other computer programs that calculate monthly runoff. Consequently, SWMHMS may find its greatest application as an educational tool for students learning principles of hydrologic modeling, such as parameter evaluation procedures and the impacts of input data uncertainty on model results.     

Hydrologic Modeling Uncertainty Resulting From Land Cover Misclassification1

Abstract: A stochastic, spatially explicit method for assessing the impact of land cover classification error on distributed hydrologic modeling is presented. One‐hundred land cover realizations were created by systematically altering the North American Landscape Characterization land cover data according to the dataset’s misclassification matrix. The matrix indicates the probability of errors of omission in land cover classes and is used to assess the uncertainty in hydrologic runoff simulation resulting from parameter estimation based on land cover. These land cover realizations were used in the GIS‐based Automated Geospatial Watershed Assessment tool in conjunction with topography and soils data to generate input to the physically‐based Kinematic Runoff and Erosion model. Uncertainties in modeled runoff volumes resulting from these land cover realizations were evaluated in the Upper San Pedro River basin for 40 watersheds ranging in size from 10 to 100 km² under two rainfall events of differing magnitudes and intensities. Simulation results show that model sensitivity to classification error varies directly with respect to watershed scale, inversely to rainfall magnitude and are mitigated or magnified by landscape variability depending on landscape composition.     

QUANTIFYING MODEL OUTPUT UNCERTAINTY DUE TO SPATIAL VARIABILITY OF RAINFALL1

Traditionally in the application of hydrologic/water quality (H/WQ) models, rainfall is assumed to be spatially homogeneous and is considered not to contribute to output uncertainty. The objective of this study was to assess the uncertainty induced in model outputs solely due to rainfall spatial variability. The study was conducted using the AGNPS model and the rainfall pattern captured by a network of 17 rain gauges. For each rainfall event, the model was run using the rainfall captured by each rain gauge, one at a time, under the assumption of rainfall spatial homogeneity. A large uncertainty in the modeled outputs resulted from the rainfall spatial variability. The uncertainty in the modeled outputs exceeded the input rainfall uncertainty. Results of this study indicate that spatial variability of rainfall should be captured and used in H/WQ models in order to accurately assess the release and transport of pollutants. A large uncertainty in the model outputs can be expected if this rainfall property is not taken into account.     

A new method for site suitability analysis: The analytic hierarchy process

A critical shortcoming of methods that are reliant upon the judgment of experts to determine site suitability is noted. The article introduces a new method, the analytic hierarchy process (AHP) with which error in judging the relative importance of factors in site suitability analysis can be both detected and corrected. The proposed approach is illustrated with an example to show how the AHP frames the site evaluation problem and can aid in decision making involving multiple criteria, factor diversity, and conditions of uncertainty. The article concludes by suggesting the potential application of the AHP in public choice decisions involving complex, controversial, and conflictual site selection processes.     

WATER QUALITY MODELING BY MONTE CARLO SIMULATION1

ABSTRACT: The applicability of the Monte Carlo simulation technique to water quality modeling is demonstrated with the aid of a simple Streeter-Phelps model. The model accounts for the stochasticity of the input parameters. Triangular probability density functions are shown to be useful in case insufficient information is available to define meaningful frequency distributions of input parameters. The model output is presented as probability distributions of stream quality parameters.     

INTEGRATING GEOGRAPHIC INFORMATION SYSTEMS AND MODFLOW FOR GROUND WATER RESOURCE ASSESSMENTS1

ABSTRACT: The Floridan Aquifer is the primary source of water in the coastal area of Santa Rosa County, Florida. In order to optimize well field design and analyze aquifer stress problems, the USGS MODFLOW code (McDonald and Harbaugh, 1988) is applied to develop a numerical computer model of the aquifer. The Geographical Information System (GIS) is the primary tool used in the development of the model grid, performance of the modeling procedure, and model analysis. The GIS is used in generating multiple grids in which to simulate both regional scale and local scale flow. The grid topology is recorded in geographic coordinates which facilitates geo-referencing and orientation of the grid to base maps and data coyerages. The GIS allows data transfer from various coverages to the nodes of the block centered grid where hydrogeologic information is stored as attributes to the grid coverage. From this grid coverage, pertinent information is queried within the GIS environment and used to generate the input files for the MODFLOW simulation. After MODFLOW execution, simulated heads and drawdown are imported into the grid coverage where residual error and recharge rates can be calculated. Contoured surfaces are then created for selected data sets including simulated heads, drawdown, residual error, and recharge rates. Model calibration is conducted utilizing the GIS to generate and process data sets associated with model simulations.     

A framework for assessing the impact of land use policy on community exposure to air toxics

Our research focuses on the linkage between land use planning policy and the spatial pattern of exposure to air toxics emissions. Our objective is to develop a modeling framework for assessment of the community health risk implications of land use policy. The modeling framework is not intended to be a regulatory tool for small-scale land use decisions, but a long-range planning tool to assess the community health risk implications of alternative land use scenarios at a regional or subregional scale. This paper describes the development and application of an air toxic source model for generating aggregate emission factors for industrial and commercial zoning districts as a function of permitted uses. To address the uncertainty of estimating air toxics emission rates for planned general land use or zoning districts, the source model uses an emissions probability mass function that weights each incremental permitted land use activity by the likelihood of occurrence. We thus reduce the uncertainty involved in planning for development with no prior knowledge of the specific industries that may locate within the land use district. These air toxics emission factors can then be used to estimate pollutant atmospheric mass flux from land use zoning districts, which can then be input to air dispersion and human health risk assessment models to simulate the spatial pattern of air toxics exposure risk. The model database was constructed using the California Air Toxics Inventory, 1997 US Economic Census, and land assessment records from several California counties. The database contains information on more than 200 air toxics at the 2-digit Standard Industrial Classification (SIC) level. We present a case study to illustrate application of the model. LUAIRTOX, the interactive spreadsheet model that applies our methodology to the California data, is available at http://www2.bren.ucsb.edu/~mwillis/LUAIRTOX.htm.