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.     

MULTIPLICATIVE,SEASONAL ARIMA MODELS FOR LAKE ERIE AND LAKE ONTARIO WATER LEVELS1

ABSTRACT: Federal agencies in the U.S. and Canada continuously examine methods to improve understanding and forecasting of Great Lakes water level dynamics in an effort to reduce the negative impacts of fluctuating levels incurred by interests using the lakes. The short term, seasonal and long term water level dynamics of lakes Erie and Ontario are discussed. Multiplicative, seasonal ARIMA models are developed for lakes Erie and Ontario using standardized, monthly mean level data for the period 1900 to 1986. The most appropriate model identified for each lake had the general form: (1 0 1)(0 1 1)₁₂. The data for each lake were subdivided by time periods (1900 to 1942;1 943 to 1986) and the model coefficients estimated for the subdivided data were similar, indicating general model stability for the entire period of record. The models estimated for the full data sets were used to forecast levels 1,2,3, and 6 months ahead for a period of high levels (1984 to 1986). The average absolute forecast error for Lake Erie was 0.049m, 0.076m, 0.091 m and 0.128m for the 1, 2,3, and 6 month forecasts, respectively. The average absolute forecast error for Lake Ontario was 0.058m, 0.095m, 0.120m and 0.136m for the 1,2,3, and 6 month forecasts, respectively. The ARIMA models provide additional information on water level time series structure and dynamics. The models also could be coordinated with current forecasting methods, possibly improving forecasting accuracy.     

A Gis‐Based Approach to Watershed Classification for Nebraska Reservoirs1

Abstract: The U.S. Environmental Protection Agency is charged with establishing standards and criteria for assessing lake water quality. It is, however, increasingly evident that a single set of national water quality standards that do not take into account regional hydrogeologic and ecological differences will not be viable as lakes clearly have different inherent capacities to meet such standards. We demonstrate a GIS‐based watershed classification strategy for identifying groups of Nebraska reservoirs that have similar potential capacity to attain a certain level of water quality standard. A preliminary cluster analysis of 78 reservoirs was performed to determine the potential number of Nebraska reservoir groups. Subsequently, a Classification Trees method was used to refine number of classes, describe the structure of reservoir watershed classes, and to develop a predictive model that relates watershed conditions to reservoir classes. Results suggest that Nebraska reservoirs can be represented by nine classes and that soil organic matter content in the watershed is the most important single variable for segregating the reservoirs. The cross‐validation prediction error rate of the Classification Tree model was 26.3%. Because all geospatial data used in this work are available nationally, the method could be adopted throughout the U.S. Hence, this GIS‐based watershed classification approach could provide water resources managers an effective decision‐support tool in managing reservoir water quality.     

MODELING TO EVALUATE MACROPHYTE INDUCED IMPACTS TO DISSOLVED OXYGEN IN A TAILWATER RESERVOIR1

ABSTRACT: Effects of aquatic macrophytes are not considered in most standard water quality models. This study used field measurements and water quality models to help determine the effects of aquatic macrophytes on dissolved oxygen (DO) concentrations in a shallow tailwater reservoir. Installation of a hydropower plant and macrophytes (primarily Potamogeton and Chara) in a large shallow portion of the lake are possible causes of reduced DO levels in the tailwater reservoir. A water quality model (WASP5) was used to quantify the various DO sources and sinks and to evaluate the effects of the hydropower operations on DO levels in the lake. It was found that the macrophytes in Lake Ogallala had a significant effect on the DO levels in the lake. At an average macrophyte density of about 6,360 g/m² (wet weight) in 2000, the DO fluctuated daily from about 3 mg/l to about 12 mg/l. At an average macrophyte density of about 2,120 g/m² (wet weight) in 2002, the DO fluctuated from about 5 mg/l to about 9 mg/l daily. The model predicted that the DO would remain near 5 mg/l without macrophytes. The photo‐synthetic and respiration rates developed in the model (4.4 mg/g‐hr and 1.4 mg/g‐hr, respectively) agree well with literature values.     

Loss Rates from Lake Powell and Their Impact on Management of the Colorado River

As demand for water in the southwestern United States increases and climate change potentially decreases the natural flows in the Colorado River system, there will be increased need to optimize the water supply. Lake Powell is a large reservoir with potentially high loss rates to bank storage and evaporation. Bank storage is estimated as a residual in the reservoir water balance. Estimates of local inflow contribute uncertainty to estimates of bank storage. Regression analyses of local inflow with gaged tributaries have improved the estimate of local inflow. Using a stochastic estimate of local inflow based on the standard error of the regression estimator and of gross evaporation based on observed variability at Lake Mead, a reservoir water balance was used to estimate that more than 14.8 billion cubic meters (Gm³) has been stored in the banks, with a 90% probability that the value is actually between 11.8 and 18.5 Gm³. Groundwater models developed by others, observed groundwater levels, and simple transmissivity calculations confirm these bank storage estimates. Assuming a constant bank storage fraction for simulations of the future may cause managers to underestimate the actual losses from the reservoir. Updated management regimes which account more accurately for bank storage and evaporation could save water that will otherwise be lost to the banks or evaporation.     

STOCHASTIC ANALYSIS OF TIME-AGGREGATED HYDROLOGIC DATA1

Stochastic models fitted to hydrologic data of different time scales are interrelated because the higher time scale data (aggregated data) are derived from those of lower time scale. Relationships between the statistical properties and parameters of models of aggregated data and of original data are examined in this paper. It is also shown that the aggregated data can be more accurately predicted by using a valid model of the original data than by using a valid model of the aggregated data. This property is particularly important in forecasting annual values because only a few annual values are usually available and the resulting forecasts are relatively inaccurate if models based only on annual data are used. The relationships and forecasting equations are developed for general aggregation time and can be used for hourly and daily, daily and monthly or monthly and yearly data. The method is illustrated by using monthly and yearly streamflow data. The results indicate that various statistical characteristics and parameters of the model of annual data can be accurately estimated by using the monthly data and forecasts of annual data by using monthly models have smaller one step ahead mean square error than those obtained by using annual data models.     

COMPARISON OF TWO AUTOREGRESSIVE MODELS FOR MONTHLY STREAM FLOW GENERATION1

ABSTRACT: Two autoregressive models for monthly stream flow generation are compared based on the reproduction of the historical record in terms of several important statistics such as the mean, standard deviation, skewness coefficient, correlation coefficient, and the reservoir storage components. In the comparison, both theoretical considerations and practical applications are employed to evaluate the performance of each model.     

RESERVOIR SEDIMENTATION AND ITS CAUSES IN ILLINOIS1

ABSTRACT: During the years 1930 to 1978 a research program has been carried out in Illinois dealing with reservoir sedimentation. Detailed surveys have been made on 107 lakes. A generalized graph allows annual reservoir capacity loss in percent to be estimated based on size of watershed, lake capacity, and watershed ratio. For the 258 square miles of land on the watershed of Lake Springfield, complete soil maps were measured using a graphic digitizer. A computer readable map was produced. The Universal Soil Loss Equation was solved to provide upland soil losses for each acre of the watershed. Average watershed soil loss was 3.96 tons per acre per year, and 24 percent of this was delivered to the lake.     

A FICKIAN ANALYSIS OF LAKE SEDIMENT UPSURGE1

ABSTRACT. The fundamental hypothesis of this paper is that the stratified-mixed states which occur annually in lakes play a dominant role in the movement of nutrient-rich material from the lake bottom upward into the water column. The stratified-mixed history has been used previously to develop a Fourier type, semi-infinite slab energy model to represent the lake surface temperature, thermal profile, and thermocline position with Julian day (Thibodeaux, 1975). The present paper extends the semi-infinite slab idea to include a Fickian type model for the upsurge of nutrients from the sediment-water interface upward. Relations will be developed for the rate of nutrient upwelling into the epilimnion and the photoactive zone of a lake. A lake time constant emerges from the model equations. This constant is thought to be important in predicting the likelihood of a fall algal bloom. Results of model verification attempts on three lakes are presented.     

LAND USE CHANGE PATTERNS BY LOCATION WITH RESPECT TO A RESERVOIR1

Much research has been done to determine the benefit of a water resources development to society as a whole. Some research has explored the benefit of such a facility to a region. Very little research exists on the effects of a reservoir on the immediately surrounding area. The general hypothesis of this study is that the spatial patterns of land use change are influenced by economic characteristics of the reservoir and reservoir area. Several hypotheses concerning the effects of relative location on a peninsula are tested using analysis of variance. The data used for the analysis is based on Lake Cumberland, a reservoir in southern Kentucky. The analysis indicates that there exists significant patterns of land use change around the lake and on peninsulas.     

太湖生态模拟系统构建与应用

湖泊生态系统模拟在湖泊富营养化研究中发挥着越来越重要的作用,是湖泊生态生态系统管理的重要手段。湖泊生态系统模型及其相关软件的发展经历了从简单的回归模型、单一的营养盐平衡模型到目前复杂的生态系统动力学模型。本文详细的介绍了湖泊生态模拟的原理、结构框架设计、功能、运行环境及参数等特性,借助太湖有关资料建立了太湖生态系统模拟模型,并对该模型进行了验证分析,验证结果表明该模型在太湖有很好的适应性。     

Statistical and Hybrid Methods Implemented in a Web Application for Predicting Reservoir Inflows during Flood Events

Reservoir management is a critical component of flood management, and information on reservoir inflows is particularly essential for reservoir managers to make real‐time decisions given that flood conditions change rapidly. This study's objective is to build real‐time data‐driven services that enable managers to rapidly estimate reservoir inflows from available data and models. We have tested the services using a case study of the Texas flooding events in the Lower Colorado River Basin in November 2014 and May 2015, which involved a sudden switch from drought to flooding. We have constructed two prediction models: a statistical model for flow prediction and a hybrid statistical and physics‐based model that estimates errors in the flow predictions from a physics‐based model. The study demonstrates that the statistical flow prediction model can be automated and provides acceptably accurate short‐term forecasts. However, for longer term prediction (2 h or more), the hybrid model fits the observations more closely than the purely statistical or physics‐based prediction models alone. Both the flow and hybrid prediction models have been published as Web services through Microsoft's Azure Machine Learning (AzureML) service and are accessible through a browser‐based Web application, enabling ease of use by both technical and nontechnical personnel.     

FACTORS AFFECTING SALINITY REDUCTION IN LAKE TARPON,PINELLAS COUNTY,FLORIDA1

ABSTRACT: Following an enclosure of a sink-hole connecting Lake Tarpon to the Gulf of Mexico, the chloride concentration of lake waters decreased. Water and chloride budgets for the lake in 1975 were prepared, and predictions using the model of Lerman and Brunskill (1971) were made as to the time required for the lake to achieve fresh water status. Model verification indicated good agreement with predictions in 1976; however, data on [C1^-] for 1977 and 1978 are not as supportive of the model used. The information concerning the Lake Tarpon watershed provided by this latter fact is discussed.     

ACCURACY OF IMPERVIOUS AREA VALUES ESTIMATED USING REMOTELY SENSED DATA1

ABSTRACT: Remote sensing offers an attractive alternative to conventional data collection employed in the estimation of certain hydrologic model parameters. In this investigation, the standard error of parameters estimated from Landsat data are examined. Relationships between the standard error and the size of the spatial-modeling units are developed that allow extending results to larger areas. Based upon the investigations conducted, a generalized model of the error relationships could not be developed.     

TEMPERATURE EFFECTS ON GREAT LAKES WATER BALANCE STUDIES1

ABSTRACT. Beginning of month water temperature profiles are estimated for each lake. These water temperature profiles along with surface water temperatures are used to determine the effects of thermal expansion and contraction of water on the net basin supply values obtained from water balance studies using end of month lake levels. It is demonstrated that net basin supply values (equivalent to precipitation on the lake minus the evaporation from the lake plus the runoff into the lake) obtained from water balance studies without accounting for the thermal expansion and contraction of water may be in error by as much as 100 percent during some months for each lake.     

COMPARATIVE EVALUATION OF STATISTICAL METHODS FOR WATER SUPPLY FORECASTING1

ABSTRACT: While the correlation coefficient and standard error of estimate are frequently used when comparing models of seasonal water yield, the following criteria may be more important in selecting one model from among several alternatives: rationality of the regression coefficients, the distribution of the residual errors, and the correctness of indicators of the relative importance of the predictor variables. These criteria were used to compare seasonal water yield models that were calibrated using multiple regression, stepwise regression, principal components regression, polynomial regression using a principal components rotation, and constrained pattern search. Hydrologic data from the Upper Sevier River basin in southern Utah were used to illustrate the comparative analysis process. The prediction equations used the April-July streamflow volume as the criterion variable.     

EFFECT OF FLOW VELOCITY ON SEDIMENT OXYGEN DEMAND: COMPARISON OF THEORY AND EXPERIMENTS1

ABSTRACT: Theoretical equations that establish the relationship between sediment oxygen demand (SOD) in a lake and the flow velocity and dissolved oxygen concentration in the bulk water already exist. These theoretical equations for oxygen consumption in the sediment express biological consumption with Michaelis-Menten kinetics, and chemical consumption by a first order reaction. Data from laboratory experiments that were conducted to validate the theoretical equations also exist. These experiments were performed in a laboratory channel with well defined flow characteristics for three types of sediments. Herein, the theoretical equations are used to model the experimental data for the three types of sediments. The values used for the parameters in the theoretical equations are determined by iteration until a best fit is obtained for the relationship of SOD to flow velocity from both the theoretical model and experimental data. The goodness of fit is measured by the standard error of prediction and the regression coefficient.     

Comparison of Machine Learning Models Performance on Simulating Reservoir Outflow: A Case Study of Two Reservoirs in Illinois,U.S.A.

Reservoir outflow is an important variable for understanding hydrological processes and water resource management. Natural streamflow variation, in addition to the streamflow regulation provided by dams and reservoirs, can make streamflow difficult to understand and predict. This makes them a challenge to accurately simulate hydrologic processes at a daily scale. In this study, three Machine Learning (ML) algorithms, Random Forest (RF), Support Vector Machine (SVM), and Artificial Neural Network (ANN), were examined and compared to model reservoir outflow. Past, current, and future hydrologic and meteorological data were used as model inputs, and the outflow of next day was used as prediction. Simulation results demonstrated that all three models can reasonably simulate reservoir outflow. For Carlyle Lake, the coefficient of determination and Nash–Sutcliffe efficiency were each close to one for the three models. The coefficient of determination, relative mean bias, and root mean square error indicated that the SVM performed better than the RF and ANN, but the SVM output displayed a larger relative mean bias than that from RF and ANN. For Lake Shelbyville, the ANN model performed better than RF and SVM when considering the coefficient of determination, Nash–Sutcliffe efficiency, relative mean bias, and root mean square error. The study results demonstrate that the three ML algorithms (RF, SVM, and ANN) are all promising tools for simulating reservoir outflow. Both the accuracy and efficacy of the three ML algorithms are considered to support practitioners in planning reservoir management.     

INPUT/OUTPUT MODELS AS DECISION AIDS FOR LAKE RESTORATION1

ABSTRACT: Over the past several years, input/output models have been used increasingly as decisionmaking aids in the design of lake restoration activities because they provide an approximation of the link between nutrient influx and lake trophic status. To evaluate the applicability of these models as design tools, a study was conducted in which “before” and “after” data were obtained for 25 lakes which experienced reductions in nutrient inflow, and comparisons were made of observed and predicted changes in lake conditions. Three input/output models were used as predictive tools to describe lake response: those reported by Dillon and Rigler (1974) and by Vollenweider (1975, 1976). Based on described trophic states of oligotrophic, mesotrophic, and eutrophic, it was found that all three models yielded accurate predictions for at least 70 percent of the study lakes. The model of Vollenweider (1976) performed slightly better than the other two (80 percent correct) on the data set studied.