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.     

A WATER RESOURCE PLANNING PROCEDURE FOR RURAL TOWNS1

ABSTRACT: Six new techniques have been developed for lake watershed analysis and water resource management. The techniques are for determining: (1) watershed land use intensity with reference to water quality, (2) lake vulnerability, (3) water quality, (4) watershed carrying capacity, (5) the economic value of the lake, and (6) the potential of undeveloped lake-shore. These analyses are designed for use by rural planning commissions with guidance and assistance from state agencies and the state university. The comprehensive rural watershed land and water use plan developed by this procedure is inexpensive in time and money, understandable by the layman, and scientificially sound. It is based on presently available information. This water resource planning procedure has been demonstrated in several town planning projects. It is suggested that this method, or modification of it, could be adopted in all rural states by action by a few administrators and without any new enabling or appropriations legislation.     

PLANNING METHODOLOGY FOR ANALYSIS AND MANAGEMENT ON LAKE EUTROPHICATION1

ABSTRACT: The effects of changing nutrient inputs through land use management, waste water treatment, or effluent diversion are not clear, and managers are discovering that decisions which were effective in reversing eutrophication for one lake are often unsuccessful when applied to another. Simple empirical relationships are often used to predict the impact of management decisions. Errors in estimation could result in either substantial costs for overdesign or failure to meet desired eutrophication levels. This paper presents and illustrates a methodology to evaluate the impact of land use and water resource management decisions on lake eutrophication. The problems of worth of additional information, and uncertainty of estimates were handled within a cost-effectiveness framework. The probability of exceeding a critical level of eutrophication was considered as a measure of effectiveness. The cost criterion is the expected value of opportunity costs, costs of analysis and costs of additional information. Uncertainty analysis techniques were used to estimate the effectiveness of various management alternatives. Bayesian methods can be utilized to determine the worth of additional information. The methodology was applied to Beseck Lake, Connecticut, and the cost and effectiveness measures estimated for a number of land management alternatives. Worth of additional information was not determined in this initial effort in uncertainty analysis for lake eutrophication management.     

A WATERSHED-LEVEL ECOLOGICAL RISK ASSESSMENT METHODOLOGY1

ABSTRACT: We present an ecological risk assessment methodology at the watershed level for freshwater ecosystems. The major component is a pollutant transport and fate model (a modified EUTROMOD) with an integrated uncertainty analysis utilizing a two-phase Monte Carlo procedure. The uncertainty analysis methodology distinguishes between knowledge uncertainty and stochastic variability. The model assesses the ecological risk of lentic (lake) ecosystems in response to the stress of excess phosphorus resulting in eutrophication. The methodology and model were tested on the Wister Lake watershed in Oklahoma with the lake and its trophic state as the endpoint for ecological risk assessment. A geographic information system was used to store, manage, and manipulate spatially referenced data for model input.     

ESTIMATING AVERAGE MONTHLY LAKE EVAPORATION IN THE NORTHEAST UNITED STATES1

ABSTRACT: A methodology to estimate the average monthly lake evaporation, E(τ), (month τ=1,12) for fresh water bodies located in the northeast United States is presented. The approach combines analysis of at‐site, lake‐specific vertical water temperature profile data and a previously developed regional air temperature based model approximation of the widely accepted modified Penman energy budget estimate of mean monthly potential evaporation, E_p(τ) (mm/day). The paper presents procedures to develop site‐specific estimates of E_p(τ) and to convert water temperature data to average monthly conductive heat flux, G(τ). With monthly estimates of G(τ), the average monthly potential evaporation, E_p(τ), is then convertible to estimates of the average monthly lake evaporation, E(τ). This new method permits a good estimate of site‐specific lake evaporation rates without the data and computational requirements of the Penman energy budget procedure nor the comparatively expensive, time consuming field eddy correlation approach.     

LAKE QUALITY DISCRIMINANT ANALYSIS1

ABSTRACT: Despite the fact that lake phosphorus loading criteria have proven to be valuable tools in lake management, they are generally subjective in nature or incomplete in form. In order to address these shortcomings, the oxic-anoxic transition point was selected as an objective quality criterion and discriminant analysis was used to construct a lake classification function. This function is dependent upon lake phosphorus loading, mean depth, and overflow rate. The value of the function may be expressed as a probability of classification (as either oxic or anoxic). When used in prediction, inclusion of the input error permits the estimation of the change in classification probability as input uncertainty is reduced. Further, the form of the discriminant function suggests that the annual volumetric loading is a more informative term for the expression of phosphorus loading than is the annual areal loading.     

Applying value of information methods to prioritize elements for water quality management with an example of linear alkylbenzene sulfonate in the Yodo River,Japan

Narrowing the decision space is crucial in water quality management at the meso-scale for developing countries, where a lack of data and financial budgets prevent the development of appropriate management plans and result in serious water quality degradation in many rivers. In this study, a framework for handling this task is proposed, comprising a lumped water quality model, with sensitivity and uncertainty analyses, and a management domain, including loss estimation and value of information analysis. Through a case study with linear alkylbenzene sulfonate (LAS) in the Yodo River, it is found that non-point sources and flow rate are factors that influence LAS concentration at the hot spot location. By considering the entire process of water quality management planning, we identify that the definition of the cost function of LAS treatment determines the appropriate estimation for the expected loss in reducing LAS under uncertain water quality conditions. The value of information analysis with “expected value of including uncertainty” and “expected value of perfect information” further helps estimate the benefit of including uncertainty in decision-making and the financial cost for obtaining more information regarding inputs that have been previously prioritized.     

MASS BALANCE MODEL ESTIMATION OF PHOSPHORUS CONCENTRATIONS IN RESERVOIRS1

ABSTRACT: Mass balance models have been common tools in lake quality management for some years. However, verification for use on reservoirs, especially in the Western United States, has been seriously lacking, In this study, such a verification is attempted using data from the U.S EPA National Eutrophication Survey. Several models from the literature are compared for accuracy in application to the western reservoir data. Model standard error and correlation between estimated and observed reservoir phosphorus concentrations are the Criteria used for comparison. Standard errors am further used to calculate uncertainty of trophic state classification based on estimated phosphorus concentration. The model proposed by Dillon and Rigler (1974) proved most accurate, with a correlation coefficient of 0.86 and standard error of 0.2, based on logarithmic transformed values. Deficiencies in the other models appear to & from coefficients fit to lake data and from inappropriate model formulation.     

FLOW ANALYSIS OF LANDSLIDE DAMMED LAKE WATERSHEDS: A CASE STUDY1

Abstract: The Chi-Chi earthquake, which occurred on September 21, 1999, and had a magnitude of 7.3 on the Richter scale, resulted in an extensive landslide that blocked the Ching-Shui Creek in Taiwan, forming a large lake with a storage volume of 40 million m³. This paper describes an analytical procedure used to perform flow analysis of the Tsao-Ling watershed, which includes the new landslide dammed lake. In this study, a digital elevation model was applied to obtain the watershed geomorphic factors and stage-area storage function of the landslide dammed lake. Satellite images were used to identify the landslide area and the land cover change that occurred as a result of the earthquake. Two topography-based runoff models were applied for long term and short term streamflow analyses of the watershed because the watershed upstream of the landslide dam was ungauged. The simulated daily flow and storm runoff were verified using limited available measured data in the watershed, and good agreement was obtained. The proposed analytical procedure for flow analysis is considered promising for application to other landslide dammed lake watersheds.     

Modification of uncertainty analysis in adapted material flow analysis: Case study of nitrogen flows in the Day-Nhue River Basin,Vietnam

Nitrogen flows impacted by human activities in the Day-Nhue River Basin in northern Vietnam have been modeled using adapted material flow analysis (MFA). This study introduces a modified uncertainty analysis procedure and its importance in MFA. We generated a probability distribution using a Monte Carlo simulation, calculated the nitrogen budget for each process and then evaluated the plausibility under three different criterion sets. The third criterion, with one standard deviation of the budget value as the confidence interval and 68% as the confidence level, could be applied to effectively identify hidden uncertainties in the MFA system. Sensitivity analysis was conducted for revising parameters, followed by the reassessment of the model structure by revising equations or flow regime, if necessary. The number of processes that passed the plausibility test increased from five to nine after reassessment of model uncertainty with a greater model quality. The application of the uncertainty analysis approach to this case study revealed that the reassessment of equations in the aquaculture process largely changed the results for nitrogen flows to environments. The significant differences were identified as increased nitrogen load to the atmosphere and to soil/groundwater (17% and 41%, respectively), and a 58% decrease in nitrogen load to surface water. Thus, modified uncertainty analysis was considered to be an important screening system for ensuring quality of MFA modeling.     

Uncertainty analysis of predicted disturbance from off-road vehicular traffic in complex landscapes at fort hood

The US Army Engineering Research Development Center (ERDC) uses a modified form of the Revised Universal Soil Loss Equation (RUSLE) to estimate spatially explicit rates of soil erosion by water across military training facilities. One modification involves the RUSLE support practice factor (P factor), which is used to account for the effect of disturbance by human activities on erosion rates. Since disturbance from off-road military vehicular traffic moving through complex landscapes varies spatially, a spatially explicit nonlinear regression model (disturbance model) is used to predict the distribution of P factor values across a training facility. This research analyzes the uncertainty in this model's disturbance predictions for the Fort Hood training facility in order to determine both the spatial distribution of prediction uncertainty and the contribution of different error sources to that uncertainty. This analysis shows that a three-category vegetation map used by the disturbance model was the greatest source of prediction uncertainty, especially for the map categories shrub and tree. In areas mapped as grass, modeling error (uncertainty associated with the model parameter estimates) was the largest uncertainty source. These results indicate that the use of a high-quality vegetation map that is periodically updated to reflect current vegetation distributions, would produce the greatest reductions in disturbance prediction uncertainty.     

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.     

基于流域视角的水环境综合治理规划研究——以江苏省淀山湖为例

以流域为单元进行水资源综合规划和管理是实现水环境改善的重要途径。本文以太湖流域第二大省界湖泊—淀山湖为例,在综合分析流域水环境质量基础上,利用GIS 分析工具划分流域治理片区并制定分区管控策略。根据流域所含骨干河流流向、骨干河流与淀山湖交汇特点、上中下游不同河段及镇域行政边界,将淀山湖流域分为吴淞江流域、千灯浦- 淀山湖流域、昆南湖荡流域、元荡湖荡流域、太浦河流域五大片区138 个子评价单元。通过水环境容量与压力两类空间叠加分析,构建形成污染重点减排区、污染综合治理区、产业绿色化提升区、生态环境保育区等四个类型区域,并提出差异化的产业准入和环境治理措施。本研究不仅为以流域为治理单元的水环境治理规划提供了较为可行的技术体系,而且为太湖流域水环境综合整治思路创新提供了可借鉴的案例。     

EVALUATION OF THE WORTH OF ADDITIONAL DATA1

ABSTRACT .Inherent in every decision process is a certain amount of uncertainty, which is reduced with information. Perfect knowledge yields no uncertainty for a process, but perfect knowledge for hydrologic and water resource systems would require a highly excessive investment. Therefore, it is the aim of this paper to delineate a procedure that places a value on this uncertainty so that it may be compared to a cost of further investment, which would provide a basis for deciding the time at which the value of additional data does not exceed the cost of that data. A decision theory approach is employed on a hydrologic problem to formalize the steps in making a decision. Examples are given.     

TROPICAL EUTROPHIC LAKE MODELING AND PARAMETER DISCRIMINATION1

ABSTRACT: Water quality data collected between 1978 and 1981 in a highly lake in Northern Venezuela, Lake Valencia, were analyzed to detect spatial and temporal trends. Based on the results of the analyses, an appropriate nutrient-algae dynamics model was formulated. Because many parameters, such as the algae concentration were constant over time, and the model is time dependent, the model had to be calibrated with the use of a large and structured trial-and-error calibration process. Through the calibration process, the most sensitive parameters of the model were identified, and are in order of importance: the chlorophyll-to-nitrogen ratio for algae, the algae settling velocity, the phosphorus release rate from the sediments, the chlorophyll-to-phosphorus ratio for algae, and the exchange coefficient in the upper layer of the lake. Model simulations showed that a reduction in the nitrogen load to the lake as well as a reduction in the phosphorus load will decrease the algae population. These model simulations had a high degree of uncertainty associated with them, making additional sampling directed towards the measurement of the sensitive parameters desirable.     

基于污染物来源的洞庭湖水环境生态补偿主客体研究

生态补偿主客体研究是制定及实施生态补偿政策的核心要素之一。本研究从系统分析的角度出发,基于2014年洞庭湖主要入湖河流水质、水量情况,核算了主要入湖河流总氮、总磷通量,并结合2014年洞庭湖生态经济区污染物排放情况,详细分析了洞庭湖总氮、总磷的来源,以此为依据界定了洞庭湖水环境生态补偿的主体与客体。结果显示,洞庭湖水体中总氮、总磷的贡献以洞庭湖生态经济区之外地区,通过四水、三口排入洞庭湖为主。基于此,本研究建议洞庭湖水环境生态补偿的主体省级层面应为湖南省和湖北省,而省外层面则为国家作为补偿主体对洞庭湖生态经济区进行补偿。     

Characterizing Uncertainty in Daily Streamflow Estimates at Ungauged Locations for the Massachusetts Sustainable Yield Estimator

Hydrologic characterization at ungauged locations is one of the quintessential challenges of hydrology. Beyond simulation of historical streamflows, it is similarly important to characterize the level of uncertainty in hydrologic estimates. In tandem with updates to Massachusetts Sustainable Yield Estimator, this work explores the application of global uncertainty estimates to daily streamflow simulations. Expanding on a method developed for deterministic modeling, this approach produces confidence intervals on daily streamflow developed through nonlinear spatial interpolation of daily streamflow using flow duration curves; the 95% confidence is examined. Archived cross‐validations of daily streamflows from 66 watersheds in and around Massachusetts are used to evaluate an approach to uncertainty characterization. Neighboring sites are treated as ungauged, producing relative errors that can be resampled and applied to target sites. The method, with some modification, is found to provide appropriately narrow confidence intervals that contain 95% of the observed streamflows in cross‐validation. Further characterizing uncertainty, multiday means of daily streamflow are evaluated. Working through cross‐validation in Massachusetts, two‐ to three‐month averages of daily streamflow show the best performance. These two approaches to uncertainty characterization inform how streamflow simulation produced for prediction in ungauged basins can be used for water resources management.     

LAKE EVAPORATION STUDIES USING SATELLITE THERMAL INFRARED DATA1

Thermal infrared radiation data were acquired by the Heat Capacity Mapping Mission (HCMM) satellite over the surface area (385 km²) of Utah Lake during periodic overpasses in 1978 and 1979. The thermal infrared data were converted to lake surface temperatures which were subsequently used in correlations with lake evaporation. Correlations between HCMM surface temperature and pan-derived evaporation exceeded r = 0.90 when HCMM night and day/night average temperatures and two-day average evaporation values were tested. Similar regression studies were done using monthly data from a conceptual evaporation model and the evaporation pan versus monthly HCMM temperature data. In this test both the HCMM day and night monthly temperature versus the monthly model or pan evaporation had correlations exceeding r = 0.95. Empirical estimates of both short and long term lake evaporation using satellite thermal infrared data seem feasible. Attempts to use the HCMM thermal information as direct input to a theoretical approach to calculating evaporation were inconclusive; however, a definite potential seems to exist.     

PHOSPHORUS MANAGEMENT TO PROTECT LAKE WATER QUALITY1

ABSTRACT: The Hallett Quarry gravel pit lakes are an active sand and gravel extraction operation located 0.4 km north of the City of Ames, Iowa. During periods of drought, these lakes serve as a supplemental water supply for Ames. A modified version of the Vollenweider input-output model was used to predict future water quality under various watershed land use, drainage, and lake configurations. The dominant factor controlling the future water quality of the lakes was found to be the nutrient input. It is recommended that a management plan to protect the future water quality should be oriented towards reducing the sources of phosphorus to the lakes.