A Comparison of Bayesian Methods for Uncertainty Analysis in Hydraulic and Hydrodynamic Modeling

We evaluate and compare the performance of Bayesian Monte Carlo (BMC), Markov chain Monte Carlo (MCMC), and the Generalized Likelihood Uncertainty Estimation (GLUE) for uncertainty analysis in hydraulic and hydrodynamic modeling (HHM) studies. The methods are evaluated in a synthetic 1D wave routing exercise based on the diffusion wave model, and in a multidimensional hydrodynamic study based on the Environmental Fluid Dynamics Code to simulate estuarine circulation processes in Weeks Bay, Alabama. Results show that BMC and MCMC provide similar estimates of uncertainty. The posterior parameter densities computed by both methods are highly consistent, as well as the calibrated parameter estimates and uncertainty bounds. Although some studies suggest that MCMC is more efficient than BMC, our results did not show a clear difference between the performance of the two methods. This seems to be due to the low number of model parameters typically involved in HHM studies, and the use of the same likelihood function. In fact, for these studies, the implementation of BMC results simpler and provides similar results to MCMC. The results of GLUE are, on the other hand, less consistent to the results of BMC and MCMC in both applications. The posterior probability densities tend to be flat and similar to the uniform priors, which can result in calibrated parameter estimates centered in the parametric space.     

The Regionalization of National‐Scale SPARROW Models for Stream Nutrients1

Schwarz, Gregory E., Richard B. Alexander, Richard A. Smith, and Stephen D. Preston, 2011. The Regionalization of National‐Scale SPARROW Models for Stream Nutrients. Journal of the American Water Resources Association (JAWRA) 47(5):1151‐1172. DOI: 10.1111/j.1752‐1688.2011.00581.x Abstract: This analysis modifies the parsimonious specification of recently published total nitrogen (TN) and total phosphorus (TP) national‐scale SPAtially Referenced Regressions On Watershed attributes models to allow each model coefficient to vary geographically among three major river basins of the conterminous United States. Regionalization of the national models reduces the standard errors in the prediction of TN and TP loads, expressed as a percentage of the predicted load, by about 6 and 7%. We develop and apply a method for combining national‐scale and regional‐scale information to estimate a hybrid model that imposes cross‐region constraints that limit regional variation in model coefficients, effectively reducing the number of free model parameters as compared to a collection of independent regional models. The hybrid TN and TP regional models have improved model fit relative to the respective national models, reducing the standard error in the prediction of loads, expressed as a percentage of load, by about 5 and 4%. Only 19% of the TN hybrid model coefficients and just 2% of the TP hybrid model coefficients show evidence of substantial regional specificity (more than ±100% deviation from the national model estimate). The hybrid models have much greater precision in the estimated coefficients than do the unconstrained regional models, demonstrating the efficacy of pooling information across regions to improve regional models.     

A Hierarchical Model for Estimating Long‐Term Trend of Atrazine Concentration in the Surface Water of the Contiguous U.S.

Atrazine is a herbicide frequently detected in both surface and groundwater in the United States (U.S.), but its spatiotemporal distribution and concentration trends have only been analyzed recently at regional or local scales. We employed a Bayesian hierarchical modeling approach to assess spatial and seasonal variation in atrazine concentration trends between 1990 and 2010 for the contiguous U.S. A Markov chain Monte Carlo simulation algorithm was used to address the problem of left‐censored data (i.e., atrazine concentration values below method reporting levels). We observed opposing temporal trends in the northern (flat or decreasing) and southern (increasing) regions of the U.S. This spatial variation in temporal trends can be partially explained by the relative amount of cropland in the region. Flat or decreasing trends in the north are more likely in regions with high cropland coverage while positive trends in the south are more likely in regions with low cropland coverage.     

A WATER QUALITY‐BASED APPROACH FOR WATERSHED WIDE BMP STRATEGIES1

ABSTRACT: Watershed management strategies generally involve controlling nonpoint source pollution by implementing various best management practices (BMPs). Currently, stormwater management programs in most states use a performance‐based approach to implement onsite BMPs. This approach fails to link the onsite BMP performance directly to receiving water quality benefits, and it does not take into account the combined treatment effects of all the stormwater management practices within a watershed. To address these issues, this paper proposes a water quality‐based BMP planning approach for effective nonpoint source pollution control at a watershed scale. A coupled modeling system consisting of a watershed model (HSPF) and a receiving water quality model (CE‐QUAL‐W2) was developed to establish the linkage between BMP performance and receiving water quality targets. A Monte Carlo simulation approach was utilized to develop alternative BMP strategies at a watershed level. The developed methodology was applied to the Swift Creek Reservoir watershed in Virginia, and the results show that the proposed approach allows for the development of BMP strategies that lead to full compliance with water quality requirements.     

Model‐Based Nitrogen and Phosphorus (Nutrient) Criteria for Large Temperate Rivers: 1. Model Development and Application

An initial inquiry into model‐based numeric nitrogen and phosphorus (nutrient) criteria for large rivers is presented. Field data collection and associated modeling were conducted on a segment of the lower Yellowstone River in the northwestern United States to assess the feasibility of deriving numeric nutrient criteria using mechanistic water‐quality models. The steady‐state one‐dimensional model QUAL2K and a transect‐based companion model AT2K were calibrated and confirmed against low‐flow conditions at a time when river loadings, water column chemistry, and diurnal indicators were approximately steady state. Predictive simulation was then implemented via nutrient perturbation to evaluate the steady‐state and diurnal response of the river to incremental nutrient additions. In this first part of a two‐part series, we detail our modeling approach, model selection, calibration and confirmation, sensitivity analysis, model outcomes, and associated uncertainty. In the second part (Suplee et al., 2015) we describe the criteria development process using the tools described herein. Both articles provide a fundamental understanding of the process required to develop site‐specific numeric nutrient criteria using models in applied regulatory settings.     

Bayesian Nonstationary Frequency Analysis of Hydrological Variables1

Ouarda, T.B.M.J. and S. El‐Adlouni, 2011. Bayesian Nonstationary Frequency Analysis of Hydrological Variables. Journal of the American Water Resources Association (JAWRA) 47(3):496‐505. DOI: 10.1111/j.1752‐1688.2011.00544.x Abstract: The present paper provides a discussion of nonstationary frequency analysis models in hydrology with a focus on the Bayesian approach. The Bayesian model provides an efficient estimation framework of hydrological quantiles in the presence of nonstationarity. In nonstationary frequency analysis models, the parameters are functions of covariates, allowing for dependent parameters and trends. The use of the nonstationary Generalized Maximum Likelihood Estimation method in hydrologic frequency analysis is discussed. This model allows using prior information concerning the variables under study and considering a number of models (linear, quadratic, etc.) of the dependence of the parameters on covariates. A discussion is also provided concerning the use of the reversible jump Monte Carlo Markov Chain procedure which allows carrying out the estimation of the posterior distributions of the parameters and the selection of the Bayesian model at the same time. An application to a case study is presented to illustrate the potential of the model.     

Analysis and Predictive Models of Single‐Family Customer Response to Water Curtailments During Drought1

Polebitski, Austin S. and Richard N. Palmer, 2012. Analysis and Predictive Models of Single‐Family Customer Response to Water Curtailments During Drought. Journal of the American Water Resources Association (JAWRA) 1‐12. DOI: 10.1111/j.1752‐1688.2012.00691.x Abstract: This research investigates customer response to demand management strategies during two drought periods in the City of Seattle. An analysis of customer response to voluntary water curtailments is conducted using k‐means clustering to identify like groups of customers and behavior patterns. The clustering method identified important variables (household income, lot size, living space, and family size) useful in determining customer response to water curtailments. Ordinary least squares and spatial lag regression models are estimated using the first and second principal components of variables identified in the clustering analysis. Larger values of income, lot size, and living space enhanced water reductions whereas larger family size tended to reduce the effectiveness of curtailments. Projections of changes in Seattle’s built environment and demographics between 2000 and 2030 were obtained from an urban simulation model (UrbanSim) and were processed through the regression models to investigate changes in future curtailment effectiveness. This research found that increasing household size hardened demands (decreased curtailment effectiveness) whereas decreasing household size increased per‐capita curtailment effectiveness. These results suggest that changes in the number of residents within a home is likely to be the most important factor in determining future curtailment effectiveness.     

Modeled Summer Background Concentration of Nutrients and Suspended Sediment in the Mid‐Continent (USA) Great Rivers1

Angradi, Ted R., David W. Bolgrien, Matt A. Starry, and Brian H. Hill, 2012. Modeled Summer Background Concentration of Nutrients and Suspended Sediment in the Mid‐Continent (USA) Great Rivers. Journal of the American Water Resources Association (JAWRA) 48(5): 1054‐1070. DOI: 10.1111/j.1752‐1688.2012.00669.x Abstract: We used regression models to predict summer background concentration of total nitrogen (N), total phosphorus (P), and total suspended solids (TSS), in the mid‐continent great rivers: the Upper Mississippi, the Lower Missouri, and the Ohio. From multiple linear regressions of water quality indicators with land use and other stressor variables, we determined the concentration of the indicators when the predictor variables were all set to zero — the y‐intercept. Except for total P on the Upper Mississippi River, we could predict background concentration using regression models. Predicted background concentration of total N was about the same on the Upper Mississippi and Lower Missouri Rivers (430 μg l^?1), which was lower than percentile‐based values, but was similar to concentrations derived from the response of sestonic chlorophyll a to great river total N concentration. Background concentration of total P on the Lower Missouri (65 μg l^?1) was also lower than published and percentile‐based concentrations. Background TSS concentration was higher on the Lower Missouri (40 mg l^?1) than the other rivers. Background TSS concentration on the Upper Mississippi (16 mg l^?1) was below a threshold (30 mg l^?1) designed to protect aquatic vegetation. Our model‐predicted concentrations for the great rivers are an attempt to estimate background concentrations for water quality indicators independent from thresholds based on percentiles or derived from stressor‐response relationships.     

Response of Algal Biomass to Large‐Scale Nutrient Controls in the Clark Fork River,Montana, United States1

Suplee, Michael W., Vicki Watson, Walter K. Dodds, and Chris Shirley, 2012. Response of Algal Biomass to Large‐Scale Nutrient Controls in the Clark Fork River, Montana, United States. Journal of the American Water Resources Association (JAWRA) 48(5): 1008‐1021. DOI: 10.1111/j.1752‐1688.2012.00666.x Abstract: Nutrient pollution is an ongoing concern in rivers. Although nutrient targets have been proposed for rivers, little is known about long‐term success of programs to decrease river nutrients and algal biomass. Twelve years of summer data (1998‐2009) collected along 383 km of the Clark Fork River were analyzed to ascertain whether a basin‐wide nutrient reduction program lowered ambient total nitrogen (TN) and total phosphorus (TP) concentrations, and bottom‐attached algal biomass. Target nutrient and algal biomass levels were established for the program in 1998. Significant declines were observed in TP but not TN along the entire river. Downstream of the city of Missoula, TP declined below a literature‐derived TP saturation breakpoint and met program targets after 2005; TN was below targets since 2007. Algal biomass also declined significantly below Missoula. Trends there likely relate to the city’s wastewater facility upgrades, despite its 20% population increase. Upstream of Missoula, nutrient reductions were less substantial; still, TP and TN declined toward saturation breakpoints, but no significant reductions in algal biomass occurred, and program targets were not met. The largest P‐load reduction to the river was from a basin‐wide phosphate laundry detergent ban set 10 years before, in 1989. We document that nutrient reductions in rivers can be successful in controlling algal biomass, but require achievement of concentrations below saturation and likely close to natural background.     

The Impact of Asynchronicity on Event‐Flow Estimation in Basin‐Scale Hydrologic Model Calibration1

Abstract: The calibration of basin‐scale hydrologic models consists of adjusting parameters such that simulated values closely match observed values. However, due to inevitable inaccuracies in models and model inputs, simulated response hydrographs for multiyear calibrations will not be perfectly synchronized with observed response hydrographs at the daily time step. An analytically derived formula suggests that when timing errors are significant, traditional calibration approaches may generally underestimate the total event‐flow volume. An event‐adaptive time series is developed and incorporated into the Nash‐Sutcliffe Efficiency objective function to diagnose the potential impact of event‐flow synchronization errors. Test sites are the 50 km² Subwatershed I of the Little River Experimental Watershed (LREWswI) in southeastern Georgia, and the 610 km² Little Washita River Experimental Watershed (LWREW) in southwestern Oklahoma, with the Soil and Water Assessment Tool used as the hydrologic model. Results suggest that simulated surface runoff generation is 55% less for LREWswI when the daily time series is used compared with when the event‐adaptive technique is used. Event‐flow generation may also be underestimated for LWREW, but to a lesser extent than it may be for LREWswI, due to a larger portion of the event flow being lateral flow.     

Linear Superposition in Total Maximum Daily Loads Applications: The Steady‐State Response Matrix Revisited1

Abstract: The steady‐state response matrix has historically proved a valuable tool in computing the water quality response to loadings and in providing insight into the relative impact of individual loading sources. The insight obtained may be is particularly useful in modern applications of increasingly complex water quality models to problems involving multiple point and nonpoint sources, such as in the assessment of total maximum daily loads (TMDLs). Where appropriate and the underlying equations linear, the steady‐state response matrix can be used to synthesize the results of more complicated models and present them in a way easily understood by policy makers. A straightforward method is presented for generating the response matrix using complex models, and example applications discussed. Example applications include a simple demonstration; incorporation of the method into the Mississippi Department of Environmental Quality’s STREAM model used in TMDL development; a TMDL modeling study of the Grand Calumet River and Indiana Harbor Canal, Indiana, using CE‐QUAL‐ICM; and a TMDL modeling study of the Big Sunflower River, Mississippi, using the Water Analysis Simulation Program model.     

Efficient Delineation of Nested Depression Hierarchy in Digital Elevation Models for Hydrological Analysis Using Level‐Set Method

In terrain analysis and hydrological modeling, surface depressions (or sinks) in a digital elevation model (DEM) are commonly treated as artifacts and thus filled and removed to create a depressionless DEM. Various algorithms have been developed to identify and fill depressions in DEMs during the past decades. However, few studies have attempted to delineate and quantify the nested hierarchy of actual depressions, which can provide crucial information for characterizing surface hydrologic connectivity and simulating the fill‐merge‐spill hydrological process. In this paper, we present an innovative and efficient algorithm for delineating and quantifying nested depressions in DEMs using the level‐set method based on graph theory. The proposed level‐set method emulates water level decreasing from the spill point along the depression boundary to the lowest point at the bottom of a depression. By tracing the dynamic topological changes (i.e., depression splitting/merging) within a compound depression, the level‐set method can construct topological graphs and derive geometric properties of the nested depressions. The experimental results of two fine‐resolution Light Detection and Ranging‐derived DEMs show that the raster‐based level‐set algorithm is much more efficient (~150 times faster) than the vector‐based contour tree method. The proposed level‐set algorithm has great potential for being applied to large‐scale ecohydrological analysis and watershed modeling.     

Long‐Term Streamflow Response to Climatic Variability in the Loess Plateau,China1

Abstract: The Loess Plateau region in northwestern China has experienced severe water resource shortages due to the combined impacts of climate and land use changes and water resource exploitation during the past decades. This study was designed to examine the impacts of climatic variability on streamflow characteristics of a 12‐km² watershed near Tianshui City, Gansu Province in northwestern China. Statistic analytical methods including Kendall’s trend test and stepwise regression were used to detect trends in relationship between observed streamflow and climatic variables. Sensitivity analysis based on an evapotranspiration model was used to detect quantitative hydrologic sensitivity to climatic variability. We found that precipitation (P), potential evapotranspiration (PET) and streamflow (Q) were not statistically significantly different (p > 0.05) over the study period between 1982 and 2003. Stepwise regression and sensitivity analysis all indicated that P was more influential than PET in affecting annual streamflow, but the similar relationship existed at the monthly scale. The sensitivity of streamflow response to variations of P and PET increased slightly with the increase in watershed dryness (PET/P) as well as the increase in runoff ratio (Q/P). This study concluded that future changes in climate, precipitation in particular, will significantly impact water resources in the Loess Plateau region an area that is already experiencing a decreasing trend in water yield.     

Modeling Stream Channel Characteristics From Drainage‐Enforced DEMs in Puget Sound,Washington, USA1

Abstract: Mapping stream channels and their geomorphic attributes is an important step in many watershed research and management projects. Often insufficient field data exist to map hydromorphologic attributes across entire drainage basins, necessitating the application of hydrologic modeling tools to digital elevation models (DEMs) via a geographic information system (GIS). In this article, we demonstrate methods for deriving synthetic stream networks via GIS across large and diverse basins using drainage‐enforced DEMs, along with techniques for estimating channel widths and gradient on the reach scale. The two‐step drainage enforcement method we used produced synthetic stream networks that displayed a high degree of positional accuracy relative to the input streams. The accuracies of our estimated channel parameters were assessed with field data, and predictions of bankfull width, wetted width and gradient were strongly correlated with measured values (r² = 0.92, r² = 0.95, r² = 0.88, respectively). Classification accuracies of binned channel attributes were also high. Our methodology allows for the relatively rapid mapping of stream channels and associated morphological attributes across large geographic areas. Although initially developed to provide salmon recovery planners with important salmon habitat information, we suggest these methodologies are relevant to a variety of research and management questions.     

Herbicide Transport in Goodwater Creek Experimental Watershed: II. Long‐Term Research on Acetochlor,Alachlor, Metolachlor,and Metribuzin1

Lerch, R.N., E.J. Sadler, C. Baffaut, N.R. Kitchen, and K.A. Sudduth, 2010. Herbicide Transport in Goodwater Creek Experimental Watershed: II. Long‐Term Research on Acetochlor, Alachlor, Metolachlor, and Metribuzin. Journal of the American Water Resources Association (JAWRA) 1‐15. DOI: 10.1111/j.1752‐1688.2010.00504.x Abstract: Farmers in the Midwestern United States continue to be reliant on soil‐applied herbicides for weed control in crop production, and herbicide contamination of streams remains an environmental problem. The main objective of this study was to analyze trends in concentration and load of acetochlor, alachlor, metolachlor, and metribuzin in Goodwater Creek Experimental Watershed (GCEW) from 1992 to 2006. A secondary objective was to document the effects of best management practices (BMPs) implemented within GCEW on herbicide transport trends. Median relative herbicide loads, as a percent of applied, were 3.7% for metolachlor, 1.3% for metribuzin, 0.36% for acetochlor, and 0.18% for alachlor. The major decrease in alachlor use and increase in acetochlor use caused shifts in flow‐weighted concentrations that were observed over the entire concentration range. The smaller decrease in metolachlor use led to a consistent decreasing time trend only for the upper end of the concentration distribution. Metribuzin also showed moderate decreases in concentration with time since 1998. Annual loads were generally correlated to second quarter discharge. Despite extensive education efforts in the watershed, conservation BMPs within GCEW were mainly implemented to control erosion, and therefore had no discernable impact on reducing herbicide transport. Overall, changes in herbicide use and second quarter discharge had the greatest effect on trends in flow‐weighted concentration and annual load.