ALTERNATIVE DEMAND MODEL ESTIMATORS FOR BLOCK RATE PRICING1

ABSTRACT: Three alternative demand model estimators for water sold under block rate tariffs are examined. The models are conceptually discussed and empirically estimated using cross-section and time-series data from Tucson, Arizona. While all three techniques produce plausible elasticity estimates, the ordinary least squares and censored sample techniques are shown to produce statistically biased results.     

GENERALIZED WATERSHED LOADING FUNCTIONS FOR STREAM FLOW NUTRIENTS1

ABSTRACT: Loading functions are proposed as a general model for estimating monthly nitrogen and phosphorus fluxes in stream flow. The functions have a simple mathematical structure, describe a wide range of rural and urban nonpoint sources, and couple surface runoff and ground water discharge. Rural runoff loads are computed from daily runoff and erosion and monthly sediment yield calculations. Urban runoff loads are based on daily nutrient accumulation rates and exponential wash off functions. Ground water discharge is determined by lumped parameter unsaturated and saturated zone soil moisture balances. Default values for model chemical parameters were estimated from literature values. Validation studies over a three-year period for an 850 km² watershed showed that the loading functions explained at least 90 percent of the observed monthly variation in dissolved and total nitrogen and phosphorus fluxes in stream flow. Errors in model predictions of mean monthly fluxes were: dissolved phosphorus - 4 percent; total phosphorus - 2 percent; dissolved nitrogen - 18 percent; and total nitrogen - 28 percent. These results were obtained without model calibration.     

Weighted Regressions on Time,Discharge, and Season (WRTDS), with an Application to Chesapeake Bay River Inputs1

Hirsch, Robert M., Douglas L. Moyer, and Stacey A. Archfield, 2010. Weighted Regressions on Time, Discharge, and Season (WRTDS), With an Application to Chesapeake Bay River Inputs. Journal of the American Water Resources Association (JAWRA) 46(5):857-880. DOI: 10.1111/j.1752-1688.2010.00482.x Abstract: A new approach to the analysis of long-term surface water-quality data is proposed and implemented. The goal of this approach is to increase the amount of information that is extracted from the types of rich water-quality datasets that now exist. The method is formulated to allow for maximum flexibility in representations of the long-term trend, seasonal components, and discharge-related components of the behavior of the water-quality variable of interest. It is designed to provide internally consistent estimates of the actual history of concentrations and fluxes as well as histories that eliminate the influence of year-to-year variations in streamflow. The method employs the use of weighted regressions of concentrations on time, discharge, and season. Finally, the method is designed to be useful as a diagnostic tool regarding the kinds of changes that are taking place in the watershed related to point sources, groundwater sources, and surface-water nonpoint sources. The method is applied to datasets for the nine large tributaries of Chesapeake Bay from 1978 to 2008. The results show a wide range of patterns of change in total phosphorus and in dissolved nitrate plus nitrite. These results should prove useful in further examination of the causes of changes, or lack of changes, and may help inform decisions about future actions to reduce nutrient enrichment in the Chesapeake Bay and its watershed.     

A SIMPLE METHOD FOR ESTIMATING BASEFLOW AT UNGAGED LOCATIONS1

ABSTRACT: Baseflow, or water that enters a stream from slowly varying sources such as ground water, can be critical to humans and ecosystems. We evaluate a simple method for estimating base‐flow parameters at ungaged sites. The method uses one or more baseflow discharge measurements at the ungaged site and longterm streamflow data from a nearby gaged site. A given baseflow parameter, such as the median, is estimated as the product of the corresponding gage site parameter and the geometric mean of the ratios of the measured baseflow discharges and the concurrent discharges at the gage site. If baseflows at gaged and ungaged sites have a bivariate lognormal distribution with high correlation and nearly equal log variances, the estimated baseflow parameters are very accurate. We tested the proposed method using long‐term streamflow data from two watershed pairs in the Driftless Area of southwestern Wisconsin. For one watershed pair, the theoretical assumptions are well met; for the other the log‐variances are substantially different. In the first case, the method performs well for estimating both annual and long‐term baseflow parameters. In the second, the method performs remarkably well for estimating annual mean and annual median baseflow discharge, but less well for estimating the annual lower decile and the long‐term mean, median, and lower decile. In general, the use of four measurements in a year is not substantially better than the use of two.     

Valuation of National Park System Visitation: The Efficient Use of Count Data Models, Meta-Analysis, and Secondary Visitor Survey Data

The National Park Service (NPS) currently manages a large and diverse system of park units nationwide which received an estimated 279 million recreational visits in 2011. This article uses park visitor data collected by the NPS Visitor Services Project to estimate a consistent set of count data travel cost models of park visitor willingness to pay (WTP). Models were estimated using 58 different park unit survey datasets. WTP estimates for these 58 park surveys were used within a meta-regression analysis model to predict average and total WTP for NPS recreational visitation system-wide. Estimated WTP per NPS visit in 2011 averaged $102 system-wide, and ranged across park units from $67 to $288. Total 2011 visitor WTP for the NPS system is estimated at $28.5 billion with a 95% confidence interval of $19.7–$43.1 billion. The estimation of a meta-regression model using consistently collected data and identical specification of visitor WTP models greatly reduces problems common to meta-regression models, including sample selection bias, primary data heterogeneity, and heteroskedasticity, as well as some aspects of panel effects. The article provides the first estimate of total annual NPS visitor WTP within the literature directly based on NPS visitor survey data.     

Global Daily Reference Evapotranspiration Modeling and Evaluation1

Abstract: Accurate and reliable evapotranspiration (ET) datasets are crucial in regional water and energy balance studies. Due to the complex instrumentation requirements, actual ET values are generally estimated from reference ET values by adjustment factors using coefficients for water stress and vegetation conditions, commonly referred to as crop coefficients. Until recently, the modeling of reference ET has been solely based on important weather variables collected from weather stations that are generally located in selected agro‐climatic locations. Since 2001, the National Oceanic and Atmospheric Administration’s Global Data Assimilation System (GDAS) has been producing six‐hourly climate parameter datasets that are used to calculate daily reference ET for the whole globe at 1‐degree spatial resolution. The U.S. Geological Survey Center for Earth Resources Observation and Science has been producing daily reference ET (ETo) since 2001, and it has been used on a variety of operational hydrological models for drought and streamflow monitoring all over the world. With the increasing availability of local station‐based reference ET estimates, we evaluated the GDAS‐based reference ET estimates using data from the California Irrigation Management Information System (CIMIS). Daily CIMIS reference ET estimates from 85 stations were compared with GDAS‐based reference ET at different spatial and temporal scales using five‐year daily data from 2002 through 2006. Despite the large difference in spatial scale (point vs. ～100 km grid cell) between the two datasets, the correlations between station‐based ET and GDAS‐ET were very high, exceeding 0.97 on a daily basis to more than 0.99 on time scales of more than 10 days. Both the temporal and spatial correspondences in trend/pattern and magnitudes between the two datasets were satisfactory, suggesting the reliability of using GDAS parameter‐based reference ET for regional water and energy balance studies in many parts of the world. While the study revealed the potential of GDAS ETo for large‐scale hydrological applications, site‐specific use of GDAS ETo in complex hydro‐climatic regions such as coastal areas and rugged terrain may require the application of bias correction and/or disaggregation of the GDAS ETo using downscaling techniques.     

Temporal and Spatial Trends in Nutrient and Sediment Loading to Lake Tahoe,California‐Nevada,USA

Since 1980, the Lake Tahoe Interagency Monitoring Program (LTIMP) has provided stream‐discharge and water quality data—nitrogen (N), phosphorus (P), and suspended sediment—at more than 20 stations in Lake Tahoe Basin streams. To characterize the temporal and spatial patterns in nutrient and sediment loading to the lake, and improve the usefulness of the program and the existing database, we have (1) identified and corrected for sources of bias in the water quality database; (2) generated synthetic datasets for sediments and nutrients, and resampled to compare the accuracy and precision of different load calculation models; (3) using the best models, recalculated total annual loads over the period of record; (4) regressed total loads against total annual and annual maximum daily discharge, and tested for time trends in the residuals; (5) compared loads for different forms of N and P; and (6) tested constituent loads against land use‐land cover (LULC) variables using multiple regression. The results show (1) N and P loads are dominated by organic N and particulate P; (2) there are significant long‐term downward trends in some constituent loads of some streams; and (3) anthropogenic impervious surface is the most important LULC variable influencing water quality in basin streams. Many of our recommendations for changes in water quality monitoring and load calculation methods have been adopted by the LTIMP.     

Do Energy‐Based PET Models Require More Input Data than Temperature‐Based Models? — An Evaluation at Four Humid FluxNet Sites

It is well established that wet environment potential evapotranspiration (PET) can be reliably estimated using the energy budget at the canopy or land surface. However, in most cases the necessary radiation measurements are not available and, thus, empirical temperature‐based PET models are still widely used, especially in watershed models. Here we question the presumption that empirical PET models require fewer input data than more physically based models. Specifically, we test whether the energy‐budget‐based Priestley‐Taylor (P‐T) model can reliably predict daily PET using primarily air temperature to estimate the radiation fluxes and associated parameters. This method of calculating PET requires only daily minimum and maximum temperature, day of the year, and latitude. We compared PET estimates using directly measured radiation fluxes to PET calculated from temperature‐based radiation estimates at four humid AmeriFlux sites. We found good agreement between P‐T PET calculated from measured radiation fluxes and P‐T PET determined via air temperature. In addition, in three of the four sites, the temperature‐based radiation approximations had a stronger correlation with measured evapotranspiration (ET) during periods of maximal ET than fully empirical Hargreaves, Hamon and Oudin methods. Of the three fully empirical models, the Hargreaves performed the best. Overall, the results suggest that daily PET estimates can be made using a physically based approach even when radiation measurements are unavailable.     

Constraining SWAT Calibration with Remotely Sensed Evapotranspiration Data

Historically, many watershed studies have been based on using the streamflow flux, typically from a single gauge at the basin's outlet, to support calibration. In this setting, there is great potential for equifinality of parameters during the optimization process, especially for parameters that are not directly related to streamflow. Therefore, some of the optimal parameter values achieved during the autocalibration process may be physically unrealistic. In recent decades a vast array of data from land surface models and remote sensing platforms can help to constrain hydrologic fluxes such as evapotranspiration (ET). While the spatial resolution of these ancillary datasets varies, the continuous spatial coverage of these gridded datasets provides flux measurements across the entire basin, in stark contrast to point‐based streamflow data. This study uses Global Land Evaporation: the Amsterdam Model data to constrain Soil and Water Assessment Tool parameter values associated with ET to a more physically realistic range. The study area is the Little Washita River Experimental Watershed, in southern Oklahoma. Traditional objective metrics such as the Nash‐Sutcliffe coefficients record no performance improvement after application of this method. However, there is a dramatic increase in the number of days with receding flow where simulations match observed streamflow.     

Approximating SWAT Model Using Artificial Neural Network and Support Vector Machine1

Abstract: With the popularity of complex, physically based hydrologic models, the time consumed for running these models is increasing substantially. Using surrogate models to approximate the computationally intensive models is a promising method to save huge amounts of time for parameter estimation. In this study, two learning machines [Artificial Neural Network (ANN) and support vector machine (SVM)] were evaluated and compared for approximating the Soil and Water Assessment Tool (SWAT) model. These two learning machines were tested in two watersheds (Little River Experimental Watershed in Georgia and Mahatango Creek Experimental Watershed in Pennsylvania). The results show that SVM in general exhibited better generalization ability than ANN. In order to effectively and efficiently apply SVM to approximate SWAT, the effect of cross‐validation schemes, parameter dimensions, and training sample sizes on the performance of SVM was evaluated and discussed. It is suggested that 3‐fold cross‐validation is adequate for training the SVM model, and reducing the parameter dimension through determining the parameter values from field data and the sensitivity analysis is an effective means of improving the performance of SVM. As far as the training sample size, it is difficult to determine the appropriate number of samples for training SVM based on the test results obtained in this study. Simple examples were used to illustrate the potential applicability of combining the SVM model with uncertainty analysis algorithm to save efforts for parameter uncertainty of SWAT. In the future, evaluating the applicability of SVM for approximating SWAT in other watersheds and combining SVM with different parameter uncertainty analysis algorithms and evolutionary optimization algorithms deserve further research.     

ESTIMATING CENTRAL TENDENCY FROM UNCENSORED TRACE LEVEL MEASUREMENTS1

ABSTRACT: The statistical analysis of data which have trace level measurements has traditionally been a two-step process in which data are first censored using criteria based on measurement precision, and then analyzed with statistical methods for censored data. The process might be more informative if data were left uncensored. In this paper, information loss attributable to censoring and measurement noise are assessed by comparing the sample mean and median of uncensored measurements with a log regression mean and median based on censored data. Measurements are derived from lognormal parent distributions which have random variability characteristic of trace level measurement. The relative performance of estimators used with error-free samples and with samples having measurement noise can be explained by differences between the probability distributions of parents and measurements. Measurement introduces bias and dispersion and transforms lognormal parent distributions toward greater symmetry. Estimates using uncensored data are less biased and more accurate than the log regression mean and median when censoring exceeds about 50 percent, and are not much worse at any fraction censored. For data with many (80 percent) results below the limit of detection, bias may be quite severe.     

Generalized Nondimensional Depth‐Discharge Rating Curves Tested on Florida Streamflow1

Abstract: A discharge rating is a relationship between stage and discharge at a specific point in a river stream or lake outlet structure. Rating curves are useful for interpolating and perhaps extrapolating flow measurements and for use directly in storage routing models. However, rating data and stations are limited. A generalized nondimensional mathematical expression that describes the rating relation of depth and discharge has been developed and tested against observations from 46 stations in West‐Central Florida. Three approaches were tested in sequence to select the best fit. The proposed model is a log‐linear equation with zero intercept and a slope that fits more than 50% of the stations were analyzed. The model is normalized by the depth and discharge values at 10% exceedance from data published by the U.S. Geological Survey. For ungauged applications, Q₁₀ and d₁₀ were derived from a relationship shown to be reasonably well correlated to the watershed drainage area. The average relative error for this parameter set shows that for the flow range up to the Q₁₀ discharge, better than 30% agreement with the USGS rating data can be expected for about 50% of the stations. Further analysis is required to determine why so many stations exhibit such similar behavior and to identify the criteria or parameters governing the differences.     

Spatiotemporal Evaluation of Simulated Evapotranspiration and Streamflow over Texas Using the WRF‐Hydro‐RAPID Modeling Framework

This study assesses a large‐scale hydrologic modeling framework (WRF‐Hydro‐RAPID) in terms of its high‐resolution simulation of evapotranspiration (ET) and streamflow over Texas (drainage area: 464,135 km²). The reference observations used include eight‐day ET data from MODIS and FLUXNET, and daily river discharge data from 271 U.S. Geological Survey gauges located across a climate gradient. A recursive digital filter is applied to decompose the river discharge into surface runoff and base flow for comparison with the model counterparts. While the routing component of the model is pre‐calibrated, the land component is uncalibrated. Results show the model performance for ET and runoff is aridity‐dependent. ET is better predicted in a wet year than in a dry year. Streamflow is better predicted in wet regions with the highest efficiency ~0.7. In comparison, streamflow is most poorly predicted in dry regions with a large positive bias. Modeled ET bias is more strongly correlated with the base flow bias than surface runoff bias. These results complement previous evaluations by incorporating more spatial details. They also help identify potential processes for future model improvements. Indeed, improving the dry region streamflow simulation would require synergistic enhancements of ET, soil moisture and groundwater parameterizations in the current model configuration. Our assessments are important preliminary steps towards accurate large‐scale hydrologic forecasts.     

Revisiting a statistical shortcoming when fitting the Langmuir model to sorption data

The Langmuir model is commonly used for describing the sorption behavior of reactive solutes to surfaces and is often fit to sorption data using nonlinear least squares regression. An important assumption of least squares regression is that the predictor variable is error free. In the case of sorption data, this assumption is not valid, and therefore the potential for parameter bias exists. Although alternative regression methods exist that either explicitly account for error in the predictor variable (Model II regression) or minimize the error in the predictor variable, these methods are not commonly used. Therefore, this paper more fully explores the differences in fitted parameters and model fits between these different data fitting methods by fitting P sorption data collected on 26 different soil samples using three different regression methods. For a majority of soils tested in this study, the differences in model fits between the three regression methods were not statistically significant. Statistical differences were observed in over a third of the soils, however, suggesting that errors in the predictor variable may be large enough to produce biased parameter estimates. These results suggest that multiple regression methods should be used when fitting the Langmuir model to sorption data to better assess the potential impact of error on model fits.     

Nutrient and Sediment Production,Watershed Characteristics,and Land Use in the Tahoe Basin,California‐Nevada1

Abstract: In efforts to control the degradation of water quality in Lake Tahoe, public agencies have monitored surface water discharge and concentrations of nitrogen, phosphorus, and suspended sediment in two separate sampling programs. The first program focuses on 20 watersheds varying in size from 162 to 14,000 ha, with continuous stream gaging and periodic sampling; the second focuses on small urbanized catchments, with automated sampling during runoff events. Using data from both programs, we addressed the questions (1) what are the fluxes and concentrations of nitrogen and phosphorus entering the lake from surface runoff; (2) how do the fluxes and concentrations vary in space and time; and (3) how are they related to land use and watershed characteristics? To answer these questions, we calculated discharge‐weighted average concentrations and annual fluxes and used multiple regression to relate those variable to a suite of GIS‐derived explanatory variables. The final selected regression models explain 47‐62% of the variance in constituent concentrations in the stormwater monitoring catchments, and 45‐72% of the variance in mean annual yields in the larger watersheds. The results emphasize the importance of impervious surface and residential density as factors in water quality degradation, and well‐developed soil as a factor in water quality maintenance.     

Seasonal and Regional Patterns in Performance for a Baltic Sea Drainage Basin Hydrologic Model

This study evaluates the ability of the Catchment SIMulation (CSIM) hydrologic model to describe seasonal and regional variations in river discharge over the entire Baltic Sea drainage basin (BSDB) based on 31 years of monthly simulation from 1970 through 2000. To date, the model has been successfully applied to simulate annual fluxes of water from the catchments draining into the Baltic Sea. Here, we consider spatiotemporal bias in the distribution of monthly modeling errors across the BSDB since it could potentially reduce the fidelity of predictions and negatively affect the design and implementation of land‐management strategies. Within the period considered, the CSIM model accurately reproduced the annual flows across the BSDB; however, it tended to underpredict the proportion of discharge during high‐flow periods (i.e., spring months) and overpredict during the summer low flow periods. While the general overpredictions during summer periods are spread across all the subbasins of the BSDB, the underprediction during spring periods is seen largely in the northern regions. By implementing a genetic algorithm calibration procedure and/or seasonal parameterization of subsurface water flows for a subset of the catchments modeled, we demonstrate that it is possible to improve the model performance albeit at the cost of increased parameterization and potential loss of parsimony.     

THE EFFECT OF DATA INDEPENDENCE IN MODEL CALIBRATION AND MODEL TESTING1

ABSTRACT: With the increased use of models in hydrologic design, there is an immediate need for a comprehensive comparison of hydrologic models, especially those intended for use at ungaged locations (i.e., where measured data are either not available or inadequate for model calibration). But some past comparisons of hydrologic models have used the same data base for both calibration and testing of the different models or implied that the results of model calibration are indicative of the accuracy at ungaged locations. This practice was examined using both the regression equation approach to peak discharge estimation and a unit hydrograph model that was intended for use in urban areas. The results suggested that the lack of data independence in the calibration and testing of regression equations may lead to both biased results and misleading statements about prediction accuracy. Additionally, although split-sample testing is recognized as desirable, the split-samples should be selected using a systematic-random sampling scheme, rather than random sampling, because random sampling with small samples may lead to a testing sample that is not representative of the population. A systematic-random sampling technique should lead to more valid conclusions about model reliability. For models like a unit hydrograph model, which are more complex and for which calibration is a more involved process, data independence is not as critical because the data fitting error variation is not as dominant as the error variation due to the calibration process and the inability of the model structure to conform with data variability.     

Estimating Sediment and Nutrient Loads in Four Western Lake Superior Streams

Total suspended solids (TSS) and total phosphorus (TP) have been shown to be strongly correlated with turbidity in watersheds. High‐frequency in situ turbidity can provide estimates of these potential pollutants over a wide range of hydrologic conditions. Concentrations and loads were estimated in four western Lake Superior trout streams from 2005 to 2010 using regression models relating continuous turbidity data to grab sample measures of TSS and TP during differing flow regimes. TSS loads estimated using the turbidity surrogate were compared with those made using FLUX software, a standard assessment technique based on discharge and grab sampling for TSS. More traditional rating curve methodology was not suitable because of the high variability in the particulates vs. discharge relationship. Stream‐specific turbidity and TSS data were strongly correlated (r² = 0.5 to 0.8; p < 0.05) and less so for TP (r² = 0.3 to 0.7; p < 0.05). Near‐continuous turbidity monitoring (every 15 min) provided a good method for estimating both TSS and TP concentration, providing information when manual sample collection was unlikely, and allowing for detailed analyses of short‐term responses of flashy Lake Superior tributaries to highly variable weather and hydrologic conditions while the FLUX model typically resulted in load estimates greater than those determined using the turbidity surrogate, with 17/23 stream years having greater FLUX estimates for TSS and 18/23 for TP.     

REGIONAL SCALE MODELING OF SURFACE AND GROUND WATER INTERACTION IN THE SNAKE RIVER BASIN1

ABSTRACT: Changes in irrigation and land use may impact discharge of the Snake River Plain aquifer, which is a major contributor to flow of the Snake River in southern Idaho. The Snake River Basin planning and management model (SRBM) has been expanded to include the spatial distribution and temporal attenuation that occurs as aquifer stresses propagate through the aquifer to the river. The SRBM is a network flow model in which aquifer characteristics have been introduced through a matrix of response functions. The response functions were determined by independently simulating the effect of a unit stress in each cell of a finite difference groundwater flow model on six reaches of the Snake River. Cells were aggregated into 20 aquifer zones and average response functions for each river reach were included in the SRBM. This approach links many of the capabilities of surface and ground water flow models. Evaluation of an artificial recharge scenario approximately reproduced estimates made by direct simulation in a ground water flow model. The example demonstrated that the method can produce reasonable results but interpretation of the results can be biased if the simulation period is not of adequate duration.