TOTAL SOLUTES LOADS AND GEOCHEMICAL YIELDS IN THE SASKATCHEWAN RIVER BASIN1

ABSTRACT: River solute loads have seldom been measured in very large, complex drainage basins, nor have the methods of calculating loads been critically examined. For sites in the Saskatchewan River Basin, Canada, rating curves were poor predictors of solute loads because correlations between discharge and total solutes concentration were weak (R² < 0.05 in most cases) and suffered from hysteresis. In contrast, the interval method produced reliable estimates in all seasons and sites tested, and was little affected by sampling schedule. The limit of precision (SE) for estimates of mean annual or seasonal solute load was 10–15 percent of the mean (5 percent in very small basins), reached with 10 years or more of data. Two-thirds or more of total annual solute load was transported during the open-water season, but the proportion carried during winter increased from 8 percent to 34 percent from the upstream to the downstream end of the basin, due to reservoirs retaining and mixing water. Annual loads of total solutes varied from 6.2 × 10⁴ tonnes in foothills tributaries to almost 4.0 × 10⁶ tonnes in the Saskatchewan River near the mouth. But, on an areal basis, the mountain and foothills region was the dominant solute source, producing 43–97 tonnes/km²/yr, compared with only 3–22 tonnes/km²/yr for prairie rivers. This difference is a consequence of greater rainfall and, hence, more rapid erosion in the mountains.     

AN ILLUSTRATION OF MODEL STRUCTURE IDENTIFICATION1

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

OPTIMAL ESTIMATION OF CONTAMINANT TRANSPORT IN GROUND WATER1

ABSTRACT: Finite element and finite difference representations of the convective-dispersive equation have been widely used in determining contaminant transport in ground water. Due to inherent uncertainties of the transport process, those representations are inexact and contain errors. Errors in field measurements are unavoidable. By combining a numerical model, a measurement equation, and the Kalman filter, optimal estimates of the state variable (contaminant concentration) can be obtained. This paper describes the algorithm and gives a numerical example of contaminant transport in a two-dimensional ground water flow. The results show significant improvement in the estimated concentration distribution by using the filtering technique.     

UNCERTAINTIES IN ESTIMATING THE WATER BALANCE OF LAKES1

ABSTRACT: Evaluation of hydrologic methodology used in a number of water balance studies of lakes in the United States shows that most of these studies calculate one or more terms of the budget as the residual. A literature review was made of studies in which the primary purpose was error analysis of hydrologic measurement and interpretation. Estimates of precipitation can have a wide range of error, depending on the gage placement, gage spacing, and areal averaging technique. Errors in measurement of individual storms can be as high as 75 percent. Errors in short term averages are commonly in the 15-30 percent range, but decrease to about 5 percent or less for annual estimates. Errors in estimates of evaporation can also vary widely depending on instrumentation and methodology. The energy budget is the most accurate method of calculating evaporation; errors are in the 10–15 percent range. If pans are used that are located a distance from the lake of interest, errors can be considerable. Annual pan-to-lake coefficients should not be used for monthly estimates of evaporation because they differ from the commonly used coefficient of 0.7 by more than 100 percent. Errors in estimates of stream discharge are often considered to be within 5 percent. If the measuring section, type of flow profile, and other considerations, such as stage discharge relationship, are less than ideal errors in estimates of stream discharge can be considerably greater than 5 percent. Errors in estimating overland (nonchannelized) flow have not been evaluated, and in most lake studies this component is not mentioned. Comparison of several lake water balances in which the risdual consists solely of errors in measurement, shows that such a residual, if interpreted as ground water, can differ from an independent estimate of ground water by more than 100 percent.     

SAMPLING FREQUENCY SELECTION FOR REGULATORY WATER QUALITY MONITORING1

ABSTRACT: The selection of sampling frequencies in order to achieve reasonably small and uniform confidence interval widths about annual sample means or sample geometric means of water quality constituents is suggested as a rational approach to regulatory monitoring network design. Methods are presented for predicting confidence interval widths at specified sampling frequencies while considering both seasonal variation and serial correlation of the quality time series. Deterministic annual cycles are isolated and serial dependence structures of the autoregressive, moving average type are identified through time series analysis of historic water quality records. The methods are applied to records for five quality constituents from a nine-station network in Illinois. Confidence interval widths about annual geometric means are computed over a range of sampling frequencies appropriate in regulatory monitoring. Results are compared with those obtained when a less rigorous approach, ignoring seasonal variation and serial correlation, is used. For a monthly sampling frequency the error created by ignoring both seasonal variation and serial correlation is approximately 8 percent. Finally, a simpler technique for evaluating serial correlation effects based on the assumption of AR(1) type dependence is examined. It is suggested that values of the parameter p₁, in the AR(1) model should range from 0.75 to 0.90 for the constituents and region studied.     

BANKFULL DISCHARGE RECURRENCE INTERVALS AND REGIONAL HYDRAULIC GEOMETRY RELATIONSHIPS: PATTERNS IN THE PACIFIC NORTHWEST,USA1

ABSTRACT: The model bankfull discharge recurrence interval (annual series) (T_a) in streams has been approximated at a 1.5‐year flow event. This study tests the linkage between regional factors (climate, physiography, and ecoregion) and the frequency of bank‐full discharge events in the Pacific Northwest (PNW). Patterns of Ta were found to be significant when stratified by EPA Ecoregion. The mean value for T_a in the PNW is 1.4 years; however, when the data is stratified by ecoregion, the humid areas of western Oregon and Washington have a mean value of 1.2 years, while the dryer areas of Idaho and eastern Oregon and Washington have a mean value of 1.4 to 1.5 years. Among the four factors evaluated, vegetation association and average annual precipitation are the primary factors related to channel form and T_a. Based on the results of the T_a analyses, regional hydraulic geometry relationships of streams were developed for the PNW, which relate variables, such as bank‐full cross‐sectional area, width, depth, and velocity, to bankfull discharge and drainage area. The verification of T_a values, combined with the development of regional hydraulic geometry relationships, provides geographically relevant information that will result in more accurate estimates of hydraulic geometry variables in the PNW.     

USE OF STATE ESTIMATION TECHNIQUES IN WATER RESOURCE SYSTEM MODELING1

ABSTRACT. A relatively straightforward illustration of the potential uses of State Estimation techniques in water resources modeling is given. Background theory for Linear and Extended Kalman Filters is given; application of the filter techniques to modeling BOD and oxygen deficit in a stream illustrates the importance of model conceptualization, model completeness, uncertainty in model dynamics and incorporation of measurements and measurement errors. Potential applications of state estimation techniques to measurement system design; model building, assessment and calibration; and data extension are explored.     

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.     

How to Constrain Multi‐Objective Calibrations of the SWAT Model Using Water Balance Components

Accurate discharge simulation is one of the most common objectives of hydrological modeling studies. However, a good simulation of discharge is not necessarily the result of a realistic simulation of hydrological processes within the catchment. We propose an evaluation framework that considers both discharge and water balance components as evaluation criteria for calibration of the Soil and Water Assessment Tool (SWAT). In this study, we integrated average annual values of surface runoff, groundwater flow, and evapotranspiration in the model evaluation procedure to constrain the selection of good model runs for the Little River Experimental Watershed in Georgia, United States. For evaluating water balance and discharge dynamics, the Nash‐Sutcliffe efficiency (NSE) and percent bias (PBIAS) were used. In addition, the ratio of root mean square error and standard deviation of measured data (RSR) was calculated for individual segments of the flow duration curve to identify the best model runs in terms of discharge magnitude. Our results indicate that good statistics for discharge do not guarantee realistic simulations of individual water balance components. Therefore, we recommend constraining the ranges of water balance components to achieve a more realistic simulation of the entire hydrological system, even if tradeoffs between good statistics for discharge simulations and reasonable amounts of the water balance components are unavoidable. Editor's note : This paper is part of the featured series on SWAT Applications for Emerging Hydrologic and Water Quality Challenges. See the February 2017 issue for the introduction and background to the series.     

Optimizing Bankfull Discharge and Hydraulic Geometry Relations for Streams in New York State1

Mulvihill, Christiane I. and Barry P. Baldigo, 2012. Optimizing Bankfull Discharge and Hydraulic Geometry Relations for Streams in New York State. Journal of the American Water Resources Association (JAWRA) 48(3): 449-463. DOI: 10.1111/j.1752-1688.2011.00623.x Abstract: This study analyzes how various data stratification schemes can be used to optimize the accuracy and utility of regional hydraulic geometry (HG) models of bankfull discharge, width, depth, and cross-sectional area for streams in New York. Topographic surveys and discharge records from 281 cross sections at 82 gaging stations with drainage areas of 0.52-396 square miles were used to create log-log regressions of region-based relations between bankfull HG metrics and drainage area. The success with which regional models distinguished unique bankfull discharge and HG patterns was assessed by comparing each regional model to those for all other regions and a pooled statewide model. Gages were also stratified (grouped) by mean annual runoff (MAR), Rosgen stream type, and water-surface slope to test if these models were better predictors of HG to drainage area relations. Bankfull discharge models for Regions 4 and 7 were outside the 95% confidence interval bands of the statewide model, and bankfull width, depth, and cross-sectional area models for Region 3 differed significantly (p < 0.05) from those of other regions. This study found that statewide relations between drainage area and HG were strongest when data were stratified by hydrologic region, but that co-variable models could yield more accurate HG estimates in some local regional curve applications.     

NUTRIENT LOADING ASSESSMENT IN THE ILLINOIS RIVER USING A SYNTHETIC APPROACH1

ABSTRACT: A synthetic relationship is developed between nutrient concentrations and discharge rates at two river gauging sites in the Illinois River Basin. Analysis is performed on data collected by the U.S. Geological Survey (USGS) on nutrients in 1990 through 1997 and 1999 and on discharge rates in 1988 through 1997 and 1999. The Illinois River Basin is in western Arkansas and northeastern Oklahoma and is designated as an Oklahoma Scenic River. Consistently high nutrient concentrations in the river and receiving water bodies conflict with recreational water use, leading to intense stakeholder debate on how best to manage water quality. Results show that the majority of annual phosphorus (P) loading is transported by direct runoff, with high concentrations transported by high discharge rates and low concentrations by low discharge rates. A synthetic relationship is derived and used to generate daily phosphorus concentrations, laying the foundation for analysis of annual loading and evaluation of alternative management practices. Total nitrogen (N) concentration does not have as clear a relationship with discharge. Using a simple regression relationship, annual P loadings are estimated as having a root mean squared error (RMSE) of 39.8 t/yr and 31.9 t/yr and mean absolute percentage errors of 19 percent and 28 percent at Watts and Tahlequah, respectively. P is the limiting nutrient over the full range of discharges. Given that the majority of P is derived from Arkansas, management practices that control P would have the most benefit if applied on the Arkansas side of the border.     

ESTIMATING STREAMFLOW AND ASSOCIATED HYDRAULIC GEOMETRY,THE MID‐ATLANTIC REGION,USA1

ABSTRACT: Methods to estimate streamflow and channel hydraulic geometry were developed for unpaged streams in the Mid‐Atlantic Region. Observed mean annual streamflow and associated hydraulic geometry data from 75 gaging stations in the Appalachian Plateau, the Ridge and Valley, and the Piedmont Physiographic Provinces of the Mid‐Atlantic Region were used to develop a set of power functions that relate streamflow to drainage area and hydraulic geometry to streamflow. For all three physiographic provinces, drainage area explained 95 to 98 percent of the variance in mean annual streamflow. Relationships between mean annual streamflow and water surface width and mean flow depth had coefficients of determination that ranged from R²= 0.55 to R²= 0.91, but the coefficient of determination between mean flow velocity and mean annual streamflow was lower (R²= 0.44 to R²= 0.54). The advantages of using the regional regression models to estimate streamflow over a conceptual model or a water balance model are its ease of application and reduced input data needs. The prediction of the regression equations were tested with data collected as part of the U.S. Environmental Protection Agency (USEPA) Environmental Monitoring and Assessment Program (EMAP). In addition, equations to transfer streamflow from gaged to ungaged streams are presented.     

GENETIC PROGRAMMING AND ITS APPLICATION IN REAL‐TIME RUNOFF FORECASTING1

ABSTRACT: Genetic programming (GP), a relatively new evolutionary technique, is demonstrated in this study to evolve codes for the solution of problems. First, a simple example in the area of symbolic regression is considered. GP is then applied to real‐time runoff forecasting for the Orgeval catchment in France. In this study, GP functions as an error updating scheme to complement a rainfall‐runoff model, MIKE11/NAM. Hourly runoff forecasts of different updating intervals are performed for forecast horizons of up to nine hours. The results show that the proposed updating scheme is able to predict the runoff quite accurately for all updating intervals considered and particularly for updating intervals not exceeding the time of concentration of the catchment. The results are also compared with those of an earlier study, by the World Meteorological Organization, in which autoregression and Kalman filter were used as the updating methods. Comparisons show that GP is a better updating tool for real‐time flow forecasting. Another important finding from this study is that nondimensionalizing the variables enhances the symbolic regression process significantly.     

Soil Moisture Data Assimilation Using Support Vector Machines and Ensemble Kalman Filter1

Abstract: A hybrid data assimilation (DA) methodology that combines two state‐of‐the‐art techniques, support vector machines (SVMs) and ensemble Kalman filter (EnKF), is applied for soil moisture DA in this work. The SVM methodology provides a statistically sound and robust approach to solving the inverse problem, and thus to building statistical models. EnKF is an extension of the Kalman Filter (KF), a well‐known tool in prediction updating. In the present research, ground measurements were used to build a SVM‐type soil moisture predictor. Subsequent observations and their statistics were assimilated to update predictions from the SVM model by coupling it with EnKF. In this way, both model predictions and ground data, as well as their statistics, are fused thus minimizing the prediction error and making the predictions and observations statistically consistent. The results are shown for two approaches; one in which update is done at every time step and the other which assumes that data is only available at alternate time steps (in window of 10 time steps) and hence update is performed at those occasions. The SVM‐EnKF coupling is shown to improve soil moisture forecasts in an example using data from the Soil Climate Analysis Network site at Ames, Iowa.     

Sensitivity and Uncertainty of Ground‐Water Discharge Estimates for Semiarid Shrublands1

Abstract: We proposed a step‐by‐step approach to quantify the sensitivity of ground‐water discharge by evapotranspiration (ET) to three categories of independent input variables. To illustrate the approach, we adopt a basic ground‐water discharge estimation model, in which the volume of ground water lost to ET was computed as the product of the ground‐water discharge rate and the associated area. The ground‐water discharge rate was assumed to equal the ET rate minus local precipitation. The objective of this study is to outline a step‐by‐step procedure to quantify the contributions from individual independent variable uncertainties to the uncertainty of total ground‐water discharge estimates; the independent variables include ET rates of individual ET units, areas associated with the ET units, and precipitation in each subbasin. The specific goal is to guide future characterization efforts by better targeting data collection for those variables most responsible for uncertainty in ground‐water discharge estimates. The influential independent variables to be included in the sensitivity analysis are first selected based on the physical characteristics and model structure. Both regression coefficients and standardized regression coefficients for the selected independent variables are calculated using the results from sampling‐based Monte Carlo simulations. Results illustrate that, while as many as 630 independent variables potentially contribute to the calculation of the total annual ground‐water discharge for the case study area, a selection of seven independent variables could be used to develop an accurate regression model, accounting for more than 96% of the total variance in ground‐water discharge. Results indicate that the variability of ET rate for moderately dense desert shrubland contributes to about 75% of the variance in the total ground‐water discharge estimates. These results point to a need to better quantify ET rates for moderately dense shrubland to reduce overall uncertainty in estimates of ground‐water discharge. While the approach proposed here uses a basic ground‐water discharge model taken from an earlier study, the procedure of quantifying uncertainty and sensitivity can be generalized to handle other types of environmental models involving large numbers of independent variables.     

STATISTICAL ANALYSIS OF THE IMPACT OF GROUND WATER PUMPAGE ON LOW-FLOW HYDROLOGY1

ABSTRACT: Ground-water pumpage withdrew 57 cubic feet per second from aquifers beneath the Yahara River Basin in 1970. Forty-six cubic feet per second were exported by the diversion of treated wastewater from the drainage basin. The low-flow hydrology of the upper Yahara River has been impacted by this diversion. Prior to 1959, the wastewater was discharged into the river, augmenting the baseflow during low-flow periods. As much as 85% of streamflow was due to effluent discharge. In 1959 the wastewater was transferred from the river basin. The result was a decrease of about one-third in mean annual streamflow, and a decrease of more than 50% in the 7Q₂ and 7Q₁₀. Regression analysis showed the annual 7-day low-flow and 60-day low-flow have a statistically significant correlation with mean annual flow. Using predictions of future mean annual discharge of the river with increasing interbasin transfers, it is shown that by 1990 there is a significant probability that in some years the 60-day low-flow in the river will be zero.     

The role of respondents’ comfort for variance in stated choice surveys: evidence from a SCUBA diving case

Preference elicitation among outdoor recreational users is subject to measurement errors that depend, in part, on survey planning. This study uses data from a choice experiment survey on recreational SCUBA diving to investigate whether self-reported information on respondents’ comfort when they complete surveys correlates with the error variance in stated choice models of their responses. Comfort-related variables are included in the scale functions of the scaled multinomial logit models. The hypothesis was that higher comfort reduces error variance in answers, as revealed by a higher scale parameter and vice versa. Information on, e.g., sleep and time since eating (higher comfort) correlated with scale heterogeneity, and produced lower error variance when controlled for in the model. That respondents’ comfort may influence choice behavior suggests that knowledge of the respondents’ activity patterns could be used to plan the timing of interviews to decrease error variance in choices and, hence, generate better information.     

A Water Allocation Decision‐Support Model and Tool for Predictions in Ungauged Basins in Northeast British Columbia,Canada

Pressures on water resources due to changing climate, increasing demands, and enhanced recognition of environmental flow needs result in the need for hydrology information to support informed water allocation decisions. However, the absence of hydrometric measurements and limited access to hydrology information in many areas impairs water allocation decision‐making. This paper describes a water balance‐based modeling approach and an innovative web‐based decision‐support hydrology tool developed to address this need. Using high‐resolution climate, vegetation, and watershed data, a simple gridded water balance model, adjusted to account for locational variability, was developed and calibrated against gauged watersheds, to model mean annual runoff. Mean monthly runoff was modeled empirically, using multivariate regression. The modeled annual runoff results are within 20% of the observed mean annual discharge for 78% of the calibration watersheds, with a mean absolute error of 16%. Modeled monthly runoff corresponds well to observed monthly runoff, with a median Nash–Sutcliffe statistic of 0.92 and a median Spearman rank correlation statistic of 0.98. Monthly and annual flow estimates produced from the model are incorporated into a map‐ and watershed‐based decision‐support system referred to as the Northeast Water Tool, to provide critical information to decision makers and others on natural water supply, existing allocations, and the needs of the environment.     

The global solar radiation estimation and analysis of solar energy: Case study for Osmaniye,Turkey

This paper investigates the prediction of solar radiation model and actual solar energy in Osmaniye, Turkey. Four models were used to estimate using the parameters of sunshine duration and average temperature. In order to obtain the statistical performance analysis of models, the coefficient of determination (R²), mean absolute percentage error (MAPE), mean absolute bias error (MABE), and root mean square error (RMSE) were used. Results obtained from the linear regression using the parameters of sunshine duration and average temperature showed a good prediction of the monthly average daily global solar radiation on a horizontal surface. In order to obtain solar energy, daily and monthly average solar radiation values were calculated from the five minute average recorded values by using meteorological measuring device. As a result of this measurement, the highest monthly and yearly mean solar radiation values were 698 (April in 2013) and 549 (2014 year) W/m² respectively. On an annual scale the maximum global solar radiation changes from 26.38 MJ/m²/day by June to 19.19 MJ/m²/day by September in 2013. Minimum global solar radiation changes from 14.05 MJ/m²/day by October to 7.20 MJ/m²/day by January in 2013. Yearly average energy potential during the measurement period was 16.53 MJ/m²/day (in 2013). The results show that Osmaniye has a considerable solar energy potential to produce electricity.     

THE RELATIONSHIP BETWEEN THE TIME BASES OF SIMULATION MODELS AND THEIR STRUCTURE1

ABSTRACT: The time base of a simulation model can be defined as a combination of two time intervals. One is the interval used for input and internal computations. The second is the interval used for the output and calibration of the model. The time base of a model is related on the one hand to the type of applications for which the simulated data are used, and on the other hand to the structure and complexity of the model. The latter may be represented by the number of parameters employed to specify the operation of the model. Using data typical to relatively small watersheds in a semiarid climate, the interaction between the complexity of a series of models and the time bases used by them was studied. This included the effects of the two factors, time base and complexity, on the values of the optimal parameters, prediction of mean annual flow, and general performance of the models. The main conclusion is that if the acceptable time base is longer, the model can be less complex needing fewer parameters. There is also an advantage in using a time base comprising a shorter input time interval and a longer output time interval.