© 2012 Khatibi et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Inter-Comparison of an Evolutionary Programming Model of Suspended Sediment Time-Series with Other Local Models

summary Accurate estimation of nutrient loads in rivers and streams is critical for many applications including determination of sources of nutrient loads in watersheds, evaluating long-term trends in loads, and estimating loading to downstream waterbodies. Since in many cases nutrient concentrations are measured on a weekly or monthly frequency, there is a need to estimate concentration and loads during periods when no data is available. The objectives of this study were to: (i) document the performance of a multiple regression model to predict loads of nitrate and total phosphorus (TP) in Iowa rivers and streams; (ii) determine whether there is any systematic bias in the load prediction estimates for nitrate and TP; and (iii) evaluate streamflow and concentration factors that could affect the load prediction efficiency. A commonly cited rating curve regression is utilized to estimate riverine nitrate and TP loads for rivers in Iowa with watershed areas ranging from 17.4 to over 34,600 km 2 . Forty-nine nitrate and 44 TP datasets each comprising 5–22 years of approximately weekly to monthly concentrations were examined. Three nitrate data sets had sample collection frequencies averaging about three samples per week. The accuracy and precision of annual and long term riverine load prediction was assessed by direct comparison of rating curve load predictions with observed daily loads. Significant positive bias of annual and long term nitrate loads was detected. Long term rating curve nitrate load predictions exceeded observed loads by 25% or more at 33% of the 49 measurement sites. No bias was found for TP load prediction although 15% of the 44 cases either underestimated or overestimate observed long-term loads by more than 25%. The rating curve was found to poorly characterize nitrate and phosphorus variation in some rivers. Published by Elsevier B.V.

[1] Water quality samples for most streams are collected at variable frequencies within monitoring periods of different lengths. On the basis of discrete concentration data obtained from these monitoring studies, loads of various pollutants passing through a gaging station for selected periods may be calculated using various load estimation methods. In this paper, nitrate-N load estimates were compared with their “true” values, calculated using 6 years of daily nitrate-N concentration and average discharge data at an agricultural watershed in central Illinois. A Monte Carlo subsampling study was conducted to simulate different sampling scenarios for variable sampling frequencies and different monitoring durations. Load calculations were compared for each sampling scenario based on rating curve, ratio estimator, and flow-weighted average estimator. In addition, two bias correction techniques (minimum variance unbiased estimator (MVUE) and smearing estimator) were applied to the rating curve method. The monitoring durations were 1, 2, 3, and 6 years, and the sampling frequencies ranged from weekly to bimonthly. The results demonstrated that a desired accuracy of the estimates could be achieved either by sampling more frequently or by monitoring the site longer. Although the ratio and the flow-weighted average estimators had a small negative bias, in most cases rating curve estimators were positively biased when applied to the study site. Also, neither of the two bias correction techniques, MVUE and smearing estimator, decreased this positive bias. On the contrary, those techniques produced a higher bias, which resulted in increased root-mean-square error (RMSE). The rating curve uncorrected for bias, the simple ratio, and the flow-weighted estimator had a significantly smaller RMSE for all sampling frequencies and all periods of record than the bias-corrected rating curve methods.

[1] This paper presents an adjusted maximum likelihood estimator (AMLE) that can be used to estimate fluvial transport of contaminants, like phosphorus, that are subject to censoring because of analytical detection limits. The AMLE is a generalization of the widely accepted minimum variance unbiased estimator (MVUE), and Monte Carlo experiments confirm that it shares essentially all of the MVUE's desirable properties, including high efficiency and negligible bias. In particular, the AMLE exhibits substantially less bias than alternative censored-data estimators such as the MLE (Tobit) or the MLE followed by a jackknife. As with the MLE and the MVUE the AMLE comes close to achieving the theoretical Frechet-Cramer-Rao bounds on its variance. This paper also presents a statistical framework, applicable to both censored and complete data, for understanding and estimating the components of uncertainty associated with load estimates. This can serve to lower the cost and improve the efficiency of both traditional and real-time water quality monitoring.

[1] Regression-type, hybrid empirical/process-based models (e.g., SPARROW, PolFlow) have assumed a prominent role in efforts to estimate the sources and transport of nutrient pollution at river basin scales. However, almost no attempts have been made to explicitly accommodate interannual nutrient loading variability in their structure, despite empirical and theoretical evidence indicating that the associated source/sink processes are quite variable at annual timescales. In this study, we present two methodological approaches to accommodate interannual variability with the Spatially Referenced Regressions on Watershed attributes (SPARROW) nonlinear regression model. The first strategy uses the SPARROW model to estimate a static baseline load and climatic variables (e.g., precipitation) to drive the interannual variability. The second approach allows the source/sink processes within the SPARROW model to vary at annual timescales using dynamic parameter estimation techniques akin to those used in dynamic linear models. Model parameterization is founded upon Bayesian inference techniques that explicitly consider calibration data and model uncertainty. Our case study is the Hamilton Harbor watershed, a mixed agricultural and urban residential area located at the western end of Lake Ontario, Canada. Our analysis suggests that dynamic parameter estimation is the more parsimonious of the two strategies tested and can offer insights into the temporal structural changes associated with watershed functioning. Consistent with empirical and theoretical work, model estimated annual in-stream attenuation rates varied inversely with annual discharge. Estimated phosphorus source areas were concentrated near the receiving water body during years of high in-stream attenuation and dispersed along the main stems of the streams during years of low attenuation, suggesting that nutrient source areas are subject to interannual variability.

[1] Mercury (Hg) is one of the leading water quality concerns in surface waters of the United States. Although watershed-scale Hg cycling research has increased in the past two decades, advances in modeling watershed Hg processes in diverse physiographic regions, spatial scales, and land cover types are needed. The goal of this study was to assess Hg cycling in a Coastal Plain system using concentrations and fluxes estimated by multiple watershed-scale models with distinct mathematical frameworks reflecting different system dynamics. We simulated total mercury (HgT, the sum of filtered and particulate forms) concentrations and fluxes from a Coastal Plain watershed (McTier Creek) using three watershed Hg models and an empirical load model. Model output was compared with observed in-stream HgT. We found that shallow subsurface flow is a potentially important transport mechanism of particulate HgTduring periods when connectivity between the uplands and surface waters is maximized. Other processes (e.g., stream bank erosion, sediment re-suspension) may increase particulate HgT in the water column. Simulations and data suggest that variable source area (VSA) flow and lack of rainfall interactions with surface soil horizons result in increased dissolved HgTconcentrations unrelated to DOC mobilization following precipitation events. Although flushing of DOC-HgTcomplexes from surface soils can also occur during this period, DOC-complexed HgT becomes more important during base flow conditions. TOPLOAD simulations highlight saturated subsurface flow as a primary driver of daily HgT loadings, but shallow subsurface flow is important for HgTloads during high-flow events. Results suggest limited seasonal trends in HgT dynamics.

[1] Fluvial loads for total nitrogen, total oxidized nitrogen, total phosphorus, orthophosphate phosphorus, and total suspended solids were estimated for three watersheds of different sizes using a regression-based method and compared with loads computed by a method based on direct hydrologic and water quality observations. Statistically significant differences between the fluvial loads estimated by the two methods were observed in all cases. Using the direct method as the basis for comparison, the regression method was found to underpredict the annual fluvial load for the watersheds analyzed. A representative “magnitude-of-difference” measure was computed. The larger watershed (area > 104 km2) had a lower magnitude-of-difference compared to the two smaller watersheds (area ∼102 km2). The five constituents analyzed also had statistically significant effect on the magnitude-of-difference, with higher magnitude-of-difference observed for total suspended solids and total phosphorus compared to other parameters. For the watersheds analyzed, estimates for the magnitudes-of-difference obtained by long-term fluvial load analysis (15 years for larger, and 9 and 12 years for two smaller watersheds) may be evaluated by shorter-term comparisons. The time required to obtain a stable magnitude-of-difference was found to vary with the watershed size and the constituent of interest in the study watersheds. Although the results from this study represent the watersheds analyzed and are not likely to be directly applicable for other watersheds, the comparison between fluvial loads estimated by regression and intensive sampling may be applied to assess the applicability of the regression method in other watersheds.

[1] Assessment of constituent loads in rivers is essential to evaluate water quality of streams and estuaries; however, uncertainty in load estimation may be large and must be considered and communicated together with estimates. In this comparative study, the usefulness of two existing methods (bootstrap and Bayesian inference) to assess uncertainty in constituent loads estimated with an improved eight-parameter rating curve is demonstrated. Bootstrap prediction intervals and Bayesian credible intervals were estimated for daily and monthly loads obtained with a rating curve applied to routine monitoring sampling data sets of nitrate (NO3-N), reactive phosphorus (RP), and total phosphorus (TP) of the Duck River, in Tasmania (Australia). Predicted loads and prediction intervals were compared to benchmark loads obtained by an independent, high frequency monitoring program. The eight-parameter rating curve resulted in better prediction of NO3-N and TP than RP loads. Both inference methods successfully generated prediction intervals. The bracketing frequency (i.e., the fraction of prediction intervals that comprised benchmark loads) of bootstrap prediction intervals was 50–65% of daily or monthly benchmark loads. Bracketing frequency of Bayesian credible intervals was consistently higher, and included 74–85% of benchmark daily loads and 80% or more of benchmark monthly loads. Both methods proved to be robust to the presence of an artificial outlier. Prediction intervals were affected by the distribution of the regression error, hence they reflected uncertainty in the regression data set and limitations in the rating curve formulation. They did not account for other sources of uncertainty, i.e., they were still conservative predictions of load uncertainty.

We used the hydrochemical model GWLF to estimate terrestrial diffuse fluxes from ungauged areas of a coastal plain catchment, the Choptank River basin. The gauged area of the basin is 17% of the land surface, and we divided the remaining ungauged area into 21 subbasins. Three comparative approaches were used: (1) application of area yield coefficients based on 11 years of observations from the gauged area to extrapolate over ungauged subbasins without modeling, (2) application of GWLF to estimate export from all subbasins using model parameters calibrated in the gauged subbasin, and (3) application of GWLF with parameter adjustments based on the local characteristics in each subbasin. Comparison of the predicted export from 6 selected subbasins with observed export data showed that application of GWLF with local adjustments reduced model errors of N export from 43% to 27%. With only one adjustment for sediment P, application of GWLF alone reduced errors of P export from 92%to 40–45%, with or without local adjustments for flow and sediment retention. The data supported the hypothesis that significant spatial variations in N and P yields introduce large errors when extrapolating from gauged to ungauged subbasins, and estimated TN and TP yield coefficients varied over 1–21 kg N and 0.1–0.5 kg P ha−1 y−1 in ungauged areas due to varying human population densities, soil drainage characteristics, and amounts of agriculture. The most accurate estimates of terrestrial diffuse sources were combined with point source discharges and wet atmospheric inputs to estimate annual average inputs of 2.5 × 106 kg N and 5.8 × 104 kg P y−1 to the Choptank estuary during 1980–1996. These results illustrate the problems of spatial extrapolation from gauged to ungauged areas and emphasize the need for application of local characteristics for accurate assessment of watershed export.

We synthesize and update the science supporting the Action Plan for Reducing, Mitigating, and Controlling Hypoxia in the Northern Gulf of Mexico (Mississippi River/Gulf of Mexico Watershed Nutrient Task Force 2001) with a focus on the spatial and temporal discharge and patterns of nutrient and organic carbon delivery to the northern Gulf of Mexico, including data through 2006. The discharge of the Mississippi River watershed over 200 years varies but is not demonstrably increasing or decreasing. About 30% of the Mississippi River was shunted westward to form the Atchafalaya River, which redistributed water and nutrient loads on the shelf. Data on nitrogen concentrations from the early 1900s demonstrate that the seasonal and annual concentrations in the lower river have increased considerably since then, including a higher spring loading, following the increase in fertilizer applications after World WarII. The loading of total nitrogen (TN) fell from 1990 to 2006, but the loading of total phosphorus (TP) has risen slightly, resulting in a decline in the TN:TP ratios. The present TN:TP ratios hover around an average indicative of potential nitrogen limitation on phytoplankton growth, or balanced growth limitation, but not phosphorus limitation. The dissolved nitrogen:dissolved silicate ratios are near the Redfield ratio indicative of growth limitations on diatoms. Although nutrient concentrations are relatively high compared to those in many other large rivers, the water quality in the Mississippi River is not unique in that nutrient loads can be described by a variety of land-use models. There is no net removal of nitrogen from water flowing through the Atchafalaya basin, but the concentrations of TP and suspended sediments are lower at the exit point (Morgan City, Louisiana) than in the water entering the Atchafalaya basin. The removal of nutrients entering offshore waters through diversion of river water into wetlands is presently less than 1% of the total loadings going directly offshore, and would be less than 8% if the 10,093 km2 of coastal wetlands were successfully engineered for that purpose. Wetland loss is an insignificant contribution to the carbon loading offshore, compared to in situ marine production. The science-based conclusions in the Action Plan about nutrient loads and sources to the hypoxic zone off Louisiana are sustained by research and monitoring occurring in the subsequent 10 years.

We propose the use of Bayesian hierarchical/multilevel ratio approach to estimate the annual riverine phosphorus loads in the Saginaw River, Michigan, from 1968 to 2008. The ratio estimator is known to be an unbiased, precise approach for differing flow-concentration relationships and sampling schemes. A Bayesian model can explicitly address the uncertainty in prediction by using a posterior predictive distribution, while in comparison, a Bayesian hierarchical technique can overcome the limitation of interpreting the estimated annual loads inferred from small sample sizes by borrowing strength from the underlying population shared by the years of interest. Thus, by combining the ratio estimator with the Bayesian hierarchical modeling framework, long-term loads estimation can be addressed with explicit quantification of uncertainty. Our study results indicate a slight decrease in total phosphorus load early in the series. The estimated ratio parameter, which can be interpreted as flow-weighted concentration, shows a clearer decrease, damping the noise that yearly flow variation adds to the load. Despite the reductions, it is not likely that Saginaw Bay meets with its target phosphorus load, 440 tonnes/yr. Throughout the decades, the probabilities of the Saginaw Bay not complying with the target load are estimated as 1.00, 0.50, 0.57 and 0.36 in 1977, 1987, 1997, and 2007, respectively. We show that the Bayesian hierarchical model results in reasonable goodness-of-fits to the observations whether or not individual loads are aggregated. Also, this modeling approach can substantially reduce uncertainties associated with small sample sizes both in the estimated parameters and loads.

We present an overview of national water databases managed by the U.S. Geological Survey, including surface-water, groundwater, water-quality, and water-use data. These are readily accessible to users through web interfaces and data services. Multiple perspectives of data are provided, including search and retrieval of real-time data and historical data, on-demand current conditions and alert services, data compilations, spatial representations, analytical products, and availability of data across multiple agencies.

We modeled nutrient export in the ChoptankRiver Basin on the coastal plain of the Chesapeakedrainage, using a modified version of alumped-parameter, hydrochemical model (GWLF).Calibration was performed using long-term (WY1980–WY1990)hydrochemistry data from a gauged site. Thecalibrated model reproduced water yields, TN, and TPexport with cumulative errors of <1% over the11-year calibration period and with annual RMS errorsof 10–50%. Model validation was done withindependent measurements at the same gauged site(WY1991 to WY1996) and at another nearby independentlygauged site (WY1991 to WY1995). Local adjustment ofthe groundwater recession coefficient and thedissolved N concentration in agricultural stormflowwas essential for successful application at the secondsite. GWLF appears to be a useful model for estimationof fluxes of water, N and P from ungauged areas withaccuracies of 10–50% at annual time scales.

We investigate the sensitivity of phosphorus loading (mass/time) in an urban stream to variations in climate using nondimensional sensitivity, known as elasticity, methods commonly used by economists and hydrologists. Previous analyses have used bivariate elasticity methods to represent the general relationship between nutrient loading and a variable of interest, but such bivariate relations cannot reflect the complex multivariate nonlinear relationships inherent among nutrients, precipitation, temperature, and streamflow. Using fixed‐effect multivariate regression methods, we obtain two phosphorus models (nonparametric and parametric) for an urban stream with high explanatory power that can both estimate phosphorus loads and the elasticity of phosphorus loading to changes in precipitation, temperature, and streamflow. A case study demonstrates total phosphorus loading depends significantly on season, rainfall, combined sewer overflow events, and flow rate, yet the elasticity of total phosphorus to all these factors remains relatively constant throughout the year. The elasticity estimates reported here can be used to examine how nutrient loads may change under future climate conditions.

We describe a method for using spatially referenced regressions of contaminant transport on watershed attributes (SPARROW) in regional water-quality assessment. The method is designed to reduce the problems of data interpretation caused by sparse sampling, network bias, and basin heterogeneity. The regression equation relates measured transport rates in streams to spatially referenced descriptors of pollution sources and land-surface and stream-channel characteristics. Regression models of total phosphorus (TP) and total nitrogen (TN) transport are constructed for a region defined as the nontidal conterminous United States. Observed TN and TP transport rates are derived from water-quality records for 414 stations in the National Stream Quality Accounting Network. Nutrient sources identified in the equations include point sources, applied fertilizer, livestock waste, nonagricultural land, and atmospheric deposition (TN only). Surface characteristics found to be significant predictors of land-water delivery include soil permeability, stream density, and temperature (TN only). Estimated instream decay coefficients for the two contaminants decrease monotonically with increasing stream size. TP transport is found to be significantly reduced by reservoir retention. Spatial referencing of basin attributes in relation to the stream channel network greatly increases their statistical significance and model accuracy. The method is used to estimate the proportion of watersheds in the conterminous United States (i.e., hydrologic cataloging units) with outflow TP concentrations less than the criterion of 0.1 mg/L, and to classify cataloging units according to local TN yield (kg/km 2 /yr).

We consider estimating the total load from frequent flow data but less frequent concentration data. There are numerous load estimation methods available, some of which are captured in various online tools. However, most estimators are subject to large biases statistically, and their associated uncertainties are often not reported. This makes interpretation difficult and the estimation of trends or determination of optimal sampling regimes impossible to assess. In this paper, we first propose two indices for measuring the extent of sampling bias, and then provide steps for obtaining reliable load estimates that minimizes the biases and makes use of informative predictive variables. The key step to this approach is in the development of an appropriate predictive model for concentration. This is achieved using a generalized rating-curve approach with additional predictors that capture unique features in the flow data, such as the concept of the first flush, the location of the event on the hydrograph (e.g. rise or fall) and the discounted flow. The latter may be thought of as a measure of constituent exhaustion occurring during flood events. Forming this additional information can significantly improve the predictability of concentration, and ultimately the precision with which the pollutant load is estimated. We also provide a measure of the standard error of the load estimate which incorporates model, spatial and/or temporal errors. This method also has the capacity to incorporate measurement error incurred through the sampling of flow. We illustrate this approach for two rivers delivering to the Great Barrier Reef, Queensland, Australia. One is a data set from the Burdekin River, and consists of the total suspended sediment (TSS) and nitrogen oxide (NO(x)) and gauged flow for 1997. The other dataset is from the Tully River, for the period of July 2000 to June 2008. For NO(x) Burdekin, the new estimates are very similar to the ratio estimates even when there is no relationship between the concentration and the flow. However, for the Tully dataset, by incorporating the additional predictive variables namely the discounted flow and flow phases (rising or recessing), we substantially improved the model fit, and thus the certainty with which the load is estimated.

We analyzed an ensemble of watershed models that predict flow, nitrogen, and phosphorus discharges. The models differed in scope and complexity and used different input data, but all had been applied to evaluate human impacts on discharges to the Patuxent River or to the Chesapeake Bay. We compared predictions to observations of average annual, annual time series, and monthly discharge leaving three basins. No model consistently matched observed discharges better than the others, and predictions differed as much as 150% for every basin. Models that agreed best with the observations in one basin often were among the worst models for another material or basin. Combining model predictions into a model average improved overall reliability in matching observations, and the range of predictions helped describe uncertainty. The model average was not the closest to the observed discharge for every material, basin, and time frame, but the model average had the highest Nash–Sutcliffe performance across all combinations. Consistently poor performance in predicting phosphorus loads suggests that none of the models capture major controls. Differences among model predictions came from differences in model structures, input data, and the time period considered, and also to errors in the observed discharge. Ensemble watershed modeling helped identify research needs and quantify the uncertainties that should be considered when using the models in management decisions.

Water quality data may not be collected at a high frequency, nor over the range of streamflow data. For instance, water quality data are often collected monthly, biweekly, or weekly, since collecting and analyzing water quality samples are costly compared to streamflow data. Regression models are often used to interpolate pollutant loads from measurements made intermittently. Web-based Load Interpolation Tool (LOADIN) was developed to provide user-friendly interfaces and to allow use of streamflow and water quality data from U.S. Geological Survey (USGS) via web access. LOADIN has a regression model assuming that instantaneous load is comprised of the pollutant load based on streamflow and the pollutant load variation within the period. The regression model has eight coefficients determined by a genetic algorithm with measured water quality data. LOADIN was applied to eleven water quality datasets from USGS gage stations located in Illinois, Indiana, Michigan, Minnesota, and Wisconsin states with drainage areas from 44 km2 to 1,847,170 km2. Measured loads were calculated by multiplying nitrogen data by streamflow data associated with measured nitrogen data. The estimated nitrogen loads and measured loads were evaluated using Nash-Sutcliffe Efficiency (NSE) and coefficient of determination (R2). NSE ranged from 0.45 to 0.91, and R2 ranged from 0.51 to 0.91 for nitrogen load estimation.

To better understand the transfer of particulate organic matter (POM) by small mountainous river systems (SMRS) to the ocean, we measured the concentration and composition of suspended particles from the Alsea River, a SMRS in the Oregon Coast Range, over a wide range of discharges that included several floods. All particulate constituents measured, including organic carbon, nitrogen and biomarkers such as lignin-derived phenols, cutin acids and amino acid-derived products, displayed concentrations that increased as a power function of discharge. In contrast to other SMRS, virtually all POM in the Alsea River samples was modern and had an average age <60 year. In spite of their similar 14C ages, marked contrasts in elemental and biomarker compositions were evident in particles collected at low and high discharges. Particles at low flows were primarily composed of organic detritus from non-vegetation sources (e.g., algal cells) whereas mineral-rich particles containing vegetation and soil-derived POM were predominant at elevated flows. Biomarker compositions of these latter particles suggest most of the POM originated from areas if the watershed with measurable hardwood contributions, which include areas affected by shallow landslides and riparian zones. We infer that the low uplift rates, lush vegetation, high net primary production and relatively thick soils that characterize the Alsea watershed are responsible for these trends. Comparison of our results with those from other systems, including the well-studied Santa Clara River (southern California), demonstrates that SMRS are part of a continuum whereby contrasts in hydroclimate, geology and vegetation lead to significant differences in the age and composition of POM exported to the ocean.

Ths report addresses the following two questions: 1) What are the loads (flux) of nutrients transported from the Mississippi-Atchafalaya River Basin to the Gulf of Mexico, and where do they come from within the basin? 2) What is the relative importance of specific human activities, such as agriculture, point-source discharges, and atmospheric deposition in contributing to these loads? These questions were addressed by first estimating the flux of nutrients from the Mississippi-Atchafalaya River Basin and about 50 interior basins in the Mississippi River system using measured historical streamflow and water quality data. Annual nutrient inputs and outputs to each basin were estimated using data from the National Agricultural Statistics Service, National Atmospheric Deposition Program, and point-source data provided by the USEPA. Next, a nitrogen mass balance was developed using agricultural statistics, estimates of nutrient cycling in agricultural systems, and a geographic information system. Finally, multiple regression models were developed to estimate the relative contributions of the major input sources to the flux of nitrogen and phosphorus to the Gulf of Mexico.