Douglas Moyer

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

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. 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

Comparison of two regression-based approaches for determining nutrient and sediment fluxes and trends in the Chesapeake Bay watershed

Nutrient and sediment fluxes and changes in fluxes over time are key indicators that water resource managers can use to assess the progress being made in improving the structure and function of the Chesapeake Bay ecosystem. The U.S. Geological Survey collects annual nutrient (nitrogen and phosphorus) and sediment flux data and computes trends that describe the extent to which water-quality conditions are changing within the major Chesapeake Bay tributaries. Two regression-based approaches were compared for estimating annual nutrient and sediment fluxes and for characterizing how these annual fluxes are changing over time. The two regression models compared are the traditionally used ESTIMATOR and the newly developed Weighted Regression on Time, Discharge, and Season (WRTDS). The model comparison focused on answering three questions: (1) What are the differences between the functional form and construction of each model? (2) Which model produces estimates of flux with the greatest accuracy and least amount of bias? (3) How different would the historical estimates of annual flux be if WRTDS had been used instead of ESTIMATOR? One additional point of comparison between the two models is how each model determines trends in annual flux once the year-to-year variations in discharge have been determined. All comparisons were made using total nitrogen, nitrate, total phosphorus, orthophosphorus, and suspended-sediment concentration data collected at the nine U.S. Geological Survey River Input Monitoring stations located on the Susquehanna, Potomac, James, Rappahannock, Appomattox, Pamunkey, Mattaponi, Patuxent, and Choptank Rivers in the Chesapeake Bay watershed. Two model characteristics that uniquely distinguish ESTIMATOR and WRTDS are the fundamental model form and the determination of model coefficients. ESTIMATOR and WRTDS both predict water-quality constituent concentration by developing a linear relation between the natural logarithm of observed constituent concentration and three explanatory variables—the natural log of discharge, time, and season. ESTIMATOR uses two additional explanatory variables— the square of the log of discharge and time-squared. Both models determine coefficients for variables for a series of estimation windows. ESTIMATOR establishes variable coefficients for a series of 9-year moving windows; all observed constituent concentration data within the 9-year window are used to establish each coefficient. Conversely, WRTDS establishes variable coefficients for each combination of discharge and time using only observed concentration data that are similar in time, season, and discharge to the day being estimated. As a result of these distinguishing characteristics, ESTIMATOR reproduces concentration-discharge relations that are closely approximated by a quadratic or linear function with respect to both the log of discharge and time. Conversely, the linear model form of WRTDS coupled with extensive model windowing for each combination of discharge and time allows WRTDS to reproduce observed concentration-discharge relations that are more sinuous in form. Another distinction between ESTIMATOR and WRTDS is the reporting of uncertainty associated with the model estimates of flux and trend. ESTIMATOR quantifies the standard error of prediction associated with the determination of flux and trends. The standard error of prediction enables the determination of the 95-percent confidence intervals for flux and trend as well as the ability to test whether the reported trend is significantly different from zero (where zero equals no trend). Conversely, WRTDS is unable to propagate error through the many (over 5,000) models for unique combinations of flow and time to determine a total standard error. As a result, WRTDS flux estimates are not reported with confidence intervals and a level of significance is not determined for flow-normalized fluxes. 2 Comparison of Two Regression-Based Approaches for Determining Nutrient and Sediment Fluxes and Trends The differences between ESTIMATOR and WRTDS, with regard to model form and determination of model coefficients, have an influence on the determination of nutrient and sediment fluxes and associated changes in flux over time as a result of management activities. The comparison between the model estimates of flux and trend was made for combinations of five water-quality constituents at nine River Input Monitoring stations. The major findings with regard to nutrient and sediment fluxes are as follows: (1) WRTDS produced estimates of flux for all combinations that were more accurate, based on reduction in root mean squared error, than flux estimates from ESTIMATOR; (2) for 67 percent of the combinations, WRTDS and ESTIMATOR both produced estimates of flux that were minimally biased compared to observed fluxes (flux bias = tendency to over or underpredict flux observations); however, for 33 percent of the combinations, WRTDS produced estimates of flux that were considerably less biased (by at least 10 percent) than flux estimates from ESTIMATOR; (3) the average percent difference in annual fluxes generated by ESTIMATOR and WRTDS was less than 10 percent at 80 percent of the combinations; and (4) the greatest differences related to flux bias and annual fluxes all occurred for combinations where the pattern in observed concentrationdischarge relation was sinuous (two points of inflection) rather than linear or quadratic (zero or one point of inflection). The major findings with regard to trends are as follows: (1) both models produce water-quality trends that have factored in the year-to-year variations in flow; (2) trends in water-quality condition are represented by ESTIMATOR as a trend in flow-adjusted concentration and by WRTDS as a flownormalized flux; (3) for 67 percent of the combinations with trend estimates, the WRTDS trends in flow-normalized flux are in the same direction and magnitude to the ESTIMATOR trends in flow-adjusted concentration, and at the remaining 33 percent the differences in trend magnitude and direction are related to fundamental differences between concentration and flux; and (4) the majority (85 percent) of the total nitrogen, nitrate, and orthophosphorus combinations exhibited longterm (1985 to 2010) trends in WRTDS flow-normalized flux that indicate improvement or reduction in associated flux and the majority (83 percent) of the total phosphorus (from 1985 to 2010) and suspended sediment (from 2001 to 2010) combinations exhibited trends in WRTDS flow-normalized flux that indicate degradation or increases in the flux delivered. Introduction Excessive nutrient (nitrogen and phosphorus) and sediment transport to the Chesapeake Bay from the watershed is detrimental to the overall structure and function of the bay ecosystem and is a major concern for local, State, and Federal entities that benefit from and work to protect the living resources of the bay. The flux (also called load) of nutrients to the Chesapeake Bay is in part natural but has been accelerated as a result of anthropogenic inputs of these nutrients through sewage disposal, agricultural runoff, urban runoff, and acid rain (Officer and others, 1984; Nixon, 1987; Schlesinger, 1997). Accelerated eutrophication through excessive nutrient flux has been linked to the loss of critical habitat for living resources within the Chesapeake Bay estuary (U.S. Environmental Protection Agency, 1983). Cooper and Brush (1991) found that accelerated algal production resulting from elevated nutrient fluxes has led to an increased occurrence of anoxic conditions in bottom waters and associated sediment throughout the Chesapeake Bay estuary. Similarly, the flux of sediment to the Chesapeake Bay results from both natural processes associated with upland erosion, lateral movement of channels into streambanks, and downcutting of streambeds (Waters, 1995) as well as anthropogenic processes such as agriculture, logging, mining, and urbanization. Anthropogenically derived sediment can overwhelm the natural assimilative capacity of the aquatic system (Cairns, 1977) and may bury filter-feeding organisms, reduce habitat available for macroinvertebrates, contribute to decreased fish populations, and impair growth of aquatic vegetation by reducing available light (Lenat and others, 1981; Dennison and others, 1993; Box and Mossa, 1999; Madsen and others, 2001). The Chesapeake Bay Program (CBP) was initiated in 1983 to direct the restoration and protection of the Chesapeake Bay. The CBP is composed of various Federal, State, academic, and local watershed organizations. In 1987, the CBP established its first nutrient reduction goal, which was to reduce nitrogen and phosphorus fluxes to the Chesapeake Bay. In 2000, the CBP recommitted to achieve the nutrient and sediment reduction goals established in 1987and established criteria for dissolved oxygen, chlorophyll, and water clarity (Chesapeake Bay Program, 2000). Despite extensive restoration efforts made by the CBP, however, established waterquality goals were not being obtained for the Chesapeake Bay and associated tributaries (Chesapeake Bay Foundation, 2010). As a result, in 2010, the U.S. Environmental Protection Agency (USEPA) established the Chesapeake Bay total maximum daily load (TMDL) for nitrogen, phosphorus, and sediment (U.S. Environmental Protection Agency, 2010). This TMDL assigns accountability for nutrient and sediment fluxes to New York, Pennsylvania, Maryland, Delaware, Virginia, West Virginia, and the District of Columbia and serves as a catalyst for rigorous implementation of management actions to mitigate the transport of excessive nutrients and sediment to the Chesapeake Bay and tidal estuaries. Since the early 1990s, the U.S. Geological Survey (USGS), in cooperation with the Virginia Department of Environmental Quality (VADEQ) and the Maryland Department of Natural Resources (MDDNR), has been responsible for monitoring nutrient and sedime

Decadal-scale export of nitrogen, phosphorus, and sediment from the Susquehanna River basin, USA: Analysis and synthesis of temporal and spatial patterns

The export of nitrogen (N), phosphorus (P), and suspended sediment (SS) is a long-standing management concern for the Chesapeake Bay watershed, USA. Here we present a comprehensive evaluation of nutrient and sediment loads over the last three decades at multiple locations in the Susquehanna River basin (SRB), Chesapeakes largest tributary watershed. Sediment and nutrient riverine loadings, including both dissolved and particulate fractions, have generally declined at all sites upstream of Conowingo Dam (non-tidal SRB outlet). Period-of-record declines in riverine yield are generally smaller than those in source input, suggesting the possibility of legacy contributions. Consistent with other watershed studies, these results reinforce the importance of considering lag time between the implementation of management actions and achievement of river quality improvement. Whereas flow-normalized loadings for particulate species have increased recently below Conowingo Reservoir, those for upstream sites have declined, thus substantiating conclusions from prior studies about decreased reservoir trapping efficiency. In regard to streamflow effects, statistically significant log-linear relationships between annual streamflow and annual constituent load suggest the dominance of hydrological control on the inter-annual variability of constituent export. Concentration-discharge relationships revealed general chemostasis and mobilization effects for dissolved and particulate species, respectively, both suggesting transport-limitation conditions. In addition to affecting annual export rates, streamflow has also modulated the relative importance of dissolved and particulate fractions, as reflected by its negative correlations with dissolved P/total P, dissolved N/total N, particulate P/SS, and total N/total P ratios. For land-use effects, period-of-record median annual yields of N, P, and SS all correlate positively with the area fraction of non-forested land but negatively with that of forested land under all hydrological conditions. Overall, this work has informed understanding with respect to four major factors affecting constituent export (i.e., source input, reservoir modulation, streamflow, and land use) and demonstrated the value of long-term river monitoring.

Riverine discharges to Chesapeake Bay: Analysis of long-term (1927–2014) records and implications for future flows in the Chesapeake Bay basin

The Chesapeake Bay (CB) basin is under a total maximum daily load (TMDL) mandate to reduce nitrogen, phosphorus, and sediment loads to the bay. Identifying shifts in the hydro-climatic regime may help explain observed trends in water quality. To identify potential shifts, hydrologic data (1927-2014) for 27 watersheds in the CB basin were analyzed to determine the relationships among long-term precipitation and stream discharge trends. The amount, frequency, and intensity of precipitation increased from 1910 to 1996 in the eastern U.S., with the observed increases greater in the northeastern U.S. than the southeastern U.S. The CB watershed spans the north-to-south gradient in precipitation increases, and hydrologic differences have been observed in watersheds north relative to watersheds south of the Pennsylvania-Maryland (PA-MD) border. Time series of monthly mean precipitation data specific to each of 27 watersheds were derived from the Precipitation-elevation Regression on Independent Slopes Model (PRISM) dataset, and monthly mean stream-discharge data were obtained from U.S. Geological Survey streamgage records. All annual precipitation trend slopes in the 18 watersheds north of the PA-MD border were greater than or equal to those of the nine south of that border. The magnitude of the trend slopes for 1927-2014 in both precipitation and discharge decreased in a north-to-south pattern. Distributions of the monthly precipitation and discharge datasets were assembled into percentiles for each year for each watershed. Multivariate correlation of precipitation and discharge within percentiles among the groups of northern and southern watersheds indicated only weak associations. Regional-scale average behaviors of trends in the distribution of precipitation and discharge annual percentiles differed between the northern and southern watersheds. In general, the linkage between precipitation and discharge was weak, with the linkage weaker in the northern watersheds compared to those in the south. On the basis of simple linear regression, 26 of the 27 watersheds are projected to have higher annual mean discharge in 2025, the target date for implementation of the TMDL for the CB basin.