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Application of a Weighted Regression Model for Reporting Nutrient and Sediment Concentrations, Fluxes, and Trends in Concentration and Flux for the Chesapeake Bay Nontidal Water-Quality Monitoring Network, Results Through Water Year 2012

January 13, 2016

In the Chesapeake Bay watershed, estimated fluxes of nutrients and sediment from the bay’s nontidal tributaries into the estuary are the foundation of decision making to meet reductions prescribed by the Chesapeake Bay Total Maximum Daily Load (TMDL) and are often the basis for refining scientific understanding of the watershed-scale processes that influence the delivery of these constituents to the bay. Two regression-based flux and trend estimation models, ESTIMATOR and Weighted Regressions on Time, Discharge, and Season (WRTDS), were compared using data from 80 watersheds in the Chesapeake Bay Nontidal Water-Quality Monitoring Network (CBNTN). The watersheds range in size from 62 to 70,189 square kilometers and record lengths range from 6 to 28 years. ESTIMATOR is a constant-parameter model that estimates trends only in concentration; WRTDS uses variable parameters estimated with weighted regression, and estimates trends in both concentration and flux. WRTDS had greater explanatory power than ESTIMATOR, with the greatest degree of improvement evident for records longer than 25 years (30 stations; improvement in median model R2= 0.06 for total nitrogen, 0.08 for total phosphorus, and 0.05 for sediment) and the least degree of improvement for records of less than 10 years, for which the two models performed nearly equally. Flux bias statistics were comparable or lower (more favorable) for WRTDS for any record length; for 30 stations with records longer than 25 years, the greatest degree of improvement was evident for sediment (decrease of 0.17 in median statistic) and total phosphorus (decrease of 0.05). The overall between-station pattern in concentration trend direction and magnitude for all constituents was roughly similar for both models. A detailed case study revealed that trends in concentration estimated by WRTDS can operationally be viewed as a less-constrained equivalent to trends in concentration estimated by ESTIMATOR. Estimates of annual mean flow-adjusted (ESTIMATOR) and flow-normalized (WRTDS) concentration for years initially constituting the end of a water-quality record showed a similar degree of variability as data for additional years were incrementally added and the initial estimates “aged.” On the basis of the results of this broad comparison of the two models, the U.S. Geological Survey is adopting WRTDS as the primary model for estimating constituent fluxes and trends throughout the CBNTN. Nutrient and sediment flux and trend estimates, based on WRTDS, are summarized narratively and tabulated in appendixes for all stations for which fluxes or trends were reported through water year 2012.

WRTDS also was used to explore the sensitivity of flux and trend estimates to three data-quality issues common in many large-scale monitoring networks and evident in some of the CBNTN records. The potential effects of inconsistency in annual sampling effort and inconsistency in storm sampling effort were explored by way of a subsampling experiment using eight of the most densely sampled long-term (1985–2012) stations in the CBNTN as baseline datasets. From each dataset, a set of 10 “design guideline” subsamples was selected, consisting of 12 monthly samples and 8 targeted storm samples per year. The selection was conducted in a manner that preserved the overall intensity of storm sampling in the baseline data. These 10 subsamples were further manipulated to create “heterogeneous” subsamples by removing storm samples prior to 2003. The maximum relative difference between flow-normalized flux estimated in a single year from any of the 10 design guideline subsamples and values estimated in the corresponding year from baseline data was smallest for dissolved inorganic nitrogen (median of 8 stations = 6 percent of baseline estimate), but more appreciable for total phosphorus and sediment (medians of 22 and 32 percent, respectively). The maximum relative difference between flow-normalized flux estimated from from the 10 heterogeneous subsamples and values estimated in the corresponding year from baseline data was more pronounced, with medians for 8 stations of 15, 30, and 53 percent of the corresponding baseline estimates for dissolved inorganic nitrogen, total phosphorus, and sediment, respectively. The worst-case maximum relative differences between flow-normalize flux estimated in a single year from the 10 heterogeneous subsamples and values estimated in the corresponding year from baseline data were 25 percent for dissolved inorganic nitrogen, 37 percent for total phosphorus, and 250 percent for sediment. The results for the heterogeneous subsamples indicate that changes in storm sampling frequency can result in appreciable distortion of estimated trends in flow-normalized flux, especially for total phosphorus and sediment. Trend lines estimated from heterogeneous subsamples tended to converge with the trend lines estimated from baseline data after 2003. In contrast, 2003–12 trends based on subsamples truncated by discarding all data prior to the induced heterogeneity in 2003 showed appreciable biases and differences in slope, relative to the corresponding 2003–12 segment of the trend computed from the design guideline subsamples. Overall, the results indicate that for particulate constituents, load and trend estimates computed using long-term records recently converted to CBNTN design guideline sampling protocols will be most reliable if the trend is computed using the entire record, but reported only for the period that design guideline sampling protocols were followed.

Inconsistencies related to changing laboratory methods were also examined via two manipulative experiments. In the first experiment, increasing and decreasing “stair-step” patterns of changes in censoring level, overall representing a factor-of-five change in the laboratory reporting limit, were artificially imposed on a 27-year record with no censoring and a period-of-record concentration trend of –68.4 percent. Trends estimated on the basis of the manipulated records were broadly similar to the original trend (–63.6 percent for decreasing censoring levels and –70.3 percent for increasing censoring levels), lending a degree of confidence that the survival regression routines upon which WRTDS is based are generally robust to data censoring. The second experiment considered an abrupt disappearance of low-concentration observations of total phosphorus, associated with a laboratory method change and not reflected through censoring, near the middle of a 28-year record. By process of elimination, an upward shift in the estimated flow-normalize concentration trend line around the same time was identified as a likely artifact resulting from the laboratory method change, although a contemporaneous change in watershed processes cannot be ruled out. Decisions as to how to treat records with potential sampling protocol or laboratory methods-related artifacts should be made on a case-by-case basis, and trend results should be appropriately qualified.

Citation Information

Publication Year 2016
Title Application of a Weighted Regression Model for Reporting Nutrient and Sediment Concentrations, Fluxes, and Trends in Concentration and Flux for the Chesapeake Bay Nontidal Water-Quality Monitoring Network, Results Through Water Year 2012
DOI 10.3133/sir20155133
Authors Jeffrey G. Chanat, Douglas L. Moyer, Joel D. Blomquist, Kenneth E. Hyer, Michael J. Langland
Publication Type Report
Publication Subtype USGS Numbered Series
Series Title Scientific Investigations Report
Series Number 2015-5133
Index ID sir20155133
Record Source USGS Publications Warehouse
USGS Organization Virginia Water Science Center