Stacey A. Archfield

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

A bootstrap method for estimating uncertainty of water quality trends

Estimation of the direction and magnitude of trends in surface water quality remains a problem of great scientific and practical interest. The Weighted Regressions on Time, Discharge, and Season (WRTDS) method was recently introduced as an exploratory data analysis tool to provide flexible and robust estimates of water quality trends. This paper enhances the WRTDS method through the introduction of the WRTDS Bootstrap Test (WBT), an extension of WRTDS that quantifies the uncertainty in WRTDS-estimates of water quality trends and offers various ways to visualize and communicate these uncertainties. Monte Carlo experiments are applied to estimate the Type I error probabilities for this method. WBT is compared to other water-quality trend-testing methods appropriate for data sets of one to three decades in length with sampling frequencies of 6-24 observations per year. The software to conduct the test is in the EGRETci R-package. Display Omitted Block bootstrap approach for water quality trends is developed.Used in conjunction with a flexible statistical model for river water quality.Trends in concentration and trends in flux can be evaluated.Confidence intervals can be estimated for trend magnitude.Based on WRTDS: Weighted Regressions on Time, Discharge, and Season.

Accelerating advances in continental domain hydrologic modeling

In the past, hydrologic modeling of surface water resources has mainly focused on simulating the hydrologic cycle at local to regional catchment modeling domains. There now exists a level of maturity among the catchment, global water security, and land surface modeling communities such that these communities are converging toward continental domain hydrologic models. This commentary, written from a catchment hydrology community perspective, provides a review of progress in each community toward this achievement, identifies common challenges the communities face, and details immediate and specific areas in which these communities can mutually benefit one another from the convergence of their research perspectives. Those include: (1) creating new incentives and infrastructure to report and share model inputs, outputs, and parameters in data services and open access, machine-independent formats for model replication or reanalysis; (2) ensuring that hydrologic models have: sufficient complexity to represent the dominant physical processes and adequate representation of anthropogenic impacts on the terrestrial water cycle, a process-based approach to model parameter estimation, and appropriate parameterizations to represent large-scale fluxes and scaling behavior; (3) maintaining a balance between model complexity and data availability as well as uncertainties; and (4) quantifying and communicating significant advancements toward these modeling goals.

Fragmented patterns of flood change across the United States.

Abstract Trends in the peak magnitude, frequency, duration, and volume of frequent floods (floods occurring at an average of two events per year relative to a base period) across the United States show large changes; however, few trends are found to be statistically significant. The multidimensional behavior of flood change across the United States can be described by four distinct groups, with streamgages experiencing (1) minimal change, (2) increasing frequency, (3) decreasing frequency, or (4) increases in all flood properties. Yet group membership shows only weak geographic cohesion. Lack of geographic cohesion is further demonstrated by weak correlations between the temporal patterns of flood change and large‐scale climate indices. These findings reveal a complex, fragmented pattern of flood change that, therefore, clouds the ability to make meaningful generalizations about flood change across the United States.

Estimation of Flow-Duration Curves at Ungaged Sites in Southern New England

Two sets of regional-regression equations are developed to estimate the daily, unregulated, period-of-record flow duration curve (FDC) at ungaged sites in southern New England. The first method assumes an underlying probability density function (pdf) for daily streamflow whose parameter values are related to the physical characteristics of the ungaged basin. The second method relates flow at selected exceedence probabilities on the FDC to physical characteristics of the ungaged basin. We consider 66 relatively unregulated gages having between 10 and 86 years of continuous, daily-streamflow measurements. A jack-knife procedure is used to compare FDCs estimated from each method to the gage data from which the regression equations were developed. FDC estimates from regression equations developed for individual exceedences led to lower mean square errors than estimates of FDCs that assumed an underlying pdf. L-moment diagrams, probability plots and simulation experiments reveal that daily streamflow are well approximated by a kappa distribution. The first four L-moments are highly correlated with each other, which were used to improve estimates of FDCs based on a regional kappa distribution.

On the probability distribution of daily streamflow in the United States

Abstract. Daily streamflows are often represented by flow duration curves (FDCs), which illustrate the frequency with which flows are equaled or exceeded. FDCs have had broad applications across both operational and research hydrology for decades; however, modeling FDCs has proven elusive. Daily streamflow is a complex time series with flow values ranging over many orders of magnitude. The identification of a probability distribution that can approximate daily streamflow would improve understanding of the behavior of daily flows and the ability to estimate FDCs at ungaged river locations. Comparisons of modeled and empirical FDCs at nearly 400 unregulated, perennial streams illustrate that the four-parameter kappa distribution provides a very good representation of daily streamflow across the majority of physiographic regions in the conterminous United States (US). Further, for some regions of the US, the three-parameter generalized Pareto and lognormal distributions also provide a good approximation to FDCs. Similar results are found for the period of record FDCs, representing the long-term hydrologic regime at a site, and median annual FDCs, representing the behavior of flows in a typical year.

Computing daily mean streamflow at ungaged locations in Iowa by using the Flow Anywhere and Flow Duration Curve Transfer statistical methods

The U.S. Geological Survey (USGS) maintains approximately 148 real-time streamgages in Iowa for which daily mean streamflow information is available, but daily mean streamflow data commonly are needed at locations where no streamgages are present. Therefore, the USGS conducted a study as part of a larger project in cooperation with the Iowa Department of Natural Resources to develop methods to estimate daily mean streamflow at locations in ungaged watersheds in Iowa by using two regression-based statistical methods. The regression equations for the statistical methods were developed from historical daily mean streamflow and basin characteristics from streamgages within the study area, which includes the entire State of Iowa and adjacent areas within a 50-mile buffer of Iowa in neighboring states. Results of this study can be used with other techniques to determine the best method for application in Iowa and can be used to produce a Web-based geographic information system tool to compute streamflow estimates automatically. The Flow Anywhere statistical method is a variation of the drainage-area-ratio method, which transfers sameday streamflow information from a reference streamgage to another location by using the daily mean streamflow at the reference streamgage and the drainage-area ratio of the two locations. The Flow Anywhere method modifies the drainage-arearatio method in order to regionalize the equations for Iowa and determine the best reference streamgage from which to transfer same-day streamflow information to an ungaged location. Data used for the Flow Anywhere method were retrieved for 123 continuous-record streamgages located in Iowa and within a 50-mile buffer of Iowa. The final regression equations were computed by using either left-censored regression techniques with a low limit threshold set at 0.1 cubic feet per second (ft3/s) and the daily mean streamflow for the 15th day of every other month, or by using an ordinary-least-squares multiple linear regression method and the daily mean streamflow for the 15th day of every other month. The Flow Duration Curve Transfer method was used to estimate unregulated daily mean streamflow from the physical and climatic characteristics of gaged basins. For the Flow Duration Curve Transfer method, daily mean streamflow quantiles at the ungaged site were estimated with the parameterbased regression model, which results in a continuous daily flow-duration curve (the relation between exceedance probability and streamflow for each day of observed streamflow) at the ungaged site. By the use of a reference streamgage, the Flow Duration Curve Transfer is converted to a time series. Data used in the Flow Duration Curve Transfer method were retrieved for 113 continuous-record streamgages in Iowa and within a 50-mile buffer of Iowa. The final statewide regression equations for Iowa were computed by using a weighted-leastsquares multiple linear regression method and were computed for the 0.01-, 0.05-, 0.10-, 0.15-, 0.20-, 0.30-, 0.40-, 0.50-, 0.60-, 0.70-, 0.80-, 0.85-, 0.90-, and 0.95-exceedance probability statistics determined from the daily mean streamflow with a reporting limit set at 0.1 ft3/s. The final statewide regression equation for Iowa computed by using left-censored regression techniques was computed for the 0.99-exceedance probability statistic determined from the daily mean streamflow with a low limit threshold and a reporting limit set at 0.1 ft3/s. For the Flow Anywhere method, results of the validation study conducted by using six streamgages show that differences between the root-mean-square error and the mean absolute error ranged from 1,016 to 138 ft3/s, with the larger value signifying a greater occurrence of outliers between observed and estimated streamflows. Root-mean-square-error values ranged from 1,690 to 237 ft3/s. Values of the percent rootmean-square error ranged from 115 percent to 26.2 percent. The logarithm (base 10) streamflow percent root-mean-square error ranged from 13.0 to 5.3 percent. Root-mean-square-error observations standard-deviation-ratio values ranged from 0.80 to 0.40. Percent-bias values ranged from 25.4 to 4.0 percent. Untransformed streamflow Nash-Sutcliffe efficiency values ranged from 0.84 to 0.35. The logarithm (base 10) streamflow Nash-Sutcliffe efficiency values ranged from 0.86 to 0.56. For the streamgage with the best agreement between observed and estimated streamflow, higher streamflows appear to be underestimated. For the streamgage with the worst agreement between observed and estimated streamflow, low flows appear to be overestimated whereas higher flows seem to be 2 Computing Daily Mean Streamflow at Ungaged Locations in Iowa by using Flow Statistical Methods underestimated. Estimated cumulative streamflows for the period October 1, 2004, to September 30, 2009, are underestimated by -25.8 and -7.4 percent for the closest and poorest comparisons, respectively. For the Flow Duration Curve Transfer method, results of the validation study conducted by using the same six streamgages show that differences between the root-meansquare error and the mean absolute error ranged from 437 to 93.9 ft3/s, with the larger value signifying a greater occurrence of outliers between observed and estimated streamflows. Root-mean-square-error values ranged from 906 to 169 ft3/s. Values of the percent root-mean-square-error ranged from 67.0 to 25.6 percent. The logarithm (base 10) streamflow percent root-mean-square error ranged from 12.5 to 4.4 percent. Root-mean-square-error observations standard-deviation-ratio values ranged from 0.79 to 0.40. Percent-bias values ranged from 22.7 to 0.94 percent. Untransformed streamflow NashSutcliffe efficiency values ranged from 0.84 to 0.38. The logarithm (base 10) streamflow Nash-Sutcliffe efficiency values ranged from 0.89 to 0.48. For the streamgage with the closest agreement between observed and estimated streamflow, there is relatively good agreement between observed and estimated streamflows. For the streamgage with the poorest agreement between observed and estimated streamflow, streamflows appear to be substantially underestimated for much of the time period. Estimated cumulative streamflow for the period October 1, 2004, to September 30, 2009, are underestimated by -9.3 and -22.7 percent for the closest and poorest comparisons, respectively.

A Decision-Support System to Assess Surface-Water Resources in Massachusetts

Federal, State and local water supply, regulatory, and planning agencies require easy-touse, technically-defensible, decision-support (DS) applications that can evaluate impacts of proposed water withdrawals, determine baseline streamflow conditions needed for sustainability of aquatic habitat, and estimate inflows to drinking-water-supply reservoirs for safe yield analyses at ungaged locations. An interactive, point-and-click DS application is developed in combination with a geographic-information system to address these needs. The DS application estimates unimpacted daily streamflow at any user-selected location – gaged or ungaged -on a perennial stream in Massachusetts. A new method is proposed to estimate a daily flow-duration curve at an ungaged site by exploiting the strong structural relationship among streamflow quantiles. This method offers improvement -particularly for low flows -over traditional regression-based approaches that relate flows at selected flow quantiles to measurable basin characteristics. A time series of daily flows is then created by transferring the timing of the daily flows at an index gage to the ungaged site at equivalent exceedance probabilities. Estimated daily streamflows show remarkably good agreement with observed daily flows and are generally comparable to the agreement obtained from a calibrated rainfall-runoff model. A jack-knife cross-validation experiment indicates that the agreement between observed and estimated flow series at an ungaged site is also remarkably good.

Panel regressions to estimate low‐flow response to rainfall variability in ungaged basins

Multicollinearity and omitted-variable bias are major limitations to developing multiple linear regression models to estimate streamflow characteristics in ungaged areas and varying rainfall conditions. Panel regression is used to overcome limitations of traditional regression methods, and obtain reliable model coefficients, in particular to understand the elasticity of streamflow to rainfall. Using annual rainfall and selected basin characteristics at 86 gaged streams in the Hawaiian Islands, regional regression models for three stream classes were developed to estimate the annual low-flow duration discharges. Three panel-regression structures (random effects, fixed effects, and pooled) were compared to traditional regression methods, in which space is substituted for time. Results indicated that panel regression generally was able to reproduce the temporal behavior of streamflow and reduce the standard errors of model coefficients compared to traditional regression, even for models in which the unobserved heterogeneity between streams is significant and the variance inflation factor for rainfall is much greater than 10. This is because both spatial and temporal variability were better characterized in panel regression. In a case study, regional rainfall elasticities estimated from panel regressions were applied to ungaged basins on Maui, using available rainfall projections to estimate plausible changes in surface-water availability and usable stream habitat for native species. The presented panel-regression framework is shown to offer benefits over existing traditional hydrologic regression methods for developing robust regional relations to investigate streamflow response in a changing climate. This article is protected by copyright. All rights reserved.

Reliability of reservoir firm yield determined from the historical drought of record

The firm yield of a reservoir is typically defined as the maximum yield that could have been delivered without failure during the historical drought of record. In the future, reservoirs will experience droughts that are either more or less severe than the historical drought of record. The question addressed here is what the reliability of such systems will be when operated at the firm yield. To address this question, we examine the reliability of 25 hypothetical reservoirs sited across five locations in the central and western United States. These locations provided a continuous 756-month streamflow record spanning the same time interval. The firm yield of each reservoir was estimated from the historical drought of record at each location. To determine the steady-state monthly reliability of each firm-yield estimate, 12,000-month synthetic records were generated using the moving-blocks bootstrap method. Bootstrapping was repeated 100 times for each reservoir to obtain an average steady-state monthly reliability R, the number of months the reservoir did not fail divided by the total months. Values of R were greater than 0.99 for 60 percent of the study reservoirs; the other 40 percent ranged from 0.95 to 0.98. Estimates of R were highly correlated with both the level of development (ratio of firm yield to average streamflow) and average lag-1 monthly autocorrelation. Together these two predictors explained 92 percent of the variability in R, with the level of development alone explaining 85 percent of the variability.