Some of the characteristics that complicate the analysis of water quality time series are non-normal distributions, seasonality, flow relatedness, missing values, values below the limit of detection, and serial correlation. Presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonic trends. The first procedure described is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported ag 'less than': the seasonal Kendall test. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation), it is robust in comparison to parametric alternatives, although neither the seasonal Kendall test nor the alternatives can be considered an exact test in the presence of serial correlation. The second procedure, the seasonal Kendall slope estimator, is an estimator of trend magnitude. It is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal. The third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow, thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed (e.g., drought effects). In this method a flow-adjusted concentration is defined as the residual (actual minus conditional expectation) based on a regression of concentration on some function of discharge. These flow-adjusted concentrations, which may also be seasonal and non-normal, can then be tested for trend by using the seasonal Kendall test. This paper is not subject to U.S. Similarly, the presence of values reported as less than the limit of detection presents no problems for the first of the three techniques.Meaningful interpretation of the results of these analyses depends on the data collection practices. These techniques are only appropriate for data collected by systematic sampling at a monthly frequency, although stratified random sampling data (with monthly strata) would also be suitable. If the results are to be interpreted as applying to the entire cross section at the station, the water sample must be vertically and horizontally integrated. It is also most important that consistent field and laboratory procedures be used at all times. The achievement of this goal depends on documentation of procedures, training of personnel, and a vigorous program of quality assurance in all phases of the data collection process. Another highly desirable feature is the collection of ancillary data such as time of day, water temperature, and discharge at the time of sample collection. These data provide a basis for explaining a portion of the observed variation in the concentration data. This can enable the analyst to distinguish effects of drought or storms, weather conditions, or effects of solar...

An increase in the flux of nitrogen from the Mississippi river during the latter half of the twentieth century has caused eutrophication and chronic seasonal hypoxia in the shallow waters of the Louisiana shelf in the northern Gulf of Mexico. This has led to reductions in species diversity, mortality of benthic communities and stress in fishery resources. There is evidence for a predominantly anthropogenic origin of the increased nitrogen flux, but the location of the most significant sources in the Mississippi basin responsible for the delivery of nitrogen to the Gulf of Mexico have not been clearly identified, because the parameters influencing nitrogen-loss rates in rivers are not well known. Here we present an analysis of data from 374 US monitor ing stations, including 123 along the six largest tributaries to the Mississippi, that shows a rapid decline in the average first-order rate of nitrogen loss with channel size--from 0.45 day (-1) in small streams to 0.005 day (-1) in the Mississippi river. Using stream depth as an explanatory variable, our estimates of nitrogen-loss rates agreed with values from earlier studies. We conclude that the proximity of sources to large streams and rivers is an important determinant of nitrogen delivery to the estuary in the Mississippi basin, and possibly also in other large river basins.

Seasonal hypoxia in the northern Gulf of Mexico has been linked to increased nitrogen fluxes from the Mississippi and Atchafalaya River Basins, though recent evidence shows that phosphorus also influences productivity in the Gulf. We developed a spatially explicit and structurally detailed SPARROW water-quality model that reveals important differences in the sources and transport processes that control nitrogen (N) and phosphorus (P) delivery to the Gulf. Our model simulations indicate that agricultural sources in the watersheds contribute more than 70% of the delivered N and P. However, corn and soybean cultivation is the largest contributor of N (52%), followed by atmospheric deposition sources (16%); whereas P originates primarily from animal manure on pasture and rangelands (37%), followed by corn and soybeans (25%), other crops (18%), and urban sources (12%). The fraction of in-stream P and N load delivered to the Gulf increases with stream size, but reservoir trapping of P causes large local-and regional-scale differences in delivery. Our results indicate the diversity of management approaches required to achieve efficient control of nutrient loads to the Gulf. These include recognition of important differences in the agricultural sources of N and P, the role of atmospheric N, attention to P sources downstream from reservoirs, and better control of both N and P in close proximity to large rivers.

Abstract. 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 permeabili•, 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/km2/yr). IntroductionThe objectives of regional water-quality assessments are to describe spatial and temporal patterns in water quality and identify the factors and processes that influence those condi- data from monitoring networks, certain commonly encountered problems make it difficult to interpret point-level waterquality data in areal terms and thus meet the objectives of regional water-quality assessments. Even when their objectives are clearly established and sampling programs are well planned, regional water-quality assessments are often complicated by (1) sparseness of sampling locations due to cost constraints, (2) spatial biases in the sampling network due to the need to target sampling toward specific pollution sources, and (3) drainage basin heterogeneity. These complications impede data interpretation in distinct ways by limiting sample sizes, reducing the regional representativeness of the sampling network, and limiting the ability to relate in-stream conditions to specific pollution sources.In this paper, we describe a method for interpreting monitoring data that reduces the commonly encountered problems of network sparseness, bias, and basin heterogeneity. The method involves construction of a statistical model relating water-quality observations to spatially referenced (and potentially temporally referenced) data on basin a...

A set of statistical methods particularly well suited for evaluating time series of monthly water-quality data are presented. The Seasonal Kendall Test for trend is defined. It is a nonparametric test based on the differences between observations in the same month of different years. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation) it is robust by comparison with the parametric alternative of regression. The Seasonal Kendall Slope Estimator, a measure of trend magnitude, is defined. It is closely related to the Seasonal Kendall Test. It is an unbiased estimator of the slope of a linear trend and in comparison to linear regression has a considerably greater precision when the data are log-normally distributed but a moderately lesser precision when the data are normal. The flow-adjusted concentration is defined as the residual (actual minus the conditional expectation) concentration, based on some regression model of concentration as a function of river discharge. By testing these flow-adjusted concentration values for trend over time, one avoids the problem of identifying trends that are artifacts of the sequence of discharges observed. Rather, one is testing for changes in the relationship between concentration and discharge.