ESTIMATING MEAN AND VARIANCE FOR ENVIRONMENTAL SAMPLES WITH BELOW DETECTION LIMIT OBSERVATIONS1

ABSTRACT: Left-censoring of data sets complicates subsequent statistical analyses. Generally, substitution or deletion methods provide poor estimates of the mean and variance of censored samples. These substitution and deletion methods include the use of values above the detection limit (DL) only, or substitution of 0, DL/2 or the DL for the below DL values during the calculation of mean and variance. A variety of statistical methods provides better estimators for different types of distributions and censoring. Maximum likelihood and order statistics methods compare favorably to the substitution or deletion methods. Selected statistical methods applicable to left-censoring of environmental data sets are reviewed with the purpose of demonstrating the use of these statistical methods for coping with Type I (and Type II) left-censoring of normally and log-normally distributed environmental data sets. A PC program (UNCENSOR) is presented that implements these statistical methods. Problems associated with data sets with multiple DLs are discussed relative to censoring methods for life and fatigue tests as recently applied to water quality data sets.     

USING UNCENSORED TRACE-LEVEL MEASUREMENTS TO DETECT TRENDS IN GROUND WATER CONTAMINATION1

ABSTRACT: Environmental decision making involving trace-levels of contaminants can be complicated by censoring, the practice of reporting concentrations either as less than the limit of detection (LOD) or as not detected (ND) when a test result is less than the LOD. Censoring can result in data series that are difficult to meaningfully summarize, graph, and analyze through traditional statistical methods. In spite of the relatively large measurement errors associated with test results below the LOD, simple and meaningful analyses can be carried out that provide valuable information not available if data are censored. For example, an indication of increasing levels of contamination at the fringe of a plume can act as an early warning signal to trigger further study, an increased sampling frequency, or a higher level of remediation at the source. This paper involves the application of nonparametric trend analyses to uncensored trace-level groundwater monitoring data collected between March 1991 and August 1994 on dissolved arsenic and chromium for seven wells at an industrial site in New York.     

Modeling Variability and Trends in Pesticide Concentrations in Streams1

Abstract: A parametric regression model was developed for assessing the variability and long‐term trends in pesticide concentrations in streams. The dependent variable is the logarithm of pesticide concentration and the explanatory variables are a seasonal wave, which represents the seasonal variability of concentration in response to seasonal application rates; a streamflow anomaly, which is the deviation of concurrent daily streamflow from average conditions for the previous 30 days; and a trend, which represents long‐term (inter‐annual) changes in concentration. Application of the model to selected herbicides and insecticides in four diverse streams indicated the model is robust with respect to pesticide type, stream location, and the degree of censoring (proportion of nondetections). An automatic model fitting and selection procedure for the seasonal wave and trend components was found to perform well for the datasets analyzed. Artificial censoring scenarios were used in a Monte Carlo simulation analysis to show that the fitted trends were unbiased and the approximate p‐values were accurate for as few as 10 uncensored concentrations during a three‐year period, assuming a sampling frequency of 15 samples per year. Trend estimates for the full model were compared with a model without the streamflow anomaly and a model in which the seasonality was modeled using standard trigonometric functions, rather than seasonal application rates. Exclusion of the streamflow anomaly resulted in substantial increases in the mean‐squared error and decreases in power for detecting trends. Incorrectly modeling the seasonal structure of the concentration data resulted in substantial estimation bias and moderate increases in mean‐squared error and decreases in power.     

A SIMPLE METHOD FOR ESTIMATING BASEFLOW AT UNGAGED LOCATIONS1

ABSTRACT: Baseflow, or water that enters a stream from slowly varying sources such as ground water, can be critical to humans and ecosystems. We evaluate a simple method for estimating base‐flow parameters at ungaged sites. The method uses one or more baseflow discharge measurements at the ungaged site and longterm streamflow data from a nearby gaged site. A given baseflow parameter, such as the median, is estimated as the product of the corresponding gage site parameter and the geometric mean of the ratios of the measured baseflow discharges and the concurrent discharges at the gage site. If baseflows at gaged and ungaged sites have a bivariate lognormal distribution with high correlation and nearly equal log variances, the estimated baseflow parameters are very accurate. We tested the proposed method using long‐term streamflow data from two watershed pairs in the Driftless Area of southwestern Wisconsin. For one watershed pair, the theoretical assumptions are well met; for the other the log‐variances are substantially different. In the first case, the method performs well for estimating both annual and long‐term baseflow parameters. In the second, the method performs remarkably well for estimating annual mean and annual median baseflow discharge, but less well for estimating the annual lower decile and the long‐term mean, median, and lower decile. In general, the use of four measurements in a year is not substantially better than the use of two.     

SOURCES OF VARIABILITY IN PHOSPHORUS AND CHLOROPHYLL AND THEIR EFFECTS ON USE OF LAKE SURVEY DATA1

Summer lake survey measurements of total phosphorus (TP) and chlorophyll a (CHLa) from 188 reserviors and natural lakes in the midwest were analyzed to determine the magnitude of major sources of variability. Median variance among replicate samples collected at the same location and time was about 7-8 percent of the mean for both TP and CHLa. Median observed temporal variability within summers was 27 percent of the mean for TP and 45 percent of the mean for CHLa. Median values of year-to-year variance in average TP and CHLa were 22 percent and 31 percent of the mean, respectively. A range of approximately two orders of magnitude was observed among individual estimates of variance in each of these categories. The magnitude of observed temporal variability was affected only slightly by variance among replicate samples on individual days and was weakly correlated with the length of time during which samples were collected from individual lakes. Observed temporal variation was similar between reservoirs and natural lakes when variances were calculated with logtransformed data. The magnitude of temporal and year-to-year variance can severely limit the power of statistical comparisons of TP and CHLa means, but has less effect on establishing relative rankings of lake means, Sources and relative magnitude of variability are important in the use of TP and CHLa data in regression models and in the planning of lake surveys and subsequent data analysis.     

ESTIMATING THE MEAN AND VARIANCE OF CENSORED PHOSPHORUS CONCENTRATIONS IN FLORIDA RAINFALL1

ABSTRACT: The total phosphorous (TP) concentrations in the South Florida rainfall have been recorded in weekly intervals with a detection limit (D_L) of 3.5 μg/L. As a large amount of the data is reported as below the D_L, appropriate statistical methods are needed for data analysis. Thus, an attempt was made to identify an appropriate method to estimate the mean and variance of the data. In particular, a method to separate the statistics for the below D_L portion from the estimated population statistics is proposed. The estimated statistics of the censored data are compared with the statistics of the uncensored data available from the recent years’ laboratory records. It was found that the one-step restricted maximum likelihood method is the most accurate for the wet TP data, and that the proposed method to combine the estimated statistics for TP < D_L portion and the sample statistics for TP ≥ D_L portion improves estimates compared to the conventional maximum likelihood estimates.     

ESTIMATING LOW-FLOW QUANTILES FROM DRAINAGE-BASIN CHARACTERISTICS IN NEW HAMPSHIRE AND VERMONT1

ABSTRACT: This study systematically develops, validates, and compares alternative approaches for estimating quantiles of the distribution of annual minimum seven-day-average flows (7Q) for ungaged, unregulated drainage basins in New Hampshire and Vermont via regression on map-measurable drainage-basin characteristics. At 47 gaging stations in the region, the hypotheses that 7Q is log normally distributed and serially independent are not rejected, and the regional average spatial correlation is R= 0.35. Step-forward examination of a suite of potential predictor variables revealed that logarithm of drainage area, mean elevation, and fraction of basin covered with sand and gravel deposits are significant predictors of quantiles of 7Q. The regression equations were incorporated into four approaches to estimate the 7Q value with a nonexceedence probability of 0.1, 7Q10. Comparison of observed values and values predicted via a delete-one jackknife resampling validation indicates that one of the approaches gives estimates with acceptable bias and precision, with median relative error of 33 percent and prediction error of 64 percent. This is equivalent to the precision obtainable with only one to two years of gaging records. In spite of this limited precision, the approaches developed herein are useful for predicting 7Q quantiles at ungaged sites. Further improvement in precision will likely be possible only by exploiting the spatial correlation of annual 7Q.     

UNCERTAINTY OF EXTREME FLOOD ESTIMATES INCORPRATING HISTORICAL DATA1

ABSTRACT: The ability to predict extreme floods is an important part of the planning process for any water project for which failure will be very costly. The length of a gage record available for use in estimating extreme flows is generally much shorter than the recurrence interval of the desired flows, resulting in estimates having a high degree of uncertainty. Maximum likelihood estimators of the parameters of the three parameter lognormal (3PLN) distribution, which make use of historical data, are presented. A Monte Carlo study of extreme flows estimated from samples drawn from three hypothetical 3PLN populations showed that inclusion of historical flows with the gage record reduced the bias and variance of extreme flow estimates. Asymptotic theory approximations of parameter variances and covariances calculated using the second and mixed partial derivatives of the log likelihood function agreed well with Monte Carlo results. First order approximations of the standard deviations of the extreme flow estimates did not agree with the Monte Carlo results. An alternative method for calculating those standard deviations, the “asymptotic simulation” method, is described. The standard deviations calculated by asymptotic simulation agree well with the Monte Carlo results.     

REGRESSION MODELS FOR ESTIMATING HERBICIDE CONCENTRATIONS IN U.S. STREAMS FROM WATERSHED CHARACTERISTICS1

ABSTRACT: Regression models were developed for estimating stream concentrations of the herbicides alachlor, atrazine, cyanazine, metolachior, and trilluralin from use‐intensity data and watershed characteristics. Concentrations were determined from samples collected from 45 streams throughout the United States during 1993 to 1995 as part of the U.S. Geological Survey's National Water‐Quality Assessment (NAWQA). Separate regression models were developed for each of six percentiles (10th, 25th, 50th, 75th, 90th, 95th) of the annual distribution of stream concentrations and for the annual time‐weighted mean concentration. Estimates for the individual percentiles can be combined to provide an estimate of the annual distribution of concentrations for a given stream. Agricultural use of the herbicide in the watershed was a significant predictor in nearly all of the models. Several hydrologic and soil parameters also were useful in explaining the variability in concentrations of herbicides among the streams. Most of the regression models developed for estimation of concentration percentiles and annual mean concentrations accounted for 50 percent to 90 percent of the variability among streams. Predicted concentrations were nearly always within an order of magnitude of the measured concentrations for the model‐development streams, and predicted concentration distributions reasonably matched the actual distributions in most cases. Results from application of the models to streams not included in the model development data set are encouraging, but further validation of the regression approach described in this paper is needed.     

A STATISTICAL APPROACH FOR PERFORMING WATER QUALITY IMPAIRMENT ASSESSMENTS1

ABSTRACT: A statistical approach for making Total Maximum Daily Load (TMDL) impairment decisions is developed as an alternative to the simple tally of the number of measurements that happen to exceed the standard. The method ensures that no more than a small (e.g., 10 percent) percentage of water quality samples will exceed a regulatory standard with a high level of confidence (e.g., 95 percent). The method is based on the 100(1‐α) percent lower confidence limit on an upper percentile of the concentration distribution. Advantages of the method include: (1) it provides a direct test of the hypothesis that a prespecified percentage of the true concentration distribution exceeds a regulatory standard, (2) it is applicable to a wide variety of different statistical concentration distributions, (3) it directly incorporates the magnitude of the measured concentrations unlike traditional approaches, and (4) it has explicit statistical power characteristics (i.e., what is the probability of missing an environmental impact). Detailed study of the simple tally approach reveals that it achieves high statistical power at the expense of unacceptably high false positive rates (30 to 40 percent false positive results). By contrast, the statistical approach results in similar statistical power while achieving a nominal false positive rate of 5 percent.     

VARIABILITY IN MEASURED BEDLO AD-TRANSPORT RATES1

ABSTRACT: Variability in bedload-transport rates during constant water discharge is an inherent part of the bedload-transport process. Although this variability has been measured extensively in the laboratory, similar information generally is not available from field measurements. During a four-day period of nearly constant water discharge, four sets of consecutively collected bedload samples, ranging from 43 to 120 samples, were obtained at the same cross channel location using a standard 65-pound Helley-Smith bedload sampler. When the measured transport rates are converted to dimensionless rates and plotted as cumulative frequency distributions, they show good agreement with a theoretical probability distribution function of rates derived for the case of ripples on dunes. The distributions show that during constant water discharge individual measured rates at a fixed point vary from near zero to four times the mean rate, and 60 percent of the sampled rates will be less than the mean. Because of the large variation in transport rates that occurs at every location in the cross section, many observations are required to establish an accurate estimate of the mean rate at any given location.     

INFLUENCE OF DIFFERENT TEMPORAL SAMPLING STRATEGIES ON ESTIMATING TOTAL PHOSPHORUS AND SUSPENDED SEDIMENT CONCENTRATION AND TRANSPORT IN SMALL STREAMS1

ABSTRACT: Various temporal sampling strategies are used to monitor water quality in small streams. To determine how various strategies influence the estimated water quality, frequently collected water quality data from eight small streams (14 to 110 km²) in Wisconsin were systematically subsampled to simulate typically used strategies. These subsets of data were then used to estimate mean, median, and maximum concentrations, and with continuous daily flows used to estimate annual loads (using the regression method) and volumetrically weighted mean concentrations. For each strategy, accuracy and precision in each summary statistic were evaluated by comparison with concentrations and loads of total phosphorus and suspended sediment estimated from all available data. The most effective sampling strategy depends on the statistic of interest and study duration. For mean and median concentrations, the most frequent fixed period sampling economically feasible is best. For maximum concentrations, any strategy with samples at or prior to peak flow is best. The best sampling strategy to estimate loads depends on the study duration. For one‐year studies, fixed period monthly sampling supplemented with storm chasing was best, even though loads were overestimated by 25 to 50 percent. For two to three‐year load studies and estimating volumetrically weighted mean concentrations, fixed period semimonthly sampling was best.     

PREDICTION OF MEAN ANNUAL FLOWS IN NORTH AND CENTRAL FLORIDA1

ABSTRACT: A frequency analysis approach for the prediction of flow characteristics at ungaged locations is applied to a region of high annual precipitation and low topography in north and central Florida. Stationary time series of annual flows are fitted with the lognormal distribution and estimated parameters of the distribution are fitted by third order trend surfaces. These explain 65 and 74 percent of the observed variances in the mean and standard deviation, respectively. Predictions of parameters are then made for several locations previously unused in the study and they are used to estimate the return periods of various flows from the lognormal distribution. Application of the Kolmogorov-Smirnov goodness-of-fit test suggests that only one of the five test stations can be considered significantly different from the observed data, confirming the applicability of this technique.     

Prediction of diffuse solar radiation using satellite data

In the project of the solar systems, the values of the solar radiation of a region must be known. The global solar radiation measurements are performed by the Turkish Meteorological Service in Turkey, while the diffuse solar radiation measurements are unavailable. In this study, some new models for predicting the monthly average daily diffuse solar radiation on a horizontal surface for Erzincan, Turkey are developed using satellite data. The evaluation of the models is carried out with the statistical analysis methods of mean bias error (MBE), root mean square error (RMSE) and correlation coefficient (r). The results are proved that the correlation equations obtained in here can be used to forecast diffuse solar radiation reasonably well.     

Multivariate analysis of trace metal levels in tannery effluents in relation to soil and water: a case study from Peshawar, Pakistan

Tannery effluents and relevant ground water and soil samples collected from various tanning industries of Peshawar were analyzed for Na, Ca, K, Mg, Fe, Mn, Cr, Co, Cd, Ni, Pb and Zn by the AAS method. The metal concentration data for the three media are reported in terms of basic statistical parameters, metal-to-metal correlations and linear regression analyses. Metal distributions in the three media were quite divergent and showed non-normal distributions with high standard deviation and skewness parameters. Sodium exhibited the highest mean levels of 1,277mg/L, 881mg/L and 12,912mg/kg in the effluent, ground water and soil samples, respectively. Among other metals, Cr concentrations were 410mg/L, 0.145mg/L, 100mg/kg and Ca, 278mg/L, 64.8mg/L, and 2,285mg/kg in the effluent, ground water and soil samples, respectively. Some significant correlations were observed between effluent and soils in terms of Na, Cr, Ni, Co and Pb. The ground water-soil interrelationship suggested that Na levels in the soil and ground water were significantly correlated with each other (r=0.486, P<0.01). Similarly, Cr in the soil is strongly correlated with Ca in ground water (r=0.486, P<0.01). These results were duly supported by the linear regression analysis of data. The source identification studies conducted using Principal Component Analysis (PCA) and Cluster Analysis (CA) evidenced that ground water and soil were being contaminated by the toxic metals emanating from the tannery effluents.     

COMPARISON OF PARAMETRIC TAIL ESTIMATORS FOR LOW‐FLOW FREQUENCY ANALYSIS1

ABSTRACT: In recent years, several approaches to hydrologic frequency analysis have been proposed that enable one to direct attention to that portion of an overall probability distribution that is of greatest interest. The majority of the studies have focused on the upper tail of a distribution for flood analyses, though the same ideas can be applied to low flows. This paper presents an evaluation of the performances of five different estimation methods that place an emphasis on fitting the lower tail of the lognormal distribution for estimation of the ten‐year low‐flow quantile. The methods compared include distributional truncation, MLE treatment of censored data, partial probability weighted moments, LL‐moments, and expected moments. It is concluded that while there are some differences among the alternative methods in terms of their biases and root mean square errors, no one method consistently performs better than the others, particularly with recognition that the underlying population distribution is unknown. Therefore, it seems perfectly legitimate to make a selection of a method on the basis other criteria, such as ease of use. It is also shown in this paper that the five alternative methods can perform about as well as, if not better than, an estimation strategy involving fitting the complete lognormal distribution using L‐moments.     

ESTIMATION OF COASTAL WATER CONTAMINATION LONG-TERM TREND USING SEASONAL LINEAR MODELS1

ABSTRACT: Bivalves are used as bioindicators to assess trends of the chemical quality of coastal and marine environments due to their ability to concentrate chemicals. These shellfish are subject to seasonal physiological changes influencing the chemical concentration. Using quarterly data, we model concentration via linear regression with a biologically based seasonal component. This was applied to cadmium concentration measured in the blue mussel (Mytilus edulis) at three sites in the Seine estuary (Normandy, France). In this case we have a high concentration season from January to June and a “low concentration” season from July to December. This season definition was checked a posteriori, using box-and-whisker plots and a statistical test of comparison of pair-wise adjusted least-squares mean differences, and it appears to be very reasonable. We averaged data by season and across sites. Our final model (R²= 0.846 with N= 27 observations) includes highly significant terms: a season effect, which accounts for 45% of the total variability, a linear and a quadratic time term. Outliers were identified by high Studentized residual values and attributed to bias in the temporal sampling schemes. The methodology developed will further be used with other shellfish and/or other trace elements and organic chemicals.     

MODELING THE BIG BLACK RIVER: A COMPARISON OF WATER QUALITY MODELS1

ABSTRACT: The Mississippi Department of Environmental Quality uses the Steady Riverine Environmental Assessment Model (STREAM) to establish effluent limitations. While the U.S. Environmental Protection Agency has approved of its use, questions arise regarding the model's simplicity. The objective of this research was to compare STREAM with the more commonly utilized Enhanced Stream Water Quality Model (QUAL2E). The comparison involved a statistical evaluation procedure based on sensitivity analyses, input probability distribution functions, and Monte Carlo simulation with site‐specific data from a 46‐mile (74‐km) reach of the Big Black River in central Mississippi. Site specific probability distribution functions were derived from measured rates of reaeration, sediment oxygen demand, photosynthesis, and respiration. Both STREAM and QUAL2E reasonably predicted daily average dissolved oxygen (DO) based on a comparison of output probability distributions with observed DO. Observed DO was consistently within 90 percent confidence intervals of model predictions. The STREAM approach generally overpredicted while QUAL2E generally matched observed DO. Using the more commonly assumed lognormal distribution as opposed to a Weibull distribution for two of the sensitive input parameters resulted in minimal differences in the statistical evaluations. The QUAL2E approach had distinct advantages over STREAM in simulating the growth cycle of algae.     

通过GIS建模对电厂噪声分布进行分析

噪声分布是有规律可循的,可通过实际测量得到,但为了提高效率,实际测量也应根据规律进行.通过空间建模,对噪声分布规律进行初步分析,在此基础上进行测量,为测量噪声提供依据,并可进行有效率评估.首先进行数据组织,然后进行空间分析建模,再运行模型,可得到理想的噪声分布情况.