Cost effective policies for alternative distributions of stochastic water pollution

This study investigates the role for cost effective coastal water management with regard to different assumptions of probability distributions (normal and lognormal) of pollutant transports to coastal waters. The analytical results indicate a difference in costs for a given probability of achieving a certain pollutant load target whether a normal or lognormal distribution is assumed. For low standard deviations and confidence intervals, the normal distribution implies a lower cost while the opposite is true for relatively high standard deviations and confidence intervals. The associated cost effective charges and permit prices are higher for lognormal distributions than for normal distributions at relatively high confidence intervals and probabilities of achieving the target. An application to Himmerfj?rden--an estuary south of Stockholm, Sweden--shows that the minimum costs of achieving a 50 per cent reduction in nitrogen load to the coast varies more for a lognormal than normal probability distribution. At high coefficient of variation and chosen probability of achieving the target, the minimum cost under a lognormal assumption can be three times as high as for a normal distribution.     

RELATIONSHIPS BETWEEN WATER QUALITY AND PHOSPHORUS CONCENTRATIONS FOR PUGET SOUND REGION LAKES1

Regression relationships were developed between summer mean total phosphorus (P) concentrations in near-surface water and both chlorophyll a concentrations and Secchi disc transparency for Puget Sound region lakes. Total P concentrations in the lakes studied ranged from 7 to 66 μ/L. The relationship between total P and chlorophyll a, based on data from 69 lakes, explained 57 percent of the variance in chlorophyll a. Predicted chlorophyll a concentrations and 95 percent confidence intervals ranged from 1 ⁺³_-0.5μg/L for 7 μg/L P to about ⁺³⁵_-10μ/L for 66 μ/L P. The relationship between total P and Secchi disc, based on data from 71 lakes, explained 53 percent of the variance in Secchi disc. Predicted Secchi disc transparencies and 95 percent confidence intervals ranged from 5.5 ^+5.5_-3.0 m for 7 μ/L P to 1.4 ^+1.5_-0.7 m for 66 μ/L P.     

TEMPERATURE AND THE PRODUCTIVITY-LIGHT RELATIONSHIP1

ABSTRACT: Seventy-three in situ primary productivity experiments over a six-month period in hypereutrophic Onondaga Lake near Syracuse, New York, demonstrated variations in the light saturation parameter, I_p, which in part describes the interaction between productivity and light. Substantial variations in I_p were observed (coefficient of variation = 60 percent). Variations in I_p were significantly correlated (greater than 99 percent confidence level) with temperature (°C). An Arrhenius-type relationship (I_p= 1.312 × 1.088 (^T-20)) accounted for approximately 37 percent of the variation in I_p and may be appropriate for other systems dominated by green algae.     

Application of Index Procedures to Flood Frequency Analysis in Turkey1

Abstract: This study investigates the regional analysis of annual maximum flood series of 48 stream gauging stations in the basins of the West Mediterranean Region in Turkey. The region is divided into three homogeneous subregions according to both Student‐t test and Dalrymple homogeneity test. The regional relationships of mean annual flood per unit area‐drainage area and coefficient of skew‐coefficient of variation are obtained. Two statistically meaningful relationships of the mean flood per unit area‐drainage area and a unique relationship between skewness and variation coefficients exist. Results show that the index‐flood method may be applicable to each homogenous subregion to estimate flood quantiles in the study area.     

NON-ZERO LOWER LIMIT IN LOW FLOW FREQUENCY ANALYSIS?1

ABSTRACT: The implications of fitting distributions with non-zero lower limits to low flow data are examined. The 3-parameter Weibull distribution is fitted to annual minimum flow series from 60 long term stations in Canada. The relations between the estimated lower limit and three sampling variables (skewness, smallest, and largest observations) were investigated. The lower limit strongly depends on the sample skewness; it varies directly with the sample skewness, which in turn is highly influenced by the largest observation. For a given skewness, the value of the estimated lower limit is determined by the value of the smallest observation. Therefore, the lower limit cannot be accurately determined, and the resulting low flow estimates will be either too small or too high.     

AN APPLICATION OF COMPUTER GRAPHICS TO ANALYSIS OF EXTREMES1

ABSTRACT: A convenient method for the statistical analysis of hydrologic extremes is to use probability papers to fit selected theoretical distributions to extremal observations. Three commonly accepted statistical distributions of extreme hydrologic events are: the double exponential distribution, the bounded exponential distribution, and the Log Pearson Type III distribution. In most cases, probability papers are distribution specific. But, for the Log Pearson Type III distribution, the probability paper is characterized by a population-specific parameter, namely, the coefficient of skewness. It is not practicable to procure probability papers for all possible values of this parameter. Therefore, a computer program is developed to generate population-specific probability papers and to perform statistical analysis of the data using computer graphics. Probability papers covering return periods up to 1000 years or more are generated for the three distributions mentioned above. Using a plot routine, available extremal observations are plotted on selected probability papers and a linear regression analysis is used to fit a straight line to the data. Predictions of hydrologic extremes for higher recurrence intervals can be made by extrapolating the fitted straight lines.     

ANTIDEGRADATION WATER QUALITY CRITERIA FOR THE DELAWARE RIVER: A DISTRIBUTION-FREE STATISTICAL APPROACH1

ABSTRACT: Existing water quality for the Middle Delaware Scenic and Recreational River is significantly better than is required by current standards, leaving a potential for degradation. A method is presented for deriving candidate antidegradation water quality criteria for this segment of the Delaware River using statistical analysis of historic (ambient) water quality data. Data for 34 water quality parameters are first evaluated for data density, serial correlation, trend, seasonality, and other factors. These preliminary analyses are based on observation of data plots and application of distribution-free statistical techniques that are insensitive to outliers and are robust to relatively mild violations of basic assumptions. Data for 12 of the parameters have sufficient density for further analysis and can reasonably be modeled as independent and identically distributed over time (either seasonally or for the entire data sets). For these 12 parameters, distribution-free statistical methods are developed and used to derive intervals within which there is high confidence (usually greater than 95 percent) that the quantiles with potential use as anti-degradation criteria (the 0.85^th, 0.90^th, and 0.95^th quantiles in this study) for a particular parameter lie.     

A COMPARISON OF TRANSFORMATION METHODS FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: The SMEMAX transformation, its modified versions and power transformation were applied to 55 long-term records of annual maximum flood flows tested previously for independence, homogeneity and completeness. Even though SMEMAX transformation reduced the coefficient of skewness to near zero for flood data, their distribution was not a true normal distribution. In almost all cases, the coefficient of kurtosis was quite different from 3.0 of the normal distribution. Empirical criteria showed that SMEMAX transformation performed well only for 40 (70 percent) of the 55 stations tested. Its performance level dropped, especially for stations which had both the coefficient of skewness and kurtosis greater than 3.0 and 10.0, respectively. Power transformation was generally better in transforming the flood data to a normal distribution. It performed well for 50 (90 percent) of the 55 stations tested. The coefficient of skewness in case of the data transformed by power transformation was much closer to the zero value than in the case of SMEMAX transformed series. The SMEMAX transformation and its two modified versions yielded identical results when flood frequency analysis was performed. Computationally, all three methods were equally simple and easy to apply for flood frequency analysis. In some cases, the coefficient of kurtosis for the transformed distributions obtained both by SMEMAX and power transformations deviated farther from that for the normal distribution than for the parent distribution.     

CALCULATION OF NONLINEAR CONFIDENCE AND PREDICTION INTERVALS FOR GROUND-WATER FLOW MODELS1

ABSTRACT: A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that includsion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.     

ANTIDEGRADATION WATER QUALITY CRITERIA FOR THE DELAWARE RIVER: A DISTRIBUTION-FREE STATISTICAL APPROACH1

ABSTRACT: Existing water quality for the Middle Delaware Scenic and Recreational River is significantly better than is required by current standards, leaving a potential for degradation. A method is presented for deriving candidate antidegradation water quality criteria for this segment of the Delaware River using statistical analysis of historic (ambient) water quality data. Data for 34 water quality parameters are first evaluated for data density, serial correlation, trend, seasonality, and other factors. These preliminary analyses are based on observation of data plots and application of distribution-free statistical techniques that are insensitive to outliers and are robust to relatively mild violations of basic assumptions. Data for 12 of the parameters have sufficient density for further analysis and can reasonably be modeled as independent and identically distributed over time (either seasonally or for the entire data sets). For these 12 parameters, distribution-free statistical methods are developed and used to derive intervals within which there is high confidence (usually greater than 95 percent) that the quantiles with potential use as anti-degradation criteria (the 0.85^th, 0.90^th, and 0.95^th quantiles in this study) for a particular parameter lie.     

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.     

Hydrologic and Phosphorus Export Behavior of Small Streams in Commercial Poultry‐Pasture Watersheds1

Romeis, J. Joshua, C. Rhett Jackson, L. Mark Risse, Andrew N. Sharpley, and David E. Radcliffe, 2011. Hydrologic and Phosphorus Export Behavior of Small Streams in Commercial Poultry‐Pasture Watersheds. Journal of the American Water Resources Association (JAWRA) 1‐19. DOI: 10.1111/j.1752‐1688.2011.00521.x Abstract: Few watershed‐scale studies have evaluated phosphorus export in streamflow from commercial poultry‐pasture operations. Continuous streamflow and mixed‐frequency water quality datasets were collected from nine commercial poultry‐pasture (AG) and three forested (FORS) headwater streams (2.4‐44 ha) in the upper Etowah River basin of Georgia to estimate total P (TP) loads and examine variability of hydrologic response and water quality of storm and nonstorm‐flow regimes. Data collection duration ranged from 18 to 22 months, and approximately 1,600 water quality samples were collected. Significant (p < 0.1) inverse relationships were detected between peak flow response variables and both drainage area and fraction of forest cover. Order‐of‐magnitude differences in TP and dissolved reactive P (DRP) concentration were observed between AG and FORS sites and among AG sites. TP yields of FORS sites ranged from 0.01 to 0.1 kg P/ha. Yields of AG sites ranged from 0.031 to 3.17 kg P/ha (median = 0.354 kg P/ha). With 95% confidence intervals, AG yields ranged from 0.025 to 13.1 kg P/ha. These small‐watershed‐scale yields were similar to field‐scale yields measured in other studies in other regions. TP yields were significantly related to area‐weighted Mehlich‐1 soil test P concentrations (p = 0.0073) and base‐flow water sample P concentrations (p ≤ 0.0005). Water quality sampling during base‐flow conditions may be a useful screening tool for P risk‐based management programs.     

Predicting δCDIC dynamics in CCS: A scheme based on a review of inorganic carbon chemistry under elevated pressures and temperatures

Stable carbon isotopes are important tools to assess potential storage sites for CO₂, as they allow the quantification of ionic trapping via isotope mass balances. In deep geological formations high p/T conditions need to be considered, because CO₂ dissolution, equilibrium constants and isotope fractionation of dissolved inorganic carbon (DIC) depend on temperature, pressure and solute composition. After reviewing different approaches to account for these dependencies, an expanded scheme is presented for speciation and carbon isotope fractionation of DIC and dissolution of CaCO₃ for pCO₂ up to 100 bar, pH down to 3 and temperatures of up to 200 °C. The scheme evaluates the influence of respective parameters on isotope ratios during CO₂ sequestration. The pCO₂ and pH are the dominant controlling factors in the DIC/δ¹³C/pH system. The fugacity of CO₂ has major impact on DIC concentrations at temperatures below 100 °C at high pCO₂. Temperature dependency of activities and equilibrium dominates at temperatures above 100 °C. Isotope ratios of DIC are expected to be about 1–2‰ more depleted in ¹³C compared to the free CO₂ at pCO₂ values above 10 bar. This depletion is controlled by carbon isotope fractionation between CO₂ and H₂CO₃* which is the dominant species of DIC at the resulting pH below 5.     

Neighborhood effects in bird distributions,Navarre, Spain

This study examines the role of neighborhood effects in the spatial distributions of selected bird species in Navarre, Spain. We employed a geographic information system (GIS) to organize the data on bird distributions and relevant environmental variables and to analyze their spatial patterns. Three bird species were selected for analysis: the European honey-buzzard (Pernis apivorus), the Eurasian hobby (Falco subbuteo), and the European pied flycatcher (Ficedula hypoleuca). Selected environmental variables of the study area were digitized to create a comprehensive data base and logistic regression models were used to evaluate the significance of each variable in the spatial distribution. The spatial patterns of bird distributions were used to extract topological relationships and to identify neighborhood effects. Although all the selected species illustrate a pattern of positive spatial autocorrelation in their distributions, the significance of neighborhood effects varies from species to species. Among the selected species, neighborhood effects are most evident in the distribution of the European pied flycatcher and are significant for the Eurasian hobby. The distribution of the European honey-buzzard is not much affected by neighborhood effects. The results suggest that examination of neighborhood effects is a prerequisite for modeling bird distributions.     

Influence of Prey and Nutritional Status on the Rate of Nitrogen Uptake by Prymnesium parvum (haptophyte)1

Lindehoff, Elin, Edna Granéli, and Patricia M. Glibert, 2010. Influence of Prey and Nutritional Status on the Rate of Nitrogen Uptake by Prymnesium parvum (Haptophyte). Journal of the American Water Resources Association (JAWRA) 46(1):121-132. DOI: 10.1111/j.1752-1688.2009.00396.x Abstract: We studied how the specific nitrogen (N) uptake rates of nitrate (NO₃⁻), urea, and the amino acids, glutamic acid and glycine, by Prymnesium parvum were affected by (1) the change from N-deficient status to N-sufficient status of the P. parvum cells, (2) presence of prey from a natural Baltic Sea plankton community, and (3) the composition of prey as affected by additions of terrestrial originated dissolved organic matter (DOM) or inorganic nutrients. Nitrogen-deficient P. parvum (16 μM NO₃⁻ and 4 μM PO₄⁻, molar N:P ratio of 4:1) were mixed with a natural Baltic plankton community and given PO₄³⁻ and (1) NO₃⁻ (control) or (2) high molecular weight DOM, >1 kDa concentrated from sewage effluent (+DOM), in a molar N:P ratio of 9-10:1. With additions of ¹⁵N-enriched substrates, rates of N uptake from NO₃⁻, urea, and the amino acids glycine and glutamic acid were measured every 24 h for 72 h. Initial N-deficient P. parvum were highly toxic (3.7 ± 0.9 × 10⁻⁴ mg Sap equiv/cell) and toxic allelochemicals were released into the medium causing the natural plankton community to lyse. Rates of N uptake differed between the “control” and the “+DOM” treatments over time; total (sum of the N substrates measured) absolute uptake rates (ρ_cell, fmol N/cell/h) at ambient culture conditions were significantly higher (ANOVA, p < 0.05) in the more toxic “control” treatments compared with the “+DOM” treatments after 48 h. In the “control” treatment, the total ρ_cell increased significantly (ANOVA, p < 0.01) from time 0 to 48 h, while in the “+DOM” treatment there was no significant increase. Released organic nutrients from the lysed plankton cells may have increased uptake rates of amino acids and urea by P. parvum. All uptake rates declined in all treatments by 72 h. Total dissolved N uptake rates at ambient culture conditions were estimated to make up about 10% of the N P. parvum are potentially capable of ingesting from particulate prey.     

A Hydrologic Drying Bias in Water‐Resource Impact Analyses of Anthropogenic Climate Change

For water‐resource planning, sensitivity of freshwater availability to anthropogenic climate change (ACC) often is analyzed with “offline” hydrologic models that use precipitation and potential evapotranspiration (E_p) as inputs. Because E_p is not a climate‐model output, an intermediary model of E_p must be introduced to connect the climate model to the hydrologic model. Several E_p methods are used. The suitability of each can be assessed by noting a credible E_p method for offline analyses should be able to reproduce climate models’ ACC‐driven changes in actual evapotranspiration in regions and seasons of negligible water stress (E_w). We quantified this ability for seven commonly used E_p methods and for a simple proportionality with available energy (“energy‐only” method). With the exception of the energy‐only method, all methods tend to overestimate substantially the increase in E_p associated with ACC. In an offline hydrologic model, the E_p‐change biases produce excessive increases in actual evapotranspiration (E), whether the system experiences water stress or not, and thence strong negative biases in runoff change, as compared to hydrologic fluxes in the driving climate models. The runoff biases are comparable in magnitude to the ACC‐induced runoff changes themselves. These results suggest future hydrologic drying (wetting) trends likely are being systematically and substantially overestimated (underestimated) in many water‐resource impact analyses.     

Evidence for Changing Flood Risk in New England Since the Late 20th Century1

Abstract: Long‐term flow records for watersheds with minimal human influence have shown trends in recent decades toward increasing streamflow at regional and national scales, especially for low flow quantiles like the annual minimum and annual median flows. Trends for high flow quantiles are less clear, despite recent research showing increased precipitation in the conterminous United States over the last century that has been brought about primarily by an increased frequency and intensity of events in the upper 10th percentile of the daily precipitation distribution – particularly in the Northeast. This study investigates trends in 28 long‐term annual flood series for New England watersheds with dominantly natural streamflow. The flood series are an average of 75 years in length and are continuous through 2006. Twenty‐five series show upward trends via the nonparametric Mann‐Kendall test, 40% (10) of which are statistically significant (p < 0.1). Moreover, an average standardized departures series for 23 of the study gages indicates that increasing flood magnitudes in New England occurred as a step change around 1970. The timing of this is broadly synchronous with a phase change in the low frequency variability of the North Atlantic Oscillation, a prominent upper atmospheric circulation pattern that is known to effect climate variability along the United States east coast. Identifiable hydroclimatic shifts should be considered when the affected flow records are used for flood frequency analyses. Special treatment of the flood series can improve the analyses and provide better estimates of flood magnitudes and frequencies under the prevailing hydroclimatic condition.     

NONLINEAR PROGRAMMING IN RIVER BASIN MODELING1

ABSTRACT: This paper explores the use of nonlinear programming in river basin water quality modelling. Applications recently reported in the literature, along with the author's experience with nonlinear programming, are reviewed. Results obtained using nonlinear programming are compared with the results obtained by other researchers using linear and dynamic programming to solve river basin water quality optimization problems. These water quality models have objective functions with continuous first partial derivatives, several inequality and variable bound constraints, and are of the form: minizie Σ^j=n_j=1Y_j(X_j) subject to Σ^j=n_j=1a_ijX_jb_i, i=1,2, …, m c_jX_jd_j, j= 1,2, …, n The variable X_i is the maximum allowable ratio of the BOD (biochemical oxygen demand) of the effluent outflow to the BOD of the wastewater inflow for treatment plant j, in the range c_j to d_j. The a_ijd and b_i are constants in the DO (dissolved oxygen) and BOD constraints. The resuks show, given certain assumptions about the data, that nonlinear programming is a better solution method for these problems than is either linear programming or dynamic programming.     

Assessing Parameter Uncertainty of a Semi‐Distributed Hydrology Model for a Shallow Aquifer Dominated Environmental System

This paper examines the performance of a semi‐distributed hydrology model (i.e., Soil and Water Assessment Tool [SWAT]) using Sequential Uncertainty FItting (SUFI‐2), generalized likelihood uncertainty estimation (GLUE), parameter solution (ParaSol), and particle swarm optimization (PSO). We applied SWAT to the Waccamaw watershed, a shallow aquifer dominated Coastal Plain watershed in the Southeastern United States (U.S.). The model was calibrated (2003‐2005) and validated (2006‐2007) at two U.S. Geological Survey gaging stations, using significant parameters related to surface hydrology, hydrogeology, hydraulics, and physical properties. SWAT performed best during intervals with wet and normal antecedent conditions with varying sensitivity to effluent channel shape and characteristics. In addition, the calibration of all algorithms depended mostly on Manning's n‐value for the tributary channels as the surface friction resistance factor to generate runoff. SUFI‐2 and PSO simulated the same relative probability distribution tails to those observed at an upstream outlet, while all methods (except ParaSol) exhibited longer tails at a downstream outlet. The ParaSol model exhibited large skewness suggesting a global search algorithm was less capable of characterizing parameter uncertainty. Our findings provide insights regarding parameter sensitivity and uncertainty as well as modeling diagnostic analysis that can improve hydrologic theory and prediction in complex watersheds. Editor's note : This paper is part of the featured series on SWAT Applications for Emerging Hydrologic and Water Quality Challenges. See the February 2017 issue for the introduction and background to the series.