Jim C. Loftis

The “data-rich but information-poor” syndrome in water quality monitoring

Water quality monitoring conducted routinely over time at fixed sites has been a part of most water quality management efforts for many years. It has been assumed that such monitoring plays a major role in management. However, the lack of routine data analysis, and reporting of information derived from such analysis, points up the fact that the exact nature of the role of routine, fixed-station monitoring is poorly defined.There is a need to very clearly define this role in the design of such systems if routine monitoring is to efficiently and effectively meet the information expectations placed on it. Design of routine monitoring systems will therefore have to consider not only the where, what, and when of sampling, but also why. A framework for including the “why” of monitoring in the design process is proposed and experience with using the framework in New Zealand is discussed.

Application of geostatistics to evaluate partial weather station networks

Abstract Climatic data are an essential input for the determination of crop water requirements. The density and location of weather stations are the important design variables for obtaining the required degree of accuracy of weather data. The planning of weather station networks should include economic considerations, and a mixture of full and partial weather stations could be a cost-effective alternative. A ‘full’ weather station is defined here as one in which all the weather variables used in the modified Penman equation are measured, and a ‘partial’ weather station is one in which some, but not all, weather variables are measured. The accuracy of reference evapotranspiration (Etr) estimates for sites located some distance from surrounding stations is dependent on measurement error, error of the estimation equation, and interpolation error. The interpolation error is affected by the spatial correlation structure of weather variables and method of interpolation. A case-study data set of 2 years of daily climatic data (1989–1990) from 17 stations in the states of Nebraska, Kansas, and Colorado was used to compare alternative network designs and interpolation methods. Root mean squared interpolation error (RMSIE) values were the criteria for evaluating Etr estimates and network performance. The kriging method gave the lowest RMSIE, followed by the inverse distance square method and the inverse distance method. Co-kriging improved the estimates still further. For a given level of performance, a mixture of full and partial weather stations would be more economical than full stations only.

What do significance tests really tell us about the environment

Routine application of significance tests does not extract the maximum information from environmental data and can lead to misleading conclusions. Reasons leading to this are: a significant result can often be reached merely by collecting enough samples; a statistically significant result is not necessarily practically significant; and reports of the presence or absence of statistically significant differences for multiple tests are not comparable unless identical sample sizes are used. These problems are demonstrated by application to pH data for grazed and retired fields, and by discussion of significance tests used in recent US regulations for groundwater quality. The advantages of equivalence tests, where the tester must state the difference of practical difference, are discussed and applied to the field pH problem. We recommend that environmental managers and scientists pay more attention to statistical power and decide on what is a practical difference. Confidence intervals for the size of the differences, accompanied where necessary by equivalence tests, are the preferred means of addressing the question: “is there a difference of practical significance?”

Water quality sample collection, data treatment and results presentation for principal components analysis--literature review and Illinois River Watershed case study.

Comprehensive water quality investigations to characterize large watersheds include collection of surface water samples over time at various locations within the watershed and analyses of the samples for multiple chemical and biological constituents. The size and complexity of the resulting dataset make overall evaluations difficult, and as a result, multivariate statistical methods can be useful to evaluate environmental patterns and sources of contamination. The most commonly applied multivariate method in watershed studies is principal components analysis (PCA), which uses correlation among multiple water quality constituents to effectively reduce the number of variables. The reduced set of variables may assist in the identification and description of spatial patterns in water quality that result from hydrologic and geochemical processes and from sources of contamination. The utility of PCA for identifying important environmental factors in a given study is obviously affected by sampling design, constituents analyzed, data quality, data treatment prior to PCA, methods of interpreting PCA results, and other factors. Unfortunately no comprehensive evaluations have been performed and no standard procedures exist for dealing with these issues. This paper examines and evaluates the current state-of-the-science by review of 49 published papers dealing with multivariate (typically PCA) techniques to evaluate watershed water quality. Additionally an example PCA for a surface water quality study in the Illinois River Watershed (IRW) is provided to illustrate methods to address the above issues and to evaluate the sensitivity of results to alternative methods. The example PCA evaluations were consistent with two dominant sources of surface water contamination in the IRW: 1) discharge to the streams from municipal wastewater treatment plants and 2) runoff and infiltration from fields with land applied poultry waste.

Detecting cumulative watershed effects: the statistical power of pairing

Abstract The statistical power for detecting change in water quality should be a primary consideration when designing monitoring studies. However, some of the standard approaches for estimating sample size result in a power of less than 50%, and doubling the pre- and post-treatment sample size are necessary to increase the power to 80%. The ability to detect change can be improved by including an additional explanatory variable such as paired watershed measurements. However, published guidelines have not explicitly quantified the benefits of including an explanatory variable or the specific conditions that favor a paired watershed design. This paper (1) presents a power analysis for the statistical model (analysis of covariance) commonly used in paired watershed studies; (2) discusses the conditions under which it is beneficial to include an explanatory variable; and (3) quantifies the benefits of the paired watershed design. The results show that it is beneficial to include an explanatory variable when its correlation to the water quality variable of concern is as low as about 0.3. The ability to detect change increases non-linearly as the correlation increases. Power curves quantify sample size requirements as a function of the correlation and intrinsic variability. In general, the temporal and spatial variability of many watershed-scale characteristics, such as annual sediment loads, makes it very difficult to detect changes within time spans that are useful for land managers or conducive to adaptive management.

Water quality monitoring—Some practical sampling frequency considerations

Water quality monitoring involves sampling a “population,” water quality, that is changing over time. Sample statistics (e.g., sample mean) computed from data collected by a monitoring network can be affected by three general factors: (1) random changes due to storms, rainfall, etc.; (2) seasonal changes in temperature, rainfall, etc.; and (3) serial correlation or duplication in information from sample to sample. (Closely spaced samples will tend to give similar information).In general, these effects have been noted, but their specific effects on water quality monitoring network design have not been well defined quantitatively. The purpose of this paper is to examine these effects with a specific data set and draw conclusions relative to sampling frequency determinations in network design.The design criterion adopted for this study of effects due to the above factors is the width of confidence intervals about annual sample geometric means of water quality variables. The data base for the study consisted of a daily record of 5 water quality variables at 9 monitoring stations in Illinois for a period of 1 year.Three general regions of frequencies were identified: (1) greater than approximately 30 samples per year where serial correlation plays a dominant role; (2) between approximately 10 and 30 samples per year where the effects of seasonal variation and serial correlation tended to cancel each other out; and (3) less than approximately 10 samples per year where seasonal variation plays a dominant role. In region 2, either seasonal variation and serial correlation should both be considered or both ignored. To consider only seasonal variation introduces more error than ignoring it. These results are network averages (over variables and stations) from one network, thus results for individual variables may deviate considerably from the average and from those for other networks.

Multivariate tests for trend in water quality

Several methods of testing for multivariate trend have been discussed in the statistical and water quality literature. We review both parametric and nonparametric approaches and compare their performance using, synthetic data. A new method, based on a robust estimation and testing approach suggested by Sen and Puri, performed very well for serially independent observations. A modified version of the covariance inversion approach presented by Dietz and Killeen also performed well for serially independent observations. For serially correlated observations, the covariance eigenvalue method suggested by Lettenmaier was the best performer.

optimizing Temporal Water Allocation by Irrigation Ditch Companies

ABSTRACT Adynamic programming (DP) algorithm is presented for allocation of irrigation water over time by ditch companies. The algorithm optimizes weekly deliveries of water to farmers and uses a single state variable, total storage in reservoirs at the beginning of each week. The DP objective is minimization of the sum of squared shortages over the irrigation season. The DP solution consists of optimal operating rules in the form of tables which indicate optimal target end-of-week storage as a function of beginning-of-week storage. One table is obtained for each week of the season. Stochastic treatment of crop water demand is compared against deterministic treatment using a case study ditch company near Fort Collins, CO. In repetitive simulations, stochastic DP always outperformed deterministic DP in terms of average sum of squared shortages, even when only two years of historical weather data were available for characterizing the reference E^ process.

Cost-effective selection of sampling frequencies for regulatory water quality monitoring

Abstract A dynamic programming code was formulated for the purpose of assigning sampling frequencies throughout a regulatory water quality monitoring network in order to optimize the statistical performance of the network while operating within a fixed budgetary constraint. The statistical objective is to achieve the greatest possible station to station uniformity in confidence interval widths about annual geometric means of the measured water quality variables and to keep the average confidence width reasonably small. The objective function is the sum (over several selected variables and all stations) of the normalized positive deviations of the predicted confidence interval widths from preselected design confidence interval widths. The code was designed to account for the effects of deterministic seasonal variation and serial correlation of the water quality observations by incorporating the results of the time series analysis of historical quality data. The economic constraint ensures that the annual operating cost of the system, including direct costs of travel and laboratory analysis, will not exceed the allowable budget. As an example situation, the dynamic programming code was used to assign sampling frequencies to the nine stations in Illinois from which historical quality data had been obtained and analyzed. Using five design quality constituents and representative travel and laboratory costs, an “optimal” design was produced. The optimal design achieved a 10% improvement in uniformity (standard deviation) of confidence interval widths when compared to a more traditional design based on the same budget and using identical sampling frequencies at every station.

spatial Interpolation of Penman Evapotranspiration

ABSTRACT FOR irrigation scheduling and hydrologic studies, it is often necessary to estimate reference evapotranspiration at points located some distance from a weather station. For regions which are served by weather station networks, one may interpolate, using evapotranspiration estimates from monitored locations. The approaches which are currently used for spatial interpolation include the Thiessen polygon, simple averaging, and inverse distance weighting. The present work examines the use of Kalman filtering as an alternate approach. The Kalman filter offers the advantages of considering reference evapotranspiration as a stochastic process and of accounting for measurement error and model error explicitly. The filter was found to be an acceptable algorithm for spatial interpolation of reference evapotranspiration based on diagonostic checks, lowest sum of squared error, and minimum variance estimates.