Shahrokh Rouhani

Problems in space-time kriging of geohydrological data

Spatiotemporal variables constitute a large class of geohydrological phenomena. Estimation of these variables requires the extension of geostatistical tools into the space-time domain. Before applying these techniques to space-time data, a number of important problems must be addressed. These problems can be grouped into four general categories: (1) fundamental differences with respect to spatial problems, (2) data characteristics, (3) structural analysis including valid models, and (4) space-time kriging. Adequate consideration of these problems leads to more appropriate estimation techniques for spatiotemporal data.

SPACE-TIME KRIGING OF GROUNDWATER DATA

A large number of geohydrological variables may be viewed as realizations of spatiotemporal random functions. In many instances, the available data are composed of long time series, located at few scattered points. To analyse such data sets it seems imperative to expand the available geostatistical techniques into the time-space domain. It is assumed that the spatial and the temporal components of the data can be characterized by intrinsic random functions. The space-time kriging is then applied to groundwater quantity data in southern Georgia. It appears that this procedure yields maps with lower estimation variances, while allowing forecasting and hindcasting.

Geostatistical schemes for groundwater sampling

Abstract Geostatistical techniques offer efficient tools for design of groundwater sampling networks. They include procedures for the selection of the best sequences of sampling points, such as: variance reduction analysis, median ranking, and risk ranking. Variance reduction analysis considers primarily the accuracy of the estimated field, while median ranking is based only on the magnitude of the estimated values. Risk ranking is a compromise between these procedures that appears to yield a more balanced guideline for cases when planners desire to acquire maximum information, while monitoring areas where the variable of interest exhibits critical values. These procedures are used for the design of a regional shallow groundwater quality monitoring network in the Dougherty Plain, located in southwest Georgia. The shallow aquifer of concern is the main recharge route to a semiconfined aquifer which is the primary source of water in this region. The desired monitoring network acts as an early warning system for groundwater pollution in deeper layers. Leakance data are utilized to identify the primary sampling locations. Statistical analyses indicate that leakance has a log-normal distribution with a constant drift and a linear spatial covariance. The results of our risk rankings demonstrate that the southern tip of the Dougherty Plain and its upper central zone should be the prime targets of our monitoring activities.

Resilience of a statistical sampling scheme

Abstract Most statistical sampling algorithms on hydrologic random fields assume that the new measurements will agree reasonably well with their predicted values. This in turn implies the stationarity of the estimated covariance function. In order to test the reliability of one such statistical algorithm (i.e., variance reduction analysis), noisy input data are generated, and results of sampling from these data are compared to the case of sampling with the unperturbed data. These comparisons and a related regret analysis reveal that the effects of the noisy data are primarily accommodated by adjustments to the covariance function parameters, while selected sets show a high degree of resilience. Variance reduction analysis seems to be a reliable method for maximizing information by sampling random fields with an unstable parameter space but a resilient action space.

Multivariate geostatistical trend detection and network evaluation of space-time acid deposition data. I: Methodology

Abstract A multivariate geostatistical technique is presented to address two key issues of trend detection and network evaluation of acid deposition data. The proposed technique is specifically designed to be compatible with the distinctive characteristics of acid deposition variables such as non-stationary of their spatial means, non-stationary of their spatial covariances, their complex periodic and non-periodic temporal trends, and the common imbalance between the availability of their spatial and temporal data. To accomplish this, the time series at each measurement point is viewed as a separate, but correlated one-dimensional regionalized variable. Each variable is assumed to be a sum of periodic (e.g. seasonal) and non-periodic (e.g. anthropogenic) temporal random variables, each characterized by its own temporal variogram. To obtain an initial estimate of the frequency of the involved periodic trends, direct quadratic spectrum estimation is conducted. Based on fitted direct and cross variograms, various forms of estimation such as co-kriging of non-periodic components can be performed. The estimated time series may then be tested for the presence of long-term trends. In addition, the fitted sill values of any variogram model at different stations form elements of a coregionalization matrix. This matrix may be regarded as the variance-covariance matrix for the particular temporal-trend scale presented by the variogram model. A coregionalization matrix can be used to generate a spatial correlogram. Viewing the estimated integral scale of each spatial correlogram as an indicator of the radius of information-influence of each measurement station, a monitoring network can be evaluated for its adequacy of coverage at different temporal-trend scales. A coregionalization matrix can also be decomposed through principal-component analysis in order to determine any potential spatial groupings and/or to generate regional indicators of changes at different temporal scales.

Multivariate geostatistical trend detection and network evaluation of space-time acid deposition data—II. Application to NADP/NTN data

Abstract A multivariate geostatistical technique was presented in the first part of this paper (Rouhani et al., 1992, Atmospheric Environment 26A, 2603–2614) with the objective of addressing two key issues of trend detection and network evaluation of the acid deposition data. The investigated data include weekly reported SO42− concentrations and depositions from 34 level-1 stations of the NADP/NTN. The duration of the available data ranges from 6 to 10 years. In order to extract the maximum amount of information from these relatively short time series, it is imperative to avoid any data reduction, such as integrating the data into seasonal or annual series. Direct quadratic spectrum estimation is applied to the data, which clearly indicates the presence of annual cycles in a large number of stations. Based on these preliminary results, measurement stations are grouped into three main eco-regions, including the Northeast/central, the West and the Midwest/Gulf regions. While the first two regions exhibit significant annual periodicities, the latter region does not show any significant cyclic characteristics. This analysis is followed by multi-scale temporal variography that further confirms the presence of periodic trends. Two types of time series are generated by co-kriging: (1) the non-periodic components at each station, and (2) the non-periodic regionalized factors for each region. Kendalls test for trend detection is applied to all generated time series, as well as to the original data. The results indicate that by geostatistical filtering of periodic components, the proposed procedure offers an efficient technique for trend detection. Using the estimated coregionalization matrices, spatial correlograms are generated for various temporal scales and regions. Viewing the estimated integral scale of each spatial correlogram as an indicator of the radius of information-influence of each measurement station, the NADP/NTN network is evaluated for its adequacy of coverage under different temporal scales.

A geostatistical tool for drought management

Abstract Drought lead time is a useful tool to enable local reservoir operators to predict the possibility of the occurrence of a hydrological drought. Universal time kriging, a geostatistical technique, can be used to predict streamflows in low-flow seasons to yield an estimate of drought lead time for a given operating policy and initial conditions. This is an indicator of the severity of an approaching drought. The case study concerns a hypothetical reservoir in western Georgia. This area has experienced a number of drought periods in recent years. Using the actual and the estimated data, drought lead times for different initial storage values are calculated. The comparison indicates that the proposed procedure yields reliable estimates of drought lead time.