MULTIVARIATE GEOSTATISTICAL TREND DETECTION AND NETWORK EVALUATION OF SPACE-TIME ACID DEPOSITION DATA .1. METHODOLOGY

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-stationarity of their spatial means, non-stationarity 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.