KALMAN FILTERING IN GROUNDWATER-FLOW MODELING - PROBLEMS AND PROSPECTS

The popularity of applying filtering theory in the environmental and h ydrological sciences passed its first climax in the 1970s. Like so man y other new mathematical methods it was simply the fashion at the time . The study of groundwater systems was not immune to this fashion, but neither was it by any means a prominent area of application. The spat ial-temporal characteristics of groundwater flow are customarily descr ibed by analytical or, more frequently, numerical, physics-based model s. Consequently, the state-space representations associated with filte ring must be of a high order, with an immediately apparent computation al over-burden. And therein lies part of the reason for the but modest interest there has been in applying Kalman filtering to groundwater s ystems, as reviewed critically in this paper. Filtering theory may be used to address a variety of problems, such as: state estimation and r econstruction, parameter estimation (including the study of uncertaint y and its propagation), combined state-parameter estimation, input est imation, estimation of the variance-covariance properties of stochasti c disturbances, the design of observation networks, and the analysis o f parameter identifiability. A large proportion of previous studies ha s dealt with the problem of parameter estimation in one form or anothe r. This may well not remain the focus of attention in the future. Inst ead, filtering theory may find wider application in the context of dat a assimilation, that is, in reconstructing fields of flow and the migr ation of sub-surface contaminant plumes from relatively sparse observa tions.