Directives for 4-D soil moisture data assimilation in hydrological modelling

Data assimilation is a procedure to provide time-dependent spatially-distributed estimates of a dynamic system using observations from various sources and with various physical constraints in an efficient way. Mathematically, it can be seen as a state estimation procedure. The spatio-temporal prediction of soil moisture is pre-eminently a problem that can be dealt with by data assimilation techniques. Even though there is considerable literature on data assimilation in the environmental sciences, the application to soil moisture estimation is still new. To date only the problem of integrating remotely sensed data or field-observations over a small area with a one-dimensional soil moisture model of the root zone has been studied. In all cases the assimilation technique comprises simplifications or variants of the weak-constraint variational technique (equivalent to the Kalman smoother). Problems involving more spatial dimensions and more diverse information sources have not yet been dealt with. This is partly because the dimensionality of the problem prohibits a straightforward extension of the common algorithms, i.e. new data assimilation algorithms need to be developed. The lack of appropriate data sets and regularization tools is also a serious impediment. As a first step towards applying soil moisture data assimilation to problems of a higher dimension, this study outlines the desirable structure of 4-D hydrological data assimilation algorithms, and discusses the consequences for data handling and the specification of hydrological models.