ABSTRACT
The evolution in time of environmental systems, in particular, geophysical ones, can be described via systems of partial differential equations. In most cases, these equations, that can be either linear or non-linear, embody the physical laws that are assumed to govern the temporal dynamics of the system, and need initial, and in some cases, boundary conditions in order to be integrated forward in time and thus predict the next state of the system. Data assimilation, that is, the combination of different sources of information, has been very successful and widely used in atmospheric sciences particularly in numerical weather forecasting where it is routinely and operationally implemented to derive weather forecasts. In regression-based approaches, the geophysical model output is considered as data and is used as a covariate in a linear regression model where the observational data is, in most cases, the outcome.
