A modified Richards equation, its adjoint, and a new perspective on land data assimilation

Summary Richards equation, which is the key relationship for addressing basic soil hydrological processes within the rhizosphere and constitutes the basis for multiple-layer soil hydrology models for meteorological studies, is modified to include two vegetation processes: the transpiration (daytime) and hydraulic lift (nighttime). The analytical form of the adjoint system is derived and can serve as the guideline for discrete forms, as implemented in a variety of multiple layer land surface models. The modified equation and its adjoint model may be used to address at least two types of inverse problems: estimation of the initial soil moisture contents from sparse observations of related quantities; and retrieval of critical soil/vegetation parameters with observations of soil moisture contents (or other related quantities) distributed over a certain period of time. The former may be of more interest for numerical weather prediction studies, whereas the latter may be more valuable for longer time integration of climate models.