“Wishful thinking” – how much rainfall information can be inferred from soil moisture and runoff?

Abstract:

In a land surface hydrologic system, rainfall is a major forcing (input) to drive the moisture and energy dynamics and the soil moisture and runoff are the result (output) of such dynamics. Land surface models (LSMs) have long been used to simulate such a dynamic system given the forcing input. The question here is whether, how much, and how the soil moisture and runoff (output) data can be used to recover rainfall (input) information or help improve our existing rainfall estimates. This is essentially to perform an inverse estimation of LSM. Such an inverse operation can help us optimally combine information (e.g. remote sensing observations) gathered across both input and output variables and improve our quantification of different components of the land surface hydrologic system and the consistency among them.

However, this is seemingly and indeed no easy task and some consider it more “wishful thinking” than practically meaningful, given the extremely complicated structure and behavior of the land surface hydrologic system. Here we explore two methods for solving the inverse LSM estimation problem (1) the Wiener Filter (WF) based deconvolution approach where the land surface is treated as a stationary linear system with fixed Impulse Response Function (IRF) w.r.t rainfall input and (2) the Particle Filter (PF) based Bayesian approach. The results suggest that while there is a limit of how much such inverse estimation can do under different conditions it is possible to recover a very significant amount of rainfall information from soil moisture and runoff.