We analyze the propagation of daily fluctuations in rainfall and potential evapotranspiration to soil moisture dynamics, using a stochastic model that accounts for these two different forms of hydroclimatic variability. The pulsing, intermittent behavior of daily precipitation is described by a compound Poisson process that models the unpredictability of both frequency and amount of rainfall events, while fluctuations in potential evapotranspiration that act continuously in time are assumed to be Gaussian. The resulting model for the soil water balance is thus a stochastic differential equation, forced by a state-dependent compound Poisson noise and a multiplicative Gaussian noise. Steady state probability distribution functions (pdfs) of soil moisture are obtained analytically along with the equations for the expected water balance and its variability. The multiplicative effect of temporal fluctuations in potential evapotranspiration on soil moisture reduces the soil water losses caused by evapotranspiration compared to the case when they are not present. Most importantly, the analysis also shows that because of their different forms and state dependence the impact of rainfall variability on soil moisture dynamics is much more significant than that of potential evapotranspiration, the fluctuations of which do not affect appreciably the soil moisture statistical properties.
All Science Journal Classification (ASJC) codes
- Water Science and Technology