Investigating soil moisture feedbacks on precipitation with tests of Granger causality

Granger causality (GC) is used in the econometrics literature to identify the presence of one- and two-way coupling between terms in noisy multivariate dynamical systems. Here we test for the presence of GC to identify a soil moisture (S) feedback on precipitation (P) using data from Illinois. In this framework S is said to Granger cause P if F(P_t|Ω_t−Δt)≠F(P_t|Ω_t−Δt−S_t−Δt) where F denotes the conditional distribution of P, Ω_t−Δt represents the set of all knowledge available at time t−Δt, and Ω_t−Δt−S_t−Δt represents all knowledge except S. Critical for land–atmosphere interaction research is that Ω_t−Δt includes all past information on P as well as S. Therefore that part of the relation between past soil moisture and current precipitation which results from precipitation autocorrelation and soil water balance will be accounted for and not attributed to causality. Tests for GC usually specify all relevant variables in a coupled vector autoregressive (VAR) model and then calculate the significance level of decreased predictability as various coupling coefficients are omitted. But because the data (daily precipitation and soil moisture) are distinctly non-Gaussian, we avoid using a VAR and instead express the daily precipitation events as a Markov model. We then test whether the probability of storm occurrence, conditioned on past information on precipitation, changes with information on soil moisture. Past information on precipitation is expressed both as the occurrence of previous day precipitation (to account for storm-scale persistence) and as a simple soil moisture-like precipitation-wetness index derived solely from precipitation (to account for seasonal-scale persistence). In this way only those fluctuations in moisture not attributable to past fluctuations in precipitation (e.g., those due to temperature) can influence the outcome of the test. The null hypothesis (no moisture influence) is evaluated by comparing observed changes in storm probability to Monte-Carlo simulated differences generated with unconditional occurrence probabilities. The null hypothesis is not rejected (p>0.5) suggesting that contrary to recently published results, insufficient evidence exists to support an influence of soil moisture on precipitation in Illinois.