Accounting for the Effect of Noise in Satellite Soil Moisture Data on Estimates of Land–Atmosphere Coupling Using Information Theoretical Metrics

Abstract

Abstract Land states can affect the atmosphere through their control of surface turbulent fluxes and the subsequent impact of those fluxes on boundary layer properties. Information theoretic (IT) metrics are ideal to study the strength and type of coupling between surface soil moisture (SM) and land surface heat fluxes (HFs) because they are nonparametric and thus appropriate for the analysis of highly complex Earth systems containing nonlinear cause-and-effect interactions that may have nonnormal distributions. Specifically, a methodology for the estimation of IT metrics from noisy time series is proposed, accounting for random errors in satellite-based SM data. Performance of the proposed method is demonstrated through synthetic tests. Efficacy of the method is greatest for estimates of entropy and mutual information involving SM; improvements to estimates of transfer entropy are significant but less stark. A global depiction of the information flow between SM and HFs is then constructed from observationally based gridded data. This is used as independent verification for two configurations of the ECMWF modeling system: unconstrained open-loop (retrospective forecasts) and constrained by data assimilation (ERA5). Compared to studies that only investigate the linear SM–HF relationships, extended regions of significant terrestrial coupling are found over the globe, as IT metrics enable detection of nonlinear dependencies. The magnitude and spatial variability of coupling strength and type from models show discrepancies with those from observations, highlighting the potential to improve SM and HF covariability within models. Although ERA5 did not perform better than the unconstrained model in very dry climates, its performance is generally superior to that of the unconstrained model across metrics.