Can Hydrological Models Reproduce Time-Lagged Dependencies?

Abstract:

Methods developed to infer causality and connectivity between processes represent an opportunity to advance the understanding and modeling of hydrological systems. This study assessed the behavior of a conceptual model to verify whether the time-lagged dependencies (TLDs) between observed (flux and state) variables can be reproduced. The conceptual model was parameterized, implemented and calibrated based on previous modeling studies and observed data (groundwater levels - GWL, streamflow - Q, weather data, and remote sensing vegetation indices - EVI, from 2008 to 2019) referred to a tropical catchment (52 km²), located in an outcrop area (agricultural use) of the Guarani Aquifer System, Brazil. The Granger causality test (GC) and the normalized time-lagged mutual information (NMI) were used to determine the relationships within and between observed and modeled datasets. Not surprisingly, causality and persistence were widely found in the study area hydrological system. The NMI indicated diverse patterns of dependencies between precipitation data (P), evapotranspiration (ET), Q, and GWL, including the seasonal effects. The GC confirmed causality between most of the variables, even when large lags (>300 days) were considered. The model was capable to reproduce exceptionally well the patterns of dependencies between observed P and ET and the model storage state variable representing the groundwater level changes. Slight differences were noted in other cases. Some of the patterns resulting from the NMI analysis suggest that both the land use and the depth of wells affect the statistical results. The satisfactory reproduction of TLDs between flux and state variables may be used in the future as evidence of model consistency. Causality analysis can provide us with additional ways to take advantage of observed data and to propose and evaluate models, transforming them into more effective scientific tools to address questions and hypotheses in hydrology.