System dynamics perspective: lack of long-term endogenous feedback accounts for failure of bucket models to replicate slow hydrological behaviors

Abstract. Hydrological models with the conceptual tipping bucket and the process-based evapotranspiration models are the most common tools in hydrology. However, these models consistently fail to replicate long-term and slow dynamics of a hydrological system, indicating the need for model augmentation and shift in approach. This study employed an entirely different approach – system dynamics – towards more realistic replication of long-term and slow hydrological behaviors by removing limits of exogenous climate on evapotranspiration and involving endogenous soil water-vegetation feedback loop. Using the headwaters of Baiyang Lake in China as a case study, the mechanisms of slow hydrological dynamics were gradually unraveled from 1982 to 2015 through wavelet analysis, Granger's causality test, and system dynamics. The wavelet analysis and Granger's causality test identified a negative-correlated, bidirectional causal relationship between evapotranspiration and the water budget across distinct climatic periodicities, suggesting a robust endogenous soil water-vegetation feedback structure operating on a long-term scale. The system dynamics approach successfully captured the slow behavior of the hydrological system under both natural and human-intervention scenarios, demonstrating a self-sustained oscillation arising within the system's boundary. Conventional hydrological models, which rely on process-based evapotranspiration models, operate on an instantaneous scale and are thus susceptible to short-time climatic and vegetation physiological variations. This results in inaccurate depletion rate of soil water stock and in turn, can lead to incorrect calculations of other hydrological variables. However, long-term and slow hydrological dynamics typically involves in endogenous state-dependent modulation and feedback related to changes in vegetation structure, thus are insensitive to exogenous disturbances and can be well replicated using system dynamics approach. This insight that the failure of hydrological models to replicate slow dynamics can be attributed to a time-scale mismatch may offer potential solutions for improving conventional hydrological models.