Can system dynamics explain long-term hydrological behaviors? The role of endogenous linking structure

Abstract

Hydrological models with conceptual tipping bucket and process-based evapotranspiration formulations 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 a shift in formulation approach. This study employed an entirely different approach - system dynamics - towards more realistic replication of the observed slow hydrological behaviors at inter-annual and inter-decadal scales. Using the headwaters of Baiyang Lake in China as a case study, the endogenous linking structure of the hydrological system was gradually unraveled from 1982 to 2015 through wavelet analysis, Granger's causality test, and a system dynamics model. The wavelet analysis and Granger's causality test identified a negatively correlated and bidirectional causal relationship between actual evapotranspiration and catchment water storage change across distinct climatic periodicities, and the system dynamics approach suggested a combined structure of a vegetation reinforcing feedback and a soil water-vegetation balancing feedback in the hydrological system. The system dynamics' structure successfully captured the slow hydrological behaviors under both natural and human-intervention scenarios, demonstrating a self-sustained oscillation arising within the system's boundary. Our results showed that the interaction between the vegetation structure and the soil-bound water dominates the hydrological process at an inter-annual scale, while the interaction between the climatic oscillation and the soil-water-holding capacity dominates the hydrological process at an inter-decadal scale. Conventional hydrological models, which typically employ physiological-based evapotranspiration formulations and assume invariable soil characteristics, ignore vegetation structure change at the inter-annual scale and soil-water-holding capacity change at the inter-decadal scale, leading to failure in predicting the observed long-term hydrological behaviors. The system dynamics model is in its early stage with applications primarily confined to water-stressed regions and long-term scales. However, the novel insights proposed in our study, including the different hierarchies corresponding to distinct mechanisms and timescales and the endogenous linking structure among stocks being a more important driver of the hydrological behaviors, offer potential solutions for better understanding a hydrological system and guidelines for improving the configuration and performance of conventional hydrological models.