Integration of hydrological models with data-driven techniques in cold regions

The complex interaction among meteorological, glaciological, and hydrological variables presents challenges for glacio-hydrological modeling, necessitating advanced methodologies to capture the intertwined system. This study aimed to combine the traditional process-based hydrological model and data-driven techniques to enhance hydrological predictions in glacierized catchments. One glacierized catchment in northern Sweden was used as the testing site. We used a process-based glacio-hydrological model (FLEX^G) and a machine learning approach (the M5Tree model) to assess and enhance the predictive capabilities of hydrological simulations. A suite of meteorological variables, such as air temperature, precipitation, evapotranspiration, relative humidity, sunshine hours, solar radiation, and wind speed, in combination with glacio-hydrological outputs from the FLEX^G model, including snow cover area, snow water equivalent, and glacier mass balance, were used as inputs to the M5Tree model. Nine distinct scenarios were examined to explore the individual and cumulative impacts of these variables on the accuracy of runoff simulation. We started with the first scenario (named as M5Tree1) in which all meteorological and glacio-hydrological variables were used; this scenario serves as a benchmark for comparison against the other scenarios. Sequentially, each scenario omitted one variable to elucidate its specific contribution to runoff modeling. The final scenario (M5Tree9) used only air temperature and precipitation as inputs, reflecting their fundamental role in hydrological processes. The Variable Mode Decomposition (VMD), as a signal decomposition technique, was employed to enhance runoff modelling accuracy. This technique facilitated the dissection of each meteorological and glacio-hydrological variable into five distinct sub-signals, offering a more nuanced understanding of their contributions to runoff dynamics. Subsequently, the scenarios were re-evaluated with inputs derived from the VMD-decomposed variables (VMD-M5Tree1 to VMD-M5Tree9). The results showed remarkable improvements in the accuracy of runoff simulation with the incorporation of VMD. Our study demonstrated the significance of meticulous variable selection and decomposition techniques (particularly VMD) in improving model accuracy. We identified the optimal combination of meteorological and glacio-hydrological variables for robust runoff simulation. This study explored a singular approach among various methods to integrate traditional models and machine learning techniques for combining their respective strengths. Future research could explore other different ways in combining traditional models and machine learning techniques to improve runoff simulation. Additionally, given the vulnerability of glacierized catchments to climate change, future studies should incorporate future climate projections to assess the adaptability of the proposed integrated modelling framework and to understand the impact of climate change on runoff in cold regions.