Hybrid multi-model ensemble learning for reconstructing gridded runoff of Europe for 500 years

Runoff is a crucial water cycle component that contributes to the water resources to sustain human life. Historical trends in runoff, when examining climate change scenarios, provide vital information about past variability and support the design of adaptation measures. However, hydrological models based on climate data, such as the Budyko model, can be biased in estimating annual runoff due to input data uncertainty. Therefore, it is vital to utilize advanced machine learning-based computing models to reduce uncertainty and reconstruct climate variables over a long period of time and sufficiently large spatial coverage, preferably at a continental scale. We propose and test a novel machine learning-based framework called Hybrid Ensemble Multi-Model Framework (HEMMF) to reconstruct the gridded runoff of Europe over a 500-year historical period (1500 to 1999). The HEMMF combines non-parametric extended data pattern recognition and data-driven methods. The extended data patterns are computed using Moran's spatial autocorrelation (SPA) index of the climate variable fields and the Budyko models output, whereas the data-driven methods contain nine different machine learning (ML) algorithms and four ensembles of ML. The extended data patterns are jointly ingested with climate-reconstructed data (precipitation, temperature, Palmer's drought severity index) as predictor variables, which serve as input for the data-driven methods. To assess the impact and contribution of SPA, the runoff is simulated based on three different input training datasets in the HEMMF: (1) a dataset containing only precipitation, temperature, Palmer's drought severity index, and four different estimates of runoff from the Budyko model, (2) a dataset containing only SPA of the first input datasets, and (3) a dataset created by merging the first and second datasets. The HEMMF offers the best reconstruction performance when using the third input dataset. This reconstructed runoff helps to explain the runoff trend, drought propagation, and runoff's link with the climate variables. The proposed methodology has the potential to be applied to past hydroclimatic data and related analyses across different temporal periods, climate scenarios, and geographical scales.