Data-driven scale extrapolation: estimating yearly discharge for a large region by small sub-basins

Abstract. Large-scale hydrological models and land surface models are so far the only tools for assessing current and future water resources. Those models estimate discharge with large uncertainties, due to the complex interaction between climate and hydrology, the limited availability and quality of data, as well as model uncertainties. A new purely data-driven scale-extrapolation method to estimate discharge for a large region solely from selected small sub-basins, which are typically 1–2 orders of magnitude smaller than the large region, is proposed. Those small sub-basins contain sufficient information, not only on climate and land surface, but also on hydrological characteristics for the large basin. In the Baltic Sea drainage basin, best discharge estimation for the gauged area was achieved with sub-basins that cover 5% of the gauged area. There exist multiple sets of sub-basins whose climate and hydrology resemble those of the gauged area equally well. Those multiple sets estimate annual discharge for the gauged area consistently well with 6 % average error. The scale-extrapolation method is completely data-driven; therefore it does not force any modelling error into the prediction. The multiple predictions are expected to bracket the inherent variations and uncertainties of the climate and hydrology of the basin.