Scaling relationships in hydrological quantities and pollutant loads across river basins

Quantities such as discharge, flow velocity, water depth, and pollutant loads are essential for understanding pollutant emissions and for effective hydrological management, including flood control, water supply, and ecosystem preservation. Despite their critical importance and advances in data collection and modeling, the challenge of predicting these quantities in ungauged or poorly monitored basins persists. In the case of pollutants, this issue is complexified by the growing number of pollutants requiring evaluation. For example, within the EU, more than 100,000 chemical compounds require assessment.

Scaling relationships, which relate system characteristics to basin size metrics, offer a promising stepping stone to address this challenge. For instance, river discharge - one of the most fundamental hydrological metrics - has been shown to scale with basin size through power-law relationships. This scaling is also influenced by additional factors such as climatic conditions, land use, and geomorphology, underscoring the need for integrated approaches to characterize the scaling relationship. Similarly, pollutant loads are often expressed through models such as the Concentration-Discharge (C-Q) relationship, which links pollutant concentrations (C) to discharge rates (Q). While such models provide valuable insights, their applicability requires robust scaling principles to account for variability in pollutant sources, and transport mechanisms. 

In this contribution, we present our framework to derive scaling relationships for key quantities in the hydrological cycle and pollutant loads within river basins, focusing on their dependence on size-related indicators of river basins. Scaling principles of metrics such as discharge, flow velocity, water depth, and groundwater volume are derived using observational datasets, such as Global Runoff Data Center and SWOT river database. For pollutant loads and emissions, where monitoring is limited to a few key indicators, scaling principles offer promising avenues to predict emissions across diverse systems. By linking hydrological and pollutant-related variables through consistent scaling principles, we aim to provide a unified approach to understanding variability across river basins of different sizes. This work underscores the value of scaling relationships in bridging theoretical insights and practical applications, offering tools for improved management of water resources and pollutant impacts.