Scaling in Surface Hydrology: Progress and Challenges

This paper presents a review of the challenges in spatial and temporal scales in surface hydrology. Fundamental issues and gaps in our understanding of hydrologic scaling are highlighted and shown to limit predictive skill, with heterogeneities, nonlinearities, and non-local transport processes among the most significant difficulties faced in scaling. The discrepancy between the physical process scale and the measurement scale has played a major role in restricting the development of theories, for example, relating observational scales to scales of climate and weather models. Progress in our knowledge of scaling in hydrology requires systematic determination of critical scales and scale invariance of physical processes. In addition, viewing the surface hydrologic system as composed of interacting dynamical subsystems should facilitate the definition of scales observed in nature. Such an approach would inform the development of careful, resolution-dependent, physical law formulation based on mathematical techniques and physical laws.