Scaling in Surface Hydrology: Progress and Challenges

Surface hydrology has experienced tremendous progress in the last few decades thanks to observational campaigns and platforms, the development of new theories and models, and the increase in computational power. Still, the spatial scales resolved in weather (~10 km) and climate (~100 km) models remain too coarse for accurate water resource management, prediction of floods, ecosystem services, and water quality, as well as accurate stream flow determination. Surface hydrologic processes are often viewed or analyzed at the scale of watersheds, which is also the scale at which water resources management occurs. Larger watersheds may be subdivided into a set of smaller watersheds. The area of a watershed ranges from a few hectares (100 m2) to thousands of square kilometers. The smaller watersheds are interconnected and constrain the surface water budget. Even over small watersheds, heterogeneities in the soil, topography, and vegetation can profoundly affect the surface water cycle (Maxwell et al. 2007; Weigel et al. 2007). Consequently, the current generation of numerical weather and climate prediction models fall short of reasonably forecasting the local surface hydrologic state (e.g., soil moisture, evapotranspiration, and surface runoff). Higher-resolution modeling is thus required (Wood et al. 2011) for accurate surface hydrologic prediction. The large range of temporal scales in hydrology, from sub-hourly to decadal and beyond, also creates challenges. Even while our ability to numerically model the range of time scales has greatly improved with increased computational power, the datasets necessary to validate models across the entire range of scales are absent. Thus, it is quite possible that a model that works well on a particular time scale may be insufficient on other time scales. A further challenge to accurate representation of the surface hydrologic state involves the scaling of physical surface hydrologic processes themselves (Entekhabi et al. 1999). At present, our understanding of the scaling (both up and down) of such processes remains relatively abstract: 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.