Physically based modeling in catchment hydrology at 50: Survey and outlook

Abstract

Integrated, process‐based numerical models in hydrology are rapidly evolving, spurred by novel theories in mathematical physics, advances in computational methods, insights from laboratory and field experiments, and the need to better understand and predict the potential impacts of population, land use, and climate change on our water resources. At the catchment scale, these simulation models are commonly based on conservation principles for surface and subsurface water flow and solute transport (e.g., the Richards, shallow water, and advection‐dispersion equations), and they require robust numerical techniques for their resolution. Traditional (and still open) challenges in developing reliable and efficient models are associated with heterogeneity and variability in parameters and state variables; nonlinearities and scale effects in process dynamics; and complex or poorly known boundary conditions and initial system states. As catchment modeling enters a highly interdisciplinary era, new challenges arise from the need to maintain physical and numerical consistency in the description of multiple processes that interact over a range of scales and across different compartments of an overall system. This paper first gives an historical overview (past 50 years) of some of the key developments in physically based hydrological modeling, emphasizing how the interplay between theory, experiments, and modeling has contributed to advancing the state of the art. The second part of the paper examines some outstanding problems in integrated catchment modeling from the perspective of recent developments in mathematical and computational science.

The evolution of process-based hydrologic models: historical challenges and the collective quest for physical realism

“…The first solution, and the most obvious, is to exploit advances in massively parallel (e.g., exa-scale) computation (Kollet et al, 2010;Wood et al, 2011;Paniconi and Putti, 2015;Fatichi et al, 2016). This solution is often implemented by running a complex model at the finest grid resolution possible over the domain of interest (e.g., Maxwell et al, 2015;Maxwell and Condon, 2016).…”

Characterizing and reducing equifinality by constraining a distributed catchment model with regional signatures, local observations, and process understanding

“…Currently, researchers approach distributed modeling and parameter set selection in a number of different ways, all of which have implications for reducing equifinality. Many studies avoid the topics of uncertainty or equifinality by assigning parameter values from measurements (e.g., Du et al, 2014), though the sheer number of parameters, heterogeneity of the catchment environment, uncertainty in model structure and inputs, and problems translating measurements from the point to the grid scale can make this difficult (Grayson et al, 1992;Surfleet et al, 2010;Paniconi et al, 2015). Other approaches involve fixing some parameters, while letting others vary, often through manual calibration.…”

“…While there are examples where different observations, including snow accumulation and melt (Thyer et al, 2004;Whitaker et al, 2003), soil moisture (Koren et al, 2008;Graeff et al, 2012), and catchment chemistry (Birkel et al, 2014), have been incorporated into the calibration and parameter set selection process, many catchments lack measurements beyond streamflow, suggesting that other sources of information are needed Grayson et al, 2002;Paniconi et and Putti, 2015). Finally, while examples exist where model simulations are compared to internal measurements of different hydrologic processes at a few points, there are fewer examples where researchers holistically evaluate the patterns of these simulated processes (Franks et al, 1998;Lamb et al, 1998;Grayson et al, 2002;Wealands et al, 2005;Koch et al, 2016).…”

“…Towards this end, distributed, physically based models were first developed as tools to represent spatially discretized processes with physically meaningful parametric relationships (Freeze and Harlan, 1969;Beven and Kirkby, 1979;Band et al, 1991Band et al, , 1993Wigmosta et al, 1994;Refsgaard and Storm, 1995;Bixio et al, 2002;Qu, 2004;Qu and Duffy, 2007;Camporese et al, 2010;Fatichi et al, 2016). Distributed models should represent the characteristics of the catchment environment in space, given that this variability impacts how water is stored, partitioned, and released across the landscape (O'Loughlin, 1981;Beven,model parameters (see Singh and Woolhiser, 2002;Kampf and Burges, 2007;Paniconi and Putti, 2015, for a review of distributed models).…”

HESS Opinions: The complementary merits of competing modelling philosophies in hydrology

“…Models at the lowresolution and low-complexity end of the continuum are criticized for lacking a robust physical or theoretical basis and for their inability to meaningfully represent spatial patterns (e.g. Paniconi and Putti, 2015;Fatichi et al, 2016), whereas models at the high-resolution and high-complexity end are often viewed as having inferior representations of sub-grid variability (e.g. Beven and Cloke, 2012) and as being not sufficiently agile to represent the dominant processes in different environments (e.g.…”