Opinion paper: How to make our models more physically-based
Abstract. Catchment-scale hydrological models that are generally called "physically-based" unfortunately only have a partial view of the physical processes at play in hydrology. Although the coupled partial differential equations in these models generally reflect the water balance equations and the flow descriptors at laboratory scale, they miss essential characteristics of what determines the functioning of catchments. The most important active agent in catchments is the ecosystem (and sometimes people). What these agents do is to manipulate the flow domain in a way that it supports the essential functions of survival and productivity: infiltration of water, retention of moisture, mobilization and retention of nutrients, and drainage. Ecosystems do this in the most efficient way, establishing a continuous, ever-evolving feedback loop with the landscape and climatic drivers. In brief, our hydrological system is alive and has a strong capacity to adjust itself to prevailing and changing environmental conditions. Although most physically based models take Newtonian theory at heart, as best they can, what they generally miss is Darwinian theory on how an ecosystem evolves and adjusts its environment to maintain crucial hydrological functions. If this active agent is not reflected in our models, then they miss essential physics. Through a Darwinian approach, we can determine the root zone storage capacity of ecosystems, as a crucial component of hydrological models, determining the partitioning of fluxes and the conservation of moisture to bridge periods of drought (Gao et al., 2014a). Another crucial element of physical systems is the evolution of drainage patterns, both on and below the surface. On the surface, such patterns facilitate infiltration or surface drainage with minimal erosion; in the unsaturated zone, patterns facilitate efficient replenishment of moisture deficits and preferential drainage when there is excess moisture; in the groundwater, patterns facilitate the efficient and gradual drainage of groundwater, resulting in linear reservoir recession. Models that do not account for these patterns are not physical. The parameters in the equations may be adjusted to compensate for the lack of patterns, but this involves scale-dependent calibration. In contrast to what is widely believed, relatively simple conceptual models can accommodate these physical processes very efficiently. Of course the parameters of catchment-scale conceptual models, even if they represent physical parameters, such a time scales, thresholds and reservoir sizes, require calibration or estimation on the basis of observations. Fortunately, we see the emergence of new observation systems from space that become more and more accurate and detailed as we go along. Recent products estimating precipitation and evaporation from space have shown to allow the estimation of the root zone storage capacity of ecosystems globally (Lan-Erlandsson et al., 2016), DEMs allow the identification of heterogeneity in the landscape, providing information on the heterogeneity of dominant runoff generating mechanisms (Gharari et al., 2011, Gao et al., 2014b), and gravity observations from space can be used to estimate sub-surface storage fluctuation and groundwater recession (Winsemius et al., 2009). As a result, it will become more and more practical to calibrate well-structured conceptual models, even in poorly gauged catchments. These insights and developments will contribute to the revaluation of conceptual models as physics-based representations of hydrological systems.
