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.

There are a growing number of large-scale, complex hydrologic models that are capable of simulating integrated surface and subsurface flow. Many are coupled to land-surface energy balance models, biogeochemical and ecological process models, and atmospheric models. Although they are being increasingly applied for hydrologic prediction and environmental understanding, very little formal verification and/or benchmarking of these models has been performed. Here we present the results of an intercomparison study of seven coupled surface-subsurface models based on a series of benchmark problems. All the models simultaneously solve adapted forms of the Richards and shallow water equations, based on fully 3-D or mixed (1-D vadose zone and 2-D groundwater) formulations for subsurface flow and 1-D (rill flow) or 2-D (sheet flow) conceptualizations for surface routing. A range of approaches is used for the solution of the coupled equations, including global implicit, sequential iterative, and asynchronous linking, and various strategies are used to enforce flux and pressure continuity at the surface-subsurface interface. The simulation results show good agreement for the simpler test cases, while the more complicated test cases bring out some of the differences in physical process representations and numerical solution approaches between the models. Benchmarks with more traditional runoff generating mechanisms, such as excess infiltration and saturation, demonstrate more agreement between models, while benchmarks with heterogeneity and complex water table dynamics highlight differences in model formulation. In general, all the models demonstrate the same qualitative behavior, thus building confidence in their use for hydrologic applications.

Water scarcity is a serious environmental problem in many European regions, and will likely increase in the near future as a consequence of increased abstraction and climate change. Water scarcity exacerbates the effects of multiple stressors, and thus results in decreased water quality. It impacts river ecosystems, threatens the services they provide, and it will force managers and policy-makers to change their current practices. The EU-FP7 project GLOBAQUA aims at identifying the prevalence, interaction and linkages between stressors, and to assess their effects on the chemical and ecological status of freshwater ecosystems in order to improve water management practice and policies. GLOBAQUA assembles a multidisciplinary team of 21 European plus 2 non-European scientific institutions, as well as water authorities and river basin managers. The project includes experts in hydrology, chemistry, biology, geomorphology, modelling, socio-economics, governance science, knowledge brokerage, and policy advocacy. GLOBAQUA studies six river basins (Ebro, Adige, Sava, Evrotas, Anglian and Souss Massa) affected by water scarcity, and aims to answer the following questions: how does water scarcity interact with other existing stressors in the study river basins? How will these interactions change according to the different scenarios of future global change? Which will be the foreseeable consequences for river ecosystems? How will these in turn affect the services the ecosystems provide? How should management and policies be adapted to minimise the ecological, economic and societal consequences? These questions will be approached by combining data-mining, field- and laboratory-based research, and modelling. Here, we outline the general structure of the project and the activities to be conducted within the fourteen work-packages of GLOBAQUA.