Water Transport in Land Surface Models: From the Richards Equation to Catchment Water Balances

An accurate estimation of water exchange between land surface and atmosphere is critical for numerical weather prediction (NWP) and climate modelling in order to capture associated feedback processes to the atmosphere. Moreover, the partitioning of available energy at the surface into turbulent sensible and latent heat fluxes is highly sensitive to water availability, thus modulating the energy cycle. As our understanding of hydrological processes may not be formulated as a closed set of equations based on first principles, these processes have to be parameterized, involving the use of ad-hoc assumptions and poorly constrained free parameters in order to achieve acceptable model performance. Errors introduced by poor parameter choices or misrepresented processes often interact and compensate each other, both within the land-surface model as well as in the interaction with other parts of the NWP or climate model. It is therefore not sufficient to measure the quality of a land-surface model in the predictive capability of the coupled land-atmosphere model for standard meteorological variables, rather if one wants to truly advance a quantitative understanding of land-atmosphere interaction, model validation and development should be process-oriented. Kilometer-scale models pose substantial challenges and opportunities to state-of-the-art land surface models as individual watersheds are resolved both in terms of land surface properties as well as in terms of a more realistic, spatially distributed precipitation forcing. Thus, the more widespread use of kilometer-scale simulations in both NWP and climate modelling necessitates a careful reassessment of parameterizations within the land-surface model. In the first part of this thesis, we develop a validation framework based on catchment mass balances and apply the framework to four different versions of the TERRA ML land surface model on the kilometer-scale. Despite large observational uncertainties, the validation framework reveals a tight link between errors in catchment integrated runoff and errors in terrestrial water storage changes. The high sensitivity of runoff errors to different formulations of the infiltration process implies that the mathematical formulation of infiltration deserves more attention. As is the case for many land surface models, the governing equation for soil water propagation in TERRA ML is the one-dimensional Richards equation. A simple numerical convergence experiment in the second part of this thesis demonstrates a systematic and drastic decrease of infiltration capacity with increasing time step and decreasing vertical resolution. Grid setups of state-of-the art land surface models are found to be too coarse to achieve reasonable numerical convergence. The same is true for time steps longer than forty seconds, which is probably shorter than time steps chosen for many global models and for standalone applications of land-surface models. A second experiment with rainfall time series obtained from convection resolving and convection parameterized models puts the poor convergence found for typical model setups into context and shows the consequences for infiltration-runoff partitioning. The convergence problem aggravates for high-intensity precipitation events, which are more often found in highresolution convection-resolving numerical weather prediction and climate models. The observed difficulties in soil water modelling lead to the question as to what extent future projections of evapotranspiration are in accordance with fundamental mass and energy constraints as formulated in the Budyko hypothesis. The third part of this thesis thus makes use of the Budyko hypothesis as a physical consistency check for climate projections and shows that it is a helpful framework to disentangle model deficiencies in energy partitioning from model deficiencies in water partitioning. While the shift of hydrological states associated with climate change is mostly occurring aligned with the Budyko curve, high latitude river basins exhibit future evapotranspiration climatologies exceeding its energy limit. This may be explained by a net downward sensible heat flux on annual means which is contributing considerably to the surface energy balance. On the one hand, the sensible heat flux may be exaggerated in the climate projection and on the other hand, the energy limit of the Budyko hypothesis completely misses this contribution to the surface energy balance. In summary, this thesis highlights the importance of mathematical, numerical and physical accuracy for model performance on diurnal to inter-annual time scales and the added value of process-oriented validation strategies to pinpoint areas, where future development efforts should be focused