Emmanuel Mouche

The integrated hydrologic model intercomparison project, IH‐MIP2: A second set of benchmark results to diagnose integrated hydrology and feedbacks

Emphasizing the physical intricacies of integrated hydrology and feedbacks in simulating connected, variably saturated groundwater-surface water systems, the Integrated Hydrologic Model Intercomparison Project initiated a second phase (IH-MIP2), increasing the complexity of the benchmarks of the first phase. The models that took part in the intercomparison were ATS, Cast3M, CATHY, GEOtop, HydroGeoSphere, MIKE-SHE, and ParFlow. IH-MIP2 benchmarks included a tilted v-catchment with 3-D subsurface; a superslab case expanding the slab case of the first phase with an additional horizontal subsurface heterogeneity; and the Borden field rainfall-runoff experiment. The analyses encompassed time series of saturated, unsaturated, and ponded storages, as well as discharge. Vertical cross sections and profiles were also inspected in the superslab and Borden benchmarks. An analysis of agreement was performed including systematic and unsystematic deviations between the different models. Results show generally good agreement between the different models, which lends confidence in the fundamental physical and numerical implementation of the governing equations in the different models. Differences can be attributed to the varying level of detail in the mathematical and numerical representation or in the parameterization of physical processes, in particular with regard to ponded storage and friction slope in the calculation of overland flow. These differences may become important for specific applications such as detailed inundation modeling or when strong inhomogeneities are present in the simulation domain.

Overland flow as a queueing process

We study the single server B/D/1 FIFO queue with Bernoulli inter-arrival times t (t{0,1}) and arbitrary deterministic service time s (s<1). This queue is introduced in hydrology to model overland flow generation during a rainfall event on a sloping flat soil surface with infiltration rate distributed randomly in space. The service time, the inter-arrival time and the waiting time stand respectively for the rainfall rate, the infiltration rate and the overland flow-rate. The main performance measure of interest in hydrology is the mean overland flow-rate. Its variation with the rainfall rate is of primary importance for peak-flow forecasting. For this purpose the queue must be solved for any real value of s. Two solutions, one exact and one approximate, are presented. The exact one is developed for rational values of s. The queue is transformed into a discrete time queue with a slot equal to 1/q, where q is the denominator of the irreducible fraction s=p/q (p and q integers). The waiting time and the queue length distributions are derived, and for each value of p and q there is a characteristic equation to solve inside the unit disk. The approximate, and simpler, solution is an extrapolation of the special case where s is a unit fraction (s=1/q) to an arbitrary value of s. Simulations show that this extrapolation seems to be acceptable only for the mean and standard deviation of the waiting time.