  In the first part of our study, we demonstrated how a simple physical
benchmark model can be used to assess assumptions of the conceptual models,
based on a lumped Probability Distributed Model (PDM) formulated by Lamb
(1999). In this second part, we extend the scope of our study to distributed
models, which aim to represent the spatial variability of model's elements
(e.g. input precipitation, soil moisture levels, flow components etc.). For
demonstration purposes, we assess the assumptions of the Grid and Grid-to-Grid
models, commonly used for flood real-time forecasting in the UK. While the
distributed character of these models is conceptually closer to the physical
model, we demonstrate that its exact implementation leads to many qualitative
and quantitative differences in the model behaviour. For example, we show that
the main assumption, namely that the speed of surface and subsurface flow is
constant, causes the Grid-to-Grid model to significantly misrepresent scenarios
with no rainfall, leading to too fast river flow decay, and scenarios with
upstream rainfall, failing to capture characteristic flash flood formation. We
argue that this analytical approach of finding fundamental differences between
models may help us to develop more theoretically-justified rainfall-runoff
models, e.g. models that can better handle the two aforementioned scenarios and
other scenarios in which the spatial dependence is crucial to properly
represent the catchment dynamics.
