Flood inundation modelling is a key applied problem where distributed model predictions are required and used to inform major decisions relating to planning and insurance. However, it has long been known (e.g. see Beven (1989)) that distributed hydraulic models, along with similar codes in catchment hydrology, suffer from two key problems: 1. A lack of distributed data to parameterize and validate the codes. 2. A lack of adequate theory to scale parameter values derived for point-based equations to effective parameter values at the grid scale or to relate point validation measurements to the time-and space-averaged quantities actually predicted by the models. Until recently, validation data for hydraulic models consisted primarily of bulk flow measurements, either at the catchment outlet or at gauging stations internal to the model domain. Measurements of internal state variables, where made, tended to consist only of data from a small number of points. As noted above, considerable difficulties exist in actually measuring the quantities predicted by distributed numerical models because of the (necessarily) discrete way in which they treat time and space. Unsurprisingly, therefore, comparison of small numbers of point state-variable measurements to grid-scale model predictions showed only mixed success (e.g. Lane et al., 1999). Model validation thus relied on bulk flow data that represented the aggregate response of the catchment to that point (e.g. Bates et al., 1998). However, for any given model and discretization, many different spatial patterns of grid-square effective parameter values can lead to the same aggregate response, but give different spatial predictions and, thus, process inferences. In fact, replication of aggregate catchment response only requires single values of model parameters spatially lumped at the catchment scale and representative of aggregate conditions. Lack of distributed validation data is, therefore, a significant cause of equifinality and leads to a tolerance of the physically unrealistic spatial lumping of parameter values and processes. These ideas have recently been taken up by Grayson and BlΓΆschl (2001) in their book Spatial patterns in catchment hydrology: observations and modelling.
Lack of parameterization data leads to a requirement to estimate the unknown values; however, as these are scale dependent, the underlying distribution may not be well known and correct values may be difficult to define a priori. Calibration of initial parameter