Disaggregation, aggregation and spatial scaling in hydrological modelling

A typical feature of the land surface is its heterogeneity in terms of the spatial variability of land surface characteristics and parameters controlling physical/hydrological, biological, and other related processes. Different forms and degrees of heterogeneity need to be taken into account in hydrological modelling. The first part of the article concerns the conditions under which a disaggregation of the land surface into subareas of uniform or “quasihomogeneous” behaviour (hydrotopes or hydrological response units – HRUs) is indispensable. In a case study in northern Germany, it is shown that forests in contrast to arable land, areas with shallow groundwater in contrast to those with deep, water surfaces and sealed areas should generally be distinguished (disaggregated) in modelling, whereas internal heterogeneities within these hydrotopes can be assessed statistically, e.g., by areal distribution functions (soil water holding capacity, hydraulic conductivity, etc.). Models with hydrotope-specific parameters can be applied to calculate the “vertical” processes (fluxes, storages, etc.), and this, moreover, for hydrotopes of different area, and even for groups of distributed hydrotopes in a reference area (hydrotope classes), provided that the meteorological conditions are similar. Thus, a scaling problem does not really exist in this process domain. The primary domain for the application of scaling laws is that of lateral flows in landscapes and river basins. This is illustrated in the second part of the article, where results of a case study in Bavaria/Germany are presented and discussed. It is shown that scaling laws can be applied efficiently for the determination of the Instantaneous Unit Hydrograph (IUH) of the surface runoff system in river basins: simple scaling for basins larger than 43 km 2, and multiple scaling for smaller basins. Surprisingly, only two parameters were identified as important in the derived relations: the drainage area and, in some cases, the elevation a.s.l.. The scaling exponent was determined as equal or approximately equal to the exponent 0.566 in Hack’s law. Therefore, it is suggested that there is some relation between the scaling laws and the fractal nature of river networks, and accordingly with the complex dynamics of the interacting hydrological and geomorphological processes in river basins.