Parallel to the development of the distributed models the lumped models have been further refined and improved to more physically based models which fully cover the whole hydrological cycle of land-bound water movement and refine its spatial resolution by subcatchments and hydrotopes. The last ones are areas of equal hydrological characteristic with respect to the vertical processes of interception, infiltration, evapotranspiration and groundwater recharge.

Some of the lumped model use the same mathematical approaches as the distributed models to simulate these vertical processes, like the Richards equation or exponential functions^{(*1)}. The subcatchments are composed of hydrotopes, in which the runoff of each hydrotop is aggregated and according to the terrain contour and stormwater network discharged into the stream channel. The horizontal flow components of overland flow and interflow are modelled by own system functions, making use of the concept of parallel reservoir cascades^{(*2)}. The translation of surface-runoff and interflow is covered by a time-area-histogram which presents the histogram of the travel time of runoff within the catchment and thus represent the drainage characteristics of the subcatchments.

Another very popular representative of these refined lumped model is the Topmodel^{(*3)}. It also uses a transfer-function which is derived from raster based values of the topography (hillslope of each raster cell) and morphology. Topmodel assumes a close correlation between mean soil moisture, topography, the pattern of saturated areas and the hillslope runoff formulation. In dependence of the resolution of subcatchments, raster cells and hydrotops today’s conceptual models can reach a degree of spatial resolution which comes close to the distributed models. Therefore they are often described as semi-distributed models.