The River Systems in Small Catchments in the Context of the Horton’s and Schumm’s Laws – Implication for Hydrological Modelling. The Case Study of the Polish Carpathians

In ungauged catchments, flood hydrographs are usually simulated/reconstructed by simple rainfall-runoff and routing models. Horton’s and Schumm’s ratios serve as the input data for many of these models. In this paper, more than 800 Carpathian catchments (up to 35.2 km² in area) were investigated in context of the “Horton’s and Schumm’s laws”. Results reveal that the “law of stream number” and “law of stream areas” are fulfilled in almost all catchments. The mean that values of the bifurcation ratio (R_B) and the area ratio (R_A) reach 3.8 and 4.8, respectively, and are thus comparable to values reported in other regions of the world. However, the “law of stream lengths” is not fulfilled in more than half of the catchments, which is not consistent with many theoretical studies reported in the literature. Only 383 (48%) catchments fulfill the “law of stream length”, with the mean value of the length ratio (R_L)=2.3. There was no relationship found between the geological/geomorphological settings that influence river system development and the spatial distribution of catchments where the “law of stream length” was or was not was fulfilled. A similar conclusion was reached for the spatial distribution of the R_B, R_L, and R_A ratios. These results confirmed that the use of Horton’s and Schumm’s ratios for the evaluation of the influence of geological/geomorphological settings on the river system development is limited. Among the lumped hydrological models, those requiring the R_B, R_L, and R_A ratios have been extensively studied over last decades. This study suggests that the application of these models may be limited in small catchment areas; therefore, more attention should be placed on the development of hydrological models where the R_B, R_L, and R_A ratios are not necessary.