An improved community structure method for catchment classification

Abstract

Catchment classification plays an important role in many hydrologic applications. There are numerous approaches for catchment classification, with different bases, assumptions, and methods. Applications of the concepts of complex networks, specifically community structure, for catchment classification are just emerging. Among the many community structure methods, the edge betweenness (EB) algorithm, which applies hierarchical clustering and modularity function, is widely used for community detection. However, the EB method is susceptible to network resolution problem, which is caused by the modularity function, in identifying the best split. Thus, it is important to address the resolution problem to obtain reliable classification. Motivated by this, the present study proposes a Modularity Density-based EB (MDEB) algorithm by considering the modularity density function, instead of the modularity function. The performance of the MDEB method and the EB method is first compared for the widely-studied Zachary’s Karate Club network. Both methods are then tested for classification of 218 catchments in Australia and 639 catchments in the United States. For each region, three different types of networks are studied, to take into account the network size and regional similarity: (1) the entire network; (2) smaller network sizes based on random selection; and (3) smaller network sizes based on drainage divisions or hydrologic units. Considering streamflow data in a single-variable sense, the MDEB method is found to perform better than the EB method in catchment classification for both the study areas at all of the above three scenarios. The MDEB method is then also attempted for classification in a multi-variable sense for the 218 catchments in Australia, by considering rainfall and potential evapotranspiration (PET) in addition to streamflow. Four different combinations of variables are considered in the multi-variable approach. The results suggest that the multi-variable classification is nearly similar to that based on the single-variable classification using streamflow, but at different correlation thresholds. The present study is a significant advancement in the application of complex networks for catchment classification, as it offers an improved community structure methodology (EB) and an approach–based on multiple variables. Such advancement is certainly promising for the development of a generic catchment classification framework.