New metrics for evaluating channel networks extracted in grid digital elevation models

Channel networks are critical components of drainage basins and delta regions. Despite the important role played by these systems in hydrology and geomorphology, there are at present no well-defined methods to evaluate numerically how two complex channel networks are geometrically far apart. The present study introduces new metrics for evaluating numerically channel networks extracted in grid digital elevation models with respect to a reference channel network (see the figure below). Streams of the evaluated network (EN) are delineated as in the Horton ordering system and examined through a priority climbing algorithm based on the triple index (ID1,ID2,ID3), where ID1 is a stream identifier that increases as the elevation of lower end of the stream increases, ID2 indicates the ID1 of the draining stream, and ID3 is the ID1 of the corresponding stream in the reference network (RN). Streams of the RN are identified by the double index (ID1,ID2). Streams of the EN are processed in the order of increasing ID1 (plots a-l in the figure below). For each processed stream of the EN, the closest stream of the RN is sought by considering all the streams of the RN sharing the same ID2. This ID2 in the RN is equal in the EN to the ID3 of the stream draining the processed stream, the one having ID1 equal to the ID2 of the processed stream. The mean stream planar distance (MSPD) and the mean stream elevation drop (MSED) are computed as the mean distance and drop, respectively, between corresponding streams. The MSPD is shown to be useful for evaluating slope direction methods and thresholds for channel initiation, whereas the MSED is shown to indicate the ability of grid coarsening strategies to retain the profiles of observed channels. The developed metrics fill a gap in the existing literature by allowing hydrologists and geomorphologists to compare descriptions of a fixed physical system obtained by using different terrain analysis methods, or different physical systems described by using the same methods.