A theoretical travel time based on watershed hypsometry

The time to hydrograph peak of a watershed basin has been found to correlate with various statistical attributes (e.g., skewness and kurtosis) of its hypsometric curve (treated as probability distribution). This paper presents a theoretical travel time that is conceptually analogous to the time to hydrograph peak and can be calculated directly from the hypsometric curve of a watershed basin based on gravity and acceleration. The theoretical travel times for 23 selected watersheds in the United States are found to correlate significantly with their corresponding hypsometric attributes. In addition, the theoretical travel times are consistent with the times of concentration estimated from the Federal Aviation Administration method. Thus, this paper offers a simple theoretical explanation to the empirically identified linkage between time to hydrograph peak and hypsometric attributes. This theoretical travel time can provide an alternative way of characterizing the effects of basin morphometry on hydrologic response.