Gamma distribution models for transit time estimation in catchments: Physical interpretation of parameters and implications for time‐variant transit time assessment

Abstract

In hydrological tracer studies, the gamma distribution can serve as an appropriate transit time distribution (TTD) as it allows more flexibility to account for nonlinearities in the behavior of catchment systems than the more commonly used exponential distribution. However, it is unclear which physical interpretation can be ascribed to its two parameters (α, β). In this study, long‐term tracer data from three contrasting catchments in the Scottish Highlands were used for a comparative assessment of interannual variability in TTDs and resulting mean transit times (MTT = αβ) inferred by the gamma distribution model. In addition, spatial variation in the long‐term average TTDs from these and six additional catchments was also assessed. The temporal analysis showed that the β parameter was controlled by precipitation intensities above catchment‐specific thresholds. In contrast, the α parameter, which showed little temporal variability and no relationship with precipitation intensity, was found to be closely related to catchment landscape organization, notably the hydrological characteristics of the dominant soils and the drainage density. The relationship between β and precipitation intensity was used to express β as a time‐varying function within the framework of lumped convolution integrals to examine the nonstationarity of TTDs. The resulting time‐variant TTDs provided more detailed and potentially useful information about the temporal dynamics and the timing of solute fluxes. It was shown that in the wet, cool climatic conditions of the Scottish Highlands, the transit times from the time‐variant TTD were roughly consistent with the variations of MTTs revealed by interannual analysis.