ABSTRACT: Black, grey and white-box approaches to understanding catchment-wide hydrologic connectivity.

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Abstract

Connectivity is associated with nonlinear hydrological responses as it is believed to lead to drastic changes in the delivery of stormwater to the stream. Quantitative evidence of connectivity is therefore needed if the concept is to serve as a diagnostic tool for hydrologic behaviours. Recent publications advocate that geostatistical connectivity is a universal measure as it transcends catchment idiosyncracies and allows for the detection of transitions and thresholds in flow processes. Yet, the geostatistical framework failed to reflect threshold change in runoff response in a temperate humid forested catchment (Mont St-Hilaire, Quebec). In this study based on a forested catchment from the Canadian Shield (St-Hippolyte, Quebec), we use three types of hydrological data analysis in searching for evidence of connectivity: (1) statistical classification techniques applied to meteorological records and storm hydrographs; (2) end-member mixing computations performed on stream and source areas geochemistry; and (3) catchment-wide multiple-depths soil moisture data subjected to pattern analysis. These methods correspond respectively to black, grey and white-box approaches towards understanding connectivity. Since the methods can be discriminated by accessibility, physical basis, robustness and spatial discretization, results obtained are compared to assess catchment behavior and prediction uncertainty. The black-box approach reveals that catchment responses, labeled as low/high magnitude and slow/quick timing, can be predicted from meteorological thresholds. It yields indirect evidence of connectivity by suggesting that a relationship between response types and antecedent conditions can be found if assumed nonlinear. The grey-box approach is helpful in identifying time-variable contributing sources to streamflow. Intermediate discharge levels are fed by an enhanced near-surface riparian-stream connection, while both riparian and hillslope areas produce overland flow when prior conditions are wet. Proportional contributions increase in a nonlinear fashion with antecedent conditions. The white-box approach is useful to observe distinct preferential states in soil moisture that are sensitive to initial conditions. A wide range of 2-D and 3-D connectivity measures (i.e. entropy, effective upslope area, integral correlation and connectivity scale lengths) exhibit a threshold-like behaviour when plotted against discharge. This study shows that process rates and thresholds inferred from the black and grey-box approaches are consistent with changing spatial connectivity of hydrologically active areas. Even though prediction uncertainty is more severe with black and grey-box approaches, our study challenges the use of a white-box, ‘resources-greedy’ approach since simplified models are effective in searching for evidence of catchment-scale connectivity.

Bibliography of Canadian Geomorphology