Integrating connectivity theory within watershed modelling part I: Model formulation and investigating the timing of sediment connectivity

Integrating connectivity theory within watershed modelling is one solution to overcome spatial and temporal shortcomings of sediment transport prediction, and Part I and II of these companion papers advance this overall goal. In Part I of these companion papers, we present the theoretical development of probability of connectivity formula considering connectivity's magnitude, extent, timing and continuity that can be applied to watershed modelling. Model inputs include a high resolution digital elevation model, hydrologic watershed variability, and field connectivity assessments. We use the model to investigate the dependence of the probability of connected timing and spatial connectivity on sediment transport predictors. Results show the spatial patterns of connectivity depend on both structural and functional characteristics of the catchment, such as hillslope gradient, upstream contributing area, soil texture, and stream network configuration (structural) and soil moisture content and runoff generation (functional). Spatial connectivity changes from catchment-to-catchment as a function of soil type and drainage area; and it varies from event-to-event as a function of runoff depth and soil moisture conditions. The most sensitive connected pathways provide the stencil for the probability of connectivity, and pathways connected from smaller hydrologic events are consistently reconnected and built upon during larger hydrologic events. Surprisingly, we find the probability of connected timing only depends on structural characteristics of catchments, which are considered static over the timescales analyzed herein. The timing of connectivity does not statistically depend on functional characteristics, which relaxes the parameterization across events of different magnitudes. This result occurs because the pathway stencil accumulates sediment from adjacent soils as flow intensity increases, but this does not statistically shift the frequency distribution.