Temporal dynamics of hydrological threshold events

The episodic nature of hydrological flows such as surface runoff and preferential flow is a result of the non-linearity of their triggering and the intermittency of rainfall. In this paper we examine the temporal dynamics of threshold processes that are triggered by either an infiltration excess (IE) mechanism when rainfall intensity exceeds a specified threshold value, or a saturation excess (SE) mechanism governed by a storage threshold. We use existing and newly derived analytical results to describe probabilistic measures of the time between successive events in each case, and in the case of the SE triggering, we relate the statistics of the time between events (the inter-event time, denoted IET) to the statistics of storage and the underlying water balance. In the case of the IE mechanism, the temporal dynamics of flow events is found to be simply scaled statistics of rainfall timing. In the case of the SE mechanism the time between events becomes structured. With increasing climate aridity the mean and the variance of the time between SE events increases but temporal clustering, as measured by the coefficient of variation (CV) of the IET, reaches a maximum in deep stores when the climatic aridity index equals 1. In very humid and also very and climates, the temporal clustering disappears, and the pattern of triggering is similar to that seen for the IE mechanism. In addition we show that the mean and variance of the magnitude of SE events decreases but the CV increases with increasing aridity. The CV of IETs is found to be approximately equal to the CV of the magnitude of SE events per storm only in very humid climates with the CV of event magnitude tending to be much larger than the CV of IETs in arid climates. In comparison to storage the maximum temporal clustering was found to be associated with a maximum in the variance of soil moisture. The CV of the time till the first saturation excess event was found to be greatest when the initial storage was at the threshold.