How does the 'window' of overland flow generating rainfall react to Clausius-Clapeyron scaling?

Rainfall on an infiltrating microcatchment or hillslope will trigger overland flow, if it is long and intense enough. It is, naturally, of interest to know, what 'enough' means in quantitative terms, i.e. with respect to a given soil and an intensity-duration-frequency (IDF) relationship of selected return interval.

Fully impervious surfaces excepted, an initial phase of the process exists, during which detention storage will be filled and water infiltrates into the soil. The end of that phase (if any) marks the lower limit to the overland flow generating rainfall 'window'. Further to the right of the IDF-curve longer events causing overland flow follow, until a point is reached, where no more overland flow forms, this time because the rainfall intensity has become too low to overcome infiltration. The interval between these two end points has been termed the 'rainfall window'. A closed form expression for its length is given subsequently, and its response to rainfall events subject to Clausius-Clapeyron scaling will be discussed. 

An IDF relationship of the form

is assumed, with r the rainfall intensity, t_d the storm duration and f the Clausius-Clapeyron scaling factor (parameters s = 0.0597 m and  b = 540 s in the examples below). Using a Green-Ampt type infiltration model and assuming p = 1, the following closed form expression has been derived:

with K_sv vertical saturated permeability and S_av averaged suction at the wetting front.

The Clausius-Clapeyron relationship, i.e. a 7% increase in rainfall depth per additional degree centigrade of warming, may yield an order of magnitude of what to expect from climate change. Here, f = 1.07 will be assumed for 1 K increase in temperature, and f = 1.14 for 2 K.

The examples given here use a present-day IDF relationship of 20 years' return interval (roughly valid in the Austrian Alps) and initial loss of 0.5 mm. The rainfall window was computed using soil data from Columbia sandy loam, Guelph loam and Ida silt loam. Future warming was assumed as 1.0 and 2.0 K, resp.

In the case of the most pervious soil of the three (Columbia sandy loam, vertical saturated permeability K_sv = 0.0139 mm/s) the (short) rainfall window showed a length of 22 min (present), 27 min (1 K warming) and 31 min (2K), an increase of 22% and 43%, resp.

The 'medium' soil, Guelph loam (K_sv = 0.00367 mm/s), started from a window length of 109 min (present), rising to 123 min and 138 min for 1K and 2K resp. (increases of 13% and 26%).

In case of the finest soil, Ida silt loam (K_sv = 0.000292 mm/s), the overland flow generating window of rainfall was longest and amounted to 44 h (present), 48 h (1K: 9% increase) and 52 h (17% increase).

In conclusion it may be stated that notable increases in the overland flow generating rainfall window are to be expected due to future warming. Overland flow events tend to become more frequent as more storms will qualify as triggers.