Runoff production on a hillslope during a rainfall event may be basically described as follows. Given a soil of constant infiltrability I, which is the maximum amount of water that the soil can infiltrate, and a constant rainfall intensity R, runoff is observed where R is greater than I. The infiltration rate equals the infiltrability when runoff is produced, R otherwise. In this simplified description, ponding time, topography, and overall spatial and temporal variations of physical parameters, such as R and I, are neglected.
In this study, we consider soils of spatially variable infiltrability. Our aim is to assess, in a stochastic framework, the runoff organization on 1D slopes with random infiltrabilities by means of theoretical developments and numerical simulations. As the modelled runoff can re-infiltrate on down-slope areas of higher infiltrabilities (runon), the resulting process is highly non-linear. The stationary runoff equation is:
Qn+1 / x = Qn / x + (R - in)+
where Qn is the runoff arriving on pixel n of size x [L2/T], R and in the rainfall intensity and infiltration function on that same pixel [L/T]. The non-linearity is due to the dependence of in on R and Qn.
A theoretical framework based on the queueing theory is developed. We implement the idea of Jones et al. (2009), who remarked that the above formulation is identical to the waiting time equation in a single server queue. Thanks to this theory, it is possible to accurately describe some outputs of our numerical model, notably the runoff repartition over the slope for uncorrelated exponential infiltrability distributions.
We analyse the influence of the infiltrability distribution (log-normal, exponential, bimodal...) on the outflow and on the spatial runoff organisation. Our first results indicate that these distributions have limited impacts on the outlet runoff for sufficiently long slopes, indicating a scale effect. However, runoff patterns organize differently depending on the distribution of I, and their connectivity is assessed using the connectivity function of (Allard, 1993).