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| Titel |
1D Runoff-runon stochastic model in the light of queueing theory : heterogeneity and connectivity |
| VerfasserIn |
M.-A. Harel, E. Mouche, E. Ledoux |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250063123
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| Zusammenfassung |
| Runoff production on a hillslope during a rainfall event may be simplified 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.
When ponding time, topography, and overall spatial and temporal variations of
physical parameters, such as R and I, are neglected, the runoff equation remains
simple.
In this study, we consider soils of spatially variable infiltrability. As 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 = max(Qn + (R - In)*Δx , 0)
where Qn is the runoff arriving on pixel n of size Δx [L2/T], R and In the rainfall
intensity and infiltrability on that same pixel [L/T]. The non-linearity is due to the
dependence of infiltration on R and Qn, that is runon. This re-infiltration process generates
patterns of runoff along the slope, patterns that organise and connect to each other differently
depending on the rainfall intensity and the nature of the soil heterogeneity. The runoff
connectivity, assessed using the connectivity function of Allard (1993), affects greatly the
dynamics of the runoff hillslope.
Our aim is to assess, in a stochastic framework, the runoff organization on 1D slopes with
random infiltrabilities (log-normal, exponential, bimodal and uniform distributions) by means
of theoretical developments and numerical simulations. This means linking the nature of soil
heterogeneity with the resulting runoff organisation. In term of connectivity, we
investigate the relations between structural (infiltrability) and functional (runoff)
connectivity.
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. Alternative
formulations for the connectivity function of Allard (which cannot be predicted
theoretically to our knowledge) are discussed with regard to predictability, efficiency in
computation and qualification of the “near-connectedness” state of the system. |
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