Abstract
This paper is concerned with the estimation of aggregated direct runoff from small watersheds during a time interval (0,t), homogeneous with respect to rainfall characteristics. The storm events are simulated by a Poisson process, whereas direct runoff is estimated by the SCS method or a linear regression model. The probability of the occurrence of direct runoff is incorporated in the proposed method by examining the possibility of each storm exceeding the watershed losses index. A closed form solution is derived for the expected total direct runoff in the interval (0,t). Finally, the proposed method is applied to a particular set of conditions.
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Abbreviations
- Q :
-
direct runoff
- P :
-
rainfall depth
- S :
-
index of watershed storage
- CN:
-
Curve Number of SCS method
- t :
-
time
- T i :
-
time interval between successive storm events (i andi+1)
- X i :
-
storm depth of theith event (case a) excess storm depth of theith event (case b)
- Y(t) :
-
total direct runoff in (0,t)
- N(t) :
-
number of storm events in (0,t)
- F(t) :
-
distribution function of the time between storm events
- G(x) :
-
distribution function of the storm depth
- F n(t),F n+1(t):
-
n-fold and (n+1)-fold convolution ofF(t), respectively
- G n(x),G n+1(x):
-
n-fold and (n+1)-fold convolution ofG(x), respectively
- E[X] :
-
expected mean value
- p :
-
probability of exceeding the thresholde,p+q=1
- *:
-
convolution operation
References
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Tsakiris, G., Agrafiotis, G. Aggregated runoff from small watersheds based on stochastic representation of storm events. Water Resour Manage 2, 77–86 (1988). https://doi.org/10.1007/BF00577061
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DOI: https://doi.org/10.1007/BF00577061