Wallingford Procedure Model
The Wallingford model is applicable to typical urban catchments in the UK. It uses a regression equation to predict the runoff coefficient depending on the density of development, the soil type and the antecedent wetness of each subcatchment.
The model predicts the total runoff from all surfaces in the sub-catchment, both pervious and impervious. This model should therefore not be mixed with another model within one subcatchment.
This is the standard model used to represent continuing losses for UK urban catchments and is applied with the initial losses model described previously. Runoff losses are assumed to be constant throughout a rainfall event and are defined by the relationship:
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where PR - is the percentage runoff PIMP - is the percentage impermeability. This parameter is the percentage imperviousness of the catchment obtained by dividing the total directly connected impervious area (both roofs and roads) by the total contributing area UCWI - is the Urban Catchment Wetness Index SOIL - is an index of the water holding capacity of the soil. The soil index (SOIL) is based on the winter rain acceptance parameter (WRAP) included in the Flood Studies Report and can be obtained from the revised soil map or from the 1:1000000 version covering the whole of the UK. The index describes broadly infiltration potential and was derived by a consideration of soil permeability, topographic slope, and the likelihood of impermeable layers. Five classes of soil are recognised as shown below:
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Eq. 1 was derived by statistical analysis. The derived relationship explained 57% of the observed variation of PR. However, when used to predict runoff volume the model provides a far greater explanatory power, as the variation of runoff volume is influenced markedly by the variation of rainfall volume. In fact, Eq. 1 explains the variability of runoff volume after the effect of rainfall volume has been removed. This latter point explains to a certain extent the marked success found in the use of Eq. 1 to predict runoff volume since the release of the Wallingford Procedure.
Inspection of Eq.1 indicates for low values PIMP, SOIL and UCWI low or even negative values of PR could be predicted. Consequently, a minimum value of PR of 20% together with a maximum of 100% is defined within the software. Eq. 1 is therefore used to define PR for separate events within this range. It should be appreciated that unrealistic PR values can be predicted with low values of SOIL (for example 0.15) in combination with both low values of PIMP (for example 30%) and UCWI.
This model predicts the total runoff from all surfaces in the sub-catchment, including both pervious and impervious. The model should therefore not be mixed with another model in one sub-catchment.
Runoff for the entire catchment is distributed between the different surfaces using weighting coefficients. All surfaces can therefore contribute some runoff even at low runoff rates, provided that initial losses have been satisfied.
The weighting is carried out as follows:
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where: fiis the weighting coefficient for surface i PRiis the percentage runoff for surface i Aiis the area for surface i Default parameters for the weighting coefficients are:
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