New PR Model
The New UK PR equation developed jointly by HR Wallingford, the Water Research Centre and the Institute of Hydrology with support from North West Water PLC has been designed as a replacement to the familiar UK PR equation defined previously
The UKWIR equation has subsequently been developed to address limitations of the New UK PR equation.
The New UK PR equation was designed primarily to overcome some of the difficulties experienced in practical application of the old equation, namely:
- The old equation stated that PR remained constant throughout a rainfall event irrespective of catchment wetness. Clearly for long duration storms lower losses towards the end of the event may be significant in terms of urban drainage design.
- Problems have been encountered in applying the PR equation to partially separate catchments and to catchments with low PIMP and low SOIL values.
To overcome these problems various new model forms were investigated using a subset of the original data as indicated in Table 1.
|
Catchment name |
Characteristics |
Results |
||||
|---|---|---|---|---|---|---|
|
Area (ha) |
PIMP (%) |
SOIL |
Events Used |
PR imp (%) |
RMS error (%) |
|
|
Blackpool |
4.82 |
42 |
0.45 |
19 |
74.5 |
12.9 |
|
Doncaster |
5.14 |
30 |
0.45 |
16 |
53.4 |
19.4 |
|
Kidbrooke |
3.42 |
68 |
0.15 |
43 |
59.9 |
12.9 |
|
Oxhey Road |
0.78 |
60 |
0.45 |
32 |
100.0 |
14.8 |
|
WPRL |
1.39 |
50 |
0.30 |
11 |
44.7 |
7.4 |
|
Bracknell |
11.60 |
46 |
0.45 |
33 |
65.2 |
16.3 |
|
Derby 3A |
8.55 |
51 |
0.45 |
32 |
53.4 |
12.4 |
|
Southampton 1 |
0.80 |
41 |
0.40 |
16 |
62.6 |
23.2 |
|
Southampton 2 |
0.60 |
42 |
0.40 |
13 |
60.5 |
7.3 |
Table 1: New model forms using a subset of original data
The advised model derived by this analysis is of the form:
|
|
where IF - effective impervious area factor PF - moisture depth parameter (mm) NAPI - API30 derived from net rainfall after subtraction of running depression storage |
This equation divides PR into two elements. First, the impervious area PR which is obtained by using an effective contributing area factor, IF. Therefore after initial losses on impervious surfaces, remaining losses are given as a constant fraction of rainfall volume. Recommended values of IF are indicated in Table 2 and can be compared with the PRimp values for the individual catchments in Table 1. These values are introduced into the software as per the constant runoff coefficient approach.
|
Surface Condition |
Effective impervious area factor, IF |
|---|---|
|
POOR |
0.45 |
|
FAIR |
0.60 |
|
GOOD |
0.75 |
Table 2: Recommended values of IF
The losses on pervious surfaces and non-effective impervious areas are represented by the second term of Eq. 1. The first part of this term represents the total percentage of the catchment occupied by pervious and non-effective impervious areas. The losses from this area are dependent on the function NAPI/PF.
NAPI is defined as a 30-day API with evapotranspiration and initial losses subtracted from rainfall. As for API5, API30 is given by:
|
|
|
The constant value C of the API has been made dependent on the soil class to reflect the faster reduction of soil moisture on lighter soils. The relationship between C and soil class is shown in Table 3.
|
Soil Class |
C |
|---|---|
|
1 |
0.1 |
|
2 |
0.5 |
|
3 |
0.7 |
|
4 |
0.9 |
|
5 |
0.99 |
Table 3: Relationship between soil class and C
The moisture depth parameter, PF, was calibrated using the data described above. A value of 200 mm was obtained (this compares well with the available water capacity of soils with grass vegetation).
Finally, it is advised that this model be used with initial loss models representative of impervious and pervious areas.
