SPRINT Model
The SPRINT routing model consists of a single linear reservoir.
The storage equation:
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where
where: k: linear reservoir constant (min) A: catchment area (ha) IMP: impervious percentage (%) p: slope (%) The range of application for this equation is 0.4ha < A < 5000ha 2% < IMP < 100% 110m < L < 17800m 0.4% < p < 4.7% |
Together with the continuity equation
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where in is the net rainfall (rainfall minus losses) |
The equation for k was derived by statistical analysis using the data quoted below:
| Source of Data | Catchment No |
Area (A) (ha) |
Impervious Area (IMP) (%) | Length (L) (m) | Slope (p) (%) |
k (minutes) |
|---|---|---|---|---|---|---|
| Schaake JC (USA) | 1 | 9.40 | 52.0 | 570 | 0.90 | 8.8 |
| 3 | 0.69 | 32.0 | 110 | 2.10 | 4.8 | |
| 6 | 0.52 | 54.0 | 110 | 6.10 | 3.1 | |
| 7 | 0.61 | 9.0 | 143 | 1.70 | 8.0 | |
| 12 | 0.39 | 100.0 | 280 | 0.70 | 5.8 | |
| 13 | 19.20 | 68.0 | 690 | 2.90 | 6.5 | |
| 17 | 12.20 | 52.0 | 635 | 2.60 | 7.3 | |
| 18 | 62.00 | 33.0 | 1710 | 1.40 | 11.5 | |
| Sarma, Delleur and Rao (USA) | 1 | 11.90 | 38.0 | 1064 | 2.10 | 11.9 |
| 2 | 158.80 | 37.4 | 3054 | 2.10 | 36.8 | |
| 5 | 1943.00 | 10.5 | 6151 | 0.24 | 238.0 | |
| 6 | 2616.00 | 15.5 | 9083 | 0.27 | 213.0 | |
| 7 | 5001.00 | 2.1 | 17864 | 0.44 | 785.0 | |
| 11 | 598.30 | 27.0 | 7033 | 0.89 | 101.0 | |
| 12 | 1069.70 | 37.0 | 8417 | 0.89 | 64.0 | |
| Wormand D (France) | 1 | 1.50 | 70.0 | 286 | 0.80 | 10.2 |
| 2 | 4.60 | 78.0 | 518 | 0.50 | 14.4 | |
| 3 | 3.00 | 52.0 | 660 | 4.70 | 13.4 | |
| 4 | 5.50 | 39.0 | 990 | 4.10 | 11.3 | |
| 5 | 5.30 | 22.0 | 433 | 1.90 | 14.9 | |
| 6 | 3.60 | 100.0 | 450 | 0.40 | 14.0 |
Data used to derive the SPRINT runoff routing equation
Examining this table reveals the following points:
- The SPRINT model is highly dependent on the variation of observations originating from the U.S.A. (especially the variation of A).
- The interpretation of k from such varied sources is likely to be different, together with the interpretation of the independent variables.
- The equation is strictly applicable to lumped catchments.
The value of k is also corrected further for areal effecs using
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where a = 0.8 for A < 6ha a = 0.7 A0.09 for 6ha < A < 250ha |
This approach differs from the UK runoff routing models for the following reasons:
- The equation is strictly applicable to lumped catchment models and not to single surface types.
- The equation relates to a single linear reservoir (halving the k value and using the double linear reservoir is known to give approximately the same result).
- The equation is not dependent on rainfall intensity.
