Rational method and its limitations

Rational method

The rational method estimates the peak discharge from a small catchment, assuming that the peak occurs when the whole catchment contributes, i.e. when the rainfall duration equals the time of concentration $t_c$, and that the runoff rate equals the rainfall excess rate.

$$Q_p = \frac{C\,i\,A}{360}$$

where $Q_p$ is in m³/s, $i$ is the average rainfall intensity (mm/h) for duration $t_c$ and the required return period (from IDF curves), $A$ is the area in hectares, and $C$ is the runoff coefficient (ratio of peak runoff to rainfall, 0 to 1). In SI units with A in km²: $Q_p = 0.278\,C\,i\,A$.

Steps

1. Find $t_c$ (e.g. Kirpich: $t_c = 0.0195\,L^{0.77}S^{-0.385}$ min, L in m, S in m/m).
2. Take the rainfall intensity $i$ for duration $t_c$ and the design return period from the IDF curve.
3. Select $C$ from tables according to land use (e.g. 0.8 – 0.95 for paved areas, 0.1 – 0.3 for forest or flat cultivated land); use a weighted $C$ for mixed surfaces: $C=\sum C_iA_i/\sum A_i$.
4. Compute $Q_p$.

The rational hydrograph is a triangle or trapezoid; the method gives only the peak. It assumes the return period of the flood equals that of the rainfall.

Limitations

1. Applicable only to small catchments (generally up to about 50 km², best below 5 km²) because the rainfall is assumed uniform in space and time.
2. Gives only the peak discharge, not the flood volume or hydrograph shape.
3. $C$ is assumed constant, although it depends on soil moisture, storm intensity, slope and season (it increases with return period).
4. Ignores storage in the catchment and channels and the effect of antecedent moisture.
5. Assumes the duration of rain equals $t_c$ and that rainfall intensity is constant in that period.
6. $t_c$ itself is empirical; different formulae give widely different values.
7. Needs reliable local IDF curves, which are scarce for Nepal's hilly catchments.