Unit hydrograph, assumptions, base flow separation

Unit hydrograph

A unit hydrograph (UH) is the direct runoff hydrograph resulting from 1 cm (unit depth) of rainfall excess falling uniformly over the whole basin at a uniform rate for a specified duration D (called the D-hour UH). It was proposed by Sherman (1932).

Assumptions

1. Rainfall excess is uniformly distributed over the entire basin.
2. Rainfall excess has a constant intensity during the duration D.
3. Time invariance: for a given basin, the DRH for a given excess-rain duration is always the same, irrespective of when the rain occurs.
4. Linearity (proportionality): ordinates of DRH are directly proportional to the rainfall excess depth.
5. Superposition: the DRH from successive rainfall bursts is obtained by adding the individual responses with their proper time lags.
6. The time base of the DRH is constant for storms of the same duration.

Limitations

• It is valid for basins of about 25 to 5000 km² only; rain and flow are non-uniform in very small or very large basins.
• Rain should not vary greatly over the basin; the UH is not reliable where there is storage (lakes, reservoirs) or for snowmelt.
• Non-linear effects at large floods are neglected, and the UH of one duration cannot be used for a very different duration without conversion (S-curve).
• It requires isolated, uniform-intensity storms and good rainfall-runoff data.

Base flow separation

The storm hydrograph = direct runoff + base flow. Base flow must be removed before deriving the UH. In the sketch, A is the point where the rising limb starts and B is the point on the recession limb where direct runoff ends. The usual methods are:

 Q
   |      /\
   |     /  \__
   |    /      \__
   |___/ A         \___ B ____
   |        base flow
   +------------------------- t

1. Straight-line method (Method I): join A to B by a straight line (horizontal when A and B are at the same discharge). B is on the recession limb N days after the peak, where $N = 0.827A^{0.2}$ (A = catchment area in km²). It is the simplest method and suits small catchments with steady base flow.
2. Method II: extend the base-flow recession curve that existed before the storm forward, until it meets the ordinate at the peak (point C). Join C to B by a straight line. The base flow is then A–C–B.
3. Variable-slope method (Method III): extend the base-flow recession curve that follows the storm backward to a point below the point of inflection of the recession limb. Join this point to A by an arbitrary smooth curve. This suits large catchments with a good recession record.

The area between the total hydrograph and the base-flow line gives the direct runoff volume; the direct runoff depth = volume / catchment area.