Unit hydrograph, assumptions and limitations

Unit hydrograph (UH)

A unit hydrograph (Sherman, 1932) is the direct runoff hydrograph resulting from 1 unit (1 cm or 1 mm) of effective rainfall falling uniformly over the whole basin at a uniform rate during a specified duration $D$. It is written as the $D$-hour unit hydrograph.

 Q |      /\
   |     /  \
   |    /    \___
   |___/         \____
   +------------------- t
   |<-- Tb (base) --->|

Assumptions

1. Constant intensity: effective rainfall is uniform in intensity over the duration $D$.
2. Uniform distribution: effective rainfall is uniformly spread over the whole drainage area.
3. Constant base time: the base time of the direct runoff hydrograph is the same for all storms of equal duration, whatever the intensity.
4. Linearity (proportionality): ordinates of DRH due to the same duration are directly proportional to the effective rainfall depth; for twice the rain, ordinates are doubled.
5. Superposition (time invariance): the hydrographs of successive rain periods can be added; the catchment response does not change with time.
6. All characteristics of the catchment are reflected in the shape of the UH.

Limitations

1. Applies to catchments of about 25 to 5000 km$^2$; very small (< 25 km$^2$) or very large basins (> 5000 km$^2$) violate the assumptions.
2. Not valid when rainfall is not uniform in space or time, or storms move across the basin.
3. Not suitable for snowmelt-dominated or heavily regulated basins, or basins with large storage (lakes, reservoirs).
4. Cannot handle effective rainfall of different durations without S-curve conversion.
5. Real catchment behaviour is not exactly linear; UH from small storms may differ from that of large floods.
6. Needs reliable rainfall and streamflow records; an ungauged basin needs synthetic methods.
7. Derived UH is valid only for that point on the stream.