### UNIT HYDROGRAPH

• It is frequently necessary to predict the flood hydrograph coming from a known storm.

• There are numerous techniques for resolving this issue.

• The most popular and commonly used method for predicting flood hydrographs resulting from a known storm is the Unit Hydrograph Method.

Sherman proposed it first in 1932.

#### Definition :

The hydrograph of direct runoff resulting from one unit depth (1cm) of rainfall surplus happening evenly over the basin and at a uniform rate for a specific duration is known as a unit hydrograph (D hours)

• A ‘unit’ is a measurement of a unit depth of rainfall excess, which is usually 1cm.

• A specific unit hydrograph’s duration is utilised as a prefix.

### The definition of a unit hydrograph implies the following:

1. To produce a direct runoff hydrograph, the unit hydrograph represents the catchment’s lumped response to a unit rainfall excess of D-h duration. It solely connects rainfall excess to direct runoff. As a result, the amount of water in the unit hydrograph must equal the rainfall excess. The area beneath the unit hydrograph is equal to the volume given by a 1cm depth of water over the catchment region, because a rainfall excess of 1cm is considered by definition.

2. For the duration D-h of the storm, the excess rainfall (ER) is assumed to have an average intensity of 1/D cm/h.

3. The storm’s distribution is thought to be uniform throughout the catchment.

**A example hydrograph of a 6 hour unit (The duration of rainfall excess is 6h)**

**The Unit Hydrograph Theory’s Assumptions**

1. Time Invariance: This means that the direct runoff response (i.e., the direct runoff hydrograph – DRH) for a given effective rainfall (ER) in a catchment is always the same, regardless of when it happens.

2. Linear Response: It is assumed that the direct runoff response to rainfall excess is linear. If an input has a linear response, it suggests that the output will also have a linear reaction.

The ordinates of the resulting DRH will be r times the corresponding ordinates of the D hour unit hydrograph if the rainfall surplus in a duration D hours is r times the unit depth. The DRH’s base will be the same as the unit hydrograph’s because the area under the D hour DRH should equal r times the area under the equivalent D hour unit hydrograph.

The assumption of linear response allows the method of superposition to be used to calculate DRHs.

If two rainfall excesses of D hour duration occur sequentially, the combined effect (i.e. the resulting DRH) is calculated by superposing the separate DRHs, with proper sequence of events taken into account.

## Application of Unit Hydrograph

1. If an appropriate unit hydrograph is available, the DRH in a catchment due to a given storm can be determined.

2. Assume that you have access to a D-h unit hydrograph and a storm hyetograph.

3. To obtain ERH, the initial losses and infiltration losses are estimated and subtracted from the storm hyetograph.

4. The ERH is then divided into M blocks, each lasting D hours.

5. The rainfall excess in each D-h duration is then applied to the unit hydrograph in a series of operations to produce various DRH curves. These DRHs’ ordinates are lagged appropriately to create the right time sequence, and then summed at each time interval to obtain the requisite net DRH owing to the storm.

4. The ERH is then divided into M blocks, each lasting D hours.

Take a look at a series of M rainfall excess numbers.

Each has a duration of D hours clip image020 At t hours from the start, u(t) is the ordinate of a D-h unit hydrograph.