# Derivation of Unit Hydrograph

## Introduction

This spreadsheet based step demonstrates the derivation of unit hydrograph by using the excess rainfall and direct runoff data from a single historical storm event.The intended audience for this step are upper level undergraduate or MS/PhD students interested in hydrology. The approach presented here should be applicable to any gauged watershed that has data for at least one storm event that satisfies the assumptions of the Unit Hydrograph theory. This step uses the data for Hall Creek in Indiana.

## Conceptual Outcomes

- Students demonstrate understanding of unit hydrograph
- Students demonstrate the understanding of unit hydrograph derivation

## Practical Outcomes

- MS Excel and spreadsheet-based derivation of unit hydrograph
- Hydrology data analyses using MS Excel

## Time Required

- 1 hour

## Reference Documents and Files

- None

## Data Inputs

Numerical Values: Excess rainfall and direct runoff data for Hall Creek in Indiana: Hall Creek Event Data (Excel 2007 (.xlsx) 24kB Nov10 14)

Numerical Value: Area of Hall Creek Watershed: 21.8 square miles

## Data Outputs

- Numerical Values: Unit Hydrograph
- Numerical Values: Baseflow time series

## Required Hardware and Software

- MS Excel

## Related Steps

Baseflow Separation Using Straight Line Method

Computing Excess Rainfall using Phi Index

Application of Unit Hydrograph to Derive Direct Runoff Hydrograph

## Instructions

### Unit Hydrograph

Unit hydrograph is a direct runoff hydrograph resulting from one unit (one inch or one cm) of constant intensity uniform rainfall occurring over the entire watershed. The concept of unit hydrograph is based on linear systems theory and follow the principles of superposition and proportionality. For example, if one inch of excess rainfall produces a direct runoff peak of 100 cfs then two inch of excess rainfall with produce a direct runoff of 2 x 100 = 200 cfs. Similarly if one inch of rainfall is followed by two inch of rainfall, the hydrographs from both rainfall pulses are simply added after accounting for the necessary time lag. The following figure demonstrates this concept.

The role of unit hydrograph in hydrology is to provide an estimate of direct runoff hydrograph resulting from given excess rainfall hyetograph. In order to use unit hydrograph as a tool for predicting direct runoff hydrograph, we first need to derive a unit hydrograph for a given watershed.

**Deriving a Unit Hydrograph**

The data from Hall Creek, when opened in MS Excel, will look like the following:

One of the key assumptions in the unit hydrograph theory is that the rainfall intensity is constant over the storm duration. However, it is difficult to find a natural storm event that satisfies this and some other assumptions of the unit hydrograph theory. The dataset provided here is representative of what you will generally get from a rainfall gauge.

As shown in the table, excess rainfall and the consequent direct runoff values are available at 15 minute intervals.

The first step is to compute the total volume of direct runoff. To do this, add all direct runoff values, and multiply the sum of all the direct runoff flows by the time interval (in seconds) of the series as shown below. (convert cubic feet per second to cubic feet of volume). After getting the total runoff volume, find the **equivalent runoff depth** by dividing the runoff volume by the basin area. Do not forget to use appropriate conversion factors in calculations to have uniformity in the units of various quantities involved. Note that, the depth thus calculated is equal to the total excess rainfall depth.

By definition, Unit Hydrograph is a direct runoff hydrograph resulting from the unit depth of effective rainfall. So, the **ordinates of required UH** can simply be obtained by dividing the ordinates of Direct Runoff Hydrograph by the equivalent depth of total direct runoff as shown below.

Once you get the unit hydrograph, the next step is to identify its duration. In the Unit Hydrograph definition, the duration of a unit hydrograph is the time period over which the excess rainfall occurred. In the dataset for Hall Creek, excess rainfall occurs from 9:30 AM to 12:00 PM, and hence the duration of the derived unit hydrograph is 2.5 hours.

The conventional graphical representation of the Direct Runoff Hydrograph and the derived Unit Hydrograph ordinates can be obtained by plotting the direct runoff and UH ordinates against time axis in Excel. The scatter plot hence obtained depicts the direct runoff hydrograph and the derived unit hydrograph of 2.5 hr duration for the given basin.

You are done with deriving unit hydrograph. Now this unit hydrograph can be used to derive runoff hydrographs from rainfall data!