# Computing Excess Rainfall using Phi Index (Constant Loss) Method

## Introduction

The objective of this step is to learn how to compute excess rainfall hyetograph from a total rainfall hyetograph using constant loss or the phi index. This steps assumes that the user already has a total rainfall hyetograph in MS Excel. This total rainfall hyetograph for a single event is then used as input to separate rainfall losses by using the phi index. There are two outputs from this step, including the rainfall abstractions and the excess rainfall hyetograph. This step also requires that the phi index or constant loss is known.

## Conceptual Student Learning Outcomes

• Student demonstrates the understanding of rainfall abstractions and excess
• Student demonstrates the knowledge of phi index or constant loss for computing rainfall abstractions

## Practical Student Learning Outcomes

• Data analysis using MS Excel
• Use of constant loss in Excel for computing excess rainfall

One hour

## Reference Documents and Files

• Procedure to compute phi-index by using data for a single storm event: Computing phi index (Acrobat (PDF) 387kB Nov9 14)

## Data Inputs

• Numerical Value(s): Microsoft Excel file containing rainfall hyetograph for one event at Hall Creek in Indiana: 15 Min Precipitation Data (Excel 2007 (.xlsx) 8kB Apr14 16)
• Numerical Value: Curve Number [Double]

## Data Outputs

• Numerical Values: Rainfall abstractions
• Numerical Values: Excess rainfall hyetograph

• MS Excel

## Instructions

### Excess Rainfall

During a rainfall event, not all rainfall will become direct runoff or contribute to the streamflow at the watershed outlet. Some of the rainfall will be lost to interception by vegetation and to soil through infiltration. The loss due to evaporation and transpiration is either negligible or absent during an individual storm event. Therefore, in order to know how much rainfall is actually contributing to the direct runoff, we much subtract the losses or abstractions from the total rainfall. The hyetograph that we get after subtracting losses from the actual rainfall is called the excess rainfall hydrograph. In this exercise, we are going to see how to compute excess rainfall by assuming constant loss. As one can imagine, the loss may be varying during a rainfall event with relatively higher infiltration at the beginning of the storm event compared to the later stages when the soil reaches saturation. The constant loss method is the simplest method for computing excess rainfall. Another approach is by using the SCS curve number (CN) method, which is discussed in a separate step.

### Computing Excess Rainfall using Constant Loss

The rainfall hyetograph provided in the input data is shown below in an Excel sheet.

Excess rainfall is computed by subtracting losses from a rainfall hyetograph. In this case, we will assume a constant loss (or phi-index) of 0.272 inch/hr. This phi-index corresponds to a rainfall depth of 0.068 (approx. 0.07) for 15 mins. In the Excel sheet, create a new column for this constant loss of 0.07 as shown below. By typing 0.07 at the top of the column, clicking the bold bottom right corner of the cell, and dragging down over the desired cells, you can instantly populate them with the same value or formula:

Create a new column next to constant loss called 'Excess Rainfall' in the first row of column D. Then use the formula Excess rainfall = observed rainfall - loss (column D= column B-column C) -- type an equal sign in a cell in column D and click the relevant cells in columns B and C, adding mathematical operation signs to make the cell input an expression as you would with a calculator. Then drag this cell (where you typed the expression) all the way down to populate the runoff column as shown below. Note that when the loss is greater than rainfall (first and last row), excess rainfall = 0.

Column D will give you excess rainfall in inches.