# How to Construct a Flood Frequency Curve

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A flood frequency curve is a valuable tool to extrapolate how often a flood of a given discharge will occur. A flood frequency curve can be constructed by plotting a graph of discharge versus recurrence interval. This can easily be accomplished provided you have a data set of annual peak discharge measured over a number of years.

Your flood discharge data should list the year and the given discharge in velocity that occurred that year. You need to calculate the order of each of the floods. Start by ordering your data according to the magnitude of the flood, from smallest to largest. Number each of the floods in order, starting with the smallest flood as number "1". The order of the flood is denoted by the letter "m". If you have 100 years of records, you will calculate flood orders for m=1, m=2, m=3,....m=100.

Calculate the recurrence interval, which is the number of times in your record that a flood of a given magnitude occurred. The formula for recurrence interval is. T= (n+1)/m Where T= recurrence interval, n=number of years in the record, m= the number you calculated in step 2, the order of the annual flood discharge. You should, therefore, calculate the recurrence interval for each year of data you have. For instance, if you have 100 years of flood records, you will have floods numbered from 1 to 100, and you will calculate 100 recurrence intervals. Write the recurrence interval beside each given flood.

Construct your graph on the semi logarithmic paper. Recurrence interval will go on the x axis; and discharge will go on the y axis. Divide the x axis with the following scale: 1, 1.5, 2, 4, 6, 8, 10, 20, 50, 100, 200. Label the axes, and title your graph “Flood Frequency Curve”.

Plot corresponding discharges and recurrence intervals.

Draw a best fit line between the data set. The resulting line is the flood frequency curve.

#### Things You'll Need

• Flood discharge data
• Calculator
• Pencil
• Semi-logarithmic graph paper
• Ruler

#### Tips

• Semi logarithmic paper has one side with a logarithmic scale. In the case of the flood frequency curve it will be the x axis. When you plot your numbers on this scale they will not be in equal increments.

Flood frequency curves are used as predictive tools in flood forecasting. By extrapolating out the curve, you can estimate how often a given river discharge will occur. Keep this in mind when you construct your graph. If you only have a 50 year flood record, you can still leave room on your graph for 200 years. That way, you can extend your line; thereby predicting how often a flood of a given discharge will occur.

For each recurrence interval, you can calculate the probability in any given year that a flood of that magnitude will be equaled or exceeded with the formula P (probability) = 1/T. T is the recurrence interval, and the resulting number will be in percent.

#### Warnings

• The longer the number of years of flood records, the more likely large discharge floods have been recorded. It is important to note that the frequency with which a flood will occur is a statistical average. It does not mean that every 100 years a flood of that magnitude will occur. It means on average, a flood of that intensity will occur every 100 years. For instance, that flood could occur in back to back years; or it could take 500 years before that level of river discharge is matched.