Conditional Flood Frequency

The term ‘conditional flood frequency’ is used in several documents on this web site. These notes define conditional flood frequency and describe some of its characteristics and applications.

Calculation or estimation of a ‘flood frequency curve’ for a watershed is a routine task in hydrologic engineering. Flood frequency curves are created from a time series of peak flow in each water-year, and show flow rates at different return periods.

 

Observed and Simulated Peak Flows, Sonoma Creek , CA , 1955 to 1981

Figure 1

 

Flood frequency plots like Figure1, assembled from a series of annual peaks, are traditional in hydrologic analysis, but they show only one aspect of flood frequency, the long-term flood frequency.

If we were to plot ‘long term’ flood frequency vs. time of year, say the one percent or the ‘100-year’ flood that would be expected to occur in each week of the year, how would this peak flow vary during the water year? What is the one percent peak flow in the first week March?

Figure 2

 

Figure 2 shows how the long term mean one percent flood peak, plotted in red, varies during the water year for a coastal California stream. The long term mean one percent or 100-yr flood in a watershed is a continuous time series, even though we often think of it as 'x' on the red curve, or the maximum of the red curve - a fixed quantity. The seasonal long term mean peak flow variability is due to both climate and soil moisture – there is very little precipitation on the California coast in July, August and September and low soil moisture levels limit peak flows in October and November. The seasonal variability in the one percent flood is often used to calculate seasonal flood control storage requirements for reservoirs.

What then is conditional flood frequency? Would the one percent flood that one would expect in March be the same in every year? This question is carefully worded: The long term mean one percent flood in March is the same every year, but what is the one percent flood that would be expected on March 1st in a particular year?

The one percent flood that would be expected on March 1st in a particular year is conditional – the green curve in Figure 2 is an example. The conditional flood frequency March 1st in any year varies with the March 1st watershed state in that year (soil moisture conditions and snow packs). HFAM calculates conditional flood frequency in the probabilistic runs so the green curve in Figure 2 would be found by calculating conditional flood frequency every week or month during a particular year.

Conditional Flood Frequency on January 1st, for Month of January

Figure 3

Figure 3 shows the upper and lower bounds of conditional flood frequency for January, calculated January 1st, for Lichau Creek, CA. Snow does not accumulated in this watershed so the variability in Figure 3 is due to watershed soil moisture conditions on January 1st only.

 

Flood Hydrographs for January 4th, 1982 for Lichau Creek, Ca

Figure 4

Hydrographs for the largest historical flood in the watershed are shown in Figure 4 when the storm begins at historic low and historic high soil moisture conditions on January 1st.

Given that conditional flood frequency exists and can be calculated, what is its practical value? In Lichau Creek is a major tributary to Petaluma River . Floods are common on Petaluma River and emergency evacuations have occurred in historic floods. The only hydrologic tools available to local police and fire departments are an Alert flood warning system, which will give about two hours warning of overbank flows, and the long term mean flood frequency curve for the river.

Conditional flood frequency provides additional information; for example, if January 1st soil moistures are at historic high levels the long term mean one percent flood will have an eight percent chance of occurring within the next month. If January 1st soil moistures are at historic low levels the long term mean one percent flood has a very low chance of occurring – even the largest storm of record, January 4st of 1982, will not cause overbank flows. This information would be useful for flood emergency planning – public officials may know actual current flood risks rather than long term mean flood risks.

Reservoir operations for flood control would benefit as well. Flood control policies for some reservoirs do include data on current flood risks, e. g. policies may vary with upstream snowpacks. Many reservoirs use the same flood control storage policy every year and watershed conditions are not considered. Thus, flood protection is more than sufficient in some years and less than a desirable level in others.

Soil Moisture Anomaly Forecast, Europe , April 2, 2008

Figure 5

The European Commission, Joint Research Center , makes a daily soil moisture forecast (Figure 5) in connection with the European Flood Alert System. These data combined with ‘ensemble’ weather forecasts and modeling would define conditional flood frequencies for major rivers.

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