# Presentation: 076980

## Evaluating and Establishing Flooding Frequencies

*Allen Thompson*
*PhD, PE*
*Biological Engineering MU*

## Current Methods in Use

- Determine if soils can be classified as hydric (*frequently flooded for long durations*)
- Soil horizons of overwash areas are analyzed for silt and sand and the respective depth of horizon to determine past flooding
- Conduct interviews with area locals

## Frequency Classification  National Soil Survey Handbook

- None – less than 1 in 500 years
- Very Rare – less than 1 in 100 years
- Rare – 1 to 5 times in 100 years
- Occasional – 5 to 50 times in 100 years
- Frequent -  more than 50 times in 100 years
- Very Frequent – more than a 50% chance

## Analytical Methods

- Flooding frequency can be analytically determined using
- Probabilities
- Statistical distributions
- Requires adequate data sets

## Occurrence of events

## Frequency Analyses

- and
-    where s is the standard deviation and K is a frequency factor

## Normal and Skewed distributions

## Mass Rainfall vs. Intensity

## Rainfall distributions

## Statistical Distributions

- Negatively Skewed Distribution

- Cumulative probability curve

- Cumulative Probability curve, linearized on a probability scale

## Data Evaluation

- Data are analyzed by one of two probability laws
- Extreme Value Law
- Log Probability Law

## Extreme Value Law

- Annual maximum values approach a pattern of frequency distribution when n is large
-  (n = number of observations)

## Log Probability Law

- Logarithms of values are normally distributed

## Return Periods

-    where T is return period in years and P is percent probability

## Frequency Analysis

- Chow (1951) has shown that many frequency analyses can be reduced to
-    where XT is the magnitude of the event of return period T and K is the frequency factor

- Determining coefficient of Skewness, Cs
- Can be approximated as

## Selection Criteria 

- Most structures are sized based on the extreme events
- Insignificant data can be excluded
- Data Selection
- Annual series
- Partial Duration series

## Annual series

- Only the largest single event per year is selected

## Partial Duration series

- All values above a given base are selected per year regardless of the number of events
*These two series are essentially equal for return periods greater than 10 years*

## Criteria for including data

- Events must be independent
- Data for the period of record must be representative of long term trends

## Empirical Methods for Probability Gumbel’s equation

- N = total number of statistical events
- m = rank of events in descending order of   magnitude

## Log Probability for Annual Precipitation 

## Adequacy of Length of Record

- Y = minimum acceptable years of record
- t =  student’s t (90% significance level for Y-6 d.f.)
- R = ratio of magnitude of 100 to 2 year event

## Rainfall intensity – duration - frequency

## Log Pearson Type III Distribution

- Developed by Benson in 1968
- Based on log Pearson type III distribution
- Distribution resembles a dimensionless hydrograph
- Obtained by using the logs of observed data with the Pearson type III distribution

## Applying Log Pearson

- Transform the n annual flood magnitudes, Xi, to their logarithmic values, Yi
- Compute the mean logarithm,
- Compute the standard deviation of the logarithm, SY

## Applying Log Pearson (cont.)

- Compute the coefficient of skewness, Cs
- Compute
-  	KT obtained Pearson’s type III distribution
- Compute XT = antilogYT
- When Cs = 0 regionalized coefficient can be used

## Regional Frequency Analysis

- Define hydrologically homogenous region
- Hydrologic data from several locations within region can be combined into a single regional frequency analysis

## Define the Region

- Considerations
- Political boundaries
- Watershed divides
- Similarity of flood frequency curves

## Floods of Selected Frequency

- USGS publishes flood frequency reports
-     - Discharge-frequency curves
- 	 - Stage-frequency curves

## Discharge-frequency curves

- Variation of peak discharge expressed as a ratio to the mean annual flood with corresponding recurrence interval
-      - Regional as well as state-wide reports
-      - Size of drainage area required to determine	for a given point in watershed

## Stage-frequency curves

- Frequencies can be computed in terms of discharge and transformed to stages if stage-discharge stable during period of record
- Caution when used to define the high-stage end of the curve for short extrapolations

## Estimates for Small Watersheds

- Empirical or semi-empirical methods
- Statistical analysis of flood records on regional basis – applied with index curves
- Synthetic flood hydrographs based on unit graphs to design storm patterns
- Correlation analysis based on factors such as rainfall intensity, land use, slope, watershed dimensions

## Other Considerations

- Flooding not associated with stream flow
-   - Poorly drained soils
-   - Perched water tables

## Questions ?