An Alternative Temporal

Rainfall Distribution for

Hydrologic Analysis and

Design

Joseph P. Wilson, PE, PHWilson Hydro, LLCPhD CandidateMissouri University of Science TechnologyRolla, Missouri

Sorry Folks, Missouri is CLOSED due to high water

MoDOTRoad Conditions

I think we can all agree that this

Is not the same as this

Session Topics

Why is the temporal distribution of rainfall important?

Rainfall temporal distributions currently used in hydrologic modeling.

Some of the issues with currently used rainfall distributions.

An updated temporal distribution.

Design Storms

Most jurisdictions in the United States use the design storm approach to hydrologic modeling for design and analysis.

A design storm is a way of representing storm rainfall with respect to depth, duration, temporal distribution, frequency and spatial distribution.

Based on the assumption that, under average conditions, a rainfall of a given frequency will produce runoff of the same frequency.

Rainfall Temporal Distributions

The selected design storm for hydrologic modeling has a significant impact on the computed results.

Rainfall Temporal Distributions are generally categorized as:

Simple geometrical shapes.

Nested intensity.

Statistical analysis of a gage network.

Simulation based on stochastic rainfall models

Based on an observed storm.

NRCS Type I, Ia, II, and III

Huff’s Quartile

Atlas 14 Distributions

New Frequency Modified Pilgrim-Cordery

Temporal Distributions for Discussion

NRCS 24-Hour Distributions

Nested Intensity.

Developed by SCS using rural rain gages, expanded on work by Hershfield.

NRCS proposing to

discontinue use.

Huff’s Quartile Distributions

Median CurvesPoint Rainfall

• Derived from 49 gage network in Illinois

• Events > 0.5”• 11 year period of

record, 1955-1966• Revisited in 1990 to

add 5 urban gages andResults included inBulletin 71.

Atlas 14 Distributions

Median Curves24-Hour Duration

• Published with Atlas 14 Region 8, 2013

• Based on precipitation depth > 2-year recurrence interval

• Distribution by duration

• 6-hour curves not based on true quartiles

They are Somewhat Similar

Frequency Modified Pilgrim-Cordery Distribution

Based on the method developed by Pilgrim and Cordery, 1975.

PC Ranking method based on arbitrary number of observed rainfall events.

Annual exceedance series used.

Depths non-dimensionalized.

Original method average period used for each rank. FMPC uses most frequent rank.

Average depth per rank assigned.

Frequency Modified Pilgrim-Cordery Method

This analysis uses the NOAA hourly rainfall for 48 stations in Missouri defined as Hydrologic Region 4 in Atlas 14, Volume 8.

Period of record ranges from 30-67 years.

The annual exceedance series was used.

Durations of 6-, 12-, and 24-hours.

48 Stations Studied

Data is Messy!

Data Processing

Period of record >30 years.

Missing data does not exceed 5%.

Accumulated totals excluded.

Consecutive totals summed for consecutive 6-, 12-, and 24-hour periods. Precipitation must occur in at least 80% of the time periods.

Overlapping time periods eliminated.

Data Processing, cont’d

The WILRAIN program was developed to process over 27 million lines of rainfall data.

A separate MODPC program was developed to derive the Frequency Modified Pilgrim-Cordery Distribution and compute the RMSE.

The programs can be applied to data from any NOAA hourly or 15-minute rainfall station or can be customized for other data formats.

FMPC Distribution - 48 Stations

Computed Error

St. Louis Lambert InternationalCumulative Mass Diagram, Hourly Data

St. Louis Regional Analysis

St. Louis Regional Analysis

St. Louis County Flood Study, MSD, FEMA

St. Louis FMPC compared to Huff’s 2nd Quartile

St. Louis FMPC compared to Huff’s 3rd Quartile

St. Louis FMPC compared to NRCS Type II

SummaryFrequency Modified Pilgrim-CorderyDistribution has a smaller RMSE than Huff’s or the NRCS Type II, and more closely represents observed data.

The method can be applied to any NOAA station recording hourly or 15-minute data.

Can be used at a single station or as a regional analysis.

It is important to use the best available data.

RecommendationsSelect the distribution that best fits your data.

Prefer a statistical based distribution.

Rainfall distributions in order of preference:

1. Frequency Modified Pilgrim-Cordery.

2. Pilgrim-Cordery.

3. Huff’s quartile/Atlas 14

4. As a last resort:

Nested intensity from local data.

Questions?

Joe.Wilson@WilsonHydro.comPhone 573-465-4209

Osage RiverTuscumbia, MO

1977