1. Design Rainfall Distributions Based on NRCC Data

2. General Considerations
Standard NRCS rainfall distributions were developed between 1960 and 1985.
NRCS is proposing adoption of NRCC data in the states where it is applicable.
Will a new set of rainfall distributions be required ?
If so, how to develop and apply them ?
Types I, II, and IA were developed in 1960’s. Type III was developed about 1985.
NRCC RF Distribution
October 2010

3. Standard Rainfall Distributions
The Type II distribution was developed from data in Technical Paper 40, The Type III was developed from data in TP-40 and Hydro-35, Two characteristics of the times strongly influenced the development of the Types I, IA, and II, especially. 1) Data were most plentiful for the 1-day duration. Very limited data were available for durations less than 1-day. For this reason, for locations where there were data at N-minute and hourly durations, ratios of these to the 24-hour (or daily) duration were developed and used to develop the 24-hour rainfall distribution. 2) Hydrologic computations were done by hand methods (there were very few computers available). This influenced the development of a small number of rainfall distributions. Tables and graphs were developed for hydrologists to estimate peak discharges and hydrographs efficiently. In these modern times, both of these limitations have been minimized.
NRCC RF Distribution
October 2010

4. Geographic Application
WinTR-20 NOAA 14 Data
March 2009

5. Ratio of shorter duration to 24 hour rainfall
The Type II distribution, especially, was developed when there were very limited data for duration less than 24 hours. These ratios were determined for rainfall stations where data were available for durations less than 24 hours.
NRCC RF Distribution
October 2010

6. NOAA 14 Data for Bergen County, NJ
Do we need a new rainfall distribution ? The Type III is used in NJ, will it still be reasonable ? Consider a location in Bergen County, NJ.
NRCC RF Distribution
October 2010

7. NRCC Data for White Plains, NY
Do we need a new rainfall distribution ? The Type III is used in southeast NY, will it still be reasonable ? Consider White Plains, NY. Comparing this table with that of Bergen County, NJ, the 24-hour 1-year to 50-year are reasonably close. The NRCC values for 100-year, 200-year and 500-year show an increasing trend.
NRCC RF Distribution
October 2010

8. Ratio of shorter duration to 24 hour rainfall, Bergen Co, NJ
The ratios for shorter durations to the 24-hour for Bergen County, NJ are highly variable and significantly different than the ratios for the Type II and Type III. These ratios are for non-smoothed data. This plot shows that the ratios are different than the Type II and Type III and also that the ratio varies from 1-year to 500-year storms. One distribution cannot reasonably fit ratios of all return periods. This is an example using data from NOAA 14. NRCS has developed this procedure for 19 states, Puerto Rico and Pacific Islands based on NOAA 14 data. Since NRCC is developing precip-frequency data for New York and New England, NRCS is extending this rainfall distribution procedure to those states as well.
NRCC RF Distribution
October 2010

9. Ratio of shorter duration to 24 hour rainfall, White Plains, NY
The ratios for shorter durations to the 24-hour for White Plains, NY are highly variable and significantly different than the ratios for the Type II and Type III. These ratios are for non-smoothed data. This plot shows that the ratios are different than the Type II and Type III and also that the ratio varies from 1-year to 500-year storms. One distribution cannot reasonably fit ratios of all return periods. This is an example using data from NRCC.
NRCC RF Distribution
October 2010

10. Steps in developing a distribution
Determine ratios of x hour / 24 hour rainfall.
Place the rainfall ratio for the shortest duration in the center of the distribution.
Symmetrically place each larger duration to include the shorter durations.
NRCC RF Distribution
October 2010

11. Example of a Nested Distribution
6 hr
0.7
0.6
In this example, the 3-hour / 24-hour ratio is Placed symmetrically about 12 hours, the 3-hour duration extends from 10.5 to 13.5 hours. Symmetrically placed about the 0.5 rainfall ratio, the ratios for the 3-hour duration extend from 0.2 to 0.8.
3 hr
WinTR-20 NOAA 14 Data
March 2009

12. Data Smoothing Procedure
Why is data smoothing recommended?
How are data smoothed ?
Each individual rainfall duration was analyzed independently. For example, the 1-year through 500-year 2-hour data were analyzed. Then the 3-hour data were analyzed. When building a rainfall distribution from the data, how much rain falls between each duration is important in order to generate smooth rising and falling hydrographs. If very long data series were available, the plot of intensity versus duration should be a smooth curve. If the curve is not smooth, other issues are involved such as probability distribution fitting (high or low outliers, differences in skew, long or short record, etc) come into play. There may be natural reasons such as mixed populations (different meteorology) in the data series.
NRCC RF Distribution
October 2010

13. Example – original data
This is an extreme case of being non-smooth. A limitation built into the precipitation-frequency analysis is that the 3-hour value must be greater than the 120-minute value, the 120-minute value be greater than the 60-minute value etc. These may be as close as 0.01 inch apart. The problem in this example is that the rainfall intensity between 60-minutes and 120-minutes is out of balance with the rainfall intensity between 120-minutes and 3-hours.
NRCC RF Distribution
October 2010

14. Example – smoothed data
After smoothing of the 120-minute and 3-hour data, the rainfall intensity between 60-minutes and 120-minutes and between 120-minutes and 3-hours are in balance.
NRCC RF Distribution
October 2010

15. Data Smoothing Procedure
Define incremental intensity:
Difference in rainfall divided by difference in duration, units inches/hour.
Data: 10-minute rain = 0.54 inches
15-minute rain = 0.67 inches
Incremental Intensity =
0.13 / (5 / 60) = 1.56 inches / hr
Incremental intensity for the 5-minute duration is the 5-minute rainfall times 12. Incremental intensity for 10-minutes is based on the difference between the 5-and 10-minute durations times 12. The incremental intensity for 30-minutes is based on the difference between the 15 and 30-minute rainfalls times 4. The incremental intensity at 24-hours is based on the difference between the 12 and 24-hour rainfalls divided by 12.
NRCC RF Distribution
October 2010

16. Data Smoothing 1-year, NJ
This curve is fairly smooth, especially in the 5-minute through 60-minute durations. If the non-smooth and smooth distributions were run in WinTR-20, there would not be a significant difference in peaks or hydrograph shape for this storm.
NRCC RF Distribution
October 2010

17. Data Smoothing Procedure
Incremental intensity is smoothed such that the 60-min and 24-hour rainfall values are not changed. 5-min through 30-min values may be changed.
120-min through 12-hour values may be changed.
There are two line segments joined at the 60-min value.
NRCC RF Distribution
October 2010

18. Data Smoothing 100-year, NJ
NRCC RF Distribution
October 2010

19. Data Smoothing, Virgin Islands
This plot is generated from data at Bethlehem Upper Works, US Virgin Islands. It is based on the 25-year rainfall. This shows two significant dips in incremental intensity near 10 minutes and 3 hours. This causes a very irregular hydrograph shape to be generated from the smooth and non-smooth rainfall distributions.
NRCC RF Distribution
October 2010

20. Data Smoothing, Virgin Islands
This plot is generated from data at Bethlehem Upper Works, US Virgin Islands. It is based on the 25-year rainfall. This shows two places before 12 hours and two after 12 hours of the rainfall distribution. This causes a very irregular hydrograph shape to be generated from the smooth and non-smooth rainfall distributions.
NRCC RF Distribution
October 2010

21. Data Smoothing, Phoenix, AZ
This is the 25-year plot of incremental intensity at the Phoenix rain gage. It shows two significant dips at 3 hours and 12 hours. This causes irregularities in the hydrograph tail. The most significant smoothing problems have been found in the southwest states and all tropical areas including Hawaii, Puerto Rico, Virgin Islands, and Pacific islands. NOAA 14 data smoothing problems for the mid-atlantic and midwest states are not so significant.
NRCC RF Distribution
October 2010

22. Data Smoothing, Phoenix, AZ
This is the 25-year plot of incremental intensity at the Phoenix rain gage. At 6 and 18 hours, there are significant changes in slope of the distribution. The most significant smoothing problems have been found in the southwest states and all tropical areas including Hawaii, Puerto Rico, Virgin Islands, and Pacific islands. NOAA 14 data smoothing problems for the mid-atlantic and midwest states are not so significant.
NRCC RF Distribution
October 2010

23. Rainfall ratio maps based on NRCC data
81 GIS maps were developed showing ratio of shorter duration to the 24-hour.
9 durations from 5-minutes to 12-hours.
9 return periods from 1-year to 500-year.
NRCC RF Distribution
October 2010

24. 1-yr ratio, 15min/24hr NRCC RF Distribution October 2010
This is the 15-minute / 24-hour ratio for the 1-year GIS layer. The 15-minute ratio is typical of the variation of 15-minute / 24-hour rainfall in both space and return period.
NRCC RF Distribution
October 2010

25. 500-yr ratio, 15min/24hr NRCC RF Distribution October 2010
This is the 15-minute / 24-hour ratio for the 500-year GIS layer. Compare this map with the previous map (1-yr). The high and low ratio areas are significantly relocated. The maximum and minimum ratios are also significantly different. This shows the problem with trying to develop a regional rainfall distribution. This is the reason that site-specific distributions are developed for WinTR-20 (the highest level NRCS hydrologic model). This variable behavior in rainfall ratios is also evident in NOAA Atlas 14 data.
NRCC RF Distribution
October 2010

26. Draft: 60 minute 25-yr ratio
The difference between the maximum and minimum ratios was divided by 3 to create three regions. One region has ratios from to 0.349, the second region has ratios from to 0.411, and the third region has ratios from to The map of tentative regions is shown on the next slide.
NRCC RF Distribution
October 2010

27. Draft: 3 distribution regions
These distribution regions are based on the draft 60-min/24-hour 25-year ratio. Within each region there is a specific limit on the range of the 60-min/24-hour ratio.
NRCC RF Distribution
October 2010

28. Steps to determine draft rainfall distribution
Determine average 25-year ratios for durations from 5-minutes to 12 hours in each of the three regions.
Develop 24-hour rainfall table at 0.1 hour increment for each region.
NRCC RF Distribution
October 2010

29. Draft: average 25-year ratios
NRCC RF Distribution
October 2010

30. Draft: RF Distributions
This shows the relation among the three distributions. We would expect higher peak discharges for Region A and lower peak discharges from Region C (if all other data were held constant).
NRCC RF Distribution
October 2010

31. Future Directions Develop software to easily use the data.
Use GIS data layers to derive site-specific rainfall data for hydrologic modeling.
NRCC RF Distribution
October 2010

32. NRCC RF Distribution
October 2010