Design Storm Rainfall Depths - An Overview of the Research Methods
By Ronald Eaglin, Linda Eaglin, and Marty Wanielista
Stormwater Management Academy
University of Central Florida
WHY DO THE STUDY?
Simply stated the depth of water associated with rain events may be more accurately
defined in light of new methods for analyses and additional data. The five water
management districts (WMDs) in Florida – Northwest Florida, St. Johns River, South
Florida, Southwest Florida, and Suwannee River – have worked with the Federal
Emergency Management Agency (FEMA) to improve and formalize their relationships
with a federal agency that shares flood protection responsibilities. The WMDs have
each executed a Cooperating Technical Partners (CTP) Memorandum of Agreement
with FEMA. Staff from the five WMDs and other partners coordinates on a regular basis
to discuss the unique issues facing Florida in implementing FEMA’s Flood Insurance
Rate Map (FIRM) Modernization program. As CTPs, the WMDs see the necessity of a
coordinated approach to implementing and managing Map Modernization and the
advantages of dealing with issues as a united front. As a product of this coordination,
the WMDs identified the need to develop consistent rainfall depth criteria across the
state for hydrologic analysis.
Regionally specific rain depths have been developed by most of the WMDs to produce
design criteria within their area boundaries. Along the boundaries between WMDs, the
rainfall depths often do not match and in fact differ by several inches in some locations.
In addition, Isopluval maps generated by each WMD differ from the national standards:
National Weather Service Technical Paper 40 (TP-40), published in 1961; National
Weather Service Technical Paper (TP-49), published in 1964; and the National Oceanic
and Atmospheric Administration Technical Memorandum NWS HYDRO-35, published in
1977. Differences in the maps are a result of using local data, different periods of
record, different best-fit distributions, and different approaches to filling in data gaps
both spatially and temporally.
Because the boundaries of the WMDs are based largely on watershed boundaries
rather than political boundaries, many counties within the state are split between
WMDs. One issue that has been raised during several Map Modernization projects is
the difference among the WMDs in the total rainfall depth for a given duration. For split
counties, determining which design storm criteria to apply for a countywide Map
Modernization project must be determined. The WMDs have suggested that developing
Isopluval rainfall depth curves for the entire state is the best alternative to manage the
design rainfall depth inconsistencies across the state. Developing updated, statewide
Isopluval rainfall depth curves provides the WMDs a consistent approach based on
defendable techniques, local data, and a longer period of record than existing maps.
1
PAST STATE WIDE DATA ANANLYSES
The last state-wide update using the then current rainfall data was completed in 1995.
Since then there have been various other studies for specific areas that in some ways
have resulting in discontinuous estimates of rainfall depths for different return periods at
the boundaries of the Water Management Districts in the State of Florida.
The 1995 update preformed by the UCF research team resulting in the development of
equal precipitation lines for the State of Florida and used rainfall data acquired from
NOAA and the Water Management Districts in digital format. The data were obtained in
both 15-minute and hourly recorded rainfall for stations in Florida, 5 stations in southern
Georgia, and one file containing only 15-minute data from southeast Georgia. The
information was then parsed into annual and partial series records containing the
required durations for the study. An extensive visual quality control check of all data
resulted in the acceptance of a total of 107 rainfall (76 hourly and 31 fifteen-minute)
stations.
A sample of 25 stations was selected based on their spatial location and amount of data
available for analysis. Distribution analysis of these 25 stations and comparison to
results obtained in reviewed research resulted in the selection of the Log Pearson Type
III distribution. The predicted rainfall volumes for the desired return periods of 2-, 3-, 5,
10-, 25-, 50-, 100-, 200-, and 500-years were generated and then converted to
intensities. These intensities were then used to determine the best equation to fit the
intensity versus duration data to the standard forms associated with IDF curves.
Since rainfall data collected and analyzed represented a single location, spatial analysis
was used to estimate the values for unrecorded areas within the boundaries of the
study. Kriging was used as the interpolation estimator for the special analysis to obtain
the best possible local averages coinciding with actual obtained values of recorded
rainfall stations. All 107 sites were used in the kriging analysis incorporating the
location of the stations and the predicted rainfall intensities at those stations. The
estimates at 625 coordinate points in the Florida grid resulting from the kriging process
provided the curve fit parameters for the selected best fit equation.
WHAT WAS DONE TO UPDATE THE DEPTH CURVES?
The proposed plan for updating the precipitation frequency estimates for the State of
Florida includes all of the steps taken in the above described analysis and was divided
into four tasks.
1.
The first task was a review of the literature to determine the extent of work
being completed for similar analyses. An annotated bibliography and summary
report resulted.
2.
In the second task, the national data used was from three major sources,
namely the National Climatic Data Center (NCDC), a digital format of the
available NOAA rainfall stations for the state of Florida, and additional quality
2
controlled digital data from the Water Management Districts. To ensure the best
possible accuracy of this project, additional visual QC checking was performed
on all data. The rainfall stations used in southern Georgia and southeast
Alabama were again used. This helped in obtaining consistency across the north
Florida borders. A DVD or other suitable storage device with all the rainfall data
that was deemed acceptable was submitted along with a report statistically
summarizing the data for each station. The proposed method for parsing the
data, performing the frequency analysis, and the spatial interpolation was also
presented in a draft technical report. The report was submitted to a WMD
committee for approval prior to starting task three.
3.
The third task involved parsing of the data and frequency analysis. The
revised data set was submitted along with a draft report documenting the data
used, methodology for parsing the data, the process for inspecting the accuracy
of the data, the methodologies for determining the sample of stations for the
frequency analysis, the range of functions used in the frequency analysis and the
result thereof. Summary tables and figures were included. Any abnormalities in
the data were documented with recommended solutions. This technical report
was presented to a committee of WMD members as a draft and revision made
based upon the committee input.
4.
The final report was composed of technical reports and posted for ease of
use on a computer site known as Wiki (an online database depository of
information). The site called the UCF Rainfall Analysis, and it currently gets on
the average over 300 hits per month.
DETAILS OF THE METHODOLOGIES USED IN TASKS 2 and 3
Step 1 – Determination of Rainfall Maxima
There is a significant quantity of rain depth data, but for some periods of time the
records are not complete. To select the data for analysis, at least eleven years must be
available. For each year of the eleven, there should be no more than 28 consecutive
days of missing data and no more than 60 intermittent days of missing data. Also
accumulations should not total more than 122 in a year. We also had available NOAA
data and the selection of each year already included the rule of no more than 30
consecutive days of missing data. The majority of the data available is in hourly depths.
From these rain depths, the annual maximum is determined for all durations under
study. A computer program was written that parses through the data for each site
determining the maximum rainfall for all durations. This program is available at the
computer site named “ucf-rainfall.pbworks.com”. The program simply starts at a given
time accumulating rainfall forward for the duration being accumulated. If this volume is
greater than the current maximum, it replaces that maximum. The process is repeated
for every starting value (rainfall value in the data set) in the data for each year. These
values were also verified by hand checking their values against the actual data for the
site. The following table shows the annual maximum volume for each year of available
data and analyzed duration for the rainfall site at Orlando International Airport.
3
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Durations (hrs)>>
1
2
1.78
3.3
2.11
2.18
1.50
2.50
2.65
3.52
2.70
3.20
1.90
2.21
1.68
2.20
2.30
4.10
3.69
3.74
1.43
2.17
1.85
2.14
2.09
2.70
1.89
2.79
1.35
1.78
1.85
2.63
1.95
2.29
1.24
1.46
1.42
2.68
2.42
4.48
2.00
2.60
1.21
2.02
1.25
1.76
2.64
4.61
1.99
2.08
2.61
3.16
3.35
3.55
1.18
1.50
2.60
4.15
2.01
2.05
1.88
2.34
1.88
2.54
1.80
2.03
6
3.35
2.31
2.66
3.56
3.89
2.64
2.50
4.40
3.75
2.59
3.70
3.70
3.04
3.03
4.41
2.42
1.64
3.47
5.19
2.60
3.04
2.39
4.73
2.77
3.47
3.80
1.52
5.28
3.98
2.44
3.75
3.37
12
3.37
2.53
2.66
3.56
3.95
3.42
3.14
4.40
3.75
2.78
4.62
4.00
3.24
3.20
5.49
2.42
1.69
4.11
5.56
2.60
4.37
2.50
4.73
3.21
3.47
3.80
1.52
5.28
4.06
2.45
5.00
4.69
24
5.15
2.72
2.66
3.56
3.95
3.71
3.18
4.40
4.09
2.79
5.04
4.06
4.19
3.59
5.87
3.29
2.53
4.32
5.65
2.60
5.45
3.01
4.94
3.85
3.47
5.01
2.35
5.28
4.06
2.52
5.36
5.09
48
8.48
3.54
3.65
3.67
4.60
3.78
3.18
5.50
4.25
3.63
5.04
4.06
4.34
5.47
5.87
3.67
2.79
5.06
5.97
3.66
5.84
4.15
6.06
4.05
3.47
5.21
2.63
5.65
4.08
2.56
5.40
6.64
72
9.31
4.06
5.73
3.67
4.64
3.78
3.80
5.57
4.59
3.86
5.04
5.02
4.34
5.66
5.87
3.67
3.45
5.12
6.04
3.98
5.85
4.78
6.30
4.62
3.85
5.66
2.85
6.04
4.46
2.97
5.41
6.64
96
10.67
4.35
5.99
3.67
4.87
3.87
3.80
5.66
5.00
4.11
5.04
5.02
4.59
7.12
5.87
4.16
4.13
5.31
6.07
4.07
5.87
4.85
6.30
5.66
3.94
7.00
3.84
6.77
5.08
4.07
5.42
6.69
120
10.74
4.89
6.04
4.12
6.19
3.97
3.80
5.66
5.13
4.18
5.04
5.94
4.59
9.29
5.87
4.52
4.13
5.79
6.14
4.19
5.95
4.85
6.40
6.51
4.89
7.16
4.15
10.16
6.32
5.03
5.58
6.69
Annual Maximum Volumes (inches) for Site 6628 (Orlando IAP)
Step 2 – Distribution Fit for the Rainfall Data
The maximum data for a given duration is now fit to a probability distribution. The
selected distribution for all data analysis was the GEV distribution. This determination
was made by visual comparison of fit comparing Normal, 2 Parameter Log Normal, 3
Parameter Log Normal, Pearson, Log Pearson, Gumbel, and GEV distributions. The
Weiss factor was applied to the data before analysis to account for the possibility of
missing actual maxima for durations close to the time increment of the data. The results
of the Distribution Fit are the GEV Parameters (Mean, 2 nd Moment, Skew, L-Moments)
and a prediction of the maximum based distribution fit. The fit value (Rainfall Volume) is
a function of return period and duration. The following table shows the results of the
GEV Distribution fit for the Orlando International Airport.
4
500
200
100
50
25
10
5
3
2
1
5.2814
4.8070
4.4445
4.0780
3.7062
3.2007
2.7971
2.4737
2.1817
2
7.5986
6.7193
6.0822
5.4673
4.8717
4.1050
3.5264
3.0830
2.6974
6
6.3531
6.0518
5.7896
5.4928
5.1555
4.6312
4.1511
3.7222
3.2976
12
6.6239
6.3878
6.1696
5.9095
5.5980
5.0829
4.5805
4.1087
3.6216
24
7.0620
6.8123
6.5834
6.3123
5.9897
5.4602
4.9479
4.4698
3.9787
48
9.8644
9.1048
8.5060
7.8842
7.2360
6.3263
5.5759
4.9587
4.3890
72
9.7250
9.0800
8.5607
8.0116
7.4287
6.5927
5.8877
5.2977
4.7450
96
13.1300
11.4717
10.3236
9.2579
8.2653
7.0452
6.1674
5.5197
4.9740
120
16.2335
13.7870
12.1575
10.6943
9.3763
7.8187
6.7427
5.9740
5.3435
GEV Volume Predictions (inches) with Weiss factors for Site 6628 (Orlando IAP)
Step 3 – Curve Fit to Final Equation Form
The final step of the analysis for a single site is to fit the distribution data to a single
curve fit form. The form of the equation selected was
Volume  a(b  D) n
Where D = Duration (in hours) and a, b, and n are curve fit parameters. An example of
the curve fit parameters for the Orlando International Airport site is shown.
a*(b+D)^n
500
200
100
50
25
10
5
3
2
a
4.57
4.29
4.06
3.80
3.52
3.31
2.99
2.64
2.32
b
1.00
1.00
1.00
1.00
1.00
0.23
0.00
0.00
0.00
n
0.21
0.20
0.19
0.19
0.19
0.17
0.16
0.17
0.17
r^2
0.68
0.77
0.84
0.90
0.95
0.98
0.99
0.99
0.99
Curve Fit Parameters with Weiss for Site 6628 (Orlando IAP)
These parameters are then used to calculate the final volume prediction for each
duration and return period. These values are calculated for every site.
5
500
200
100
50
25
10
5
3
2
Actual
1
5.2861
4.9279
4.6315
4.3349
4.0155
3.4286
2.9900
2.6400
2.3200
4.216
2
5.7559
5.3442
5.0024
4.6821
4.3371
3.7935
3.3407
2.9702
2.6101
4.917
6
6.8768
6.3311
5.8762
5.4999
5.0946
4.5174
3.9827
3.5801
3.1461
5.392
12
7.8315
7.1655
6.6096
6.1863
5.7305
5.0663
4.4498
4.0278
3.5396
5.618
24
8.9843
8.1667
7.4840
7.0047
6.4886
5.6907
4.9717
4.5315
3.9822
5.901
48
10.3480
9.3432
8.5048
7.9601
7.3736
6.3972
5.5548
5.0982
4.4802
8.502
72
11.2516
10.1186
9.1740
8.5865
7.9538
6.8519
5.9271
5.4620
4.7999
9.326
96
11.9437
10.7106
9.6831
9.0630
8.3952
7.1943
6.2063
5.7357
5.0405
10.684
120
12.5113
11.1948
10.0985
9.4518
8.7553
7.4719
6.4319
5.9575
5.2354
10.751
GEV Volume Predictions (inches) Curve Fit for Site 6628 (Orlando IAP)
Actual Maximum Volumes with Weiss
Step 4 – Spatial Analysis
Each site now has 81 rainfall volume predictions for the 9 return periods and the 9
rainfall volumes that were part of the analysis. The final step is to develop a set of
rainfall volume isohyetes representing all the stations that were part of the analysis. The
first step was to choose a spatial analysis methodology that adequately represents the
data. A standard spatial kriging analysis was selected as the best methodology.
Methods compared were inverse distance to a power, standard kriging, minimum
curvature, modified Shepards method, natural neighbor, nearest neighbor, polynomial
regression, radial basis functions, triangulation with linear interpolation, moving
average, and local polynomial. These were applied to fifteen sites and selection was
made based on the reproduction of actual rainfall volumes from the sites. The krig
analysis was performed on all data and the results were published for each duration and
return period.
6
31
30
29
28
27
26
25
-87
-86
-85
-84
-83
-82
5 Year 1 Hour Using Standard Kriging
7
-81