These geospatial data sets consist of surface grids of precipitation depths for seven frequencies at 12 durations used in a regional precipitation frequency analysis for Oklahoma. Eighty-four depth-duration-frequency surfaces were interpolated from precipitation-station data. The grid-cell spacing is 2,000 meters. Each depth-duration-frequency surface was interpolated using the same interpolation function and parameters.
Data were used from precipitation gage stations with at least 10 years of record within Oklahoma and about 50 kilometers into bordering states. Data were analyzed for seven frequencies (expressed as recurrence intervals of 2-, 5-, 10-, 25-, 50-, 100-, and 500-years) and 12 durations (15-, 30-, and 60-minutes; 1-, 2-, 3-, 6-, 12-, and 24-hours; and 1-, 3-, and 7-days).
Statistical methods were used to estimate precipitation depths for each duration-frequency at each station. These station depth-duration-frequency estimates were interpolated to produce continuous grids with grid-cell spacing of 2,000 meters. Contour lines derived from these surfaces (grids) were used to produce the maps in the "Depth-Duration Frequency of Precipitation for Oklahoma," by R.L. Tortorelli, Alan Rea, and W.H. Asquith, U.S. Geological Survey Water-Resources Investigations Report 99-4232.
These geospatial data sets may be used to determine an interpolated value of depth-duration-frequency of precipitation for any point in Oklahoma.
These data sets were used to produce the maps in the Depth-Duration Frequency of Precipitation for Oklahoma (Tortorelli, Rea, and Asquith, 1999).
L-moment statistical methods were used to estimate
depth-duration-frequency relations for each precipitation
station. See Tortorelli, Rea, and Asquith, (1999) for discussion
of the statistical methods.
L-coefficient of variation and L-skew were averaged for each
station with its four nearest neighbors. The values were weighted
by the number of years of record at each station. The means
were not averaged. The IDW function in ARC/INFO was used with
an exponent of zero to average the values for each point and
its four nearest neighbors. The effect was to spatially smooth the
frequency distribution parameters while leaving the mean values unchanged.
The frequency distribution parameters were used to calculate the
depth-duration-frequency (DDF) relation for each precipitation station.
The ARC/INFO GRID function, POINTINTERP (ESRI, 1997)
was used to interpolate surface grids of each DDF on a 2-km cell size.
The exponential smoothing option was used for POINTINTERP,
with a decay radius of 50 km and a neighborhood radius of 100 km.
The POINTINTERP function calculates distance-weighted averages for
each grid cell of all observed values within the neighborhood radius
of 100 km. The weight function is an exponential decay function
that goes to 0 at the neighborhood radius of 100 km.
Length-of-record weighting for the grid interpolation was
accomplished by multiplying the DDF values by the number of
years of record for each station, then interpolating a surface
of the multiplied values using the POINTINTERP function. Then
POINTINTERP was used to interpolate a surface of the years of
record using the same decay and neighborhood parameters. Then
for each grid cell the values of the first surface were
divided by the values of the second surface. This had the
effect of weighting the final surface by the period of
record. The result of this length-of-record weighting is that
the final interpolated surface is closer to the observed
values at stations having longer periods of record than at
stations with shorter periods of record.
After interpolation the DDF grids were masked to include just
the area of Oklahoma plus a 20-km buffer. This was done to (1)
minimize the effects of poorer interpolations near the edges
of the data (at 50 km outside Oklahoma), and (2) assist in
interpolating depth values at the State border. Contour
lines were then derived from each surface, choosing an
appropriate contour interval. It is intended that the maps be
used to estimate the precipitation depth values within the
The DDF grids were checked to ensure that the DDF values
increase monotonically (are continuously increasing) with
increasing duration and increasing frequency. For example,
(1) within the 12-hour duration, the 100-year DDF is larger
than the 50-year DDF for all grid cells, and (2) within the
100-year frequency, the 24-hour DDF is larger than the 12-hour
DDF for all grid cells. Only a few very small deviations from
monotonically increasing DDFs were observed. All were near the
edges of the grids at the 500-year frequency at durations
6-hours and above and all were outside Oklahoma.
An excerpt from the Arc Macro Language (AML) program used to
interpolate the surfaces follows:
/* Add items and calc products for period-of-record weighting tables additem sites%dur%.pat porw2yr 9 9 n 4 additem sites%dur%.pat porw5yr 9 9 n 4 additem sites%dur%.pat porw10yr 9 9 n 4 additem sites%dur%.pat porw25yr 9 9 n 4 additem sites%dur%.pat porw50yr 9 9 n 4 additem sites%dur%.pat porw100yr 9 9 n 4 additem sites%dur%.pat porw500yr 9 9 n 4 sel sites%dur%.pat calc porw2yr = yrsrec * freq2yr calc porw5yr = yrsrec * freq5yr calc porw10yr = yrsrec * freq10yr calc porw25yr = yrsrec * freq25yr calc porw50yr = yrsrec * freq50yr calc porw100yr = yrsrec * freq100yr calc porw500yr = yrsrec * freq500yr quit /* run pointinterp() to make Depth-Duration-Frequency surfaces /* First set cell size and snap to snap grid grid setwindow -700000 1120000 190000 1640000 setcell 2000 ayrs = pointinterp ( sites%dur%, yrsrec, #, EXP_SMOOTH, 50000, 0, 100000 ) &do freq &list 2yr 5yr 10yr 25yr 50yr 100yr 500yr porw%freq% = pointinterp(sites%dur%,porw%freq%,#,EXP_SMOOTH,50000,0,100000) setmask /proj/temp1/okrain/sitemaps/okbuff20g surf%freq% = porw%freq% / ayrs setmask off &end /* of do-freq-listRelated Data sets--
The precipitation stations data sets and contour data sets
derived from each surface are being published with these data
Other References Cited--
Asquith, W.H., 1998, Depth-duration frequency of precipitation for Texas:
U.S. Geological Survey Water-Resources Investigations Report 98-4044, 107 p.
Environmental Systems Research Institute, Inc. (ESRI), 1997,
ARC/INFO Command Reference, ARC/INFO Version 7.1.1 on-line
help: Redlands, CA.
Tortorelli, R.L., Rea, Alan, and Asquith, W.H., 1999, Depth-duration frequency
of precipitation for Oklahoma: U.S. Geological Survey Water-Resources Investigations
Report 99-4232, 113 p.
Any use of trade, product, or firm names is for descriptive purposes
only and does not imply endorsement by the
Although this Federal Geographic Data Committee-compliant metadata
file is intended to document the data set in nonproprietary form,
as well as in ARC/INFO format, this metadata file may include some
E(i) = X(i) - S(i) where E(i) = error associated with precipitation depth for a duration frequency at station i; X(i) = value of the precipitation depth for a duration-frequency at the station (control point); and S(i) = value of the precipitation depth for a duration-frequency at the station from the surface.The error defined is only indicative of the true error because each station was used in the surface developments. An independent means to measure error is not available.
The error analysis results for precipitation depth are listed in the file "table1.htm" accompanying this metadata. The table shows the comparison of the statewide mean, the standard deviation of differences between the statewide mean and each control point (station) value, and the coefficient of variation. The mean surface (contour) error, mean absolute surface (contour) error, maximum and minimum surface errors, root mean square error, and percent change from standard deviation to root mean square error for each depth-duration frequency also are listed. Each statistic is a weighted value, except for the maximum and minimum surface errors, which means the length of record of each station was considered in the computation. Maximum and minimum surface errors are listed to show the range of errors found in each depth-duration frequency of precipitation surface.
The weighted mean surface error is the mean difference between values of the control points and values from the surface. Mean surface errors near zero are desirable, because this indicates how well the interpolation routine worked. This error reflects any potential bias in the surface.
Root mean square error (RMSE) is analogous to the standard deviation (SD), and, therefore, the RMSE is comparable to the SD of the control points (differences between the statewide mean value and individual station values). The percent change from SD to RMSE, 100*[(RMSE SD) / SD], indicates the improvement in the precipitation depth estimate by using the surfaces (or contour maps) rather than simply using the corresponding statewide mean. If the percent decrease from the statewide standard deviation to the root mean square error is not at least 15 percent (Asquith, 1998), then a contour map is not better than a single statewide mean.
Percent changes from standard deviation to root mean square error for the (1) 15-minute to 60-minute durations ranged between -34.7 to -52.0 percent; (2) 1-hour to 24-hour durations ranged between -42.1 and -70.4 percent; and (3) 1-day and 7-day durations ranged between -51.8 and -70.3 percent. Therefore, the use of the surfaces (contour maps) results in more accurate estimates of the precipitation depth than simply using a statewide mean.
Each depth-duration-frequency surface is identified by its
name and position in the directory structure. For example, the
SURF100Y data set in the 7day subdirectory contains
precipitation depths for the 100-year 7-day precipitation
event. All depths are in inches.
Although these data have been used by the U.S. Geological Survey, U.S. Department of the Interior, no warranty expressed or implied is made by the U.S. Geological Survey as to the accuracy of the data.
The act of distribution shall not constitute any such warranty, and no responsibility is assumed by the U.S. Geological Survey in the use of this data, software, or related materials.
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