DIGITAL DATA SETS OF DEPTH-DURATION FREQUENCY OF PRECIPITATION FOR OKLAHOMA
By Alan Rea and Robert L. Tortorelli
U.S. Geological Survey Open-File Report 99-463
Prepared in cooperation with the
Oklahoma Department of Transportation
Oklahoma City, Oklahoma
1999
Data were used from precipitation gage stations with at least 10 years of record within Oklahoma and a zone extending about 50 kilometers into bordering states. Three different rain gage networks provided the data (15-minute, 1-hour, and 1-day). Precipitation annual maxima (depths) were determined from the station data for each duration for 110 15-minute, 141 hourly, and 413 daily stations. 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. The geospatial data sets are presented in digital form for use with geographic information systems. These geospatial data sets may be used to determine an interpolated value of depth-duration-frequency of precipitation for any point in Oklahoma.
The geospatial data sets are presented in digital form for use with geographic information systems. The data sets consist of surface grids of precipitation depths 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) for Oklahoma. Eighty-four depth-duration-frequency surfaces were produced from precipitation-station data. Contour lines derived from each surface and the precipitation-station data from which the surfaces were interpolated also are included. Contour intervals vary from 0.05 to 0.5 inch. These geospatial data sets may be used to determine an interpolated value of depth-duration-frequency of precipitation for any point in Oklahoma. A geospatial data set of county boundaries for Oklahoma (Rea and Becker, 1997) is provided for spatial reference.
Data were used from precipitation gage stations with at least 10 years of record within Oklahoma and a zone extending about 50 kilometers into bordering states. Three different rain gage networks provided the data (15-minute, 1-hour, and 1-day). Precipitation annual maxima (depths) were determined from the station data for each duration for 110 15-minute, 141 hourly, and 413 daily stations. Statistical methods (Tortorelli, Rea, and Asquith, 1999) 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.
Length-of-record weighting for the grid interpolation was done by multiplying the depth-duration frequency of precipitation values by years of record for each station, then interpolating a surface of the multiplied values using the POINTINTERP function in ARC/INFO GRID. Then POINTINTERP was used to interpolate a second surface of the years of record. Then for each grid cell the values of the first surface were divided by the values of the second surface. This method weighted the final surface by distance and years of record. As a result the final interpolated surface is closer to the observed values at stations having more years of record than at stations with less years of record. Contour lines derived from these surfaces (grids) were used to produce the maps in the Depth-Duration Frequency of Precipitation for Oklahoma (Tortorelli, Rea, and Asquith, 1999).
Additional information about the statistical methods is in Tortorelli, Rea, and Asquith (1999). Additional information about the spatial interpolation methods is included in the metadata for the surfaces data sets.
The data sets are provided in nonproprietary and ARC/INFO
file formats. No software is provided with these data sets. Users will
need geographic information system (GIS) software to use the data sets.
The U.S. Geological Survey does not recommend or endorse any particular
software package for use with these data sets. For links to more information
on GIS software and capabilities, see: The
GIS FAQ (Frequently Asked Questions), GIS
Companies on the WWW, USGS
GIS Information.
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 table 1. The table shows the comparison of the statewide mean for the control points, the standard deviation of differences between the statewide mean and each control point (station) value, and the coefficient of variation for the control points. 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 map.
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 of 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.
The data sets provided are available in nonproprietary and ARC/INFO
file formats. See the following table for an explanation of the file formats.
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The sites are stored as comma-delimited ASCII text files. The first record in each file contains a field identifier. This format is compatible with many spreadsheet and data-base management systems. Additional information about the field contents may be found in the "Entity_and_Attribute_Information" section of the metadata for the sites data sets.
The surfaces are stored in an ASCII grid format. This is a simple space-delimited array of values preceded by header information. The header information identifies the number of columns and rows in the array, the X- and Y-coordinates of the lower left corner, the grid-cell size, and the value used to indicate missing data.
The contour data sets are stored in the generic, public-domain Digital Line Graph (DLG-3) Version 3, Optional format, and have file extensions of ".DLG". Designed for data interchange, the DLG-3 format allows the simple creation of a vector polygon or line data structure. The topological linkages are explicitly encoded for node, area, and line elements. The files are composed of 8-bit ASCII characters organized into fixed logical records of 80 bytes. A detailed description of the DLG-3 Optional format may be found in the data users guide 3, Digital Line Graphs from 1:2,000,000-scale maps (U.S. Geological Survey, 1990). The major and minor codes used in this application of the DLG format are not the same as those used in many USGS standard digital data products. The "Entity_and_Attribute_Information" section of the metadata file contains more information about the major and minor codes used. A free viewer capable of reading DLG files is available at http://mcmcweb.er.usgs.gov/viewers/dlg_view.html.
The ARC/INFO data sets are stored as coverages (points and lines) or grids (surfaces). ARC/INFO export files with ".E00" file extensions also are provided for the COUNTY and COUNTYDD coverages. A free viewer called ArcExplorer is capable of reading the ARC/INFO data sets. ArcExplorer is available from http://www.esri.com.
A documentation file (known as metadata) is provided for each type (sites,
surfaces, and contours) of data set. The documentation files comply with
the Federal Geographic Data Committee (FGDC) Content Standards for Digital
Geospatial Metadata (Federal Geographic Data Committee, 1994). The FGDC-compliant
metadata files contain detailed descriptions of the data sets, and include
narrative sections that describe the procedures used to produce the data
sets in digital form. The metadata files are stored as HTML files, with
".HTM" file extensions.
| A_NOTICE.TXT | Liability disclaimer |
| INDEX.HTM | This file |
| SITES.HTM | Metadata for the sites data sets |
| SURFACES.HTM | Metadata for the surface data sets |
| CONTOURS.HTM | Metadata for the contour data sets |
| TABLE1.HTM | Table containing results of error analysis |
| COUNTY.HTM | Metadata for county data set (from Digital Atlas of Oklahoma) |
| USGS.GIF | USGS logo in Graphics Interchange Format (GIF) |
| DIR_EXAM.GIF | Example graphic of portion of directory structure (GIF) |
The four subdirectories contain the following:
| raw_data | Original storm accumulation data files (see readme.txt) |
| fnl_data | Storm accumulation data files after review and removal of questionable data (see readme.txt) |
| arc_data | Data sets in ARC/INFO format |
| pd_data | Data sets in nonproprietary format |
Procedures used to review the storm accumulation data files and remove questionable data are described in the "Data_Quality_Information" section of the metadata for the sites data sets.
The surfaces and contours data sets are intended to estimate precipitation depth values within Oklahoma. A geospatial data set of county boundaries for Oklahoma (Rea and Becker, 1997) is provided for spatial reference. The geospatial data set is named "COUNTY" and is provided in DLG format (\pd_data\county.dlg) and in ARC/INFO coverage format in the arc_data subdirectory. The geospatial data set also is provided in the arc_data subdirectory stored in decimal degrees and named "COUNTYDD".
The arc_data and pd_data subdirectories each contain a subdirectory
for each duration. The individual data sets are stored under the duration
subdirectories. An example showing the arc_data subdirectory and its 12-hour
duration subdirectory is shown below:
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Each duration subdirectory contains contours,
sites, and surfaces data sets. As shown in the example, the ARC/INFO data
sets each consist of directories and a parallel "info" directory.
A "latlong" subdirectory under each duration subdirectory in arc_data contains copies of the contour and sites data sets stored in decimal degrees. The pd_data subdirectory is structured similarly, except the data sets are individual files in delimited ASCII, DLG, or ASCII grid format. The pd_data subdirectory contains the county-boundary data set in DLG format, named "county.dlg". The nonproprietary-format files are provided in Albers Equal Area projection only. |
The Albers Equal Area map projection (Snyder, 1987) was chosen for
the data sets. This projection is appropriate for maps of the conterminous
United States because of the visual presentation and equal-area characteristics,
which facilitates areal analysis. The projection is cast on the North American
Datum of 1983. This projection slightly distorts shapes and distances (scale)
in order to maintain equal-area properties. Scale is true along the standard
parallels, which are to the north and south of Oklahoma. Scale distortion
in Oklahoma reaches a maximum of slightly less than 1 percent at the northern
border of the state. The following table provides map projection information.
Albers Equal Area projection parameters
[GRS1980, Geodetic Reference System 1980; NAD83, North American Datum
1983]
| Projection parameters: | |
|---|---|
| Spheroid | GRS1980 |
| Datum | NAD83 |
| First standard parallel | 29 30 00 North |
| Second standard parallel | 45 30 00 North |
| Central meridian | 96 00 00 West |
| Latitude of projection origin | 23 00 00 North |
| Coordinate system parameters: | |
| False easting | 0 |
| False northing | 0 |
| Planimetric units of measure | meters |
A "latlong" subdirectory under each duration subdirectory in arc_data
contains copies of the contour and sites data sets stored in decimal degrees.
The "COUNTYDD" coverage in the arc_data subdirectory also is stored in
decimal degrees. These coordinates are based on the North American Datum
of 1983.
ARC/INFO software was used in the development of the data sets. The
data sets were processed using the ARC/INFO Revision 7.1.1 software package,
on a SUN Enterpise 4000 running Solaris Version 2.5.1. Final processing
used ARC/INFO Revision 7.2.1.
Asquith, W.H., 1998, Depth-duration frequency of precipitation for
Texas: U.S. Geological Survey Water-Resources Investigations Report 98-4044,
107 p.
Federal Geographic Data Committee, 1994, Content standards for digital geospatial metadata (June 8): Federal Geographic Data Committee, Washington, D.C., 78 p. URL: https://www.fgdc.gov/Metadata/Metadata.html
Rea, Alan and Becker, C.J., 1997, Digital atlas of Oklahoma: U.S. Geological Survey Open-File Report 97-23, 2 CD-ROMs.
Snyder, J.P., 1987, Map projections--A working manual: U.S. Geological Survey Professional Paper 1395, 383 p.
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.
U.S. Geological Survey, 1990, Digital line graphs from 1:2,000,000-scale
maps, data users guide 3: U.S. Geological Survey National Mapping Program
Technical Instruction, 70 p.
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