In cooperation with the Texas Department of Transportation
Depth-Duration
Frequency of
Precipitation for Texas
By William H. Asquith
U.S. Geological Survey
Water-Resources Investigations Report 98–4044
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Abstract
The U.S. Geological Survey, in cooperation with the Texas Department of Transportation, conducted a study of the depth-duration frequency of precipitation for Texas. Depth-duration frequency is an estimate of the depth of precipitation for a specified duration and frequency or recurrence interval. For this report, precipitation durations of 15, 30, and 60 minutes; 1, 2, 3, 6, 12, and 24 hours; and 1, 2, 3, 5, and 7 days were investigated. The recurrence intervals for the frequencies range from 2 to 500 years.
The time series of precipitation annual maxima for 173 fifteen-minute, 274 hourly, and 865 daily National Weather Service precipitation stations with at least 10 years of record in Texas provide the basis of depth-duration frequency for each identified duration. In total, about 3,030; 10,160; and 38,120 cumulative years of record are available for the 15-minute, hourly, and daily stations, respectively.
L-moment statistics of the precipitation annual maxima were calculated for each duration and for each station using unbiased L-moment estimators. The statistics calculated were the mean, L-scale, L-coefficient of variation, L-skew, and L-kurtosis. The mean for each station and duration was corrected for the bias associated with fixed-interval recording of precipitation. The generalized logistic distribution was determined, using L-moment ratio diagrams, as an appropriate probability distribution for modeling the frequency of annual maxima for durations of 15 minutes to 24 hours; whereas, the generalized extreme-value distribution was determined as appropriate for durations of 1 to 7 days.
The location, scale, and shape parameters of the distributions for each duration and each station were calculated from the L-moments. These parameters were contoured using spatial interpolation, based on the geostatistical method of kriging, to produce 37 maps that depict the spatial variation and magnitude of each parameter. Contour maps of the shape parameter for the generalized extreme-value distribution for durations of 1 to 7 days are not presented; the root mean square errors of preliminary maps for 1- to 7-day shape parameters were not appreciably smaller than the statewide standard deviation. Therefore, a single statewide mean shape parameter was used for 1- to 7-day durations. The depth-duration frequency for any location in Texas can be estimated using the contour maps and the equation of the corresponding distribution.
CONTENTS
Abstract
Introduction
Purpose and Scope
Previous Studies
Climate of Texas
Data Base of Precipitation Annual Maxima
Data Sources
Correction of Precipitation Annual Maxima for Fixed-Interval Recording
Acknowledgments
Regionalization of Precipitation Annual Maxima
L-moments
Generalized Logistic and Generalized Extreme-Value Distributions
Spatial Averaging of L-coefficient of Variation and L-skew and Estimation of L-scale
Contouring Distribution Parameters
Depth-Duration Frequency of Precipitation for Texas
Examples of Depth-Duration Frequency Computation
Precipitation Intensity-Duration Frequency Curve
Comparison to Previous Studies
Summary
Selected References
Appendix 1. Fifteen-minute precipitation stations in Texas with at least 10 years of annual maxima data through 1994
Appendix 2. Hourly precipitation stations in Texas with at least 10 years of annual maxima data through 1994
Appendix 3. Daily precipitation stations in Texas with at least 10 years of annual maxima data through 1994
PLATE
1. Map showing locations of 15-minute, hourly, and daily recording precipitation stations in Texas with at least 10 years of annual maxima data through 1994
FIGURES
1. Graph showing relation
between precipitation depth and storm duration for world record, Texas record,
and Texas
data-base maxima
2. Map showing modified National Weather Service climatic regions of Texas
3. Boxplots showing record-length
distribution for 15-minute, hourly, and daily precipitation stations in climatic
regions
of Texas
4–7. Graphs showing:
4. Time series of 1-day precipitation annual maxima for long-term stations (1778, 2266, and 2444) and
distribution of available record in corresponding climatic regions of Texas5. Time series of 1-day precipitation annual maxima for long-term stations (3262, 3873, and 3992) and
distribution of available record in corresponding climatic regions of Texas6. Time series of 1-day precipitation annual maxima for long-term stations (4058, 5272, and 9522) and
distribution of available record in corresponding climatic regions of Texas7. L-moment ratio diagrams for selected precipitation durations in Texas
8–9. Boxplots showing:
8. Effects of spatial averaging on the statewide distribution of L-coefficient of variation for each
precipitation duration9. Effects of spatial averaging on the statewide distribution of L-skew for each precipitation duration
10–18. Maps showing location (x) parameter of generalized logistic (GLO) distribution for:
10. 15-minute precipitation duration in Texas
11. 30-minute precipitation duration in Texas
12. 60-minute precipitation duration in Texas
13. 1-hour precipitation duration in Texas
14. 2-hour precipitation duration in Texas
15. 3-hour precipitation duration in Texas
16. 6-hour precipitation duration in Texas
17. 12-hour precipitation duration in Texas
18. 24-hour precipitation duration in Texas
19–23. Maps showing location (x) parameter of generalized extreme-value (GEV) distribution for:
19. 1-day precipitation duration in Texas
20. 2-day precipitation duration in Texas
21. 3-day precipitation duration in Texas
22. 5-day precipitation duration in Texas
23. 7-day precipitation duration in Texas
24–32. Maps showing scale (a) parameter of generalized logistic (GLO) distribution for:
24. 15-minute precipitation duration in Texas
25. 30-minute precipitation duration in Texas
26. 60-minute precipitation duration in Texas
27. 1-hour precipitation duration in Texas
28. 2-hour precipitation duration in Texas
29. 3-hour precipitation duration in Texas
30. 6-hour precipitation duration in Texas
31. 12-hour precipitation duration in Texas
32. 24-hour precipitation duration in Texas
33–37. Maps showing scale (a) parameter of generalized extreme-value (GEV) distribution for:
33. 1-day precipitation duration in Texas
34. 2-day precipitation duration in Texas
35. 3-day precipitation duration in Texas
36. 5-day precipitation duration in Texas
37. 7-day precipitation duration in Texas
38–46. Maps showing shape (k) parameter of generalized logistic (GLO) distribution for:
38. 15-minute precipitation duration in Texas
39. 30-minute precipitation duration in Texas
40. 60-minute precipitation duration in Texas
41. 1-hour precipitation duration in Texas
42. 2-hour precipitation duration in Texas
43. 3-hour precipitation duration in Texas
44. 6-hour precipitation duration in Texas
45. 12-hour precipitation duration in Texas
46. 24-hour precipitation duration in Texas
47. Graph showing precipitation intensity-duration curves of 100-year storm for selected localities in Texas
48. Map showing depth of 100-year storm for 6-hour precipitation duration in Texas
49. Graph showing precipitation intensity-duration curves of 100-year storm for Amarillo and Orange, Texas
TABLES
1. Correction factors for mean annual maxima of precipitation
2. Summary of goodness-of-fit and heterogeneity measures for Texas
3. Summary statistics of distribution-parameter maps for each precipitation duration in Texas
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