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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 Texas

 5. 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 Texas

 6. 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 Texas

 7. 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 duration

 9. 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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