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Statistical Characteristics of Storm Interevent Time, Depth, and Duration for Eastern New Mexico, Oklahoma, and Texas

By William H. Asquith, Meghan C. Roussel, Theodore G. Cleveland, Xing Fang, and David B. Thompson 

U.S. Geological Survey
Professional Paper 1725

In cooperation with the Texas Department of Transportation


Abstract

The design of small runoff-control structures, from simple floodwater-detention basins to sophisticated best-management practices, requires the statistical characterization of rainfall as a basis for cost-effective, risk-mitigated, hydrologic engineering design. The U.S. Geological Survey, in cooperation with the Texas Department of Transportation, has developed a framework to estimate storm statistics including storm interevent times, distributions of storm depths, and distributions of storm durations for eastern New Mexico, Oklahoma, and Texas. The analysis is based on hourly rainfall recorded by the National Weather Service. The database contains more than 155 million hourly values from 774 stations in the study area. Seven sets of maps depicting ranges of mean storm interevent time, mean storm depth, and mean storm duration, by county, as well as tables listing each of those statistics, by county, were developed. The mean storm interevent time is used in probabilistic models to assess the frequency distribution of storms. The Poisson distribution is suggested to model the distribution of storm occurrence, and the exponential distribution is suggested to model the distribution of storm interevent times. The four-parameter kappa distribution is judged as an appropriate distribution for modeling the distribution of both storm depth and storm duration. Preference for the kappa distribution is based on interpretation of L-moment diagrams. Parameter estimates for the kappa distributions are provided. Separate dimensionless frequency curves for storm depth and duration are defined for eastern New Mexico, Oklahoma, and Texas. Dimension is restored by multiplying curve ordinates by the mean storm depth or mean storm duration to produce quantile functions of storm depth and duration. Minimum interevent time and location have slight influence on the scale and shape of the dimensionless frequency curves. Ten example problems and solutions to possible applications are provided.

Table of Contents

Abstract

Introduction

Purpose and Scope

Previous Studies

Storm Research Sponsored by the Texas Department of Transportation

Other Studies

Database of Hourly Rainfall

Acknowledgments

Analysis of Site-Specific Statistical Characteristics of Hourly Rainfall

Minimum Interevent Time of Rainfall

Storm Interevent Time and Distribution of Depth and Duration

Quantile Functions of Storm Depth and Duration

Statistical Characteristics of Storm Interevent Time, Depth, and Duration

Regionalization of Storm Statistics

Maps of Mean Storm Interevent Time, Depth, and Duration

Tables of Mean Storm Interevent Time, Depth, and Duration

Example Applications

Site-Specific Approach

Example 1: Estimation of Storm Occurrence

Example 2: Estimation of Interevent Times of Storms

Example 3: Estimation of the Empirical Distribution of Storm Depth

Example 4: Estimation of the Continuous Distribution of Storm Depth

Example 5: Statistical Simulation of Rainfall Intensity

Regional Approach by County

Example 6: Regional Estimation of Storm Occurrence

Example 7: Computation of the Storm-Captured Percentage

Example 8: Regional Estimation of the Empirical Distribution of Storm Depth

Example 9: Estimation of the Uncertainty of a Regional Estimate of a Storm Depth Percentile

Example 10: Estimation of the Expected Storage in a BMP Using Mean Storm Interevent Time, Depth, and Duration

Summary

References

Appendix 1—L-Moments and Sample L-Moments

L-moments

Sample L-moments

Appendix 2—Storm Statistics for Hourly Rainfall Stations in Eastern New Mexico

  2–1.1. — 2–1.7.  Number of storms, total duration, and mean storm interevent time defined by:
    2–1.1.  6-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–1.2.   8-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–1.3.   12-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–1.4.   18-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–1.5.   24-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–1.6.   48-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–1.7.   72-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
  2–2.1. — 2–2.7.  L-moments of storm depth defined by:
    2–2.1.   6-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–2.2.   8-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–2.3.   12-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–2.4.   18-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–2.5.   24-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–2.6.   48-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–2.7.   72-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
  2–3.1. — 2–3.7.  L-moments of storm depth defined by:
    2–3.1.   6-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–3.2.   8-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–3.3.   12-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–3.4.   18-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–3.5.   24-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–3.6.   L-moments of storm duration defined by 48-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–3.7.   72-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
  2–4.1. — 2–4.7.  Empirical distribution of storm depth defined by:
    2–4.1.   6-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–4.2.   8-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–4.3.   12-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–4.4.   18-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–4.5.   24-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–4.6.   48-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–4.7.   72-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
  2–5.1. — 2–5.7.  Empirical distribution of storm duration defined by:
    2–5.1.   6-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–5.2.   8-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–5.3.   12-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–5.4.   18-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–5.5.   24-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–5.6.   48-hour minimum interevent time for hourly rainfall stations in eastern New Mexico
    2–5.7.   72-hour minimum interevent time for hourly rainfall stations in eastern New Mexico

Appendix 3—Storm Statistics for Hourly Rainfall Stations in Oklahoma

  3–1.1. — 3–1.7.  Number of storms, total duration, and mean storm interevent time defined by:
    3–1.1.   6-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–1.2.   8-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–1.3.   12-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–1.4.   18-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–1.5.   24-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–1.6.   48-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–1.7.   72-hour minimum interevent time for hourly rainfall stations in Oklahoma
  3–2.1. — 3–2.7.  L-moments of storm depth defined by:
    3–2.1.   6-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–2.2.   8-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–2.3.   12-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–2.4.   18-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–2.5.   24-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–2.6.   48-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–2.7.   72-hour minimum interevent time for hourly rainfall stations in Oklahoma
  3–3.1. — 3–3.7.  L-moments of storm depth defined by:
    3–3.1.   6-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–3.2.   8-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–3.3.   12-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–3.4.   18-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–3.5.   24-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–3.6.   48-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–3.7.   72-hour minimum interevent time for hourly rainfall stations in Oklahoma
  3–4.1. — 3–4.7.  Empirical distribution of storm depth defined by:
    3–4.1.   6-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–4.2.   8-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–4.3.   12-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–4.4.   18-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–4.5.   24-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–4.6.   48-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–4.7.   72-hour minimum interevent time for hourly rainfall stations in Oklahoma
  3–5.1. — 3–5.7.  Empirical distribution of storm duration defined by:
    3–5.1.   6-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–5.2.   8-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–5.3.   12-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–5.4.   18-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–5.5.   24-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–5.6.   48-hour minimum interevent time for hourly rainfall stations in Oklahoma
    3–5.7.   72-hour minimum interevent time for hourly rainfall stations in Oklahoma

Appendix 4—Storm Statistics for Hourly Rainfall Stations in Texas

  4–1.1. — 4–1.7.  Number of storms, total duration, and storm interevent time defined by:
    4–1.1.   6-hour minimum interevent time for hourly rainfall stations in Texas
    4–1.2.   8-hour minimum interevent time for hourly rainfall stations in Texas
    4–1.3.   12-hour minimum interevent time for hourly rainfall stations in Texas
    4–1.4.   18-hour minimum interevent time for hourly rainfall stations in Texas
    4–1.5.   24-hour minimum interevent time for hourly rainfall stations in Texas
    4–1.6.   48-hour minimum interevent time for hourly rainfall stations in Texas
    4–1.7.   72-hour minimum interevent time for hourly rainfall stations in Texas
  4–2.1. — 4–2.7.  L-moments of storm depth defined by:
    4–2.1.   6-hour minimum interevent time for hourly rainfall stations in Texas
    4–2.2.   8-hour minimum interevent time for hourly rainfall stations in Texas
    4–2.3.   12-hour minimum interevent time for hourly rainfall stations in Texas
    4–2.4.   18-hour minimum interevent time for hourly rainfall stations in Texas
    4–2.5.   24-hour minimum interevent time for hourly rainfall stations in Texas
    4–2.6.   48-hour minimum interevent time for hourly rainfall stations in Texas
    4–2.7.   72-hour minimum interevent time for hourly rainfall stations in Texas
  4–3.1. — 4–3.7.  L-moments of storm duration defined by:
    4–3.1.   6-hour minimum interevent time for hourly rainfall stations in Texas
    4–3.2.   8-hour minimum interevent time for hourly rainfall stations in Texas
    4–3.3.   12-hour minimum interevent time for hourly rainfall stations in Texas
    4–3.4.   18-hour minimum interevent time for hourly rainfall stations in Texas
    4–3.5.   24-hour minimum interevent time for hourly rainfall stations in Texas
    4–3.6.   48-hour minimum interevent time for hourly rainfall stations in Texas
    4–3.7.   72-hour minimum interevent time for hourly rainfall stations in Texas
  4–4.1. — 4–4.7.  Empirical distribution of storm depth defined by:
    4–4.1.   6-hour minimum interevent time for hourly rainfall stations in Texas
    4–4.2.   8-hour minimum interevent time for hourly rainfall stations in Texas
    4–4.3.   12-hour minimum interevent time for hourly rainfall stations in Texas
    4–4.4.   18-hour minimum interevent time for hourly rainfall stations in Texas
    4–4.5.   24-hour minimum interevent time for hourly rainfall stations in Texas
    4–4.6.   48-hour minimum interevent time for hourly rainfall stations in Texas
    4–4.7.   72-hour minimum interevent time for hourly rainfall stations in Texas
  4–5.1. — 4–5.7.  Empirical distribution of storm duration defined by:
    4–5.1.   6-hour minimum interevent time for hourly rainfall stations in Texas
    4–5.2.   8-hour minimum interevent time for hourly rainfall stations in Texas
    4–5.3.   12-hour minimum interevent time for hourly rainfall stations in Texas
    4–5.4.   18-hour minimum interevent time for hourly rainfall stations in Texas
    4–5.5.   24-hour minimum interevent time for hourly rainfall stations in Texas
    4–5.6.   48-hour minimum interevent time for hourly rainfall stations in Texas
    4–5.7.   72-hour minimum interevent time for hourly rainfall stations in Texas

Glossary

Figures

1–3.   Maps showing locations of National Weather Service hourly rainfall stations in:
  1.   Eastern New Mexico
  2.   Oklahoma
  3A.   Western Texas
  3B.   Northeastern Texas
  3C.   Southeastern Texas
4.   Graphs showing empirical distributions of (A) storm depth and (B) storm duration for 3,331 storm events defined by an 8-hour minimum interevent time for station 0016 Abilene Regional Airport, Texas
5.   L-moment diagram at two scales (A and B) showing relation between L-skew and L-kurtosis of the distributions of storm depth and storm duration defined by the 8-hour minimum interevent time and theoretical relations for selected probability distributions
6–9.   Graphs showing:
  6.   Dimensionless kappa distribution frequency curves for (A) storm depth and (B) storm duration for the selected minimum interevent times in Texas
  7.   Dimensionless kappa distribution frequency curves for storm depth and storm duration for 24-hour minimum interevent time for eastern New Mexico, Oklahoma, and Texas
  8.   Dimensionless exponential gamma and kappa distributions of storm depth for 24-hour minimum interevent time in Texas, graphed with (A) a linear y-axis scale and (B) a base-10 log y-axis scale
  9.   Storm depth and storm duration for 3,331 storm events defined by an 8-hour minimum interevent time for station 0016 Abilene Regional Airport, Texas
10–16.   Maps showing mean storm interevent time defined by:
  10.   6-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  11.   8-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  12.   12-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  13.   18-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  14.   24-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  15.   48-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  16.   72-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
17–23.   Maps showing mean storm depth defined by:
  17.   6-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  18.   8-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  19.   12-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  20.   18-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  21.   24-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  22.   48-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  23.   72-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
24–30.   Maps showing mean storm duration defined by:
  24.   6-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  25.   8-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  26.   12-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  27.   18-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  28.   24-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  29.   48-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas
  30.   72-hour minimum interevent time in eastern New Mexico, Oklahoma, and Texas

Tables

1–3.   National Weather Service hourly rainfall stations in:
  1.   Eastern New Mexico
  2.   Oklahoma
  3.   Texas
4.   Selected storm statistics for station 4570 Jayton, Texas, illustrating influence of minimum interevent time on statistics
5–6.   Regionwide or statewide record-length, weighted-average:
  5.   Storm depth L-moments
  6.   Mean storm interevent time and storm duration L-moments
7–8.   Dimensionless gamma and kappa distributions fit to record-length, weighted-average:
  7.   Storm depth L-moments
  8.   Storm duration L-moments
9–11.   Summary statistics and diagnostic statistics of mean:
  9.   Storm interevent time maps for each minimum interevent time
  10.   Storm depth maps for each minimum interevent time
  11.   Storm duration maps for each minimum interevent time
12–20.   Mean storm:
  12.   Interevent time by county for eastern New Mexico
  13.   Depth by county for eastern New Mexico
  14.   Duration by county for eastern New Mexico
  15.   Interevent time by county for Oklahoma
  16.   Depth by county for Oklahoma
  17.   Duration by county for Oklahoma
  18.   Interevent time by county for Texas
  19.   Depth by county for Texas
  20.   Storm duration by county for Texas
21.   Example simulations of storm interevent time from example 2 using 24-hour minimum interevent time for station 0211 Amarillo Weather Service Office Airport, Texas
22.   Distribution of storm depth for examples 3 and 4 based on site-specific statistics for station 4311 Houston Alief, Texas
23.   Regional values for selected storm depth percentiles in Randall County, Texas

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