Historic, archived document

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Monthly

Precipitation

Probabilities

by Climatic

Divisions

23 Eastern States From the Great Lakes to the Golf Coast

Miscellaneous Publication No. 1 1 6

U.S. DEPARTMENT OF AGRICULTURE, Economic Research Service and Administration U.S. DEPARTMENT OF COMMERCE, Environmental Science Services

PREFACE

This publication provides basic long-term data on the variability and

dependability of an area's natural rainfall supply potential* In addition to

providing a better understanding of the precipitation phenomena of an area,

the data will also aid in the development of water resource management plans

for the area. For example, the need for supplemental irrigation can be de-

rived; adequacy of precipitation for municipal and industrial water supply can

be determined; and the design and management of reservoir storage for flood

control or low-flow augmentation can be estimated. These data will also be

used in research work in the evaluation of projects or operations in a given

area.

The research report was completed as a cooperative effort between the

U.S. Department of Commerce. Environmental Science Services Administration,

and the U.S. Department of Agriculture. Economic Research Service.

Acknowledgment is made to Grady McKay, ESSA National Weather Records Center,

Asheville, N. C, for the basic computer program used and to Priscilla Prophet,

Computer Laboratory, Michigan State University, for data processing and pro-

gramming assistance.

Washington, D. C. 20250 November 1969

H^H CONTENTS Page Summary ...... 1

Introduction 1

Data 3

Results and Interpretation 4

Selected References 7

State Map - Climatic Divisions - Alabama 8

Table 1. Comparison - Montgomery with Prairie Division 9

2. Precipitation Probability Values for Climatic Divisions. . . 10 Northern Valley - Appalachian Mountain

3. Precipitation Probability Values for Climatic Divisions. . . 11 Upper Plains - Eastern Valley

4. Precipitation Probability Values for Climatic Divisions. . . 12 Piedmont Plateau - Coastal Plain

5. Precipitation Probability Values for Climatic Divisions. . . 13 Gulf

State Map - Climatic Divisions - Arkansas 14

Table 6. Comparison - Little Rock with Central Division 15

7. Precipitation Probability Values for Climatic Divisions. . . 16 Northwest - North Central

8. Precipitation Probability Values for Climatic Divisions. . . 17 Northeast - West Central

9. Precipitation Probability Values for Climatic Divisions. . . 18 East Central - Southwest

10. Precipitation Probability Values for Climatic Divisions. . . 19 South Central - Southeast

State Map - Climatic Divisions - Florida 20

Table 11. Comparison - Lakeland with South Central 21

ii Table 12. Precipitation Probability Values for Climatic Divisions 22 Northwest - North

13. Precipitation Probability Values for Climatic Divisions 23 North Central - Everglades and SW Coast

14. Precipitation Probability Values for Climatic Divisions 24 Lower East Coast - Keys

- - State Map Climatic Divisions Georgia , 25

Table 15. Comparison - Atlanta with North Central, 26

16. Precipitation Probability Values for Climatic Divisions 27 Northwest - Northeast

17. Precipitation Probability Values for Climatic Divisions 28 West Central - Central

18. Precipitation Probability Values for Climatic Divisions 29 East Central - Southwest

19. Precipitation Probability Values for Climatic Divisions 30 South Central - Southeast

State Map - Climatic Divisions - Illinois 31

Table 20. Comparison - Peoria with Central Division, 32

21. Precipitation Probability Values for Climatic Divisions 33 Northwest - Northeast

22. Precipitation Probability Values for Climatic Divisions 34 West - East

23. Precipitation Probability Values for Climatic Divisions 35 West Southwest - Southwest

24. Precipitation Probability Values for Climatic Divisions 36 East Southeast - Southeast

State Map - Climatic Divisions - Indiana 37

Table 25. Comparison - Indianapolis with Central Division. 38

26. Precipitation Probability Values for Climatic Divisions 39 Northwest - North Central

27. Precipitation Probability Values for Climatic Divisions 40 Northeast - West Central

28. Precipitation Probability Values for Climatic Divisions 41 East Central - Southwest

iii Table 29. Precipitation Probability Values for Climatic Divisions South Central - Southeast

State Map - Climatic Divisions - Iowa

Table 30. Comparison - Des Moines with Central Division

31. Precipitation Probability Values for Climatic Divisions Northwest - North Central

32. Precipitation Probability Values for Climatic Divisions Northeast - West Central

33. Precipitation Probability Values for Climatic Divisions East Central - Southwest

34. Precipitation Probability Values for Climatic Divisions South Central - Southeast

State Map - Climatic Divisions - Kentucky

Table 35. Comparison - Lexington with Blue Grass Division

36. Precipitation Probability Values for Climatic Divisions Western - Central

37. Precipitation Probability Values for Climatic Divisions Eastern

State Map - Climatic Divisions - Louisiana

Table 38. Comparison - Baton Rouge with East Central Division,

39. Precipitation Probability Values for Climatic Divisions Northwest - North Central

40. Precipitation Probability Values for Climatic Divisions Northeast - West Central

41. Precipitation Probability Values for Climatic Divisions Central - Southwest

42. Precipitation Probability Values for Climatic Divisions South Central - Southeast

State Map - Climatic Divisions - Maryland

Table 43. Comparison - Baltimore with Upper Southern

44. Precipitation Probability Values for Climatic Divisions Southern Eastern Shore - Central Eastern Shore

iv Table 45. Precipitation Probability Values for Climatic Divisions 62 Lower Southern - Upper Southern

46. Precipitation Probability Values for Climatic Divisions 63 Northern Eastern Shore - Northern Central

47. Precipitation Probability Values for Climatic Divisions 64 Appalachian Mountain - Allegheny Plateau

- - State Map Climatic Divisions Michigan , 65

Table 48. Comparison - Lansing with South Central Lower Division 66

49. Precipitation Probability Values for Climatic Divisions 67 West Upper - East Upper

50. Precipitation Probability Values for Climatic Divisions 68 Northwest Lower - Northeast Lower

51. Precipitation Probability Values for Climatic Divisions 69 West Central Lower - Central Lower

52. Precipitation Probability Values for Climatic Divisions 70 East Central Lower - Southwest Lower

53. Precipitation Probability Values for Climatic Divisions 71 Southeast Lower

State Map - Climatic Divisions - Minnesota 72

Table 54. Comparison - St. Cloud with Central Division 73

55. Precipitation Probability Values for Climatic Divisions 74 Northwest - North Central

56. Precipitation Probability Values for Climatic Divisions 75 Northeast - West Central

57. Precipitation Probability Values for Climatic Divisions 76 East Central - Southwest

58. Precipitation Probability Values for Climatic Divisions 77 South Central - Southeast

State Map - Climatic Divisions - Mississippi 78

Table 59. Comparison - Meridian with Southeast Division, 79

60. Precipitation Probability Values for Climatic Divisions 80 Upper Delta - North Central

61. Precipitation Probability Values for Climatic Divisions 81 Northeast - Lower Delta Table 62. Precipitation Probability Values for Climatic Divisions Central - East Central

63. Precipitation Probability Values for Climatic Divisions Southwest - South Central

64. Precipitation Probability Values for Climatic Divisions Coastal

State Map - Climatic Divisions - Missouri

Table 65. Comparison - Springfield with West Ozarks Division

66. Precipitation Probability Values for Climatic Divisions Northwest Prairie - Northeast Prairie

67. Precipitation Probability Values for Climatic Divisions West Central Plains - East Ozarks

68. Precipitation Probability Values for Climatic Divisions Bootheel

State Map - Climatic Divisions - New York

Table 69. Comparison - Syracuse with Central Lakes Division,

70. Precipitation Probability Values for Climatic Divisions Western Plateau - Eastern Plateau

71. Precipitation Probability Values for Climatic Divisions Northern Plateau - Coastal

72. Precipitation Probability Values for Climatic Divisions Hudson Valley - Mohawk Valley

73. Precipitation Probability Values for Climatic Divisions Champlain Valley - St. Lawrence Valley

74. Precipitation Probability Values for Climatic Divisions Great Lakes

State Map - Climatic Divisions - North Carolina

Table 75. Comparison - Greensboro with Northern Piedmont Division

76. Precipitation Probability Values for Climatic Divisions Southern Mountains - Northern Mountains

77. Precipitation Probability Values for Climatic Divisions Central Piedmont - Southern Piedmont

78. Precipitation Probability Values for Climatic Divisions Southern Coastal Plain - Central Coastal Plain

vt Table 79. Precipitation Probability Values for Climatic Divisions. 102 Northern Coastal Plain

State Map - Climatic Divisions - Ohio 103

Table 80. Comparison - Columbus with Central Division, 104

81. Precipitation Probability Values for Climatic Divisions. 105 Northwest - North Central

82. Precipitation Probability Values for Climatic Divisions. 106 Northeast - West Central

83. Precipitation Probability Values for Climatic Divisions. 107 Central Hills - Northeast Hills

84. Precipitation Probability Values for Climatic Divisions. 108 Southwest - South Central

85. Precipitation Probability Values for Climatic Divisions. 109 Southeast

State Map - Climatic Divisions - Pennsylvania 110

Table 86. Comparison - Harrisburg with Lower Susquehanna Division. 111

87. Precipitation Probability Values for Climatic Divisions. 112 Pocono Mountains - East Central Mountains

88. Precipitation Probability Values for Climatic Divisions. 113 Southeastern Piedmont - Middle Susquehanna

89. Precipitation Probability Values for Climatic Divisions. 114 Upper Susquehanna - Central Mountains

90. Precipitation Probability Values for Climatic Divisions. 115 South Central Mountains - Southwest Plateau

91. Precipitation Probability Values for Climatic Divisions. 116 Northwest Plateau

State Map - Climatic Divisions - South Carolina 117

Table 92. Comparison - Columbia with Central Division, 118

93. Precipitation Probability Values for Climatic Divisions. 119 Mountain - Northwest

94. Precipitation Probability Values for Climatic Divisions. 120 North Central - Northeast

95. Precipitation Probability Values for Climatic Divisions. 121 West Central - Southern

vii State Map - Climatic Divisions - Tennessee 122

Table 96. Comparison - Nashville with Middle Division. 123

97. Precipitation Probability Values for Climatic Divisions 124 Eastern - Cumberland Plateau

98. Precipitation Probability Values for Climatic Divisions 125 Western

State Map Climatic Divisions - Virginia 126

Table 99. Comparison - Richmond with Eastern Piedmont Division . 127

100. Precipitation Probability Values for Climatic Divisions 128 Tidewater - Western Piedmont

101. Precipitation Probability Values for Climatic Divisions 129 Northern - Central Mountain

102. Precipitation Probability Values for Climatic Divisions 130 Southwestern Mountain

State Map - Climatic Divisions - West Virginia 131

Table 103. Comparison - Charleston with Southwestern Division 132

104. Precipitation Probability Values for Climatic Divisions 133 Northwestern - North Central

105. Precipitation Probability Values for Climatic Divisions 134 Central - Southern

106. Precipitation Probability Values for Climatic Divisions 135 Northeastern

- State Map Climatic Divisions - Wisconsin. . 136

Table 107. Comparison - Madison with South Central Division 137

108. Precipitation Probability Values for Climatic Divisions 138 Northwest - North Central

109. Precipitation Probability Values for Climatic Divisions 139 Northeast - West Central

110. Precipitation Probability Values for Climatic Divisions 140 Central - East Central

111. Precipitation Probability Values for Climatic Divisions 141 Southwest - Southeast

viii MONTHLY PRECIPITATION PROBABILITIES BY CLIMATIC DIVISIONS- -23 EASTERN STATES

FROM THE GREAT LAKES TO THE GULF COAST

by

Norton D. Strommen State Climatologist, Michigan Environmental Data Service, Environmental Science Services Administration

and

James E. Horsfield Agricultural Economist Natural Resource Economics Division, Economic Research Service

SUMMARY

This publication presents precipitation probability data by climatic divisions for 23 eastern States. The explanation of the development and application of the data use Maryland as an example. Data for other States can be interpreted in a similar manner.

INTRODUCTION

Through statistical analysis of past weather records, the future weather for an area can be projected. Today, with greater emphasis on area develop- ment potential and efficient use of our natural resources, many planners, researchers, and engineers seek more detailed climatological information.

Precipitation probabilities interest these people, especially information on the variability and the dependability of the amount that can be expected.

Precipitation probabilities derived from historical data can aid understanding of these aspects of precipitation and serve as basic data for the evaluation of an area's natural water supply potential. Precipitation probabilities can

-1- also be used to show the differences between mean precipitation and amount which can be expected to occur half the time—information that is useful for research on irrigation planning and other water resource problems. In consid- ering simple statistical frequency distribution curves, the arithmetic mean is one of the variables used to determine the normal distribution. In the normal distribution, the vertical line of symmetry occurs at the mean of the distri- bution, and is also the median and the mode value. The normal distribution provides a good fit for most climatological variables that are unbounded above and below, such as temperature. Precipitation is bounded at the lower end by zero. Appropriately, some distribution other than the normal distribution should be expected to provide the best fit for precipitation data.

This publication presents precipitation probability values derived by using the gamma probability function where the frequency distribution present- ed by Thorn (1) 1/ for the random variable x is given by -x/3 m-1 f(x) = ^— 2 m 6 T(m) where x = precipitation amount

m

m gamma parameter as found from the equation:

2 12 (In x - I Z In x) m -6m-l = N

x ~*x in- 1 r(m) = gamma function, /ex dx, <_ x <_<», m>0

1/ Underscored numbers in parentheses refer to items in the Selected References, p. 7.

-2- It does not present the details of the development and application of this

method. The user is instead referred to articles by Thorn (l f 2, 4, and 6);

Friedman and Janes (3); and Barger, Shaw, and Dale (5), all of whom have shown that the gamma probability function gives a good fit for precipitation in a climatological data series. Utilizing this method, monthly precipitation probability values for each climatic division for 23 States have been calcu- lated as have monthly probabilities for at least one major weather station in each of these States.

DATA

The precipitation data for the climatic divisions were compiled at the

National Weather Records Center at Asheville, N.C., and were published in summary form in Climatography of the United States No. 85-* 2/ in 1963 and the State Monthly Climatological Data series. These data consist of the arithmetic averages of monthly precipitation data from the cooperative clima- tological stations within each climatic division for the period 1931-65. The boundaries of climatic divisions have been carefully drawn to give a division as much uniformity in its observed climate as possible. To illustrate how point and area values compare, the precipitation probability totals or values for a single station (point) within one of the climatic divisions of each

State have been provided for comparative purposes with the division data. For

Maryland, Baltimore, located in the Upper Southern Climatic Division, was used

(p. 60). The good agreement between the station and the climatic division averages suggest that in most cases, the division probabilities adequately represent the expected precipitation amounts. In mountainous areas where very substantial terrain changes occur, local climatic differences are substantial

If The asterisk represents the special number assigned to each State,

-3- and Che point versus division data will exhibit larger departures, particular- ly in the relatively low and relatively high probability categories. Because of these large climatic changes in short distances in the mountains, extreme care must be used in the application or interpretation of these data. Also, points in the fringe area of the larger climatic divisions might also exhibit somewhat larger departures from the division data. A third factor which could cause some difference is the distribution of the climatological stations with- in the division. This factor may have produced a greater bias in earlier years when stations tended to be clustered in the urban areas. The effect of this is now minimized by the systematic location of climatological stations on a grid of points, with a single station designed to represent an area of approximately 600 square miles.

The precipitation data for the individual stations used in this study were taken from annual summaries for each station and, in general, cover the period 1931-67.

RESULTS AND INTERPRETATION

The calculated probability values or totals are presented in tables, by months. Included in the tables are the monthly mean precipitation amounts and the two parameters, gamma and beta of the gamma probability function, which describe the incomplete gamma function. As an example, in table 44, the

Southern Eastern Shore Climatic Division of Maryland (p. 61), we find under the 30-percentile column (shown in the table as 0.30), and across from January,

2.71. This indicates that in 3 years out of 10, the January precipitation total is expected to be equal to or less than 2.71 inches, or alternatively, that in 7 years out of 10, the January precipitation total is expected to exceed 2.71 inches. At the 70-percentile level for January, we find 4.27, indicating that in 7 years out of 10, the precipitation total is expected to

-4- -

be equal to or less than 4.27 Inches or that In 3 years out of 10, it is ex- pected to be greater than 4.27 inches.

In using the gamma probability function, two parameters must be estimated.

The shape parameter, gamma, is inversely related to the skevness. That is, a smaller gamma indicates that a few large values cause positive skewness and that the mean departs further from the median value. A large gamma causes the probability function to approach normality. Beta, the scale parameter, indi- cates range or dispersion with a larger beta indicating a greater tendency to deviate from either the mean or the median.

These characteristics can be illustrated with data from Maryland's Lower

Southern Climatic Division (p. 62). For example, in January, we find the 50- percentile value is 3.24 inches while in August, it is 4.32 inches. In general, this indicates that larger precipitation amounts can be expected in August than in January. By comparing the differences in the expected precipitation amounts for the high and low probabilities for these 2 months, we can assess the de- pendability of the precipitation. In January, the range between the 5-percent ile precipitation amount and the 95-percentile amount is 5.33 inches. In

August, the range between the same probabilties is 8.99 inches. Thus, while a larger amount of precipitation can generally be expected in August, relative to January, the August precipitation amounts over a period of years will show greater variation.

This type of information can be extremely valuable in planning for munic- ipal or industrial water supplies or irrigation needs. It indicates both the distribution of the potential supply over the year and the probability that facilities will be necessary for the storage or release of water from month to month. It also emphasizes the inadequacies inherent in using the simple average of area precipitation for planning. In the cases computed for this

-5- study, the 50-percentile value is less than the arithmetic average which has generally been used. This occurs because precipitation totals are bounded by zero on one end of the scale but are unlimited on the other end. Thus, the occurrence of large monthly totals in a series tends to push the monthly aver- age amount above the amount that can be expected one-half of the time; that is, the 50-percentile value.

The mean value, however, has some advantages as it is easily computed, the sum of a number of events divided by the number of events. The mean may be combined directly with further accumulated means, for example, the monthly means can be combined to give the annual mean. The mean is also estimated from sample data as efficiently as any other statistic in a given distribution.

-6- SELECTED REFERENCES

1. Thorn, H.C.S., "A Note on the Gamma Distribution," Statistical Laboratory, Iowa State College, 1947 (Manuscript).

2. Thorn, H.C.S., "A Frequency Distribution for Precipitation,* 1 Abstract in

Bulletin American Meteorological Society , Vol. 32, No. 10, Dec. 1951.

3. Friedman, D.G. and Janes, B.E., "Estimation of Rainfall Probabilities," University of Connecticut, Agricultural Experiment Station Bulletin 332. 22 pp., 1957.

4. Thorn, H.C.S., "A Note on the Gamma Distribution," Monthly Weather Review , Vol. 86, No. 4, Apr. 1958, pp. 117-122.

5. Barger, G.L., Shaw, R.H. , and Dale, R.F., "Gamma Distribution Parameters from 2 and 3-week Precipitation Totals in the North Central Region of the United States," Agricultural and Home Economics Experiment Station, Iowa State University, 183 pp., 1959.

6. Thorn, H.C.S., "Direct and Inverse Tables of the Gamma Distribution," Tech .

Report No . 2, Environmental Data Service, ESSA. Apr. 1968. pp. 1-30. -8- i 1 <

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