: 

National Climatic Data Center 

DATA DOCUMENTATION 

FOR 

DATA SET 9712D (DSI-9712D) 

Air-Freezing Index Statistics for the United States 

December 26, 2002 

National Climatic Data Center 

151 Patton Ave. 

Asheville, NC 28801-5001 USA 
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Table of Contents 

Topic Page Number

1. Abstract................................................... 3 

2. Element Names and Definitions: ............................ 5 

3. Start Date................................................. 8 

4. Stop Date.................................................. 8 

5. Coverage................................................... 8 

6. How to order data.......................................... 8 

7. Archiving Data Center. .................................... 8 

8. Technical Contact.......................................... 8 

9. Known Uncorrected Problems................................. 8 

10. Quality Statement.......................................... 9 

11. Essential Companion Data Sets.............................. 9 

12. References................................................. 9 
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1. Abstract: A climatography of the Air-freezing Index (AFI) has been 

developed for 3,110 stations in the United States and is presented here as a 

digital data set. The AFI is a measure of the combined magnitude and duration 

of air temperatures above and below freezing during any given winter season. 

The AFI, the thermal properties of the soil, and the surface soil cover are 

the major parameters used to determine the ground freezing potential of a 

given climate. 

Data Set Overview: 

This data set consists of two statistics stored as separate records within 

this data-set file. The first statistic represents the computation of 29 

seasonal AFI totals for each winter season that occurred during the 1951-1980 

period. These winter season AFI totals were computed separately for each 

climate station. The second statistic represents an estimate of various 

return periods of the AFI for each station using the 29 seasonal totals for 

that station as input. The return periods included in this data set are 1.1-

years, 1.25 years, 2-years, 2.5-years, 3.3-years, 5-years, 10-years, 20-years, 

25-years, 50-years, and 100-years. A return period is defined as a measure of 

the average amount of time between which an event of a given magnitude will be 

equaled or exceeded (Gumbel, 1958). Thus, a 100-year return period of the AFI, 

as an example, would be equaled or exceeded once every 100 years on average. 

Work by Steurer (1985, 1989) used serially complete daily maximum and minimum 

temperature data from 1951-1980 to generate the 29 seasonal totals of the AFI 

for 3,110 stations in the United States. A detailed description of the 

computation procedures used to generate the AFI is presented by Steurer and 

Crandell (1995) along with a graph that depicts a sinusoidal cumulative AFI 

curve for a typical mid-latitude station. See References. 

Generally, the daily AFI is defined as the departure of the daily mean 

temperature above or below 32 degrees Fahrenheit. The daily AFI departures 

are then summed each day throughout the freezing season and plotted as a 

cumulative AFI total. A freezing season is defined as beginning on August 1 

and ending on July 31 of the next year. Starting at zero, the daily AFI 

cumulative curve for a typical mid-latitude station would become positive and 

turn upward at the beginning of the freezing season when the daily average 

temperature was above freezing, then become negative and turn downward as 

daily average temperatures consistently dropped below 32 degrees Fahrenheit in 

the Winter, and then turn upward again in the Spring or Summer when daily mean 

temperature consistently was above freezing. The AFI for a winter season is 

defined as the difference between the highest and lowest inflection points on 

this cumulative time curve of daily AFI departures. However, for sites that 

do not exhibit a typical four-season climate such as in the Southern United 

States, there may not be a well-defined cumulative AFI time curve. Instead 

there may be several maxima and minima that correspond to cold outbreaks that 

occur throughout the winter months. Since each cold outbreak is essentially a 

separate event for these warmer climate stations, only the difference between 

the maximum and its corresponding minimum of the largest cold outbreak event 

is assigned the seasonal AFI total. 

Data Applications

When the temperature remains below freezing for a period of time, ice lenses 

can form in the soil that result in frost heave and possible damage to 

overlying structures (Jones et al., 1982). Structural damages caused by frost 

action in soils are most notable in the pavement of highways and airfields, in 
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hydraulic structures such as dams and canals, and in residential and 

commercial buildings. An important application of the AFI is the estimation 

of the effect of freezing conditions upon the soil foundations of structures. 

In non-permafrost environments, a conventional method of controlling frost 

action in soils is to locate a structural foundation below the depth of frost 

penetration. The depth of frost penetration has empirically been determined 

by using the AFI in conjunction with the soil type and surface soil cover 

(Linell and Lobacz, 1980). 

A frost-protected shallow foundation (FPSF) is another method used to protect 

structural foundations from frost heave (Farouki 1992; Morris 1988). FPSF 

incorporates the strategic placement of insulation to raise the frost depth 

around a building, thereby allowing foundations as shallow as 0.4 meters (16 

inches), even in the most severe climates. The amount of insulation required 

to protect a foundation has been found to be a function of the AFI ("Frost" 

1993). Cost savings to the buyer of new homes using FPSF have been estimated 

to range from 1 to 4 percent over the cost of conventional slab-on-grade 

construction or an annual savings of $300 million nationally. Additional 

long-term savings are expected from increased energy efficiency ("Frost” 

1994). 

Description of the AFI Return Period Estimates 

Various statistics can be used to represent the AFI. The ones more commonly 

used in the United States are the mean, the design value (Jones et al., 1982), 

and the 100-year return period (Steurer, 1989). The mean is a measure of 

average conditions and is simply the average of the seasonal AFI totals for 

ten or more winter seasons. Jones et al. (1982) indicate that the mean index 

is used primarily in the construction phase of temporary structures. For more 

permanent structures, the design AFI can be used. Here, the seasonal totals 

for the three coldest winters in a 30-year period are averaged. To provide an 

index that reflects conditions during the coldest winter seasons, work by 

Steurer (1989) resulted in the development of an estimate of the 100-year 

return period of the AFI using the Weibull probability distribution. 

A total of 29 seasonal totals of the AFI was computed at each climate station 

and used to compute an estimate of the 100-year return period for that 

station. These statistics were produced for 3,110 stations in the United 

States based upon the period 1951-1980. A return period is defined as a 

measure of the average amount of time between which an event of a given 

magnitude will be equaled or exceeded (Gumbel, 1958). A return period is 

described by the equation 1/p where p is the probability of the event 

occurring over a specified period of time. Using this equation, a 2-year 

return period of the AFI would occur on average in 50% of the years (1/.5), 

while a 100-year return period would occur on average in only 1% of the 

years (1/.01). A common misuse of return periods is to expect, as an example, 

the 100-year return period to occur exactly every 100 years. It is quite 

possible to equal or exceed the 100-year return period of the AFI in two 

successive years or not reach it in more than 500 years. But when the average 

is considered, the length of time between events will be 100 years for a valid 

100-year return period estimate (Linsley et al., 1949). 

Different methods have been used to obtain an estimate of the AFI for other 

locations around the world. Different AFI computation procedures have been 

performed for locations in Norway (Heiersted, 1976) and Finland (Anderson, 

personal communication, 1993). Work by Steurer and Crandell (1995) 

investigated the differences among the USA method, which used return periods, 
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and Norway, and Finland methods. They found that the USA method was more 

representative of the freezing effect for all U.S. climate regimes. This was 

in terms of calculating an unbiased AFI that considered all freezing and 

thawing events during the winter regardless of their duration or time of 

occurrence. As a result of this work, U.S. building codes as regulated by the 

1995 Edition of the Council of Building Officials (CABO) One and Two-Family 

Dwelling Code were changed to accept FPSF as a mechanism to offset increased 

construction costs and provide more energy-efficient housing (Crandell, 

personal communication, 1994). 

However, Steurer and Crandell (1995) pointed out that there were potential 

shortcomings in fitting one probability distribution to every possible climate 

regime, especially when the sample size was relatively small (Kite, 1977). 

To address the problem of a small sample size, a longer-term data set was used 

in another study performed by Steurer (1996) that contained temperature data 

for 1901-1987. This 138-station network of U.S. observing sites is considered 

by some climate researchers to be a high quality and long-term temperature 

data sets in terms of temporal homogeneity and spatial coverage (Hughes et al, 

1992). A total of 25 of the 138 available stations were selected for this 

study. The stations that were chosen had few missing data and also maintained 

the same observation time throughout the 1901-1987 period. This resulted in a 

sample size of 86 winter seasons or data points for each station. This latter 

work revealed that the Weibull probability distribution was still determined 

as the best choice for use in estimating the 100-year return period of the AFI 

for all U.S. climate regimes. 

2. Element Names and Definitions: 

The data are archived in a fixed length ASCII format. The total data volume 

is about 1 megabyte. The data are sorted by station using the station number 

as the primary key followed by statistic identifier number. 

Each record is of fixed length and composed of 156 characters. The record 

format is: 

Element Name Width Position 

Station Number 6 001-006 

Statistic Identifier 2 007-008 

If Statistic Identifier in positions 007-008 = 01 then the following record 

layout is used: 

 1951-1952 Winter Season AFI 5 009-013 

 1952-1953 “ 5 014-018 

 1953-1954 “ 5 019-023 

 1954-1955 “ 5 024-028 

 1955-1956 “ 5 029-033 

 1956-1957 “ 5 034-038 

 1957-1958 “ 5 039-043 

 1958-1959 “ 5 044-048 

 1959-1960 “ 5 049-053 

 1960-1961 “ 5 054-058 

 1961-1962 “ 5 059–063 

 1962-1963 “ 5 064-068 

 1963-1964 “ 5 069-073 

 1964-1965 “ 5 074-078 
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 1965-1966 “ 5 079-083 

 1966-1967 “ 5 084-088 

 1967-1968 “ 5 089-093 

 1968-1969 “ 5 094-098 

 1969-1970 “ 5 099-103 

 1970-1971 “ 5 104-108 

 1971-1972 “ 5 109-113 

 1972-1973 “ 5 114-118 

 1973-1974 “ 5 119-123 

 1974-1975 “ 5 124-128 

 1975-1976 “ 5 129-133 

 1976-1977 “ 5 134-138 

 1977-1978 “ 5 139-143 

 1978-1979 “ 5 144-148 

 1979-1980 “ 5 149-153 

 Not used 3 154-156 

If Statistic Identifier in positions 007-008 = 02 then the following record 

layout is used: 

 Station Name 30 010-039 

 Latitude 5 041-045 

 Longitude 6 047-052 

 Elevation 4 054-057 

 Annual Mean Temperature 6 059-064 

 AFI 1.1-year return period 8 066-073 

 AFI 1.25-year return period 8 074-081 

 AFI 2-year return period 8 082-089 

 AFI 2.5-year return period 8 090-097 

 AFI 3.3-year return period 8 098-105 

 AFI 5-year return period 8 106-113 

 AFI 10-year return period 8 114-121 

 AFI 20-year return period 8 122-129 

 AFI 25-year return period 8 130-137 

 AFI 50-year return period 8 138-145 

 AFI 100-year return period 8 146-153 

 Not used 3 154-156 

Station Number is an integer variable that refers to the Cooperative station 

number for this station. Range of values is 010252-666073 

Statistic Identifier is an integer variable that defines the type of record 

that follows. Range of values is 01 and 02. 

If Statistic Identifier = 01 then the following element names are used: 

 1951-1952 Winter Season AFI is an integer variable that defines the AirFreezing Index that was compute for the 1951-1952 winter season. Range 

of values is 0 through 99999. Units are whole degrees Fahrenheit-Days. 

 1952-1953 Winter Season AFI through 1979-1980 Winter Season AFI are 

described above under 1951-1952 Winter Season AFI

If Statistic Identifier = 02 then the following element names are used: 

Station Name is a 30-character alphanumeric variable that defines the 

station name assigned as part of the Cooperative Observer Network 
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Latitude is a 5-character alphanumeric variable that defines the 

latitude of the station. The format is N9988 where N indicates North 

latitude, 99 indicates degrees and 88 indicates minutes. All stations 

are North Latitude in this data set. 

 Longitude is a 6-character alphanumeric variable that defines the 

longitude of the station. The format is W99988 where W indicates West 

longitude, 999 indicates degrees, and 88 indicates minutes. All stations 

are West Longitude in this data set. 

Elevation is a 4-character integer variable that defines the elevation 

of the station in whole feet. The range of values is -194 to 9332 feet 

 Annual Mean Temperature is a real variable which represents the 1951-

1980 normal of the annual mean temperature. Units are tenths of a 

degree Fahrenheit. Range of values is 9.0 to 76.7 degrees Fahrenheit. 

 AFI 1.1-year return period is an integer variable that defines the Air 

Freezing Index (AFI) at the1.1-year return period. A return period is 

described by the equation 1/p where p is the probability of the event 

occurring over a specified period of time. Using this equation, a 

1.1-year return period of the AFI would occur on average in 90% of the 

years (1/.9). The range of values is -9999, -8888, and 0 through 99999. 

 Units are whole degree Fahrenheit-Days. A value of -9999 indicates 

that the probability of occurrence of this return period is less than 

the return period probability, or in other words, the average daily 

temperature did not fall below 32 degrees Fahrenheit in every winter 

season during the 1951-1980 period. A value of -8888 indicates no 

freezing index values were recorded at base 32 degrees Fahrenheit during 

the 1951-1980 period or, in other words, the average daily temperature 

never fell below 32 degrees Fahrenheit during the entire1951-1980 

period. Refer to Topic 22 below for the further descriptions of the 

Air-Freezing Index and return periods. 

 AFI 1.25-year return period is described above under the AFI 1.1-year 

return period. A 1.25-year return period would occur on average in 80% 

of the years (1/.8) 

 AFI 2-year return period is described above under the AFI 1.1-year 

return period. A 2-year return period would occur on average in 50% of 

the years (1/.5) 

 AFI 2.5-year return period is described above under the AFI 1.1-year 

return period. A 2.5-year return period would occur on average in 40% 

of the years (1/.4) 

AFI 3.3-year return period is described above under the AFI 1.1-year 

return period. A 3.3-year return period would occur on average in 30% 

of the years (1/.3) 

 AFI 5-year return period is described above under the AFI 1.1-year 

return period. A 5-year return period would occur on average in 20% of 

the years (1/.2) 

 AFI 10-year return period is described above under the AFI 1.1-year 
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return period. A 10-year return period would occur on average in 10% of 

the years (1/.1) 

 AFI 20-year return period is described above under the AFI 1.1-year 

return period. A 20-year return period would occur on average in 5% of 

the years (1/.05) 

 AFI 25-year return period is described above under the AFI 1.1-year return 

period. A 25-year return period would occur on average in 4% of the years 

(1/.04) 

 AFI 50-year return period is described above under the AFI 1.1-year return 

period. A 50-year return period would occur on average in 2% of the years 

(1/.02) 

 AFI 100-year return period is described above under the AFI 1.1-year 

return period. A 100-year return period would occur on average in 1% of 

the years (1/.01) 

3. Start Date: This data set represents a group of summary statistics. The 

beginning period of record used in generating these statistics was 19510101. 

4. Stop Date: The ending period of record used in generating these statistics 

was 19801231. 

5. Coverage: Continental United States, Alaska, Hawaii, and Puerto Rico. 

a. Southernmost Latitude: 18 Degrees 03 Minutes N. 

b. Northernmost Latitude: 71 Degrees 18 Minutes N. 

c. Westernmost Longitude: 176 Degrees 39 Minutes W. 

d. Easternmost Longitude: 65 Degrees 39 Minutes W.

6. How to Order Data: 

 Ask NCDC’s Climate Services about the cost of obtaining this data set. 

 Phone: 828-271-4800 

 FAX: 828-271-4876 

 E-mail: NCDC.Orders@noaa.gov

7. Archiving Data Center: 

 National Climatic Data Center 

 Federal Building 

 151 Patton Avenue 

 Asheville, NC 28801-5001 

 Phone: (828) 271-4800. 

8. Technical Contact: 

 National Climatic Data Center 

 Federal Building 

 151 Patton Avenue 

 Asheville, NC 28801-5001 

 Phone: (828) 271-4800. 
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9. Known Uncorrected Problems: There are no known uncorrected problems in this 

data set. 

10. Quality Statement: Extensive validation and interpolation procedures were 

performed on the daily maximum and minimum temperatures used to derive the Air 

Freezing Indexes at each station. The resulting indexes where visually 

checked based upon a map analysis. 

11. Essential Companion Datasets: There are no additional data sets required 

in order to use this data set. 

12. References:

Farouki, O. (1992). European foundation designs for seasonally frozen ground. 

Monograph 92-1, U.S. Army Corps of Engrs., Cold Regions Res. & Engrg. Lab., 

Hanover, N.H. 

Frost protected shallow foundations in Residential Construction, 1993. Phase 

I Report Prepared for the U.S. Department of Housing and Urban Development, 

NAHB Res. Ctr., Upper Marlboro, Md. 

Frost protected shallow foundations in Residential Construction, 1994. Phase 

II Final Report Prepared for the U.S. Department of Housing and Urban 

Development, NAHB Res. Ctr., Upper Marlboro, Md. 

Gumbel, E.J. (1958). Statistics of Extremes. Columbia University Press, New 

York, New York, 375 pp. 

Heiersted, R.S. (1976). Frost I Jord (Frost Action in Ground). Committee on 

Frost Action in Soils, Royal Norwegian Council for Scientific and Industrial 

Res., Nr. 17, Oslo, Norway (in Norwegian). 

Hughes, P.Y., E.H. Mason, T.R. Karl, and W.A. Brower (1992). United States 

Historical Climatology Network daily temperature and precipitation data. 

ORNL/CDIAC, NDP-042. Carbon Dioxide Information Analysis Ctr., Oak Ridge Nat. 

Lab., Oak Ridge, TN. 140 pp. 

Jones, C.W., D.G. Miedema, and J.S. Watkins (1982). Frost action in soil 

foundations and control of surface structure heaving. Report No. 

REC-ERC-82-17, Bureau of Reclamation, Denver, Colo., 69 pp. 

Kite, G.W. (1977). Frequency and risk analysis in hydrology. Water Resources 

Publications, Fort Collins, Colo., 224pp. 

Linnel, K.A. and E.F. Lobacz (1980). Design and construction of foundations in 

areas of deep seasonal frost and permafrost. Special Report 80-34, U.S. Army 

Corps of Engrs., Cold Regions Res. & Engrg. Lab., Hanover, N.H. 

Linsley, R.K., M. Kohler, and J.L.H. Paulus (1949). Applied Hydrology. 

McGraw-Hill Book Co., New York, New York, 689 pp. 

Morris, R.A. (1988). Frost-protected shallow foundations: Current 

state-of-the-art and potential application in the U.S. Report prepared for 

the Society of the Plastics Industry, NAHB Res. Ctr., Upper Marlboro, Md. 

Steurer, P.M. (1985): Creation of a serially complete database of high 

quality daily maximum and minimum temperatures. Nat. Oc. and Atmospheric 
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Admin., Nat. Climatic Data Ctr., Asheville, N.C. 

Steurer, P.M. (1989). Methods used to create an estimate of the 100-year 

return period of the air-freezing index. Frost-protected shallow foundation 

development program-Phase II final report, Appendix A. Prepared for the 

Society of the Plastics Industry, NAHB Res. Ctr., Upper Marlboro, Md. 

Steurer, P.M. and J.H. Crandell (1995). Comparison of methods used to create 

an estimate of the air-freezing index. J. Cold Reg. Engrg., 9(2), 64-74. 

Steurer, P.M. (1996). Probability distributions used in the 100-year return 

period of the air-freezing index. J. Cold Reg. Engrg., 10(1), 25-35.