Global Annual Freezing and Thawing Indices

This data set consists of global, annual freezing and thawing indices calculated from monthly mean air temperatures compiled by Legates and Willmott (1990). The data have been interpolated to a 0.5° latitude by 0.5° longitude lattice.

Table of Contents

  1. Contacts and Acknowledgments
  2. Data Access
  3. Detailed Data Description
  4. References and Related Publications
  5. Document Information

Citing These Data

As a condition of using these data, you must cite the use of this data set using the following citation. For more information, see our Use and Copyright Web page.

Zhang, T. 1998. Global Annual Freezing and Thawing Indices, [indicate subset used]. Boulder, Colorado USA: NASA DAAC at the National Snow and Ice Data Center.



Ground-based Observations



Spatial Coverage


Spatial Resolution


Temporal Coverage


Temporal Resolution



  • Freezing Index
  • Thawing Index

Data Format

ASCII Binary

Metadata Access

View Metadata Record

Data Access


1. Contacts and Acknowledgments

Investigator(s) Name and Title

Principal Investigator

Tingjun Zhang
University of Colorado
National Snow and Ice Data Center

Technical Contact

NSIDC User Services
National Snow and Ice Data Center
University of Colorado
Boulder, CO 80309-0449  USA
phone: +1 303.492.6199
fax: +1 303.492.2468
form: Contact NSIDC User Services

2. Data Access

Data are available via FTP.

3. Detailed Data Description

In permafrost regions, annual freezing and thawing indices have been used to predict permafrost distribution and active layer extent, providing researchers with important information on climate variability as well as offering engineers information specific to cold region structural design. These indices can also be used in more temperate, permafrost-free regions to classify snow-type, estimate depth of ground-frost penetration, and predict the maximum thickness of sea, river and lake ice.

The freezing and thawing indices are defined as the cumulative number of degree-days below and above 0 degrees Celsius for a given time period (Permafrost Subcommittee 1988). Generally, four main types of freezing and thawing indices have been used: (i) approximate freezing and thawing indices; (ii) total annual freezing and thawing indices; (iii) seasonal freezing and thawing indices; and (iv) design freezing and thawing indices.

Global annual freezing and thawing indices were calculated at NSIDC from air temperature data compiled by Legates and Willmott (1990).

Strictly speaking, the indices should be called the 'Global Approximate Annual Freezing and Thawing Indices'. The global annual freezing and thawing indices measure the magnitude of air temperatures below (e.g. Northern Hemisphere late fall, winter and early spring) and above (e.g. Northern Hemisphere late spring, summer and early fall) 0 degrees Celsius over the course of one year. Most of the global mean monthly air temperatures were compiled between 1920 and 1980 over the terrestrial surface and between 1950 and 1979 over the oceanic surface (Legates and Willmott 1990). The global annual freezing and thawing indices are generally representative of the freezing and thawing climatology during that period.

The source data compiled by Willmott and Legates is a global climatology of mean monthly surface air temperatures. Terrestrial station records and oceanic grid-point records were interpolated to a 0.5 degree latitude by 0.5 degree longitude lattice using a spherically-based interpolation algorithm (Willmott and Legates 1990).

Willmott and Legates' data were acquired from various sources including Wernstedt 1972, Willmott et al. 1981, the National Center for Atmospheric Research (Spangler and Jenne 1984), the Commonwealth Scientific and Industrial Research Organization (CSIRO 1962-1971), the Australian Department of National Development (ADND 1965), and individual research stations in Antarctica (van Rooy 1957; Schwerdtfeger 1984), China and the Far East (Nuttonson 1947; Terjung et al. 1985). Oceanic surface air temperature data were obtained from the Comprehensive Ocean-Atmospheric Data Set for the period 1950-1979 (Fletcher et al. 1983; Slutz et al. 1985; Woodruff 1985; Woodruff et al. 1987).

Potential errors in the freezing and thawing indices may include error from relocation of individual stations, exposure of instruments to the elements, human error in instrument readings, and instrument malfunction due to relocation. In addition errors may have resulted from the compilation of the station air temperatures into the 0.5 by 0.5 grids. A detailed discussion of these errors can be found in Legates and Willmott (1990). Errors may also result from using monthly mean air temperature to calculate the annual freezing and thawing indices without making corrections for positive (above 0 degree Celsius) and negative (below 0 degree Celsius) degree-days in spring and fall, respectively. In the high Arctic, errors in calculating the annual freezing and thawing indices using both monthly mean and daily mean air temperatures are generally less than five percent (Zhang et al. 1996). However, in temperate regions, the errors can potentially become larger.


Gridded data are available in *either* ASCII or binary format. The ASCII files are flat arrays (720 columns by 360 rows) consisting of a maximum of five characters (i.e. tens of thousands) to the left of the decimal place and two to the right (i.e. hundredths). Each ASCII entry is separated by a space. The binary data files are flat arrays (720 columns by 360 rows) of 4-byte floating point values.

The resolution of the data is 0.5 degrees latitude by 0.5 degrees longitude with the first grid cell located at 90 degrees North latitude, 180 degrees West longitude. The freeze_a.dat ASCII files (or freeze.dat binary files) contain the annual freezing index for each 0.5 by 0.5 grid cell, while the thaw_a.dat (and thaw.dat) files contain the annual thaw index. Each uncompressed file contains approximately one megabyte of data. Below is a short program to read the data using FORTRAN77:

	parameter (COL = 720, ROW = 360)
	OPEN(40, FILE = 'freez.dat', ACCESS = 'DIRECT',
    	RECL = 1036800, FORM='UNFORMATTED')
	READ(40, REC = 1), ((DATA(I,K), K = 1, COL), I = 1,ROW)

File and Directory Structure

Data are available on the FTP site in the This directory contains four files:

  • freez.dat
  • freez_a.dat (ASCII)
  • thaw.dat
  • thaw_a.dat (ASCII)

File Size

Dat files are approximately 1 MB. ASCII files are approximately 2.2 MB.

Spatial Coverage


Spatial Resolution


Temporal Coverage


Temporal Resolution


References and Related Publications

ADND. 1965. Fitzroy Region, Queensland - Climate. Canberra, Australian Department of National Development Resources Information and Development Branch.

CSIRO. 1962-71. Land Research Series Nos. 6-14, 17-22, 24-29. Melbourne, Commonwealth Scientific and Industrial Research Organization.

Fletcher, J.O., R.J. Slutz, and S.D. Woodruff. 1983. Towards a comprehensive ocean-atmosphere data set. Tropical Oceanic and Atmospheric Newsletter. 20:13-14.

Legates, D. R. and C. J. Willmott. 1990. Mean Seasonal and Spatial Variability in Global Surface Air Temperature. Theoretical and Applied Climatology 41:11-21.

Nuttonson, M.Y. 1947. Ecological Crop Geography of China and its Agro-climatic Analogues in North America. Washington, D.C. American Institute of Crop Ecology. 28 pages.

Permafrost Subcommittee. 1988. Glossary of Permafrost and Related Ground-ice Terms. Associate Committee on Geotechnical Research, National Research Council of Canada.

Schwerdtfeger, W. 1984. Weather and Climate of the Antarctic. The Netherlands, Elsevier. Developments in Atmospheric Science No. 15. 261 pages.

Slutz, R.J., S.J. Lubker, J.D. Hiscox, S.D. Woodruff, R.L. Jenne, D.H. Joseph, P.M. Steurer, and J.D. Elms. 1985. Comprehensive Ocean-atmospheric Data Set; Release 1. Boulder, CO. NOAA Environmental Research Laboratories, Climate Research Program. 268 pages.

Spangler, W.M.L., and R.L. Jenne. 1984. World Monthly Surface Station Climatology. Boulder, CO. National Center for Atmospheric Research, Scientific Computing Division. 14 pages.

Terjung, W.H., J.T. Hayes, H-Y. Ji, P.E. Todhunter, and P.A. O'Rourke. 1985. Potential Paddy Rice Yields for Rainfed and Irrigated Agriculture in China and Korea. Annual Association of American Geographers. 75:83-101.

van Rooy, M.P. 1957. Meteorology of the Antarctic. South Africa, Government Printer. 240 pages.

Wernstedt, F.L. 1972. World Climatic Data. Lemont, P.A., Climatic Data Press. 552 pages.

Willmott, C.J., J.R. Mather, and C.M. Rowe. 1981. Average Monthly and Annual Surface Air Temperature and Precipitation Data for the World. Part 1: the Eastern Hemisphere. Part 2. The Western Hemisphere.

Woodruff, S.D. 1985. The comprehensive ocean-atmospheric data set. Third Conference on Climate Variations Symposium on Contemporary Climate 1850-2100, American Meteorological Society, 14-15.

Woodruff, S.D., R.J. Slutz, R.L. Jenne, and P.M. Steurer. 1987. A comprehensive ocean-atmosphere data set. Bulletin of the American Meteorological Society, 68:1239-50.

Zhang, T. T.E. Osterkamp, and K. Stamnes. 1996. Some characteristics of the climate in northern Alaska, USA. Arctic and Alpine Research 28(4):509-518.

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Document Information

Document Creation Date

August 1998

Document Revision Date

April 2015

Document URL