Willmott and Feddema's Moisture Index Archive:
Gridded Monthly Climatologies

(Version 1.01)

produced and documented by

Cort J. Willmott and Kenji Matsuura
(with support from NASA's Seasonal to Interannual ESIP)

For additional information concerning this archive,
please contact us at:

Center for Climatic Research
Department of Geography
University of Delaware
Newark, DE 19716
(302) 831-2294



Archive (Version 1.01) released August 1, 1999


Climatic means of monthly air temperature (T) and unadjusted (for raingage undercatch) precipitation (P) were taken from the station and oceanic-grid-point records compiled by Legates and Willmott (1990a and b). These in-situ averages then were used to spatially reinterpolate average-monthly T and P fields to a 0.5x0.5 degree spatial grid, which covers the entire globe. The interpolations were, in part, based on Willmott et al.'s (1985a) spherical implementation of Shepard's spatial-interpolation algorithm, although an average of 20 nearest stations influenced each grid-point estimate, instead of the seven suggested by Shepard. Two separate sets of gridded T fields were alternately interpolated, first using "traditional" interpolation alone (Willmott et al., 1985a, as outlined above), and second by "DEM-assisted" interpolation as described by Willmott and Matsuura (1995). It is likely that the DEM-assisted T fields are more realistic over the land surfaces, with regional and seasonal exceptions. These gridded T and P data fields are available from this site (Global Air Temperature and Precipitation: Regridded Monthly and Annual Climatologies, V. 2.01). Our estimates of the average-monthly moisture indices from T and P (see below) were made at (and are available for) only the land-surface grid points, which number 86,609.


Average-monthly water-balance fields first were estimated from the gridded average-monthly T and P fields according to Willmott et al.'s (1985b) modified version of the Thornthwaite water-balance procedure. The computational algorithm was derived from Willmott (1977). Climatic water-balance calculations were separately made for each of the 86,609 grid nodes, thereby conserving mass (in z only) at each grid node. Two complete sets of water-balance estimates were produced and archived: one based on the traditionally interpolated average-monthly T fields; and the other based on a DEM-assisted gridding of average-monthly T. These 0.5-degree resolution water-balance estimates also are available through this site (Terrestrial Water Balance Data Archive: Regridded Monthly Climatologies, V. 1.01). Using our estimated average-monthly potential evapotranspiration (Eo) and P values, average-monthly moisture indices were calculated according to Willmott and Feddema (1992) at the same resolution as the water-balance fields. Two sets of moisture indices were estimated and archived: one based on Eo from traditionally interpolated air temperature and other based on DEM-assisted, interpolated air temperature (mentioned above).


There are two sets of files in this archive. One based on Eo calculated from traditionally interpolated air temperature and the other based on Eocalculated from DEM-assisted, interpolated air temperature. Please note that each mean-annual moisture index was computed from the 12-month total Eo and P.

Fortran Format
11 - 8 Longitude (decimal degrees)
29 - 16Latitude (decimal degrees)
3-1417 - 112 Monthly Moisture Indices
15113 - 120 Annual Moisture Indices


Legates, D. R. and C. J. Willmott, 1990a. Mean Seasonal and Spatial Variability in Gauge-Corrected, Global Precipitation. International Journal of Climatology, 10, 111-127.

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

Willmott, C. J., 1977. WATBUG: A FORTRAN IV Algorithm for Calculating the Climatic Water Budget. Pubs. in Climatology, 30, 1-55. (Also published as Report 1 in The Use of the Climatic Water Budget in Water Resources Management and Control. Newark, DE: University of Delaware, Water Resources Center, 1977).

Willmott, C.J. and K. Matsuura, 1995. Smart Interpolation of Annually Averaged Air Temperature in the United States. Journal of Applied Meteorology, 34(12), 2577-2586.

Willmott, C.J., C.M. Rowe, and W.D. Philpot, 1985a. Small-Scale Climate Maps: A Sensitivity Analysis of Some Common Assumptions Associated with Grid-Point Interpolation and Contouring. The American Cartographer, 12, 5-16.

Willmott, C. J., C. M. Rowe, and Y. Mintz, 1985b. Climatology of the Terrestrial Seasonal Water Cycle. Journal of Climatology, 5, 589-606.

Willmott, C. J. and J. J. Feddema, 1992. A More Rational Climatic Moisture Index. Professional Geographer, 44(1), 84-88.