Terrestrial Water Balance Data Archive:
Regridded 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 May 12, 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 through this site under the title "Global Air Temperature and Precipitation: Regridded Monthly and Annual Climatologies (Version 2.01)." Our estimates of the climatic water balance 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 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 are based on semi-empirical relationships between observed average monthly P and an estimated average monthly potential evapotranspiration (Eo), derived from an average monthly T. Soil water-holding capacity (w*) was held constant, e.g. at 150 mm. A snow-cover water budget also was evaluated and coupled with the soil-moisture balance according to Willmott et al. (1985b). Water-balance variables estimated and archived here include: average-monthly Eo in mm, average-monthly actual evapotranspiration (E) in mm, average-monthly deficit (def) in mm, mid-monthly soil-moisture depth (w) in mm, mid-monthly water equivalent of the snow pack (ws) in mm, average-monthly snow melt (M) in mm, and average-monthly surplus (S) in mm.


Separate "...Water Balance Climatologies" were produced and archived for several different soil water-holding capacities, namely w*=150, w*=100, w*=75 and w*=50mm. Furthermore, the entire suite of water-balance computations were performed and archived twice; once, with "..traditionally interpolated.." air-temperature fields; and, once, with forced with "..DEM-aided.." air-temperature fields. Each of the two alternately interpolated air-temperature fields was used to estimate potential evapotranspiration (Eo) and the other components of the water balance. Please see the associated README file for additional information.

Each directory (traditionally interpolated and DEM-aided) has seven files. The beginning of each file name describes the content of the file as follows. If the name includes "_d", it is based on DEM-aided, interpolated air-temperature fields. The "n" refers to the soil water-holding capacity.

def(_d)n...: deficit
E(_d)n... :actual evapotranspiration
Eo(_d)n... :adjusted potential evapotranspiration
M(_d)n... :snow melt
S(_d)n... :surplus
w(_d)n... :mid-monthly soil moisture
ws(_d)n... :mid-monthly snow cover
All files have the structure.
Field Columns Variable Fortran Format
1 1 - 8 Longitude (decimal degrees)
2 9 - 16 Latitude (decimal degrees)
3-14 17 - 112 Monthly values (mm)


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.