Principal Investigators:

David R. Legates and Cort J. Willmott

Summary:

Primary References:

* Legates, David R. and Cort J. Willmott. 1990. "Mean seasonal and spatial variability in gauge­corrected global precipitation." International Journal of Climatology, vol. 10. pp. 111­127.

* Legates, David R. and Cort J. Willmott. 1990. "Mean seasonal and spatial variability in global surface air temperature." Theoretical and Applied Climatology, vol. 41, pp. 11­21.

Legates and Willmott Average Monthly Surface Air Temperature and Precipitation (re-gridded)
 

• Integrated dataset
• Design
• Source
• Additional references
• File Lists

Dataset Description

INTEGRATED DATA­SET

Data­Set Citation:

Projection:

Spatial Representation:

Temporal Representation:

Data Representation:

VARIABLE UNITS PRECISION

1) Measured precipitation mm/month 1mm
2) Gauge corrected precipitation mm/month 1mm
3) Surface Air temperature C x 10 .1 C
4) Standard deviation (expressed in the same units and precision as above) of the interpolated cell values for each measurement (precipitation, corrected precipitation, and temperature) are provided as separate layers as an estimate of uncertainty introduced by the re-gridding process -- these three standard deviation ("SD") files were not part of the original data-set.
5) RMS Std. error of corrected precip. mm/month 1mm

Note that this variable was re-gridded by a different method than the first three: The re-gridding method employed a root-mean-square average to combine the 4 quadrant values into the newly registered grid cell for the GED.

Layers and Attributes:

Dataset Description

DESIGN

Variables:

(1) Measured precipitation mm/month 1mm
(2) Gauge corrected precipitation mm/month 1mm
(3) Standard error of corrected precipitation mm/month 1mm
(4) Surface Air temperature degrees Celsius 0.1 C

Origin:

Geographic Reference:

Centroid­registered grid cells on 30­minute lat/long meridians. Original grid (361x721) extends from pole to pole and originates at the International Date Line.

Geographic Coverage: Global

Geographic Sampling:

Time Period:

Temporal Sampling

Dataset Description

SOURCE

Source Data Citation:

Contributor:

Distributor:

NCAR

Date of Production:

Lineage & Contacts:

(2)Archived and Distributed by:
Roy Jenne
National Center for Atmospheric Research
Boulder, CO 

Dataset Description

ADDITIONAL REFERENCES

Sevruk, B. 1989. "Reliability of precipitation measurement." In: Precipitation Measurement, B. Sevruk (ed.), Proceedings of the WMO/IAHS/ETH International Workshop on Precipitation Measurement, St. Moritz, Switzerland, Dec. 3­7, 1989. Zurich: Swiss Federal Institute of Technology, pp. 519­526

Shepard, D. 1968. "A two-dimensional interpolation function for irregularly-spaded data." In: Proceedings of 23rd National Conference of the Association for Computing Machinery. ACM Pub. P-68. Princeton, NJ: Brandon/Systems Press, Inc.

Willmott, C.J., Rowe, C.M., and Philpot, W.D. 1985. "Small-scale climate maps: a sensitivity analysis of some common assumptions associated with grid-point interpolation and contouring. The American Cartographer, 12(1): 5-16. 

Dataset Description

File Lists

• Dataset Files
• Reprint Files

Legates and Willmott Average Monthly Surface Air Temperature and Precipitation (re-gridded)
 

• Gauge Corrected Precipitation (re-gridded)
• Standard Error for Gauge Corrected Precipitation (re-gridded)
• Measured Precipitation (re-gridded)
• Surface Air Temperature (re-gridded)
• Average Monthly Air Temperature and Precipitation (Source Examples)

Gauge Corrected Precipitation (re-gridded)

Description:

 Structure:

 Series:

 System Files:

Notes:

 Standard Error for Gauge Corrected Precipitation (re-gridded)

Description:

 Structure:

 Series:

 System Files:

Notes:

 Measured Precipitation (re-gridded)

Description:

 Structure:

 Series:

 System Files:

 Notes:

 Surface Air Temperature (re-gridded)

Description:

Structure:

 Series:

 System Files:

Notes:

 Average Monthly Air Temperature and Precipitation (Source Example)

Description:

 Structure:

 Series:

 System Files:

Notes:

Legates and Willmott Average Monthly Surface Air Temperature and Precipitation (re-gridded)
 

John Kineman and Mark Ohrenschall
National Geophysical Data Center
Boulder, Colorado

OVERVIEW

The Legates and Willmott data are referenced to a latitude/longitude grid with the data values located at intersections of the .5-degree latitude and longitude meridians, globally. This can be seen as a grid of half-degree cells with the cell centers located at the .5 degree meridian intersections. Note also that the "cell" boundaries of this type of grid extend beyond the "edges" of the global lat/long grid extending between +/- 180 degrees longitude and +/- 90 degrees latitude. This differs from the convention adopted for the GED, of edge alignment with a nested set of GED "conventional" latitude and longitude meridians, one of which is .5-degrees (i.e., the GED "nested" grids - see User's Guide). In the GED convention, the cell boundaries are aligned with the edges of the global window and with each "nested" meridian. The difference between these two grid conventions is cell registration, but it poses a problem for integration or intercomparison with other data in the database since differently registered grid cells do not occupy the same location, and thus must be either interpolated or accepted with a spatial offset of 1/2 the diagonal of a cell (e.g., systems that would automatically grid-sample to obtain the edge-registered grid values from a centroid-registered grid).

In a raster GIS, each number in a digital image file is referenced to a "cell," which covers some area on the surface of the earth. Given data values spaced a half-degree apart on a latitude/longitude grid, each value is considered to refer to a half-degree "cell" on the surface of the earth (although with true "point" data sets the value more properly refers to the centroid of the cell). In practice, the spatial meaning of cell values may vary considerably between data-sets, depending on design criteria of the original investigators. The Legates and Willmott data are carefully interpolated from irregularly spaced point observations to values that have a spatial resolution approximately equal to the cell size (i.e., .5-degree). It is therefore not correct to assume a spatial uncertainty of .5-degrees, as commonly used "nearest-neighbor" resampling would. Unfortunately, owing to the complex nature of rainfall data and the spatial interpolation techniques that were applied (see references), any method of re-gridding introduces problems.

In resampling from the Legates and Willmott grid to the Global Ecosystems Database grid two methods were tested: (2) combining resampling and interpolation to represent the data on a GED-compatible 10-minute grid, and (2) regridding (interpolation) to the GED conventional half-degree grid using a simple 2x2 quadrant average for each cell in the new grid. The first of these products was distributed on the 1991 Prototype CD-ROM of the GED Database (Version 0.1 - Beta Test). Partly based on the 1991 review, the decision was made to include the second product on the current release of the GED database (Version 1.0). Both of these solutions are considered inferior to re-producing the data from source material, however this will require more time and resources.

METHOD USED IN THE PROTOTYPE

The method used for the prototype was to expand (by pixel replication) the Legates and Willmott grid by a factor of six in both row and column dimensions, window on the inner 2160 rows and 4320 columns (excluding the outer-most three rows and columns), and then contract (with cell averaging) by a factor of two. The result was a 10-minute grid that can nest with other gridded images in the Global Ecosystems Database. While the new 10-minute grid was to some degree interpolated from the original grid, the advantage of this method was that the original grid values are preserved amongst interpolated values, and the original data-set can be recovered from the new grid by sampling. Its disadvantage was that it was unclear how to use this mixed grid in normal processing, and the artificially fine grids (10-minutes) require a lot of storage space and may mislead users into assuming greater regional resolution than actually exists. In other words, the expanded grid would have to be aggregated to a coarser grid to have proper meaning anyway.

METHOD USED IN THE CURRENT VERSION

The method used for the current release was a simple grid interpolation, averaging 4 cell values to obtain a 1/2 cell offset data-set on a .5-degree grid that is compatible with the GED convention. This, unfortunately, also smooths the original data, thus reducing its variability and changing its spatial meaning. Statistically, the new grid represents averages of four 1/2-degree "quadrant" cells covering a 1x1 degree region, taken at 1/2-degree grid increments. The data should be interpreted with this in mind, as it is a questionable procedure for many uses to interpolate variables such as precipitation in this way (although the original values are themselves interpolated and spatially general). It may be more appropriate to use this interpolated GED grid for coarser studies, at 1-degree or greater resolution.

To assess the uncertainty in the re-gridding process, companion data files are provided for each variable giving the standard deviation (sample s.d., i.e., 1/n-1) for each cell's 4 source values. This may serve as a reliability indicator for the interpolated values.

According to the NCAR documentation, the gauge-error data (for the gauge-corrected precipitation estimates) is expressed as a standard error, however the literature references discuss gauge-errors in percent. It was decided to interpolate the gauge-error file as standard error estimates, using a simple root-mean-square algorithm.

Further investigation of these methods is warranted.

SOURCE FILE FORMATTING

The Legates and Willmott data came as four files on tape, one file for each parameter, with an 80-character fixed-record format containing latitude, longitude, and 13 data fields for the twelve monthly averages and the annual average. Since each record did have geo-referencing, a cell sequencing was unnecessary, nonetheless the data files had cell sequencing north to south within longitude columns, with column sequencing from west to east, beginning at 90 degrees north and 180 degrees west. Each data value was referenced by half-degree multiples, including 90 degrees north, 90 degrees south, 180 degrees west, and 180 degrees east.

DATA PROCESSING

In processing the data, the first task was running a custom-written program to resequence the cells and extract the data fields to produce an Idrisi image for each parameter for each monthly and annual image. Next, a program was written to average a moving window of 4 original cell values, writing the averages and standard deviations of the 2x2 average to the new grid.

Data was rewritten by remapping and resampling center of cell (ie..registered grids) to corner of cell (ie.. lower left registered grids). This change allowed half-degree edge-alligned cells to be compatible with the rest of the nested grid structure present on this disc.

CONCLUSION

The representation of the Legates and Willmott data is a compromise to achieve integration with multi-thematic data. As with any data-set, the user must assess its value for the purpose at hand. These "re-gridded" data will loose regional variability information due to the smoothing effect of the interpolation. The amount of loss may be estimated by the standard deviation values provided with the re-gridded data, and by experimenting with the sample source file provided with the database. Nevertheless, an obvious future improvement would be to re-calculate the data-set on the desired grid from station observations, using the original (or improved) interpolation methods.