VESPER: Variogram Estimation and Spatial Prediction plus ERror

The large number of measurements made by continuous yield monitoring, mobile electrical conductivity systems, kinematic GPS and other ‘on-the-go’ field sensors have created large data sets (more than 1000 points) within a single field. In most geostatistical software, spatial interpolation requires two separate steps: calculating and modelling/fitting of variogram for the whole area (data points) followed by kriging estimates for unsampled points in the area. There is a need to develop new spatial prediction software in order to accommodate the large number of data and to take into account the local spatial structure. A range of prediction options that considers the nature and quality of the original data and the end use of the mapped output is also required.

VESPER is a PC-Windows program developed by the Australian Centre for Precision Agriculture (ACPA) for spatial prediction that is capable of performing kriging with local variograms (Haas, 1990). Kriging with local variograms involves searching for the closest neighbourhood for each prediction site, estimating the variogram from the neighbourhood, fitting a variogram model to the data and predicting the value and its uncertainty. The local variogram is modelled in the program by fitting a variogram model automatically through the nonlinear least-squares method. Several variogram models are available, namely spherical, exponential, Gaussian and linear with sill. Punctual and block kriging is available as interpolation options. This program adapts itself spatially in the presence of distinct differences in local structure over the whole field.

Applications of the program include generating yield maps (Whelan et al., 1996), interpolation of digital elevation models, and assessment of topsoil salinity problems (Walter et al., 1999). The program also allows conventional kriging with a whole area variogram, with options for manual adjustment and fitting of the whole-area variogram. The user-friendly interface permits the creation of a field boundary and generation of an interpolation grid. Future development will incorporate local regression kriging into the program with more advanced guidance for users incorporated with the interface.

A screenshot from VESPER
A screenshot from VESPER

VESPER is a publication of the Australian Centre for Precision Agriculture (ACPA). It is made available for use by the PA Lab.
If it is used for research or commercially please cite the following reference:

Minasny, B., McBratney, A.B., and Whelan, B.M., 2005. VESPER version 1.62. Australian Centre for Precision Agriculture, McMillan Building A05, The University of Sydney, NSW 2006. (

More information on VESPER can be found by downloading this paper and the User Manual.


The PA Lab has taken all care to ensure these programs are operationally sound. However, these programs are supplied 'as is' and no warranty is provided or implied. The PA Lab assumes no liability for damages, direct or consequential that may result from the use of these programs.


  • Haas, T.C., 1990. Kriging and automated variogram modeling within a moving window. Atmospheric Environment 24A, 1759-1769.
  • Walter, C., McBratney, A.B., Douaoui, A., Minasny, B., 2001. Spatial prediction of topsoil salinity in the Chelif valley, Algeria, using local kriging with local variograms versus local kriging with whole-area variogram. Aust. J. Soil Res. 39, 259-272. Article
  • Whelan, B.M., McBratney, A.B., Viscarra-Rossel, R.A., 1996. Spatial prediction for precision agriculture. In: Proceedings of the 3rd international conference on precision agriculture, Minneapolis, Minessota, June 23-26, 1996, pp 331-342.

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