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Atmospheric studies often require the generation of high-resolution maps of ozone distribution across space and time. The high natural variability of ozone concentrations and the different levels of accuracy of the algorithms used to generate data from remote sensing instruments introduce major sources of uncertainty in ozone modeling and mapping. These aspects of atmospheric ozone distribution cannot be confronted satisfactorily by means of conventional interpolation and statistical data analysis. We suggest that the techniques of Modern Spatiotemporal Geostatistics (MSG) can be used efficiently to integrate salient (although of varying uncertainty) physical knowledge bases about atmospheric ozone in order to generate and update realistic pictures of ozone distribution across space and time. The MSG techniques rely on a powerful scientific methodology that does not make the restrictive modeling assumptions of previous techniques. A numerical study is discussed involving datasets generated by measuring instruments onboard the Nimbus 7 satellite. In addition to exact (hard) ozone data, the MSG techniques process uncertain measurements and secondary (soft) information in terms of total ozone-tropopause pressure empirical relationships. Nonlinear estimators are used, in general, and non-Gaussian probability laws are automatically incorporated. The proposed total ozone analysis can take into consideration major sources of error in the Total Ozone Mapping Spectrometer solar backscatter ultraviolet tropospheric ozone residual (related to data sampling, etc.) and produce high spatial resolution maps that are more accurate and informative than those obtained by conventional interpolation techniques.