Water vapor concentration structures in the atmosphere are well approximated horizontally by Gaussian random fields at small scales (≲6 km). These Gaussian random fields have a spatial correlation in accordance with a structure function with a two-thirds slope, following the corresponding law from Kolmogorov's theory of turbulence. This is proven by showing that the horizontal structure functions measured by several satellite instruments and radiosonde measurements do indeed follow the two-thirds law. High-spatial-resolution retrievals of total column water vapor (TCWV) obtained from the Ocean and Land Color Instrument (OLCI) on board the Sentinel-3 series of satellites also qualitatively show a Gaussian random field structure.
As a consequence, the atmosphere has an inherently stochastic component associated with the horizontal small-scale water vapor features, which, in turn, can make deterministic forecasting or nowcasting difficult. These results can be useful in areas where high-resolution modeling of water vapor is required, such as the estimation of the water vapor variance within a region or when searching for consistency between different water vapor measurements in neighboring locations. In terms of weather forecasting or nowcasting, the water vapor horizontal variability could be important in estimating the uncertainty of the atmospheric processes driving convection.
