Parameter Weighting

In the Parameter Weighting operation, one parameter (Scientific Data Set, or (SDS)) is weighted by another when computing any average (or a similar statistical quantity such as standard deviation). The averaging can be done either spatially or temporally.

The parameter-weighted average of a quantity x is computed as ﴾ ∑ (w_{i} ∙ x_{i} ) ﴿ / ﴾ ∑ w_{i} ﴿ , where the sums in both numerator and denominator are taken over all grid cells i (in the spatial/temporal averaging region) for which the parameter being averaged, x_{i }, and the weighting parameter, w_{i} , both have valid values.

Notes: At present, Parameter Weighting is only applied to the MODIS data product "Aerosol Small Mode Fraction" which is weighted by Aerosol Optical Depth (AOD). In this case, a valid weight is defined to be any AOD ≥ 0. (Note that this definition is equivalent to resetting any negative measurement of AOD to 0 for the purpose of the weighting operation.)

If area-weighting is also being applied, the above formula still holds, but with the weights (w_{i}’s), replaced by their product with the area of their grid cell: (w_{i} ∙ a_{i }).

This Technical Summary page is under development -- for information on this operation while the documentation is being prepared, please send a message to GES DISC Help.