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The obtained precision values were validated following a method presented by Piccolo and Dudhia (2007). It is generally accepted that at low latitudes ozone concentrations are relatively stable above the tropopause. Based on this we assume, as did the study by Toohey et al. (2010), that two measurements of low latitude stratospheric ozone taken a day apart should be approximately the same.  Any difference between the profiles could be attributed to random measurement and retrieval noise.   We assemble a set of the differences between matched pairs and find the variance of these differences.  This variance is related to  the random error associated with a profile.  

Mathematically we can say that the difference between two profiles is  so we find the variance in the set of differences:

For a large set of matched pairs the mean uncertainty in the profiles is

and is related to the variance of differences by the equation   

or we can write

and this value should match the average precision value.  

They are compared in the figure below using 

or

For this study we considered scans to be a matched pair if they were taken within a 1.01 day window, and were within 1.5° longitude  and 0.5° latitude of each other.