MLS Radiance Variance Calculations
         When the radiances become saturated at the bottom of each scan, they measure the air temperature in the saturation layer. Therefore, fluctuations of the saturated radiances can be reported as the temperature perturbations in that layer.

        There are several ways to estimate the radiance variance from the saturated measurements. The method used by Wu and Waters [1996b] is a simple chi-square analysis of the saturated radiances at the bottom of each limb scan. The estimated variance ( coefficient for estimated variance) is computed as follows
equation for estimated variance                    (1)
where yi and zi are radiances and tangent heights, respectively, and n is the number of saturated radiances. Parameters a and b are determined from the least-squares fit to the radiances, and thus yield  n-2 as the degree of freedom. Note that a variance is produced for each channel in each scan. Variances from different channels and scans are completely independent so as to minimize planetary-scale perturbations. The estimated variance may fluctuate about the true variance and the uncertainty is approximately
formula for the uncertainty whe the estimated variance fluctuates about the true variance                             (2)
To reduce this uncertainty, we generally average a large number of the estimated variances sampled over a week, a month or a season.

        One may increase the variance signal-to-noise ratio by combining the radiances from the symmetric channels that have the similar weighting function and noise figure before the least-squres fitting. The pair combination will reduce the instrument variance roughly by one half, namely

formula for reduction in instrument variance                        (3)
where y1i and y2i are the radiances from the pair channels that are symmetric about the line center.

        Finally, we report the atmospheric component, coefficient for atmospheric component, which is called the GW variance, by subtracting out the instrument noise. The variance due to the instrument noise is constant throughout the mission but channel-dependent. The derived GW variances are mostly due to meso-scale temperature perturbations in the saturation layer but of relatively long (>10km) vertical scales.