Reduction of bias from parameter variance in geophysical data estimation: Method and application to ice water content and sedimentation flux estimated from LiDar

This paper addresses issues of statistical misrepresentation of the a priori parameters (henceforth called ancillary parameters) used in geophysical data estimation. Parameterizations using ancillary data are frequently needed to derive geophysical data of interest from remote measurements. Empirical fits to the ancillary data that do not preserve the distribution of such data may induce substantial bias. A semianalytical averaging approach based on Taylor expansion is presented to improve estimated cirrus ice water content and sedimentation flux for a range of volume extinction coefficients retrieved from spaceborne lidar observations by CALIOP combined with the estimated distribution of ancillary data from in situ aircraft measurements of ice particle microphysical parameters and temperature. It is shown that, given an idealized distribution of input parameters, the approach performs well against Monte Carlo benchmark predictions. Using examples with idealized distributions at the mean temperature for the tropics at 15 km, it is estimated that the commonly neglected variance observed in in situ measurements of effective diameters may produce a worst-case estimation bias spanning up to a factor of 2. For ice sedimentation flux, a similar variance in particle size distributions and extinctions produces a worst-case estimation bias of a factor of 9. The value of the bias is found to be mostly set by the correlation coefficient between extinction and ice effective diameter, which in this test ranged between all possible values. Systematic reporting of variances and covariances in the ancillary data and between data and observed quantities would allow for more accurate observational estimates.