Abstract
In interpreting radiation data from the Vertical Temperature Profile Radiometers aboard the NOAA satellites, the following problem arose: given a satellite retrieval of the atmospheric temperature profile and a measurement of radiance from the earth's atmosphere in a single spectral interval (535 cm−1) where water vapor is the principal optically active species, how can we estimate the atmospheric profile of water vapor mixing ratio? Our proposed solution has two steps. The first is to estimate the mixing-ratio profile by linear least-squares regression on the saturation mixing-ratio profile, the latter having been computed from the retrieved temperature profile. Associated with this estimate are residual errors. In the second step the measured radiance is used to reduce these errors, as follows: The covariance matrix of the errors is estimated and its principal eigenfunction is derived. The solution for the mixing-ratio profiles is assumed to be a linear combination of this eigenfunction and the regression estimate of the mixing-ratio profile. The unknown coefficient in this solution is determined through a solution of the radiative transfer equation by Newton's method. In simulation, this method produced accurate solutions for mixing-ratio profiles and total precipitable water; the absolute error in the latter averaging 13% of the true value. This number increased to 26% when a uniform 2 K bias was introduced into the estimates of the temperature profiles.
