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- Author or Editor: Michael P. Weinreb x
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Abstract
Mixing ratios of stratospheric constituents can be inferred from satellite- or balloon-based infrared solar occultation measurements. The nonlinear system of equations that relates the measurements to the mixing ratios is often solved by the “onion-peeling” technique. We show how to implement onion-peeling with an algorithm in which limb paths are represented by equivalent homogeneous paths. The essential computations are confined to the tangent layers instead of the full multilayer limb paths. The algorithm yields the same solutions as conventional onion-peeling but requires significantly less computation time.
Abstract
Mixing ratios of stratospheric constituents can be inferred from satellite- or balloon-based infrared solar occultation measurements. The nonlinear system of equations that relates the measurements to the mixing ratios is often solved by the “onion-peeling” technique. We show how to implement onion-peeling with an algorithm in which limb paths are represented by equivalent homogeneous paths. The essential computations are confined to the tangent layers instead of the full multilayer limb paths. The algorithm yields the same solutions as conventional onion-peeling but requires significantly less computation time.
Abstract
A priori estimates of the vertical distribution of tropospheric water vapor are needed to solve the radiative transfer equation in the 15 μm CO2 band to derive tropospheric temperatures from radiances measured at orbiting satellites. This paper shows how errors in estimates of water vapor mixing ratio propagate into these solutions for temperature, and in simulation establishes the sensitivity of the rms errors in a collection of temperature soundings from the NOAA 2 satellite to errors in mixing ratio. The simulations predict that errors found in available estimates of mixing ratio degrade the solutions for temperature in the low troposphere so that they provide little new information over that already in the forecasts of the National Meteorological Center.
Abstract
A priori estimates of the vertical distribution of tropospheric water vapor are needed to solve the radiative transfer equation in the 15 μm CO2 band to derive tropospheric temperatures from radiances measured at orbiting satellites. This paper shows how errors in estimates of water vapor mixing ratio propagate into these solutions for temperature, and in simulation establishes the sensitivity of the rms errors in a collection of temperature soundings from the NOAA 2 satellite to errors in mixing ratio. The simulations predict that errors found in available estimates of mixing ratio degrade the solutions for temperature in the low troposphere so that they provide little new information over that already in the forecasts of the National Meteorological Center.
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.
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.
Abstract
An accurate approximation to calculate atmospheric profiles of transmittance in instrumental spectral intervals is presented. The approximation assumes a known transmittance model; i.e., that the transmittance in the spectral interval of the instrument is known as a function of quantity of absorber, temperature, and total pressure in homogeneous paths. An inhomogeneous atmosphere is treated as a sequence of homogeneous layers. One applies the model by successively rescaling the quantity of absorber. The method is exact for monochromatic radiation. It avoids the computation of mean line strengths, and it is computationally fast. As an example, transmittance profiles are computed for two spectral intervals in which water vapor is the chief absorber. The results are in excellent agreement with the “exact” point-by-point calculation.
Abstract
An accurate approximation to calculate atmospheric profiles of transmittance in instrumental spectral intervals is presented. The approximation assumes a known transmittance model; i.e., that the transmittance in the spectral interval of the instrument is known as a function of quantity of absorber, temperature, and total pressure in homogeneous paths. An inhomogeneous atmosphere is treated as a sequence of homogeneous layers. One applies the model by successively rescaling the quantity of absorber. The method is exact for monochromatic radiation. It avoids the computation of mean line strengths, and it is computationally fast. As an example, transmittance profiles are computed for two spectral intervals in which water vapor is the chief absorber. The results are in excellent agreement with the “exact” point-by-point calculation.
