Henry E. Fleming

Atmospheric transmittance of an absorbing gas: a computationally fast and accurate transmittance model for absorbing gases with constant mixing ratios in inhomogeneous atmospheres

At a given pressure level the atmospheric transmittance for an absorbing gas with a constant mixing ratio varies only with the temperature profile of the atmosphere. A simple transmittance model based on temperature differences is derived for monochromatic radiation. This model then is extended to the more important case of polychromatic radiation through the use of scaling approximations. The resulting algorithm for calculating transmittances for an arbitrary temperature profile is simple to use, accurate, and computationally fast because only arithmetic operations are required. In fact, resulting transmittances agreed with line-by-line calculations to within 0.0031 for the cases tried. Details for calculating the expansion coefficients are provided.

Atmospheric transmittance of an absorbing gas. 2: A computationally fast and accurate transmittance model for slant paths at different zenith angles

Models exist which allow the calculation of atmospheric transmittance at a given zenith angle for an absorbing gas with a constant mixing ratio. However, many applications require transmittances at several zenith angles. A simple, fast, and accurate model for calculating the angular dependence is given. This model is computationally fast because only the four arithmetic operations are used. Details for calculating the expansion coefficients are provided. When this technique is combined with a procedure for calculating transmittances at a fixed angle, it is possible to calculate transmittances for slant paths at arbitrary zenith angles and temperature profiles, provided the mixing ratio is constant. This technique was evaluated with a method capable of calculating transmittances at zero zenith angle with an accuracy of 0.0031. For zenith angles ranging from 0 degrees to 40 degrees , transmittances agree with line-by-line calculations to within 0.0038.

Equivalence of regularization and truncated iteration in the solution of III-posed image reconstruction problems

Abstract The equivalence of minimum-norm least-squares solutions of systems of linear equations and standard iterative methods of solution is well established. On the other hand, while it is generally understood that truncated iteration is a form of regularization, comparatively few papers have formalized the relationship between direct methods of regularization and truncated iteration. A brief review of such papers is presented. The main result of this paper is to carry this idea one step further and prove that solutions by direct regularization are in fact identical to solutions of a certain type of truncated-iterative method, and conversely. This equivalence is proved by construction for a very general form of regularization method in which the coefficient matrix has full rank and is rectangular.

The forward problem and corrections for the SSM/T satellite microwave temperature sounder

The relationship between atmospheric temperatures and the brightness temperatures measured by the Special Sensor Microwave/Temperature (SSM/T) radiometer is addressed. Physical algorithms for retrieving temperature profiles explicitly employ the physics of radiative transfer. Consequently, it is necessary to do the forward problem accurately before attempting the retrieval problem. The various problems that arise in doing forward calculations over oceans are discussed. These problems include determining when the measurements are cloud contaminated, the amount of liquid water in the fields of view, the surface emissivity under both clear and cloudy conditions, the corrections for liquid water contamination of the measurements, the adjustments for deficiencies in the radiative transfer model, and the compensation for measurement discrepancies by using shrinkage estimation. These procedures are developed for SSM/T data, and their validity is checked by comparing the forward calculations with the corresponding satellite measurements. Application of the procedures to an independent data set confirms their veracity. >

COMPARISON OF LINEAR INVERSION METHODS BY EXAMINATION OF THE DUALITY BETWEEN ITERATIVE AND INVERSE MATRIX METHODS

Linear numerical inversion methods applied to atmospheric remote sounding generally can be categorized in two ways: (1) iterative, and (2) inverse matrix methods. However, these two categories are not unrelated; a duality exists between them. In other words, given an iterative scheme, a corresponding inverse matrix method exists, and conversely. This duality concept is developed for the more familiar linear methods. The iterative duals are compared with the classical linear iterative approaches and their differences analyzed. The importance of the initial profile in all methods is stressed. Calculations using simulated data are made to compare accuracies and to examine the dependence of the solution on the initial profile.

Accuracies of three computationally efficient algorithms for computing atmospheric transmittances.

Three algorithms for calculating polychromatic atmospheric transmittance functions have been tested using a set of eleven distinct temperature profiles in order to compare transmittance accuracies achievable by the three methods. The comparison of rms errors demonstrates that the iterative method of McMillin and Fleming (1976) is the most accurate of the efficient algorithms currently available for gases with constant mixing ratios; its accuracy approaches that of the spectroscopic parameters and the computational approximations used in the ground-truth line-by-line calculations. The method of Arking et al. (1974), while less accurate, has the advantage of being perfectly general and easily adapted to cases where spectral bandwidths are varied

Trade-Offs in the Design of Satellite Sounding Instruments

Abstract In the design of satellite sounding instruments there are many factors that determine the accuracies of the retrieved temperature and moisture profiles. However, the three major factors are: instrument noise, number of channels and weighting function half-widths. The effect of these three factors on retrieved temperatures are examined through simulation studies to determine trade-offs among them. We conclude that the trade-offs among the three factors suggest that year different instrument designs can yield similar accuracies. Consequently, the instrument design that provides optimum performance can be recognized only after a trade-off analysis is made. If the design with the best performance is to be selected, it is particularly important that the designs be given equal benefit of factors which are not intrinsic design differences.

APPLICATION OF THE TRUNCATED NORMAL DISTRIBUTION TECHNIQUE TO THE DERIVATION OF SEA SURFACE TEMPERATURES

The truncated normal distribution technique is applied to the derivation of sea surface temperatures from high-resolution satellite measurements in the 11-μm window region. The purpose of this technique is to remove cloud contamination from the measurements. This procedure produces sea surface temperature maps on a mesoscale level so that a reasonably small-scaled temperature structure, such as that found in the Gulf Stream, can be determined. Because not all the cloud contamination is removed by the truncated normal distribution technique, the resulting temperature fields are modified by an error detection and correction technique. Results from both simulated and real data are presented. No attempt has been made to account for atmospheric attenuation by water vapor; therefore, the results are accurate in only a relative sense .