Efficient nonlinear inversion for atmospheric sounding and other applications

Retrieving atmospheric and/or surface state variables using remote observations typically involves minimizing a nonlinear cost function in measurement space. Many methods exist for minimizing nonlinear functions, but the applicability of one method over another has a large dependence on the degree of nonlinearity of the cost function and the initial guess error. We present a minimization method, called DRAD, that is applicable to highly nonlinear cost functions and to problems where little a priori information about the retrieved variables is available. To illustrate the method, water vapor and temperature profiles are retrieved using simulated Atmospheric Infrared Sounder observations. We focus on the efficiency of DRAD for retrievals generated for a wide range of initial guess errors. For a comparison, we also generate retrievals using the Levenberg-Marquardt method.

Optimal use of the information provided by indirect measurements of atmospheric vertical profiles

A procedure for the optimal utilization and representation of the information retrieved from atmospheric observations is discussed. We show that the "measurement-space solution" exclusively contains the information present in the observations, but is not suitable for a representation of the retrieved profile in the form of a graph. The new method of the "null-space regularization", which provides in a complement space an external constraint and makes the solution compliant with this representation, is presented. In this way the measurement and the constraint are separately determined and are given in a vertical grid that can be freely chosen as fine as desired. The method is applied to simulated measurements and is used to define a procedure for data fusion.

Analytical determination of the regularization parameter in the retrieval of atmospheric vertical profiles

In the retrieval of vertical profiles of atmospheric constituents, regularization methods are frequently used to improve the conditioning of the solution. The regularization reduces the retrieval errors and causes the vertical resolution to deteriorate. One obtains a trade-off by tuning the strength of the regularization by way of a regularization parameter. A new analytical method for determining the regularization parameter is presented. This method is suitable for operational retrievals, for which an unattended procedure is required. The performance of the new method is compared with that of the L-curve method, and the results show that a better trade-off between retrieval errors and vertical resolution is obtained.

Retrieval of CO from nadir remote-sensing measurements in the infrared by use of four different inversion algorithms

Four inversion schemes based on various retrieval approaches (digital gas correlation, nonlinear least squares, global fit adjustment, and neural networks) developed to retrieve CO from nadir radiances measured by such downward-looking satelliteborne instruments as the Measurement of Pollution in the Troposphere (MOPITT), the Tropospheric Emission Spectrometer (TES), and the Infrared Atmospheric Sounding Interferometer (IASI) instruments were compared both for simulated cases and for atmospheric spectra recorded by the Interferometric Monitor for Greenhouse Gases (IMG). The sensitivity of the retrieved CO total column amount to properties that may affect the inversion accuracy (noise, ancillary temperature profile, and water-vapor content) was investigated. The CO column amounts for the simulated radiance spectra agreed within 4%, whereas larger discrepancies were obtained when atmospheric spectra recorded by the IMG instrument were analyzed. The assumed vertical temperature profile is shown to be a critical parameter for accurate CO retrieval. The instrument's line shape was also identified as a possible cause of disagreement among the result provided by the groups of scientist who are participating in this study.

Methods for determining regularization for atmospheric retrieval problems

The atmosphere of Earth has already been investigated by several spaceborne instruments, and several further instruments will be launched, e.g., NASA's Earth Observing System Aura platform and the European Space Agency's Environmental Satellite. To stabilize the results in atmospheric retrievals, constraints are used in the iteration process. Therefore hard constraints (discretization of the retrieval grid) and soft constraints (regularization operators) are included in the retrieval. Tikhonov regularization is often used as a soft constraint. In this study, different types of Tikhonov operator were compared, and several new methods were developed to determine the optimal strength of the constraint operationally. The resulting regularization parameters were applied successfully to an ozone retrieval from simulated nadir sounding spectra like those expected to be measured by the Tropospheric Emission Spectrometer, which is part of the Aura platform. Retrievals were characterized by means of estimated error, averaging kernel, vertical resolution, and degrees of freedom.