Search

Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our “Generic Atmospheric Radiation Line-by-line Infrared Code”, utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using “exact” AD Jacobians as a reference. The results indicate that the “standard” two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy. [ABSTRACT FROM AUTHOR]

Abstract: A suite of programs for high resolution infrared-microwave atmospheric radiative transfer modeling has been developed with emphasis on efficient and reliable numerical algorithms and a modular approach appropriate for simulation and/or retrieval in a variety of applications. The Generic Atmospheric Radiation Line-by-line Infrared Code — GARLIC — is suitable for arbitrary observation geometry, instrumental field-of-view, and line shape. The core of GARLIC's subroutines constitutes the basis of forward models used to implement inversion codes to retrieve atmospheric state parameters from limb and nadir sounding instruments. This paper briefly introduces the physical and mathematical basics of GARLIC and its descendants and continues with an in-depth presentation of various implementation aspects: An optimized Voigt function algorithm combined with a two-grid approach is used to accelerate the line-by-line modeling of molecular cross sections; various quadrature methods are implemented to evaluate the Schwarzschild and Beer integrals; and Jacobians, i.e. derivatives with respect to the unknowns of the atmospheric inverse problem, are implemented by means of automatic differentiation. For an assessment of GARLIC's performance, a comparison of the quadrature methods for solution of the path integral is provided. Verification and validation are demonstrated using intercomparisons with other line-by-line codes and comparisons of synthetic spectra with spectra observed on Earth and from Venus. [Copyright &y& Elsevier]

Radiation is a key process in the atmosphere. Numerous radiative transfer codes have been developed spanning a large range of wavelengths, complexities, speeds, and accuracies. In the infrared and microwave, line-by-line codes are crucial esp. for modeling and analyzing high-resolution spectroscopic observations. Here we present Py4CAtS—PYthon scripts for Computational ATmospheric Spectroscopy, a Python re-implemen-tation of the Fortran Generic Atmospheric Radiation Line-by-line Code GARLIC, where computationally-intensive code sections use the Numeric/Scientific Python modules for highly optimized array processing. The individual steps of an infrared or microwave radiative transfer computation are implemented in separate scripts (and corresponding functions) to extract lines of relevant molecules in the spectral range of interest, to compute line-by-line cross sections for given pressure(s) and temperature(s), to combine cross sections to absorption coefficients and optical depths, and to integrate along the line-of-sight to transmission and radiance/intensity. Py4CAtS can be used in three ways: in the (Unix/Windows/Mac) console/terminal, inside the (I)Python interpreter, or Jupyter notebook. The basic design of the package, numerical and computational aspects relevant for optimization, and a sketch of the typical workflow are presented. In conclusion, Py4CAtS provides a versatile environment for "interactive" (and batch) line-by-line radiative transfer modeling. [ABSTRACT FROM AUTHOR]