tion matrix and U is the identity matrix. is computed by summing up the lines with a signicant contribution (line-by-line model). e line shape is the Voigt function, its complex form including dispersion eects is used for assessing the Zeeman eects [13]–[15]. e matrix expo-nential is the computation bottleneck of the model when a general algorithm is used. A fast function has then been implemented using the Caley-Hamilton development and the analytical solution of eigenvalues (2 independent values) [13]. Radiances are computed over ne tangent-height and frequency grids and convolved with the instru-mental functions (e.g., antenna pattern or spectrometer channels). e case of unpolarized radiation is computed using a similar equation but with scalar parameters instead of matrices and vectors.e standard approach for retrieving the forward model (FM) unknown parameters (atmospheric and obser-vation parameters) from a measurement y can be expressed as:() Equation 2Where x is a vector (size=n) representing all the un-known parameters in the forward model, y (size=m) con-tains all the spectra measured during a vertical scan, and K is the Jacobian matrix dy/dx (size=[n, m]). is equation gives the most probable vector x for which the FM matches the noisy measurement. Usually iterations are performed to deal with non-linearities in the forward model, K would be weighted with the measurement errors and an a priori knowledge of x would be used as a con-straint. Here, these issues have been omitted for simplica-tion but are described in [4]. e matrix K allows us to infer the information content of the measurement and to map into the x-space the measurement error described in the y-space. We characterize the measurement perfor-mances by the precision and the spatial resolution of the retrieved geophysical parameters [8][9][13]. Quick tour of AMATERASUe rst version of AMATERASU (V1) uses functions derived from the code MOLIERE [12] to compute the absorption coecient, the radiative transfer for unpolar-ized radiation and the instrumental eects. Each function, implemented in Fortran2000, are compiled into a DLL (Windows) or shared library (Linux, MacOs), and wrapped into python functions using the standard foreign-function library ctypes and the scientic library Numpy (https://numpy.org/). e model is a set of python functions, al-lowing a quick implementation of tools that match the experience specicities (e.g., atmospheric conditions, ob-servation characteristics, retrieval algorithms). Calculations can be performed dynamically in a command line interface or using standalone scripts. e rich set of scientic and plotting libraries available in the python environment can be exploited. Additional functions are also provided to handle atmospheric and observation characteristics (e.g., instrumental eect, spectroscopic parameters, ray-path refraction, hydrostatic equilibrium) as well as the inverse problem.e new functions implemented with TF can be used together with V1 ones. e main motivation for using TF was to use GPUs to boost the calculation runtimes. Figure 5 shows a calculation of the molecular oxygen (O2) line at 773.84 GHz selected for SMILES-2. e LOS tangent height is 100 km and it is measured with a polarized instrument. e molecule of O2 is a magnetic dipole that interacts with the geomagnetic eld (B). e spectral transition is split into the so-called and π Zeeman lines (right panel). ese lines are polarized, and their frequency separation depends 3FiF4 Discretization of the line-of-sight into homogeneous small ranges. Figure taken from [12].110 情報通信研究機構研究報告 Vol. 65 No. 1 （2019）4 衛星センサによる宇宙からの地球環境観測
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