Parameterizing the instrumental spectral response function and its changes by a super-Gaussian and its derivatives

Abstract. The instrumental spectral response function (ISRF) is a key quantity in DOAS analysis, as it is needed for wavelength calibration and for the convolution of trace gas cross sections to instrumental resolution. While it can generally be measured using monochromatic stimuli, it is often parameterized in order to merge different calibration measurements and to plainly account for its wavelength dependency. For some instruments, the ISRF can be described appropriately by a Gaussian function, while for others, dedicated, complex parameterizations with several parameters have been developed.

Here we propose to parameterize the ISRF as a super-Gaussian, which can reproduce a variety of shapes, from point-hat to boxcar shape, by just adding one parameter to the classical Gaussian. The super-Gaussian turned out to describe the ISRF of various DOAS instruments well, including the satellite instruments GOME-2, OMI, and TROPOMI.

In addition, the super-Gaussian allows for a straightforward parameterization of the effect of ISRF changes, which can occur on long-term scales as well as, for example, during one satellite orbit and impair the spectral analysis if ignored. In order to account for such changes, spectral structures are derived from the derivatives of the super-Gaussian, which are afterwards just scaled during spectral calibration or DOAS analysis. This approach significantly improves the fit quality compared to setups with fixed ISRF, without drawbacks on computation time due to the applied linearization. In addition, the wavelength dependency of the ISRF can be accounted for by accordingly derived spectral structures in an easy, fast, and robust way.