The Radiance Differences between Wavelength and Wavenumber Spaces in Convolving Hyperspectral Infrared Sounder Spectrum to Broadband for Intercomparison

Abstract

Converting the hyperspectral infrared (IR) sounder radiance spectrum to broadband is a common approach for intercomparison/calibration. Usually the convolution is performed in wavenumber space. However, numerical experiments presented here indicate that there are brightness temperature (BT) differences between wavelength and wavenumber spaces in convolving hyperspectral IR sounder spectrum to broadband. The magnitudes of differences are related to the spectral region and the width of the spectral response functions (SRFs). In addition, the central wavelength and central wavenumber should be determined separately in wavelength and wavenumber spaces, respectively; they cannot be converted to each other directly for broadband BT calculations. There exist BT differences (BTDs) between interpolating the resolution of SRF to hyperspectral IR sounder spectrum, and vice versa, for convolution. This study provides clarity on convolution, central wavelength/wavenumber determination, and spectral resolution matching between broadband SRFs and hyperspectral IR sounder radiances for intercomparison/calibration.

Inter‐Calibration of Geostationary Imager Infrared Bands Using a Hyperspectral Sounder on the Same Platform

“…To be more specific, for AGRI, the calibration uncertainty is more relevant to the temperature of scene, and the inconsistency between AGRI and GIIRS BT observations is more noticeable in low temperature scenes (e.g., overcast, high cloud situation). The relatively larger calibration uncertainty in low temperature scenes could be partly attributed to the fact that the nonlinearity of the Planck function for cooler BTs is more significant than for warmer BTs when converting the radiance to BT (Berk, 2008; DeSlover, 1996; Di et al., 2019; Weinreb et al., 1981). Since the GIIRS radiances are spectrally averaged to GIIRS bands by linearly applying SRFs, the nonlinearity might cause uncertainty in the inter‐comparisons when the scene is cold.…”

“…Based on evaluation with forecasts from an NWP model (Liu et al., 2022; Yin et al., 2020), the calibration uncertainty is relatively larger around 750 cm −1 for GIIRS/FY‐4A. Therefore, only AGRI bands 12 (A12) and 13 (A13) are used for inter‐calibration in this study; the GIIRS radiances are spectrally averaged to A12 and A13 using the following formula (Di et al., 2019): $$$\hat{rad}=\frac{\int \nolimits_{\nu 1}^{\nu 2}rad(\nu )f(\nu )d\nu }{\int \nolimits_{\nu 1}^{\nu 2}f(\nu )d\nu }$$$ Where $$\nu $$ is the wavenumber, $$f(\nu )$$ is the corresponding AGRI band SRF; $$rad(\nu )$$ is the GIIRS radiance observation at channel ν, $$\hat{rad}$$ is the convolved AGRI band radiance from GIIRS. Then BT is converted from $$\hat{rad}$$ using the following formula: $$$BT=\left\{\frac{{c}_{2}\ast {\nu }_{c}}{\mathit{ln}\left[1+\left({c}_{1}\ast {\nu }_{c}^{3}\right)/\hat{rad}\right]}-b{c}_{1}\right\}/b{c}_{1}$$$ where $${\nu }_{c}$$ is the central wavenumber of AGRI band; c 1 and c 2 are the Planck ...…”

“…Based on evaluation with forecasts from an NWP model (Liu et al, 2022;Yin et al, 2020), the calibration uncertainty is relatively larger around 750 cm −1 for GIIRS/FY-4A. Therefore, only AGRI bands 12 (A12) and 13 (A13) are used for inter-calibration in this study; the GIIRS radiances are spectrally averaged to A12 and A13 using the following formula (Di et al, 2019):…”

Evaluation of Environmental Moisture from NWP Models with Measurements from Advanced Geostationary Satellite Imager—A Case Study

“…Note the accuracy of surface properties is not important for this typhoon case study because the environment is moist enough to be practically opaque to the surface contributions. Although HIRTM is developed for all-sky hyperspectral IR sounder radiance simulation, it can also be applied for broad band sensor IR band radiance calculations with appropriately applying the imager spectral response functions (SRFs) [26]. The simulated bands in this study are three AHI WV absorption bands (i.e., AHI channel 8 centered at 6.25 µm, channel 9 at 6.95 µm and channel 10 at 7.35 µm) from Himawari-8.…”