Rapid, accurate computation of narrow-band sky radiance in the 940 nm gas absorption region using the correlated k-distribution method for sun-photometer observations

Abstract

Abstract We developed lookup tables for the correlated k-distribution (CKD) method in the 940 nm water vapor absorption region (WV-CKD), with the aim of rapid and accurate computation of narrow-band radiation around 940 nm (10,000–10,900 $${\mathrm{cm}}^{-1}$$ cm - 1 ) for ground-based angular-scanning radiometer data analysis. Tables were constructed at three spectral resolutions (2, 5, and 10 $${\mathrm{cm}}^{-1}$$ cm - 1 ) with quadrature values (point and weight) and numbers optimized using simulated sky radiances at ground level, which had accuracies of ≤ 0.5% for sub-bands of $$10 {\mathrm{cm}}^{-1}$$ 10 cm - 1 . Although high-resolution WV-CKD requires numerous quadrature points, the number of executions of the radiative transfer model is reduced to approximately 1/46 of the number used in the line-by-line approach by our WV-CKD with a resolution of 2 $${\mathrm{cm}}^{-1}$$ cm - 1 . Furthermore, we confirmed through several simulations that WV-CKD could be used to compute radiances with various vertical profiles. The accuracy of convolved direct solar irradiance and diffuse radiance at a full width at half maximum (FWHM) of 10 nm, computed with the WV-CKD, is < 0.3%. In contrast, the accuracy of convolved normalized radiance, which is the ratio of diffuse radiance to direct solar irradiance, at an FWHM of 10 nm computed with the WV-CKD is < 0.11%. This accuracy is lower than the observational uncertainty of a ground-based angular-scanning radiometer (approximately 0.5%). Finally, we applied the SKYMAP and DSRAD algorithms (Momoi et al. in Atmos Meas Tech 13:2635–2658, 2020. https://doi.org/10.5194/amt-13-2635-2020 ) to SKYNET observations (Chiba, Japan) and compared the results with microwave radiometer values. The precipitable water vapor (PWV) derived with the WV-CKD showed better agreement (correlation coefficient γ = 0.995, slope = 1.002) with observations than PWV derived with the previous CKD table (correlation coefficient γ = 0.984, slope = 0.926) by Momoi et al. (Momoi et al., Atmos Meas Tech 13:2635–2658, 2020). Through application of the WV-CKD to actual data analysis, we found that an accurate CKD table is essential for estimating PWV from sky-radiometer observations.

Keywords

• Atmospheric gas absorption
• Correlated k-distribution
• Radiative transfer