A new k-interval selection technique for fast atmospheric radiance calculation in remote sensing applications

A new technique is proposed to generate the k-interval parameters, including the number of k-intervals, the equivalent absorption coefficients, and the quadrature weights when using the correlated k-distribution method for the computation of spectrally integrated three-dimensional (3D) atmospheric radiance. The main difference between the proposed technique and the traditional exponential sum fitting technique is that only quadrature weights are involved in the optimization process. To avoid the ill-conditioned problem in the proposed technique, the absorption coefficients with high value are dealt with by the delta log(k) (log(k)) technique instead of involving them in the fitting procedure. The performance of the proposed technique is illustrated by radiance calculation results of cloudless and cloudy atmosphere for three different band settings. Results show that there are less relative errors with the proposed optimization technique than with the log(k) technique under the same number of k-intervals. However, as the absorption becomes stronger, the performance of the proposed technique gradually decreases to the log(k) technique. The relative root-mean-square error (RMSE) of radiance for 3D cloudy atmosphere can be controlled in less than 2% when the number of k-intervals is less than 10 particularly for weak absorption band, the RMSEs are less than 1% with only 6 terms.