An Accurate Method for Correcting Spectral Convolution Errors in Intercalibration of Broadband and Hyperspectral Sensors
Authors: Wu Wan , Liu Xu , Xiong Xiaoxiong , Li Yonghong , Yang Qiguang , Wu Aisheng , Kizer Susan , Cao Changyong 
Published: August 2018

The intercalibration between a broadband and a hyperspectral satellite Earth observation system requires the convolution of the hyperspectral data with the spectral response functions (SRFs) of the corresponding broadband channels. There are two potential issues associated with the convolution procedure. First, the finite resolution of a hyperspectral spectrum, that is, the deviation from the highly accurate line‐by‐line monochromatic radiances, will contribute to convolution errors. The magnitude of the errors depends on the spectral resolution and the SRF shape of the hyperspectral instrument. This type of the convolution error has not been well recognized, and there is a lack of corresponding discussion in most published papers. Although it is small as compared with the instrument accuracy of existing hyperspectral sounders, the error is deemed to be significant when it is compared with the stringent calibration requirement imposed by future climate missions like the Climate Absolute Radiance and Refractivity Observatory. Second, some broadband channels are insufficiently covered by the hyperspectral data, causing spectral gaps that lead to convolution errors. Although several methods have been developed to fill the spectral gaps and hence compensate for the second type of convolution error, the correction accuracy may still need improvement especially when a large spectral gap needs to be filled. This paper presents a methodology to accurately quantify and compensate for both types of convolution errors. This methodology utilizes the available hyperspectral information to correct the scene‐dependent convolution errors due to either the limited spectral resolution or spectral gaps. We use simulations to characterize the intercalibration errors between the Moderate resolution Imaging Spectroradiometer (MODIS) and current operational infrared sounders. We demonstrate that convolution errors can be effectively removed to meet the highly accurate intersatellite calibration requirement proposed by the Climate Absolute Radiance and Refractivity Observatory. Our methodology is also validated using real satellite data for the intercalibration between Aqua MODIS and Aqua Atmospheric Infrared Sounders (AIRS). Our study demonstrates that the accurate characterization and correction for the convolution errors greatly reduces the scene‐dependent and spectrally dependent errors, being critical to the consistency check between Infrared Atmospheric Sounding Interferometer (IASI) and AIRS using the double‐difference method. The convolution correction also facilitates the evaluation for other intercalibration errors (e.g., the drift of MODIS SRFs). Our derived SRF shift values from MODIS‐AIRS (after convolution error corrections) and from MODIS‐IASI intercalibration are consistent with each other. We further extend the methodology to study the calibration of a broadband channel which is either completely or largely uncovered by a hyperspectral measurement. The large spectral gap filling methodology is validated by demonstrating the accurate prediction of the MODIS radiance of band 29 using the Cross‐track Infrared Sounder spectra, with the real IASI spectral data being used as the reference.