The radiometric calibration based on pseudo-invariant calibration site (PICS) can calculate the apparent radiance directly by using the reflectance model of top of atmosphere (TOA) established by high precision remote sensing sensors without ground synchronous observation. This enables high precision and high frequency radiometric calibration of optical remote sensing sensors. Currently, the trend in radiometric calibration based on PICS is to relax the stability constraints of the surface and atmosphere to increase the number of stable sites, thereby obtaining more satellite transit frequency and achieving higher frequency on-orbit radiometric calibration. However, current multispectral models can only predict the TOA reflectance of a few channels, limiting the use of the stable site model. In this paper, we present a method for hyperspectral reflectance expansion from multispectral reflectance, which realizes the expansion of the existing multispectral model in spectral dimension. We construct the TOA hyperspectral reflectance model of the East of Dazaohuo stable sites and the West of Xiao Qaidam Lake stable sites. Compared with the multispectral model, the precision of the TOA hyperspectral reflectance model in the original five channels is not significantly reduced and can provide on-orbit radiometric calibration service for optical sensors in transit of 400?2500 nm.

The GF5B/AHSI is a hyperspectral sensor with 330 imaging channels covering the 400?2500 nm band range, and its historical spectrum over the stable sites remains stable (Fig. 2). In our paper, the mean value of its historical data is selected as the reference TOA reflectivity spectrum. Assuming a linear relationship between the ratio of TOA hyperspectral reflectance to its corresponding channel reflectance, the reference spectrum is normalized to the spectral responses of moderate-resolution imaging spectroradiometer (MODIS) as equivalent channel reflectance to have a uniform scale within the model. Subsequently, information on solar attitude, observation attitude and day of year (DOY) is extracted, and the channel TOA reflectance over the transit stable sites is predicted by the multispectral model. Then, the ratio of TOA channel reflectance to equivalent channel reflectance during satellite transit is calculated, linearly interpolated across the spectral band as a spectral scaling factor, and applied to scale the reference spectrum. This process realizes the spectral dimension expansion of the model and constructs the TOA hyperspectral reflectance model of the stable sites.

Landsat8/OLI data from 2013 to 2021 and Sentinel2/MSI data from 2018 to 2021 are used to verify the proposed method. The results show an average relative difference between the model’s predicted values and the satellite’s observed values of no more than ±4%, with a root mean square error (RMSE) of each band of no more than 1.5% (Table 2, Table 3). Compared with the TOA multispectral model, the average relative difference of the blue wave segment based on Sentinel2/MSI data increases from -1.02% to -1.61%, and the RMSE from 0.36% to 0.42%. The average relative difference of the shortwave infrared band increases from -0.12% to -0.94%, and the RMSE from 0.61% to 0.68%. The precision of the other three bands is consistent with that of the multispectral model, indicating that the precision of the method in the original several channels is not significantly reduced. At the West of the Xiao Qaidam Lake site, the average relative difference between the model-predicted value and the satellite-observed value is less than ±3.1%, with an RMSE for each band of less than 1.1% (Table 6, Table 7). The verification results of the two stable site models show that the predicted values of TOA hyperspectral reflectance of the stable sites maintain high consistency with the satellite observation values. Meanwhile, the model also analyzes the uncertainty of the calibration result based on the calibration process of GF6/WFV sensors. The uncertainty of eight bands of GF6/WFV is less than 4.5%, which is 0.49% lower than the average uncertainty of the original multispectral reflectance model.

In this paper, we present a method for hyperspectral reflectance expansion from multispectral reflectance, utilizing the mean value of GF5B/AHSI data as the reference spectrum and normalizing it to the MODIS spectral response as equivalent channel reflectance. The channel TOA reflectance over the transit stable sites is predicted by the multispectral model. Then, the ratio of TOA channel reflectance to equivalent channel reflectance during satellite transit is calculated, and the ratio is linearly interpolated across the spectral band as a spectral scaling factor. This factor is then used to scale the reference spectrum, realizing the spectral dimension expansion of the model. In our study, Sentinel2/MSI data and Landsat8/OLI data are used to evaluate the precision of the East of Dazaohuo and West of Xiao Qaidam Lake sites. The results demonstrate high agreement between the model’s predicted values and satellite observation values. The precision across each band of the model is similar, indicating that the model’s precision itself can remain stable. Based on the calibration process of GF6/WFV sensors, an uncertainty analysis of model calibration results is conducted. The uncertainty of eight bands of GF6/WFV sensors is less than 5.4%, further verifying the reliability of the model. The uncertainty analysis of the calibration results helps characterize the uncertainty of the calibration results and ensures consistency and traceability of satellite sensors calibration results. In future studies, the TOA hyperspectral reflectance model can also generate time series calibration results for satellite sensors, providing long-term trend information for individual sensors. Moreover, based on multiple stable site models, multi-site calibrations can also be performed to further improve the on-orbit calibration frequency of sensors, which is significantly important for the commercial calibration of domestic satellite sensors.