A Multi-Channel Calibration method for Multi-Filter Rotating Shadow-band Radiometer

In order to improve the accuracy of solar radiation related parameters' for crop modeling, a new calibration method (Multi-Channel Calibration) for Multi-Filter Rotating Shadow-band Radiometer (MFRSR) is proposed. It uses the Angstrom Law that links aerosol optical depth (AOD) at multiple wavelengths as the primary constraint. It also uses the bi-channel Langley Regression to provide an additional constraint. Starting with any initial guess of calibration coefficient (V₀) at 870 nm, two consecutive steps, both involves calling trust region based non-linear optimization module (CONDOR), are implemented to solve (1) the intermediate parameter Angstrom coefficient and the set of biased V_0s at other channels corresponding to the initial one at 870 nm channel; and (2) the final V_0s of all permissible channels. The result shows that Unlike Langley method, the Multi-Channel Calibration method return V₀ at all permissible channels. Besides, the new method can converge to the same (less than 0.5%) final V_0s with the starting guess in a wide range. Most important, the comparison between AODs derived from those final V_0s and those of AERONET sunphotometers suggests the upper limit of the error of those final V_0s is less than 1.03%, which is a great improvement over the Langley V_0s (7.45%).