Abstract. During spring and summer, melt ponds appear on the sea ice surface in the Arctic and play an important role in sea ice-albedo feedback effect. The melt pond fraction (MPF) can be retrieved using multi-band linear equations, but the calculation is complicated by the ill-conditioned reflectance matrix. In this paper, we calculated the condition numbers which represent the degree of the ill-conditioned reflectance matrix in the results of the MPF from a MODIS-based unmixing algorithm. The condition number is introduced here as a criterion for the sensitivity of the solution in the system to the error in the input value. By combining 3 bands among 5 visible and near-infrared bands of MODIS data, the results show that the three-band combination with the lowest sensitivity to the error of input is B245. To improve the algorithm, we introduce pre-processing to remove open water from the four surface types and then remove one reflectance equation from the original set. The best two-band combination algorithm is B15. Compared with the discrimination results from Landsat5-TM, the RMS is 0.14. This algorithm is applied in pan-Arctic scale, the MPF results are larger than that from University of Hamburg, especially in the Pacific sector.
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