A Relaxed Matrix Inversion Method for Retrieving Water Constituent Concentrations in Case II Waters: The Case of Lake Kasumigaura, Japan

The matrix inversion method (MIM) is an effective algorithm for estimating water constituent concentrations in case II waters. To apply this method, appropriate and accurate specific inherent optical properties (SIOPs) for each constituent in water are essential. However, many routine observations of lake water quality do not in fact provide SIOPs, thus limiting the application of the MIM. In this paper, an alternative MIM method based on linear matrix inversion theory was proposed to relax the requirement of SIOPs measurement. For this, so-called ESIOPs (Estimated SIOPs) were first derived by an unusual application of MIM based on adequate calibration samples; then the water constituent concentrations for the whole study area were retrieved by the standard application of MIM based on the derived ESIOPs. For each calibration sample, measurement of the reflectance spectrum and corresponding water constituent concentrations, which can be obtained from periodical satellite data and routine field surveys, is required. The performance of the proposed method was evaluated using the simulation data from Hydrolight and three MEdium Resolution Imaging Spectrometer Instrument (MERIS) images. The results showed that this method yielded satisfactory estimations of the water constituent concentrations for the noise-contaminated simulation data sets. For MERIS data in our study area (Lake Kasumigaura, Japan), the average bias (mean normalized bias or MNB) and relative random uncertainty (normalized root mean square error, or NRMS) were in the range of -11.2% to 3.4% and 4.8% to 29.7% for each water constituent concentration. These findings imply that the algorithm proposed in this study is theoretically reasonable and practically applicable.