Retrieval of Secchi disk depth from a reservoir using a semi-analytical scheme

The mechanistic model reported in Lee et al. (2015) estimating the Secchi disk depth (ZSD) was applied to an oligo- to mesotrophic reservoir in Brazil. The model was originally validated with data covering lake, oceanic, and coastal waters; however, the model used the quasi-analytical algorithm (QAA) designed for optically deep waters as input and was applied to oceanic and coastal waters to derive absorption [a] and backscattering [bb] coefficients. The hypothesis is that the use of QAAv5 (http://www.ioccg.org/groups/Software_OCA/QAA_v5.pdf) to estimate both a and bb (step M1) to retrieve Kd (step M2) and ZSD (step M3) will lead to errors caused by M1 preventing an accurate estimate in oligo- to mesotrophic water. To test this hypothesis, data collected in three field trips were used to apply the mechanistic model based on the spectral bands from OLI/Landsat-8, (often applied to oceanic and coastal waters), and multispectral instrument (MSI)/Sentinel-2 bands (applied to QAA designed for very turbid inland water). The impact of step M1 over steps M2 and M3 was analyzed by the error analysis. The mean absolute percentage error (MAPE) for Kd using QAAv5 ranged between 10.35% and 19.76%, while the error using QAAM14 varied between 12.68% and 28.29%. Regarding the errors of step M3 and applying QAAv5, the total root-mean-square difference (RMSD) varied from 0.55 to 1.18m and MAPE ranged between 12.86% and 31.17%, while the RMSD ranged between 0.70 and 1.50m and MAPE varied from 14.33% to 39.13% when using QAAM14. However, the result from QAAv5 showed a better correlation with in situ data, although underestimating Kd and ZSD. Therefore, a modified version of QAAv5 (QAAR17) was evaluated. The results showed an improvement of Kd (MAPE ranging between 8.89% to 18.76%) and ZSD (RMSD ranging between 0.32 and 0.90m and MAPE ranging between 8.65 and 19.75%), bringing the values close to the 1:1 line. The largest error was observed for the data of the second field trip, where the bio-optical properties showed a horizontal gradient along the reservoir. In addition, the magnitude of the remote sensing reflectance (Rrs) also varied depending on the water quality. Thus, with respect to ZSD mapping, this research showed that environments with a high variability in Rrs can limit the accurate estimation of inherent optical properties (IOPs) based on QAAv5. Therefore, the limiting step of the model was attributed to M1, which means that the mechanistic model from Lee et al. (2015) can be considered an universal approach if M1 is modified based on the type of water.