Towards global long-term water transparency products from the Landsat archive

Secchi Disk Depth (Z(sd)) is one of the most fundamental and widely used water-quality indicators quantifiable via optical remote sensing. Despite decades of research, development, and demonstrations, currently, there is no operational model that enables the retrieval of Z(sd) from the rich archive of Landsat, the long-standing civilian Earth-observation program (1972 - present). Devising a robust Z(sd) model requires a comprehensive in situ dataset for testing and validation, enabling consistent mapping across optically varying global aquatic ecosystems. This study utilizes Mixture Density Networks (MDNs) trained with a large in situ dataset (N = 5689) from 300+ water bodies to formulate and implement a global Z(sd) algorithm for Landsat sensors, including the Thematic Mapper (TM), Enhanced Thematic Mapper Plus (ETM+), and Operational Land Imager (OLI) aboard Landsat-5, -7, -8, and -9, respectively. Through an extensive Monte Carlo cross-validation with in situ data, we showed that MDNs improved Z(sd) retrieval when compared to other commonly used machine-learning (ML) models and recently developed semi-analytical algorithms, achieving a median symmetric accuracy (epsilon) of similar to 29% and median bias (beta) of similar to 3%). A fully trained MDN model was then applied to atmospherically corrected Landsat data (i.e., remote sensing reflectance; R-rs) to both further validate our MDN-estimated Z(sd) products using an independent global satellite-to-in situ matchup dataset (N = 3534) and to demonstrate their utility in time-series analyses (1984 - present) via selected lakes and coastal estuaries. The quality of R-rs products rigorously assessed for the Landsat sensors indicated sensor-/band-dependent epsilon ranging from 8% to 37%. For our Z(sd) products, we found epsilon similar to 39% and beta similar to 8% for the Landsat-8/OLI matchups. We observed higher errors and biases for TM and ETM+, which are explained by uncertainties in R-rs products induced by uncertainties in atmospheric correction and instrument calibration. Once these sources of uncertainty are, to the extent possible, characterized and accounted for, our developed model can then be employed to evaluate long-term trends in water transparency across unprecedented spatiotemporal scales, particularly in poorly studied regions of the world in a consistent manner.