Optimal Solar Zenith Angle Definition for Combined Landsat-8 and Sentinel-2A/2B Data Angular Normalization Using Machine Learning Methods

Data from Landsat-8 and Sentinel-2A/2B are often combined for terrestrial monitoring because of their similar spectral bands. The bidirectional reflectance distribution function (BRDF) effect has been observed in both Landsat-8 and Sentinel-2A/2B reflectance data. However, there is currently no definition of solar zenith angle (theta(sz)) that is suitable for the normalization of the BRDF-adjusted reflectance from the three sensors' combined data. This paper describes the use of four machine learning (ML) models to predict a global theta(sz) that is suitable for the normalization of bidirectional reflectance from the combined data in 2018. The observed theta(sz) collected globally, and the three locations in the Democratic Republic of Congo (26.622 degrees E, 0.356 degrees N), Texas in the USA (99.406 degrees W 30.751 degrees N), and Finland (25.194 degrees E, 61.653 degrees N), are chosen to compare the performance of the ML models. At a global scale, the ML models of Support Vector Regression (SVR), Multi-Layer Perception (MLP), and Gaussian Process Regression (GPR) exhibit comparably good performance to that of polynomial regression, considering center latitude as the input to predict the global theta(sz). GPR achieves the best overall performance considering the center latitude and acquisition time as inputs, with a root mean square error (RMSE) of 1.390 degrees, a mean absolute error (MAE) of 0.689 degrees, and a coefficient of determination (R-2) of 0.994. SVR shows an RMSE of 1.396 degrees, an MAE of 0.638 degrees, and an R-2 of 0.994, following GPR. For a specific location, the SVR and GPR models have higher accuracy than the polynomial regression, with GPR exhibiting the best performance, when center latitude and acquisition time are considered as inputs. GPR is recommended for predicting the global theta(sz) using the three sensors' combined data.

Automated summary

This study utilizes machine learning models to predict a global solar zenith angle suitable for the normalization of reflectance in 2018, and compares the performance of different models at a global scale and at three specific locations.