Propagation of sensor noise in oceanic hyperspectral remote sensing

In previous works, the authors have shown via numerical simulation that sensor noise, even assuming otherwise perfect knowledge of the environment, can cause large scale variations in the retrieval of concentrations of biophysical parameters in a water body, and also investigated methods for using statistical measures (such as the Mahalanobis distance) to help mitigate these issues. In this work, we derive explicit formulas that can be used to estimate how uncertainty in the sensor radiance is propagated to uncertainty in the remote sensing reflectanceR_rs(λ), without the need for simulations. In particular, the formulas show that the variation in R_rs(λ)is affected by not only the noise characteristics of the sensor, but also by the conditions (atmospheric parameters, viewing angles, altitude) under which the data is collected. We include validation results for the formulas over a wide range of atmospheric conditions, and show by example how the collection conditions can affect the uncertainty in R_rs(λ).