An Entropy Framework for Evaluating Reflectance Observations for Climate Studies

This study evaluated the comparative entropy represented in shortwave (300-1,750 nm) passive remote sensing measurements from conceptual instruments with varying systematic measurement uncertainties and spectral resolutions. The focus was on spectral and broadband reflectance averaged over large spatial scales typically relevant for climate change studies. Information theory was applied to quantify how the normalized Shannon entropy changed for different conceptual instruments and over different spatial scales. Reflectance measurements from the Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY) were used to represent the observed reflectance, and simulated reflectance from climate Observing System Simulations Experiments (OSSEs) were used to represent decadal- and centennial-length data sets free from instrument artifacts. Similar to previous studies, the simulated OSSE spectra were shown to be a sufficient proxy for the observed reflectance. As hypothesized, the normalized entropy decreased with increasing measurement uncertainty and increasing spectral bandwidth. Additionally, the entropy decreased for increasingly large spatial scales, particularly for measurement uncertainties larger than 2%. When applied to OSSE reflectance simulated from a forced CMIP3 climate model simulation, the change in entropy with measurement uncertainty and spectral resolution provided insight into measurement attributes needed to monitor a changing climate system and highlighted the importance of sufficiently high accuracy and spectral resolution for detecting and attributing climate trends. These preliminary studies illustrate the value of this information theory-based framework in instrument design by calculating the entropy, used to represent information in measurements from different conceptual instruments.