Inferring and Interpreting the Visual Geometric Albedo and Phase Function of Earth

TL;DR

This paper delivers a definitive measurement of Earth's visual geometric albedo $A_g$ and characterizes its phase function by combining a curated, phase-resolved broadband visual dataset with a physically motivated, statistical forward model that includes Lambertian surfaces, ocean glint, Rayleigh scattering, thick clouds, aerosols, and ozone absorption. The analysis yields $A_g = 0.242^{+0.005}_{-0.004}$, spherical albedo $A_s = 0.294^{+0.002}_{-0.002}$, and phase integral $q = 1.22^{+0.02}_{-0.03}$, with band-specific albedos provided in $B$, $V$, and $R$ bands; models including clouds and aerosol forward scattering best reproduce Earth’s crescent-phase brightness. A key finding is that aerosol forward scattering can mimic ocean glint, producing a false negative for surface habitability in optical phase curves, and that redder or near-infrared observations, possibly with polarization, are needed to disentangle ocean signatures from aerosol effects. The work demonstrates a practical analytic two-parameter surrogate for Earth’s phase curve and provides a framework for applying phase-curve retrievals to exoplanets, contributing to mission planning and interpretation of directly imaged Earth-like worlds.

Abstract

Understanding reflectance-related quantities for worlds enables effective comparative planetology and strengthens mission planning and execution. Measurements of these properties for Earth, especially its geometric albedo and phase function, have been difficult to achieve due to our Terrestrial situation -- it is challenging to obtain planetary-scale brightness measurements for the world we stand on. Using a curated dataset of visual (0.4--0.7 um) phase-dependent, disk-averaged observations of Earth taken from the ground and spacecraft, alongside a physical-statistical model, this work arrives at a definitive value for the visual geometric albedo of our planet: $0.242^{+0.005}_{-0.004}$. This albedo constraint is up 30--40% smaller than earlier, widely-quoted values. The physical-statistical model enables retrieval-like inferences to be performed on phase curves, and includes contributions from optically thick clouds, optically thin aerosols, Rayleigh scattering, ocean glint, gas absorption, and Lambertian surface reflectance. Detailed application of this inverse model to Earth's phase curve quantifies contributions of these different processes to the phase-dependent brightness of the Pale Blue Dot. Model selection identifies a scenario where aerosol forward scattering results in a false negative for surface habitability detection, which implies that aerosol forward scattering can effectively mimic an ocean glint signature in broadband visual phase curves. Observations of phase curves for Earth at redder-optical or near-infrared wavelengths could disentangle ocean glint effects from aerosol forward scattering. Finally, a review of albedos and planetary photometry is provided as well as a simple two-parameter fit to Earth's visual phase curve to ease adoption into other tools.

Figures (17)

• Figure 1: Phase-dependent measurements of Earth's broadband visual (0.4--0.7 $\upmu$m) apparent albedo, including historic observations from danjon1928. Mission or observing technique is indicated by datapoint color and shape. Uncertainties are indicated, which are sometimes smaller than the point size. As a reminder, the geometric albedo is equal to 2/3 of the apparent albedo at full phase.
• Figure 2: Schematic demonstrating how the adopted variability model parameterizes a variability-driven apparent albedo spread as a function of phase angle. Key parameters are the fractional variability ($\Delta \ln A$), the variability breakpoint phase angle ($\alpha_{0}$), and the high-phase variability power law index ($n$).
• Figure 3: Comparison between the phase- and wavelength-dependent parametric model developed in this work (dashed) to high-fidelity simulated Earth spectra from the Virtual planetary Laboratory Three-Dimensional Spectral Earth Model robinsonetal2010. Crescent- (red) and gibbous-phase (blue) spectra are shown, and the spectral range highlights the visual band. The simple model sufficiently reproduces results from the high-fidelity tool.
• Figure 4: Visual band phase curves, shown as apparent albedo, demonstrating the phase-dependence of the various components of the model developed in this work. Earth phase curve data from Figure \ref{['fig:earth_data']} are shown as points for comparison. Component phase curves do not include a spatial weighting for coverage on the disk, and the Rayleigh curve is for Rayleigh scattered light that has not been also reflected by the surface.
• Figure 5: Data-model comparisons for best-fitting models from case numbers 02 (left), 05 (middle), and 07 (right), with components as given in Table \ref{['tab:models']}. All models reproduce the phase curve observations well with reduced chi-squared values very near to unity. As a reminder, the geometric albedo is equal to 2/3 of the apparent albedo at full phase.