Earth is a complex system, and as a result any model that aims to simulate Earth's appearance to a distant observer should reflect this complexity. Our spectral Earth model aims to accurately simulate Earth's disk-integrated spectrum at any arbitrary viewing geometry and wavelength, which necessitates a comprehensive and rigorous treatment of a large number of physical processes (e.g.,
ocean glint, realistic cloud scattering, vertically and spatially resolved temperature, and gas mixing ratio profiles). However, as we have shown, this does not necessarily imply that more simplified models cannot reproduce specific details of Earth's appearance [e.g.,
ocean glint in Williams and Gaidos (2008
)]. In either case, any model of Earth's appearance should be validated against observational data, which ensures its accuracy as a predictive or interpretive tool.
Our new model is capable of reproducing the time variable color and absolute brightness of Earth, as observed in the visible and NIR EPOXI data, and can do so for multiple dates of EPOXI observations. Typical RMS errors for the model lightcurves are within 3–4%, and the 24-hour average visible radiance for the model matches the EPOXI observations to within calibration uncertainties. The model also simultaneously provides a good fit to the shape and absolute brightness of the high-resolution AIRS mid-IR observations.
Although our fit to the lightcurves is generally good (), the largest RMS errors are seen for the 750 and 850
nm filters, which indicates that our poorest match to the shapes of the EPOXI lightcurves occurs at these wavelengths. These filters are relatively clear of atmospheric absorbers and are largely unaffected by the strong Rayleigh scattering seen in bluer filters. As a result, these filters are the most sensitive to the surface, and mismatches in these filters may indicate that more than five surface types are needed to better reproduce the EPOXI data at these wavelengths.
Even though our model reproduces the 24-hour average visible radiance of Earth to within instrument uncertainties (), discrepancies at short wavelengths are typically in the sense of the data being brighter than the model, which suggests either a systematic calibration error or residual minor defects in the model. The difference in the 24-hour average brightness between the data and the model is largest in the 350 and 450
nm filters. A small fraction of the light incident on an ocean surface actually enters the water and is scattered back out (Cox and Munk, 1954
), which is an effect not accounted for in our model. Adding this ocean “volume scattering” behavior to our simulations could improve our fits to Earth's radiance, as water is most transparent in the 350 and 450
Notable disagreements between the model and data in the NIR spectra occurred near 1.4, 1.9, and 4.1μ
m. The 1.4 and 1.9μ
m discrepancies occur at the base of water vapor absorption features, which indicates problems with the input MODIS water vapor distribution data, the HITRAN line lists, and/or the vertical placement of clouds in our model. The height of clouds in the atmosphere controls the column depth of water vapor that is available to absorb radiation incident on the top of the atmosphere. For this reason, low clouds allow a longer column through the atmosphere and more absorption by water vapor in the spectrum than high clouds. MODIS data does not contain a complete description of the full three-dimensional distribution of clouds in Earth's atmosphere, and we must estimate standard altitudes for our liquid and ice clouds. While the altitudes that we assumed seem to offer a reasonably good fit overall to the NIR data, these fits could be improved by allowing our clouds to have a varying vertical distribution that is determined by CloudSat data (Stephens et al., 2002
The disagreement near 4.1μ
m is in the wing of a CO2
absorption feature. Efforts to fit this shape by altering cloud coverage and thickness were unsuccessful. N2
O has a weak absorption feature between 4.0 and 4.1μ
m, but altering atmospheric N2
O levels also failed to reproduce the observed shape. SO2
absorbs in this region, but the strength of this feature is even less than the N2
O feature. It is possible that we are missing a trace gas that absorbs in this region, or that our CO2
linelist is incomplete, although a test in which the more recent HITRAN 2008 database (Rothman et al., 2009
) was used did not improve our fit in this region.
The original version of the model (Tinetti et al., 2006a
) failed to reproduce the observed lightcurves primarily because this version of the model required a less rigorous parameterization of clouds to reproduce limited Earth-observing data sets. Most importantly, this earlier version of the model assumed that all ice clouds were quite thin with an extinction optical depth of order unity, which is true for only ~10% of all ice clouds in the MODIS data. The model presented in this work has a much improved treatment of spatially and temporally varying clouds, and parameterizes them based solely on input data collected from the MODIS instruments. Our cloud parameterization technique is rigorous and versatile, allowing us to reproduce all three sets of EPOXI observations, which span almost three months in time, without needing to tune model parameters to each data set.
In summary, our model is designed to be comprehensive and versatile enough to model Earth's appearance over a very large wavelength range and at arbitrary viewing angle and phase. The level of model complexity required to simulate Earth's spectrum simultaneously over a large wavelength range, where different physical processes dominate, may at first appear daunting, especially if considering the reverse problem of retrieval of the correct planetary characteristics from a limited data set. However, the more optimistic view is that, in cases where a more comprehensive model is required to fit Earth data accurately, this indicates that the data contained enough information to allow us to discriminate the more complex environmental characteristics from more simplistic models. This would be a desirable circumstance when attempting to learn about extrasolar planetary environments from observations. Additionally, in the process of fitting the EPOXI data, we have been able to quantify when model complexity is and is not required for a particular application or wavelength range subset.
For example, modeling moderate resolution NIR spectra does require multiple categories of clouds, providing cloud altitude, phase, and optical thickness resolution. As demonstrated in , a single cloud category produces a disk integrated spectrum that is too bright in the NIR continuum and underestimates water vapor absorption in some regions (near 1.4μ
m) while overestimating water vapor absorption at other wavelength regions (near 1.1μ
m). The lack of ice clouds leads to discrepancies near 1.5μ
m where ice particles absorb. A model with two cloud categories reproduces the spectral data more accurately than the single-cloud model but struggles with the shape of the 1.1 and 1.4μ
m water features. Residuals for the two-cloud model can be over 40% larger than the residuals for the four-cloud model in these regions. The four-cloud model therefore appears to be optimal for simultaneously fitting both the visible and NIR spectral regions and would be most useful for studying the detectability of Earth's globally averaged characteristics for TPF-like designs that span both the visible and NIR.
The absolute brightness and temporal variability of the EPOXI lightcurves can be reproduced by models without a large number of cloud categories due to the broadband nature of these data and the fact that observations at these wavelengths are relatively insensitive to atmospheric absorption. In essence, the broadband lightcurves provide evidence for white, highly reflective structures that vary in time on the planet, and observations in the 950
nm filter demonstrate an absorption feature from water vapor. The higher spectral resolution NIR data provide information regarding the phase and vertical distribution of these structures. Furthermore, insofar as both liquid water and ice clouds are required to reproduce the observations near 1.5μ
m, the broadband data and moderate resolution spectra demonstrate that water is found in the atmosphere as vapor, liquid, and ice.
Sensitivity tests indicate that high atmospheric resolution is not needed to reproduce the EPOXI visible photometric data. This is not surprising, as at visible the temperature structure and distribution of trace gases within the atmosphere should have only small effects on the lightcurves. Even data in the 950
nm filter, which contains a large water vapor absorption feature, can still be fit due to variations in the brightness of the continuum outside the absorption feature and the fact that clouds control the column depth of water vapor that is available to absorb radiation. Earth exhibits large variations in both water vapor mixing ratios and surface temperatures, which indicates that models with low atmospheric resolution are poor choices for modeling high-resolution spectral data or mid-IR data, especially if the model aims to generate observations for arbitrary viewing geometries (e.g.,
polar versus equatorial views).
Reflectance models that ignore scattering and absorption in the atmosphere and treat clouds as Lambertian reflectors cannot reproduce the 24-hour averaged brightness of Earth. The short-wavelength filters have lower reflectivity than the data because Rayleigh scattering has been ignored, while longer-wavelength filters (e.g.,
nm filter, which contains a strong water feature) show enhanced reflectivity because atmospheric absorption has been ignored. Reflectance models can, however, reproduce the shapes of the EPOXI lightcurves as these models are designed to reproduce relative brightness variations due to structures (e.g.,
clouds, continents) rotating into and out of view. While simple, computationally inexpensive models, like reflectance models, may be useful as retrieval tools in scenarios where observational data are limited or of poor quality, these models are not optimal when compared to more rigorous and comprehensive spectral models for applications that require accurate predictions.
Our validated model has a variety of applications. Robinson et al.
) used the model to demonstrate that surface oceans on Earth-like extrasolar planets may be detectable, even after considering the confusing effects of forward scattering from clouds. The Tinetti et al.
) model could not perform such a study, as it did not simulate specular reflection from ocean surfaces; and reflectance models, while excellent at reproducing glint, could not address the important issue of phase-dependent aerosol scattering when investigating the detection of ocean glint in the presence of clouds (Williams and Gaidos, 2008
). Cowan et al.
) used the model presented here to simulate observations of a distant Earth to validate and better understand a retrieval method for exoplanets.
Our comprehensive model is uniquely capable of investigating a variety of Earth's traits over wavelength ranges, synoptic views, and vantage points that are unavailable to Earth-observing spacecraft or satellites. For example, future applications could include model-generated disk-integrated, UV, visible, or IR spectra of Earth for a variety of sub-observer points and phases. These simulated data sets could be used, among other applications, to investigate the wavelength-dependent effect of clouds on our ability to measure thermal radiation from the surface or to simulate Earth as seen from a lunar vantage point over a complete lunar orbit. We could also investigate the effects of an unresolved, airless satellite on the spectrum of its host by pairing our simulations with a model of the spectrum of the Moon. Finally, our Earth model could also be used to generate synthetic observations for “blind” tests of retrieval models, where other individuals or teams attempt to retrieve planetary characteristics without knowing the input to our Earth model (e.g., season, viewing geometry, phase). In general, simulated data can be used to test techniques aimed at characterizing habitable planets that may be employed by TPF-class missions.