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LPSC2008 #2554 SYNTHETIC SPECTRA FROM A GCM SIMULATION OF A MODEL EXO-EARTH.

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LPSC2008 #2554

SYNTHETIC SPECTRA FROM A GCM SIMULATION OF A MODEL EXO-EARTH.

S. I. Ipatov (1) and J. Y-K. Cho (2)

(1) Department of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, D.C. (siipatov@hotmail.com),

(2) Astronomy Unit, School of Mathematical Sciences, Queen Mary, University of London, London, UK (J.Cho@qmul.ac.uk)

This poster can be found on http://www.dtm.ciw.edu/~ipatov/lpsc2008atm.ppt

- The outputs from the general circulation model (GCM) simulations were used to compute model spectra for atmospheres of Earth and exo-Earth rotating with period equal to 1 and 100 days, respectively. The following common features in the synthetic spectra were obtained: (1) both planets have a broad CO_2 absorption band centered around 14 μm; (2) clouds tend to muffle long-wave spectral signatures; (3) there is essentially no difference in the spectra near the equator for an exo-Earth and Earth; however, in some regions (e.g., near the South Pole), there can be a distinguishable difference, indicating that viewing angle matters; (4) when integrated over the planetary disk, the differences in spectral signal observed from different directions are reduced; however, even when integrated signal, differences between Earth and an exo-Earth can still be seen (e.g., spectra at 11 km altitude viewed from directions of South and North Poles are not the same), but the differences are very small if one observes the whole disk from different directions close to the equator. In summary, one-dimensional modeling, which cannot explicitly incorporate circulation, is clearly limited because of anisotropy. Our results suggest that spectral signal cannot be used to infer rotation rate since viewing geometry is in general not known a priori. For observations, our calculations also suggest that ~5-10 and ~13-16 µm bands would be the best wavelength ranges to consider, at least for a model exo-planet which is Earth-like in all respects except for the rotation period. Analyzing spectra at wavelength of about 9.5-10 micron, one can make a conclusion whether an extra-solar planet has ozone or not.

- Several Earth-like planets outside the solar system have recently been detected by S. Udry et al (A&A, 2007,469, L43-L47). Estimated 35% of stars harbor Earth-like planets. Hence, many more are expected to be detected in the near future. To assess the detectability of biosignatures that may be present on these planets, we have performed a series of general circulation model (GCM) simulations of putative “extrasolar Earths”. These planets are identical in all respects to the model Earth, except for different rotation periods. In this work, we use the outputs from the GCM simulations to compute model spectra. Such synthetic spectra can be useful for guiding and interpreting observations.

- The GCM used is CCM3, a global atmospheric model. It is a spectral model that solves the primitive equations. The model includes parameterizations of various important physical processes and boundary conditions such as shortwave and longwave radiation, moist convection, cloud fraction, and land surface types. Temperature-pressure profiles at each grid point over the globe, along with distributions of radiatively active species, are used to generate the spectra off-line.
- For the spectra calculation, we use SBDART, a code that computes plane-parallel radiative transfer in the atmosphere in clear and cloudy conditions (Ricchiazzi et al. BAMS, 1998, 79, 2101-2114). The code solves the radiative transfer equation and is based on a collection of highly developed, reliable physical models.

- We have checked the SBDART code using climatological temperature and species distributions of the Earth (which is also the initial conditions of our GCM simulations) as inputs. We have also checked the code against results described by Ricchiazzi et al. (1998). We analyze the total upward flux at 1 km and 11 km altitudes in the wavelength range between 1 and 18 µm and also between 0.3 and 1 µm. The GCM simulation resolution is T85L19, which corresponds to 128 longitude (0-357 deg) and 64 latitude (from -88 deg to 88 deg) points and 18 layers (pressure levels) over the full globe.
- SBDART is used to compute the mean spectrum for different regions over the model planet. For all regions, we compare the spectra for the initial atmosphere with atmospheres after 2 years of model runs for planets with rotation period P from 0.167 to 100 days. Here we present results from P = 1 and P = 100 cases – “Earth” and “exo-Earth”, respectively. We considered spectra from the common initial condition, Earth, and exo-Earth. SBDART makes calculations of spectrum for one point on the Earth (for a pair of values of longitude and latitude), but it analyses the atmosphere at different heights. Using SBDART as a subroutine, we calculated the mean spectrum for some region on a planet.

- Two models were considered. All calculations of spectra were made for initial state, Earth, and exo-Earth.
- Model 1. Model for which mean radiative flux depends on the area considered, but not on the angle at which we see different parts of this area.
- For model 1 for calculation of the mean radiative flux for some region, the weighting coefficient for one SBDART run is proportional to the area corresponding to the pair (lon, lat) of longitude and latitude. This area is proportional to cos(lat), but did not depend on lon. Model 1 corresponds to the abstract model when one sees all points of considered surface at the same angle. The size of the area corresponding to each pair (lon, lat) is 2.8 deg × 2.8 deg, and this pair shows the center of the region.
- Model 1a. For series of runs 1a, we considered a fixed latitude and all values of longitude (0-360 deg). Different values of latitude (-88 deg [the South Pole], -82 deg, -77 deg, -66 deg, -43 deg, 1 deg [equator], 46 deg, 77 deg, and 88 deg [the North Pole]) were considered.
- Model 1b. For series of runs 1b, we calculated mean values of flux based on SBDART runs for all pairs (lon, lat), i.e., we considered all surface of a planet.
- Model 1c. For model 1c, mean values of flux were based on SBDART runs for the southern hemisphere (-90 deg ≤lat≤0, 0≤lon≤360 deg).
- Model 2. Model for which mean radiative flux depends on the angle at which one sees different parts of this area.
- For model 2, the mean flux is calculated for the case when a half of a planet is observed from some point located far from the planet. In this model we take into account that we see different parts of surface at different angles. If one looks from the equator at lon=lon0, then the total weighting coefficient k for one SBDART run equals to abs(cos(lat)×cos(lat)×cos(lon-lon0)). One cos(lat) is due to that the area corresponding to a single SBDART run is smaller for latitudes close to poles (same as for model 1), and another cos(lat) is due to that one sees areas at different latitudes at different angles. If one looks from a pole, then k=abs(cos(lat)×sin(lat)).

- Below we consider cloud and temperature maps on planets. Cloud coverage was calculated as 1-[(1-CLD1)×(1-CLD2)×...(1-CLD18)], where CLD1,…,CLD18 are values of cloud coverage at 18 different values of height.
- GCM simulations show significant differences in the distribution of fields important for spectra, due to different rotation periods. The differences in the distribution are not simple. For example, the distribution of total cloud (Fig. 1) is fairly zonal for both the Earth and the exo-Earth, but less “banded” on the exo-Earth: three bands in the meridional direction, from the North Pole to the South Pole, are present on the Earth but only one (near the equator) on the exo-Earth with P = 100 days. In the latter planet, the southern polar region is nearly devoid of clouds, and cloud coverage is close to 1 near the equator. For Earth and initial maps, there are a lot of clouds near both poles; for the Earth map there are even less clouds near the equator than at the poles.
- Near the equator the temperature maps (Fig. 2) do not differ much for P=1 day and P=100 days. For exo-Earth, the temperatures T are more uniform than for Earth. For example, for exo-Earth, the region of T>290 K is smaller than that for Earth. For all surface of exo-Earth T>230 K, but there are some regions with T<230 K for Earth. The main difference in T-maps for Earth and exo-Earth is near the South Pole. At the South Pole, the temperature is warmer for exo-Earth than for Earth and initial state. Near the South Pole, the line T=240 K is long for the Earth and is absent for exo-Earth. For initial planet, there was even line T=220 K near the South Pole. The difference between T-maps for exo-Earth and Earth was less than the differences between these maps and the initial T-map. The temperature at the North Pole (265 K) was greater than that at the South Pole.

- Fig. 1. Cloud maps.
- (a) Cloud map for the model Earth case (P=1 day) ;
- (b) Cloud map for the model exo-Earth (P=100 days).

- Fig. 2. Surface temperature maps.
- (a) Surface temperature (K) for the model Earth case (P=1 day).
- (b) Surface temperature (K) for the model exo-Earth (P=100 days).

- Longitudinal averages of outgoing long-wave flux at fixed latitudes (not adjusted for surface element orientation) show that the flux is greatest at the equator and decreases toward the poles on both the Earth and the exo-Earth (Table 1, Figs. 3-4). For model 1a for initial planet, the maximum value Fmax of flux (usually reached at wavelength λ≈10 μm) at the South and North Poles was respectively by a factor of 4 and 1.7 smaller than at the equator. The values of Fmax for initial planet (or Earth, or exo-Earth) almost didn’t depend on lat at lat≤-77deg (Table 1). For the same planet, the values of flux at λ~10-12 μm at lat=-77 deg were greater by a factor of 1.1 than that at the South Pole, and were greater by a factor of 1.05 at lat=77 deg than at the North Pole. For the South Pole, such values were greater for Earth and exo-Earth than for initial state by a factor of 1.3 and 1.7, respectively. For the North Pole, maximum values of flux were close for Earth, exo-Earth, and initial state. For the flux at 1 km, the spectra plots were close for the three planets at -43 deg≤lat≤88 deg.
- For both planets, spectra near the equator (at 1 and 11 km altitudes) at the end of the GCM run duration are essentially the same. Moreover, the spectra are not different from that of the initial state. In contrast, the fluxes of the two planets differ significantly near the poles in the ~5-10 μm and ~13-16 μm bands. The difference is well seen also at latitude lat≤-43 deg and lat≥77 deg. The differences between the fluxes at 11 km and 1 km are smaller if we compare Earth and initial state, than if we compare exo-Earth and initial state. For all plots and h=11 km, there was a local minimum of flux at λ~14-16 μm, and a smaller local minimum at 9.5 μm. All of the above features are primarily due to the different cloud coverage on the exo-Earth compared to that on the model Earth.

- Fig. 3. Spectra (outgoing LW flux) at the equator (model 1a) for two different altitudes, 1 km (upper line) and 11 km (lower line). The spectra is nearly identical for the model Earth case (P=1 day) and the model extrasolar planet (P = 100 days). In the model Earth case, the spectrum is almost same as in the initial state.
- Fig. 4a. Longitudinally averaged spectra at latitude = -77 deg (model 1a) for initial state. The lines are as in Fig. 3.

- Fig. 4b. Longitudinally averaged spectra at latitude = -77 deg (model 1a) for model Earth (P=1 day). The lines are as in Fig. 3. Compare with the spectra at the equator in Fig. 3: the flux is significantly reduced at all wavelengths.
- Fig. 4c. Longitudinally averaged spectra at latitude = -77 deg (model 1a) for model exo-Earth (P=100 days). The lines are as in Fig. 3. Compare with the spectra at the equator in Fig. 4b: absorption in the ~5-10 µm range is significantly reduced, although not in the ~13-16 µm range at 11 km altitude.

- Fig. 5a. Disk-integrated spectra including the weighted contribution of the surface element orientation for Earth (model 2). The planet is seen from the South Pole.
- Fig. 5b. Spectra as in Fig 5a for the exo-Earth.

- Table 1. Maximum flux (in W/m^2/micron) at wavelength about 10-12 micron for several values of latitude (model 1a)
- latitude, deg -88 -82 -77 -66 -43 1 46 77 88
- initial 6.5 8 7.5 13 23 30 25 18 17.5
- earth 9 10 9.5 13.5 23 30 25 18 17.5
- exo-Earth 12 12.5 12.5 14 22 29.5 25 18 17
- Table 2. Maximum flux (in W/m^2/micron) from half of planet surface at wavelength about 10.0-10.4 micron at altitude equal 1 km (maximum values at 11 km are usually smaller by a factor of 1.01-1.02 than those at 1 km) for several directions of view on a planet (model 2)
- South Pole North Pole Equator Equator
- lon=90 deg lon=270 deg
- initial 6.61 8.09 8.27 8.49
- earth 6.63 7.97 8.05 8.31
- exo-Earth 6.61 7.77 8.25 8.09

- For all surface of a planet (model 1b), the plots of flux vs. λ were very close for Earth, exo-Earth, and initial state. The value of Fmax for all surface of the southern hemisphere (model 1c) is about 15 W m^{-2} micron^{-1} and is smaller than that (16 W m^{-2} micron^{-1}) for a whole surface (model 1b) by about 7% (these values are about twice less than those for the equator). It means that there is a difference between plots for the southern and northern hemispheres (e.g., it may be caused by Antarctica). For models 1b and 1c, the differences between values of Fmax for Earth, exo-Earth, and initial planet are smaller (<2%) than that for two hemispheres. Therefore the influence of a line of sight on observed flux can be greater than that of a period of rotation (see also results for model 2). For the southern hemisphere at wavelength about 14-16 μm, the flux at 11 km for exo-Earth was greater by a factor of 1.2 than that for Earth and initial state.
- The maximum value Fmax of flux for spectrum plots is greater for hotter T-regions. Cloud coverage was maximum in a wide region near the equator and it was minimum near the South Pole of exo-Earth. Such peculiarities of cloud coverage may help to understand why differences between the fluxes at 1 and 11 km at the South Pole differ from those at the equator.

- When the influence of viewing geometry is taken into account (model 2), the total flux when the planet is viewed is reduced by a factor of 2 (compared to model 1) since the line of sight is not perpendicular to the surface elements.
- However, the general behavior is not different than that described above, when the flux for each surface element is simply integrated unadjusted for variation in the orientation. This is consistent with the similarity of the spectra in the equatorial region on both planets: areas from the higher latitudes do not contribute significantly.
- The peak values of the spectra (see Table 2) also differ by no more than 5% when the planet is viewed centered at lon = 90 deg or 270 deg with lat = 0 – or from the North Pole (with full longitude range). For the view centered on the South Pole, the peak is smaller by a factor of 1.2 compared to that for the view centered on the North Pole, again showing the asymmetry of the two poles. In the South Pole view, the difference between the fluxes at 11 and 1 km at ~6-8 μm band for the exo-Earth is smaller than that for the Earth (Fig. 5).

- The previous discussion was for analysis of plots with wavelength between 1 and 18 microns. In Fig. 6 we present spectra for wavelength between 0.3 and 0.8 micron for total upward flux at 11 and 1 km. The plot is presented for the North Pole of exo-Earth, but plots for other latitudes (model 1a), Earth, and the initial state look similar to Fig. 6 (e.g., all plots have a local minimum at 0.76 micron). The form of spectrum at 11 km is the same as that at 1 km, but the values are greater by about a factor of 5. Note that at wavelength between 3 and 18 microns, the flux at 11 km always doesn’t exceed that at 1 km.
- At wavelengths less than 1 micron, there are no practically differences for plots for Earth, exo-Earth, and initial state (therefore such wavelengths are not recommended for studies of differences in period of planet rotation). At the equator and the North Pole, the Earth plot could be higher than the exo-Earth plot by not more than 7 %; at the South Pole the difference is smaller (in contrast to larger wavelengths). The difference “Earth – exo-Earth” is greater than the difference “Earth – initial”. For the South Pole, the fluxes could be a few percent smaller than those for the North Pole or for the equator, and plots for the equator could be a little lower than those for the North Pole, the relative difference is greater for 1 km than for 11 km.

- Fig. 6. Spectra (outgoing flux) at the North Pole (model 1a) for two different altitudes, 1 km (lower line) and 11 km (upper line). The plot is for the model of extrasolar planet (P = 100 days), but spectra are nearly identical for the model Earth case (P=1 day) and in the initial state. For such wavelengths, spectra are also similar for different latitudes.
- Fig. 7. Spectra at the North Pole (model 1a) for the model Earth case (P = 1 day) if ozone is absent. The local minimum at wavelength about 9.4-10 micron was absent on plots of total upward flux at 11 km for ozone density equal to 0 though such minimum was on plots for two other models that include ozone (there was no difference in plots for the latter two models).

- Spectrum plots were considered for a model with some distribution of ozone with height and also for a model for which ozone density equaled to 0.00005 g/m^3 at all heights and at all points on surface. The plots for these two models (at wavelengths between 0.3 and 18 microns) practically coincided, and it was not possible to see any difference. It means that the model with a fixed ozone density equaled to 0.00005 g/m^3 can be considered if we do not know exact distribution of ozone.
- We also considered the third model with zero ozone density. For this model, the difference with two other models was only at two wavelength intervals. The local minimum at wavelength about 9.4-10 micron was absent in plots of total upward flux at 11 km for ozone density equal to 0 (Fig. 7) though such minimum was in plots for two other models (for flux at 1 km there was no such difference). At wavelengths less than about 0.35 micron (SBDART does not consider wavelength less than 0.25 micron), there were some differences in plots (both for fluxes at 1 and 11 km) obtained for the model without ozone from the plots for two other models. As ozone is important for life, the interval of wavelengths about 9.4-10 micron may be important for future observations of earth-like planets.

- In this work, we observe the following common features in the synthetic spectra: (1) both planets (Earth and exo-Earth with rotation period equal to 1 and 100 days, respectively) have a broad CO_2 absorption band centered around 14 μm; (2) clouds tend to muffle long-wave spectral signatures; (3) there is essentially no difference in the spectra near the equator for exo-Earth with 100-day rotation period (compared with Earth at P = 1 day); however, in some regions (e.g., near the South Pole), there can be a distinguishable difference, indicating that viewing angle matters; (4) when integrated over the planetary disk, the differences in spectral signal observed from different directions are reduced; however, even when integrated signal, differences between Earth and an exo-Earth can still be seen (e.g., spectra at 11 km altitude viewed from directions of the South and North Poles are not the same), but the differences are very small if one observes the whole disk from different directions close to the equator.
- In summary, one-dimensional modeling, which cannot explicitly incorporate circulation, is clearly limited because of anisotropy. Our results here suggest that spectral signal cannot be used to infer rotation rate since viewing geometry is in general not known a priori. For observations, our calculations also suggest that ~5-10 and ~13-16 µm bands would be the best wavelength ranges to consider, at least for a model exo-planet which is Earth-like in all respects except for the rotation period. Analyzing spectra at wavelength of about 9.5-10 micron, one can make a conclusion whether an extra-solar planet has ozone or not.
- This work was supported by the NASA grant NNG04GN82G.