1e-14 1e-12 1e-10 1e-08 1e-06 0.0001 0.01 1
0.01 0.1 1 10 100 1000
Flux (W m-2 A-1 )
wavelength (micron)
Scaled central star spectra
K-type starSun F-type star
Figure 7.1: High resolution spectra of the three central stars considered. Red shows the spectrum of the Sun, taken from Gueymard (2004). Green shows the spectrum of the K-type star Eridani and blue shows the spectrum of the F-type star σ Bootis, both scaled to a total energy ux of 1366mW2.
Binning of the stellar spectra
For modeling the inuence of the stellar radiation upon an atmosphere, the stellar spectra are binned to the resolution and wavelength range covered by the radiative transfer scheme covering the stellar wavelength regime used in the model. As described in section 5.3.2.1, the 3D model oers the possibility of calculating the radiative transfer in two dierent res-olutions. In the standard RAD4ALL scheme, the stellar radiation is binned in four bands, one spanning the UV and visible wavelengths and three bands covering the near infrared.
The stellar spectra binned to four bands are shown in the upper panel of Fig. 7.2.
For the high resolution radiative transfer scheme FUBRAD (sec. 5.3.2.1), the UV and visible wavelength regime is split into 49 bands and the wavelength coverage is expanded to lower wavelengths, i.e. down to Lyman α instead of 250 nm for the standard scheme.
Therefore dierences in the stellar energy ux distribution are more pronounced in the binned spectra as can be seen in the middle panel of Fig. 7.2.
For comparison with the 1D model, the same stellar spectra are binned according to the wavelength bands in the short-wave radiative transfer in the 1D radiative-convective cli-mate module. As described in section 5.2, the covered wavelengths range from 237 nm to 4.454μm, and are split into 38 bands. The corresponding spectra are shown in the lower panel of Fig. 7.2.
This work mainly applies FUBRAD in the 3D model, which calculates the stellar radiation in 52bands for pressures smaller than 70 hPa (see section 5.3.2.1). For all scenarios no
1e-11 1e-10 1e-09 1e-08 1e-07 1e-06 1e-05
200 300 400 600 800 1000 1500 2000 3000 4000 Fstellar (W m-2 nm-1 )
λ (nm) K-StarSun
F-Star 1e-11
1e-10 1e-09 1e-08 1e-07 1e-06 1e-05
Fstellar (W m-2 nm-1 )
K StarSun F Star 1e-11
Figure 7.2: Spectral energy ux distribution of the three central stars (Sun in red, K-type star in green, F-type star in blue) as considered by the short wavelength radiation schemes in the models.
Upper panel: Binning of the central star spectra into four bands as used in standard RAD4ALL radiative transfer scheme of the 3D model. Middle panel: Binning of the central star spectra into 52 bands as needed for the high resolution radiative transfer scheme FUBRAD of the 3D model.
Lower panel: Binned stellar spectra (38 bands) as used by the short wavelength radiative transfer scheme of the 1D climate model.
scaling of the ux in the Chappuis band is applied, as discussed in Chapter 6.
7.2. 3D MODEL SCENARIOS 111 Table 7.2: Orbital parameters
Star stellar type MStar (MSun) a(AU) P (days)
Eridani K-dwarf 0.856 0.6 184.00
Sun G-dwarf 1.000 1.00 365.25
σ Bootis F-dwarf 1.244 1.89 450.00
7.2 3D model scenarios
The scenarios and the corresponding model inputs for the 3D model are summarized in Table 7.3.
7.2.1 Adjustment of orbit
Clearly, for consistent planetary scenarios in the 3D model the orbital period also has to be adjusted. The orbital periods, hence orbital distances are chosen to obtain a total energy input at the top of the atmosphere (TOA) from the star of one solar constant (1366mW2).
These have been calculated via Kepler's third law (Pa32 =const= M4Starπ2G) from the orbital distances acalculated in sec. 7.1.
P =
4π2
MStarGa3 (7.2)
The resulting orbital distances and periods resulting in an energy input by the star at TOA of one solar constant (1366mW2) are summarized in Table 7.2.
The stellar masses of Eridani and σ Bootis have been taken from Takeda et al. (2007).
Fig. 7.3shows the variation of the incident stellar ux over a time period of ve Earth years and latitude for a planet around the Sun, a K-type and an F-type star. While the planet revolves the K-type star about ten times in ve Earth years, the planet around the F-type star completes only four orbits. The eccentricity and the axial tilt of all scenarios are those of the present Earth.
Figure 7.3: Zonal mean incident radiation (W/m2) at TOA over ve Earth years for planets orbiting dierent types of stars. Left: Sun, Middle: K-type star, Right: F-type star.
Figure 7.4: Earth's ozone climatology by Fortuin and Kelder (1998). Left: Zonal mean ozone concentrations in ppmv for January. Right: Zonal mean ozone concentrations in ppmv for January.
Figure 7.5: Annual mean of the Earth's ozone climatology by Fortuin and Kelder (1998) in ppmv.
7.2.3 Lower boundary
7.2.3.1 Sea surface temperatures
Two dierent setups are chosen concerning the sea surface temperatures (SSTs) and sea ice concentrations. For the investigation of the stellar radiation upon the stratosphere (see sec. 11.1) xed sea surface temperatures and sea ice concentrations are prescribed using
7.2. 3D MODEL SCENARIOS 113 the AMIP II climatology (Taylor et al., 2000), which is derived to obtain observed monthly mean sea surface temperatures for present day conditions.
To study the inuence of the stellar radiation upon the climate, the mixed layer ocean (MLO) model, described in section 5.3.8.6, is coupled to the atmosphere. It calculates the SSTs and the sea ice concentration and depth interactively. The correction uxes (q-uxes) needed to reproduce present day climate are calculated from the reference scenario with solar radiation and xed SSTs, here called sunsst. This is done by the following equation (see also sec. 5.3.8.6).
Q=Hclim−Csw∂Tclim
∂t (7.3)
where Qis the q-ux, Tclim are the xed sea surface temperatures for which the net heat ux Hclim is calculated by the atmosphere model. Csw is the heat capacity of sea water.
These uxes can induce a forcing of the calculated SSTs towards a one Earth year season-ality. This boundary condition is not known for Earth-like planets around dierent types of stars, especially when including a change in the orbital period. Therefore, in this work three sets of q-uxes were used for the calculation of the sea surface temperatures.
q-ux1 These uxes, shown in Fig. 7.6, are calculated as they are used for Earth climate studies by calculating a monthly mean Hclim from a reference scenario with xed sea surface conditions (sunsst). The model then calculates the q-ux for every time step (see Eq. 7.3) by interpolation of the input values (monthly meanHclim and sea surface temperatures). These are used in the scenarios sunmlo, klomloalb and fmlo.
q-ux2 These are calculated as the q-ux1, but with a annual mean Hclim, see Fig. 7.7.
These are introduced to the model for the scenarios sunorb, korb, forb.
q-ux3 These are monthly mean q-uxes calculated oine from the q-ux1. For these no interpolation is carried out, hence they are constant over a period of one Earth month. They are used in the scenarios sunorbmq, korbmq and forbmq.
The annual global mean energy input to the atmosphere by these q-uxes is about 15 Wm−2, which is rather small compared to energy input by the star. Hence, especially the variability will be inuenced by the dierent q-uxes.
The inuence of these q-uxes for the Earth around the Sun are shown in Chapter 8 and discussed for the Earth-like planets around dierent types of stars in Chapter 10.
Figure 7.6: Monthly mean of q-ux1 (mW2) in January (left) and July (right).
Figure 7.7: Monthly mean of q-ux2 (mW2) in January (left) and July (right).