6.4 Albedo and ice sheets

6.4.1 Albedo as a function of ice sheet extension

In nature, the planetary albedo mainly depends on the ice extent, cloud cover and land surface properties.

In SimClimat, only the effect of ice sheet extent is taken into account. The albedo is calculated as a function of ice sheet extent $phi_{g}(t)$ by a piece-wise linear function. The albedo is bounded between the albedo of the ice (taken at 0.9) and the albedo of the Earth without ice, taken at 0.25. This formulation of the albedo as a function of the latitude of ice sheets, which itself depends on the temperature (section 6.4.2, explains the shape of the $F_{in}$ curve (the solar energy absorbed by the Earth) as a function of temperature in figure 8.

6.4.2 Ice sheet extent as a function of temperature and of summer insolation at 65°N

The latitude of the ice sheets is in degrees of latitude. It is calculated as a function of global temperature and of the summer insolation at 65°N, $I$ (in order to take into account the variations of orbital parameters).

We calculate the ice sheet extent at equilibrium $phi_{g}^{eq}$:

$$phi_{g}^{eq}=acdot T+b+ccdot(I-I_{actuel})$$

$I$ is calculated as a function of the solar constant, eccentricity, obliquity and precession (section 6.4.3).

The parameters $a$, $b$ and $c$ are tuned to satisfy the constraints summarized in section 2.1: $a$=0.73, $b$=49.53 and $c$=0.2.

The ice sheets respond to climate forcing with a time scale $tau_{g}$= 3000 years. To represent this effect, the ice sheet latitude $phi_{g}(t)$ is calculated as a function of $phi_{g}(t-dt)$ assuming that $phi_{g}(t)$ tends towards $phi_{g}^{eq}$ with the time constant $tau_{g}$:

$$phi_{g}(t)=phi_{g}(t-dt)+left(phi_{g}^{eq}-T(t-dt)right)left({1-e}^{^{-dt/tau_{g}}}right)$$

6.4.3 Summer insolation at 65°N

The summer insolation at 65°N, $I$, is calculated as a function of the solar constant $S_{0}$, eccentricity $x$, obliquity $o$ and precession $p$ following this formula:

$$I=frac{S_{0}}{4}cdot cosleft(frac{(65-o)cdotpi}{180}right)*l... ...ht)}{1-frac{x}{2}*sinleft(frac{-pcdotpi}{180}right)}right)^{2}$$

where $x_{actuel}$ and $p_{actuel}$ the present-day eccentricity and precession. Angles $o$ and $p$ are given in °.