The climate system model is basically our "energy balance" Model B, plus a model for the emissivity of the atmosphere based on the amount of water vapor and carbon dioxide it contains. Unline Model B, the climate system model includes some of the key feedbacks in the climate system, such as ice-albedo, cloud-albedo, and water vapor-temperature. It also takes into account anthropogenic carbon release and carbon uptake by the biosphere and oceans.
The climate system is always in radiative equilibrium in the model, i.e. the solar energy absorbed at the surface is equal to the longwave energy emitted to space by the atmosphere and ground. However, the exact nature of the energy balance (i.e. the emissivity, albedo, and surface temperature) may vary from year to year in response to changes in the external forcings and changes in the model itself. This feature will allow you to determine not only the "equilibrium" climate under a new combination of the model parameters, but also how long it will take the system to reach this new state.
When you are working with the model, keep in mind that the difference between the global mean surface temperature today versus the last Ice Age maximum is thought to be about 5 degrees Celsius.
So*(1-alpha) --------------------- = Tg^4 (1) 4*sigma*(1-epsilon/2)Here, So is the solar constant (which you can control directly), and alpha and epsilon are the albedo and bulk emissivity of the atmosphere, respectively.
We will (rather crudely) treat epsilon as the sum of the emissivities of the two major greenhouse gases, water vapor (H2O) and carbon dioxide (CO2):
epsilon = epsilon{CO2} + epsilon{H2O} (2)
The values for the emissivities of these gases, and for the planetary albedo,
are determined by the functional relationships and feedbacks discussed below.
change in C -------------- = F - gamma*(C-Co) - beta*(C-Co) (3) change in timewhere Co is the preindustrial amount of carbon in the atmosphere (which is set at 280 ppm for all runs), F is an anthropogenic input rate, gamma determines the carbon flux between the atmosphere and the ocean based on the difference between C and Co, and beta determines the carbon flux between the atmosphere and the biosphere. In this model, all of the anthropogenic carbon release must be accounted for by either uptake by the biosphere or an increase in the amount of carbon in the atmosphere.
You have direct control over Co and F in the model, and beta will be discussed below in section 4c (for now you can assume it's a constant). The uptake by the ocean (gamma) is assumed to be independent of everything except (C-Co). Note that the model does not account for the uptake of carbon by the carbon-silicate cycle, because this occurs on extremely long timescales. Also note that if C = Co AND the anthropogenic forcing is zero, then the concentration of carbon in the atmosphere will remain fixed (at Co).
epsilon{CO2} = A + B*ln(C/Co) (4)
Here A and B are just numbers, and all the other symbols have been defined
above. The coefficients A and B are different from the numbers you were
given in homework #3, because here we are treating carbon dioxide and
water vapor independently.
Note that equation (4), unlike equations (2) and (3), is strongly nonlinear,
so that a small increase in carbon could lead to a small increase in emissivity
or a very large increase in emissivity, depending on the current value of
epsilon{CO2}.
Note that the carbon dioxide emissivity, as determined by equations (2), (3), and (4) above, is independent of the ground temperature. However, if the biological carbon sink depends on the surface temperature (i.e. if beta is a function of temperature), then carbon dioxide will also be part of a feedback loop in the model. This option is discussed in section 4c.
epsilon{H2O} = function of Tg (5)
The details of this relationship are rather messy, although you should know
from your first lab assignment that the greenhouse effect of water vapor
is basically constant at low temperatures, increases rapidly at intermediate
temperatures, and reaches a maximum value at around 30 degrees Celsius.
Two things occur at high
temperatures which cause the relationship to break down: the atmosphere becomes
"optically saturated" with respect to water vapor, and the high concentration
of water vapor in the atmosphere causes clouds to form. The first effect is
accounted for in our "function of Tg" above; the second effect is accounted
for in the "cloud-albedo feedback" below.
However, the amount ice (or snow) cover and cloud cover depends on the ground temperature, with lower temperatures leading to higher snow and ice cover, and higher temperatures leading to higher cloud cover (due to enhanced evaporation, as discussed above). Thus the albedo of the planet is a function of its surface temperature, with the highest albedo values corresponding to temperatures that are significantly warmer or colder than the present value.
We will model these feedbacks as follows:
alpha = function of Tg (6)Here, alpha will increase if the ground temperature gets lower or higher than its present value. It is assumed that the albedo will increase gradually at first, then get stronger as the ground temperature deviates farther from the present value, until at really cold or really warm temperatures, the planetary albedo reaches its maximum possible value (representing either an ice-covered or cloud-covered planet).
In addition to specifying the "baseline" planetary albedo in the model, you may choose to have one, both, or neither of these feedbacks active. The exact functional form of the albedo versus the surface temperature will be displayed when you run the model.
beta = function of Tg (7)In this function, the removal rate of carbon by the biosphere approaches zero when the temperature gets either extremely warm or extremely cold, and the optimal climate for the biota (hence, the highest removal rate) is for temperatures near 15 degrees Celcius. (Note that we have "swept a lot under the rug" with this feedback.) The exact nature of the "function of Tg" will become apparent when you use the model, and you can choose to have this "beta" feedback inactive, active but weak, or active and strong.
To run the climate system model you will have to submit a form from the webpage. This form will include your selection for the values of key parameters (So, Co, F, etc.) and your choice of model functions (e.g. albedo type, biota type, etc.).
The results will be displayed on your screen. A new page will come up with eight plots on it. The first four plots (all in a line) are just to remind you of the exact nature of the climate model that you're working with and the values for the solar constant and other parameters that you have chosen. The next four plots show the temporal evolution of some key variables in your climate model. These include the evolution of ground temperature, atmospheric CO_2 concentration, albedo and emissivity, and the rate which carbon is being removed by the biosphere.