### Climate model

webDICE includes a model of how emissions of CO_{2} affect
temperatures. The model has two components. The first is how carbon
moves around the earth, between the oceans and the atmosphere. This
component determines long emissions of CO_{2} stay in the
atmosphere. The second is how the emissions that stay in the atmosphere
increase temperatures. This latter component is called
radiative forcing.

The model of how emission move around the earth assumes that emissions from economic activity are released into the atmosphere. Some of these emissions are absorbed by the upper layers of the ocean and from there into the lower ocean. The rate of absorption into the upper and lower ocean determines how long emissions stay in the atmosphere. There are no parameters choices for the climate model, but in Advanced Move, you can choose the default model, which is used in Nordhaus’s DICE models, or the ‘BEAM, simplified‘ model, which is a more accurate but slightly slower running model. (Optimization using BEAM may be particularly slow and possibly time out.) more

The default climate model in DICE simulates the carbon cycle using
a linear there-reservoir model where the three reservoirs are the
deep oceans, the upper ocean and the atmosphere. Each of these reservoirs
is well-mixed in the short run. A transition matrix governs the transfer
of carbon among the reservoirs. If $M_{i}(t)$, is he mass of carbon
(gigatons) in reservoir $i$, then:
\[
\left[\begin{array}{c}
M_{AT}(t)\\
M_{UP}(t)\\
M_{LO}(t)
\end{array}\right]=\left[\begin{array}{ccc}
\phi_{11} & \phi_{12} & 0\\
1-\phi_{11} & 1-\phi_{12}-\phi_{32} & \phi_{23}\\
0 & \phi_{32} & 1-\phi_{23}
\end{array}\right]\left[\begin{array}{c}
M_{AT}(t-1)\\
M_{UP}(t-1)\\
M_{L0}(t-1)
\end{array}\right]+\left[\begin{array}{c}
E(t-1)\\
0\\
0
\end{array}\right],
\]
where the parameters $\phi_{i,j}$ represent the transfer rate from
reservoir $i$ to reservoir $j$ (per time period), and $E(t)$ is
emissions at time $t$. The model only includes CO_{2} in its
emissions factor and atmospheric carbon concentration. Other greenhouse
gases are assumed to be exogenous and enter the
forcing equation
separately.