### Radiative forcing

Radiative forcing determines how much the CO2 in the atmosphere increases temperatures. It is a measure of the difference between incoming energy from the sun and the energy radiated back out to space from the earth. Any differ results in temperatures increasing. You can choose how much a given amount of CO2 in the atmosphere increases temperatures by choosing the value of the climate sensitivity. The default value is 3.2, which means that a doubling of atmospheric CO2 produces a 3.2°C temperature increase. more

Radiative forcing quantifies the change in the earth’s energy balance from the addition of greenhouse gasses and other climate forcers to the atmosphere. DICE links the amount of carbon dioxide added to the atmosphere since 1750 to radiative forcing. Radiative forcing is then related to temperature change. This relationship is governed by climate sensitivity. This parameter is a way of representing the equilibrium temperature from doubling the concentration of CO2. The default setting of the model specifies a 3.2°C rise in temperature for a doubling of CO2. The user can set this between 1°C and 5°C.

The relationship between greenhouse gases and radiative forcing $F(t)$ is given by $F(t)=\eta\frac{\ln\left(M_{AT}(t)\right)-\ln\left(M_{AT}^{1750}\right)}{\ln(2)}+F_{EX}(t)$ where $F_{EX}(t)$ represents forcing from gases other than CO2 in time period $t$ and $\eta$ represents the increase in forcing from the doubling of CO2 in the atmosphere. These other forcings are estimated in a given period by a linear function of the difference between forcings from non-CO2 today and an estimate of those forcings in the year 2100: $F_{EX}(t)=F_{EX}(0)+0.1\left(F_{EX}(2100)-F_{EX}(0)\right)\cdot t.$

Radiative forcing leads the warming in the atmosphere, which then warms the upper ocean, gradually warming the deep ocean. The model is: \begin{align*} T(t) & =T(t-1)+\xi_{1}\left[F(t)-\lambda T(t-1)-\xi_{2}\left(T(t-1)-T_{LO}(t-1)\right)\right]\\ T_{LO}(t) & =T_{LO}(t-1)+\xi_{3}\left(T(t-1)-T_{LO}(t-1)\right) \end{align*} where the $\xi_{i}$ are the transfer coefficients reflecting the rates of flow and thermal capacities of the sinks. In particular, $1/\xi_{1}$ is the thermal capacity of the atmosphere and the upper oceans, $1/\xi_{3}$ is the transfer rate from the upper ocean to the deep ocean, and $\xi_{2}$ is the ratio of the thermal capacity of the deep oceans to the transfer rate from the shallow to deep ocean.

The key parameter is $\lambda$, or climate sensitivity, is a way of representing the equilibrium temperature from doubling the concentration of CO2. If we solve the temperature equation for a constant temperature (i.e. equilibrium), we get $\Delta T/\Delta F=1/\lambda$. If $T_{2xCO_{2}}$ is the equilibrium impact of a doubling of CO2 concentrations, we get $T_{2xCO_{2}}=\Delta F_{2xCO_{2}}/\lambda$ where $\Delta F_{2xCO_{2}}$ is the change in radiative forcing from a doubling of CO2. Therefore, setting $\lambda$ allows us to set the climate sensitivity.