I am trying to understand climate tipping points better and I am looking for a place to ask the following question. If Earth Science SE isn't the right place, a recommendation of a better place would be welcome.

Let me refer to the paper Analysis and Predictability for Tipping Points with Leading-Order Nonlinear Terms and consider the dynamical system described by this set of stochastic differential equations:

$$\dot{T} = f(C,\dot{C}) + \sigma(T)\cdot\dot{W}$$

$$\dot{C} = g(T) + \varepsilon$$

with $T$ the mean global temperature, $C$ the mean concentration of atmospheric carbondioxide, $\sigma$ the $T$-dependent noise level, $W$ a one-dimensional Brownian motion, and $\varepsilon$ the (small) anthropogenic increase of atmospheric carbondioxide.

The function $f(C,\dot{C})$ captures the increase of $T$ by increasing $C$. When doubling of $C$ compared to $C_0 = 200\ \textsf{ppm}$ in 1850 or so results in an increase of $T$ by $3°C$, $f(C,\dot{C})$ takes the form

$$f(C,\dot{C}) = 3\cdot\dot{C}/C$$

The function $g(T)$ captures the fact, that the oceans emit an increasing net amount of $C$, depending on temperature. Let's assume that

$$g(T) = \gamma\cdot(T - T_0)$$

with $T_0$ the mean global temperature in 1850 or so.

The function $\sigma(T)$ captures the stochastic variance of temperature by internal variability which itself depends on the temperature. It may be assumed as

$$\sigma(T) = \sigma_0 + \sigma_1\cdot(T - T_0).$$

Question 1: Is the given form of $f(C,\dot{C})$ roughly correct? Which functions $g(T)$ and $\sigma(T)$ would be more realistic?

Question 2: What can be said about attractors and long-term behaviour of this system?

Question 3: Can this dynamical system give rise to tipping points?


The Urban heat island effect offset's reliable temp data. Fact is, decades of computer models predicted temperature gains that never happened. If you want an extrapolation of overall temp in relation to CO2 outputs here ya go (Below) Vs. model predictions. Note the Temperature curve failed to Obey the CO2 curve. It's not to say CO2 doesn't have SOME factor in temp.

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