# Simple model that exhibits a climate tipping point

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?