# Math behind climate modeling.

Let me start with a purely mathematical question. What are the partial differential equations used in modeling our climate? I do mean the exact mathematical description.

What are the initial conditions ?

As far as I know, there should be at least 3 kind of equations.

1. The equation about Mass continuity (for mass).
2. The equation for motion (of Gaz).
3. Thermodynamics equation (for temperature).

In order to study our climate I'm pretty sure that we need to take in account some "mathematized" chemical equations but I would not ask about them.

Here is my main question: How precise is the prediction of these equations for our planet climate under the assumption that we know the initial conditions with exact precision ? (the last point is not realistic form physical viewpoint, I agree)

• Definitely not an answer, but to my understanding the Navier-stokes equations are the governing differential equations in many fluid-dynamics based situations; for example, the conservation form of the Cauchy momentum equation $\frac{\partial}{\partial t}(\rho\ u)+\nabla\cdot(\rho u\otimes u)=-\nabla\cdot p I+\nabla\cdot\tau+\rho\ g$, where an explanation of the variables and constants involved can be found here en.wikipedia.org/wiki/…. – Alec Rhea Nov 4 '17 at 8:36
• What makes you think the models are primarily pdes? Reasonable models would have stochastic components, discrete components, statistical trended components, etc – Matt F. Nov 4 '17 at 12:14