Should be correspondingly. ðŸ˜Ÿ

Also one equation missing. Will try to find out why.

Note this is the best estimate unless more is known about A as in the Bounded Derivative Theory.

Jerry

]]>I had to redo the last equation because latex2wp does not take macros. ]]>

Can I post this on a new thread

\title{Analysis of Perturbed Climate Model Forcing Growth Rate}

\author{G L Browning}

\maketitle

Nick Stokes (on WUWT) has attacked Pat Frank’s article for using a linear growth in time of the change in temperature due to increased Green House Gas (GHG) forcing in the ensemble GCM runs. Here we use Stokes’ method of analysis and show that a linear increase in time is exactly what is to be expected.

1. Analysis

The original time dependent pde (climate model) for the (atmospheric) solution y(t) with normal forcing f(t) can be represented as

where y and f can be scalars or vectors and A coresspondingly a scalar or matrix. Now supose we instead solve the equation

where is the Green House Gas (GHG) perturbation of f. Then the equation for the difference (growth due to GHG) is

Multipy both sides by _{t} = \exp( A t ) \Delta f . Integrate both sides from 0 to t

Assume the initial states are the same, i.e., is 0. Then multiplying by yields

Taking norms of both sides the estimate for the growth of the perturbation is

where we have assumed the norm of as in the hyperbolic or diffusion case. Note that the difference is a linear growth rate in time of the climate model with extra CO2 just as indicated by Pat Frank.

]]>I have written Stephen a number of messages and he has not reponded. In particular I asked him if he would allow me to post the above tutorial on a new thread, and I would like to post the estimate I mentioned above on a new thread. He has not responded, so I assumed he is busy. Thus I tried on this thread to figure out how to post the tutorial. There is a bug in CA Assistant so it took me a number of attempts. As you can see the tutorial raises a number of issues with climate and weather modelers use of numerical methods. The estimate clarifies the Stokes attacks on Pat Frank’s paper.

Jerry

]]>An estimate of a perturbation to the forcing of a pde yields an estimate of linear growth in time times the maximum perturbation, exactly as in youe linear model. Nick seems to have missed that fact? I can reproduce that estimate if you want.

Jerry

]]>Your discussion of the innards of the models and the dissipation problem are beyond my knowledge, though I can get a general gist of your point.

The problem of the molasses atmosphere that you raise is one that is generally ignored in all the discussions of climate models, their simulations, and their reliability.

I look forward to seeing how your conversation with Nick evolves.

In the meantime, I was happy to see that your were amused by the success of the linear emulator.

In my 2015 talk at the DDP conference, I observed that you can use a hand-calculator to duplicate the air temperature projection of an advanced climate model running on a super computerc. ðŸ™‚

]]>Interesting. When I asked what happened to my first post, suddenly both of them appeared. And Nick has chosen to ignore them because he has no answer for hard mathematics.

Jerry

]]>I will recreate it here if it disappears.

Jerry

]]>read my last comment on WUWT.

Actually there may be two because one seemed to disappear.

Jerry

]]>