Nathan wrote:

>The filter code takes the value for a month and replaces it with a 12-month average. Specifically, it averages over the value for the month being replaced, the values for the preceding 5 months, and for the following 6 months.

So if $q= (q_1, q_2,\ldots,q_N)$ is a list of time ordered monthly measurement values

then

$filter(q_i)= 1/12*\sum_{j=0}^{11} q_{i-5+j}$

Is that correct?

And $Diff12(q_i)$ would then be filter $(q_{i+1})-filter(q_i)$ or would it be $filter(q_{i})-filter(q_{i-1})$?

But that would then just be the yearly difference in monthly concentrations shifted by e.g. 5 months, i.e. in the first case

$q_{i+7}-q_{i-5} = q_{i-5 + 12} - q_{i-5}$

divided by 12 .....If I didnt miscalculated something in my head.

So by looking at the co2 curve of concentrations, which looks periodic in year, this difference looks more like being a constant or maybe
eventually slightly increasing. So I'd expect a slightly wiggly straight line on a first glance for the diff12 curve of the co2 concentrations.
In particular if I look at fig 1 then the yearly differences of monthly measurement values look like to be in the range of 0.02 "original data" (what ever this is) and not as being in the range of 0.2 as indicated in fig. 2 in the real climate post. And if I divide by 12 then this gets even worse.

Whereas the corresponding differences for the temperatures could be in the 0.2 range (but what about the factor 1/12?)