There's been more feedback discussion at Climate Audit. And since people are talking from different professional points of view (lots from EEs lately) I thought it would be useful to try to draw together the terminologies, and relate the concepts.

Here's a TOC:

## Monday, September 26, 2011

## Sunday, September 18, 2011

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## A faulty tapering

I see there's renewed interest at Climate Audit in discussing Bart's code for relating temperature and cloud radiative fluxes (CRF). I've discussed it a lot there, and on the past few posts here. But I'm bogged down there explaining what I believe is a simple error, which I'd like to explain here in more detail.

There is questioning at CA as to whether the whole approach is the right way to try to analyse feedback between these variables. There is a confused notion of causality. I agree with that. But here the aim is more limited.

There is questioning at CA as to whether the whole approach is the right way to try to analyse feedback between these variables. There is a confused notion of causality. I agree with that. But here the aim is more limited.

## Thursday, September 15, 2011

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## Green's Functions and Dessler's data

Green's functions? What's that?

Well, I want to talk about applying Bart's analysis to Dessler's ERA data. Tallbloke asked for this, and so, a while ago did Steve McIntyre.

But the previous discussion at CA was couched in terms of impulse response, and that caused confusion. The word is correct, but to many people it means a causal response in time. You bang something, you get a response afterward. Not before.

To do such an analysis, you need Laplace transforms. But Bart used a FFT, which has no preferred direction. The effect of an impulse spreads in both directions, as in spatial diffusion, for example. And his response function is two-sided.

There doesn't seem to be a universal word conveying that. It's like a digital filter, but people think of that as smoothing, rather than a mapping. Or a weighted moving average.

Well, I want to talk about applying Bart's analysis to Dessler's ERA data. Tallbloke asked for this, and so, a while ago did Steve McIntyre.

But the previous discussion at CA was couched in terms of impulse response, and that caused confusion. The word is correct, but to many people it means a causal response in time. You bang something, you get a response afterward. Not before.

To do such an analysis, you need Laplace transforms. But Bart used a FFT, which has no preferred direction. The effect of an impulse spreads in both directions, as in spatial diffusion, for example. And his response function is two-sided.

There doesn't seem to be a universal word conveying that. It's like a digital filter, but people think of that as smoothing, rather than a mapping. Or a weighted moving average.

###
## Feedback, frequency and Bart's comments at CA

More discussion of this thread at CA. PaulM suggested continuing discussion here, and to facilitate that, I've copied some of the key subthreads on this page. There are related threads here and here. Tallbloke also has a thread here

In one of his recent comments Bart posted this diagram of the system he was modelling:

It's a standard feedback system - just two boxes. But to me it raises this query - how can you isolate the box that you want? Electrically, if you look at input-output of box T2, you can't avoid the fact that T1 is in parallel with it. So you's disconnect the box and do the impulse response or whatever out of circuit. It seems to me that weve been trying to do that analysis in circuit, and getting tripped up with causality issues.

In one of his recent comments Bart posted this diagram of the system he was modelling:

It's a standard feedback system - just two boxes. But to me it raises this query - how can you isolate the box that you want? Electrically, if you look at input-output of box T2, you can't avoid the fact that T1 is in parallel with it. So you's disconnect the box and do the impulse response or whatever out of circuit. It seems to me that weve been trying to do that analysis in circuit, and getting tripped up with causality issues.

## Tuesday, September 13, 2011

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## August GISS - Very small rise - TempLS map comparison

GISS rose from 0.59°C (Jul) to 0.61°C (Aug). The rise came partly because they adjusted July down by 0.01 0.59°C. TempLS had measured no change (actually down 0.006°C). I'll show the comparison of world distributions below the jump:

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## FFT, impulse response, clouds, GMST

There has been a lot of interest in the thread at CA which started out looking at correlations between a figure that notionally expresses (unreliably) the part of TOA radiant energy flux attributable to clouds and surface temperature. There is a contention, favored by Spencer and Lindzen, that ST may be affecting clouds, which is a kind of feedback, which in fact is spoken of as a forcing.

There's lots to be said about whether these notions are true, but in this post I want to talk about a kind of analysis proposed by commenter Bart at that site.

Instead of looking at correlations, he proposed in effect to find an impulse response function which will transform temperature (T) into that quantity ΔR_cloud (or dR) by convolution:

\[ dR(t) = \int_{-\infty}^\infty h(t-\tau) T(\tau) d\tau\]

You can this of this as being like applying a smoothing filter but it doesn't smooth - it turns T into dR. The basic idea is that Fourier transformation turns that convolution into a product. Then you can work out the FT \(\hat{h}\) from

\[\hat{h} = \hat{dR}/ \hat{T}\]

invert the FT, and it's done. Along the way there are lots of complex variables, but the answer comes out real.

## Monday, September 12, 2011

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## Impulse responses and the Spencer/Dessler Cloud models

I've been involved in discussions at this CA thread, which has gone into FFT analysis of the relation between temperature and cloud contribution to TOA energy flux, as discussed a lot re papers from Dessler and Spencer and Braswell.

I should hasten to add that the analysis at CA is based on the use of all CERES data, which Dessler did not do. He gave good reasons for his choice to use reanalysis instead. Consequently, I don't think this alternative approach is telling us anything useful about clouds. However, there is interesting maths.

Commentator Bart there proposed a model in which an impulse function is found by FFT which, when convolved with surface temp (Hadcrut3) will reproduce that "cloud forcing" function, in his notation dR (for δR_cloud). He has produced a lot of Matlab analysis. His contention is that the low frequency behaviour of the impulse response shows strong negative feedback. I don't now agree with that - I think he is looking at very low frequency results which can't be supported by the short period (about 10 years) of data. Furthermore the integral of the impulse response that he cites is the low frequency limit where it becomes just the ratio of the time gradients of the two data sets as determined by OLS regression.

Anyway, I translated his code into R and did some comparison calculations, which I put n a page attached to this blog. I'm now transferring it to this post, in case people want to comment. I'm hoping to write a more detailed analysis soon. The data being used, referred to in the code as flux.csv, is here.

I should hasten to add that the analysis at CA is based on the use of all CERES data, which Dessler did not do. He gave good reasons for his choice to use reanalysis instead. Consequently, I don't think this alternative approach is telling us anything useful about clouds. However, there is interesting maths.

Commentator Bart there proposed a model in which an impulse function is found by FFT which, when convolved with surface temp (Hadcrut3) will reproduce that "cloud forcing" function, in his notation dR (for δR_cloud). He has produced a lot of Matlab analysis. His contention is that the low frequency behaviour of the impulse response shows strong negative feedback. I don't now agree with that - I think he is looking at very low frequency results which can't be supported by the short period (about 10 years) of data. Furthermore the integral of the impulse response that he cites is the low frequency limit where it becomes just the ratio of the time gradients of the two data sets as determined by OLS regression.

Anyway, I translated his code into R and did some comparison calculations, which I put n a page attached to this blog. I'm now transferring it to this post, in case people want to comment. I'm hoping to write a more detailed analysis soon. The data being used, referred to in the code as flux.csv, is here.

## Friday, September 9, 2011

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## August GMST - TempLS no change

This is the second month of running a TempLS analysis ahead of the major indices, and coincidentally with the same result. August's mean land/sea temperature anomaly came out the same as July - 0.45°C, relative to the 1961-1990 base period. The data and plots are at the latest ice and temperature data page.

Below is the graph (lat/lon) of temperature distribution for August, using GISS colors, levels and base period

And here, from that data page, is the plot of the last four months:

Below is the graph (lat/lon) of temperature distribution for August, using GISS colors, levels and base period

And here, from that data page, is the plot of the last four months:

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