Skip to comments.BIG NEWS part VI: Building a new solar climate model with the notch filter
Posted on 06/22/2014 4:26:28 PM PDT by Ernest_at_the_Beach
Open Science live The story so far: Dr David Evans is building the O-D notch-delay solar model. Its a much simpler big-picture approach than Global Climate Coupled Models. They use an ambitious bottom-up system where the models add up every small aspect in every small cell of the Earths climate atmosphere and oceans and try to predict everything, but the trap is the errors small errors in 10,000 calculations add up to big-mush. Davids approach is top-down. He looks at the whole system from the outside, and doesnt try to understand or predict each individual part. Its a way of starting at the start to shed light on the big forces and processes that happen as energy arrives on Earth, gets reflected, or blended, and eventually changes the surface temperature. His model wont tell us what happens to rainfall in Sudan in 2050, but it might do what current models dont and that is predict the global temperature.
The important development here is to complete the path of the energy flow in the most brutally simple way from Sun > Earth > Space. We know the sun provides heat through TSI or Total Solar Irradiance. But this is almost constant it produces heat for sure, but possibly not much of the variation in temperature on Earth that we are interested in. The discovery of the notch filter means some other force (yet to be specified) from the sun acts with a delay of probably 11 years. This delayed force turns out to cause a lot of the variation in temperature. But Earth is not going to immediately warm or cool with every change. Energy collects in all kinds of pools and buckets before it ends up warming the atmosphere. So the effects of both incoming paths immediate solar and delayed solar get combined and run through a low pass filter which blends and smooths the bumps.
Having discovered the pattern in the way TSI is tranformed into temperature, David builds the model with the filters to produce the same transfer function as he found in empirical data. Hopefully the model will mimic the overall processes without needing to know the details of all the parts. In a sense all models have to do this at some level. No climate model tracks each molecule or follows each photon. Will it work? It does a good job of hindcasting (and well talk about that soon), but the real test will take a few years. Enjoy the quest to figure it out.
By the way, one of my favourite graphs is below Figure 4 some curves are intrinsically beautiful. Jo
Dr David Evans
This is the last of the three posts in which we build the solar model. We assembled a notch filter, a delay filter, and a low pass filter in cascade in part III, in part IV we took a diversion to physically interpret the notch and the delay, and in part V we added the RATS multiplier to model the atmosphere on the yearly timescales of the TSI datasets.
In this post we assemble these four elements in their correct order, and add the immediate path for the TSI changes that obviously warm the Earth directly. This will complete the model. We finish by examining the step response of the model.
The notch-delay solar model so far is simply a computational path from TSI to (surface) temperature that contains a notch filter, a delay filter, a low pass filter, and the RATS multiplier (which is a trivial filter whose transfer function is a constant). There are no other filters we can discern from the empirical transfer function, or from elementary physical theory. So with no more to add, lets put these four in order.
The transfer functions of these four filters, when multiplied together, form the empirical transfer function. The transfer function of two filters in cascade is the products of their two transfer functions, so these four filters must be in cascade (that is, the output of one is the input of the next). But multiplication is commutative, so the empirical transfer function does not indicate their order. For that we turn to physical reasoning.
The filter whose place is most obvious is the low pass filter. It models the Earth as a bucket of heat with unreflected TSI pouring in the top, and its output is the radiating temperature. We can now place the other filters around it.
In the flow of computation the RATS multiplier goes immediately after the low pass filter, because its input is the radiating temperature and its output is the surface temperature. We then have the computational path covered from the unreflected TSI all the way to the output of the entire model.
The notch and delay filters intrinsically go together and are inseparable, and it does not matter if they go notch-delay or delay-notch. The only place left for them to go is between the input to the entire model, namely the TSI, and the input to the low pass filter, which is the unreflected TSI.
Therefore the notch and delay filters are modulating the albedo of the Earth.
The development to date only shows the delayed path from TSI to surface temperature. But obviously any changes in TSI also cause direct and immediate changes in the unreflected TSI, by changing the incoming heat from the Sun, so there is also an immediate path from TSI to the input of the low pass filter. This immediate path must therefore be in parallel with the notch-delay path from TSI to unreflected TSI.
Putting it all together, here is the notch-delay solar model. If the recent global warming was associated almost entirely with solar radiation, and if it had no dependence on carbon dioxide, this is how it would work:
Note the parallel paths:
The parameters for the model were found by fitting the model to the observed temperatures since 1610, when yearly TSI data became available, though focused mainly on the last 100 and 200 years. Composite TSI and composite temperature records were created out of the TSI and temperature records analyzed earlier. In forming the composites, the offset of each dataset was adjusted so that the average values for overlapping datasets are the same, datasets were faded in and out of a composite gradually rather than entering the average abruptly, and instrumental data was preferred over proxy data. The fitting process found the model parameters such that the model best reproduced the composite temperature from the composite TSI and best produced a transfer function like the empirical transfer function found earlier.
The most important parameter is the delay parameter, which was found to most likely be 11 years but definitely between 10 and 20 years. The break period of the low pass filter was found to most likely be 5 years, though the possible range is from 4 to 25 years because it might be hiding over to the low frequency side of the notch. (It is very unlikely to be more than about the five years that other researchers have found, but the fitting process held open the possibility.) The most likely set of parameters is called the P25″ set of parameters. The values in P25 were rounded off to form the P0″ set of parameters, which has been used to illustrate the transfer functions and step responses of the filters during this development.
Here is the transfer function of the entire model:
It reproduces the amplitude of the empirical transfer function (see Figure 5), in the grayed area.
Here is the step response of the model, in dark blue.
Note that the step response is causal it is zero before the step stimulus is applied.
The step responses of each of the two paths in the model are also shown.
The final value of the delayed path response in the P0 parameter-set shown is 14 times larger than the final value of the immediate path response. The parameter fitting showed that this was the most likely value, and that the delayed path seems to always be between 10 and 20 times as powerful as the immediate path. Thus, the influence of changes in force X (or TSI via the the delayed path) on temperature is 10 to 20 times as powerful as the changes in TSI (or TSI via the immediate path).
The step response shown in Figure 4 is pristine and clean, with sharp edges, because it is a theoretical model, built of simple components that were inspired by, but do not incorporate, the messy empirical transfer function. If we could measure the step response of the system (TSI in, temperature out) then no doubt it would be lumpy, crinkly, and messy with no sharp edges, because in reality it is far more complicated than the model above. We aim to approximate a messy complicated reality with a simple model.
All of the above and everything in the preceding posts are based on the solar assumption, that all the recent global warming is associated with TSI. Now that the parameter values have been estimated, we can dispense with the solar assumption.
In the next post we will run some climate simulations, to see how well the model does at hindcasting.
*Jo adds that some people find Figure 4 looks unnaturally perfect (I did say it was my favorite). Thats true its the model step response. The actual real one probably looks more complex. But there are no perfect steps either.
My that was very well explained hooey.
Okay, I know I am not the sharpest crayon in the FR box — but what in the world is a “notch filler” and what does it mean in this context?
Having RATS and TSI defined/elucidated could be very helpful. I assume this has been done in an earlier iteration of this presentation, but . . .. That was then; this is now.
So, if this shows that any change on earth comes from OUTSIDE the earth....
Then there goes the (crackpot) theory that earth changes come about as a result of what is ON the earth.... such as “ global warming is caused by people”.
Notch filters let certain items through, or block certain items from entering.
Think of a narrow gate.
See part 5. You have to read the entire explanation, starting with part 2. It’s all on Joanne’s blog, and well worth the time.
I guess it is an Electrical Engineering term.///>P?Iy was discussed in the early parts....
A radio has a “notch filter”.
The tuner is a notch that allows the signal from the tuned station to pass, and blocks all those on other frequencies.
It was discussed in the early parts....
Typically filters - signal filters - are characterized by what frequencies they let through, how much attenuation they provide, and how quickly they "roll off" (eg. db per MHz) from passing signal through (pass-band) to stop-band.
So a "low pass" filter might let normal speech frequencies through, but block higher frequencies associated with hiss, static, noise... Or a "high pass" filter might let the main carrier signal through, and block DC and low frequency interference (eg. 60 Hz, which seems to be everywhere).
A notch filter removes signals in a specific band, letting signals of frequencies above or below the notch through. It may be useful if you're getting interference from a local RF source. The counterpart is the "band-pass" filter which only lets a specific band through, blocking signal above and below.
I skimmed through the article. I think this is poorly named. I believe they adopted the notch filter name because the author's analysis and model only accounts for very slowly varying inputs (low frequency, a dozen years long or so) and for very rapidly (yearly, high frequency). The author is apparently ignoring some "mid frequency" inputs that may vary every year or two. Hence his model notches-out these inputs/effects. Not sure that's a good analysis/modeling approach, and I'm not sure I'd call that a notch filter design either. Probably adopted 'cause it sounds catchy and high-tech. You know climate change types, they're all about the sound bite, not so big on the science.
Danke. Spaceba. Arregato.
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.