Some time ago I had a brief discussion with Leif Svalgaard on ClimateAudit blog inspired by an exchange between Leif and David Archibald when the latter complained that Leif’s TSI reconstruction was “too flat”.

The sunspots exhibited cyclic variability in terms of the frequency of the cycles and that most thermostats work by pulse width modulation and some digital music with pulse frequency modulation. Both these work in a similar manner the thermal inertia of whatever the thermostat is controlling smooths the temperature variability and the pulse frequency modulation’s demodulator is a simple low pass filter often just a series resistor and shunt capacitor. In both these cases only the duty cycle or the frequency varies but not the amplitude. Below is a description of how this behaviour can be simulated with an electrical circuit emulator called ‘qucs’.

Any system for storing energy and releasing at a slower rate can function as a low pass filter like a fly wheel for rotational mechanical energy, capacitor or inductor properly configured an oven hot plate with a pot of food on it. I decided to test the concept so I downloaded sunspot data from the Boulder site and run the crudest integrator on it, the running average. with a 20 window and the result is here:

The result bears a resemblance if not precisely correlated to the data for the same period that can be seen on the CRU site though somewhat more muted:

nhshgl

It was suggested that I should have centered the running average but as far as I’m aware no physical integrator has a memory of future values. In any case while I was installing a new revision of an electron schematic capture and simulation program I thought I might run a simulation on Leif’s corrected TSI data through an RC low pass filter simulation the result is below.

qucs-0014-tsifilter

I got the “Quite Universal Circuit Simulator” (qucs) from here.

I obtained the source from Leif Svalgaard research page here:

I extracted a csv file from this using the using awk command

awk ‘ $0 ~ /[21][06-9]/ {if (NF == 5 ) print $3″,”$5}’ SsnTsi.txt > vfile.csv

for those without awk could probably persuade a spreadsheet program to produce one from the above file.

This just leaves out any missing data of which here are a few months worth but qucs can hold the data.

vfile.dat is the qucs data file used as input this can be obtained using

qucsconv -i vfile.txt -if csv -of qucsdata -o vfile.dat

The vfile.dat that I used is attached below.

Now I have no idea what sort of directory structure windows uses but for Mac and unix users qucs does everything in a hidden ~/.qucs directory you can either run qucs start a new project and copy the schematic by hand the important parameters will be visible on the pdf attached in the schematic.

Or you can move the compressed file into the ~/.qucs directory and unpack it and run and you will see the project in the qucs Projects window double click on “TSIfilter” then double click on TSIfilter.sch and the schematic with charts from my last run should appear ( I left it in when I compressed).

At this point you can run the simulation yourself by clicking on the gear icon or using the menu -> Simulation ->Simulate.

You can change the properties if everything in the page by right clicking on the component page (including charts) and a menu will appear allowing you to change the values and the properties and see what sort of difference it makes.

in the zip file shold be the schematic the file from Leif Svalgaards site with the sunspot and TSI data the csv file obtained from this and the vfile.dat file generated from the .csv file as well as data files from the last run before I compressed it which incidentally is not the run that produced the PDF file attached. Does it prove anything? I don’t know I don’t think it is rigorous enough but I had fun doing it and it does look like it shares a finger print with the recent temperature record and it might give some of you a feel for how a simple model can work. Have fun with it.

Qucs project file: tsifilter_prj