Sol y Vol Smoothing Choices

When I do a rough fit of the Sol y Vol combination of sun spot number derived Total Solar Irradiance (TSI) and the Crowley and Unterman volcanic sulphates forcing estimate there are a lot of choices than can be made.  I selected a 27 month base smoothing period because of internal lags in the tropics.  There is a huge seasonal swing of near 100 Wm-2 due to Earth's eccentric orbit that has to have some reasonable settling time.  13 month is a standard smoothing choice which would show more detail than 27 months.  The longer the time period selected the more information that is lost.  Any time frame I select will be question by someone with an agenda or someone thinking I have an agenda.  Such is life.

This is a comparison of the BEST global data using the 27 month cascade smoothing and the Vol part for the northern hemisphere.  Believe it or not, that is not a bad fit.  Since there is considerable uncertainty in the earliest part of the temperature data and determining volcanic forcing from sulphate deposits in glacial ice in not an exact science, this is the kind of correlations that should be expected in a complex system.  Volcanic forcing due to sulphates in the atmosphere obviously cannot cause surface cooling before they occur, but there is no reason to expect that every volcano happens to have the same atmospheric conditions when they erupt or that there are smaller volcanoes that may not be included in the data that may have some impact  Also every perturbation of the system can have a different impact on temperature depending on the dynamic state at the time of the perturbation.  The quick and dirty settling time estimate for the southern hemisphere indicates 45 years until 50% of the hemispheric imbalance works its way through the system.  90 years later there can still be a pulse of 25% of the initial impact on the ocean surface temperature which would just contribute more noise to the surface air temperature recorded by BEST.  So I tend to personally prefer the general detail offered by the 27 month smoothing.

This uses a 13 month cascade smooth.  There is a little difference in the fit but not enough to write home about unless you are trying to isolate a specific period.  In both cases I showed the impact of each filtering stage.  I blurred the BEST monthly data to show the realistic range of uncertainty.  With the blur regions of higher variability show darker bands indicating the fit in those areas is likely to be more uncertain that in the less variable bands.  In the land data there is also lots of "other" factors, glacial and snow cover advance/retreat which can be impacted by natural warming, i.e. recovery from LIA conditions, black carbon from the use of fossil fuels, agriculture albedo impact due to snow removal, dust and smoke from slash and burn clearing, crop selection and rotation, water cycle changes due to everything from beaver hat fads to irrigation and swamp drainage.  Under all this uncertain expecting a tight fit over the whole period is just a bit goofy.  The oceans tend to not have as many issues.

This is the Hadley Center SST version 3 with the 13 moth cascade smoothing.  The overall fit is generally better but with issues more likely related to ocean settling times.  The Vol used is still NH only which misses half the globe with more heat capacity.  We are also missing 100 years of data which had more volcanic impact that would likely have some delay moving through the system. 

The same data with the 27 month smooth shows less detail which may be a problem for some, but should be easier to "roughly" fit.  The extra smoothing make is it simpler to determining the weakly dampen settling periods.  Once that is done there can always be an attempt to fill in some of the finer points, but I think starting with too much detail too early just leads to missed opportunities. 

Note that these last two charts have light blue and red bands.  The blue band is the mean of the entire period and the red the mean of the 1951 to 2010 period.  Both are blurred to simulate the nominal instrumental error range.  No smoothing method will ever replace accuracy. What the 27 month stacked or tiered smoothing does though is create a simple band pass filter.  By having a larger number of tiers you can isolate the more synchronize 27 month events.

This is a bit of an extreme example where I used 17 tiers to isolate the ~62 year AMO/Global pseudo- cyclic oscillation.  If the period happens to be fairly constant you can make a prediction based on this recurrent pattern.  I wouldn't count on it though since volcanic perturbations may not be so predictable :)