Hi Stephen -

I can say a ton about frequency response and phase shift.  The foundation 
for all of that work was done in this paper for solar reduction:
https://www.earth-syst-dynam.net/7/469/2016/esd-7-469-2016.html
It turned out that we could use a similar control algorithm with a factor 
of ten scaling (for reasons that I can go into).

Sulfate aerosols are more difficult than solar reduction because you don't 
get the same control (you can't wall off the stratosphere), and there are 
nonlinearities in the response.  Those two topics are covered by the papers 
with Simone Tilmes and Doug MacMartin as first authors, respectively.  The 
paper with me as first author was putting all of that together and 
evaluating the performance of the control algorithm.

More directly to your question, we went for a bandwidth corresponding to a 
~5 year timescale, and we have a one year time delay because we're 
adjusting every year based on annual averages.  I don't specifically 
remember what the phase shift was, but our phase margins were good enough 
that we weren't all that worried about convergence or peaking.  If you're 
curious, I can try digging up some Bode plots.

Best,

Ben

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