My take on this now ( and I assume it’s the same as your take) is that the GISS process can be thought of as estimating the deviation of the temperature in month a from its long term average. And it does this as as the average of the deviation of months b and c from their respective long term averages. In other words,

DEVa=[(Tb-TB) +(Tc-TC)]/2. Then the estimated temperature for month a is TA+DEVa which leads to your result for Tq.

Thinking about it like this makes it sound more reasonable. I would hope, however, that GISS tested this method against other alternatives.

I’m going back to lurking.

]]>It should be deltaTn = Tn – TN. When I was solving the problem back in September, I figured Hansen was adding a bias to the month’s average in order to get the month’s estimate. So my second step in that derivation is correct. I got sloppy with the Latex in the fourth step, which should read deltaTn = Tn – TN instead of deltaTn = TN – Tn. The signs are backwards in the fifth step as well. Fortunately, I had worked it out in a notebook and was trying to copy from my notebook into the Latex, and I did copy the sixth and final step correctly.

When I get a chance tonight I will post a complete and corrected derivation – hopefully without the typos. What I posted in the past is incomplete in that it does not specify when rounding of results occurs, nor does it specify when the seasonal averages are calculated.

]]>In your post of Sept 6 to which you referred me, the next to last line in your derivation of Tq is

Ta=TA+(TB+TC)/2 -(Tb+Tc)/2 where Ta is the estimated temperature for mont a that is missing data. (This comes about from deltaTn=TN-Tn) Since Tq= (Ta+Tb+Tc)/3 then by substitution

Tq=[TA+(TB+TC)/2 -(Tb+Tc)/2 +Tb+Tc]/3 = [TA+(TB+TC)/2+ (Tb+Tc)/2]/3=TA/3+(Tb+TC)/6+(Tb+Tc)/6.

On the other hand if deltaTn=Tn-TN then I get your result for Tq.

]]>Thank you for pointing out the error in comment #76. It should read Tq= rather than Ta=.

I do not get your resulting equation, however. I would need to see your step-by-step derivation to comment on it. While I now see that I had an error in the intermediate result in the post I referred you to, the resulting equation is still correct (as far as I can tell). I’ve rerun it a bunch of times on GISS data and I get the same results as Hansen.

One trap to watch out for is that the December value you must use is from the previous year, not the current year. That is a programming error I recall stumbling into.

]]>In # 76 above you said that Ta was the temperature of the missing month. I looked at your earlier derivation cited in your reply in #89, and it seems that your equation for Ta in # 76 is supposed to be the estimate for the quarter that is missing the temperature in month a. However, in reviewing your earlier derivation for the quarterly estimate, I can’t get your result. I get (using the notation in #76 above) that

Tq=TA/3+(Tb+Tc)/6+(TB+TC)/6, which I think makes more sense since it properly weighs the 3 months. ]]>