Gaze into the crystal ball …
Specifically, let’s forecast global average temperature for the remainder of the year. Many people are expecting temperatures to increase because we’ve moved from la Nina to el Nino conditions. Indeed that’s correct, but the expected influence over the remainder of the year is actually rather small. There are three factors I’ll use in my forecast. First is volcanic forcing, second is el Nino, third is global warming.
I did a multiple regression fit of GISS global temperature from 1975 to the present, to volcanic forcing (as estimated by Ammann et al. 2003, A monthly and latitudinally varying volcanic forcing dataset in simulations of 20th century climate, Geophysical Research Letters, 30, 1657), the multivariate el nino index or MEI, and a linear trend in time, allowing for a lag in the impact of volcanic forcing and MEI. The best fit was for a lag of 9 months for volcanic forcing, 4 months for MEI. But the residuals from that fit showed a small but significant annual cycle. That’s because GISS data are anomaly relative to the 1951-1980 baseline, and the annual cycle has changed since then; winter has warmed more than summer and the effect is more pronounced in the northern hemisphere than the southern.
So I added an annual cycle to the fit by including a 2nd-order Fourier series in the fit. The best lags are still 9 months for volcanic and 4 months for MEI, and the fit looks like this:
The residuals look like this:
The fit is quite good. The residuals do exhibit some autocorrelation. So I fit an AR model to them, picking the best order by AIC, which yielded an AR(2) model.
Finally, I combined the predicted signal using the multiple regression model with the predicted noise using the AR(2) model to generate predictions for the next 4 months. It’s not really possible to extend this model beyond that time, because that would require as-yet-unobserved values of the MEI. And what are the predictions?
| Time | Prediction |
| September | 0.59 |
| October | 0.59 |
| November | 0.60 |
| December | 0.64 |
Indeed the prediction is for mild warming over the next four months, but nothing like record-breaking temperatures.
If these predictions turn out to be exactly correct, then 2009 will come in as the 5th-warmest year on record. Lest any denialist claim that’s evidence of global cooling (I guess they’ll do that anyway), if the prediction is right on the money that will actually be evidence of global warming — it would mean that the model got it right, and the model includes global warming but not cooling.
The chance of the predictions being exactly correct is very small! After all, the residuals from the model have standard deviation about 0.12 deg.C, and we can in fact expect about that much deviation in the predictions. Nonetheless, this forecast gives us some idea what to expect over the next four months: mildly warmer temperatures than the first 2/3 of the year.
22 responses so far ↓
Gavin's Pussycat // September 13, 2009 at 3:54 pm |
That fit looks pretty damn good…
So you had 10 parameters: 4 Fourier, two for linear trend and intercept, two delays, and two regression coefficients?
What were the Akaike weights? Anything change for AR(1)?
Ted // September 13, 2009 at 4:36 pm |
So, just curious … is the ‘global warming’ forcing less than or more than the residuals? (It sounds like less … is that right?) Also, what does your model say about 1 year, 5 years, 10 years?
[Response: You're confused. The global warming impact is much larger than the noise on long-term averages and trends, but much smaller on a single month's change.
As for this model, I already stated that it can't be extended more than 4 months because that would require as-yet unobserved values of MEI.]
At what point in the future does the model’s output make a prediction outside of the expected variability? In other words, when does the g.w. component ensure a prediction that deviates enough from a prediction without the g.w. component in order to say something meaningful about the climate?
Thanks.
[Response: See this.]
jyyh // September 13, 2009 at 5:27 pm |
Thank you for this, adding such equations as the alteration between winter-summer in these is currently beyond me. If I remember correctly, the methane concentrations haven’t been measured for long and widely enough to get rid of some of the remaining residual spikes? At least I haven’t seen such dataset be mentioned anywhere.
Georg Hoffmann // September 13, 2009 at 6:05 pm |
@Tamino
Lean&Rind added furtermore solar activity to the multivariate regression. They came up with an explained variability of 76%. Can you make a statistical statement if the 11 yr cycle adds significant focing to the regression?
Visually I have the impression their fit is better than yours. Much better to justify their choice of adding solar activity?
http://www.scienceblogs.de/primaklima/2009/09/warum-eigentlich-klimamodelle-wenns-ne-lineare-regression-auch-tut.php
CapitalClimate // September 13, 2009 at 7:40 pm |
Since I’ve seen your other work, I know you know what you’re doing, but isn’t this kind of individual monthly prediction likely to be distorted and misrepresented by those with an agenda? (Not that anyone would have an agenda when it comes to science. What was I thinking?)
[Response: What could I write about that wouldn't be distorted and misrepresented by denialists?]
dhogaza // September 13, 2009 at 8:03 pm |
You could write “climate science is a fraud” and be a hero …
CapitalClimate // September 13, 2009 at 8:15 pm |
Just sayin’: no sense making it extra easy.
Hank Roberts // September 13, 2009 at 8:26 pm |
http://www.kevinandkell.com/2009/strips/kk20090913.gif
Deep Climate // September 13, 2009 at 10:54 pm |
It’s true that winters have warmed more than summers – if you go far back enough.
But when I looked at the severe UAH annual cycle, I also saw a moderate surface annual cycle that resulted in higher recent trends in autumn (1979-2008), especially in GISS, with other seasons more or less equal .
See:
http://deepclimate.files.wordpress.com/2009/03/global-month-trends1.gif
Here are seasonal linear trends to end of 2008 in the latest GISS data (downloaded today).
From To *DJF* *MMA* *JJA* * SON*
=============================
1961-2008 0.143 0.137 0.127 0.135
1975-2008 0.169 0.163 0.168 0.195
1988-2008 0.155 0.158 0.140 0.240
(Of course, DJF is winter and JJA is summer and so on).
Batman // September 14, 2009 at 12:45 am |
“What were the Akaike weights? Anything change for AR(1)?”
I’m also curious if you did any type of penalization for the number of parameters.
luminous beauty // September 14, 2009 at 2:41 am |
Hank,
Why shouldn’t flowers have issues, too?
Deep Climate // September 14, 2009 at 2:56 am |
The last comment were the global figures. Here are seasonal linear trends to end of 2008 for Northern Hemisphere only.
From To *DJF* *MMA* *JJA* * SON*
=============================
1961-2008 0.200 0.183 0.159 0.179
1975-2008 0.262 0.252 0.239 0.284
1988-2008 0.235 0.224 0.225 0.384
Deep Climate // September 14, 2009 at 3:26 am |
To two decimal points, I have 0.56 as the 2009 global temp anomaly if the above predictions came to pass.
If so, that would not only put 2009 in the top 5, but there would be a four-way virtual tie for second place (with 1998, 2002, and 2007 – all at 0.56).
Rattus Norvegicus // September 14, 2009 at 3:56 am |
We’re number #1!
My educated guess is that 2010 will beat 1998, even w/o an extraordinarily strong El Nino. Bets anyone? (Bet limited to a beer in Bozeman).
Gavin's Pussycat // September 14, 2009 at 4:35 am |
Batman,
actually the number of parameters is not a problem as here, monthly values are used of which there are plenty.
(I see that I overlooked that instead of one parameter, volcanism introduces as many as there are latitude zones. Still a small number.)
The Akaike thing refers (as I understand it) to choosing AR(2) (as opposed to AR(1) or AR(3)). For the residuals time series.
[Response: Only 1 for volcanism, since I globally averaged (area-weighted) the Ammann volcanic forcing data.]
Deep Climate // September 14, 2009 at 12:38 pm |
Rattus,
I agree with you for GISS. Not so sure for HadCRU – it may depend on how strong El Nino peaks. (Of course any guess I might make is no doubt less “educated” any way).
“Number #1″?
Deep Climate // September 14, 2009 at 12:56 pm |
A tentative hypothesis concerning recent autumnal warming in NH: It may be related to trends north of 60 deg.
For instance, Barrow in Tamino’s Reply to Lucy Skywalker post:
http://tamino.files.wordpress.com/2009/09/barrow.gif?w=500&h=299
GISS uses far north stations to estimate Arctic temperatures, so naturally would have more of an “autumnal bump” if these stations are the source.
Magnus A // September 14, 2009 at 1:58 pm |
[Explain why you delete this comment!]
[Response: Because your agenda is obvious: to slander me. You show your foolishness by attempting to do so about a post whose methods and results are nowhere near controversial. Clearly you have nothing to contribute to intelligent discussion.]
[edit]
TrueSceptic // September 14, 2009 at 4:50 pm |
Tamino,
Isn’t it sometimes better to allow posts that expose the dishonesty of those making them?
And shouldn’t it be “libel”, not “slander”?
[Response: Indeed it is. As to giving them enough rope to hang themselves, sometimes I do.]
Deep Climate // September 14, 2009 at 2:00 pm |
The last word on seasonal warming for now:
NH 30-year seasonal trends in GISS
From To *DJF* *MMA* *JJA* * SON*
=============================
1972-2002 0.287 0.234 0.223 0.229
1978-2008 0.244 0.263 0.239 0.282
Clearly there has been dramatic warming in fall in the last few years. I still think this will turn up largely in the north, but the Barrow example may turn out to be less relevant than I thought, as the seasonal graph only went to 2001.
Slioch // September 14, 2009 at 8:50 pm |
Psst… Deep Climate … MAM
Or do you guys on the sunny side of the pond juggle the months around as well?:)
Deep Climate // September 14, 2009 at 10:16 pm |
Slioch wrote:
Oops … sorry about that. I should have cut and paste the heading, as I did for the numbers. (Spring should be MAM, not MMA of course).