A reader on RealClimate wanted to see Fourier transforms of various signals related to paleoclimate. So, without much explanation and little helpful information(!), here they are.
Precession cycle:
Obliquity cycle:
Eccentricity cycle:
Insolation at 65oN latitude in July:
The LR04 stack:
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8 responses so far ↓
David B. Benson // February 16, 2007 at 8:27 pm |
Very useful. Thank you!
tim // February 17, 2007 at 1:42 am |
does this seem to show eccentricity has more impact than obliquity?
[Response: not necessarily. (note: these Fourier transforms are for the last million years only, to correspond with the graphs on the RealClimate post) It does show that for the last million years, the 100,000-year cycle in paleoclimate has been stronger than the 41,000-year cycle. But whether that 100,000-year cycle is actually caused by eccentricity changes is an open question.]
David B. Benson // February 17, 2007 at 8:21 pm |
I’m having difficulty going from the first three graphs to the fourth, insolation at 65N in July. Pointers?
[Response: I'm not exactly sure what you're asking. Using earth's orbital configuration, we can compute the daily average insolation (incoming solar energy) at any given latitude, on any given day. This depends strongly on precession and obliquity, but not significantly on eccentricity (except that eccentricity modulates precession). The calculation is rather complex!
Can you be more specific about what has you puzzled?]
David B. Benson // February 17, 2007 at 9:14 pm |
I fail to understand why, with twice the power, the obliquity signal in the insolation is so small. Also, but less important, there is no low frequency power in the isolation at all.
Perhaps you have already anwered by stating that the computaion is complex…
[Response: Aha! First a note: the power in a Fourier spectrum isn't the size of the signal, it's the statistical significance of the signal.
For obliquity, almost all of the variation happens at a period (about 41,000 years) which changes very little, so all the power goes into that one frequency. For precession, the "effective period" changes quite a bit -- sometimes 24,000 years, sometimes 22,000 years, sometime 19,000 years, so the total power of the precession signal gets spread around among those frequencies. That's why the spectrum for precession shows three tall peaks, but the obliquity spectrum only shows one tall peak. If you sum the power levels for the peaks, then obliquity and precession are much more on par.
As for why precession dominates the 65N July insolation, that's because the primary effect of precession is to alter insolation near midsummer/midwinter, while the primary effect of obliquity is to alter the average over the entire year. Precession has a much larger effect on seasonal contrast (summer - winter), but no effect at all on the annual average.
The absence of very low frequency is because eccentricity has a negligibly small effect on summer/winter contrast. Both precession and obliquity are zero-sum, i.e., an increase in insolation in one season or one latitude is exactly compensated by a decrease in another season/latitude. But eccentricity actually affects the GLOBAL total insolation, although only by a small amount (about 0.4 W/m^2 max).]
David B. Benson // February 18, 2007 at 12:39 am |
This is now much clearer! Thank you.
I am, just for fun, programming a paleoclimate simulator, with sole forcing being the orbital forcings.
What you have above provides me with estimates for the coefficients at the various frequencies. But if you care to, what are appropriate coefficients for each of the
19, 22, 24, 41, 47?, 95, 125, 400 ky cycles?
I just need the variability, not the averages, to plug into the constants k for each of the k(cos 2pi(t/T)) terms.
[Response: You can get the actual numbers for the orbital forcing terms here. If this isn't what you're looking for, let me know.]
Vishwa Narayan // February 19, 2007 at 1:22 am |
Excellent blog. Highly informative, rational, objective.
Please tell me more about the effect of water vapour on global warming. (Or point me at information sources).
How much warming is predicted by the existing water vapour in the atmosphere?
Has any one looked at changes, if any, in the amount of water vapour in the atmosphere? Are the current quantities “average”?
Also, can you point me at data showing
- the IR radiation of the earth (e.,g radiated wavelength vs intensity)
- the absorption of this IR by GHGs such as CO2, methane, water vapor, etc., (as a function of wavelength?)
Thank you very much
Vishwa
David B. Benson // May 6, 2007 at 8:47 pm |
Tamino — This is somewhat off-topic, but a piece of statistics I don’t know where to begin finding the answer: We have hypothesis H and evidence E (i.e., data). The hypotheis actually contains a parameter which I used rms deviations of predictions versus the evidence to find the best fit. So far, so good.
However, I would like to be able to compute liklyhood ratios P[E|H]/P[E|K] for a competing hypothesis K. But I don’t know how to compute P[E|H], the probability of the evidence E given the hypothesis H, even under the assumption that the errors in the evidence are independent normally distributed random variables with known mean and variance given by the determined rms value.
Any light you can shead will be greatly appreciated!
[Response: It's *really* hard to know, because there's not much detail about what the evidence or hypotheses are like, what kind of processes are at work, etc. Can you give more details?
But here's a possibility: you say you used predictions versus evidence to estimate your parameter. Then I assume you can predict results from hypothesis H -- and likewise you could do the same for hypothesis K. You can also generate independent random errors. So, run a *lot* of simulations for hypothesis H, to generate a *distribution* of results. This might enable you to estimate P(E|H). Then you could do the same to estimate P(E|K).]
David B. Benson // May 7, 2007 at 8:41 pm |
Tamino, thanks for the suggestion. Here is what I have done. The evidence is a series of data points, i=1,N. Hypothesis H generates computed values c_i, i=1,N. By modifying the parameter of H, I get the smallest (unbaised estimator of) the variance, v. I then compute each of the normal probabilites N(d_i,v)(c_i) and multiply them all together, claiming this the probability of the evidence given the hypothesis, P[E|H].
Similarly for hypothesis K. Then the liklyhood ratio is obtained. (Actually, it is more usual to consider the logarithm (base 10) of the liklyhood ratio.
The resulting number, for the test case of a good hypothesis versus an obviously bad hypothesis gives an intuitively expected log liklyhood ratio of about 5.6. (So I think what I have done is the corrrect procedure…)