Posted on April 27th, 2011 in Isaac Held's Blog
Black: Climatological seasonal cycle of temperature in Minneapolis (two years are shown for clarity). Averaging (Tmax +Tmin)/2 over >100 years for each calendar day. Data kindly provided by Charles Fisk. Red: Fit with annual mean plus fundamental annual harmonic
Two common questions that I (and many others) often get are “How can you predict anything about the state of the atmosphere 100 years from now when you can’t predict the weather 10 days in advance?” and “How do you know that the climate system isn’t far more complicated than you realize or can possibly model?” I often start my answer in both cases with the title of this post. It may sound like I am being facetious, but I’m not; the fact that summer is warmer than winter is an excellent starting point when addressing both of these questions.
I don’t think that we have to spend much time on the first question here. We all successfully and continually predict the state of the atmosphere several months in advance whenever we plan our summer or winter vacations. Of course, the seasonal cycle is forced; no one can predict the chaotic day-to-day weather months in advance. More reasonably, we do try to predict whether the temperature averaged over the next summer will be warmer or colder than average in some region, part of the challenge we call seasonal forecasting.
Analogously, when we talk about predicting the trend in the climate over the next 100 years due to a projected increase in carbon dioxide, we are talking about a forced response, fully analogous to predicting the extent to which summer is different from winter on average. The forcing in this case is through a reduction in the outgoing infrared flux rather than a redistribution of the solar flux, so the details are different. And the time scales are different. And — the biggest difference of all , of course– we have experienced a lot of seasonal cycles and don’t have to rely on theories/models to tell us what the forced response is going to be. But just because we have a lot more observational input into one problem than the other does not change the fact that the two physical problems are very closely analogous. The analogy to seasonal forecasting, whether next summer will be warmer or wetter than average, is the challenge of predicting the decadal-to-multi-decadal internal variability, generated by the oceans, that will modify the emerging forced signal.
Moving on to the question of complexity:
I grew up in the Twin Cities of St. Paul and Minneapolis, so I found a lot of interest in this elegant little web site (also here). I’ve plotted the seasonal cycle of surface air temperature in Minneapolis in the figure above. The max and min temperatures are averaged together for each day; the individual days are then averaged over 120 years or so. No smoothing is applied. The seasonal cycle appears to be very smooth. In fact, it is almost exactly sinusoidal. (While growing up, I always thought that it was colder than it had any right to be in mid-winter;I can now point to the small mid-winter departure from a pure sine wave as support for this claim.) Despite the potential for complexity (I can assure you that clouds have a very different character in summer and winter in Minneapolis), I think we can agree that this is a pretty simple and intuitive temperature response.
Not all seasonal cycles of temperature are this sinusoidal. In the Arctic, for example, the summer gets truncated because temperatures are pegged to freezing and the energy goes into melting ice. Over parts of the oceans with a large seasonal cycle in the depth of the surface well-mixed layer, the warm season is more peaked and the cold season flatter because the heat capacity of the part of the ocean that is tightly coupled to the surface is larger in winter. More counter-intuitive is the spatial structure of the phase of the seasonal cycle near the equator in the eastern Pacific (see Horel, 1982). Looking for interesting structure in the seasonal cycle can be fun — see Mapes,et al in prep.
Why is the seasonal cycle in Minneapolis temperatures so simple despite the nonlinear chaotic behavior of the weather making up these averages? Is it because the seasonal cycle is so large compared to internal variability, so that it just overpowers any attempt of the internal variability to couple with it and create more counter-intuitive behavior. This sort of thing can happen in periodically forced nonlinear oscillators. Would the seasonal cycle get more complicated if one reduced its amplitude — by decreasing the obliquity of the Earth (the angle between the axis of rotation and the normal to the orbital plane), leveling the playing field between the seasonal cycle and internal modes of variability? I doubt it, primarily because one still would have a lot of separation in frequency between the bulk of the intrinsic variability, with characteristic time scales of days, and the seasonal cycle. (Are there any modeling studies with very small obliquity?) The deep tropics may be a counterexample, involving the interplay between intrinsic ENSO dynamics and the seasonal cycle, in which “Devil’s staircase” type of complexity is a possibility — but even here the system seems too noisy for this kind of complexity to dominate.
What kind of internal dynamics might plausibly couple nonlinearly with the response to the anthropogenic carbon pulse? The decadal to multi-decadal variability typically associated with the thermohaline circulation in the Atlantic seems too fast. Even if one had a lower frequency candidate, my impression is that it is a lot harder to generate serious nonlinearity when internal variability interacts with pulse-like, as opposed to periodic, forcing.
At the extreme, there is the possibility that the climate system, and climate models, exhibit structural instability — that climate does not vary smoothly as parameters are varied, not just at isolated bifurcations but more generically. See here and here and here for different perspectives on this issue. This is not an easy topic, and one that I have a lot to learn about. But I wouldn’t advise you to cancel your summer vacation plans just yet.