Weather and climate: noise and timescales

To see that our nation is not quite innocent, click the frog and review a shameful "climate change" event sponsored by the Czech government.

A few days ago, an alarmist nicknamed Tamino (Grant Foster) wrote a shallow posting about the extrapolation of trends:

What if?

Foster argues that one can't blindly extrapolate trends, especially not the cooling ones. Well, I agree with the first part of the sentence but unlike Foster, I think that one should blindly extrapolate neither cooling nor warming trends. I agree that the absence of a warming trend since 1998 (and the fact that 2008 was the coolest year since 2000; and it was also cooler than 1998, of course) doesn't mean that we know that there won't be any warming in the next 50 years. But in the same way, the existence of some warming in the last 100 years doesn't mean that there will be the same - or even much larger - warming in the 21st century.

Related: Rasmussen: Only 41% of Americans believe that climate change is man-made

And the absence of a warming trend in the last 10 years indicates that it is somewhat likely that there won't be any warming trend in the following 10 years, either. In other words, even if "man-made climate change" exists, it is almost certainly not going to be an urgent problem at the time scale of a decade or shorter. Every sensible person should agree that short-term observations of either sign cannot be extrapolated to an arbitrarily far future.

But every sensible person should also agree that the observed temperatures do matter, and as their total volume grows bigger, their importance for our conclusions should increase, too. If someone talks about an "underlying trend" but his "underlying trend line" is allowed to deviate from the observed temperatures for arbitrarily long times and by arbitrarily large amounts, the "underlying trend line" is clearly scientifically meaningless and should have no impact for a rational decision-making.




Although these weather vs climate issues have been discussed on this blog many times, there has been no article that could be viewed as a comprehensive introduction - even though one year ago, we wrote about the weather, climate, and noise, too. So let us begin with another one.

The atmosphere is being affected by all kinds of effects. They are associated with various time scales, long ones and short ones. The extrapolation fallacy usually starts with the linearization of one particular effect which is extrapolated to a very far future. Not surprisingly, an infinite temperature change is always predicted for an infinite future moment by such a method. But things almost never work like that.

The first criterion to classify the atmospheric effects - or processes that influence the temperature as a function of time - is the following:

1. processes that are understood
2. processes that are not understood

Of course, there can exist and there do exist items in between. The second classification deals with

1. periodic processes
2. aperiodic processes

Again, there can exist processes that are approximately periodic but not exactly periodic: the 11-year and 22-year solar cycles are examples. Day-and-night cycles and the seasons are periodic and understood, the apparently important 22-year cycles caused by the Sun's and Earth's magnetic fields are (approximately) periodic but badly understood.

And there's a lot of aperiodic processes that are partly understood - such as the "monotonic" warming effects caused by the increasing CO2 concentrations (let us not argue about the amplitude at this point). And of course, there's a lot of aperiodic processes that are badly understood. Various ocean cycles similar to the Pacific Decadal Oscillation are understood at most qualitatively.

We usually say that the aperiodic processes that are not understood well are "chaotic". That doesn't mean that they will remain scientifically unpredictable forever. But with a certain limited degree of understanding, their detailed features look chaotic to us which is why we try to classify them as "chaotic" and associate their quantitative description with random numbers. But we must also be careful: there are different statistical distributions; there are many "kinds" of random functions, if you wish. The laymen (and not-quite laymen) often incorrectly assume that all kinds of "random contributions" are always of the same character. They are not.

And many processes that are not understood well don't even have names because we don't know what they are.

So far I have only sketched a few categories of effects. Each category has a lot of entries and many entries will remain unclassified, anyway. The observed temperature are results of the superposition (and sometimes nonlinear interactions!) of all these effects. As you would expect, the atmosphere (or the weather or the climate) is a pretty complicated system. Nevertheless, our understanding of this system is improving with time (or at least, it was getting improved before the climate science was hit by the wave of the postmodern alarmist quasi-religion).

Let me discuss various effects that influence the atmosphere and order them according to their typical time scale. The discussion will be much more than a list so you may find many of the detailed sentences useful, too.

Minutes and hours

Clouds and rain, rainbows and thunderstorms can come and go within minutes or hours and influence the local weather. They can also stay for weeks or months - and but I won't be talking about the same mundane meteorological phenomena (and other phenomena such as hurricanes or tornadoes) again. When we compute the average of the weather at a given place for a given day over periods comparable to 30 years or longer, we usually talk about the local climate.

We can get rid of the clouds in our theoretical model by taking the average over a long time. But we may also partly eliminate it by taking the average over huge regions or the whole Earth. In both cases, we should avoid oversimplified assumptions about the average. For example, the average global cloudiness of the atmosphere in January may be oscillating itself, being influenced by many other (slower) processes - understood and misunderstood ones, periodic and aperiodic ones, natural and man-made ones. We will mention some of them later.

One day

Most children know that days and nights are periodically alternating because the Earth is spinning around its axis.

Sometimes we see the Sun, sometimes we don't. ;-) During the day, the temperature is higher because the Earth is absorbing more energy (mostly in the visible spectrum) than it emits (in the infrared spectrum). During the night, it is the other way around. This cycle is, of course, extremely well understood and I don't want to spend too much time with it.

Because the maximum temperature is often reached around 2 p.m. local time, you see that the reaction of the Earth's surface to imbalances in the energy budget may be almost immediate (a few hours). However, there exist many processes associated with the Earth that are much slower than a few hours - and they may take thousands of years and give us new sources of "cycles" and "variability". The magnification of the time scales may be due to a huge heat capacity or other internal degrees of freedom of our planet that might be neglected in a naive treatment. You will see.

One year

We will omit various weather phenomena that take weeks or months and continue with the most important weather cycle, the seasons. We usually talk about four of them even though their multiplicity as well as their boundaries are clearly a matter of social conventions. Nature doesn't hire a new minister of the weather whenever the winter ends and the spring begins. ;-)

It may sound remarkable to the average inhabitants of the Northern Hemisphere, but the Earth is actually closer to the Sun now than it is during the summer. The reason for the cold weather in January is that the Earth orbits around the Sun and because the axis of the Earth's spinning is not orthogonal to the plane of the rotation around the Sun, we are sometimes facing the Sun by a part of the surface where the Southern Hemisphere is overrepresented (that's why they have the summer now) and sometimes it's the other way around.

Let me expect that the readers have learned this in the fifth-grade geography classes. ;-)

Two years: ENSO cycles

The days and nights and the seasons are the most obvious cycles influencing the weather. But there are other effects, too. The rest of this article will be about cycles and effects that take more than one year. Most people are unfamiliar with them. So they usually say that the interannual changes are "random". Moreover, they usually expect that such "random" changes from one year to another should be independent for each year.

Such expectations are completely wrong. Many of the effects that take more than one year can be understood. More importantly, most of the effects that take more than one year are also not "random" in the sense that they have their own internal inertia or autocorrelation, if you wish. If such an effect makes one year hotter, it is pretty likely that the following year will also be hotter because of this effect (and sometimes even more so).

The cycles of El Nino and La Nina episodes are our first example. El Nino (Spanish: little boy or Baby Jesus) means that the equatorial Pacific Ocean is warmer than the average, a pattern that brings heat and cold, precipitation or drought to various regions in the world. La Nina (Spanish: little girl) is the opposite thing. You need to create sensibly good models of the atmosphere, the ocean, and their interactions, including their turbulence, to describe these phenomena.

The typical periodicity of these ENSO (El Nino - Southern Oscillation) phenomena is between 1 and 4 years. They completely dominate this slightly trans-annual time scale. That's why the average jump of the global mean annual temperature per 1,2,3,4 years is actually nearly constant (0.1 °C is the standard deviation) even though you would expect that the typical jumps of the temperature after 4 years will be significantly higher than the jumps after 1 year.



Five years: the upper ocean's inertia

There is another time scale that I mention now even though it is not associated with any "cycles" but rather with an exponential decrease. The upper layers of the world's ocean - the layers (100-400 meters) that can exchange the heat with the atmosphere effectively enough - have a certain heat capacity. If you calculate how much time it takes to warm up or cool down this volume of water "almost" to the external temperature of the atmosphere, you will get a few years. A similar duration was used by Stephen Schwartz to calculate the climate sensitivity.

Note that this result is pretty much independent of the temperature difference because if the temperature difference is much higher, the oceans will be warming up faster, too. The existence of this heat capacity of water is the reason why the oceans may stabilize the temperature. It takes roughly five years until the active portions of the oceans adapt to the external temperature. They bring a specific "lag" or "inertia" to the climate system. But they are not the only source of "lags" and there exist slower lags, too.

The 11-year solar cycle

The Sun's magnetic field is changing its direction and strength in cycles that take 22 years in average. However, it is natural to expect that important physical quantities don't depend on the magnetic field itself but only its absolute value: the sign should be irrelevant. For mathematical reasons, it is more natural to talk about the second power of the absolute value. The latter has an 11-year periodicity.

We observe this periodicity as the fluctuating number of the sun spots. The sun spots may have the opposite magnetic "fingerprint" in the odd cycles and the even cycles but people have been assuming that these sign differences shouldn't matter. It was always natural to imagine that the 11-year solar cycle should periodically influence the temperature on Earth except that this 11-year signal has always been rather weak in the climatic data.

22-year solar cycle

But in fact, the longer, 22-year solar cycle seems to be visible in the temperature data. How is it possible physically? How can the sign matter? Well, the sign is physical because it is also the relative sign of the Sun's and Earth's magnetic field: the Earth's magnetic field is changing much more slowly. Because of subtle interactions - and combined effects - of these two magnetic fields on the Earth's atmosphere and the cosmic rays, the sign of the Sun's magnetic field almost certainly matters which is why we shouldn't be surprised by observed "fingerprints" of this cycle in the temperature data.



25 years: big volcano eruptions

Several times a century or so, we experience a gigantic volcano eruption that is able to flood the atmosphere with smoke, increase the reflection of the solar rays, and cool the Earth by as much as 0.5 °C.

Mt Pinatubo had such an effect in 1991 when it erupted. Some people are eagerly waiting for even bigger explosions, such as one in the Yellowstone Supervolcano.

While the cooling from such an explosion is not permanent and disappears in five years or so (together with the aerosols), it is clear that a higher frequency of eruptions could be able to lower the Earth's temperature at all times. There are other geological effects that can possibly have an influence on the climate, by producing or absorbing unexpected amounts of geothermal heat, but it is likely that many of these effects are not understood as of today.

The cooling effect of the eruptions is being mimicked in some geoengineering projects to cool the Earth. Also, aerosols emitted (from chimneys etc.) in a few decades after the World War II are likely to have contributed to the limited warming (or slow cooling) in that epoch. However, the actual size of this cooling contribution is notoriously unknown and people are not even sure that the overall effect was a cooling one.



30 years: Pacific Decadal Oscillation and other cycles

At the time scale of 1 decade, 30 years, or slightly longer, you may identify many other quasiperiodic phenomena that are qualitatively similar to the ENSO dynamics but they are slower. The Pacific Decadal Oscillation (PDO) is arguably the most important example even though similar cycles exist in the Atlantic Ocean (North Atlantic Oscillation...) and other places, too. A year ago or so, we switched to the cool phase of the PDO which means that the U.S. West Coast's sea is cooler than normal, wrapping a warmer-than-normal region deeper in the Pacific Ocean.

These cycles are slower than the El Nino/La Nina cycles because their basic dynamics comes not only from the equatorial Pacific Ocean but from larger portions of the world's ocean. You should realize that quite generally, every cycle influences the faster cycles by changing their "external parameters" (which are not really constant, if you look at the system from the viewpoint of eternity, including some very slow cycles).

So it seems natural to think - and the data seem to suggest - that the PDO cool phase increases the frequency of (faster) La Ninas while the PDO warm phase has increased the frequency of El Ninos which has probably contributed to the warming in the last 30 years (and the first 40 years of the 20th century, too).

Man-made greenhouse gases: 200 years

Clearly, this (heavily overhyped) effect is not periodic. Nevertheless, it is still associated with a time scale. I chose it to be two centuries because it can be expected that after a time scale comparable to 200 years, the fossil fuels will either be nearly depleted or largely replaced by another technology.

The burning of all fossil fuels may realistically quadruple the CO2 concentration in the atmosphere, to a number as high as 1,000 ppm. That would still leave the atmosphere very comfortable for humans (who need 10,000 ppm to feel dizzy) and other animals and much better for plants. The warming expected out of the burning of all fossil fuels is close to twice the climate sensitivity linked to the CO2 doubling.

Your humble correspondent and all other sensible people would estimate this doubled climate sensitivity to be probably below 2 °C while the IPCC might put it at 6 °C because their primary mission is fear-mongering and cherry-picking of the evidence meant to affect the public and the politicians and to establish a global eco-socialism.

At any rate, this is the maximum, "most catastrophic" temperature change that we can ever cause by burning all this useful material. And those 2 °C wouldn't be with us forever.

Removing excessive CO2: 500 years

After a time scale comparable to 500 years, most of the added atmospheric CO2 is going to be reabsorbed by the Earth and its layers including the biosphere (because of a faster plant growth) and especially the ocean (whose absorption increases, and the carbon will be slowly moving to its deep layers whose capacity to store carbon is virtually unlimited).

That will be returning the temperature to the original value or the value expected from the current albedo and concentration of greenhouse gases, too. Even with the most unrealistic "large" expectations for the sensitivity, it is thus unlikely that the burning of all fossil fuels would cause serious climatic problems at any particular time scale: we need several centuries to burn everything, but it is the same time scale at which Nature is already able to start to eliminate the effects.

Slow solar cycles: 400-1,000 years

I've mentioned the 11-year and 22-year solar cycles that can be observed from the number of sun spots. But sometimes, e.g. during the Maunder minimum or the Dalton minimum, the number of sun spots is low even during the maximum for a given 11-year cycle. So the 11-year cycles are being modulated by slower processes. I estimated their duration (of one approximate cycle) to be 400-1,000 years. These oscillations are arguably important for the alternation of epochs such as the Medieval Warm Period and the Little Ice Age.

The multi-centennial temperature swings caused by these slow solar cycles may be around 2-3 °C so they are probably as important as the warming we will ever generate by the burned fossil fuels.

Deep ocean circulation: 1,500 years

I said that the upper, "fast" layers of the ocean can only store the heat (most of the extra amount they receive) for 5 years or so. But there are many slower circulation patterns in the ocean that effectively replace water in the deeper layers after a millenium or two. But these processes are almost unable to influence the climate at shorter time scales because it takes a lot of time to transfer the heat to the deep ocean: you can't move too much heat by these "deep ocean" channels too quickly. Only if you average the temperatures over millenia, you may observe the "memory" of the deep ocean.

As you can see, whenever you average the climate over periods whose duration is comparable to "T", the processes and cycles whose duration is close to "T" are the most important ones, too. Why? The processes that are faster (shorter period than "T") get averaged out while the processes that are slower (longer period than "T") look almost constant and you treat their characteristic quantities as external, nearly constant parameters of your climate system.

Every physicist who is familiar with the philosophy of the Renormalization Group understands why it is important to choose the relevant degrees of freedom (quantities describing the climate, in this case, and their dynamics) depending on the time scale we want to understand.

Glaciation and Milankovitch cycles: tens of thousands of years

Finally, we are getting to the ice ages and interglacials. After tens of thousands of years, the temperature changes by 8 °C or so (the typical differences between the highs and lows of 20,000-year-long periods). The classical explanation of these cycles are the Milankovitch cycles - various astronomical, periodic or quasiperiodic oscillations of the Earth's orbit, including changes of its eccentricity, precession (changing tilt and "wobbling" of the Earth's axis), and so on.

These temperature swings also cause the concentration of all trace gases in the atmosphere, including the carbon dioxide, to oscillate. The warmer oceans you have, the less capable they are to store the gases, which means that they release them to the atmosphere (outgassing). During the warm interglacials, the CO2 concentration was around 280 ppm while during the ice ages, it was close to 180 ppm.

However, it is important to realize that the CO2 swings were just by-products of the temperature swings. Today, the CO2 in the atmosphere is influenced by other processes than temperature - including the SUVs - but these new processes don't respect the old relationship between the CO2 and temperature.

The old link only worked for outgassing - the influence of temperature on the gas concentrations - and has nothing to say about the opposite influence of CO2 on the temperature. So as we know very well, the additional increase of CO2 concetration by new 100 ppm (from 280 ppm to 380 ppm) hasn't warmed (and won't warm) the Earth by additional 8 °C. The greenhouse effect - an extra warming caused by CO2 - almost certainly exists but it hasn't appeared in any clearly visible form in the observational data yet because it is much weaker than the dominant processes (or the processes that have been dominant on Earth so far).

But I would like to argue that a huge part of the glaciation cycles may be due to the Earth's internal memory and variability. In a recent text about the probability of clustered temperature records, I argued that the Brownian motion is the best simple model to visualize the changes of global mean temperature over time scales between 1 and 10,000 years: the temperature change scales like the square root of the time separation (although the optimal exponent could slightly differ from 0.5, after all, but stay between 0 and 1). We used this simplified table of typical natural climate change after various time intervals:

• 1 year: 0.1 °C
• 100 years: 1 °C
• 400 years: 2 °C
• 900 years: 3 °C
• 2500 years: 5 °C
• 10000 years: 10 °C

I also argued that all the temperature changes for time separations longer than 4 years should be divided by 2 or so because the 1-year variability is overstated because of the ENSO cycles. So the maximum temperature change (jump) in the table could be closer to 5 °C rather than 10 °C. Notice that these estimates make sense. At time scales longer than 10,000 years, the "damping" - self-regulating mechanisms - become important and prevent the temperature from leaving the sensible, user-friendly interval.

So this table indicates that I think that the internal variability of the Earth is able to keep the temperature "away from a central value" for thousands of years so that the Brownian motion can be the best description of the "random" climate swings for the whole region of time scales between 4 years and 10,000 years. You should ask what are the actual "slow" variables of the Earth that may be changed in one direction for such a long time.

Obviously, the radiative balance tries to return the Earth's temperature to the theoretical central value dictated by the solar radiation within hours: that's why the daily temperature peaks around 2 p.m. or so. The upper oceans are able to store the heat (of either sign) for 5-10 years. But we also argued that the deep ocean takes millenia to circulate. And who knows, the geothermal processes may matter, too. All the "difficult" phenomena make the right "central value" for the Earth's temperature oscillate and these oscillations can be much slower than we could a priori imagine.

You know, if the Earth were just a piece of stone, it would adjust its temperature to the external influx of solar radiation very quickly, after hours. Obviously, it doesn't do so. There are many substantial fluctuations that the Earth's climate makes possible. They arise from the apparent complexity of the Earth's climate (and other features of its internal architecture). You might even argue that such climate change is necessary for life to exist.

One key parameter that determines the "naive equilibrium temperature" is the albedo - or the amount of incoming energy that is reflected by the Earth. The strength of the greenhouse effect plays a similar role on the outgoing side of the energy budget but let me talk about the albedo only. The amount of cloudiness is one factor that influences the albedo. This average cloudiness seems to be a "random number" but once again, it can be random in a very different way than you think. More concretely, it can stay at values very distant from the long-term average for pretty long periods of time. Even if you don't have any "obvious" explanation why the clouds are doing so.

This is similar to the currency exchange rates or any other functions of time in the financial markets. The world can work for exchange rates and prices that differ by a factor of 2 or more from the values achieved in the last year. There is no "robust" explanation why the rates are so much different from the last year. Most of the dynamics is irrational. But this degree of freedom simply does exist and behaves pretty much independently from others. It has its own inertia and doesn't care much about the other degrees of freedom.

That's how both financial markets and the climate behave. So the average amount of cloudiness or albedo may oscillate by many percent (or dozens of percent), changing the temperature by many degrees, and such changes can last for centuries or millenia. That's how the world almost certainly works whenever there exist no "very fast" mechanisms that abruptly try to return the system (and its "new" degrees of freedom) back to the equilibrium (dictated by the other degrees of freedom that everyone considers independent).

The glaciation cycles can also be influenced by slower, currently badly understood quasiperiodic processes inside the Sun.

Spiral arms of the Milky Way: hundreds of millions of years

As the Solar System is bubbling through different regions of our Galaxy, the amount of galactic cosmic rays is oscillating, too. These cosmic rays influence the rate of cloud formation and historical data have been used to show that they the longest periodicities in the concentration of galactic stuff help to change the temperature by plus minus 2 °C.

These historical facts also strengthen the theory that similar effects also operate at shorter time scales - where they become much faster and where the solar activity may be an important regulator of the amount of incoming cosmic rays (and thus the cloudiness).



Continental drift: hundreds of millions of years

There are many other processes that I haven't mentioned. Some of them are very slow. The continental drift radically changes the shape of the Earth's continents after hundreds of millions of years. Because continents may move from equatorial regions to the poles and vice versa, the continental drift also influences the effective average albedo relevant for the incoming solar radiation. In this long time frame, there are many other changes that should be studied, including huge changes of the thermohaline circulation, dramatic changes to the composition of the atmosphere (e.g. the arrival of the Earth's oxygen in the past), and others.

Of course, the effects of the continental drift on the local climate are much more dramatic because the continents are actually moving. That's why you can find evidence of tropical life in the Antarctica. But I suppose that most people will agree that it is not a task for the politicians in the 21st century to fight against the continental drift. After billions of years, the Sun's output may change significantly. The Sun will eventually die, too.

Unfortunately, many people are extremely irrational about related effects whose typical time scales is comparable to 100 years. They neglect dozens or hundreds of other effects, both slower and faster ones, even though these other phenomena are known to be at least equally important for our scientific understanding of the climate as their favorite process (the enhanced greenhouse effect in this case). And such an approach is simply unscientific.

And that's the memo.