What is the MJO? Part 5 - interannual and intraseasonal, prediction, beating chaos

The El Nino – Southern Oscillation (ENSO) phenomenon is another natural mode of climate variability with distinct, well-defined scales. ENSO refers to both El Nino events and their counterparts, La Nina events, in which the eastern equatorial Pacific ocean becomes either unusually warm or unusually cold. These ocean changes occur simultaneously with atmospheric changes. Rainfall, wind, and temperatures shift from their typical patterns over large regions of the earth, especially (but not only) in the tropics. The intrinsic spatial scale of an El Nino event is basically the size of the tropical part of the Pacific ocean. The intrinsic time scale, the time between successive El Ninos or La Ninas, is 2-7 years. We call this time range interannual, and say that ENSO is the dominant mode of interannual variability.

Again, as with every mode of climate variability (other than those set directly by the earth's orbit and rotation: the diurnal, annual, and tidal cycles) the period of ENSO has to be expressed as a range (2-7 years), not a single number. If it were a single number – say, 3 years - it would mean that El Ninos were perfectly predictable, since once one happened we would know the next would be exactly three years later. No such luck. Still, the time scale is well enough defined to stand out above the “noise” of the random year-to-year fluctuations of the climate. As with synoptic weather, we do have a body of theory for ENSO which explains its scales in terms of the underlying fluid dynamics. Since about the 1980s, we also have some ability to predict El Nino and La Nina several months to a year ahead of time, using computer models derived from that same fluid dynamics.

The MJO occupies the range of time scales between ENSO and day-to-day weather variability – between a few days and a couple of years. Arguably it is the only truly coherent mode of variability with a well-defined periodicity in that time scale range, weeks to months.

Understanding these coherent modes, with known space and time scales, enables us to predict the behavior of the atmosphere and ocean further in the future than we would otherwise be able to. Ed Lorenz showed in the 1960s that because the atmosphere is chaotic, weather – the specific weather that will occur on a specific day – can’t be predicted very far in advance; probably not more than about two weeks. However, because ENSO influences the climate – the average weather over a period of weeks, months, or longer – and because El Nino and La Nina events tend to take a year or so to develop, mature, and then decay, knowing the state of ENSO allows us to make seasonal climate forecasts. These are predictions about how the weather over the next several seasons will differ from normal, though they don’t say anything about any particular day. Because we have computer models that simulate the evolution of the climate system, sometimes we can even go further and predict the appearance of an El Nino or La Nina event before it starts.

Understanding of the MJO allows us (just since pretty recently) to make intraseasonal forecasts. These are also predictions of the average weather over a period, rather than for a single day. Because the MJO time scale is so much shorter than that of ENSO, however, the we are predicting the average weather just for a period of a week or two. These forecasts are somewhere in between weather and climate prediction. Because their time scales are not very much longer than those of weather forecasts, though, in some circumstances they can almost allow us to predict the weather further in advance than Lorenz told us was possible.

What is the MJO? Part 4 - more background on modes of variability

Besides the scales imposed by the planet itself and its motions in the solar system, the atmosphere and ocean can generate their own scales. A characteristic of fluids is that their motions can, at least in principle, have any scale that their total dimensions allow. In any turbulent fluid motion – for example, a smoke plume billowing from a smokestack - there are whirls or “eddies” of many different sizes, from the total size taken up by the fluid (say, the total width of the smokestack plume) down to something much smaller. This multiplicity of scales is almost a working definition of turbulence, in fact, and the atmosphere and ocean are turbulent in this sense.

In a turbulent fluid, like in other physical systems (e.g., atomic gases) we can compute a “spectrum”, in either space or time. If we have enough measurements of the fluid motion, we can compute a spatial spectrum which tells us how much energy is in eddies of each size, or a temporal spectrum which tells us how much energy is in fluctuations of each frequency. The idea and the math involved are exactly the same as for the wavelength and frequency spectra of atomic gases, but the results are completely different. In a fluid undergoing pure turbulent motion, there are no distinct frequencies or wavelengths which have either much more or less energy than those nearby – no spectral lines. Rather, the spectrum is smooth, but "red". This has nothing to do with the color red now, but just means there is more energy in large scales than small. The bigger and slower the eddy, the more energy it has, but no specific size or speed is favored - there are no particular natural scales that emerge from the dynamics.

The atmosphere and ocean are turbulent, but they are not pure turbulence. On top of the overall continuous red spectrum, there are a few “peaks” – not precise frequencies as in atomic gases, but distinct frequency ranges (just like the range of heights in a group of human beings, different but all not too far from a typical value) – with which the fluids oscillate preferentially. These correspond to particular weather or climate phenomena, and the task of atmosphere and ocean science is to explain these phenomena. Just as in other sciences, any successful explanation must explain the scales.

One example is the “synoptic” low and high pressure systems that produce most of the weather in the middle and high latitudes. These have time scales of a few days – most of the time, we know that’s about how long the weather we’re experiencing at the moment is likely to last – and spatial scales of a few thousand km (say, the size of the United States, or some good fraction of it; look at the weather map today, and see how big the region is that is under roughly the same weather pattern as where you live). The space and time scales are related by a speed; if you know how far away the next weather change is, and you know how fast it is moving, you can figure out how soon it will arrive. That speed is also an important scale of the system, a velocity scale. For the midlatitude weather, it’s a few meters per second; this happens to be (not entirely by accident) similar to the scale of the actual wind velocity near the surface of the earth.

The scales of midlatitude synoptic weather systems were successfully explained by the theory of baroclinic instability developed by Jule Charney and Eric Eady in the 1940s, building on earlier work of Carl-Gustav Rossby and others. The enterprise of modern numerical weather prediction – the practice of using computers to solve equations derived from physics in order to produce the weather forecasts that we all rely on – grew out of that theory. The scales are ultimately related to the natural scales of the system – the size and rotation rate of the earth, etc. – but not in a simple way. The inherent dynamics of the fluid system plays an essential role in setting the scales of the weather systems we observe.

What is the MJO? Part 3 - on modes of variability, and space and time scales

The MJO is a distinct, coherent mode of variability, with well-defined space and time scales. There are not many such modes in the climate system, and it behooves us to understand the few that there are very well. They provide most of the useful predictability that we can use in making forecasts, and are also fundamental to our understanding of the system as a whole.

When we say the MJO is a distinct, coherent mode of variability, what do we mean by that? We mean that while the weather tends to fluctuate in ways that are chaotic and difficult to predict, certain patterns are there which give a certain degree of order to the chaos. These patterns are distinguished by particular scales in space and time – how big they are and how long they last. In this post I will give a little more context to this idea, before going on to discuss the MJO in particular.

In the sciences, an essential part of explaining anything is explaining its scales, meaning the magnitudes of key quantities expressed in physical units. For example, some of the scales of a biological species – say, homo sapiens - are its physical size (height and weight), its lifetime, the mass of its brain relative to its total body mass, etc. All these quantities vary from one individual to another, but they are well bounded within a fairly narrow range – no adult human being is two inches tall or 20 feet tall, for example. Any theory of human evolution which doesn’t include some explanation of these scales (about two meters for height, a few decades to maybe a century for lifetime, etc.) would be pretty poor.

To take an example from physics, it was discovered in the 19^th century that atomic gases have distinct spectra, meaning that when stimulated they emit light only of very specific colors. Since light is a wave, a color corresponds to a particular wavelength as well as a specific frequency. Hydrogen, say, emits light at a precise set of frequencies, but not at any others in between those. Why is that, and what determines which frequencies they are? Quantum mechanics emerged in the early 20^th century in part to answer these questions.

In the climate system, there are a few natural space and time scales that are imposed by external factors. The size of the earth itself – its radius and surface area - determine the horizontal size of the atmosphere and oceans, since obviously those have to fit on the planet. That gives us at least one inherent spatial scale.

What about time scales? The length of the day is set by the rate of rotation of the earth on its axis, and the length of the year is set by the orbit of the earth around the sun. These two astronomical rotation periods drive the most regular, and thus most predictable variations in the weather and climate. We know without a doubt that night will be darker, and usually cooler compared to day; and (outside the tropics at least) that winter will be colder compared to summer. We take for granted that we know and understand these very large and important modes of variability – the diurnal and annual cycles – very well, and that all the effort we put into predicting weather and climate is about predicting just the differences from those well-known cycles. It’s worth keeping in mind, though, that their real causes weren’t always so well understood.

What is the MJO? Part 2

MJO as a fluctuation of the monsoon

Over the wettest parts of the tropics, the climate tends to be monsoonal. This means two things:

1. There is a wet season and a dry season,

2. The wind blows in different directions in the two seasons. Westerly (from the west to the east) in the rainy season, and easterly (from the east to the west) in the dry season.

In monsoonal climates, most of the rain that falls in the entire year falls in the wet season; the dry season tends to be almost completely dry. Temperature, on the other hand, doesn’t differ all that much between the seasons. This is the opposite of what happens in some midlatitude climates. For example, in New York City, the temperature is tremendously different in summer and winter, but the amount of precipitation is pretty similar in the two seasons (though some of it is snow in the winter). Another difference is when it is hottest or coldest. In monsoon climates, the rainy season comes at what would be the peak of summer, when the sun is high and you would think it would be hottest; but all the clouds and rain cool things down. The hottest time is actually the late dry season, just before the monsoon, which would be “spring” at higher latitudes.

We think of the monsoons as occurring over land. India in particular is the most famous monsoon region. The Indian monsoon is not just India’s, but extends into southeast Asia as well. Northern Australia and northern South America also have monsoons, as does West Africa, and (arguably) southwestern north America. But the land monsoons are not the whole story. Actually the climate is monsoonal over large regions of tropical ocean also. The tropical Indian ocean experiences the monsoon just as much as India itself does, and so does the tropical western Pacific (say, from Asia to the date line, within 10 or 20 degrees of the equator). By this we mean that over these parts of the oceans, there is a season when it rains a lot and a season when it doesn’t, and the wind shifts from easterly in the dry season to westerly in the rainy season.

Just like summers and winters at higher latitudes, monsoon seasons aren’t exactly the same from one year to the next. Some wet seasons are wetter and some drier than others. Some start earlier, or later; or end earlier or later. Once the rains do start, they may keep going for a long time, but on the other hand they may stop and start. Sometimes there are “breaks” in the middle of monsoon season, during which it may rain little or not at all.

While rainy periods and breaks don’t come and go with complete regularity, there is some rhythm to them. The weather tends to switch from rainy to dry a few times over the course of a rainy season. This is what we mean by “intraseasonal” variability. The period of “intraseasonal oscillations” – the time for one complete cycle to complete itself - is sometimes quoted as 40-50 or 30-60 days, but it’s just as well to think of it as “a few times in a season”. These intraseasonal oscillations affect the land monsoon regions, but are actually strongest over the oceans.

What Roland Madden and Paul Julian discovered in the early 1970s is not just that these active and break periods occur over the oceans (to people living on the islands or adjacent continents this surely was known already) but that there are connections between all the active and break cycles occurring in different places. The activeness or breakness – the “phase”, in jargon – occupies a large chunk of real estate at any given time, but moves at a leisurely pace from west to east. (In northern hemisphere summer, the Indian and southeast Asian monsoon season, it can also move from south to north.) This is the MJO – the eastward-propagating, intraseasonal variability of the monsoons, especially (but not only) over the oceans.

What is the MJO? Part 1

The words Madden-Julian Oscillation (MJO) refer to a tendency of the weather in some regions of the tropics to fluctuate between rainier and drier states a few times over the course of a season. In the rainy state, the wind close to the earth’s surface tends to blow from west to east (“westerly”), while in the dry state it blows from east to west (“easterly”). A given state tends to last a month or two, and to cover a region of size several thousand km in the east-west direction. Changes from rainy to dry (or vice versa) tend to progress slowly from west to east so that – for example - if it is rainy in one place, it will probably become rainy soon in places nearby to the east of there. The MJO most strongly affects the weather over the tropical Indian and western Pacific oceans, but also influences places far from there, including at higher latitudes.

In the scientific literature you will find statements like this. “The MJO is a mode of natural variability in the tropical climate system characterized by planetary spatial scale, intraseasonal (30-60 day) time scale, and eastward propagation.” Translating that into English one bit at a time:

“A mode of natural variability” has two parts, “mode of variability” and “natural”. “Natural” means “not caused by humans”. The MJO would be there in the absence of human perturbations to the climate. It is not a result of global warming (though it is quite possible that some of its properties will change as the climate warms). “Mode of variability” means that it is a tendency for some aspects of the climate to change in a particular ways. The changes are generally back and forth between two states, rather than permanent. In this case the aspects that change most dramatically include rain, clouds, and wind.

“In the tropical climate system” means that the MJO occurs primarily in the tropics; “climate system” means in this context that both the atmosphere and ocean are involved (although for the MJO we believe that the most important action is in the atmosphere, while the ocean mainly responds to that).

“Planetary spatial scale” means that if a given state of the MJO (i.e., rainy or dry, or in jargon, “active” or “suppressed”) is in place somewhere, the same state tends to be in place everywhere around there for a long distance. “Long” here means at least thousands of km. Really the term “planetary spatial scale” means “not many times smaller than the circumference of the earth”. The circumference of the earth at the equator is 40,000 km, so planetary scale means maybe at least 5,000-10,000 km.

“Intraseasonal (30-60 day) time scale” means that 30-60 days is the typical “period”, or time it takes for a given state of the MJO (rainy or dry) to repeat itself after having first switched to the other state. The time to switch from one state to the other would then be half that period. The range 30-60 days, rather than just a single number, indicates that the switching back in forth is not that regular. In mathematical terms we would say the MJO is not truly “periodic”, but only “quasi-periodic”. (This is typical of nearly all natural climate and weather fluctuations, and is what makes them difficult to predict far in advance; truly periodic fluctuations are the diurnal cycle (day-night) and the seasonal cycle, both of which are easy to predict because their periods are known exactly and never change.) The word “intraseasonal” refers to the fact that 30-60 days is a little shorter than a season (especially in tropical regions where one might say there are really only two seasons in a year) so that within a given season there is time for a few MJO cycles.

“Eastward propagation” means that if a rainy MJO phase is happening somewhere, it will happen a little later in places east of there. In particular, MJO events tend to start in the Indian ocean and move across Indonesia to the western Pacific. The speed at which they move is around 5 meters per second. After reaching the western Pacific, MJO events continue moving eastward, into the eastern Pacific, then across the Americas into the Atlantic; but in those parts of the world the change in the weather that accompanies the MJO is often not as strong as it was over the Indian and western Pacific oceans.