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.