# Large-Scale Atmospheric Equatorial Waves

By: TomTaylor, 10:24 PM GMT on March 28, 2013

AussieStorm had a question last night about equatorial rossby waves and I realized that atmospheric equatorial waves are something almost none of us pay attention to on the blog. In fact, I'd be willing to bet most of us on the blog have no idea what an equatorial rossby wave is. Realizing this, I thought it was a good opportunity to write a blog...

Atmospheric equatorial kelvin waves, rossby waves, and mixed gravity-rossby waves are an important source of intraseasonal variability in the tropics. In a sense, these waves are very similar to the Madden-Jullian Oscillation (MJO). Like the MJO, there exists an upward (enhanced convection) and downward motion (suppressed convection) phase of the wave. Structurally, however, there are some key differences between these waves, which I will get into later. In this blog I will try and outline my basic understanding of atmospheric equatorial waves below. I will admit, I don't understand much of the physical or mathematical reasoning behind equatorial waves (which most sites on the internet seem to beat to death), but for our intents and purposes on the blog, the understanding of the mathematical representation is completely unnecessary. Also, keep in mind this blog is referring to large-scale atmospheric equatorial waves. That does not include African Easterly Waves, which are an entirely different subject.

Figure 1: Directional Propagation of Equatorial Atmospheric Kevlin, Rossby, and Mixed Rossby-Gravity Waves. Notice how kelvin waves travel eastward, while rossby waves and mixed rossby-gravity waves travel westward. Also note how these waves stay along or near the equator.

As previously mentioned, there are few different types of equatorial waves that exist. In the atmosphere, there are kelvin waves, rossby waves, and mixed rossby-gravity waves. Equatorial kelvin and rossby waves also exist in the ocean, but that's a whole 'nother story. Anyway, these waves are called equatorial waves because they exist and stay near the equator, only traveling zonally (east or west, as seen in the graphic above). Specifically, kelvin waves travel eastward, while rossby and mixed gravity-rossby waves travel westward. For each of these waves, the wavelength is very long (on the order of several thousand miles), the period is long (about a week), and the amplitude is low. In other words, they span very long distances zonally (east-west), travel slowly, and create only subtle variations in the atmosphere -- most of these waves weren't understood or even observed until the advent of satellites. As I mentioned earlier, these waves are very similar to the MJO. The difference between these waves and the MJO are the direction in which they propagate (only kelvin waves travel in the same direction as the MJO), the wavelength (MJO's wavelength can be as long as the Earth's circumference, the waves discussed here are only a few thousand miles long), the amplitude (MJO has a greater amplitude meaning it will cause greater anomalies in upward or downward motion), and the phase period (MJO's phase is 30-60 days, the waves discussed here are about a week) which can be thought of as the amount of time it takes for one wave to pass bye (i.e. how long it takes to get from the upward motion phase of one wave to the upward motion phase of the next wave). Since the amplitude of these waves is low and the wavelength and period of these waves is long, you probably won't notice an atmospheric equatorial wave passing overhead, though you may notice slightly more convective activity. As a comparison, in the mid-latitudes, the passing of a rossby wave is quite significant as changes in temperature, wind, humidity, etc. are all easily felt simply by walking outside. Aside from differences in the direction in which these waves propagate, there are also fundamental differences in the structure of these waves, as shown below.

Structure of Atmospheric Equatorial Waves

Figure 2: Idealized Atmospheric Equatorial Kelvin Wave Structure. Notice the trough and ridge of the wave is centered on the equator. This means the kelvin wave exhibits maximum amplitude directly over the equator. The convectively active side of the wave is on the west side of the eastward traveling low since this is where the greatest convergence is. The opposite side experiences suppressed convective activity for the exact opposite reason -- divergence. Also note the wave travel speeds at the top of the diagram. The exact velocities aren't very important, but it is worth noting that a dry, or convectively inactive, wave travels slower than a moist, or convectively active, wave. Kelvin waves have a period of about one to two weeks depending on levels of convective activity. Since kelvin waves travel eastward, they are important in the maintenance of the MJO, though kelvin waves travel at a faster velocity than the MJO. The wavelength of a kelvin wave varies between 30-90 degrees of longitude (usually right around 60 degrees of longitude), with a zonal wavenumber is usually 2 to 3 (meaning you will rarely ever see more than 3 kelvin waves across the tropics).

Figure 3: Idealized Atmospheric Equatorial Rossby Wave Structure. Notice with the rossby wave, there exists symmetric lows and highs (areas of upward and downward motion) on either side of the equator, unlike the kelvin wave. This means the maximum amplitude of the wave will be found on either side of the equator (not centered on the equator). Additionally, since the rossby wave is traveling westward, the maximum convergence is to the east of the low, creating a convective maximum in this region. And again, notice the slower wave propagation for the moist (convectively active) wave. The equatorial rossby wave also has a slower propagation than the kelvin wave. Rossby waves have a similar wavelength and wavenumber as kelvin waves (about 40-100 degrees of longitude and no more than 3 waves at a time) but because of there slower travel speed, they have a phase period of a little more than two weeks (though they tend to dissipate before a wave makes a complete passage over a given location).

Figure 4: Idealized Atmospheric Equatorial Mixed Rossby-Gravity Wave. Ideally, the mixed rossby-gravity wave consists of a region of low pressure (upward motion) and high pressure (downward motion) sitting opposite each other across the equator, as seen in the top half of the image. When a mixed rossby-gravity wave becomes convectively active, however, these regions of upward and downward motion become distorted, with the low lagging behind. Convectively active regions are denoted by the cloud shading. Of all the waves, mixed rossby-gravity waves have the shortest wavelength of around 15-40 degrees in longitude. As a result, they also have the fastest phase period (4-5 days) and the highest wave number (up to 4-5 waves around the tropics at any given time).

Significance of Atmospheric Equatorial Waves

The significance of these waves lies in the fact that they create anomalies in the atmosphere. The anomalies are fairly small as I mentioned the amplitude of these waves is relatively small (compared to the extratropics or the MJO), but they are anomalies nonetheless. These anomalies are significant because they bring periods of enhanced upward or downward motion to regions within the tropics (exactly like the MJO). These waves may or may not be convectively-coupled (CCKW sound familiar? CCKW stands for Convectively-Coupled Kelvin Wave, for those unaware). Convectively-coupled simply means the upward motion portion of the wave is associated with convection. The more convection associated with the wave, the greater the upward motion the wave will have. If a wave has more upward motion, it will have greater cyclonic vorticity, which results in a slower traveling wave. Thus, like the MJO, the more convection associated with the wave, the slower it will travel. An additional complication of this is that waves tend to be much more active and move slower over the western Pacific and Indian Ocean (again, like the MJO which is also more active and travels slower over these regions) as a result of the warmer waters in the Indian and western Pacific region (warmer waters allow for more convection).

Figure 5: Areas of Enhanced and Suppressed Convective Activity. The total Outgoing Longwave Radiation (OLR) anomaly signal is shown in the first image, followed by the OLR anomaly produced by the MJO (second image), equatorial rossby wave (third image), kelvin wave (fourth image), and finally, the mixed rossby-gravity wave (fifth image). Areas of decreased OLR (blue shading) and increased OLR (yellow shading) represent areas of enhanced and suppressed convection, respectively. As we see in this image, the areas of enhanced (blue shading) and suppressed (yellow shading) convection match the structure of the waves shown previously. Also note how the scale of the upward motion (blue) and downward motion (yellow) regions for each of the waves. With the MJO it is largest, followed by the kelvin wave, followed by the rossby and mixed rossby-gravity waves. In other words, after the MJO, kelvin waves will provide the greatest source of intraseasonal variability in the tropics, followed by rossby and mixed rossby-gravity waves.

Since these waves are more active in the Indian Ocean and western Pacific the presence of the upward motion phase of these waves provides a significant source of TC genesis. The reason these waves are most significant in these basins is because the waters are warmer (allowing for greater atmospheric equatorial wave activity) and the lack of African Easterly Waves. Since waters are cooler in the NE Pacific and Atlantic ocean, these large-scale atmospheric equatorial waves are not a significant source for TC genesis. In fact, rossby waves and mixed-gravity waves are almost completely insignificant to TC genesis in the Atlantic. Kelvin waves are more significant to Atlantic TC activity because they have a greater amplitude and larger area of upward motion than the rossby and mixed gravity-rossby waves. Still, even kelvin waves really only play a minor roll in TC genesis in the Atlantic. It is also worth noting that these atmospheric waves can excite the development of oceanic kelvin and rossby waves. Oceanic equatorial waves can warm (kelvin wave) or cool (rossby wave) equatorial waters leading to events like an El Nino or La Nina.

To summarize, atmospheric equatorial waves are long period (slow moving), long wavelength (seperated by long distances), low amplitude (hard to detect) waves. If you're a kelvin wave you travel east, if you're a rossby or mixed rossby-gravity wave you travel west. These waves are most active and most significant in the warmer waters of the Indian Ocean and west Pacific. If you want to track these waves in the atmosphere, check out Mike Ventrice's page. Matthew Wheeler's Page is very useful as well. Much of the diagrams and information I presented here was provided by the MetEd Introduction to Tropical Meteorology 2nd Edition Textbook. You do need to register to MetEd to view the textbook, but registration is completely free.

Updated: 10:40 PM GMT on March 28, 2013