On the Hovmoeller plot

In this post I will explain one of the standard graphical methods that we in meteorology, oceanography and climate science use, the Hovmoeller plot. We use this when we want to visualize phenomena that move in time and space, but we don’t want to have to look at (or make) a movie. We want to see the motion in a single, two-dimensional picture. We often use the Hovmoeller plot to visualize the MJO, and I will focus on a particular Hovmoeller plot that is used in MJO forecasting and research.

For example, here is a Hovmoeller plot that was produced by the DYNAMO forecast team as part of this week’s forecast. (Sorry it's a little blurry, our team of graphics experts here at Madden-Julian Conversation is on vacation this week.) This specific plot was produced by Matt Wheeler at the Centre for Australian Weather and Climate Research in Melbourne, Australia.

This plot shows, in colors, outgoing longwave radiation anomalies, averaged from 7.5S-7.5N latitude, as a function of longitude and time. Time is on the y axis, and runs downward, while longitude is on the x-axis. Projections on the MJO and other coherent tropical modes are superimposed in the contours. Let’s break that down one piece at a time.

Outgoing longwave radiation (OLR) is the energy flux (amount of energy per area per time) in infrared radiation coming up from the earth into space. Because it’s infrared, it is basically heat radiated by the earth and the atmosphere (i.e., it is not reflected sunlight, which is mostly visible light rather than infrared). How much radiation is emitted from something depends on what that something is made of – some things are good emitters and some things are bad emitters – and on its temperature. The warmer something is, the more radiation it emits. Radiation is emitted from the earth’s surface itself, land or sea; from gases in the atmosphere, especially water vapor; and from clouds.

If there are no clouds, the atmosphere is partially transparent. Most of the gases that make up the atmosphere are not great emitters, with the most important exception being water vapor, which is a relatively good emitter. So most of the radiation comes either from the surface, or from lower layers of the atmosphere where there most of the water vapor is. The atmosphere gets colder the higher you go, so the surface and lower layers are relatively warm compared to the upper atmosphere. Thus the OLR is high in clear skies, because the radiation is coming from warm places. On the other hand if there are thick, high clouds – say, the kind that go with heavy tropical rain - those are really good emitters, and also good absorbers. So they block the radiation that would otherwise come up from below, and the radiation the satellite sees is what is emitted from the tops of the clouds. The OLR will be low in this case, because the tops of the clouds are at high altitude, where it is very cold, so they don’t emit as much radiation as they would if they were lower down where it is warmer.

So to summarize, low OLR = high clouds, and probably rain; high OLR = clear skies. Low OLR is blue in the picture, high is red.

What’s shown in the picture is not the total OLR, but the OLR anomaly. If you were to just plot the total OLR, a lot of what you’d see would be the “climatology”, meaning “what is normally there”. The climatology is is computed by taking the average from many years of data for that place at the same time of year. Some places tend to have a lot of clouds and rain (e.g., Indonesia) and they would be blue, while others tend to be dry (e.g., Arabian peninsula) and they would be red. But we don’t need data now to tell us what normally happens at this time of year, we are interested in what is happening now. We want to know how that is different from the climatology. So we take the OLR at a given time and place, and subtract from it the climatology, to get the anomaly. Note that “anomaly” here doesn’t mean “something really unusual”, as it does in normal English usage; it just means “the difference between present conditions and the average of what has happened at this place at this time of year in the past”.

Ok. So there is an OLR anomaly defined every day at every point on the map – mathematically, it is a function of three variables: latitude, longitude, and time. That is too much information to visualize in a two-dimensional picture, so we average in latitude. We are interested in the deep tropics, right near the equator, so we average the OLR anomaly between (in this case) 7.5 degrees south and 7.5 degrees north.

The result is a near-equatorial OLR anomaly that is a function of longitude and time. Those are the two axes on the plot, longitude and time, and the color represents the OLR anomaly value. Blue means rainier than usual, red means drier than usual. Now, by tracking diagonal bands of color, we can see weather patterns moving. WARNING: MATHEMATICS ALERT. Call longitude x and time t. Now, remember your algebra: a line on the graph would the form t=ax+b, where b is the intercept (which in this case tells us the time at which the line hits the Greenwich meridian, at zero longitude) and a is the slope. Such a line describes a trajectory, something moving in longitude with time at a constant speed. The slope of the line is inversely related to the speed. In other words, the shallower the slope, the faster the line moves, as it crosses more longitudes in a shorter time. Because time runs down in this plot, a line sloping down to the right (a<0) means motion to the east, while a positive slope (a>0), means something moving to the west.

In the lower left corner of the plot, you see a ragged blue blob sloping down to the right; that’s the active phase of our recent MJO event. Let's point it out:

It was at 40E, in the western Indian ocean, around mid-october, and reached 120E, around Indonesia, just recently. This blob slants downward such that it takes 10 days or so to cross the Indian ocean, which corresponds (if you do the math) to a speed of a few meters per second. Above it, you see an orange-red blob with the same slant, which is the suppressed phase of the MJO that preceded the active phase.

The solid horizontal line running across the whole plot in early November represents the date on which the plot was made. Anything above that line is an observation of what happened, while anything below it is a statistical forecast. What is a statistical forecast? Basically it is a forecast based on the assumption that weather patterns will continue evolving as they normally do, based on past experience. In the case of the MJO, this means that a region of low OLR (rainy) that starts in the western Indian ocean and moves eastward at the typical speed (again, a few meters per second) will continue to go eastward at that speed into the western Pacific. Here, look at the blue contours that lie on top of the blue shaded region. Those contours result from a mathematical smoothing of the OLR anomaly, in an attempt to extract just what is the MJO – it’s the “envelope”, or large-scale pattern one might see if one let one’s eyes go unfocused, as opposed to the misshapen rougher features that indicate random weather variability within the envelope. The statistical forecast is essentially produced - as you can see by eye - by letting the contours of the envelope stick out below the date on which the forecast was made, with the same slope that they had before that date.

What are the other contours on the plot, some of which slant down to the left rather than to the right, and which have different slopes indicating different propagation speeds? These are other coherent tropical wave modes, known as Kelvin waves, Rossby waves, and others. We'll write about these in a later post.

A visit to Smart-R

I spent two hours in the Smart-R radar truck Friday noon. Smart-R is a typical mobile Doppler weather radar. Its antenna has a diameter of 2.4 meters, scanning in two directions: either vertically at constant azimuthal angle, or horizontally at constant elevation angle. A combination of different scan angles, called scan strategy, determines how radar "sees" cloud. It takes 10 minutes for Smart-R to finish a scan cycle. Here is a photo looking to southeast from half a mile away. Smart-R is tiny sitting in the red circle of this photo:

A closer look:

The bicycle to the left of the truck is the one Adam bought at upper west side of Manhattan and Daehyun brought all the way here. See the trees on the right of the truck; these are also in the first photo (all those tree to the right). These trees cause significant blockage of radar signals. Let's take a look at the workstation inside the truck:

Two radar images were on the top. There are lots of green area in the right top of the monitor from 5 clock to 10 clock. These are blind spots of Smart-R because of the tree blockage I mentioned above. Smart-R also leaves 15 degrees in north-northwest for people to walking to the truck. So Smart-R detects cloud systems only from 11 clock to 4 clock. Other than trees, buildings and ships and cranes can all possibly create blockages that we really want to avoid. There will be some construction work close to Smart-R during DYNAMO, and cranes will be a big concern.

At the moment, Smart-R is maintained by a small group of people: Courtney, Johathan and Emily. During my two weeks here, I have been working with them and Chidong, our big boss, to gather some statistical information from Smart-R data. Here is one of my outputs:

The colors are relative humidity collected from weather balloons; the blue curves shows counts of daily "Echotop", a quantity from Smart-R indicating the height of cloud top; the green curve in the bottom show the daily rain rate from Scott at S-Pol. This picture shows how the height of cloud top, relative humidity and rainfall varied over October. It's interesting to DYNAMO scientists because it may indicate some inherent relationship among these variables. In the end, we will use statistics like this to learn a great deal about climate in Indian ocean over the the 6 month period of DYNAMO.

Back to the big picture for a minute

We have just had a fantastic first month of DYNAMO. The project was designed to study how MJO events start in the Indian Ocean. With only a two-month intensive observing period, though, it was not guaranteed that we would see a really good case of MJO initiation. Sometimes the MJO is inactive, and with a typical MJO cycle lasting 1-2 months, there was a chance there would be an event but we wouldn’t catch it at its start. Instead, nature has cooperated beautifully. When the experiment started in late September, we were in a suppressed phase, with clear weather over much of the Indian ocean. Then, during the first weeks of October, we had a gradual transition to moister, more active conditions, transitioning to a full-on MJO in mid-late month. Now, the MJO is moving eastward into the “maritime continent” (the region around Indonesia and the Malay peninsula) and the Indian ocean is drying out again.

Just to illustrate the big picture, here is a series of satellite images spaced roughly five days apart, starting on October 1 and continuing to now. These are infrared images, meaning that it doesn’t matter if it’s night or day. (All but the last of these images are from 12 GMT, which is 5pm in the Maldives.) White represents thick, high clouds (which generally go with rain), black is clear skies and dry conditions, and the lighter grays generally indicate partially humid or cloudy conditions. (This is the “water vapor channel”, meaning that the image becomes lighter either due to clouds or to high atmospheric humidity, or both.)

October 1: There is convection in the eastern and Indian Ocean, in the Bay of Bengal and near Sumatra; and in the southern Indian ocean, south of the equator. (Note Gan island, marked in the image, is right about on the equator.) This convection may be normal seasonal monsoon activity, or partly associated with the MJO event that passed through a little earlier, before the experiment had really begun. The westernmost Indian ocean, just off Africa, and the Arabian sea as well, are dead quiet.

October 5: very similar to the previous image. Nothing much has changed.

October 10: somewhat similar again, except the Indian Ocean weather has dried out even more. Almost the entire western portion is completely tranquil, except for a thin "intertropical convergence zone" - thin line of convective clouds - in the southern hemisphere. This is the suppressed phase of the MJO.

October 15: Small signs of a little more action brewing. The southern ITCZ is a little stronger, and a little convection starting to be seen in the Arabian sea just west of southern India. Between this image and the next one, the MJO reached a record amplitude for "phase 1", where it's over the Atlantic and Africa. So we're not quite seeing it in the Indian Ocean yet, but at this point all the models and forecasters were very confidently - more confidently than usual - predicting that it would be coming soon.

October 20: The MJO cometh. The whole basin is looking more active esp. in the western Indian ocean north of the equator. If you look closely you can see two prongs of active convection in the west, one around 10N (parallel to the tip of India) and another around 5S (parallel with Diego Garcia, marked as "FJDG"), with a dry slot in between. This feature has persisted for weeks and is due to westerly (west-east) winds bringing in dry air from Africa and the subtropics. We'll write about that more later.

October 25: Now we're talking. Looks something like the previous image, but more white in the picture, indicating more convective clouds and rainfall throughout the basin.

October 30: The MJO has matured in the Indian ocean - we call this "phase 3". The western region is starting to dry out again as the convection moves east. In the northern Arabian Sea you can see some swirling in the clouds indicating formation of a tropical depression. Tropical cyclones often form in the latter periods of MJO active phases, just like now. This system has hung around for a long time and as I write this was recently named Tropical Cyclone Keila, just as it fizzles (not before bringing some rain to Oman and Yemen, it looked like from the satellite images).

November 4, 2130 GMT: The active phase is just about past us and the Indian ocean weather quiets down. The easternmost region is again the most active. However, the remnants of the MJO are visible in the twin blobs of white about 10 degrees either side of the equator just west of the DYNAMO array. The one in the middle of the Arabian Sea may well turn into another tropical cyclone, according to some of the models.

Expect more dry days

At Gan, we have been experiencing a few days with little rain, after some rainy days that Eric and Daehyun had discussed.

I did not expect this lack of rain on my flight here. There are other interesting things going on, though. Every 15 minutes, clouds over the sky are recorded by the four cameras facing the four directions on board the S-Pol. This is today's animation from sunrise to sunset from the camera facing east. Most of the clouds are not raining. They are moving toward the camera, because of the prevailing wind blowing west at upper levels. Around the noon time, there are some big raining cloud.

This was a picture facing northeast from my camera at the moment. This raining cloud did not move toward us, but moved northeastwards. It didn't bring any rain.

It turns out that this cloud is a tiny one on the radar screen, single convective cells. On the mobile Doppler radar screen, the Smart-R, it was a few kilometers away from us and tiny over a 300x300 area of the radar scope. They are within red circles in this radar image.

This cell was not organized, it did not grow high to 10 km, and it lasted only one and half hour. So this was not something particularly interesting for storm-chasers. It was something can be easily ignored. But our radar here captured its full life cycles. The radar is going to be running for 6 months. It will capture many, many of these single convective cells, also capture something much bigger, like cloud systems hundreds of kilometers, often called mesoscale convective systems.

The long period of radar observations during DYNAMO will give precious statistics of cloud systems over this part of Indian ocean. This is very important for developing numerical models for predicting global tropical weather and climate. Surely, it will take many years.

Another thing I want to mention. So far I haven't seen any cloud spinning. This is unlike what I observed at east coast of US or in Texas, where circulations can fire up convective systems. In the tropics, these clouds are more influenced by local vertical temperature and moisture profiles. Some people would say thermodynamics largely control these clouds; now I tend to agree with them. I do wish to do some research to find out how important is the regional circulation dynamics (e.g., gravity waves) for the clouds in the tropics.

What we see locally is only a little piece of the big MJO puzzle. In the big picture, this lack of rain is believed to caused by the suppressed phase of the MJO. The MJO phase diagram that Eric discussed looks like this:

Now the convective phase has moved to eastern Indian ocean and is expected to move further east. So there might be more days ahead with little rain. (These are good days for diving and snorkeling.) In the tropics, we also have many tropical waves. I hope to see some mesoscale scale systems from those waves locally soon.

OK, More Blogging (Including Bats)

At the time of writing this, I’m sitting just outside Male Airport waiting for my flight to Qatar, and sweating profusely. I took the 1 hour and 10 minute flight from Gan to Male that spans the entire western side of our northern balloon sounding array. The array very roughly forms a square and includes Colombo (Sri Lanka), Gan Island where I stayed for two weeks, Male, and a ship. The ship had been the R/V Revelle, but it has temporarily left its station. Hence, our sounding array has temporarily broken down. The flight was about 350 miles, and very roughly gives you an idea of how long our sounding arrays are on one side, although this distance is shorter than the distance between most stations in our two sounding arrays.

For much of my time on Addu Atoll, I was very disappointed that I could not get a good picture of the Addu Atoll Flying Foxes (bats). These things could carry off a small dog. Well, my luck changed while waiting at the airport for my flight. One fellow was sitting up in a fruit tree right outside the airport terminal, munching away.These bats are endangered just for this reason. They eat fruit (e.g. mangoes, papaya) and are hence killed by farmers protecting their crops. Most of my in-focus pictures feature the bat with a mouth full of food and hence the animal has a dopey and un-dignified look.

Here is a slightly out of focus picture without any eating involved. Now, doesn’t that look more dignified?

The Maldives are truly an amazing place. I took this picture on the plane to Male showing a few of the thousands of atolls making up the Maldives. The shapes of the landforms range from linear to donut-shaped, often with a deep abyss in the center. I snorkeled on my last day along the edge of the abyss that forms the center of Addu Atoll. It was a truly amazing experience.

A quiet day

Sunrise was at 0552 am at Hithadhoo today. No rain, a few isolated thunderstorms far away from the S-Pol site, our field office. This was a quiet day. Sunset was at 0555pm. 25 minutes before sunset, I left Container 9 beginning to ride the bike back from S-Pol to the resort. Today I started to use the bike that Eric left me. At the leaving time I took a picture of our container and the weather radar. Radar is obvious in the picture below. I labeled the Container 9 and lightning rods. Members of modeling groups, Smart-R people, and other visitors sit in Container 9.

Lighting rods are all around S-Pol. What's interesting is they are seldom used, because there are virtually no lightning since the beginning of DYNAMO. There are plenty of thunderstorm and rain, but no lightning. That's odd. Where is lightning? Look at the picture here:

This is a satellite image I borrowed from the DYNAMO data catlog. On top of this infrared satellite image of clouds are many purple plus signs; they are lightnings at 2am Oct 23. Plenty of them at Arabian Sea, but not at S-Pol, 0.59S, 73.1E. This is the typical situation of lightning over these days. Why this is happening is a mystery to me.

On my way back, I took another picture, 5 minutes ahead of sunset:

In a quiet day like this, we have little to expect from the radar screen. But chances to spot clouds are still plenty in a tropical island. 25 minutes after the sunset I got back in my room, in the dark.

Leaving the Maldives

I am leaving the Maldives tomorrow, and hence this will likely be my last post from the field. I leave with some bit of regret as I enjoyed the people of the Maldives as well as the enriching experience of being out in the field, but also feel that I leave with so much more to learn about the tropical atmosphere. I have gained a newfound appreciation of the complexity of the tropical atmosphere over the last couple of weeks, something that is difficult to gain from sitting at a desk in Fort Collins. Gust fronts propagate this way that blow up intense precipitation cells, upper level stratiform clouds move the opposite direction, dry air advects in from Africa and the Middle East in the west, and equatorial waves breeze through quickly, fundamentally altering the winds over the entire basin in the matter of a day or so. These are just some of the things I observed. I think that we also observed the initiation of a very interesting MJO event during my time here, and I experienced some of the heavy rains associated with this event. While we aren’t close to a complete understanding of how this event started in the Indian Ocean, we do know a few things so far. The central Indian Ocean near our observation array started out very dry in early October, and winds were generally from the west near the surface. At some point around October 10, the winds shifted rather abruptly to the east over much of the ocean. Accompanying this wind shift, moistening seemed to initiate on the equator first, and then soon was followed by moistening of the western Arabian Sea by east winds blowing moist air across India from the Bay of Bengal. We saw this moistening and shift in wind direction very nicely from the array of soundings we deployed during the project, and these will provide an invaluable resource to diagnose what precisely caused the moistening, in addition to model investigations we plan to do next. One other thing we realized during this project is that some of our commonly used indices used to diagnose the existence of the MJO may not perform well during all events. However, our understanding of what happened here is in its infancy. Tomorrow I leave on my 40+ hour adventure back to Fort Collins and reality. The Maldives will seem like a distant dream in a few days, I am sure. However, the DYNAMO field program is nowhere near over. My colleague Shuguang Wang arrived in the Maldives a couple of days ago to continue the experience of the modelers. Next, Adam Sobel and Zhiming Kuang arrive in November. They will likely experience many fascinating things on Addu Atoll and in the tropical atmosphere that are different from what I experienced here and will add to our fascination and understanding. This experience makes me want to come back to the field soon, as I feel that there are even more things that I need to learn. You may hear more from me in future blog posts, but these will likely be from behind my desk in Fort Collins or sitting on my living room couch (it was 3 degrees in Fort Collins last night! It will be quite the shock to the system to transition from our balmy 85 degree weather.)