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Living in a world of uncertainty

29 July 2015
Running meteorological models with different initial conditions helps forecasters and illustrates the atmosphere’s chaotic nature.

Have you ever experienced a small turn of events that resulted in a completely unexpected, unplanned outcome? Unexpected events happen in science too—more frequently than you might imagine.

Such was the case for mathematician and meteorologist Edward Lorenz of MIT. In the early 1960s he accidentally stumbled on one of the most significant findings in atmospheric science. Lorenz was using a simple computer model, which integrated a set of equations forward in time to make a prediction based on the initial state of the atmosphere. Curious about his model solutions, Lorenz decided to change the mathematical precision of the initial state. To his surprise, his minuscule changes resulted in a completely different forecast—almost as if he had used a different model! The finding led Lorenz to conclude that the atmosphere is a chaotic system, and that even the smallest errors in the initial estimate of the atmospheric conditions can limit our ability to predict weather phenomena.

Lorenz's discovery half a century ago has greatly influenced the way meteorologists predict and study weather today. Given that the atmosphere is a chaotic system, numerical forecasts will inevitably contain errors, due to instabilities of the atmospheric flow. To reduce the chances of large forecast errors, initial conditions must be known precisely and model uncertainties must be minimized. Unfortunately, direct observations are not available in much of the world, including most of the oceans, as well as remote locations where it is impossible to install and maintain weather instruments. Even with the existing observation networks, which include hundreds of weather balloons launched every day around the world, atmospheric measurements still include systematic instrumental errors.

The lack of a uniform and accurate set of observations to initialize numerical weather prediction models means that a single forecast is prone to large errors associated with both initial conditions and model uncertainty. To overcome the limitations, atmospheric scientists use ensemble prediction systems to generate multiple realizations of the future state of the atmosphere.

An ensemble prediction system generally consists of a single model, which is initialized several times, each with a different set of conditions. The initial conditions are taken from a distribution of random perturbations generated using a Monte Carlo algorithm. Each member of the ensemble differs from the other members solely by small perturbations of the initial conditions. Due both to the perturbations and the chaotic behavior of the atmosphere, each member of the forecast will produce a different prediction. By way of this forecasting method, we can consider the whole range of scenarios and then assess the uncertainty associated with a particular weather phenomenon.

Using ensemble forecasts also allows meteorologists to calculate the probability that a certain event will happen, which would be impossible if only one forecast was available. For example, imagine a tropical cyclone about to make landfall somewhere along the US East Coast. A single run with a particular model may forecast landfall in North Carolina, but the members of an ensemble prediction system may forecast landfall anywhere between North Carolina and New Jersey. With an ensemble prediction system, it’s possible to calculate the likelihood that the tropical cyclone will make landfall in any particular city or town between North Carolina and New Jersey.

Ensemble forecasting is applied to a variety of weather phenomena, but here I’ll focus on tropical cyclones. My collaborators and I created a 96-member ensemble with the Advanced Hurricane Weather Research and Forecasting (AHW) model, which is a state-of-the-art atmospheric model used to study and predict tropical cyclones. The AHW model was run twice daily from August to November, in 2009–13, in association with the Hurricane Forecast Improvement Project (HFIP).

The first step was to obtain an initial estimate of the atmospheric conditions. Small, random perturbations were added to the initial conditions to create 96 different ensemble members. For each ensemble, a six-hour forecast was combined with observations (such as weather balloons, buoys, ships, satellite, and aircraft) using a technique called data assimilation. The technique takes into account errors associated with both the observations and the model in order to reach the best possible estimate of the atmospheric conditions. The assimilation of observations was repeated every six hours until the desired time of model initialization was reached. At that time, a five-day forecast was initialized for each of the 96 ensemble members.

Figure 1 shows an example of AHW ensemble forecasts for two tropical cyclones: tropical storms Katia and Ophelia, which formed during the 2011 Atlantic hurricane season. The five-day forecasts for Katia were initialized on 0000 UTC 30 August 2011; the five-day forecasts for Ophelia were initialized on 1200 UTC 28 September 2011. Both tropical cyclones had just been named tropical storms by the National Hurricane Center at the moment of forecast initialization.

Figure 1. Tracks (a, c) and intensities forecast for tropical cyclones Katia (a, b) and Ophelia (c, d) produced with the Advanced Hurricane WRF (AHW) ensemble prediction system. Gray lines depict each of the 96 ensemble members, and black lines depict the observations. (Adapted from R. Rios-Berrios, R. D. Torn, C. A. Davis, J. Atmos. Sci., in press.)

Figure 1. Tracks (a, c) and intensities forecast for tropical cyclones Katia (a, b) and Ophelia (c, d) produced with the Advanced Hurricane Weather Research and Forecasting (AHW) ensemble prediction system. Gray lines depict each of the 96 ensemble members, and black lines depict the observations. (Adapted from R. Rios-Berrios, R. D. Torn, C. A. Davis, J. Atmos. Sci., in press.)

The members of the AHW ensemble predicted for Katia a variety of tracks and intensities (depicted by the minimum sea-level pressure, where lower values correspond to a stronger tropical cyclone) . The track forecasts show fairly good agreement between members that Katia would move west-northwestward until reaching a longitude of approximately 60° W. After the storm reached 60° W, some members predicted that Katia would move westward into the Caribbean, whereas other members predicted that Katia would begin to move northwestward away from the Antilles. In reality, Katia moved further north than most members predicted, which illustrates the difficulty in predicting tropical cyclone tracks, even with 96 different forecasts.

The intensity forecasts also showed remarkable variability between members. The predicted zero-hour minimum pressure ranged between 1000 and 1015 hectopascals, whereas the 126-hour minimum pressure ranged between 945 and 1010 hPa. That difference in intensity implies that anything between a weak tropical storm and a major hurricane was possible! Weather forecasters can interpret the wide range as a low-confidence forecast. Notice, however, that even though the forecast variability between zero and 36 hours was small, none of the members captured the observed intensity.

Track and intensity forecasts for Ophelia also exhibited variability between ensemble members. Most members reproduced Ophelia’s general trajectory well, but some members predicted that Ophelia would move faster and farther west than it did in reality. In terms of intensity, once again the AHW ensemble was characterized by large uncertainty in the minimum pressure. As was the case for Katia, some members predicted that Ophelia would become a major hurricane, whereas other members predicted that Ophelia would remain a weak tropical storm. The largest difference between the members appeared around the 84-hour forecast, instead of 126 hours, as in the forecasts of Katia. After 84 hours, Ophelia started weakening and the variations between ensemble members started decreasing.

The two sets of AHW forecasts illustrate several benefits and drawbacks of using ensemble prediction systems. For both tropical cyclones, the AHW ensemble members made a variety of predictions as to where the tropical cyclones would go and how strong they would be during the five-day period. The only differences between the members were small perturbations to the initial conditions. That variety highlights the large impact that uncertainties in initial conditions have on numerical weather forecasts.

What is more, the ensembles exhibited large variability in the intensity forecasts for both tropical cyclones. That variability, caused by rapidly growing errors in the model, impedes weather forecasters in predicting tropical cyclone intensity. In the case of Katia, the ensemble had good agreement in the intensity between zero and 36 hours, but none of the members correctly matched the observed intensity. The lack of agreement illustrates a challenge of weather forecasting: Even with a large of number of ensemble members, meteorologists may not be able to predict the exact state of the atmosphere a couple of days in advance.

Yet ensemble forecasts can also be useful tools for researching atmospheric phenomena. Using the same forecasts as above, and taking a closer look at the ensemble members, it is possible to diagnose the physical processes behind the different intensity evolutions. As an example, compare one member that predicted Katia would intensify with another member that predicted Katia would remain weak throughout the five-day forecast period. Figure 2 shows the simulated radar reflectivity of both members at the 48-hr forecast (valid at 0000 UTC 1 September 2011). The simulated radar reflectivity is used to diagnose the structure and precipitation associated with each member. Even though the snapshots are taken early in the forecast, the two members already look substantially different from each other. Generally, the member that predicts intensification has more clouds and precipitation than the member that does not predict intensification.

Figure 2. Simulated radar reflectivity averaged between 1 and 3 km above the surface, valid at 0000 UTC 1 September 2011. Panel (a) shows the reflectivity for an ensemble member that predicted Katia would intensify, while panel (b) shows the reflectivity for an ensemble member that Katia would remain a weak tropical storm.

Figure 2. Simulated radar reflectivity averaged between 1 and 3 km above the surface, valid at 0000 UTC 1 September 2011. Panel (a) shows the reflectivity for an ensemble member that predicted Katia would intensify, while panel (b) shows the reflectivity for an ensemble member that Katia would remain a weak tropical storm.

My colleagues and I performed a detailed analysis of the Katia forecasts and found that the members with more clouds and precipitation were initialized with greater amounts of water vapor in the lowest 2 km. The additional amount of water vapor was essential to promote deep convective clouds (see figure 2a) that aided intensification via the release of latent heat and creation of cyclonic rotation. By contrast, those members with less water vapor in the initial conditions struggled to keep convective clouds organized around Katia, thereby failing to promote intensification (see figure 2b).

Comparing two Ophelia members highlights how uncertainty in initial conditions can quickly evolve into different forecast states. Figure 3 shows the 12-hour forecast (valid at 0000 UTC 29 September 2011) of a member that predicted Ophelia would intensify and another member that predicted Ophelia would remain weak throughout the five-day forecast period. Even after just 12 hours following model initialization, the two members have already evolved into substantially different states. The member that predicts intensification has more clouds and precipitation, especially north and west of Ophelia. By contrast, the other member exhibits fewer regions of precipitation and even suggests the presence of dry air in the vicinity of the storm.

Figure 3. Simulated radar reflectivity averaged between 1 and 3 km above the surface, valid at 0000 UTC 29 September 2011. Panel (a) shows the reflectivity for an ensemble member that predicted Ophelia would intensify, while panel (b) shows the reflectivity for an ensemble member that Ophelia would remain a weak tropical storm.

Figure 3. Simulated radar reflectivity averaged between 1 and 3 km above the surface, valid at 0000 UTC 29 September 2011. Panel (a) shows the reflectivity for an ensemble member that predicted Ophelia would intensify, while panel (b) shows the reflectivity for an ensemble member that Ophelia would remain a weak tropical storm.

In a detailed analysis of the forecasts, my colleagues and I found that intensifying members also had greater amounts of water vapor in the initial conditions, albeit at 4–6 km above the surface, not 2 km, as was the case for Katia. The greater amounts of water vapor also promoted deep convective clouds (see figure 3a), particularly north of Ophelia. Convective clouds then prevented other weather features (for example, an upper-tropospheric trough) from getting close to Ophelia, with the effect that Ophelia continued intensifying until reaching cool waters. The members with less water vapor and drier air in their initial conditions had fewer convective clouds (figure 3b), which allowed other weather features to come close to Ophelia and weaken the cyclonic circulation of the tropical cyclone.

This article illustrates the use of AHW ensembles for forecasting Atlantic hurricanes, but many more applications exist in the field of meteorology. Operational forecasting centers, such as the National Oceanic and Atmospheric Administration (NOAA) and the European Centre for Medium-Range Weather Forecasts (ECMWF), have developed their own ensemble prediction systems to provide real-time guidance to weather forecasters. That guidance can be used to predict any weather phenomena—from the minimum and maximum temperature at a particular location, to extreme weather events such as tornadoes and winter storms.

Ensemble models can also be used for a variety of long-term applications that include seasonal forecasts and climate variability assessment. Many scientists also use ensemble models to explore ways to improve numerical weather prediction models or to better understand weather and climate phenomena.

With increasing computer capabilities and more observational networks, further applications of ensemble prediction systems will emerge in the coming decades. It is fascinating to think that Lorenz, simply by changing numbers in a simple computer model, could prompt a discovery that would transform our approach to forecasting and studying weather and climate events!

Rosimar Rios-Berrios is a PhD student at the University at Albany, State University of New York, where she studies the dynamics of tropical cyclone formation and intensification under the direction of Ryan D. Torn and Christopher A. Davis.

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