A mathematician at ICTS is trying to answer this complex question.
BY NAVEYA GOPAL & DEBDUTTA PAUL
ಈ ಲೇಖನವನ್ನು ಕನ್ನಡದಲ್ಲಿ ಓದಲು ೨ನೇ ಪುಟಕ್ಕೆ ಹೋಗಿ.
Cyclones are a natural phenomenon that often hit coastal communities with violent thunderstorms, causing widespread damage to lives and livelihoods. Predicting the storm’s path can help minimise the havoc by initiating precautionary efforts.
Scientists have found it challenging to accurately predict the course of cyclones. For example, the cyclone Biparjoy, which started in the east-central Arabian Sea in June 2023, lasted 13 days. Its path changed nine times, which made it hard to predict. A mathematician at ICTS-TIFR may have a solution.
Cyclones are low-pressure systems accompanied by violent, circular winds. Ocean surface temperatures above 26 degrees help them form, and the Earth’s rotation sets them to spin. Across the globe, they go by different names: hurricanes, typhoons, and cyclones.
Being in the tropical zone, India frequently suffers the wreak of cyclones, usually more from the Bay of Bengal than the Arabian Sea. The cyclones travel from their origin for a few days to a week before hitting land. During this period, the forecasters strive to comprehend the path and intensity and provide communities a better chance to prepare.
Mathematicicans can predict the origin and evolution of a cyclone by modelling the conditions of the oceans and the atmosphere. However, these mathematical models consist of too many parameters. For example, temperature and pressure on the ocean’s surface and the ambient air play a crucial role. Moreover, local effects can affect its path. These include a difference in temperatures of different layers of water and air, even in small localities along the cyclone’s path, and local storms or vertical flow of air. If forecasters knew all these parameters, they would put their mathematical models on computers, churning out the exact paths.
Existing techniques
There are two primary challenges to the prediction exercise. One, no model can account for all the factors that determine the growth and trajectory of a cyclone. Two, the more realistic models that consider the complex interrelationship of all these factors may take too long to run on even the most advanced computers.
Researchers across the globe mitigate this problem in many ways. Meteorologists use data recorded over many decades from past cyclones in the same ocean or during similar times of the year to build the mathematical model. Then, they use the current cyclone’s past and present movement, observed between six to 12 hours, to update the model, which predicts the cyclone’s successive stages. However, this technique is only suitable for forecasts up to 24 hours.
Some researchers use techniques which predict a particular cyclone’s path by averaging over the behaviour of previous cyclones in the same ocean. But there’s a catch: the atmospheric and oceanic conditions that determine a cyclone’s path have changed drastically over the years.
The Indian Meteorological Department (IMD) combines the two techniques. But, there is another problem with this approach. Since none of the mathematical models are perfect, there is always some uncertainty in the predicted path introduced by the lack of precise estimates of the parameters in the model. Small uncertainties of the parameters can grow large with time and quickly become intractable. The IMD technique mitigates the uncertainty by giving a set of possible tracks. Thus, the prediction is not precise. The scientists at IMD constantly strive to make the predictions more precise.
Chicken-and-egg problem
Cyclones require warm water to form the eye, the storm’s centre. The ambient conditions in the ocean and the atmosphere around the eye determine which path it takes and how quickly it progresses. The storm, in turn, affects these conditions as it moves. So, predicting the eye’s path is a chicken-and-egg problem.
To get around it, some scientists use measurements of the atmospheric and oceanic conditions to estimate the initial conditions that led to the cyclone’s formation. Then, they run the numerical model with these initial conditions to predict the future path. However, since they use the observations to estimate the initial conditions, they are left with no way to test the model.
According to Vishal Vasan, a mathematician at ICTS-TIFR, Bengaluru, scientists can fix this problem by using data from the cyclone and feeding it back into their model.
In the absence of direct observations of the cyclone itself, scientists use observations from satellites and ground-based stations to draw conclusions about their cyclone models. But, India has about 500 ground stations, which are sparse for such a wide area. Scientists use the ground stattions to indirectly and infrequently measure specific parameters, like temperature, velocity of winds, pressure, moisture levels, raindrop size, and the amount of chemical species like sulfites and nitrites. Moreover, they use the satellites to measure the total amount of water in an air column, the amount of clouds in specific areas, and concentrations of chemical compounds like oxygen level. They also measure the heating on the Earth’s surface, which indirectly tells them about the amount of air heating in those areas.
The prospective solution
Vishal wants to create a standard procedure to club the sparse, infrequent observations with the known mathematical models. In mathematical jargon, this kind of problem is called an inverse problem. Mathematicians, he said, can frame many other physical problems in this language. For example, engineers locate natural gas reserves from observations of sound waves in different locations; particle physicists measure the properties of particles that scatter other known particles by observing the initial and final trajectories of the latter.
Solving the inverse problem will help mathematicians develop systematic ways to answer specific questions regarding specific models. If Vishal is successful, by observing the cyclone’s path and using the scientists’ models, one can derive the cyclone’s surrounding conditions and its velocity. “If I use simplified models with complicated data, I can estimate the atmospheric state,” he said.
The atmospheric state, in turn, will predict the cyclone’s future path. He concluded, “We hope that we converge to a solution faster than the cyclone is moving. Otherwise this exercise is a complete waste of time!”
The authors thank Professor Vishal Vasan for helpful discussions.