Researchers have developed a method for extrapolating sea surface temperatures from sparse data that is significantly more accurate than other commonly used computational methods and slightly more accurate than the best-performing AI model, while taking a fraction of the time to train. The work has implications for both short-term weather forecasting and longer-term climate predictions.

“Sea surface temperatures (SST) are a key factor in understanding everything from marine ecosystems and climate to weather predictions, but there are limitations to our ability to collect that data, so we often have sparse, or limited data,” says Mohammad Farazmand, associate professor of mathematics at North Carolina State University and corresponding author of the research.

SST data are collected from sources such as buoys and satellites, but there are limitations to each method. Buoys are more accurate but limited in number, while satellites cover more area, but atmospheric conditions can interfere with their accuracy. So oceanographers use complicated mathematical models to get the most accurate estimations of sea surface temperatures.

“Historically, federal agencies like the National Oceanic and Atmospheric Administration (NOAA) have used a combination of complicated differential equations to calculate these temperatures from sparse data,” Farazmand says.

“Recently some AI or machine learning models have been developed, but they are expensive both computationally and in terms of the time needed to train them. We wanted to see how our method stacked up against different computational methods such as Discrete Empirical Interpolation Method (DEIM) and some of the newer AI models.”

DEIM doesn’t rely solely on complicated mathematical models. Instead, it specifies a basis, or combination of patterns, that encodes information about the specific field you’re trying to estimate – in this case, SST. However, DEIM does not work well with sparse data.

Farazmand and the team developed a new method, Sparse Discrete Empirical Interpolation Method (S-DEIM). To compensate for missing, or sparse, data, S-DEIM utilizes historical data to estimate a so-called kernel vector, for which there is no closed-form mathematical formula.

The team compared the S-DEIM method to both DEIM and the highest performing AI model, a convolutional neuronal network (CNN), using a dataset containing 30 years of NOAA data. They withheld the last year of data from the models and asked them to predict what that final year’s SSTs would be. Then they compared the models’ predictions to that historical data.

S-DEIM was 40% more accurate than DEIM, and 2% more accurate than CNN. Additionally, the S-DEIM model took only one minute to train compared to 1 ½ hours for the CNN.

The researchers hope to continue improving the S-DEIM method’s accuracy.

“This work shows that S-DEIM is capable of utilizing sparse data to provide accurate results while reducing training and computational time,” Farazmand says.

The work appears in the Journal of Geophysical Research: Machine Learning and Computation and was part of a research experience for undergraduates (REU) partially supported by the National Science Foundation (NSF) under award DMS-2349611 as well as through grant DMS-2220548 (Algorithms for Threat Detection Program) and award DMS-2342344. REU participants and co-authors are Cassidy All, University of Colorado Boulder; Kevin Ho, Mississippi State University; Maya Magnuski, Bard College; and Christopher Nicolaides, Indiana University. Louisa Ebby, graduate student at NC State, also contributed to the work.

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