Sea Ice Forecasting & Machine Learning

Overview

The Arctic is warming at twice the rate of the planet. This warming rate serves both as a barometer of current conditions and a leading indicator of future climate change. Less sea ice and more open water are lowering albedo (the ability to reflect light) of the Arctic. This means that more of the Sun’s heat is absorbed by the Earth rather than reflected into the atmosphere. The immediate repercussions are an acceleration of the increase in temperatures in the Arctic region, as well as, ultimately, of the entire planet. This promotes the thawing and erosion of polar permafrost, thus releasing significant quantities of CO₂ and methane which, in themselves, drive up the risk of surpassing potential tipping point for global warming.

At 3.74 million square kilometers as of September 15, 2020, Arctic sea ice extent (SIE) ranked second to lowest since its measurement by satellite imagery began in 1978 – behind the record low of 2012. Indeed, in the last 40 years, the extent of Arctic summer sea ice has decreased by about 40%. An animated visualization of the phenomenon is available here. A continued decline in the SIE could accelerate global warming and threaten the composition of the Arctic ecosystem. The downtrend is well established. Most climate and statistical models project that it will disappear in September (the lowest point of the seasonal cycle) somewhere between 2040 and 2060. This melting obviously has climatic implications, but also economic and geopolitical consequences. Obvious examples include the opening of new, faster routes for the transport of goods (rather than the traditional routes via the Suez or Panama Canals) and the question of the control of this passage in the Arctic Territory.

Models

For all these reasons, there is increasing interest in forecasting Arctic sea ice extent in September (the equinox). In fact, the interest is such that the Sea Ice Prediction Network annually organizes the Sea Ice Outlook (SIO), a survey collecting projections from various groups of researchers. The forecasts are presented at four different horizons (June, July, August, September) and are based on a variety of models, ranging from simple statistical models to structural climate models, including machine learning techniques (ML). UPenn-UQAM forecasts are based on standard and ML econometric methods, detailed in a succession of scientific articles (Diebold and Rudebusch (2022, Journal of Econometrics), Goulet Coulombe and Göbel (2021, Journal of Climate), Diebold and Göbel (2022, Economics Letters), as well as Diebold, Göbel and Goulet Coulombe (2023, Energy Economics)). The five models are:

1. Feature-Engineered Linear Regression (FELR);
2. Pocket Feature-Engineered Linear Regression (Pocket FELR);
3. Feature-Engineered Machine Learning (FEML);
4. Pocket Feature-Engineered Machine Learning (Pocket FEML);
5. Vector Autoregression of the Arctic (VARCTIC).

These models’ objective is, among other things, to provide short-term and medium-term forecasts of the SIE each year. The first two are linear regressions. The predictors are constructed from different methods of aggregating recent SIE values which are available daily. Therefore, most UPenn-UQAM forecasts are available and updated daily rather than monthly (as aggregated by the SIO). “Pocket” means a “pocket” version of the model, i.e., more parsimonious in the choice of included predictors. This may be preferable in an environment where the number of observations to estimate parameters (or said differently, to train the algorithm) is limited (~ 40 years of data). FEML models are a Macroeconomic Random Forest version (Goulet Coulombe, 2020) of FELRs where the coefficients of the latter change over time according to a ML algorithm. This allows FEMLs to account for some relevant nonlinearities that were missed by FELRs. In addition, these use a wider set of variables such as air temperature, CO₂ emissions and ice thickness. The VARCTIC model similarly exploits a large set of variables, but includes them in a Bayesian VAR model and the forecasts are obtained iteratively at a monthly frequency.

Forecasts for September 2026

The forecasts of the models mentioned above are presented in Figure 1. The downtrend is particularly evident there. The pink area corresponds to the “out-of-sample” period that will be used to assess the past performance of the proposed approaches in Figure 3. The last point in each line is the current prediction (as of September 30) of each algorithm for September 2026. Forecasts from 2012 to 2025 are those made on the same date (i.e., September 30 of 2012 to 2025) for that year’s SIE and give an idea of the historical reliability of the various forecasts (which will be more systematically assessed in the next section).

The final value observed at the end of September 2025 is 4.75 million square kilometers — substantially higher than in 2024 (4.36), almost matching the observations of 2021 (4.92) and 2022 (4.87).

Hence, calling for a break in the clear downward trend might be premature. Nonetheless, there are three possible interpretations (or factors to weigh in) to explain the “higher” realizations of 2021 and 2022. Firstly, there is the possibility of the negative COVID shock on CO₂ emissions finally making its way into sea ice extent measurements. In Goulet Coulombe and Göbel (2021)’s results (and that of others too), it takes a minimum of 1.5 years for a negative CO₂ shock to have a noticeable positive and durable effect on sea ice extent. Secondly, we are at the onset of a new cycle for ocean heat content that could damper the abrupt trend we have been observing for the last 20 years. Recent observations could reflect that. Thirdly, it could be any other form of random upward shock, and the linear carbon models or quadratic trend models remain on track for an early disappearance of summer arctic sea ice. As one can tell, these are merely suggestions since — albeit being driven by known physical laws — the climate system remains “observationally chaotic” to climate scientists and statisticians. This will obviously sound familiar to fellow (macro)econometricians.

Naturally, there is vast uncertainty surrounding the forecast at a horizon of four months, which gradually shrinks as we approach the fixed target. Consequently, it is informative to look at the history of the forecasts produced daily since June 1, as well as the confidence intervals around them. Figure 2 shows the models’ daily predictions for this year’s September SIE — coinciding with the annual SIE minimum — in quasi real-time.

Past Forecasts and Historical Performance

To know which model to use and when, we can use a measure of past performance at each forecast horizon. Errors are obtained from a pseudo-out-of-sample recursive forecasting exercise, which ensures that models with the ability to overfit the target are not mechanically put to an advantage. The measurement used is the root mean squared error (RMSE), which is standard in the literature and penalizes large errors more than small ones. The results are nearly identical using the mean absolute error.

First, Pocket FELR stands out as the best benchmark until the end of June with a smaller RMSE over the entire period. Given the small estimation sample, it is not altogether surprising that the predictive gains provided by FEML are of limited size—ML models typically outperform simple models when many observations are available. Over the last 10 years, the simpler benchmarks — FELR & Pocket FELR — have turned out to be remarkably robust. If we thus wanted to “keep it sophisticatedly simple”, FELR seems to be the appropriate choice.

Looking at the complete forecast path of 2025, up until early September, all models predicted an SIE lower than the observed value of 4.75. Pocket FEML hereby turned out to be the most volatile of the four forecasters, especially in the first half of the forecasting period where it even reached lows of around 3.63 million km². From late July onward, all models almost marched in lockstep towards the final reading of 4.75 million km². The VARCTIC, which can only resort to information with a two-month lag, has been almost exactly on target throughout the whole forecast period, before edging slightly lower on the last submission date. Still, the observed SIE minimum of 2025 was covered by its 90% credible interval.