The following estimates and forecasts are based on the academic works of Philippe Goulet Coulombe, professor at ESG, as well as his collaborators Francis X. Diebold (University of Pennsylvania) and Maximilian Göbel (University of Lisbon). See, in particular, Diebold, Goulet Coulombe, and Göbel (2022). La version française de cette page est disponible ici.
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:
- Feature-Engineered Linear Regression (FELR);
- Pocket Feature-Engineered Linear Regression (Pocket FELR);
- Feature-Engineered Machine Learning (FEML);
- Pocket Feature-Engineered Machine Learning (Pocket FEML);
- 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 (less than 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 2025
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 2025. Forecasts from 2012 to 2024 are those made on the same date (i.e., September 30 of 2012 to 2024) 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).
Figure 1 — Historical evolution of Arctic sea ice extent and forecasts from different models on September 30 of each year since 2012. Pink shading corresponds to the out-of-sample assessment period used for the calculations in Figure 3 and the confidence intervals reported in Figures 2 and 4. The slider allows you to zoom in on certain historical periods. The user can decide about including or excluding certain models by clicking on them in the legend.
The final value observed at the end of September 2024 is 4.36 million square kilometres — about the same as in 2023 (4.37), but markedly lower than 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.
Figure 2 — History of forecasts and their confidence intervals for September 2025. The x-axis corresponds to the date on which the forecast was made. The slider allows you to zoom in on certain historical periods. The user can decide about including or excluding certain models by clicking on them in the legend.
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.
Figure 3 — Out-of-sample performance of models over the period 2014-2024. Since this is the RMSE, the lower the measurement, the better the model performs. The x-axis corresponds to the date on which the forecast was made. The slider allows you to zoom in on certain historical periods. The user can decide about including or excluding certain models by clicking on them in the legend.
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. Nevertheless, the performance of Pocket FEML from 90 to 45 days ahead is weakly dominating Pocket FELR and clearly superior to the other two options. Improvements over the simpler model sometimes go as high as 0.2 million square kilometers. In sum, the recommendation is simple: it is advisable to use Pocket FELR in June, Pocket FEML in July. From August onwards the models are generally in alignment. If we thus wanted to “keep it sophisticatedly simple“, FELR seems to be the appropriate choice.
Figure 4 — History of forecasts and their confidence intervals for September 2021. The x-axis corresponds to the date on which the forecast was made. The slider allows you to zoom in on certain historical periods. The user can decide about including or excluding certain models by clicking on them in the legend.
Looking at the complete forecast path of 2024, between mid-June and the end of July, all models predicted an SIE higher than the observed value of 4.36. The peak of above 5.00 million km2 was reached in early July, before all models embarked on a steady downward path, culminating in the forecast period’s trough in early August, which was about 1.00 million km2 lower than the peak. Starting from mid-August onwards, all models transitioned towards the final reading of 4.36 million km2. The VARCTIC, which can only resort to information with a two-month lag, was still bullish in mid August, as its median projection pointed to a higher September SIE in 2023. Still the observed SIE minimum of 2023 was covered by the its 90% credible interval. In mid-September, also the VARCTIC almost nailed the target in line with other models.
References
Diebold, Francis X., and Glenn D. Rudebusch. “Probability assessments of an ice-free Arctic: Comparing statistical and climate model projections.” Journal of Econometrics, in press.
Diebold, Francis X., and Maximilian Göbel. “A benchmark model for fixed-target Arctic sea ice forecasting.” Economics Letters 215 (2022): 110478.
Diebold, Francis X., Goulet Coulombe, Philippe, and Maximilian Göbel. “Assessing and Comparing
Fixed-Target Forecasts of Arctic Sea Ice: Glide Charts for Feature-Engineered Linear Regression and Machine Learning Models.” arXiv:2206.10721.
Goulet Coulombe, Philippe. “The macroeconomy as a random forest.” Available at SSRN 3633110 (2020).
Goulet Coulombe, Philippe, and Maximilian Göbel. “Arctic amplification of anthropogenic forcing: a vector autoregressive analysis.” Journal of Climate 34.13 (2021): 5523-5541.