1. Introduction
The Arctic is warming 4 times as fast as the rest of the world (Chylek et al. 2022), resulting in significant sea ice loss (Stroeve et al. 2007) throughout all months of the year. The rate of decrease in sea ice is consistent with increasing global mean surface temperatures, as a direct consequence of increasing greenhouse gases in the atmosphere (Vihma 2014). Some studies have quantified this relationship. Each metric ton of emitted CO2 corresponds to 3 ± 0.3 m2 of September sea ice loss (Notz and Stroeve 2016). Each 1°C of global mean surface temperature increase corresponds to 3–4 million km2 of summer sea ice loss (Niederdrenk and Notz 2018). The changes in sea ice are both a decline in extent and an overall thinning of the ice present (Meier et al. 2007; Stroeve and Notz 2018; Kwok 2018). As the sea ice pack loses overall mass, ocean waves, subsurface heat in the ocean, and winds will increasingly affect ice extent (Thomson et al. 2022), by compacting or expanding regions of thin ice types at the edge of the pack. The resulting changes in the ice edge in the western Arctic can be up to 40 km day−1, far faster than predicted by climatology (Smith et al. 2018). Current predictions for the Arctic indicate the evolution of sea ice from perennial to seasonal cover, with forecasts of the first ice-free Arctic summer ranging from 2030 (Screen and Deser 2019) to 2050 (Notz and SIMIP Community 2020). These rapidly changing conditions can result in unforeseen hazards. With sea ice retreat opening large areas of the Arctic to access by commercial and military fleets, forecasts in the time frame of several days to a week are needed for ships to proceed safely. Further, the Arctic is also the home to many indigenous populations who rely on the sea ice cover for travel and subsistence, some of whom have expressed interest in high-resolution short-term sea ice forecasts (Segal et al. 2020).
Therefore, understanding sea ice extent, concentration, and anomalies, as well as their trends, can provide the much-needed information required as ships navigate this area, drilling platforms are established, and residential communities adapt to their changing environment. An example of information modified by the changing Arctic are efforts to provide seasonal predictions of the summertime minimum Arctic sea ice path (MIP), or, put more simply, calculating a path through the Northeast and/or Northwest Passages that will involve the minimum possible distance (and, hence time and fuel) spent in waters where the sea ice concentration exceeds 15%. A recent study has used a combination of daily passive microwave ice concentrations and the low-resolution version of the Seamless System for Prediction and Earth System Research (SPEAR_LO), to assess skill in seasonal prediction of the MIP and quantify some of the errors in the MIP forecast (Winton et al. 2022). Pertinent to the effort described in the present publication, the authors suggest the MIP forecasts can be improved by, among other methods, improving the forecast system. Significant efforts in developing climate forecasts for the Arctic on the decadal time frame are underway (Tietsche et al. 2014; Notz and SIMIP Community 2020; Dai et al. 2020; Malmgren-Hansen et al. 2019), as well as shorter-term analyses on the monthly scale (Hogg et al. 2020); however, these are insufficient for the short-term forecasts required, as they are computationally intensive and at lower resolution in both space and time than needed for single vessel operations.
Work toward understanding the limits of sea ice predictability has been extensive. The Sea Ice Prediction Network (SIPN), which hosts and organizes the Sea Ice Outlook (SIO), in collaboration with many contributors and institutions through the National Snow and Ice Data Center (NSIDC), is in the second phase of its on-going studies to quantify the uncertainty involved in sea ice modeling and forecasting (Blanchard-Wrigglesworth et al. 2023), albeit at temporal and spatial scales larger than is of use for navigation (Andersson et al. 2021). The Polar Prediction Project, run through the World Meteorological Organization, among many others, is engaged in a parallel effort (Jung et al. 2016).
Operational manual analyses of current sea ice conditions are provided by many different national institutions, using the highest resolution satellite imagery available, which, for SAR systems, can be as fine as five meters. The Canadian Ice Service (CIS), for example, uses the Radar Satellite (RADARSAT) synthetic aperture radar (SAR), operating now on four satellites, the dual-polarization RADARSAT-2 and the three hybrid-polarization SARs of the RCM (RADARSAT Constellation Mission), to provide daily analyses of the coastal waters above and around Canada. The Norwegian Ice Service analyzes data from the Sentinel-1a and Sentinel-1b SAR systems to provide daily updates on the Barents and Greenland Seas. The U.S. Naval/National Ice Center (NIC) provide sea ice coverage for the entire Arctic and Antarctic. A manual ice analysis relies on trained operators synthesizing satellite data and model outputs at many different resolutions and within a strict time window—generally 12–24 h for a daily analysis, or 2–3 days for a weekly analysis—from the listed “valid” time of the analysis. Due to these underlying resolutions, the analysis for current ice conditions produced will itself have variable spatial resolution. In an effort to provide a fixed-resolution global daily product, the Multisensor Analyzed Sea Ice Extent (MASIE) dataset (Fetterer et al. 2010) was developed, at both 1 km × 1 km and 4 km × 4 km resolutions, as will be described in full in section 2a.
Ships in transit inside the Arctic basin require knowledge not just of where the ice is now for safe operations, but where it will be, and in what state, several days to a week ahead, to chart courses and plan for supplies and harborage. The operational ice services, described above, produce forecasts, but these are either generalized text messages or low-resolution predictions based on climatology, forecaster intuition, or continuity from current conditions. The NIC has recently begun to produce a 48-h daily forecast of the ice edge for the Eastern and Western Hemispheres of the Arctic, but it is of insufficiently high resolution to provide guidance for vessels navigating the Arctic. As such, they do not take full advantage of the current state of weather modeling and forecasting. Further, more high-resolution SAR satellite systems will shortly be available, with the SAR systems on Sentinel-1c and Sentinel-1d, with planned launch dates of April 2023 and 2024, respectively, and the joint NASA/Indian Space Research Organization (ISRO) SAR (NISAR) satellite, with a planned launch date in 2024. NISAR has a requirement to provide sea ice motion on a 5-km grid using data with a 3-day sampling for 70% of sea ice covered areas of the Arctic up to 77.5°N, its coverage limit, with the Sentinel-1 systems filling in the areas to the north (Joughin et al. 2021).
Early research pertaining to machine learning approaches for understanding sea ice included retrievals of ice locations and type. Leigh et al. (2014) use the map guided ice classification (MAGIC) algorithm of Clausi et al. (2010) to identify thicker ice types in dual-polarization RADARSAT imagery. Zakhvatkina et al. (2019) surveyed the wealth of automated approaches considered in the past two decades to distinguish open water and sea ice, which have included wavelet transforms, Bayes classification, maximum likelihood estimators, neural networks, and support vector machine (SVM) approaches.
Recent studies specific to sea ice forecasting using machine learning have been conducted at monthly to seasonal time scales, and most commonly at passive microwave resolution (25 km). Regional sea ice concentration forecasts for September have been produced using a complex network of monthly interconnections to which linear Gaussian process regression has been applied (Drobot et al. 2006). The monthly forecasts exhibit some skill above climatology (Gregory et al. 2020). Bayesian logistic regression has been used to forecast September minimum ice cover at one-month to seven-month lead times (Horvath et al. 2020). The technique permitted a direct measure of uncertainty for assessing reliability. Both these efforts targeted global outputs. A deep neural network accessing a multimodel ensemble for the Barents–White–Kara Seas made near-future (2017–30) predictions of sea ice concentration, where the ensemble product had a forecast correlation coefficient of 0.888 (Kim et al. 2019).
At shorter time scales, U-Net and long short-term memory (LSTM) methods have been applied to forecast monthly to seasonal sea ice edges, sea ice extent, and sea ice concentration. Andersson et al. (2021) developed IceNet, a probabilistic, deep learning sea ice forecasting system trained on climate simulations and observational data to forecast the next six months of monthly averaged sea ice concentration maps at 25-km resolution. It outperforms SEAS5, a dynamical model for seasonal ice forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF), more effectively bounding the ice edge and improving ice concentration predictions. Ali et al. (2021) used an ensemble of attention-based LSTM models to produce one-month-ahead forecasts of monthly sea ice extent at 25-km resolution that had an R2 score of 0.982 against monthly test data. One member of the ensemble was a daily trained, with monthly output, LSTM that contributed substantially to the high degree of resultant accuracy of the ensemble. Liu et al. (2021) used a convolution LSTM (ConvLSTM) to make daily predictions of sea ice concentration at 25-km resolution in comparison with a convolutional neural network (CNN) for the Northeast Passage. Both the ConvLSTM and CNN were run out from 1- to 10-day forecasts. The structural similarity (SSIM) between the ConvLSTM and the sea ice concentration (SIC), dropped from 0.955 (where the ideal is 1.0) at 1 day to 0.91 at 10 days, while the SSIM for the CNN dropped from 0.925 at 1 day to 0.89 at 10 days, showing the superiority of ConvLSTM for daily sea ice concentration forecasts. Kim et al. (2021) used both a ConvLSTM and CNN to create a multitasked model for monthly sea ice extent and sea ice concentration, significantly improving on existing sea ice models.
This intent of this effort is to create a machine learning sea ice forecasting model at 1-km resolution and 1-day time scale, overall, finer than has been produced previously, for guidance of interest to ship navigation. To progress toward the goal, the predictions from a small set of machine learning algorithms will be analyzed to down-select to a single model for optimum speed and accuracy. A small region of the Arctic that is representative of most of the processes affecting the Arctic Basin, will be the initial study area for maximum retrieval of successful model results while working with limited time and support. That area is the Beaufort Sea (Fig. 1).
Boundary of study area (red line), following International Hydrographic Organization designation.
Citation: Artificial Intelligence for the Earth Systems 2, 4; 10.1175/AIES-D-22-0070.1
The article is divided into several sections. Section 2 describes the historical and forecasted atmospheric and oceanic inputs, as well as the operationally derived sea ice extent data, used to train, validate, and test the machine learning models. Section 3 presents the candidate machine learning models tested to develop these short-term forecasts, and presents the conclusions that led to our final selection. Section 4 shows the validation results, accuracy, skill score, and variability of the short-term forecast model, discusses initial ablation studies that examined how the model worked as well as it did, and presents a significant example of the usefulness of these short-term forecasts for navigation. Section 5 offers conclusions and some ideas for future work.
2. Data
The study area chosen for analysis was the Beaufort Sea (Fig. 1). We have followed the statutory designation for the borders of this marginal sea (International Hydrographic Organization 1953). On the north (and west) it is a line from Point Barrow, Alaska, to Land’s End, Prince Patrick Island (76°16′N, 124°08′W). On the east it is from Land’s End through the southwest coast of Prince Patrick Island to Griffiths Point, then a line to Cape Prince Alfred, the northwestern extreme of Banks Island, through its west coast to Cape Kellet, the southwestern point, and then a line to Cape Bathurst on the mainland (70°36′N, 127°32′W). On the south, it is the Alaska coast from Cape Bathurst on the east to Point Barrow. The shape of the line on the north and west is not specified as a part of the standard, so, because the intent was to use gridded data, straight latitude/longitude lines have been chosen for simplicity. It should be noted that, with the passage of time, uncertainties have persisted over international boundaries (Fourcy and Lorvelec 2013) and disputes have arisen over the Beaufort Sea boundaries (Baker and Byers 2012). For the purposes of research, these areas of disagreement are inconsequential to the geophysics forcing the growth, motion, and melting of the sea ice itself. The bathymetry of the Beaufort Sea varies from the Arctic Ocean basin depths of over a kilometer to extensive coastal shelves on the north slope of Alaska and along the western portions of the Canadian Arctic Archipelago. The Beaufort Sea has two predominant current features: the anticyclonic Beaufort Gyre in the northwest (Wang and Danilov 2022) and the freshwater influx from the Mackenzie River delta in the southeast (Solomon et al. 2021). To first order, the Beaufort high and Arctic Oscillation are the forcing functions for the winds (Wang and Danilov 2022). The sea ice cover varies from completely ice covered in the winter to extensively ice free in the summer, with a remnant multiyear (MY) sea ice component in the northeast. The Beaufort Sea thus contains in itself examples of most of the important features of the Arctic Basin, making it a logical choice for an initial seedling study, such as is reported here.
The time period of the study was selected to be the period of freeze-up, from 1 September through 30 November, or all data in a given year available during that three-month window. Forecasts were made for the same time window. Specifically, observed freeze-up dates and locations for each of the years were not used as inputs to the model, but were compared to model results as part of the evaluation. The active freeze-up period was chosen for analysis as a compromise between the static winter and the highly variable summer melt seasons.
Inputs into the sea ice forecasting model are stacks of aligned geospatial data layers. Each stack captures the state of the region at a moment in time. Each layer in a stack is a two-dimensional spatial array of a weather or geographic variable. There are layers for air and sea temperatures, u and υ components of wind velocity at 10-m height, u and υ components of water currents at 2-m depth (as a part of ablation studies), classification of Earth’s surface, and sea ice extent data. Each layer is a two-dimensional gridded dataset in the Equal-Area Scalable Earth (EASE) coordinate system (Brodzik et al. 2014) at 1-km resolution. Source data were resampled using bicubic interpolation for quantitative values and nearest neighbor interpolation for categorical values to create each layer. The layers are geographically aligned to form a stack, a three-dimensional dataset.
The sea ice forecasting model used data from 2016, 2018, 2019, and 2020 between September and November, inclusive. In the initial stages of model development, National Oceanographic and Atmospheric Administration (NOAA)/National Weather Service (NWS) Global Forecast System (GFS) forecasts out to 14 days were downloaded, but the GFS forecasts out that far were not available for all of September through November in 2015 and 2017, so those years were set aside. As development proceeded, seven forecast days were chosen as the standard. Toward the end of the study, since seven forecast days were available for 2015 and most of 2017, a sixfold cross-validation study was conducted for the short-term forecast model as developed. The results were compared against the fourfold cross validations (see section 4b).
a. MASIE dataset
The MASIE–Northern Hemisphere (MASIE-NH) dataset, from the NSIDC, classifies Earth’s surface into land, lake, coastline, open ocean, and sea ice (Fetterer et al. 2010). For the purposes of forecasting sea ice, the first three of these classifications are unchanging, while the back-and-forth between open ocean and sea ice is of primary concern. Land, lakes, and coastline are excluded from the prediction area in the sea ice forecasting model. The MASIE-NH classification of ocean and sea ice is the ground truth of the sea ice forecasting model. Analysts at the NIC synthesize satellite data, weekly operational charts, and their remote sensing expertise into the operational sea ice product included in MASIE-NH. The sea ice extent product denotes ice concentrations of >15%. MASIE-NH was selected as the source for ground truth data for the sea ice forecasting model because it fully covers the Beaufort Sea each day and because its use of satellite data mitigates some of the analyst bias observed in other operational sea ice products. The data provided at one km resolution on a daily basis are used in this study. It should be noted that the data are subset from the MASIE-NH dataset directly, rather than using the Beaufort Sea MASIE subregion (Walsh et al. 2019), which deviates somewhat from the internationally defined boundaries (International Hydrographic Organization 1953). Having the whole MASIE-NH dataset in hand for the freeze-up period means, if additional funds are obtained, the analysis can be extended seamlessly to adjacent areas without delay.
b. MEaSUREs-MUR dataset
Multi-scale Ultra-high Resolution (MUR) Sea Surface Temperature (MEaSUREs-MUR) is a dataset of sea surface temperature (SST) estimates that NASA’s Jet Propulsion Laboratory makes available (Chin et al. 2017). MUR fuses microwave and infrared satellite data, which boast broader coverage and higher resolution, respectively. The data fusion is conducted using wavelet transforms in a multiresolution variational analysis (MRVA) that works across time windows centered on the “valid” date for each day’s analysis. The time windows are five days wide for the satellite data used, seven days wide for in situ data, and one day wide for model calculations. The SST values produced through MRVA are generated once a day and plotted on a 0.01° × 0.01° grid. To prepare these SST data for use in the sea ice forecasting model of the present study, they are transformed onto the 1 km × 1 km EASE grid using bicubic interpolation.
c. GFS dataset
The GFS is a NOAA/NWS model for forecasting weather variables (NCEP et al. 2015)—see the extensive references available at NOAA for documentation of the model’s capabilities and products (https://vlab.noaa.gov/web/gfs/documentation). From GFS, the sea ice forecasting model obtains values for the u and υ components of wind velocity—that is, the velocity of wind coming from the west and south, respectively—as well as air temperature at 2 m above Earth’s surface. GFS is informed by sensors on land and throughout the oceans, and each model run incorporates the most recently collected measurements to tune the model to the ground truth. GFS outputs forecasts at about 13-km resolution and with various time offsets from the model run time. The GFS model is run every 6 h, but to match the time resolution of the other data layers, the sea ice forecasting model uses data from only one model run a day, the 18-h forecast run, the forecast generated to be valid 18 h after a baseline time (0-h run). For estimates of the past days’ weather conditions, the sea ice forecasting model relies on GFS 0-h forecasts. Although they are not observations of weather conditions, the 0-h forecasts incorporate the most up-to-date sensor data—true observations—and the nature of modeled data makes it possible to obtain wind and air temperature values throughout the region of interest, even far from physical sensors. Data are transformed to the EASE grid using bicubic interpolation. Recent analysis (Nagarajan et al. 2015) has calculated the GFS wind centered root-mean-square error (CRMSE) for 7-day forecast winds to be between 0.5 and 1.5 m s−1.
d. HYCOM dataset
Predictions of ocean eastward and northward currents, temperature, salinity, and surface elevation are available from the Global Ocean Forecasting System (GOFS) 3.1 model (Metzger et al. 2017), which consists of the 41-layer Hybrid Coordinate Ocean Model (HYCOM) plus the Navy Coupled Ocean Data Assimilation (NCODA) system’s global 1/12° analysis (Naval Research Laboratory 2021).
GOFS 3.1 uses atmospheric forcing from the Navy Global Environmental Model (NAVGEM) 2.0 (Hogan et al. 2014), specifically the 10-m winds and calculates the wind stress using HYCOM SST and taking into account HYCOM surface currents (Metzger et al. 2017). NCODA assimilates available satellite altimeter sea surface height anomalies; satellite, ship, and buoy SST; in situ vertical temperature and salinity profiles from ice-tethered profilers, expendable bathythermographs, conductivity–temperature–depth sensors, gliders, and Argo floats; and satellite-derived sea ice concentration.
The northernmost temperature, salinity, and current validation testing done for GOFS 3.1 was in the Greenland–Iceland–Norwegian (GIN) Seas for a 1-yr period (Metzger et al. 2017). The temperature versus depth root-mean-square error (RMSE) averaged over the upper 500 m for the GIN Seas is 0.26°C at the nowcast (or analysis) time and the mean error is 0.00°C. The salinity versus depth RMSE averaged over the upper 500 m for the GIN Seas is 0.04 psu at the nowcast time and the mean error is 0.00 psu. The 15-m depth current speed mean error is 2 cm s−1 at the nowcast time with a RMSE of 15 cm s−1. The 0-h forecast ice edge location error in the Bering–Chukchi–Beaufort Seas is 22.2 km (Metzger et al. 2017). The ice drift 24-h forecast compared against ice-bound drifting buoys had an absolute ME of 4.8 cm s−1 in the pan-Arctic and 4.7 cm s−1 in the Bering–Chukchi–Beaufort Seas. The RMSE was 7.3 cm s−1 in the pan-Arctic and 7.0 in the Bering–Chukchi–Beaufort Seas. The vector correlation was 1.29 in the pan-Arctic and 1.26 in the Bering–Chukchi–Beaufort Seas. A vector correlation of 0 indicates no correlation and 2 indicates perfect correlation.
3. Methods
To run on a given day, the initial version of the sea ice forecasting model uses the prior seven days’ full stacks of data, plus the partial stack of the forecasted weather data from GFS for the coming seven days, concatenated along the channel axis into a three-dimensional data cube to forecast daily sea ice extent for the coming week. The inclusion of the seven previous days and seven following days of data reduces the number of useable data cubes from 91 to 78 yr−1. The 60 channels of the data cube consist of the following:
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Ocean/land/coastline/lake classifications, one-hot encoded as there is not an ordinal relationship between the classes: 4 channels.
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GFS wind and air temperature values from forecasts produced on each day’s 18-h GFS model run: (7 days) × (3 variables) = 21 channels.
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MUR sea surface temperature values computed each day from satellite measurements: (7 days) × (1 variable) = 7 channels.
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MASIE-NH sea ice extent derived by NIC analysts from satellite observations: (7 days) × (1 variable) = 7 channels.
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GFS forecasts of wind and air temperature for each of the coming seven days (i.e., 24-, 48-, …, and 168-h forecasts): (7 days) × (3 variables) = 21 channels.
Informed by prior days’ weather and ocean conditions and by coming days’ forecasted weather, the sea ice forecasting model predicts the sea ice extent for the coming days. For training the models, different random 256 × 256 pixel spatial subregions of the larger Beaufort Sea are used for each training step, conditioned on the presence of both ice and open water on the sample day within the subregion. This helps with augmenting the training data given the limited dataset size available, and focuses the network on the sea ice edge regions, where both ice and open water are present. The resulting data cubes used for the initial model are thus 60 × 256 × 256 in size.
In this study, five different models were investigated, including the baseline U-Net model, U-Net plus ConvLSTM, bidirectional encoder representation from image transformers (BeiT), channel U-Net plus distance mask, and a persistence model. U-Net had proven productive for forecasts of sea ice conditions on longer (monthly to seasonal) time scales, so it was selected as the baseline model (Andersson et al. 2021). The U-Net plus ConvLSTM (Ali et al. 2021; Liu et al. 2021; Kim et al. 2021) and channel U-Net plus distance mask models were experiments with potential improvements to U-Net. The BeiT model (Bao et al. 2021) was used to provide comparison with a different model architecture, and persistence is the reference for machine learning model intercomparisons (Walsh et al. 2019; Niraula and Goessling 2021). Each of these models is described in more detail below. The output data from each model are per-pixel sigmoid, that is, two-class (water/ice), predictions of sea ice and open water, which are converted to an ice mask by thresholding for water/ice at 0.5.
a. Models investigated
1) Model 1: Baseline U-Net
The model was trained with a batch size of 16 with an Adam optimizer with an initial learning rate of 0.001 and beta values of 0.9 and 0.999. A multistep learning rate schedule was used, with learning rate decaying by a factor of 10 at 40 epochs and again at 80 epochs, with training stopped at 100 epochs after convergence.
2) Model 2: U-Net plus ConvLSTMs
Additionally, a second approach has also been implemented where ConvLSTM cells (Shi et al. 2015) are inserted between the encoder and decoder portions of the U-Net architecture. In this architecture, the inputs are the grouped layers for each day (with ice masks and sea surface temperatures replaced with zeros for future days), and the outputs are the ice masks for each day. The network is trained to reproduce ice masks over the entire 14-day period (7 historical days + 7 forecasted days).
3) Model 3: BEiT
BEiT (Bao et al. 2021) adapts techniques from natural language processing. Imagery differs from language in that it has no defined vocabulary for identifying the image patches that are the input blocks for autoencoding prediction. Instead, images are split into a grid of patches, each of which is assigned a visual token. Masked image modeling is used to recover the visual tokens as a part of self-supervised pretraining. After pretraining, a downstream task layer is applied for fine-tuning using image classification and semantic segmentation. As part of original development, BeiT was scaled up to the same size as vector-valued infinite task learning (ViT-L), which it was found to outperform (Lambert et al. 2021).
4) Model 4: Channel U-Net plus distance masks
Distance masks were added to the channel U-Net model as a means to provide nonlocal information early in the neural network. Instead of using binary masks in the data stack for the five MASIE classes (land, lake, coastline, open ocean, and sea ice), the binary masks were replaced with distance masks. The pixel value in a distance mask for a particular class type is the distance to closest edge for that class type (i.e., where the MASIE product transitions from that class label to a different class label), with a positive distance value used if the pixel is of that class, and a negative distance value used if the pixel is not of that class.
5) Model 5: Persistence
The persistence model, where the ice extent for each day of the seven days of forecast is assumed to be the same as the first, serves as the baseline model for intercomparison (Vislocky and Fritsch 1997). It would be ideal to have operational daily forecasts of ice extent for comparison, but, with one limited exception, these do not exist for the short 1–7-day time scales of interest for this study. The exception is the daily 48-h ice edge (not sea ice extent) forecast produced, as a low-resolution image, by the NIC, which would only provide a comparison for one of our cases, and even then, not for the entire time period used in this study. A careful examination of persistence as a monthly predictor for ice extent has revealed several interesting trends. Walsh et al. (2019) have compared the Sea Ice Prediction Network’s Sea Ice Outlook of ice extent in May, June, July, August, and September over the 2008–18 time window to persistence defined as mean ice extent trend for the same time window taken from the NSIDC sea ice index. The averaged SIO had an error for July of 0.32 million versus 0.43 million km2 for May for persistence, however, for June, July, and August, the errors for persistence were 0.22, 0.25, and 0.09 million km2, respectively. In September, the SIO and persistence errors were equivalent (0.68 million vs 0.67 million km2).
b. Model intercomparison
1) Evaluation methodology
Model outputs are, as described in the previous section, per-pixel sigmoid (two-class: water/ice) predictions of sea ice presence. The loss function is calculated as the binary cross entropy of the sigmoid predictions. The base metric used to evaluate the models is average accuracy, that is, the percentage of the 256 × 256 grid points that are correctly classified as sea ice or open water. This is computed by first thresholding the sigmoid outputs at 0.5, where >0.5 is ice, and <0.5 is water, to create an inferenced, full-region binary ice mask. Second, the ice mask is compared to the source MASIE-NH sea ice classification for each ocean/ice pixel. Then, a mean accuracy is calculated for both the entire forecast window and on a per-day basis. Finally, these values are averaged over all the data samples for the validation year to produce the average accuracy.
2) Evaluation
Figure 2 shows the comparison of the four test models for accuracy versus day. Average accuracies, as well as other processing metrics, are given in Tables 1 and 2. The four models performed similarly with average accuracies between 94.8% and 95%. For the day-to-day comparison, the four model forecasts on the seventh day dropped from 97% to between 92.9% and 93.2% accuracy, while the persistence model accuracy had dropped to under 91%.
Model accuracy vs forecast day for the models used. Standard deviations are left off the graph for clarity, but are on the order of ±1%.
Citation: Artificial Intelligence for the Earth Systems 2, 4; 10.1175/AIES-D-22-0070.1
1–7-day average accuracy per model, i.e., the percentage of the 256 × 256 grid points that are correctly classified as sea ice or open water, as listed in section 3a. Models investigated.
Processing metrics for each model except persistence, in section 3a order. Batch size = number of training samples run through the model before doing each stochastic gradient descent (SGD) step.
With the accuracy of the four candidate models being so closely aligned (Table 1), different metrics were used to select the model of choice (Table 2). Although the ConvLSTM model had the highest accuracy, it took the longest time to train and used the most graphics processing unit (GPU) memory. Instead, we selected the adapted U-Net model, which took the least time to train and used the least amount of GPU memory, while having nearly the same average accuracy and skill score as ConvLSTM. Ablation studies with model 2 (U-Net plus ConvLSTM) were run for specific cases in parallel with model 1 (U-Net) to verify that the selection of model 1 for development did not adversely affect the forecast product (see section 4b, ablation studies).
4. Results and discussion
a. k-fold validations
With the limited data available (78 samples yr−1), k-fold cross validation is used to quantitatively evaluate model results. As there is significant overlap in information between one day’s forecast and the next, the individual folds are based on years. It is customary to have training, validation, and testing datasets, where the validation stage is used for hyperparameter tuning and the test stage for final evaluations. With these limited data, the dataset used for hyperparameter tuning was the fold with 2019 as the validation holdout. Table 3 shows the k-fold validation for the years 2016 and 2018–20. Data from 2015 to 2017 were excluded from these initial studies because not all model data were available for the original desired forecasting range of 14 days. The highest average skill score was for 2018, at 0.27, the lowest, for 2020, at 0.07, for an average of 0.18. The highest accuracy was also for 2018, at 96%, with 2020 tying 2016 for the lowest accuracy, at 94%, for an average of 95%. The low accuracy and skill score for 2020 are thought to be related to the anomalously low ice extent during that ice season. It was, in fact, the second lowest September ice extent on record, overpredicted by the Seasonal Ice Outlook of the Seasonal Ice Prediction Network as well (Andersson et al. 2021). In 2016, the U-Net model predictions were close to those of persistence. In 2018, the September ice extent, while low climatologically, was not as extreme as in 2020. Ice growth in 2018 was helped by rapid freezing in mid-to-late autumn, when more than 1 million km2 (386 000 mi2) of ice can form within a 7-day period (Stroeve and Notz 2018). Monthly forecasts, by virtue of reporting values for a multiday average, will be less likely to show effects from extreme 1-day events, unless that change persists over temporal scales equivalent to the month time window. The daily inputs used to forecast, and the daily outputs reported in this study will, ideally, show a response to these short-term variations and lead to improved forecasting skill.
The k-fold cross validation for model 1.
Figure 3 shows the overall average accuracy for the adapted U-Net model. These accuracies are functionally equivalent to the accuracies reported for the attention-based LSTM ensemble of models that predict monthly sea ice extent up to one month ahead (Ali et al. 2021). Further, the same trend was seen in Fig. 13 of Liu et al. (2021) for SSIM as a function of increasing days of continuous prediction. The variability cloud shown in Fig. 3 is the standard deviation of the respective metrics. While accuracy decreases for each forecast day farther into the future (as expected), the accuracy decreases at a slower rate than the persistence model, and, indeed, more slowly than the drop in SSIM.
Average accuracy of k-fold (fourfold) validation results. The APL Ice Prediction Model is model 1 of section 3a(1). Each of years 2016, 2018, 2019, and 2020 were held out for validation, while the model was trained on the remaining three. The average of the four runs is represented by the line, while the cloud represents the standard deviation.
Citation: Artificial Intelligence for the Earth Systems 2, 4; 10.1175/AIES-D-22-0070.1
This leads to increasing skill scores for each day (Fig. 4), ending with a skill score of around 0.27 by day 7, showing that the forecast model has some positive benefits relative to the persistence model. The skill score improved from day to day, but, for the first day, each model and run showed a decrease in skill from simple persistence. Although no single cause could be found for this drop in skill, it is possibly related to either transition issues with the forecasting from historical to future conditions, or, that persistence was as valid a forecast as the short-term model due to the slow state of changes in ice extent in the data. This aspect of the forecast model remains under study.
Skill score of k-fold (fourfold) validation results. The APL Ice Prediction Model is model 1 of section 3a(1). Analysis as described in Fig. 3.
Citation: Artificial Intelligence for the Earth Systems 2, 4; 10.1175/AIES-D-22-0070.1
Figure 5 shows the IIEE for the adapted U-Net model and the persistence model. At one forecast day, the IIEE for the two models are essentially equivalent. At seven forecast days, the adapted U-Net model has an IIEE of 6.8 × 104 versus 9.3 × 104 km2. Although these are large numbers, it should be recalled that the region of interest covers 1 022 219 km2, for a 9.1% error for the persistence model, versus a 6.7% error for the adapted U-Net model. Since the forecasts are for the freeze-up period, a time of rapid change in the ice edge, this decreased IIEE suggests the U-Net model is appropriately forecasting that change.
IIEE for persistence and APL ice prediction model. The APL Ice Prediction Model is model 1 of section 3a(1). Analysis as described in Fig. 3.
Citation: Artificial Intelligence for the Earth Systems 2, 4; 10.1175/AIES-D-22-0070.1
b. Ablation studies
The original model used seven days of historical data. The first ablation study sought to determine whether the model needed to use the full seven days of historical data. Tests using two, three, and seven historical days were performed, while continuing to run the model out through seven forecast days. As Figs. 6 and 7 show, seven days of data may not be necessary, as the model accuracies (Fig. 6) and skill scores (Fig. 7) were substantially similar to the original case of seven historical forecast days. Similarly, Liu et al. (2021) had found that longer time series did not decrease the accuracy of their predictions. In fact, they found that two days provided the best sea ice concentration prediction. The lack of variation in the results could possibly be due to the generally slow rate of change of ice extent seen during the years of freeze-up tested, as mentioned in the previous section. In areas of the Arctic where freeze-up can happen rapidly in areas of still, conditioned water, as seen in 2018, the forecasts could diverge substantially, depending on whether the historical days included or excluded the initiation of the accelerated freeze-up. Alternatively, it is possible the consistent use of seven forecast days was more definitive for model predictions. This aspect of the forecasting process is under continuing examination.
Per-pixel model accuracy using fewer historical days (forecast days in model remains unchanged at seven for all cases). Vertical bars represent standard deviation across all pixels in an instantiation. Two, three, and seven historical days are nearly identical, and all are above the persistence model.
Citation: Artificial Intelligence for the Earth Systems 2, 4; 10.1175/AIES-D-22-0070.1
Per-pixel skill score for reduced number of historical days in model. Analysis as described in Fig. 6.
Citation: Artificial Intelligence for the Earth Systems 2, 4; 10.1175/AIES-D-22-0070.1
Additional studies examined the effects of including other data types, a check against the U-Net plus ConvLSTM (model 2) case, and inclusion of all the years between 2015 and 2020. In the following discussion, it should be noted that the standard deviation of the fourfold validation skill score at the seventh forecast day is ∼0.05. Although the skill score varies under the conditions of the ablation studies to be reported, the maximum difference between the cases is still less than this measured standard deviation.
Two modified data types were included, first, the HYCOM surface-level ocean currents, and second, a correction of the wind components from north and east to aligned specifically with the EASE grid. When the HYCOM ocean currents from each day’s GOFS run were included for testing, this added 14 channels [(7 days) × (2 variables)] to the model. As can be seen in Table 4, both additions decreased the average skill score of the model, from 0.197 to 0.179. The decrease in skill score with the inclusion of the ocean surface currents was initially surprising, but, other studies have indicated short-term ice extent changes, over the temporal scales of interest here, are more wind driven than current driven (Smedsrud et al. 2011; Schweiger and Zhang 2015). The conversion from u, υ components to EASE grid orientation, to maintain invariance in translation, showed a similar decrease in skill score. It was not expected for transformation from one orthogonal basis to another to have an effect on model performance, but again, these differences are less than the variability seen in the original fourfold validations (Fig. 3).
Additional studies. Y = yes; N = no. Maximum skill scores are in bold.
For comparison, the U-Net plus ConvLSTM model was run with both the modified variables. For the baseline U-Net model (model 1), while each additional variable separately depressed the skill score, when used together, the skill score decreased only from 0.197 to 0.188. The reason for the reduced skill score when both additional variables were included, versus the inclusion of either separately, remains an open question. But, for the comparison of models 1 and 2, the more computationally intensive model 2 shows a slightly lower skill score, 0.186 versus 0.188, further bolstering the case for the choice of model 1. Toward the end of the study period, the data from the freeze-up in 2015 (full dataset) and 2017 (62 useable data cubes instead of 78) were incorporated to examine the full sixfold validation case, specifically for the inclusion of the two additional variables. Using all six years raised the average skill score to 0.196, almost back to its initial level of 0.197.
c. Sample operational case
Figure 8 shows a case where the model was able to forecast, nearly correctly, conditions of operational significance for ship trafficability. The MASIE ice extents showed the passage out of the Amundsen Gulf closing, that is, ice separating the open water north of Point Barrow from the polynya between Banks Island and the Mackenzie River delta, on 25 October 2019, while the model showed it closing on the 26 October 2019, but with the potential for ice formation in the gap on 25 October. Even if relying only on the short-term forecast model, a non-ice-strengthened vessel would have been provided sufficient information, seven days in advance, to be aware to be clear of the gap prior to 25 October, rendering it safe in its voyage. An ice-strengthened ship would also have had sufficient warning for safe transit.
(left) Short-term 7-day forecasts vs (right) MASIE ice extent. Days are (top) 24 Oct, (middle) 25 Oct, and (bottom) 26 Oct 2019. Note increase in probability of ice occurrence in forecast for Amundsen Gulf gap on 25 Oct 2019.
Citation: Artificial Intelligence for the Earth Systems 2, 4; 10.1175/AIES-D-22-0070.1
5. Conclusions
A deep learning model, based on the U-Net architecture, has been developed to provide short-term (7 day) forecasts for ice extent in the Beaufort Sea during freeze-up in 2016, 2018, 2019, and 2020. The inputs to the model include classifications of the surface into ocean, land, coastline, and lake, wind and air temperature values and forecasts from GFS, sea surface temperatures, and MASIE-NH sea ice extent. The short-term forecasts by this model, which we are tentatively designating the Applied Physics Laboratory (APL) model, were found to predict changes in ice extent that closely duplicated the MASIE ground truth data, thus providing useful forecasts at the temporal and spatial scales needed for shipping navigating sea ice when climatology cannot offer guidance. Model accuracy was assessed against a persistence model. While the average accuracy of the persistence model dropped from 97% to 90% for forecast days one to seven, the deep learning model accuracy dropped only to 93%. A k-fold (fourfold) cross-validation study found that on all except the first day, the deep learning model, which includes a U-Net architecture with a Resnet-18 backbone, does better than the persistence model. Skill scores improve the farther out in time. At seven days, the average skill score from the k-fold (fourfold) validation results was 0.27.
The integrated ice edge error (IIEE) was calculated for the U-Net model and for the persistence model. The average k-fold (fourfold) values, at seven forecast days, for the persistence model had a 9.1% error, while the U-Net model error was 6.7%, showing the U-Net model is capturing forecasting skill the persistence model does not. The year, 2018, with the highest skill score relative to persistence reinforces the improved accuracy of the U-Net model because the freeze-up during that year was rapid, significantly deviating from a persistence model, whether at a week time scale or at the long monthly time scales used by most models to date. But the U-Net model successfully captured these changes.
Several open questions, based on the ablation studies conducted, remain for future examination, such as, the number of historical data days required to successfully predict sea ice behavior, as the preliminary results are similar to those of Liu et al. (2021). In the future, this short-term modeling approach will be extended to ice motion, ice concentration, and ice thickness. Part of the challenge in pursuing motion and thickness conditions arises from the relative sparseness of ground truth data at scales of interest to navigation to use to train the model, which may lead to modifications in our approach. Further, this study will be extended to provide short-term forecasts in the season when ships are most likely to be present in the Arctic, namely, the summer melt period, when new openings and routes become available. Finally, the study will be extended to forecasting other newly navigable regions of the Arctic, such as the Canadian Arctic Archipelago.
Acknowledgments.
The authors would like to acknowledge the support of the APL Janney program, which covered the preparation of this manuscript, and of Robert Armiger and Marisa Hughes, who directed the internally directed research program that funded the original study. Funding for the development of HYCOM has been provided by the National Ocean Partnership Program and the Office of Naval Research. Data assimilative products using HYCOM are funded by the U.S. Navy. Computer time for running HYCOM was made available by the DoD High Performance Computing Modernization Program. The output is publicly available at https://hycom.org.
Data availability statement.
The MASIE data used are openly available at the National Snow and Ice Data Center at https://nsidc.org/data/G02186/versions/1. The MEaSUREs-MUR data are openly available at https://podaac.jpl.nasa.gov/dataset/MUR-JPL-L4-GLOB-v4.1. The GFS forecast data are available at https://rda.ucar.edu/datasets/ds084.1/. A user will need to register for a free research account at https://rda.ucar.edu/index.html?hash=data_user&action=register prior to accessing the data. The HYCOM data are available at https://www.hycom.org/dataserver.
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