Thin Sea Ice Thickness Prediction Using Multivariate Radar-Physical Features and Machine Learning Algorithms

Abstract

Climate change in the Arctic is causing significant declines in sea ice extent and thickness. This study investigated lab-grownsea ice thickness using Linear Regression and three Machine Learning algorithms: Decision Tree, Random Forest, and Fully Connected Neural Network. To comprehensively track thin sea ice growth using various parameters, a combination of up to 13 radar and physical parameters including surface-based C-band NRCS values in VV, HH, and HV polarizations, air temperature, surface temperature, Cumulative Freezing Degree Moments, humidity, wind speed, surface cover salinity, ice surface salinity, bulk ice salinity, frost flower height and snow depth were input to the four multivariate models in two time series datasets. The results showed that Random Forest was the superior model, with =0.01 cm, for thicknesses of 1–8 cm and 27–47 cm. Using the Permutation Importance method, the role of the employed parameters in the thickness prediction process were ranked and showed that the key parameters were Cumulative Freezing Degree Moment, salinity parameters (surface cover, ice surface, and bulk ice salinities), and C-band co-polarized radar backscattering. The results of this study enhance thickness prediction capacity and accuracy, while providing insights for future research and real-time sea ice thickness prediction in Arctic regions.

1. Introduction

In recent decades, due to climate change and Arctic amplification, Arctic sea ice has been declining in both extent and thickness. However, Arctic sea ice is a vital component in regulating the Earth’s climate, since its high albedo relative to the surrounding sea water results in significant solar radiation being reflected back into space [1,2,3]. Due to the raised concerns about the potential impacts on global climate patterns, there is a growing focus on monitoring and predicting polar sea ice. Although both the extent and thickness of sea ice have been declining, the thickness has been studied less than the extent [4] due to measurement challenges, data scarcity, and technological limitations. However, declining sea ice thickness is as concerning as its extent because as sea ice gets thinner, it accelerates heat escape from the ocean to the atmosphere, absorbs more solar energy, affects ocean circulation by leading more fresh water to enter the ocean [5], and threatens the life of species in the Arctic ecosystem [3].

To comprehensively monitor and predict sea ice thickness, various models are utilized and are classified into two major groups: physical model simulations and statistical methods [6,7]. Microwave remote sensing, due to its ability to penetrate clouds and darkness, is considered a conventional and efficient source of data for models predicting Arctic sea ice thickness [8].

1.1. Sea Ice Thickness Prediction Methods

Physical simulation models encompass a broad range of approaches used to estimate sea ice thickness, including both predictive sea ice dynamics and interpretive methods [9]. Predictive models numerically solve equations related to sea ice dynamics and thermodynamics by considering ice–ocean–atmosphere interactions [10,11,12,13]. The primary model was presented back in 1979 by introducing the Louvain–la-Neuve Model (LIM) [14], and then gradually, more developed versions of LIM were presented [15,16]. Moreover, the Los Alamos Sea Ice Model (CICE) and its developed versions are considered conventional models in sea ice prediction. Interpretive physical models, on the other hand, aim to simulate and understand observational data [9]. For instance, Shih et al. [17] developed a composite model for polarimetric backscattering signatures of sea ice, considering how factors like temperature, salinity, crystal sizes, and brine volumes influence wave interactions and polarimetric signatures. Although these models have been updated as sea ice science progresses, modeling challenges still exist in many parameterization processes including ice thickness distribution, wave–ice interaction, rheology, melt ponding, land-fast ice, and floe size distribution [18]. Additionally, as sea ice provides boundary conditions to both the atmosphere and the ocean simultaneously, implementing an accurate model is challenging [19]. In terms of prediction’s accuracy and performance, in a study by Arctic Research Consortium [20], 2021, physical models with their statistical model counterparts were compared and it was shown that generally statistical models outperform physical models, especially at longer lead times than several weeks ahead. Therefore, there is a tendency among researchers to explore statistical models more in sea ice thickness prediction [7].

Statistical methods are mainly based on calculations to extract relevant trends and patterns through a dataset, and the prediction of sea ice thickness is generally considered a regression problem [21]. The core concept of these methods is to use regression analysis to find a relationship between sea ice thickness and parameters (e.g., heat flux, temperature, salinity, wind speed, and humidity) involved in ice growth [6]. Based on the literature [4,7], these methods can be categorized into two subgroups, traditional regression methods and Machine Learning algorithms.

Traditional regression methods include statistical techniques such as Linear Regression, Least Squares, Markov Model, Bayesian Hierarchical Models, and Gaussian Processes (GPs). Linear Regression has been used to examine the relationship between sea ice thickness, surface air temperature and snow depth [22], to improve estimations of snow depth and ice freeboard measurements [23,24,25], and to optimize model parameters in optimization algorithms [26] for sea ice thickness estimation. Similarly, Least Squares was used as a complementary method in estimating sea ice thickness in freeboard methodology to minimize uncertainties [27]. The Multivariate Markov model was also applied to explore the predictability of sea ice thickness [7]. Probabilistic methods have been utilized to estimate sea ice thickness in a Bayesian technique [28] and a spatio-temporal hierarchical Gaussian random field [29].

Although traditional statistical methods have enhanced the performance of prediction models, there are still some shortcomings. They have a limited ability to capture the complexity of sea ice time series because of their relatively simple assumptions such as including one-dimensional or multivariate linear regression that fails to describe complex nonlinear relationships [30].

Machine Learning algorithms leverage computational power to identify patterns and make predictions. These methods provide higher accuracy than traditional regression methods in handling complex and non-linear relationships, especially in large datasets. Neural Networks, Decision Trees, Random Forests, and Deep Learning algorithms are the most conventional Machine Learning methods in sea ice thickness studies [21]. Neural Networks have been used to estimate ice thickness from polarimetric SAR observations [31], to estimate changes in Arctic sea ice thickness with in situ data [32], to develop a hybrid method with an optimization genetic algorithm [33], and to estimate various sea ice thicknesses with L-band microwave radiometry and environmental features [34].

Lee et al. [35] used a Decision Tree model to detect leads on CryoSat-2 satellite data to improve the accuracy of sea ice thickness estimations in leads. The model split the data based on the most significant features that differentiated leads from other ice types. By assembling several trees, Random Forest algorithms have been created that mainly achieve higher accuracy in their estimations [36]. Random Forests have been used to estimate sea ice thickness with multiple environmental parameters [37], to predict Arctic thin sea ice thickness with brightness temperature measurements from the Soil Moisture and Ocean Salinity (SMOS) satellite [38], to estimate sea ice thickness using polarimetric parameters from Sentinel-1 [39], and to correct biases in Arctic sea ice thickness products by selecting relevant factors including sea ice concentration, sea surface temperature, atmospheric temperature, wind speed, ocean currents, snow depth, and salinity [40].

During the last decade, there has been a tendency to use Deep Learning models, which are a specialized subset of Machine Learning techniques with multi-layered neural networks that can automatically learn complex patterns and hierarchical representations from large volumes of data [21,41]. In the context of sea ice thickness estimation, Deep Learning has shown enhanced performance in modeling complex data [21]. Some applications of Deep Learning in sea ice prediction include sea ice thickness prediction using a Convolutional Neural Network (CNN) on fused data from AMSR2 and SMOS datasets, a Fully Connected Neural Network on various parameters such as brightness temperature, surface temperature, and sea ice concentration [34], developing an ensembled 1D CNN [42], developing a self-attention CNN to estimate the daily prediction in the Arctic winter [43], integrating Deep Learning with Bayesian inference, and using temporal models such as PredRNN and PredRNN++ [44]. For more details, refer to Li et al. [21]. Although these models have improved estimation accuracy, their performances highly depend on the availability of large datasets.

1.2. Microwave Remote Sensing in Sea Ice Studies

As described in the previous section, the vast majority of studies in sea ice thickness estimation used satellite data in the microwave portion of the electromagnetic spectrum. Satellite-based sensors are commonly used in sea-ice monitoring due to their ability to provide wide-area coverage and frequent observation [8]. However, surface-based microwave data can be as applicable as satellite-based data in sea ice monitoring for several reasons. Firstly, it provides ground-truth measurements that can be used to validate and calibrate satellite-based microwave observations [45]. This helps ensure the accuracy and reliability of satellite data, which is crucial for understanding changes in sea ice extent, concentration, and thickness [46]. Surface-based microwave data also allow for detailed measurements of sea ice properties at specific locations, providing valuable information on local conditions and processes. This can be particularly useful for studying the formation and evolution of sea ice, as well as for understanding the impact of local environmental factors on sea ice behavior [47]. In recent years, there has been an increasing emphasis on integrating data from satellite-based and surface-based sensors to improve the accuracy and reliability of sea ice monitoring [48,49]. The outputs of surface-based scatterometers are commonly reported as Normalized Radar Cross Section (NRCS) and correspond to outputs of conventional satellite platforms [45].

According to previous research [49], thin sea ice growth can be monitored by C-band (5.5 GHz) NRCS values and other relevant physical and environmental observations such as air/surface temperature, wind speed, humidity and salinity. Scatterometers have been used in sea ice studies for various applications. Isleifson et al. [50] demonstrated the capability of a C-band scatterometer to detect and monitor frost flowers on sea ice and their influence on microwave backscattering signatures. Nghiem et al. [51] conducted laboratory experiments to investigate how frost flowers affect radar backscatter, providing foundational insights into their electromagnetic behavior. More recently, Isleifson et al. [48] examined thin first-year sea ice covered by frost flowers and snow using a combination of scatterometers, LiDAR, and drone-based sensors. This multi-sensor approach allowed for a more detailed characterization of surface features and improved understanding of radar signal interactions with complex ice surfaces.

Additionally, surface-based radar altimetry, particularly in the Ku-band (12–18 GHz) and Ka-band (30–40 GHz), has been employed to estimate the thickness of snow-covered sea ice by combining data from both bands [52,53]. These studies investigate how snow properties, such as salinity and depth, influence radar backscattering over first-year sea ice [53], and introduce correction factors to account for vertical shifts in the radar scattering horizon caused by snow characteristics [54].

1.3. Research Objectives

Machine Learning algorithms have the potential to draw connections between sea ice thickness and geophysical parameters. Surface-based microwave remote sensing has also proved its efficiency in sea ice growth monitoring, especially in the C-band for thin ice. Although research has been performed on estimating sea ice thickness using Machine Learning algorithms and/or surface-based microwave data, there is a lack of comprehensive studies that aggregate both approaches to enhance prediction accuracy and investigate the most influential parameters in sea ice thickness directly. The overarching objective of this study is to establish the most effective technique for predicting ice thickness using a time-series dataset. To achieve this objective, the study addresses the following research questions: (1) Which Machine Learning models perform efficiently in predicting sea ice thickness? (2) How can the integration of surface-based microwave radar and environmental parameters improve sea ice thickness prediction? and (3) What are the key parameters in sea ice thickness prediction, and how significant is their contribution to the prediction process? This study aims to comprehensively answer these questions using a time series dataset containing salient physical parameters in sea ice growth, C-band NRCS values, and some common Machine Learning algorithms.

2. Materials and Methods

Two datasets have been used in this study, both collected at the Sea-ice Environmental Research Facility (SERF), at the University of Manitoba, Winnipeg, Canada. Figure 1 demonstrates the pictures of SERF 2017 and 2021 experiments site at the end of the experiments. SERF consists of an outdoor pool that measures 9.1 m by 18.2 m with a depth of 2.45 m. This research site simulates Arctic conditions in winter and provides a substantial controlled environment for fieldwork and physical sampling. SERF has been equipped with on-site sensors for recording physical and meteorological parameters, including a Vaisala HMP45C for measuring air temperature and humidity, a Gill WindSonic Anemometer for wind speed, and an Apogee SI-111 infrared sensor for surface temperature. For measuring the salinity parameters, physical samples of ice were melted and the conductivity and temperature of the melt of each sample were measured using a conductivity meter, Thermo Scientific Orion Star A212. The sample salinities were calculated from the conductivity, according to the formulation of Fofonoff [55]. Further details about SERF are available elsewhere [45,48]. In the first dataset, frost flowers grew on the ice surface, and in the second dataset, in addition to frost flowers, two snowfalls covered the ice layer. Therefore, both datasets include sophisticated sea ice features, and these datasets are considered two analogs to winter conditions in the Arctic.

2.1. Dataset 1: SERF 2017 Experiment

The first dataset used in this paper was derived from data collected at SERF from 23:00 on 12 January to 08:40 on 14 January 2017 [45]. Figure 1a demonstrates the SERF 2017 experiment site and the C-band scatterometer setup at the end of the experiment, when the pool surface was covered with sea ice and frost flower. Sea ice thickness in this dataset ranged from 1 cm up to approximately 8 cm. The dataset includes meteorological and surface measurements, and C-band polarimetric (center frequency = 5.5 GHz) response of the sea ice in VV, HH, and HV. Measurements were conducted with 30° swaths in azimuth. Based on the published results [45], lower incidence angles (i.e., 25°) represented sea ice growth more clearly. Therefore, in this study, we focused on the NRCS values at a 25° incidence angle. The experiment lasted 33.67 h, and by 5 min data recording time intervals by the C-band scatterometer, 405 timestamps were recorded. For each timestamp, 13 parameters were observed including C-band NRCS values in VV polarization (dB), C-band NRCS values in HH polarization (dB), C-band NRCS values in HV polarization (dB), air temperature (°C, near-surface h = 70 cm), surface temperature (°C), Cumulative Freezing Degree Moments (CFDM), humidity (%), wind speed (m/s), surface cover salinity (PSU), ice surface salinity (PSU), bulk ice salinity (PSU), frost flower height (cm), and ice thickness (cm). Therefore, the collected dataset was formatted to a time series with 405 rows (timestamps) and 14 columns (the 13 observed parameters and one column for time).

CFDM is an adaptation of the traditional Cumulative Freezing Degree Days [46]. CFDM represents the cumulative sum of the air temperature differences below freezing point, calculated at more frequent intervals (here, every 5 min) rather than daily. As described in [45], bulk samples of the sea ice volume were extracted using a saw and melted at room temperature. The conductivity and temperature of the samples were measured using a conductivity meter. The salinities of the samples were calculated from the conductivity, according to the formulation of Fofonoff [55]. Figure 2 represents the data trends over experiment time [45].

In Figure 2b, the solid black vertical line marks the time of the first frost flower salinity measurement, taken on 13 January at 08:40. Prior to this time, frost flowers had not yet formed, and therefore, salinity data were unavailable from the start of the experiment until this point. To address the resulting gap, frost flower salinity values were initially assumed equal to the ice surface salinity and then linearly interpolated up to the time of the first measurement. This approach ensured continuity in the dataset during the early hours of the experiment. Once frost flowers formed, their high salinity caused a sharp increase in surface cover salinity. The subsequent decline in frost flower salinity between 08:40 and 14:40 was attributed to rising air temperatures, which reduced brine retention and led to drainage into the underlying ice layer, reflected in a corresponding increase in surface ice salinity. By 21:30, a slight rise in both frost flower and surface salinity was observed, likely driven by a combination of cooling air temperatures, increased wind speed, and peak humidity, which enhanced brine mobility and wicking. Overnight, both salinity values declined slightly by 08:40 on 14 January, likely due to reduced brine availability and stabilized environmental conditions, including lower wind speeds and humidity, which slowed brine transport and accumulation [45].

2.2. Dataset 2: SERF 2021 Experiment

The second dataset used in this paper was a subset of data collected at SERF from 10:19 on 12 February to 4:50 on 20 February 2021, [48]. Figure 1b demonstrates the SERF 2021 experiment site and the scatterometers setup after the experiment ended, showing snow-covered sea ice with snow depth of 4 cm. The original dataset includes radar parameters in Ku- and C-bands as well as LiDAR and thermal drone imagery; however, in this study, only C-band parameters were taken into account to keep the consistency with the first dataset. Sea ice thickness was in the range of 27–47 cm. In addition to the parameters that were recorded in Dataset 1, snow depth was measured as well. Therefore, for each timestamp, 14 parameters were observed including C-band NRCS values in VV polarization (dB), C-band NRCS values in HH polarization (dB), C-band NRCS values in HV polarization (dB), air temperature (°C), surface temperature (°C), Cumulative Freezing Degree Moments (CFDM), humidity (%), wind speed (m/s), surface cover salinity (PSU), ice surface salinity (PSU), bulk ice salinity (PSU), frost flower height (cm), snow depth (cm), and ice thickness (cm) [48]. The experiment lasted about 186 h, and by 15 min time intervals (as the time interval of data recording for the C-band scatterometer was set to 15 min), 1511 timestamps were recorded. Considering 1511 timestamps (as rows), the 14 observed parameters, and one column for time (as columns), the time series dimension was 1511 × 15. Figure 3 represents the data trends over experiment time.

Physical sampling procedures were similar to those used in Dataset 1 (Section 2.1) and are described in detail in [48]. Figure 3b illustrates the evolution of three salinity measurements during the sea ice growth experiment. Throughout the experiment, bulk ice salinity remains relatively stable, showing only minor changes as the ice gradually undergoes desalination through gravity drainage and diffusion [51]. In contrast, both surface cover salinity and sea ice surface salinity exhibit significant fluctuations in response to environmental transitions. During the early phase of the experiment (12–13 February), surface cover salinity was notably high due to the presence of highly saline frost flowers, formed as brine wicked upward from the ice layer to the surface. The first snowfall event on 18 February led to a sharp decline in surface salinity, primarily due to dilution and surface flooding. This was followed by another snowfall on 19 February, which caused a further abrupt decrease in both sea ice surface salinity and surface cover salinity.

2.3. Methodology

After reformatting the data into a time series, the pre-processing phase commenced by searching for any time-points that lacked a value (NaN values). These cells existed in the dataset because various parameters might have been observed in different time intervals. NaN values were data gaps, so linear interpolation was used to fill the gaps and estimate a value for time-points that have NaN values in the raw data. One limitation of this approach was the assumption that the salinity of the surface features followed a linear trend. This assumption allowed the use of the models, but it might not accurately reflect the true nature of salinity changes.

We used a multivariate predictor approach [36], where the ice thickness was the target variable and the other parameters were considered the features. Dataset 1 had 12 features (including 11 radar/physical features and frost flower height) and Dataset 2 had 13 features (including 11 radar/physical features, frost flower height, and snow depth). To better manage and analyze the results, three scenarios were designed based on the type of the features used to predict sea ice thickness. In Scenario 1, all available features were used to predict sea ice thickness. In Scenario 2, cover-related features (frost flower height and snow depth) were excluded and the other 11 parameters were input to the models. In Scenario 3, only remotely-sensed features were used including CFDM, air temperature, relative humidity, wind speed, radar VV, HH, and HV. Scenario 1 considered a direct approach of using all of the available measurements. It was the most comprehensive dataset available in this study. Scenario 3 considered only remotely sensible data, which would be more practical for a larger-scale regional study or where detailed surface measurements would not be available. In other words, it is similar to data that might be available from satellite sensors, local weather stations, or reanalysis products (e.g., ERA5). Scenario 2 was an intermediate step, where assumed knowledge of snow cover/frost flower cover thickness was removed, to see its impact on retrieving sea ice thickness.

All features and the target variable were normalized using the min-max scaling method so that the results would not be affected by very small or large numbers [56]. Then, the datasets were split randomly into training (80%) and testing (20%) subsets. In the model processing phase, the hyperparameters of the applied model were first tuned. Next, the models were trained using the training data. The performance of the models were then evaluated using the testing data providing the error of the predictions (here, RMSE). Finally, to visualize the results, predicted and actual values were plotted.

2.4. Applied Models

In this study, we used Linear Regression and three conventional multivariate Machine Learning models: Decision Tree, Random Forest, and Fully Connected Neural Network (FCNN). In all models, the 12 features in Dataset 1 and 13 features in Dataset 2 have been considered the independent variables (features) and the dependent variable was sea ice thickness (target). In Linear Regression, the goal was to find the best-fitting line that predicts the target based on the features, and its formula has been represented by Hope [57]. In the Decision Tree approach, the datasets were split into subsets based on the value of input features, creating a tree-like model of decisions. The process involved Nodes (a decision point where the data is split based on a feature value), and Leaf Nodes (the final nodes (leaves), which represent the predicted values) [58]. A Random Forest is an ensemble learning method that combines multiple decision trees to improve the predictive performance and control overfitting [36]. In this study, the Random Forest model was defined with 200 trees and a specified random state for reproducibility. FCNN, as a deep learning model that consists of multiple layers (input, hidden, and output layers), enables the model to capture non-linear relationships in the data. The model was trained using backpropagation, where the gradients are computed, and the weights were updated to minimize the loss. This is a standard technique in deep learning [41]. In this study, a sequential model, which is a linear stack of layers, was defined. The first layer included 200 neurons with ReLU activation and an input shape matching the number of features. The second layer included 100 neurons with ReLU activation. The final layer included 1 neuron (since it is a regression task) with no activation function. The model was compiled using the Adam optimizer. The model was trained on the training data for 100 epochs with a batch size of 32. The trained model made predictions on the test data. The predicted values were then inversely transformed back to their original scale for comparison with actual values. Root Mean Squared Error (RMSE) was calculated for additional evaluation.

For the models implemented with the specified architectures and hyperparameter settings in this study, the processing time per run was approximately one minute. This rapid execution was largely attributed to the relatively small size of the datasets, Dataset 1 (405 × 14) and Dataset 2 (1511 × 15), which did not impose significant computational demands.

2.5. Permutation Importance Method

Permutation Importance is a technique used to evaluate the importance of features in a predictive model. It helps to understand which features have the most influence on the model’s predictions [59]. First, the performance of the model is evaluated on the original dataset to establish a baseline. This could be measured using metrics such as RMSE for regression. For each feature, the values of that feature are randomly shuffled in the dataset. This breaks the relationship between the feature and the target variable, while keeping the distribution of the feature the same. The model’s performance is evaluated again using the dataset with the shuffled feature. The performance drop indicates the importance of that feature. If shuffling a feature significantly decreases the model’s performance, it means that the feature is important for the model’s predictions. This process is repeated for each feature in the dataset. The importance of each feature is determined by the decrease in the model’s performance when that feature is shuffled [59,60]. Permutation Importance scores do not necessarily sum to one because they are raw, unnormalized measures of how much each feature affects model performance. A positive score means that shuffling the feature worsens the model’s accuracy, indicating it is important. A negative score means the model performs slightly better when the feature is shuffled, suggesting it may be adding noise [36,61].

In this study, Python 3.10 was utilized as the programming language, and specifically, the Pandas library for data manipulation and preprocessing, NumPy for numerical computations, and Scikit-learn for implementing and evaluating the Machine Learning models were employed. Additionally, Matplotlib was used for visualizing the results, and Eli5 was utilized to calculate feature importance through Permutation Importance. These tools collectively facilitated a comprehensive and efficient analysis of sea ice thickness prediction.

3. Results

Using the two datasets and four models including Linear Regression, Decision Tree, Random Forest, and FCNN, sea ice thickness was predicted in three distinct scenarios with various combinations of features. Figure 4 illustrates the error (RMSE) values of ice thickness prediction using these models.

3.1. Sea Ice Thickness Prediction Using Dataset 1

As described in Section 2.1 and Figure 1a and Figure 2, Dataset 1 was derived from the SERF 2017 experiment, which lasted 33.67 h and encompassed 12 features, including air temperature, surface temperature, CFDM, humidity, wind speed, C-band NRCS values in VV polarization, C-band NRCS values in HH polarization, C-band NRCS values in HV polarization, surface cover salinity, ice surface salinity, bulk ice salinity, and frost flower height. Ice thickness, ranging from 1 to 8 cm, was considered the target [45]. Using Dataset 1, sea ice thickness was predicted by four statistical and Machine Learning models (Linear Regression, Decision Tree, Random Forest, and FCNN). According to Figure 4, Random Forest with RMSE = 0.01 cm in Scenarios 1 and 2 and RMSE = 0.02 cm in Scenario 3, was the superior model compared to other three models on Datset 1. FCNN with RMSE = 0.03 cm in Scenarios 1 and 2 and RMSE = 0.02 cm in Scenario 3 was in the second stage followed by Decision Tree with RMSE = 0.03 cm in Scenarios 1 and 2 and RMSE = 0.04 cm in Scenario 3. These results represent that the performances of these three models on Dataset 1 were close. However, Linear Regression showed the highest RMSE values with RMSE = 0.04, 0.05, and 0.06 cm for Scenarios 1–3, respectively.

RMSE values of Random Forest, Decision Tree and FCNN on Dataset 1 in different scenarios did not change significantly, and in most cases these values remained fixed. Linear regression showed the highest changes in RMSE in scenarios, as the RMSE of Scenario 3 is 0.02 cm (50%) more than the RMSE of Scenario 1.

Figure 5 demonstrates the actual versus predicted values of ice thickness for Dataset 1 using the Random Forest model in Scenario 1. Similar plots were generated for other models and scenarios; however, only the plot for Random Forest, as the superior model, has been presented here. The horizontal and vertical axes represent the actual and predicted sea ice thickness values for the test samples, respectively. For Dataset 1, the number of test samples is 81, corresponding to 20% of the total dataset. The ideal prediction scenario is represented by the diagonal dashed line, where predicted values perfectly match the actual measurements. The close clustering of all sample points along this diagonal line indicates a very low prediction error, further supported by the calculated RMSE of 0.01 cm. This demonstrates the high accuracy and reliability of the model’s performance on the test data.

Using the Permutation Importance method (Section 2.5) for Random Forest on Dataset 1 and Scenarios 1–3, the features used in sea ice thickness predictions were ranked. This ranking demonstrated the effectiveness of the features in the prediction process based on their weights. The higher the weight, the higher the rank of the feature, and therefore, the greater importance. As

Table 1. Parameter ranking using Permutation Importance method by Random Forest results on Dataset 1 (which included 12 features: 11 radar/physical features plus frost flower height) in the three scenarios.

	Scenario 1		Scenario 2		Scenario 3
Rank	Feature Name	Weight	Feature Name	Weight	Feature Name	Weight
1	CFDM	0.1516	CFDM	0.1559	CFDM	0.2177
2	Bulk Ice Salinity	0.0422	Bulk Ice Salinity	0.0456	C-VV	0.0278
3	Ice Surface Salinity	0.0353	Ice Surface Salinity	0.0394	C-HH	0.0216
4	Surface Cover Salinity	0.0153	Surface Cover Salinity	0.0112	Air Temperature	0.0119
5	C-VV	0.0093	C-VV	0.0112	Wind Speed	0.0014
6	C-HH	0.0056	C-HH	0.0037	Humidity	0.0013
7	Air Temperature	0.0027	Air Temperature	0.0025	C-HV	−0.0009
8	Humidity	0.0017	Wind Speed	0.0024	-	-
9	Surface Temperature	0.0004	Humidity	0.0011	-	-
10	Wind Speed	0.0004	Surface Temperature	0.0002	-	-
11	C-HV	−0.0003	C-HV	−0.0006	-	-
12	Frost Flower Height	−0.0012	-	-	-	-

shows, CFDM was ranked first in all three scenarios. In Scenarios 1 and 2, salinity features including bulk ice, ice surface, and surface cover salinities, ranked second to fourth, respectively, with slight differences among them. In Scenario 3, the exclusion of salinity features resulted in radar parameters in VV and HH polarizations being ranked second and third, respectively, while these features were ranked fifth and sixth in Scenarios 1 and 2. Other features achieved different grades depending on environmental conditions and circumstances. Meteorological features such as wind speed, humidity, air temperature and surface temperature consistently ranked lower in all scenarios, with weights close to zero. This highlights the relatively lower importance of these meteorological features in the prediction process compared to CFDM, salinity-related features, and C-VV and C-HH. Features with negative weights, including cross-polarized radar parameter (C-HV) and frost flower height, have shown low effectiveness in the prediction results and have been noise. Their data did not help the model identify the pattern between them and sea ice thickness.

3.2. Sea Ice Thickness Prediction Using Dataset 2

As described in Section 2.2 and Figure 1b and Figure 3, Dataset 2 was derived from the SERF 2021 experiment, which lasted about 186 h and encompassed 13 features, including air temperature, surface temperature, CFDM, humidity, wind speed, C-band NRCS values in VV polarization, C-band NRCS values in HH polarization, C-band NRCS values in HV polarization, surface cover salinity, ice surface salinity, bulk ice salinity, frost flower height, and snow depth. Ice thickness, ranging from 27 to 47 cm, was considered the target [48]. Using Dataset 2, sea ice thickness was predicted by four statistical and Machine Learning models (Linear Regression, Decision Tree, Random Forest, and FCNN). According to Figure 4, Random Forest with RMSE = 0.01 cm in all three scenarios was the superior model compared to other three models on Dataset 2. Decision Tree with RMSE = 0.03 cm in Scenarios 1 and 2 and RMSE = 0.04 cm in Scenario 3 was in the second stage followed by FCNN with RMSE = 0.08, 0.10, and 0.11 cm in Scenarios 1–3, respectively. Similar to the results of the models on Dataset 1, Linear Regression showed the highest RMSE values with RMSE = 0.25, 0.29, and 0.34 cm for Scenarios 1–3, respectively. Consequently, Random Forest emerged as the most effective model for predicting sea ice thickness on Dataset 2, while Linear Regression was the least effective.

RMSE values of Random Forest and Decision Tree on Dataset 2 in different scenarios did not change, while Linear regression showed the highest changes in RMSE in all scenarios, as the RMSE of Scenario 3 is 0.09 cm more than the RMSE of Scenario 1. Moreover, Random Forest and Decision Tree showed consistent RMSE values when comparing the results of Datasets 1 and 2. However, the RMSE values of FCNN and particularly Linear Regression increased significantly (approximately sixfold) in Dataset 2 compared to Dataset 1.

Figure 6 demonstrates the actual versus predicted values of ice thickness for Dataset 2 using the Random Forest model in Scenario 1. Similar graphs were generated for other models and scenarios; however, only the graphs for Random Forest, as the superior model, have been represented here. The horizontal and vertical axes represent the actual and predicted sea ice thickness values for the test samples, respectively. For Dataset 2, the number of test samples is 303, corresponding to 20% of the total dataset. The ideal prediction scenario is represented by the diagonal dashed line, where predicted values perfectly match the actual measurements. The close clustering of all sample points along this diagonal line indicates a very low prediction error, further supported by the calculated RMSE of 0.01 cm.

Similar to Section 3.1 for Dataset 1, the Permutation Importance method was applied on Random Forest results on Dataset 2 and Scenarios 1–3 to rank the effectiveness of the features in the ice thickness prediction based on their weights. As

Table 2. Parameter ranking using Permutation Importance method by Random Forest results on Dataset 2 (which included 13 features: 11 radar/physical features plus frost flower height and snow depth) in the three scenarios.

	Scenario 1		Scenario 2		Scenario 3
Rank	Feature Name	Weight	Feature Name	Weight	Feature Name	Weight
1	CFDM	0.0381	CFDM	0.0398	CFDM	0.1031
2	Surface Cover Salinity	0.0181	Surface Cover Salinity	0.0193	C-VV	0.0018
3	C-VV	0.0012	C-VV	0.0019	C-HH	0.0010
4	C-HH	0.0008	C-HH	0.0004	C-HV	0.0002
5	Frost Flower Height	0.0006	C-HV	0.0001	Wind Speed	0.0000
6	Snow Depth	0.0005	Surface Temperature	0.0001	Air Temperature	−0.0001
7	C-HV	0.0003	Wind Speed	0.0000	HumidityV	−0.0002
8	Air Temperature	0.0001	Air Temperature	−0.0001	-	-
9	Wind Speed	0.0000	Humidity	−0.0002	-	-
10	Surface Temperature	−0.0001	Bulk Ice Salinity	−0.0036	-	-
11	Humidity	−0.0001	Ice Surface Salinity	−0.0084	-	-
12	Bulk Ice Salinity	−0.0039	-	-	-	-
13	Ice Surface Salinity	−0.0076	-	-	-	-

shows, CFDM was ranked first in all three scenarios. In Scenarios 1 and 2, surface cover salinity was ranked second. In Scenario 3, the exclusion of surface cover salinity resulted in radar parameters in VV, HH, and HV polarizations being ranked second to fourth, respectively. While these features were ranked lower in Scenarios 1 and 2. Other features achieved different grades, depending on environmental conditions and circumstances. Meteorological features such as wind speed, humidity, air temperature and surface temperature consistently ranked lower in all scenarios, with weights close to zero. Unlike the results of Dataset 1, bulk ice salinity and ice surface salinity in Scenarios 1 and 2 ranked at the lowest compared to other features with negative weights indicating their low effectiveness in the ice thickness prediction.

4. Discussion

As can be seen in Figure 4, the results of the methodology were almost the same in both datasets, while the ice thickness of the datasets varied. In both datasets, the Random Forest model was the superior one with low error values (RMSE = 0.01 cm), in most scenarios. These results confirm the performance of the Random Forest model in multivariate sea ice thickness prediction. The Decision Tree model was in the second stage in both datasets, with a stable error value of 0.03 cm in most scenarios. The Decision Tree model is the basis of the Random Forest model as the Random Forest model consists of numerous Decision Trees [36]. Therefore, it can be concluded that the concept of decision-making based on trees is efficient in multivariate sea ice thickness prediction.

Linear Regression in both datasets and FCNN in Dataset 2 were the models with the highest error values, while the reasons for their weakness in this study are different. The Linear Regression model could not predict sea ice thickness as accurately as Random Forest and Decision Tree because it was not able to model the non-linearity and complex patterns in the datasets. Although some features like CFDM could be modeled linearly, there were some other features such as radar NRCS values that do not follow a linear pattern (see Figure 2 and Figure 3). Therefore, Linear Regression seems to be very simple for predicting such multivariate datasets.

On the other hand, FCNN resulted in low error values on Dataset 1, but its error increased significantly on Dataset 2. FCNN is a Deep Learning model, and it was supposed to yield higher performance. However, Deep Learning models usually are more efficient with larger datasets, as they have a lot of coefficients required to be specified. Therefore, its performance on such small datasets, like Dataset 1 in this study, is not desirable compared to other simpler Machine Learning algorithms. Although Dataset 2 is larger than Dataset 1, the RMSE values for Dataset 2 were higher than those for Dataset 1. This discrepancy may be attributed to the increased complexity of Dataset 2, which includes factors such as frost flowers, two snowfall events, and a wider range of ice thickness. Consequently, more frequent data observations would be required to accurately model these complexities. Another contributing factor could be that FCNNs are known to suffer from overfitting when the complexity of the model, hyperparameter tuning, and the size of the dataset are not optimally aligned [62,63]. Typically, FCNNs require tailored tuning and design for each specific dataset to achieve the most accurate results. In this study, however, the same settings and architecture were applied to both datasets. Consequently, it is a justified outcome that the model settings did not yield the same level of accuracy for the second dataset as they did for the first. In this case, methodologies to reduce overfitting, such as regularization techniques [64], should be applied. However, selecting the appropriate method and integrating it into the Deep Learning model can be computationally intensive and time-consuming. Conversely, Random Forest has yielded high accuracy results even without the application of these additional methods.

As mentioned in the data description (Section 2.1 and Section 2.2), the two datasets included different ice surface covers. The ice cover in the first dataset was frost flowers and bare ice; however, the ice cover in the second dataset was frost flower and snow (due to two snowfalls during the experiment). Although the ice cover varied, the performances of the models were not affected significantly. This can be inferred in two ways in this study. Firstly, by comparing the RMSE values of the models in Scenarios 1 and 2 across both datasets, no remarkable improvement can be observed in Scenario 1, which includes surface cover features (frost flower height and snow depth), over Scenario 2, which lacks these features. Indeed, most models’ RMSE values remained consistent despite the exclusion of these features. Secondly, according to Table 1 and Table 2, in Dataset 1, frost flower height was ranked 12th, the lowest level, and in Dataset 2, frost flower height and snow depth were ranked sixth and seventh, respectively, indicating their low levels of importance in predictions. This suggests that in predicting thin sea ice thickness, if a proper model is fed with a multivariate time series, it can predict sea ice thickness independently of small-sized frost flowers (approximately 1.5 cm) and shallow snow depths (approximately 4 cm). This can be an innovation, as in the Arctic regions one of the most challenging parts is the estimation of sea ice thickness under the layers of snow.

Considering Table 1 and Table 2, in both datasets CFDM was the most important parameter in sea ice thickness prediction. As mentioned earlier (Section 2.1), CFDM is a cumulative index that sums the differences between air temperature and the freezing point over time. Physically, this means that higher CFDM values correspond to colder air temperatures and longer durations of freezing conditions. As the air temperature drops further below the freezing point, the CFDM increases more rapidly, indicating stronger potential for ice growth. This direct relationship explains why CFDM closely follows the pattern of sea ice thickness development. Colder and more prolonged freezing conditions naturally lead to thicker ice. This correlation is clearly reflected in Figure 2d and Figure 3d, where a similar pattern of CFDM to the ice thickness growth can be seen. Therefore, CFDM’s superior ranking in the Random Forest model is justified by its strong physical connection to the temperature-driven process of sea ice formation.

In this study, the temperature was continuously below the freezing point of seawater and therefore the ice growth was a continuous process. Under other meteorological conditions, temperatures might rise above the freezing point, and would affect the rate of ice growth. This is a limitation of our current study and should be investigated to extend the applicability of our analyses to longer time scales and broader regions of interest in Arctic sea ice.

Comparing Table 1 and Table 2, bulk ice salinity was identified as the second most important feature for predicting sea ice thickness in Scenarios 1 and 2 of Dataset 1. In contrast, surface cover salinity, which includes the salinity of snow and frost flowers, ranked second in Scenarios 1 and 2 of Dataset 2, while bulk ice salinity dropped to among the least important features (12th and 10th, respectively). This contrast is primarily attributed to differences in sea ice thickness and surface conditions between the two datasets. Dataset 1 featured much thinner ice (up to 8 cm), allowing bulk ice salinity to more directly reflect the overall ice condition. In Dataset 2, with thicker ice (27–47 cm), internal salinity played a less significant role, while surface cover salinity became more influential due to its stronger interaction with surface thermodynamics. The thicker ice likely restricted brine mobility from deeper layers, making surface features more relevant for predicting ice thickness.

Although surface cover salinity ranked fourth out of twelve features in Scenarios 1 and 2 of Dataset 1, the differences in feature importance were not substantial, and it still falls within the moderately important category. Its relevance stems from its strong association with surface conditions that influence ice growth. In early ice formation stages, high surface salinity typically indicates the presence of frost flowers, which form under very cold conditions, signaling active brine movement from the ice to the surface and rapid ice growth [45,51]. However, snowfall significantly reduces surface cover salinity, as snow is low in salinity and dilutes the saline surface layer [48]. Additionally, snow acts as an insulating layer, limiting heat loss from the ice to the atmosphere and thereby slowing or halting ice thickening [2].

Among the radar polarizations used in the model, C-VV was ranked highest in importance for predicting sea ice thickness. This result is physically reasonable and aligns with previous studies [17,47,48], as C-VV polarization is particularly sensitive to surface roughness and dielectric properties of sea ice, both of which are closely linked to ice thickness [45]. VV polarization tends to produce stronger backscatter from thin ice compared to other polarizations, making it more responsive to subtle changes in ice thickness [49]. C-HH polarization was ranked just below VV, with a similar pattern of response but generally lower normalized radar cross-section (NRCS) values. In contrast, cross-polarized feature (C-HV) was ranked much lower and was among the least important features in sea ice thickness prediction. HV polarization is primarily sensitive to volume scattering within the ice, which is less directly correlated with ice thickness, especially in thin sea ice [49,65]. Its backscatter signal tends to be weaker and more variable, making it less reliable for thickness estimation in this context. Generally, these results confirm that C-band NRCS values in VV and HH polarizations are determining factors in tracking sea ice thickness.

It was assumed that the salinity of the surface features followed a linear trend, which permitted the use of linear interpolation to fill data gaps. This assumption presents a limitation that can be addressed in two ways. First, physical sampling data could be collected more frequently, although repeating physical sampling as frequently as every 5 min for Dataset 1 and 15 min for Dataset 2 would be challenging. Second, a more sophisticated model could be developed to describe the salinity evolution, particularly as a function of air and surface temperatures. However, this approach would increase the complexity of the methodology and the computational burden of the models. Despite this limitation, it is noteworthy that the results achieved were successful even without such corrections. This underscores the capability of the Machine Learning models, especially Random Forest.

Although meteorological parameters like air temperature, surface temperature, humidity, and wind speed are important in ice formation, Table 1 and Table 2 show that they were parameters of low importance in predicting ice thickness. Because these features did not significantly change during the experiment time, their weights remained in low amounts in the training process. Moreover, some of these parameters were highly correlated with other features that had higher weights. For instance, by a sharp increasing trend of CFDM, the model would allocate less weight to the air temperature. Surface temperature is also highly dependent on the air temperature; hence, these parameters gained low rankings. The role of humidity can be traced in forming frost flowers, as reported by [45], regarding increased NRCS values and locally increased surface cover salinity. Therefore, all these meteorological features still have determining roles in ice formation; however, in the Random Forest algorithm, they were involved less than other features in the prediction process. This proves that feature selection can be limited to high-importance features. Choosing optimum features can improve accuracy and efficiency in future research.

Using lab-grown sea ice in a controlled environment, such as SERF in this study, offered several advantages for studying sea ice processes. It enabled the precise monitoring of key variables such as air temperature, salinity, and ice growth, enabling detailed observation of specific phenomena like frost flower formation and salinity evolution. This controlled setting also facilitated repeatability and consistency across experiments, which is often difficult to achieve in natural Arctic conditions. However, there were some limitations and challenges associated with this approach. One of the main difficulties was ensuring that all experimental equipment operated in harmony to collect the full range of desired physical and meteorological parameters. Unanticipated technical issues or the absence of certain sensors could lead to gaps in data and reduce the credibility of results, particularly in studies focused on sea ice thickness. Additionally, simulating the full complexity of Arctic environmental conditions, such as snowfall, wind, and temperature fluctuations, was difficult. Furthermore, setting up radar scatterometers in a small pool environment presented its own challenges. Ensuring that the radar antenna was correctly aligned with the ice surface and not inadvertently capturing backscatter from surrounding structures, such as pool edges, barriers, or metal roofing, required careful calibration and significant effort was made to ensure that the measurements are not impacted, as demonstrated in previous studies (see Isleifson et al. [45], for example). In contrast, field measurements in the Arctic benefit from vast open areas that minimize such interference. These limitations should be considered when interpreting results from lab-based experiments and comparing them to natural sea ice conditions.

5. Conclusions

Climate change in the Arctic is significantly reducing sea ice extent and thickness. Monitoring sea ice thickness is vital, as its decline has significant implications on the Arctic ecosystem and climate. To overcome challenges of sea ice thickness estimation using physical models, Machine Learning models can be instrumental in this field. The overarching objective of this study was to address this gap by investigating the effectiveness of Machine Learning models in predicting thin sea ice thickness using two time-series datasets with thickness ranges of 1–8 cm and 27–47 cm, various ice covers, and three different combinations of radar/physical features (Scenarios 1–3).

To achieve this objective, the performances of four common statistical and Machine Learning algorithms (Linear Regression, Decision Tree, Random Forest, and Fully Connected Neural Network) were investigated. The results demonstrated that for both datasets, Random Forest was the most effective model, providing accurate and consistent predictions of sea ice thickness, with RMSE = 0.01 cm in most scenarios.

By analyzing the results of the models in three scenarios, it was confirmed that integrating surface-based microwave radar parameters (C-band NRCS values) and physical features enhances the accuracy of sea ice thickness predictions. Some physical features played a more significant role in the predictions, as their weights during the training process were higher than other features. The most important features included Cumulative Freezing Degree Moment (CFDM), salinity parameters (surface cover, ice surface, and bulk ice salinities), and radar parameters at low incident angles, VV, and HH polarizations. The contribution of these parameters was validated through the superior performance of the Random Forest model.

Applying an advanced and well-trained Machine Learning model, such as Random Forest, demonstrated the feasibility of predicting thin sea ice thickness with small surface cover dimensions, including frost flowers (approximately 1.5 cm) and shallow snow depth (approximately 4 cm). The results of this study can be a guideline for further studies on Arctic sea ice thickness using machine learning models, which will enhance our understanding of the most relevant parameters for detecting sea ice thickness using remote sensing tools. Additionally, it can lead toward near real-time observation and rapid prediction of sea ice thickness in high latitude regions more accurately.