# WV-Net: A foundation model for SAR ocean satellite imagery

Yannick Glaser, Justin Stopa, Linnea M. Wolniewicz, Ralph Foster, Doug

Vandemark, Alexis Mouche, Bertrand Chapron, Peter Sadowski

► To cite this version:

Yannick Glaser, Justin Stopa, Linnea M. Wolniewicz, Ralph Foster, Doug Vandemark, et al. WV-Net: A foundation model for SAR ocean satellite imagery. Artificial Intelligence for the Earth Systems, 2025, 4 (4), 21p. 10.1175/AIES-D-25-0003.1. [https://hal.science/hal-05329456v1](https://hal.science/hal-05329456v1)

HAL Id: hal-05329456

Submitted on 31 Oct 2025

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# WV-Net: A Foundation Model for SAR Ocean Satellite Imagery

YANNIK GLASER,ª JUSTIN E. STOPA,ᵇ LINNEA M. WOLNIEWICZ,ª RALPH FOSTER,ᶜ DOUG VANDEMARK,ᵈ
ALEXIS MOUCHE,ᶜ BERTRAND CHAPRON,ᶜ AND PETER SADOWSKI,ᶜ,ª

ª Information and Computer Sciences, University of Hawai'i at Mānoa, Honolulu, Hawaii

ᵇ Ocean Resources and Engineering, University of Hawai'i at Mānoa, Honolulu, Hawaii

ᶜ Applied Physics Laboratory, University of Washington, Seattle, Washington

ᵈ Ocean Processes Analysis Laboratory, University of New Hampshire, Durham, New Hampshire

ᵉ Université de Bretagne Occidentale, CNRS, IRD, Ifremer, Laboratoire d'Océanographie Physique et Spatiale, Brest, France

(Manuscript received 3 February 2025, in final form 21 July 2025, accepted 5 September 2025)

**ABSTRACT:** The European Space Agency's Sentinel-1 (S-1) satellite mission has captured more than 10 million images of the ocean surface using C-band synthetic aperture radar (SAR WV mode). While machine learning is a promising approach for detecting and quantifying various geophysical signatures in these images, scientists are limited by the cost of manual data annotation for any particular task. We propose to use contrastive self-supervised learning on the full archive of unannotated WV-mode images to train a semantic embedding model named WV-Net. In experiments, we show that WV-Net embeddings outperform those from models that were pretrained with natural images (ImageNet) on four downstream tasks: multilabel classification [0.96 average area under the receiver operating characteristic (AUROC) vs 0.95], wave height regression [0.50 root-mean-square error (RMSE) vs 0.60], near-surface air temperature regression (0.90 RMSE vs 0.97), and unsupervised image retrieval [0.41 class-averaged mean average precision (mAP) vs 0.37]. WV-Net embeddings also scale better in data-sparse settings, and fine-tuned WV-Net models are more robust to hyper-parameter choices. The WV-Net foundation model is publicly available and can be adapted to a variety of data analysis and exploration tasks in geophysical research.

**SIGNIFICANCE STATEMENT:** Satellite imagery of the ocean from the Sentinel-1 (S-1) mission contains global and temporal information about ocean waves, atmospheric patterns, biological signatures, sea ice, and ships. However, the dataset is currently not fully utilized due to the size and complexity of the data. Our WV-Net foundation model makes this large dataset more accessible to researchers by providing a pretrained model that converts images into semantic vector embeddings, making the dataset amenable to analysis using advanced data-driven methods.

**KEYWORDS:** Clustering; Data science; Deep learning; Dimensionality reduction; Other artificial intelligence/machine learning

## 1. Introduction

Machine learning is becoming increasingly important for analyzing remote sensing data. The number of Earth observation satellites in orbit has grown from 150 in 2008 (Tatem et al. 2008) to over 1150 in 2022 (Union of Concerned Scientists 2022). Missions like the European Space Agency's (ESA) Sentinel-1 (S-1) mission generate large amounts of high-resolution images with global coverage. ESA has taken an open-data policy making high-resolution synthetic aperture radar (SAR) imagery readily available for applications ranging from environmental monitoring to climate modeling (Torres et al. 2012). Fully leveraging the torrent of S-1 SAR imagery requires automated analysis tools with many potential applications for machine learning (e.g., Topouzelis and Kitsiou 2015; Wang et al. 2019a). However, the machine learning approach generally requires large datasets of training images that have been annotated by experts.

Transfer learning is one common solution to this challenge. A deep neural network model is first pretrained on a large

dataset from a related domain and then fine-tuned on the target task, requiring significantly less labeled data than would be necessary when training from randomly initialized network parameters. The pretrained model is called a foundation model because it can be reused for multiple downstream tasks. Foundation models pretrained to classify natural images [primarily the ImageNet dataset (Deng et al. 2009)] are routinely fine-tuned for remote sensing (Hu et al. 2015; Wang et al. 2018; Nogueira et al. 2017). However, transferring a model from a natural image classification task to a remote sensing task can be problematic because the image characteristics are very different. Guo et al. (2020), among other works, formalize this difference based on image characteristics like perspective, object-centricness, presence of color, and whether the images are of natural objects, concluding that EuroSAT imagery has limited similarity to ImageNet, making transfer learning more difficult. This is known as the domain gap, and the deep learning literature has repeatedly shown that a wide domain gap between pretraining and target data domains can hinder transfer learning performance (Yosinski et al. 2014; Leong et al. 2022; Raghu et al. 2019). Rolf et al. (2024) even go so far as to argue that satellite imagery should be treated as an entirely separate modality from natural images due to its

Corresponding author: Yannik Glaser, yglaser@hawaii.edu
distinct qualities, such as unique spatial and temporal scales, the ability to capture multispectral imagery beyond standard RGB channels, and the extremely sparse annotation-to-data-volume ratio often associated with satellite data.

Self-supervised learning (SSL) provides an approach to pre-training a foundation model on unannotated, domain-specific data. Instead of predicting annotations in a supervised manner, SSL algorithms define some other pretext task for pretraining. This approach has long been utilized in natural language processing (Church 2017; Pennington et al. 2014) and has been one of the driving factors for the success of large language models (Devlin et al. 2018; Radford et al. 2018; Brown et al. 2020). Recently, contrastive learning has reemerged as a successful self-supervised form of pretraining, especially for computer vision (Chen et al. 2020a; Caron et al. 2021b; Zhou et al. 2022). Contrastive algorithms have produced impressive results on natural image datasets, resulting in general-purpose models that perform on par or better than models being trained in a supervised manner from scratch on the target dataset (Caron et al. 2021b; Chen et al. 2020a). Thus, SSL presents opportunities for analyzing remote sensing data. Recent studies have shown that pretraining on remote sensing data instead of natural images yields superior performance on downstream tasks (Neumann et al. 2019), with most proposed methods being self-supervised (Fuller et al. 2022; Cong et al. 2022; Reed et al. 2023; Ayush et al. 2021). To date, these efforts have focused on remote sensing imagery of landmasses or coastal regions.

The objective of this work is to build the first foundation model for open-ocean sea surface images. Our foundation model is pretrained on imagery from S-1 wave (WV) mode, which was designed to capture ocean waves at 5-m resolution in 20 km × 20 km footprints (Hasselmann et al. 2013; Stopa and Mouche 2017; Quach et al. 2021). These images capture a variety of ocean phenomena (Jackson et al. 2004) and have global coverage, with millions of images archived over the last decade. Thus, the data have been used to study ocean fronts (Rascle et al. 2017), air-sea interactions including organized turbulence in the marine boundary layer (Young et al. 2000; Vandemark et al. 2001; Stopa et al. 2022), and other physical, atmospheric, and biological processes (Wang et al. 2019b). By building a foundation model specific to SAR WV images, we hope to accelerate this research.

Two hypotheses are tested. First, we test whether contrastive SSL can train a SAR WV-mode foundation model that outperforms standard foundation models pretrained on natural images. Second, we test whether performance of the model can be improved by using domain knowledge to design data augmentations. These hypotheses are tested experimentally using a dataset of almost 10 million S-1 WV images, along with three smaller subsets of annotated images that exemplify target supervised tasks for transfer learning. This paper will serve to introduce the model and demonstrate its robustness and superior transfer performance on a set of diverse downstream applications. While in-depth analysis of the model's application to these downstream tasks is beyond the scope of this paper, follow-up work is being prepared that more closely explores individual applications. The optimized foundation model is made publicly available under the name WV-Net,

and we expect it to be useful for a variety of downstream applications such as studying air-sea interactions, improving constraints on numerical weather predictions, and monitoring sea ice.

## 2. Methods

### a. Datasets

The European Space Agency's S-1 mission has been operating two SAR satellites for almost a decade. The satellites are equipped with C-band instruments that operate continuously day and night, unaffected by cloud cover. While S-1 has four imaging modes, we focus exclusively on the WV mode that is used over open ocean. Each satellite produces approximately 60 000 WV images per month, and in total, there are approximately 165 months and 9.9M images. Raw S-1 level-1 5-m data are preprocessed to effectively highlight the textures and saved as 8-bit PNG files with 20 × 20 footprints and 50-m resolution, preprocessing is further detailed in appendix B. The images contain features of interest at multiple spatial scales (Fig. 1), sometimes in the same image. Below, we describe three subsets of the data that have been annotated for supervised learning tasks; these tasks are used to evaluate WV-Net as a foundation model.

#### 1) GOALI CLASSIFICATION DATASET

The GOALI dataset (J. E. Stopa et al. 2025, unpublished manuscript) consists of 10 000 WV images that were manually annotated by human experts for multilabel classification, meaning any image can have multiple labels simultaneously. The labels indicate geophysical phenomena observable in the image. To this, we add 6400 images from Wang et al. (2019b) that have been reannotated in a way consistent with GOALI, for a total of annotated 16 400 images. The GOALI images are multilabeled with the following phenomena: wind streaks (WS), microscale convective cells (MC), negligible atmospheric variability (NV), rain cells (RC), cold pools (CP), submesoscale air-mass boundaries (AB), low wind areas (LW), atmospheric gravity waves (AW), biological slicks (BS), ocean fronts (OF), internal oceanic waves (IW), icebergs (IB), ships (SH), ship wakes (SW), and other unidentified phenomena (UD). Sample images are shown in Fig. 1, while a representative example from each class is shown in Fig. D1 of appendix D. This dataset is currently unpublished work but will be made publicly available in the future.

#### 2) WAVE HEIGHT REGRESSION DATASET

Quach et al. (2021) annotated hundreds of thousands of WV images with significant wave height ($H_s$) by collocating S-1 satellites with altimeter satellites. Here, we use a subset of 200 000 images and randomly split the data into sets of 50 000, 50 000, and 100 000 for training, validation, and final evaluation, respectively.

#### 3) AIR TEMPERATURE REGRESSION DATASET

Stopa et al. (2022) showed that the sea surface roughness observed in SAR is related to atmospheric stratification
<figure><img src="image_2.png" /><figcaption>FIG. 1. (a)–(d) Sample images of different geophysical phenomena observable in the global S-1 WV archive, titled by their dominant classes. Multiple classes can be present in the same image. (e)–(h) Augmented versions of the low wind image illustrating the default SimCLR augmentation policies. (i)–(l) Augmented low wind images illustrating the augmentation policies evaluated in this work. In the actual SimCLR framework, usually multiple augmentations are applied in sequence to the same image.</figcaption></figure>

and therefore air-sea temperature differences. Using ERA5 reanalysis data (Hersbach et al. 2020) as ground truth annotations for the sea surface temperature (SST) and air temperature ($T_{v10}$), we attempt to predict the difference from SAR images. The air temperature is corrected using the COARE algorithm (Edson et al. 2013) to account for moisture content and derived as a virtual air temperature at height 10 m above the sea surface (TV10). The annotated dataset consists of 76 000 images, which are split into 50 000 training, 11 000 validation, and 15 000 testing images.

b. Model details

WV-Net is trained using the SimCLR contrastive SSL framework (Chen et al. 2020a) with standard, fully convolutional ResNet50 as the backend architecture (He et al. 2015). These choices were based on an initial exploratory analysis of framework and backend combinations detailed in appendix A. The SimCLR SSL pretext task is to learn similar representations for two augmented views of an image while discouraging

similarity with the representations of any other image in the training data (Fig. 2).

A SimCLR training step begins by randomly sampling a min-batch of N training images. Each image $x_k$ is transformed twice by random sequences of augmentation policies (sampled from a pool of transformations) to produce two views of the original image, $\tilde{x}_{2k-1}$ and $\tilde{x}_{2k}$, resulting in 2N total images. Each view is encoded by a backend network (here, a ResNet50) and then a smaller projector neural network, resulting in the embedding vectors $z_{2k-1}$ and $z_{2k}$. The loss for any positive pair of embeddings $z_i$ and $z_j$ originating from the same image is

$$l_{i,j} = -\log \frac{\exp[\text{sim}(z_i, z_j)/\tau]}{\sum_{k=1}^{2N} \exp[\text{sim}(z_i, z_k)/\tau]}, \quad (1)$$

where $\tau$ is a temperature scalar, $\mathbb{I}$ is the indicator function mapping the positive sample pair to 0 to prevent it from adding to the denominator of the loss, and $\text{sim}(\cdot, \cdot)$ is the cosine similarity:
<figure><img src="image_3.png" /><figcaption>FIG. 2. In the SimCLR algorithm, images are randomly augmented to create several views of the same image. An encoder network—consisting of a backbone and a smaller projection head—learns to produce an embedding that is similar to embedded views from the same original image and dissimilar to embedded views from all other images. Only the encoder backbone is used for transfer learning.</figcaption></figure>

$$ \mathrm{sim}(\mathbf{u}, \mathbf{v}) = \frac{\mathbf{u}^\mathrm{T}\mathbf{v}}{\|\mathbf{u}\|\|\mathbf{v}\|} \qquad (2) $$

The final loss is the sum of losses $l_{ij}$ for all positive pairs in a batch where the goal is to maximize the positive pairs' similarity while minimizing the similarity to the rest of the batch. Unless otherwise specified, all hyperparameters are adopted from the original SimCLR work (Chen et al. 2020a) with linear learning rate scaling. Also, in accordance with the original SimCLR formulation, the projection head is a two-layer multilayer perceptron (MLP) with a 2048-unit hidden layer and 128-unit linear output size. Details on the implementation are provided in appendix C.

### c. Augmentations

SAR WV-mode images are very different from natural images, so experiments were conducted to optimize the choice of augmentations used to train WV-Net. In addition to the augmentations proposed in the original SimCLR (Chen et al. 2020a) paper, we explore a variety of augmentations proposed

in the contrastive learning literature, transformations from traditional computer vision, and a transform from signal processing that was inspired by the SAR imaging process.

* SimCLR augmentations: These include random cropping and zooming, random flipping, random color jitter, and random Gaussian blur (see Figs. 1e–h for examples).

* Literature-inspired augmentations: Mixup (Zhang et al. 2018) and Cutout (DeVries and Taylor 2017) are policies that have been shown to work well in contrastive learning frameworks (Jin and Heizmann 2024; Chen et al. 2020a; Verma et al. 2021).

* Computer vision augmentations: Many traditional image processing transformations seem well suited for this application. We combined random rotation, random color inversion, and random sharpness transformations into a single augmentation policy called CVAug. We also modified the crop-and-zoom augmentation that is universal among multiview contrastive learning frameworks to create a no-zoom crop policy that focuses on random cropping with only minimal scaling. Since WV images are captured from a satellite
in constant orbit and have a consistent 20-km footprint, phenomena captured do not vary in scale as much as features in natural images might. Thus, by reducing the zoom component, scale invariance is not as heavily incentivized in the model allowing features to be more specific.

*   **Domain-inspired augmentation:** WV images are often dominated by ocean surface waves, so representing the image in the frequency domain and dropping random frequency components emphasizes or de-emphasizes particular features that could be relevant to sea surface state. This is a common signal-processing operation called random notch filtering.

Examples for each augmentation policy can be seen in Fig. 1, and details for the augmentation policy implementations and more rationales on each policy's inclusion are provided in appendix E. All augmentations are added to the overall transform pool from which to sample during training. That means that each augmentation policy, be it from the original SimCLR policies or one of the added policies described here, gets applied with some probability to each image. An image may be transformed by any combination of policies, including all or none, and the sampling is repeated for every image in every batch.

### d. Evaluation protocols

To evaluate the quality of the WV-Net embeddings, we conduct experiments in which the embeddings are used for a multilabel classification task, two regression tasks, and an unsupervised image retrieval task. The experiment protocols are summarized below with more details in appendix F.

#### 1) MULTILABEL CLASSIFICATION

Four common protocols are used to evaluate the embeddings for transfer learning to a multilabel classification task: the k-nearest neighbors (kNNs) approach from Wu et al. (2018b), the linear probing protocol from Chen et al. (2020a), the MLP probing protocol suggested by Bordes et al. (2023), and full end-to-end fine-tuning following recent trends in evaluation (He et al. 2021; Bao et al. 2022; Zhou et al. 2022; Dong et al. 2022). The primary metric used for evaluation is the microaveraged area under the receiver operating characteristic (AUROC) curve. The F1 score is also reported.

#### 2) REGRESSION

Three protocols are used for two regression tasks: linear probing, MLP probing, and end-to-end fine-tuning. These protocols are identical to the classification protocols except no kNN-based model is considered. Models are evaluated using the mean absolute error (MAE) and root-mean-square error (RMSE).

#### 3) IMAGE RETRIEVAL

The embeddings are evaluated for one-shot image retrieval performance, following the kNN-retrieval approach from Caron et al. (2021b). Experiments are conducted on the rarest classes from the combined classification dataset, occurring in

no more than 1000 images (<0.05% of the total dataset), consisting of seven total classes. Models are evaluated in terms of mean average precision (mAP) averaged over all classes.

### 3. Results

Experiments were conducted to test two hypotheses: 1) a self-supervised model trained on WV data will outperform a model trained on ImageNet, and 2) the self-supervised model can be improved by selecting pretext tasks based on domain-specific properties of the satellite images. We first performed experiments to optimize the set of augmentations used in the SimCLR training algorithm. WV-Net was then trained using the optimized augmentations for an extended period. This model is compared to an ImageNet model, a model pretrained in a supervised manner on Sentinel-1 land-cover data (Clasen et al. 2025), and a WV model pretrained with the default SimCLR augmentations, testing hypotheses (1) and (2), respectively.

#### a. Optimization of WV-mode specific data augmentations

The set of augmentations was optimized using a local search strategy. One augmentation policy at a time was introduced to the baseline SimCLR policies, and the performance was evaluated. All models were trained for 100 epochs total, where one epoch consists of training on a random 30% subsample—roughly 3.8M unique samples—of the full unlabeled dataset, this sample is redrawn every 20 epochs, allowing for reduced computational cost while still exposing the model to the majority of the full unlabeled data at some point during training. All models are trained using 4 V100-32GB GPUs, 16 CPU cores, and 200 GB of RAM with a global batch size of 512, taking about 6 days to complete 100 epochs. The resulting models are then evaluated on the classification task and the $H_s$ regression task. Results for linear probing are shown in Table 1, and a complete table for all transfer settings can be found in appendix D. The linear probing results are illustrative of the overall trends observed in this part of the study and show that Mixup and CVAug consistently improve performance for both the classification and regression tasks. However, the domain-inspired notch filter policy, cutout (DeVries and Taylor 2017), and reduced zooming in the crop-and-zoom augmentation did not improve performance—thus, these augmentations were not included in the final model.

#### b. Transfer learning

Based on the optimization experiments above, we selected four augmentations to add to the baseline SimCLR augmentation pool: mixup, random color inversion, random rotation, and a random sharpness transform. The parameterization of these transforms remains unchanged. These are used to train the final model, called WV-Net.

In experiments, WV-Net was then compared to the baseline SimCLR model trained on WV images (without additional augmentations), the ImageNet model trained using supervised learning, and BigEarthNet-S1, a model pretrained on the Sentinel-1 land-cover dataset by Clasen et al. (2025). The two SSL models (WV-Net and baseline SimCLR) are pretrained for 200 epochs with a global batch size of 1024 (and accordingly,
<table><caption>TABLE 1. Comparison of different augmentation methods used during training with SimCLR. The original (baseline) SimCLR method trained on satellite data does better than a standard ImageNet model, and these results can be improved with modifications to the set of augmentations. The classification scores are microaveraged AUROC and microaveraged F1 scores (higher is better). The wave height scores are the RMSE and MAE (lower is better). Models that outperform baseline SimCLR are in bold.</caption><thead><tr><th rowspan="2">Evaluation method</th><th rowspan="2">Model</th><th colspan="2">Classification</th><th colspan="2">Wave height</th></tr><tr><th>AUROC↑</th><th>F1 score↑</th><th>MAE↓</th><th>RMSE↓</th></tr></thead><tbody><tr><td rowspan="7">Linear</td><td>ImageNet</td><td>0.952</td><td>0.730</td><td>0.447</td><td>0.601</td></tr><tr><td>Baseline SimCLR</td><td>0.953</td><td>0.735</td><td>0.428</td><td>0.580</td></tr><tr><td>Baseline + Cutout</td><td>0.943</td><td>0.705</td><td><strong>0.380</strong></td><td><strong>0.516</strong></td></tr><tr><td>Baseline + CVAug</td><td><strong>0.954</strong></td><td><strong>0.742</strong></td><td><strong>0.413</strong></td><td><strong>0.555</strong></td></tr><tr><td>Baseline + Mixup</td><td><strong>0.953</strong></td><td><strong>0.738</strong></td><td><strong>0.392</strong></td><td><strong>0.531</strong></td></tr><tr><td>Baseline + Notch</td><td>0.949</td><td>0.720</td><td><strong>0.427</strong></td><td><strong>0.578</strong></td></tr><tr><td>Baseline - Zoom</td><td><strong>0.955</strong></td><td>0.722</td><td>0.485</td><td>0.647</td></tr></tbody></table>

a learning rate of 1.2) on 8 V100-32GB GPUs, using 400 GB of RAM and 36 CPU cores. Training takes about 12 days to complete.

Table 2 compares the performance of the models on three supervised learning tasks using four protocols. WV-Net outperforms the other models on most tasks under most evaluation scenarios. The BigEarthNet-S1 model performs especially poorly, illustrating the shortcomings of supervised pretraining and the wide gap between SAR WV data and land-focused imagery (because performance was so much worse than even the ImageNet model on the classification task, we skipped evaluation on the regression tasks). This underscores the need for a dedicated WV foundation model as even pretraining on other imagery acquired with the same sensor can lead to suboptimal performance. The only task where other models perform better than WV-Net is the air temperature prediction task, where WV-Net performs the worst in the MLP scenario and slightly worse than the baseline SimCLR model when fine-tuned end to end. In general, the linear models perform the best on the classification task, while the MLP and fine-tuned models perform the

best on the wave height and air temperature regression tasks, respectively.

While WV-Net improved performance on each of the three transfer learning tasks, some tasks saw larger improvements than others. The wave height regression task was particularly difficult for the ImageNet model—even with model fine-tuning the model failed to extract features relevant to the task, while WV-Net had no problem (Table 2). This is likely due to the importance of subtle texture features that are very different from the large-scale visual features required for object classification in natural images. On the multilabel classification task, we observed more modest improvements across the individual classes, with some of the classes having slightly lower AUROC than with the ImageNet model, but WV-Net performs better overall (see appendix F for class-specific ROC curves).

Figure 3 also illustrates that performance trends hold for data-constrained settings. Even with as little as 100 total samples, WV-Net embeddings achieve above 0.85 microaveraged AUROCs in all transfer learning settings, consistently beating ImageNet embeddings as dataset size is increased.

<table><caption>TABLE 2. Comparison of final model performances. AUROC and F1 scores correspond to the image classification, and MAE and RMSE are used for the regression tasks to estimate significant wave heights and air-sea temperature differences. The best score for each task under different evaluation scenarios is highlighted in bold.</caption><thead><tr><th rowspan="2">Evaluation method</th><th rowspan="2">Model</th><th colspan="2">Classification</th><th colspan="2">Wave height (m)</th><th colspan="2">Air temperature (°C)</th></tr><tr><th>AUROC↑</th><th>F1 score↑</th><th>MAE↓</th><th>RMSE↓</th><th>MAE↓</th><th>RMSE↓</th></tr></thead><tbody><tr><td rowspan="4">kNN</td><td>ImageNet</td><td>0.925</td><td>0.675</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>BigEarthNet-S1</td><td>0.894</td><td>0.599</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Baseline SimCLR</td><td>0.925</td><td>0.669</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>WV-Net (ours)</td><td><strong>0.936</strong></td><td><strong>0.697</strong></td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td rowspan="4">Linear</td><td>ImageNet</td><td>0.952</td><td>0.730</td><td>0.447</td><td>0.601</td><td>0.682</td><td>0.974</td></tr><tr><td>BigEarthNet-S1</td><td>0.929</td><td>0.650</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Baseline SimCLR</td><td>0.954</td><td>0.739</td><td>0.395</td><td>0.532</td><td>0.655</td><td>0.920</td></tr><tr><td>WV-Net (ours)</td><td><strong>0.958</strong></td><td><strong>0.754</strong></td><td><strong>0.370</strong></td><td><strong>0.500</strong></td><td><strong>0.637</strong></td><td><strong>0.902</strong></td></tr><tr><td rowspan="4">MLP</td><td>ImageNet</td><td>0.931</td><td>0.715</td><td>0.479</td><td>0.656</td><td>0.702</td><td>0.996</td></tr><tr><td>BigEarthNet-S1</td><td>0.906</td><td>0.630</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Baseline SimCLR</td><td>0.930</td><td>0.716</td><td>0.355</td><td>0.491</td><td><strong>0.691</strong></td><td><strong>0.960</strong></td></tr><tr><td>WV-Net (ours)</td><td><strong>0.948</strong></td><td><strong>0.744</strong></td><td><strong>0.335</strong></td><td><strong>0.459</strong></td><td>0.763</td><td>1.01</td></tr><tr><td rowspan="3">Fine-tuned</td><td>ImageNet</td><td>0.931</td><td>0.759</td><td>2.696</td><td>3.001</td><td>0.661</td><td>0.964</td></tr><tr><td>Baseline SimCLR</td><td>0.934</td><td>0.760</td><td>0.418</td><td>0.586</td><td><strong>0.623</strong></td><td><strong>0.902</strong></td></tr><tr><td>WV-Net (ours)</td><td><strong>0.939</strong></td><td><strong>0.777</strong></td><td><strong>0.377</strong></td><td><strong>0.530</strong></td><td>0.635</td><td>0.923</td></tr></tbody></table>
<figure><img src="image_4.png" /><figcaption>FIG. 3. Performance of WV-Net vs ImageNet embeddings on the downstream classification task as a function of the number of labeled training samples. WV-Net almost always outperforms ImageNet, for any evaluation method and any number of labeled training samples.</figcaption></figure>

### c. Image retrieval

The image-retrieval task illustrates the capability of the learned embeddings from the SSL model to delineate between features of interest without any fine-tuning. WV-Net outperforms ImageNet embeddings in almost all of the rare classes and remains competitive in all other cases, as detailed in Table 3. Because the dataset is multilabel and several classes can be present in a single image, identifying all classes from a single example can be noisy and lead to mAP scores that appear lower than for single-label datasets common in natural image applications. When scoring for any class overlap between the anchor and retrieved images, mAP for both models approaches 1.0, illustrating that they can retrieve images that share some dominant characteristics. The fact that WV-Net otherwise outperforms ImageNet suggests that the SSL embeddings are more sensitive to secondary classes present in the images, allowing for more fine-grained delineation. For reference, Table G1 shows image retrieval performance for the remaining, nonrare classes, with WV-Net still displaying consistently higher or competitive mAP scores.

Figure 4 shows an example of the top three retrieved images for a reference atmospheric gravity waves (AW) image, or anchor. This class makes up less than 0.5% of the overall dataset. Given the anchor image in Fig. 4, WV-Net embeddings give an average precision of 0.95 for the top 20 retrieved images, outperforming the 0.11 average precision of Image-Net embeddings. It appears that the samples retrieved using

ImageNet mostly share similar contrasts in the SAR backscatter, while WV-Net consistently identifies the correct characteristics associated with the class. However, Fig. G4 in appendix G illustrates that given an anchor image where the class is less obvious (AB with subtle AW signatures), WV-Net embeddings also fail to capture the relevant class characteristics. Nevertheless, Table 3 again shows that, on average, WV-Net is more robust to the anchor choice for the AW and most other classes. This is similar to the uncertainty that humans have when characterizing images that contain multiple features. This may also explain the overall low mAP scores shown for the SH (ship) and SW (ship wake) classes in Table 3, because these are generally small, isolated objects in the image where other phenomena dominate the ocean surface backscatter. More examples are provided in Figs. G5 and G6 in appendix G. Figure G5 shows retrieval for randomly sampled anchors of each class, and Fig. G6 shows anchors specifically sampled from the subset of images that only contain a single tagged class. These figures further illustrate that selecting “pure” anchors can improve image retrieval. Further, when multiple classes are present in the anchor, WV-Net embeddings especially seem to retrieve images from all classes present, perhaps indicating a more evenly distributed embedding space.

### 4. Discussion and limitations

One limitation of this work is the computational cost of pretraining. Model performance could likely be improved

<table><caption>TABLE 3. Comparison of image retrieval performance. mAP scores shown on rare classes in the GOALI dataset for ImageNet and WV-Net embeddings with the better-performing model for each class highlighted in bold.</caption><thead><tr><th>Model</th><th>AW (N = 101)</th><th>IW (N = 304)</th><th>OE (N = 142)</th><th>SI (N = 955)</th><th>IB (N = 762)</th><th>SH (N = 236)</th><th>SW (N = 167)</th></tr></thead><tbody><tr><td>ImageNet</td><td>0.013</td><td>0.184</td><td><strong>0.130</strong></td><td>0.845</td><td>0.223</td><td>0.016</td><td><strong>0.024</strong></td></tr><tr><td>WV-Net (ours)</td><td><strong>0.127</strong></td><td><strong>0.297</strong></td><td>0.119</td><td><strong>0.901</strong></td><td><strong>0.398</strong></td><td><strong>0.021</strong></td><td>0.020</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>FIG. 4. Image retrieval example for the atmospheric gravity wave class. (left) The anchor image is the query for kNN retrieval, and the six images to the right are top-3 neighbors from (top) ImageNet and (bottom) WV-Net embeddings. This example shows successful image retrieval with the class present in the lower half of the anchor image.</figcaption></figure>

with larger models, longer training, and more extensive hyperparameter optimization. Carefully tuning the temperature parameter during pretraining can impact task performance, especially for small batch sizes (relative to other contrastive models), such as those employed here (Bordes et al. 2023). Contrastive SSL models have been shown to scale effectively with model capacity (Chen et al. 2020a,b), thus we expect that training a larger model such as ResNet152(x2, x4) with our setup would result in even better performance on downstream tasks.

Similarly, masked-image modeling and vision transformers (ViTs) have been shown to outperform convolutional architectures given enough training time and data (He et al. 2021; Tolstikhin et al. 2021). While ViTs were included in the initial model analysis (appendix A), the models were relatively small. It is possible that, given a larger ViT model and enough training time, this could be a competitive approach to the one presented here.

The downstream tasks presented are only a small subset of potential applications. For example, models could be trained to detect the organized large-scale eddies or lack of them (NV, WS, and MC), which are present in nearly 85% of all images. Supplementing the results with a dense prediction task like detecting organized large-scale eddies could provide further insights into the behavior of WV-Net. Previous works such as Sikora et al. (1995), Young et al. (2002, 2005) have based their analysis of the physical dynamics associated with the marine atmospheric boundary layer (MABL) on hundreds of SAR images. WV-Net could help change the study of the MABL by systematically mapping millions of observations in time and space, enabling studies like Stopa et al. (2022) to broaden their scope to the entire S-1 archive, changing the field from data poor to data rich. Even rarely occurring observations such as small-scale eddies (<100 m), atmospheric gravity waves in the open ocean, or lines in the sea (Yoder

et al. 1994) can be well detected by WV-Net with minimal additional annotations.

## 5. Conclusions

Using self-supervised contrastive learning on almost 10 million images, we have created WV-Net, the first foundation model for S-1 WV imagery. Experiments on downstream classification, regression, and image-retrieval tasks support the two hypotheses: 1) a model pretrained with self-supervised contrastive learning on unannotated domain-specific imagery outperforms models pretrained with supervised learning on natural images, and 2) self-supervised contrastive models can further be improved for non-natural-image tasks by carefully selecting pretext tasks, or augmentations. However, we found that the best augmentation strategies were not necessarily the ones that leveraged any particular domain knowledge, such as random notch filtering. Instead, we found that the best augmentations were the original SimCLR augmentations plus mixup, rotations, color inversions, and sharpness transforms.

WV-Net outperforms models pretrained on natural images and even land-cover S-1 data from the same satellite platform. While the performance improvement of WV-Net over Image-Net models is small for some tasks, the advantage is consistent across tasks. Of the three supervised learning tasks, the largest performance improvement is observed for the wave height prediction task, which requires extracting fine-scale features that may be washed out in the ImageNet model, where final layers primarily capture high-level semantic concepts as opposed to low-level texture features (Yosinski et al. 2014). Furthermore, experiments demonstrate that WV-Net embeddings can yield state-of-the-art performance without the need for end-to-end fine-tuning, drastically reducing the need for computational resources and time. In fine-tuning settings, WV-Net also demonstrates
greater robustness to hyperparameter choices, alleviating the need for broad hyperparameter sweeps. WV-Net is also more data-efficient than competing approaches, requiring less labeled data and even displaying strong image retrieval performance with no labeled data at all. Together, these properties make WV-Net a valuable tool for the remote sensing research community. WV-Net weights and code to run the model will be made available online (https://github.com/hawaii-ai/WVNet/).

More generally, this work demonstrates the value of designing domain-specific foundation models. While WV-Net is designed specifically for WV-mode images from the Sentinel-1 mission, our approach can be applied to other remote sensing imaging technologies with different physical scales. These include other important ocean monitoring technologies like Surface Water and Ocean Topography (SWOT), other SAR modes, or scatterometers. Our experiments show the value of designing a pretext task that is appropriate for the domain, highlighting the value of close collaboration between machine learning and domain scientists.

*Acknowledgments.* R. F. and D. V. were supported by NASA Physical Oceanography Grants NNX17AH17G and 80NSSC20K0822. J. E. S. was supported through Grant 2132150 from the National Science Foundation and NASA Physical Oceanography Grant 80NSSC20K0822. Y. G. was supported by the NASA Physical Oceanography Grant 80NSSC20K0822. A. M. and B. C. were supported by ESA Contract 4000135827/21/NL—Harmony Science Data Utilisation and Impact Study for Ocean. A. M. was also supported by ESA Sentinel-1 Mission Performance Center 465 (4000107360/12/I-LG). We thank ESA for providing the data and IFREMER for computing resources used in this study. L. M. W. was supported by the National Science Foundation Graduate Research Fellowship Program under Grant 2236415. P. S. and Y. G. were supported by Grant 2008344 from the National Science Foundation. Computing resources funded in part by NSF CC* Awards 2201428 and 2232862 are gratefully acknowledged.

*Data availability statement.* All SAR wave mode images are freely available at ESA's Copernicus Browser (https://browser.datalab.copernicus.eu/) and also at the Alaska Satellite Facility (https://asf.alaska.edu/data-sets/sar-data-sets/sentinel-1/sentinel-1-data-and-imagery/).

# APPENDIX A

## Comparison of Contrastive Learning Frameworks and Backend Models

Since there are multiple possible choices for contrastive self-supervised frameworks, we chose to evaluate one representative member of each of the framework families proposed by Balestriero et al. (2023). SimCLR (Chen et al. 2020a) for the deep metric learning family, bootstrap your own latent (BYOL) (Grill et al. 2020) for the self-distillation family, and swapping assignments between multiple views of the same image (SwAV) (Caron et al. 2021a). Similarly, there are multiple

<table><caption>TABLE A1. Validation set performance of different contrastive framework and backend architecture combination. Best model per task is highlighted in bold.</caption><thead><tr><th>Framework</th><th>Backend architecture</th><th>Classification (AUROC)</th><th>Wave height (RMSE)</th></tr></thead><tbody><tr><td rowspan="3">SimCLR</td><td>ResNet50</td><td><strong>0.935</strong></td><td><strong>0.564</strong></td></tr><tr><td>ConvNeXt</td><td>0.911</td><td>0.991</td></tr><tr><td>ViT</td><td>0.881</td><td>1.153</td></tr><tr><td rowspan="3">BYOL</td><td>ResNet50</td><td>0.931</td><td>0.922</td></tr><tr><td>ConvNeXt</td><td>0.889</td><td>1.133</td></tr><tr><td>ViT</td><td>0.885</td><td>1.155</td></tr><tr><td rowspan="3">SwAV</td><td>ResNet50</td><td>0.925</td><td>0.780</td></tr><tr><td>ConvNeXt</td><td>0.915</td><td>1.126</td></tr><tr><td>ViT</td><td>0.927</td><td>1.168</td></tr></tbody></table>

potential choices for families of backend architecture that have shown promise in a broad range of computer vision tasks, we chose a ResNet50 (He et al. 2015) to represent a standard convolutional architecture, ConvNeXt-T (Liu et al. 2022) to represent a more modern version of a convolutional architecture, and a ViT-S/16 (Dosovitskiy et al. 2021) to represent vision transformers. The model sizes were chose to have roughly the same number of trainable parameters and constrained to fit the available compute budget. All hyperparameters were set in accordance with the original framework papers. Table A1 details the performance results for fine-tuned models on the classification and wave height tasks, showing clear dominance by the SimCLR + ResNet combination.

# APPENDIX B

## SAR Data Processing

Sentinel-1 launched two satellites, S-1 A and B, in April 2014 and 2016, respectively (Torres et al. 2012). A third, S-1 C, is scheduled to be launched in November 2024. S-1B went out of commission in December 2021. The S-1 satellites are identical polar-orbiting, sun-synchronous satellites (Torres et al. 2012). S-1 operates in the C-band SAR with a center frequency of 5.405 GHz or wavelength of 5.5 cm S-1 has a 12-day repeat cycle, flies with an altitude of 690 km, has an inclination of 98.2°, and a repeat period of 98.7 min. When both S-1A and S-1B were in operation, they were 180° out of phase equating to a 6-day repeat cycle.

Each satellite produces approximately 60 000 images per month. S-1A and S-1B went into routine acquisition mode in October 2015 and July 2016, respectively, so in total, there are approximately 165 months and 9.9 M S-1A/S-1B images. The WV images are 20 km × 20 km scenes and alternate between incidence angles of 23.8° (WV1) and 36.8° (WV2). The along-track separation is 100 km with 5-m pixel spacing. S-1 uses both vertical–vertical (VV) or horizontal–horizontal (HH) polarization, but only one polarization can be obtained for one image. The majority of the WV archive is in VV.

The S-1 *geotiff* is saved in range–azimuth coordinates. The images in this study have the north direction facing upward; therefore, the descending passes are flipped in the
range and azimuth directions to make their relative geophysical representation the same. The raw 20-km WV images have 4000–5000 pixels in the range and azimuth directions. We implement a similar strategy to Wang et al. (2019b) by reducing the raw data size while highlighting the geophysical phenomena that influence the sea surface roughness. The scales resolved by this processing are larger than the typical azimuth cutoff of 100 m (Stopa et al. 2015) and extend to 5 km in three steps: 1) incidence normalization, 2) downscaling, and 3) intensity normalization.

1) Incidence normalization: The radar backscatter $\sigma_0$ depends on the local surface wind, incidence angle $\phi$, relative wind-platform angle $\theta$, and polarization. The model CMOD5N of Hersbach (2010) is used to ameliorate these effects by assuming a constant wind speed of $10 \text{ m s}^{-1}$ and a relative wind-platform angle $\phi$ of $45^{\circ}$ to estimate the sea surface roughness (SSR) as

$$SSR = \frac{\sigma_0}{\text{CMOD5N}(10 \text{ m s}^{-1}, \theta, \phi = 45^{\circ}, \text{VV})} \quad (B1)$$

2) Downscaling: A moving boxcar window of $10 \times 10$ pixels or 50 m is applied to the SSR data. Every 10th pixel is then selected to reduce the data by a factor of 100 resulting in an image size of 400–500 pixels in both range and azimuth.

3) Intensity normalization: The image intensity is enhanced by normalizing each image against data within the 1st (P01) and 99th (P99) percentile:

$$SSR_n = 255 \left( \frac{SSR - P01}{P99 - P01} \right) \quad (B2)$$

This alters the SSR to lie within the interval [0, 255], where values of SSR $\le$ P01 = 0 and SSR $\ge$ 255. This normal imagery is then an unsigned 8-bit integer, and the matrix is saved as a portable network graphics (png) file. Thus, the dataset is effectively composed of grayscale images.

# APPENDIX C

## Implementation Details

All deep learning models are implemented using a combination of PyTorch (Paszke et al. 2019) and PyTorch Lightning (Falcon et al. 2019), while other machine learning models used for transfer learning are implemented in scikit-learn (Pedregosa et al. 2011). Pretrained weights are the default “IMAGENET1K_V2” weights available in the PyTorch torchvision package(TorchVision Maintainers et al. 2016) for all models except for ViTs, which are obtained from the torch image models library (Wightman et al. 2023) under the name “vit_tiny_patch16_224.augreg_in21k_ft_in1k.”

# APPENDIX D

## GOALI Classes

Figure D1 shows representative examples from each of the 12 GOALI classes.
<figure><img src="image_6.png" /><figcaption>FIG. D1. Twelve representative examples of the geophysical phenomena observed in the global Sentinel-1 WV archive. The panels are defined as (a) negligible atmospheric variability (NV), (b) wind streaks (WS), (c) a mixture of WS and microscale cells (MC), (d) MC, (e) rain cells (RC) also notice the two circular patterns in the bottom of the image that represent cold pools (CP), (f) submesoscale air-mass boundary (AB) also contains WS/MC on the left-hand side, (g) a low wind area (LW) containing biological slicks (the black lines) (BS) and MC, the circular structure of the BS are likely due to a small-scale eddy, (h) atmospheric gravity waves (AW), (i) unidentified ocean or atmosphere (UD), (j) ocean front (OF) along with MC and BS, (k) internal oceanic wave, and (l) sea ice with icebergs.</figcaption></figure>

# APPENDIX E

## Comparison of Augmentations

This is a more detailed description of each introduced augmentation policy along with the reasoning behind why it may be beneficial to include in a WV-mode-specific contrastive learning model. For the baseline SimCLR color jitter, since WV images are grayscale, as part of image preprocessing, the single grayscale channel is repeated three times and scaled within a 0–1 range. The images are then effectively treated as RGB throughout the augmentations and model.

1) Cutout is a geometric transform where one or multiple rectangles within the image are zeroed out or replaced

with Gaussian noise (DeVries and Taylor 2017) (see Fig. 1i). We expect that including the cutout augmentation could, on one hand, replicate some of the driving factors behind the success of masked-image-modeling in geospatial data (He et al. 2021; Cong et al. 2022) and also force the model to pay attention to all areas of the images despite the majority of the dataset being comprised of homogeneous textures across the 20-km frames. In this study, cutout can be applied up to three times, each application having a probability of $p = 0.5$, each with a random scale between 2% and 30% of the image, and a random aspect ratio between 0.3 and 3.33. The areas may overlap and are zeroed out.

2) CVAug (or computer vision augmentations) is a composite of classical computer vision transforms that, intuitively,
may complement learning on remote sensing data. Random color inversion is included to encourage a level of invariance to the pixel-intensity information and highlight textures. Random rotation is included because the model should be rotational invariant. A sharpness transform is included to obscure or highlight texture features, incentivizing more balanced representations that do not overrely on global textures. Each augmentation is applied with probability $p = 0.5$, the sharpness being increased by a factor of 0.5 and the rotation between $\pm 170^{\circ}$ (see Fig. 1j).

3) Notch filtering or stopband filters are common in signal processing, typically applied to reduce noise. Khan et al. (2017) use the term spectral dropout to describe dropping weak Fourier coefficients from a layer's input distribution. Here, random dominant Fourier features from the raw input vector are dropped instead. Since ocean waves with scales of 50–800 m visually dominate most of the images, this augmentation should force the network to consider less dominant features. The notch filter is applied with probability $p = 0.5$ and zeroes out up to 15 of the first 30 Fourier features obtained by doing a 2D Fourier transform over the image. However, the most dominant frequency, the first Fourier component, is excluded (see Fig. 1k).

4) Mixup was first proposed as a data augmentation for supervised learning (Zhang et al. 2018). It creates new training examples by taking a weighted combination of random feature vectors and their labels. Mixup has found popularity in SSL by only combining feature vectors (Kim et al. 2020; Shen et al. 2022; Kalantidis et al. 2020). Further work framed mixup in terms of other noise-injection methods such as adding Gaussian noise to images, showing that it improves over random noise masks because the corrupted example is closer to the data manifold (Verma et al. 2021). Mixup is applied with probability $p = 0.5$ and a random mixup strength, $m$, between 0.1 and 0.4. Explicitly, the augmented image, $C$, created by mixup is written $C = (1 - m)A + mB$, where $A$ is the original image and $B$ is another, randomly sampled, image from the same batch (see Fig. 1l).

5) No-zoom crop reduces the zooming component from the crop-and-zoom augmentation and is motivated by conserving the physical spatial scales within the satellite images. While the textures and objects can still vary in scale, this is not as prominent as in natural images because the satellite is in a consistent orbit around the Earth, and the WV images have a nearly fixed footprint of 20 km. Therefore, less pronounced zooming is intended to keep the characteristics of augmented images closer to what could be observed on the ocean's surface, ideally preventing the network from learning features on data enlarged so much that it has no bearing on downstream applications. In this setting, the cropped region can be no less than 90% of the original image.

Table E1 gives the model performances trained with different augmentations for all transfer scenarios. Columns

labeled classification show the performance on the multilabel image detection of oceanic and atmospheric phenomena. The columns labeled wave height show the performance for the significant wave height regression task. Note that the models labeled “Baseline” are the baseline SimCLR model with one added or removed augmentation. For classification, the baseline SimCLR models outperform the ImageNet transfer learning model for all evaluation criteria except the kNN and MLP F1 scores, where the ImageNet weights have a slight advantage. The ImageNet model performs well despite not being pretrained on SAR imagery. For regression, the fine-tuned ImageNet models did not converge to a competitive performance to predict wave heights. This could likely be overcome to an extent with careful, model-specific hyperparameter selection. This illustrates that transfer learning from models with larger domain gaps is sometimes more tuning intensive than transferring weights from a model trained on similar data. Overall, this supports the hypothesis that even without domain-specific augmentations, simply training a self-supervised model on SAR WV data is an improvement over transferring weights from models trained on natural images.

Further, the models highlighted in bold improve over the baseline SimCLR performance by adding augmentations. Across tasks and evaluation scenarios, the addition of various augmentations seems beneficial, but CVAug and mixup stand out for consistently outperforming baseline SimCLR weights. While the classification scores of all models are relatively close (AUROC$_{s} > 0.92$ within 0.03), the wave height regression performance shows more pronounced differences with similar performance trends. Interestingly, while adding the cutout augmentation generally results in lower classification performance, it does benefit most regression models. The effects of the cutout augmentation are likely related to the scales of the phenomena—where ocean waves have typical scales of 100–600 m and many of the classified features are related to the atmosphere and have typical scales of 1–5 km.

Beyond absolute downstream performance, it is also important to understand how the models perform in data-constrained environments. An advantage of transfer learning is that it drastically reduces the need for labeled examples, lowering the barrier of entry for solving science problems with machine learning. Figure E1 shows the MLP transfer performance of the differently pretrained models for low numbers of training samples for image classification. Mixup and CVAug robustly perform better than most other models with micro-AUROC statistics greater than 0.92 and only trained with 900 images. The performance differences are larger than those observed on the full training dataset in Table E1. Therefore, for rare classes, or in situations when the training datasets are small, CVAug and mixup notably improve the model performance.
<table><caption>TABLE E1. Augmentation study results—showing the transfer performance of differently pretrained models. Note that rows 2–6 for each model setup correspond to WV-Net with different augmentations included. The classification scores are microaveraged AUROC and microaveraged F1 scores (higher is better). The wave height scores are the RMSE and MAE (lower is better). Models that outperform baseline SimCLR are in bold.</caption><thead><tr><th rowspan="2">Evaluation method</th><th rowspan="2">Model</th><th colspan="2">Classification</th><th colspan="2">Wave height</th></tr><tr><th>AUROC↑</th><th>F1 score↑</th><th>MAE↓</th><th>RMSE↓</th></tr></thead><tbody><tr><td rowspan="7">kNN</td><td>ImageNet</td><td>0.925</td><td><strong>0.675</strong></td><td>—</td><td>—</td></tr><tr><td>Baseline SimCLR</td><td>0.928</td><td>0.674</td><td>—</td><td>—</td></tr><tr><td>Baseline + Cutout</td><td>0.920</td><td>0.660</td><td>—</td><td>—</td></tr><tr><td>Baseline + CVAug</td><td><strong>0.935</strong></td><td><strong>0.690</strong></td><td>—</td><td>—</td></tr><tr><td>Baseline + Mixup</td><td><strong>0.930</strong></td><td><strong>0.676</strong></td><td>—</td><td>—</td></tr><tr><td>Baseline + Notch</td><td>0.926</td><td>0.668</td><td>—</td><td>—</td></tr><tr><td>Baseline - Zoom</td><td>0.927</td><td>0.661</td><td>—</td><td>—</td></tr><tr><td rowspan="7">Linear</td><td>ImageNet</td><td>0.952</td><td>0.730</td><td>0.447</td><td>0.601</td></tr><tr><td>Baseline SimCLR</td><td>0.953</td><td>0.735</td><td>0.428</td><td>0.580</td></tr><tr><td>Baseline + Cutout</td><td>0.943</td><td>0.705</td><td><strong>0.380</strong></td><td><strong>0.516</strong></td></tr><tr><td>Baseline + CVAug</td><td><strong>0.954</strong></td><td><strong>0.742</strong></td><td><strong>0.413</strong></td><td><strong>0.555</strong></td></tr><tr><td>Baseline + Mixup</td><td><strong>0.953</strong></td><td><strong>0.738</strong></td><td><strong>0.392</strong></td><td><strong>0.531</strong></td></tr><tr><td>Baseline + Notch</td><td>0.949</td><td>0.720</td><td><strong>0.427</strong></td><td><strong>0.578</strong></td></tr><tr><td>Baseline - Zoom</td><td><strong>0.955</strong></td><td>0.722</td><td>0.485</td><td>0.647</td></tr><tr><td rowspan="7">MLP</td><td>ImageNet</td><td>0.931</td><td><strong>0.715</strong></td><td>0.479</td><td>0.656</td></tr><tr><td>Baseline SimCLR</td><td>0.933</td><td>0.709</td><td>0.406</td><td>0.561</td></tr><tr><td>Baseline + Cutout</td><td>0.919</td><td>0.681</td><td><strong>0.360</strong></td><td><strong>0.494</strong></td></tr><tr><td>Baseline + CVAug</td><td><strong>0.941</strong></td><td><strong>0.728</strong></td><td><strong>0.385</strong></td><td><strong>0.533</strong></td></tr><tr><td>Baseline + Mixup</td><td><strong>0.938</strong></td><td><strong>0.725</strong></td><td><strong>0.373</strong></td><td><strong>0.514</strong></td></tr><tr><td>Baseline + Notch</td><td>0.924</td><td>0.694</td><td>0.410</td><td>0.564</td></tr><tr><td>Baseline - Zoom</td><td>0.926</td><td>0.687</td><td>0.488</td><td>0.645</td></tr><tr><td rowspan="7">Fine-tuned</td><td>ImageNet</td><td>0.931</td><td>0.759</td><td>2.696</td><td>3.001</td></tr><tr><td>Baseline SimCLR</td><td>0.932</td><td>0.765</td><td>0.424</td><td>0.604</td></tr><tr><td>Baseline + Cutout</td><td><strong>0.933</strong></td><td>0.749</td><td>0.448</td><td>0.629</td></tr><tr><td>Baseline + CVAug</td><td><strong>0.935</strong></td><td><strong>0.768</strong></td><td>0.433</td><td>0.614</td></tr><tr><td>Baseline + Mixup</td><td><strong>0.935</strong></td><td><strong>0.770</strong></td><td><strong>0.393</strong></td><td><strong>0.556</strong></td></tr><tr><td>Baseline + Notch</td><td><strong>0.934</strong></td><td>0.748</td><td><strong>0.419</strong></td><td><strong>0.598</strong></td></tr><tr><td>Baseline - Zoom</td><td>0.931</td><td><strong>0.765</strong></td><td>0.444</td><td>0.624</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>FIG. E1. Performance of various embeddings (Micro-AUROC, higher is better) vs the number of labeled training samples in the multilabel classification task. This experiment used the MLP transfer learning protocol.</figcaption></figure>

# APPENDIX F

## Evaluation Protocols

### a. Multilabel classification

For all classification tasks, a subset of classes from the GOALI dataset (WS, MC, NV, RC, CP, AB, LW, BS, OF,

IW, and SI) will be considered as they comprise the majority the phenomena of interest for downstream applications and together comprise the vast majority of the dataset. All other labels are grouped into a catch-all “Other” class. The classification data are stratified and randomly split into 60%, 20%, and 20% of the original 10000 images for training, validation and hyperparameter tuning, and final model testing, respectively. All 6400 images from Wang et al. (2019b) are held out for testing.

The kNN classifier is trained according to the protocol from Wu et al. (2018a) with 15 neighbors, chosen based on a hyperparameter sweep. Cosine similarity [Eq. (2)] is used as the distance metric for the kNN model.

The protocol from Chen et al. (2020a) is directly adopted for linear probing with no modifications.

The proposed MLP architecture from Bordes et al. (2023) [two hidden layers with 2048 ReLU (Agarap 2019) units] is adopted, and the model is trained for 200 epochs using the Adam optimizer (Kingma and Ba 2017) with a constant learning rate of 0.001.

The fine-tuning procedure from Chen et al. (2020a) is followed with the batch size reduced to 256 and the learning rate scaled to 0.05 accordingly.
The fine-tuned classification models are trained to minimize the sum of binary cross-entropy losses over all individual classes to allow for the multilabel property:

$$ \mathcal{L}_{\text{cls}} = - \sum_{i=1}^{N} \left[ \sum_{c=1}^{C} y_{i,c} \log(\hat{y}_{i,c}) + (1 - y_{i,c}) \log(1 - \hat{y}_{i,c}) \right] \quad (\text{F1}) $$

The microaveraged AUROC is computed by summing the predictions for each class and then calculating an AUROC curve for the aggregated predictions. The F1 score is related to the *precision*, or how many positive predictions made by the model were correct, and *recall*, or how many of the positive class samples present in the dataset were correctly identified by the model, and is calculated in terms of the true positives (TP), false positives (FP), and false negatives (FN) as

$$ F1 = \frac{2}{\frac{1}{\text{precision}} + \frac{1}{\text{recall}}} = \frac{\text{TP}}{\text{TP} + 0.5(\text{FP} + \text{FN})} \quad (\text{F2}) $$

### b. Image retrieval

For the image retrieval task, 100 experiments are conducted on IW, OE, SI, AW, IB, SH, and SW, the rarest classes from the combined classification dataset. For each experiment, a random sample of each class is drawn, and then the 20 closest neighbors are retrieved based on the embeddings generated by an ImageNet model and our WV-Net model with no supervised training on the labeled data. mAP is calculated for each class and then averaged over all classes.

### c. Regression

Linear probing and MLP protocols are left unchanged from the classification protocols except for adjusting the output

function. Hyperparameters were minimally adjusted for the end-to-end fine-tuning scenario since the hyperparameters used for the classification task showed instability. The final parameters are $10^{-6}$ weight decay, a backbone learning rate of 0.007, an output-layer learning rate of 0.025, and a dropout rate of 0.5. All other hyperparameters are left unchanged. The fine-tuned regression models use a softplus output unit and are trained using a weighted combination of the mean absolute (or L1) error (MAE) and the mean squared error (MSE) weighted in favor of the MSE:

$$ \mathcal{L}_{\text{reg}} = \sum_{i=1}^{N} 0.1*|y_i - \hat{y}_i| + (y_i - \hat{y}_i)^2. \quad (\text{F3}) $$

All regression models are primarily evaluated using the root-mean-square error (RMSE) and MAE.

## APPENDIX G

### WV-Net Performance Details

Figures G1–G6 and Table G1 show additional performance details for downstream tasks. Figure G1 shows a class-wise AUROC breakdown for the GOALI classification task, while Figures G2 and G3 show scatter plots for the wave height and sea surface temperature tasks, respectively. Table G1 supplements Table 3 with results for the more common classes in the dataset, showing consistent performance trends. Figure G4 illustrates a failing case for image retrieval where class-specific features are not as prominent, leading to both, the ImageNet model and WV-Net, retrieving images with no class overlap. Last, Figures G5 and G6 show image retrieval performed for randomly selected anchors. Figure G5 uses completely randomly sampled anchors while Figure G6 anchors are single-class wherever possible but otherwise also random.

<figure><img src="image_8.png" /><figcaption>FIG. G1. ROC curve comparison for WV-Net and ImageNet models fine-tuned on multilabel classification task.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>FIG. G2. Scatterplot comparison for WV-Net and ImageNet models fine-tuned for the wave height regression task. Note that the ImageNet weights failed to converge even with limited hyperparameter tuning for this task.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>FIG. G3. Scatterplot comparison for WV-Net and ImageNet models fine-tuned for the air temperature regression task.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>FIG. G4. Image retrieval example for atmospheric gravity waves showing unsuccessful image retrieval with the class hard to discern in the anchor image. This sample illustrates an anchor for which both architectures have uncertainty since the target class in the anchor image is not well pronounced.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>FIG. G5. WV-Net image retrieval examples for random anchors. Besides ensuring that every class is represented at least once, anchors are sampled completely randomly.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>FIG. G6. WV-Net image retrieval examples for random, single-class anchors. Anchors are randomly sampled for each class from examples that only contain that class where possible.</figcaption></figure>
<table><caption>TABLE G1. Comparison of image retrieval performance for dominant classes. mAP scores for most prevalent classes in the GOALI dataset for ImageNet and WV-Net embeddings with the better-performing model for each class highlighted in bold.</caption><thead><tr><th>Model</th><th>NV<br>(N = 2243)</th><th>WS<br>(N = 11458)</th><th>MC<br>(N = 11644)</th><th>CP<br>(N = 1745)</th><th>RC<br>(N = 2174)</th><th>AB<br>(N = 3422)</th><th>LW<br>(N = 1646)</th><th>BS<br>(N = 1631)</th><th>OF<br>(N = 1350)</th></tr></thead><tbody><tr><td>ImageNet</td><td>0.475</td><td>0.648</td><td>0.672</td><td>0.318</td><td>0.477</td><td><strong>0.353</strong></td><td>0.714</td><td><strong>0.569</strong></td><td>0.200</td></tr><tr><td>WV-Net (ours)</td><td><strong>0.561</strong></td><td><strong>0.662</strong></td><td><strong>0.752</strong></td><td><strong>0.345</strong></td><td><strong>0.510</strong></td><td>0.343</td><td><strong>0.778</strong></td><td>0.566</td><td><strong>0.286</strong></td></tr></tbody></table>

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