A Coordinate-Based Framework for Sea Surface Wind Speed Reconstruction from Sparse Multi-Source Observations

Highlights

What are the main findings?

• The proposed SwiftWind, a coordinate-based framework, fuses downsampled ASCAT measurements, sparse in situ observations, and GFS 6 h forecast fields to achieve accurate sea surface wind speed fields reconstruction.
• The model efficiently reconstructs wind speed fields under sparse conditions, enabling inference at arbitrary locations through geographic coordinate encoding and adaptive latent mechanism.

What are the implications of the main findings?

• SwiftWind offers a practical and scalable architecture for wind speed field reconstruction in real-world scenarios, providing a new perspective on data fusion in remote sensing applications.
• The model is crucial for maritime navigation and offshore operations, bridging remote sensing technologies with meteorological support.

Abstract

Accurate sea surface wind speed fields are essential for marine navigation, offshore operations, and air–sea interaction studies. However, limited communication bandwidth makes it difficult to receive forecasts from land-based centers, motivating wind speed reconstruction using sparse observations. To address this challenge, we propose SwiftWind, a coordinate-based deep learning framework for sea surface wind speed reconstruction at arbitrary locations by fusing multi-source observations. SwiftWind embeds non-gridded, variable-length observations through adaptive latent representations and latitude–longitude coordinate encoding. We conduct Observing System Simulation Experiments (OSSEs), real-world observational experiments, and arbitrary-location inference experiments. Under ERA5-based evaluation, SwiftWind consistently outperforms existing data-driven baselines, including Fourier Neural Operator (FNO) and Vision Transformer (ViT) models, demonstrating robustness to observation number, noise level, and spatial distribution. Compared to the GFS 6 h forecast fields, SwiftWind achieves approximately 20–23% reductions in RMSE and 19–22% reductions in MAE under real-world observational settings. In independent buoy validation, SwiftWind performs comparably to ViT and slightly worse than FNO, likely due to differences in scattered-point processing and buoy distribution. These findings indicate that SwiftWind is suitable for near-real-time onboard wind speed reconstruction under sparse-observation conditions.

1. Introduction

Sea surface wind speed fields play critical roles in air–sea interactions, ocean circulation, and weather processes [1,2,3]. In practice, accurate wind information is essential for maritime navigation [4], oil-spill response [5], and offshore wind-resource assessment [6]. However, reconstructing sea surface wind speed fields from sparse observations remains particularly challenging. From an operational perspective, ships navigating in the open ocean are often constrained by communication bandwidth and can only receive a small amount of observational data [7]. Moreover, the transmission of forecast products from land-based centers is further limited by communication latency and data volume [8]. As a result, although many navigation and route-planning decisions rely on timely and spatially continuous wind information [9], the available onboard data is typically insufficient to support near-real-time decision-making [10]. Therefore, there is a strong demand for an efficient reconstruction approach that can rapidly infer sea surface wind speed fields from limited observations while remaining suitable for onboard implementation.

Modern observational systems are increasingly multi-source and heterogeneous, exhibiting substantial differences in data density, spatial coverage, and measurement accuracy [11,12]. However, observations of sea surface wind speed remain insufficient [13]. Current wind measurements mainly originate from two sources. Satellite-based measurements offer broad spatial coverage but rely on indirect retrievals and are limited by long revisit times and significant data gaps, such as those from ASCAT [14,15], HSCAT [16] and SAR [17]. In contrast, in situ platforms, such as ships, provide direct wind measurements but are highly sparse, irregularly distributed, and largely confined to shipping routes. These observations provide complementary information to satellite measurements and effectively function as mobile in situ sensors over the open ocean [18]. Jointly leveraging satellite measurements and conventional in situ observations to reconstruct sea surface wind speed fields represents a valuable research direction. It also enables exploration of how a small number of moving in situ observations can effectively compensate for data gaps in satellite measurements.

Existing techniques for this problem can be broadly grouped into two categories: data sssimilation (DA) methods and deep learning (DL) approaches. DA methods integrate heterogeneous observations with short-term forecasts used as background fields to produce analysis states that approximate the true atmospheric conditions, including variational, Kalman filter, and Ensemble-based schemes [19,20,21]. Numerous studies have demonstrated that recent advances in DA have substantially improved weather forecast accuracy [22,23,24]. However, DA methods typically face a trade-off between computational cost and accuracy due to the nonlinear nature of atmospheric dynamics and the need for large ensembles [25,26,27]. Moreover, their reliance on accurate background error covariance estimates and observation operators makes them difficult to deploy in resource-limited and near-real-time shipborne environments [28].

The second category comprises DL models for sparse data reconstruction, which aim to recover complex spatial fields from noisy and partial sensor measurements. Such problems are typically characterized by extremely low observational coverage. Wind speed reconstruction from sparse multi-source observations is a representative example of this setting, where data-driven models can learn statistical structures from heterogeneous measurements even when explicit governing equations or observation operators are difficult to specify [29]. Nevertheless, real-world oceanic observations pose additional challenges: many sensors are sparse, moving and going on or off with time, such as Voluntary Observing Ships (VOSs) [30], and observations are typically located at irregular, non- gridded positions.

Existing DL approaches can be broadly categorized according to their model architectures. Convolutional Neural Networks (CNNs) have been adapted for sparse reconstruction by assuming an underlying structured grid and introducing mask arrays to identify sensor locations, such as Voronoi tessellation of observations, which allow for arbitrary sensor placement within two-dimensional mesh [31]. Another work uses Graph Neural Networks (GNNs), which naturally support unstructured data by constructing graph topologies to encode spatial relationships. But the performance of GNNs strongly depends on well-designed graph structures, limiting their generalization across different datasets and spatial domains [32]. Physics-Informed Neural Networks (PINNs) [33] alleviate data scarcity by embedding governing physical constraints into the learning process [34]. They have been applied to tropical cyclone wind and pressure reconstruction using dropsondes, satellite observations, and Doppler radar data [35,36,37], as well as large-scale sea surface wind reconstruction from sparse scatterometer observations [38]. However, PINNs often suffer from slow convergence, high computational cost, and limited scalability to large domains. In addition, attention-based architectures are well suited to handle diverse input structures in many settings. Transformer-based models have shown strong capability in point-cloud completion by treating point clouds as unordered sets and learning geometric relationships through attention, which illustrates their effectiveness for irregular and unstructured inputs [39]. In particular, the Perceiver IO [40] framework is capable of processing arbitrary size and unstructured input data. Based on this model, the Senseiver [41] has shown strong performance in sparse data reconstruction, but it has not yet been extensively tested on real-world irregular observations.

Overall, practical sea surface wind speed reconstruction from sparse observations remains challenging. Existing models often struggle to accommodate variable-length, irregularly distributed, and mobile observations without additional preprocessing or carefully designed structures. These issues become more pronounced when fusing multi-source observations with different sampling patterns and data characteristics.

This article proposes SwiftWind, a flexible coordinate-based deep learning framework for reconstructing sea surface wind speed fields from sparse multi-source observations combined with coarse background priors. By using geographic coordinate encoding, SwiftWind enables wind speed inference at arbitrary locations. All experiments demonstrate that SwiftWind enables fast and accurate wind speed field reconstruction.

The main contributions of this article are as follows:

(1)

SwiftWind achieves accurate reconstruction of dynamically evolving sea surface wind speed fields, demonstrating its robustness for high-variability geophysical processes under sparse-observation conditions.

(2)

SwiftWind integrates adaptive latent array, latitude–longitude coordinate encoding and mask-based attention mechanism, enabling wind speed inference at arbitrary locations.

(3)

SwiftWind provides a scalable framework for multi-source data fusion in real-world scenarios and has the potential to support near-real-time onboard wind speed reconstruction.

The rest of this article is organized as follows: Section 2 introduces the datasets and study area. Section 3 illustrates the details of SwiftWind model. Section 4 presents the experimental results. Section 5 provides the discussion. Section 6 concludes this article.

2. Datasets and Study Area

2.1. Data Description

The datasets used in this study are described in detail below.

(1) The Advanced Scatterometer (ASCAT) is a C-band (5.3 GHz) active microwave radar instrument onboard the MetOp-A (launched in 2006, decommissioned in 2021), MetOp-B (launched in 2012) and MetOp-C (launched in 2018) satellites operated by European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) [42,43]. ASCAT employs three vertically polarized antennas to observe the ocean surface at multiple azimuth angles. For each Wind Vector Cell (WVC), ASCAT acquires a triplet of backscatter measurements, which are used to retrieve 10 m ocean surface wind speed and direction through a Geophysical Model Function (GMF). This multi-angle sampling strategy significantly reduces ambiguity and enhances the accuracy of wind vector retrievals [14]. In this study, we use the 25 km ASCAT wind products derived from MetOp-A, -B, and -C, as processed by KNMI. The data span the following periods: MetOp-A from January 2017 to November 2021, MetOp-B from January 2017 to December 2023 and MetOp-C from January 2019 to December 2023. These periods are selected to ensure data availability and temporal consistency during the training phase.

(2) The International Comprehensive Ocean-Atmosphere Data Set (ICOADS), developed by National Oceanic and Atmospheric Administration (NOAA), offers surface marine data spanning 1662 to present. ICOADS integrates global marine meteorological observations from diverse platforms, including ships, moored and drifting buoys and other ocean platforms. The dataset includes critical surface variables such as air temperature, sea surface temperature, and wind speed and direction [44]. This non-gridded dataset exhibits sparse yet widespread spatial coverage, providing valuable in situ observational records. In this study, we use wind speed observations from January 2017 to December 2023.

(3) The Global Forecast System (GFS) is a numerical weather prediction model developed and operated by the National Centers for Environmental Prediction (NCEP). It generates forecasts for various atmospheric and land-surface variables, including temperature, wind, precipitation, soil moisture, and atmospheric ozone concentration [45]. The model is run four times daily at 00, 06, 12, and 18 UTC and the forecast output is available at 3 h intervals from 0 to 240 h, and 12 h intervals from 240 to 384 h, with a spatial resolution of 0.25°. In data assimilation systems, model forecasts are typically used as background fields to provide first-guess estimate of the atmospheric state. In this study, we use 10 m u and v wind components from GFS with a lead time of 6 h (GFS-6h) as the background field for sea surface wind speed reconstruction.

(4) ERA5, developed by the European Centre for Medium-Range Weather Forecasts (ECMWF), is the fifth-generation atmospheric reanalysis dataset and represents a state-of-the-art global reanalysis product [46]. It integrates the ECMWF Integrated Forecast System (IFS) with a wide range of global observations (such as satellites, surface stations, ships and radars) through a four-dimensional variational (4DVar) data assimilation scheme. ERA5 provides various meteorological variables, including temperature, pressure, wind components, specific humidity and geopotential height, spanning from 1940 to the present. With a temporal resolution of 1 h and a spatial resolution of 0.25°, the dataset offers high-resolution and gridded representations of sea surface wind fields. In this study, we use the 10 m u and v wind components from January 2017 to December 2023.

During the model training process, data from January 2017 to June 2022 are used for training, data from July 2022 to December 2022 are used for validation, and data from January 2023 to December 2023 are used for testing.

2.2. Data Processing

To illustrate the spatial distribution and coverage characteristics of the observations used for model training, we select an illustrative snapshot at 00:00 UTC on 13 January 2019, as shown in Figure 1a. The ASCAT swaths in this panel are collected within a ±30 min window around the target time. As shown in the figure, the three scatterometers provide a relatively large number of observations, while ICOADS observations are much sparser but partially compensate for data gaps. It should be noted that ASCAT coverage is intermittent and strongly depends on satellite overpasses. At many hourly target times, observations from ASCAT are sparse or unavailable within the study region. To further demonstrate this variability, five additional examples with different observation coverage conditions are provided in Figure S3 of the Supplementary Materials. In practice, both the number and spatial distribution of observations vary substantially over time due to satellite orbital configurations and actual shipping routes.

In addition, Figure 1b presents the probability density distributions of observation counts per time step. Here, one time step refers to one hourly ERA5 analysis time, corresponding to an individual wind speed field sample at a specific hour. The distributions reveal clear contrasts between conventional and satellite-based observations. Although ICOADS provides fewer observations at each time step, its records are available at nearly all times. In contrast, scatterometer observations have much higher counts when available, but are frequently missing because of orbital sampling. This complementary behavior highlights the necessity of incorporating conventional observations to enhance satellite measurements. Before model training, a quality control procedure is applied to remove records with missing wind information, invalid geographical coordinates, and obvious wind speed outliers.

To provide a complementary observational benchmark beyond the ERA5-based evaluation, we split the ICOADS dataset and construct a withheld buoy subset. This additional data split is designed to supplement the ERA5-based assessment with direct observational validation. Specifically, 14 buoy stations are selected and completely excluded from model training and validation. These stations are chosen because buoy observations have relatively fixed locations and more consistent observational characteristics than moving ship reports, making them more suitable for hold-out validation. The spatial distribution of the withheld buoy stations is shown in Figure 2, and their geographical coordinate information is provided in the Supplementary Materials, Table S1.

To improve training efficiency, it is necessary to standardize the scale of the input data. In this study, all input variables are normalized according to the following formula:

$$X_{\mathrm{norm}}={\displaystyle \frac{X-\mu }{\sigma }},$$

(1)

where X denotes the original value, $X_{\mathrm{norm}}$ is the normalized value, and $\mu$ and $\sigma$ represent the mean and standard deviation of the corresponding variable, respectively. The statistics $\mu$ and $\sigma$ are computed from the training dataset and are fixed when applied to the validation and test datasets to ensure consistency.

2.3. Study Area

In principle, the proposed SwiftWind model is potentially generalizable and can be applied to global regions. To reduce computational cost while accounting for the spatial distribution of available observations and providing a clear validation of the model effectiveness, we select a regional domain spanning from 10° S to 40° N and from 90° E to 150 ° E as the study area. The specific location and extent of this study region are explicitly displayed in Figure 1a.

3. Methods

3.1. Overview of SwiftWind

Figure 3 provides an overview of the SwiftWind framework. SwiftWind is built upon the Perceiver IO [40] and Senseiver [41] architectures, with specific modifications adapted to the input data of multi-source observations and background fields. It is designed on the task of real sea surface wind speed field reconstruction, with detailed innovations presented in the following sections. SwiftWind adopts an encoder–decoder architecture that takes the GFS-6h background fields together with scattered wind observations as inputs and reconstructs hourly wind speed fields with a grid spacing of 0.25° (corresponding to approximately 25–28 km over the study region). In addition to gridded reconstruction, SwiftWind supports queries at arbitrary coordinates, enabling flexible validation using independent ASCAT measurements that are excluded from training.

The detailed neural network architecture is illustrated in Figure 4. The innovation of SwiftWind is mainly to aggregate wind speed measurements and spatial location information from all available observations into a latent representation through multiple layers of attention mechanisms. Wind speed values at query locations are then decoded based on their relevance to the aggregated observational information, allowing the background fields to be effectively refined. For the temporal information, SwiftWind does not directly model the temporal dimension. Instead, the input data are divided into hourly samples, with a time window of ±30 min around each hour. Since the reference field ERA5 is available at hourly intervals, the model uses hourly observations to refine the background field, and finally obtains hourly wind speed fields.

The core of SwiftWind relies on the adaptive latent array module ($Q_{\mathrm{input}}$ and $Q_{\mathrm{out}}$ in Figure 4), which performs attention-based interactions between observations, background priors, and query points to inference accurate wind speed fields. In addition, latitude–longitude coordinate encoding is employed to explicitly represent the spatial locations of observations, and mask-based attention mechanism is introduced to enable cross-attention with a variable number of input observations. Detailed descriptions of these components are provided in the following sections.

3.2. Latitude–Longitude Coordinate Encoding

For each observation point with latitude and longitude coordinates $x_i=({\mathrm{lat}}_i,{\mathrm{lon}}_i)$, we define the positional encoding process to convert these spatial coordinates into a form suitable for model training. The goal is to create a representation that enables the model to effectively capture the spatial relationships between observation points, allowing it to generalize across different regions of interest. Specifically, the model needs to be able to recognize and make inferences for any arbitrary latitude–longitude coordinate, leveraging the full range of available spatial information.

The first step is to convert the geographical coordinates from degrees to radians, as defined in Equation (2). Then, the coordinates are standardized by subtracting the mean $\mu$ and dividing by the standard deviation $\sigma$, as shown in Equation (2). This transformation enables the model to be robust to variations in the input data.

$$x_{\mathrm{rad}}=x·{\displaystyle \frac{\pi }{180}},\tilde{x}={\displaystyle \frac{x_{\mathrm{rad}}-\mu }{\sigma }},$$

(2)

where x represents the original latitude–longitude coordinates in degrees, $x_{\mathrm{rad}}$ denotes the corresponding coordinates in radians, and $\tilde{x}$ is the standardized version of the coordinates.

Next, we employ a set of linearly spaced frequencies $\left\{f_k\right\}$ to construct the Fourier positional encoding, as defined in Equations (3) and (4). Here, B denotes the number of frequency bands used in the Fourier-based positional encoding. This results in a $4B$-dimensional representation $\gamma \left(x_i\right)$, which captures both low- and high-frequency spatial patterns and enhances the model’s ability to represent complex spatial variations, such as geographical features and large-scale atmospheric patterns. These frequency components are crucial for enabling the model to learn long-range dependencies and fine-grained spatial features, improving its accuracy.

Conceptually, this Fourier positional encoding shares a similar underlying principle with traditional Fourier analysis. While traditional Fourier analysis transforms a spatial-domain function into the frequency domain by decomposing it into a superposition of sinusoidal waves with varying amplitudes and phases, our encoding approach maps the low-dimensional spatial coordinates onto a set of sinusoidal basis functions with varying frequencies [47,48]. This multi-frequency representation serves as the mechanism for SwiftWind to recognize longitude-latitude coordinates. As demonstrated in the ablation study (Section 5.1.2), this encoding practice significantly improves the performance compared to directly inputting raw coordinate values, confirming its effectiveness in capturing complex spatial patterns.

$$f_k=1+{\displaystyle \frac{k-1}{B-1}}\left(2^B-1\right),k=1,\dots ,B$$

(3)

$$\begin{array}{cc}\hfill \gamma \left(x_i\right)=& [sin\left(f_k{\tilde{x}}_i^{\left(\mathrm{lat}\right)}\right),cos\left(f_k{\tilde{x}}_i^{\left(\mathrm{lat}\right)}\right),\hfill \\ \hfill & sin\left(f_k{\tilde{x}}_i^{\left(\mathrm{lon}\right)}\right),cos\left(f_k{\tilde{x}}_i^{\left(\mathrm{lon}\right)}\right){]}_{k=1}^B,\hfill \end{array}$$

(4)

where $\gamma \left(x_i\right)$ represents the Fourier encoding for each observation point $x_i$, capturing the spatial variations at multiple frequency scales.

The final observation embedding $h_i$ is obtained by concatenating the Fourier-encoded positional representation $\gamma \left(x_i\right)$ with the observed wind speed value $y_i$, as described in Equation (5). This embedding effectively combines both the spatial and observational information. Overall, this process effectively recognizes observation locations and supports wind speed querying at any geographic coordinate for pointwise inference.

$$h_i=\left[y_i,\gamma \left(x_i\right)\right].$$

(5)

3.3. Mask-Based Attention Mechanism

In real-world cases, the number of available observations can vary substantially across time steps, which complicates efficient batching for training and inference. To enable pointwise fusion with attention while maintaining a fixed tensor shape within each batch, we pad each sample to the maximum sequence length $N_{max}$ in the batch and construct an additive attention mask $\mathbf{M}$. The mask is applied to attention operations to ignore padded positions, enabling efficient and consistent processing of variable-length inputs. The mask is defined as in Equation (6).

$$M_j=\left\{\begin{array}{cc}0,\hfill & \mathrm{if}\mathrm{position}j\mathrm{is}\mathrm{valid},\hfill \\ -\infty ,\hfill & \mathrm{if}\mathrm{position}j\mathrm{is}\mathrm{padded}.\hfill \end{array}\right.$$

(6)

In the attention mechanism, the query set $\mathbf{Q}$, key set $\mathbf{K}$, and value set $\mathbf{V}$ are obtained through linear projections of the corresponding input features. $\mathbf{Q}$ is used to probe what information is needed, $\mathbf{K}$ is used to measure the relevance of each candidate input to that query, and $\mathbf{V}$ contains the information that is aggregated according to the resulting attention weights. The standard scaled dot-product attention [49] is defined as follows:

$$\mathrm{Attention}(\mathbf{Q},\mathbf{K},\mathbf{V})=\mathrm{softmax}\left({\displaystyle \frac{\mathbf{Q}{\mathbf{K}}^{\top }}{\sqrt{d_k}}}\right)\mathbf{V},$$

(7)

where $d_k$ denotes the dimensionality of the key vectors.

To prevent padded positions from participating in attention computation, the padding mask $\mathbf{M}$ is incorporated into the attention scores before the softmax operation. The masked attention [50] is thus formulated as follows:

$$\mathrm{MaskedAttention}(\mathbf{Q},\mathbf{K},\mathbf{V})=\mathrm{softmax}\left({\displaystyle \frac{\mathbf{Q}{\mathbf{K}}^{\top }}{\sqrt{d_k}}}+\mathbf{M}\right)\mathbf{V}.$$

(8)

By incorporating the padding mask into the attention mechanism, the model can robustly handle variable-length observation sets and ensure that attention is computed only over valid observations, which is critical for real-world scenarios with irregular and sparse measurements.

3.4. Adaptive Latent Array Module

In the encoder, each observation embedding $h_i$ is first projected through a linear transformation to obtain $z_i$ as in Equation (9).

$$z_i=W_h{h}_i+b_h,$$

(9)

where $W_h$ and $b_h$ denote the trainable weight matrix and bias vector, respectively. The $z_i$ serves as the key array $\mathbf{K}$ and value array $\mathbf{V}$ in the subsequent multi-head cross-attention mechanism (the detailed computational formulation in the Supplementary Materials). A learnable latent array ${\mathbf{Q}}_{\mathrm{in}}^{\left(0\right)}$ is initialized as the query input. The latent representations are iteratively updated through stacked blocks of cross-attention and self-attention, formulated as in Equation (10). For notational brevity and to clearly present the core attention mechanism, the standard residual connections and MLP blocks are omitted from Equation (10); their detailed architecture is explicitly illustrated in Figure 4. Furthermore, $N1,N2,N3$ in Figure 4 denote the number of stacked blocks for each respective module, which are determined by hyperparameters. This stacked structure is designed to increase the model depth, thereby enhancing the capability of feature learning and extraction.

$${\mathbf{Q}}^{(t+1)}=\mathrm{SelfAttn}\left(\mathrm{CrossAttn}\left({\mathbf{Q}}^{\left(t\right)},\mathbf{K},\mathbf{V};\mathbf{M}\right)\right).$$

(10)

This iterative update enables the latent array to aggregate information from all valid observations while encoding spatial dependencies. The final encoder output ${\mathbf{H}}_{\mathrm{enc}}$ represents the aggregated latent representation.

In the decoder, another learnable latent array ${\mathbf{Q}}_{\mathrm{out}}^{\left(0\right)}$ is initialized and concatenated with the positional encoding $\gamma \left({\mathbf{x}}_q\right)$ and the background wind speed $y_{\mathrm{background},q}$ at an arbitrary query location ${\mathbf{x}}_q$, yielding:

$${\mathbf{Q}}_{\mathrm{query}}=\left[{\mathbf{Q}}_{\mathrm{out}}^{\left(0\right)},\gamma \left({\mathbf{x}}_q\right),y_{\mathrm{background},q}\right].$$

(11)

This query representation incorporates both spatial information and large-scale prior context. It is linearly projected to match the latent dimension and serves as the query array in the decoder cross-attention, where the encoder output provides the key and value arrays:

$${\mathbf{H}}_{\mathrm{dec}}=\mathrm{CrossAttn}\left({\mathbf{Q}}_{\mathrm{query}},\mathbf{K}={\mathbf{H}}_{\mathrm{enc}},\mathbf{V}={\mathbf{H}}_{\mathrm{enc}}\right).$$

(12)

The decoder output is subsequently passed through a linear layer to produce a residual correction $\Delta {\widehat{y}}_q$ relative to the background field. The final reconstructed wind speed field is obtained as follows:

$${\widehat{y}}_q=y_{\mathrm{background},q}+\Delta {\widehat{y}}_q.$$

(13)

Here, $\Delta {\widehat{y}}_q$ denotes the model-reconstructed residual, and ${\widehat{y}}_q$ represents the reconstructed wind speed at the query location. This residual formulation explicitly constrains the network to focus on refining the large-scale background flow using information from sparse observations, leading to more stable optimization and improved physical consistency.

Through this architecture, SwiftWind effectively integrates sparse observations with coarse background fields, learns spatially coherent latent representations via attention mechanisms, and supports flexible queries at arbitrary geographic coordinates.

3.5. Experimental Setup

To comprehensively assess the capability of SwiftWind under different observational scenarios, several groups of experiments are designed, as summarized in

Table 1. Summary of experimental design, comparison baselines, and purpose.

Experiment	Inputs	Grid Spacing	Baseline Model	Reference	Purpose
Observing System Simulation Experiments	Pseudo-obs and GFS-6h	0.25°/1 h	FNO, ViT	ERA5	Reconstruction accuracy under controlled conditions
Real-world Observational Experiments	ASCAT-A/B/C, ICOADS, GFS-6h	0.25°/1 h	FNO, ViT	ERA5, withheld buoys	Robustness to observation sparsity and noise
Arbitrary-location Inference Experiments	ASCAT-A/B/C, ICOADS, GFS-6h	point/1 h	–	Independent ASCAT (non-gridded)	Arbitrary-location inference accuracy verification

.

We compare SwiftWind against two representative deep learning baselines: the Fourier Neural Operator (FNO) and the Vision Transformer (ViT). These two models are selected because they represent two widely used modeling paradigms for field reconstruction. FNO is a neural-operator model designed to learn mappings between infinite dimensional function spaces [51]. FNO parameterizes the integral operator in the Fourier domain and updates the feature representation through spectral convolution layers. ViT represents the input field as a sequence of image patches, where each patch is embedded into a feature vector and processed by self-attention layers to capture spatial relationships [52].

Firstly, Observing System Simulation Experiments (OSSEs) are conducted by randomly sampling pseudo-observations from the ERA5 reanalysis. These synthetic observations are noise-free and uniformly distributed, providing a simplified representation of real oceanic observations. The OSSEs aim to evaluate SwiftWind’s ability to reconstruct rapidly varying sea surface wind speed fields from sparse observations under controlled conditions.

Secondly, real-world observation experiments are performed using downsampled ASCAT-A/B/C scatterometer measurements together with ICOADS observations to reconstruct wind speed fields. These experiments are designed to assess model performance under realistic conditions, where observations are sparse, irregularly distributed, and exhibit strong temporal variability, which is critical for practical offshore and maritime applications.

Finally, since grid-based models (FNO and ViT) and the GFS-6h background cannot provide direct counterparts at arbitrary locations, arbitrary-location experiments are conducted by validating the reconstructed wind speed fields against independent ASCAT measurements that are not used in model training. These non-gridded observations are used to verify the model’s ability to accurately infer wind speeds at arbitrary locations.

SwiftWind is trained on four NVIDIA A100 GPUs (40 GB memory each) using the PyTorch-lightning (v2.0.0) framework. The model is optimized with the Mean Squared error (MSE) loss function. The same SwiftWind architecture is used across the main experimental settings, while several training-related hyperparameters are slightly adjusted according to validation performance.

Table 2. Representative hyperparameter settings of SwiftWind in the real-world observational experiments.

Batch Size	Learning Rate	Number of Latents	Number of Layers
128	$1\times {10}^{-4}$	256	2
Encoder Preprocess Channels	Encoder Latent Channels	Decoder Preprocess Channels	Decoder Latent Channels
64	64	64	64
Cross-Attention Heads	Encoder Self-Attention Heads	Decoder Cross-Attention Heads	Coordinate Encoding Bands
2	2	1	32

reports a representative configuration used in the real-world observational experiments. The hyperparameter settings for other cases are only slightly adjusted and remain broadly consistent with this configuration. After training, the inference of hourly wind speed fields for the entire year 2023 on a single NVIDIA A100 GPU takes approximately 120 s.

3.6. Evaluation Metrics

The model performance is evaluated using three commonly adopted metrics: the Mean L2 loss, Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). These metrics characterize the overall accuracy and error characteristics of the reconstructed wind fields at each time step, compared with the ERA5 reference. For wind speed queries at arbitrary locations, two additional indicators are employed: the Mean Bias Error (MBE) and the Pearson correlation coefficient (r), which quantify the systematic bias and linear correlation between the reconstructed values ${\widehat{y}}_t$ and the reference values $y_t$, respectively. The definitions of these metrics are given in Equations (14)–(18), where T denotes the total number of evaluated samples.

$$\mathrm{Mean}\mathrm{L}2\mathrm{Loss}={\displaystyle \frac{{∥{\widehat{y}}_t-y_t∥}_2}{{∥y_t∥}_2}},$$

(14)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{T}}\sum _{t=1}^T{\left({\widehat{y}}_t-y_t\right)}^2},$$

(15)

$$\mathrm{MAE}={\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T}\left|{\widehat{y}}_t-y_t\right|,$$

(16)

$$\mathrm{MBE}={\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T}\left({\widehat{y}}_t-y_t\right),$$

(17)

$$\mathrm{r}={\displaystyle \frac{{\sum }_{t=1}^T\left({\widehat{y}}_t-\overline{\widehat{y}}\right)\left(y_t-\overline{y}\right)}{\sqrt{{\sum }_{t=1}^T{\left({\widehat{y}}_t-\overline{\widehat{y}}\right)}^2{\sum }_{t=1}^T{\left(y_t-\overline{y}\right)}^2}}}.$$

(18)

4. Results

4.1. Observing System Simulation Experiments

We conduct OSSEs using simulated sparse observations randomly sampled from the ERA5 reanalysis (as the reanalysis reference field). These samples are combined with the GFS-6h forecasts to reconstruct the full wind speed fields. The workflow is shown in Figure 5a. Five observation densities are tested, with the number of observation points set to 1000, 500, 300, 100, and 50, respectively. A fixed random seed is adopted to ensure reproducibility. Within the 0.25° study domain, a total of 32,413 ocean grid points remain after removing land points, corresponding to observation coverages of 3.1%, 1.5%, 0.9%, 0.3%, and 0.15%, respectively. These OSSEs enable a systematic evaluation of SwiftWind under different levels of observational sparsity, providing a controlled simplification of realistic oceanic observing conditions.

To provide a clear and intuitive illustration of the OSSEs, including the experimental design, reconstruction results, and evaluation procedures, we summarize the OSSEs’ results in a single composite figure (Figure 5). The same evaluation approach is used in the real-world experiments, with results shown in separate figures for clearer interpretation.

Figure 5b shows representative reconstructed wind speed fields and their deviations from ERA5 under different observation densities. As the number of observations increases, all models exhibit progressively improved reconstruction quality and can recover the dominant large-scale wind structures. Compared with the baseline models (FNO and ViT), SwiftWind consistently yields smaller and spatially smoother errors and better preserves fine-scale circulation features. Spatially, reconstruction errors are generally lower over open-ocean regions than near coastal areas, with the largest deviations appearing in the northern and central parts of the domain. When more than 300 observation points are available, SwiftWind clearly outperforms FNO and ViT. In contrast, when the observation density drops below this level, the performance of all three models becomes comparable, with only minor visual differences. This behavior arises because wind speed field reconstruction is an ill-posed inverse problem, where insufficient observational constraints lead to increased solution uncertainty and degraded reconstruction accuracy. Moreover, since the observation locations are fixed, excessively sparse coverage reduces the model’s ability to learn spatial correlations across different regions.

These qualitative results are further confirmed by quantitative evaluations, as shown in Figure 5c. To further quantify performance, we compute the mean L2 loss, RMSE, and MAE over the year 2023 using hourly evaluation samples, resulting in 8760 time steps. As the number of observations increases, the accuracy of SwiftWind improves steadily and surpasses that of the other models at all sampling levels. When the number of observations reaches 1000, the mean L2 loss, RMSE, and MAE are approximately 0.1171, 0.7554 m/s, and 0.5322 m/s, corresponding to improvements of 49.02%, 49.04%, and 50.96% relative to GFS-6h, respectively (more results in

Table 3. Quantitative comparison of SwiftWind and two baseline models (FNO and ViT) under different numbers of observations.

Number of Obs.	Model	Mean L2 Loss		RMSE (m/s)		MAE (m/s)
		Value	Improv.	Value	Improv.	Value	Improv.
1000	FNO	0.1340	41.66%	0.8644	41.69%	0.5915	45.50%
	ViT	0.1536	33.13%	0.9909	33.15%	0.6842	36.96%
	SwiftWind	0.1171	49.02%	0.7554	49.04%	0.5322	50.96%
500	FNO	0.1535	33.17%	0.9905	33.18%	0.7024	35.28%
	ViT	0.1671	27.25%	1.0780	27.28%	0.7573	30.22%
	SwiftWind	0.1384	39.75%	0.8929	39.76%	0.6366	41.34%
300	FNO	0.1660	27.73%	1.0712	27.73%	0.7760	28.50%
	ViT	0.1790	22.07%	1.1548	22.09%	0.8255	23.94%
	SwiftWind	0.1605	30.13%	1.0357	30.13%	0.7642	29.59%
100	FNO	0.1846	19.63%	1.1910	19.65%	0.8851	18.45%
	ViT	0.1935	15.76%	1.2486	15.77%	0.9119	15.98%
	SwiftWind	0.1759	23.42%	1.1352	23.42%	0.8415	22.46%
50	FNO	0.1899	17.33%	1.2252	17.34%	0.9177	15.44%
	ViT	0.1981	13.76%	1.2782	13.77%	0.9407	13.32%
	SwiftWind	0.1836	20.07%	1.1849	20.06%	0.8835	18.59%
–	GFS-6h	0.2297	–	1.4823	–	1.0853	–

The table reports the mean L2 loss, RMSE, and MAE, together with their relative improvements over the GFS-6h background field. The bold values indicate the best results.

). Even under sparse conditions (fewer than 300 points), SwiftWind still exhibits slightly lower errors than baselines from a statistical perspective. The bottom panels of Figure 5c show the boxplots of time-series statistics, where SwiftWind maintains better consistency with ERA5 throughout the entire test period. As reflected by the narrower interquartile range and lower median values in the boxplots, SwiftWind yields more stable and reliable reconstructions, suggesting reduced temporal variability and improved robustness.

Apart from the time-series analysis, SwiftWind also exhibits excellent spatial error characteristics. For each grid point, we calculate MAE against ERA5 over the entire testing period. Figure 5d displays the spatial distribution of MAE. We find that three different models exhibit distinct and representative spatial error patterns. SwiftWind shows spatially smooth and coherent MAE distribution, indicating that it can dynamically model spatial dependencies between any two locations, enabling global long-range correlation capture instead of relying solely on neighboring grid points. In contrast, FNO displays localized errors, mainly due to its reliance on nearest-neighbor-interpolated input fields, while ViT exhibits a grid-like error pattern, reflecting the limitations of its fixed patch-based representation in maintaining spatial continuity across patch boundaries. In terms of MAE magnitude, SwiftWind consistently outperforms the other two models. Spatially, the error distribution aligns well with the qualitative results in Figure 5b, with lower errors observed over open-ocean areas and relatively higher errors occurring near coastal regions, particularly around the domain near Japan. Overall, SwiftWind achieves smaller and more spatially coherent errors, demonstrating superior spatial consistency and generalization capability compared with baseline models.

We further evaluate model performance using the radially averaged power spectral density (RAPSD) of wind speed fields, as shown in Figure 5e. RAPSD characterizes the scale-dependent distribution of wind speed variability across spatial frequencies, with higher spatial frequencies corresponding to smaller spatial scales. SwiftWind, FNO, ViT, and the GFS background all show spectral curves broadly consistent with ERA5 at low spatial frequencies, indicating that the large-scale structures are well reconstructed. At higher spatial frequencies, however, SwiftWind agrees more closely with ERA5 than the other models, indicating a stronger capability to recover small-scale variability. As the number of observations increases, the RAPSD curve of SwiftWind becomes increasingly close to that of ERA5 and nearly overlaps with it. This spectral agreement further supports the quantitative accuracy of our model and suggests that it better preserves realistic multi-scale wind structures.

To clarify whether the improvement in SwiftWind arises mainly from background error correction or from temporal filling, we further conduct a temporal-offset analysis in the OSSEs. The hourly test samples are grouped according to the temporal offset between each target hour and the native 6-hourly GFS background field used as input. Specifically, offset 0 h corresponds to the native GFS cycles, while offsets 1–3 h correspond to off-cycle target hours. Here, we use the 500-observation OSSEs as a representative case and the results are shown in

Table 4. Temporal-offset analysis of SwiftWind, two baseline models (FNO and ViT), and the GFS background field in the 500-observation OSSEs.

Offset (h)	Model	Mean L2 Loss	RMSE (m/s)	MAE (m/s)
0	FNO	0.1450	0.9347	0.6657
	ViT	0.1571	1.0131	0.7147
	SwiftWind	0.1338	0.8629	0.6184
	GFS-6h	0.2055	1.3248	0.9656
1	FNO	0.1456	0.9430	0.6714
	ViT	0.1578	1.0220	0.7209
	SwiftWind	0.1337	0.8655	0.6201
	GFS-6h	0.2076	1.3442	0.9819
2	FNO	0.1487	0.9657	0.6867
	ViT	0.1614	1.0484	0.7386
	SwiftWind	0.1351	0.8773	0.6275
	GFS-6h	0.2159	1.4023	1.0281
3	FNO	0.1532	0.9967	0.7075
	ViT	0.1666	1.0844	0.7631
	SwiftWind	0.1375	0.8950	0.6385
	GFS-6h	0.2280	1.4838	1.0919
All	FNO	0.1535	0.9905	0.7024
	ViT	0.1671	1.0780	0.7573
	SwiftWind	0.1384	0.8929	0.6366
	GFS-6h	0.2297	1.4823	1.0853

Note: Offset denotes the temporal difference between each hourly target field and the native 6-hourly GFS background field used as input. Offset 0 h corresponds to the native GFS cycles, while offsets 1–3 h correspond to off-cycle target hours. The bold values indicate the best results.

. The offset-0 results mainly reflect the ability of the model to correct background field errors. At offset 0 h, SwiftWind reduces the RMSE from 1.3248 m/s for GFS to 0.8629 m/s, indicating that its improvement is not solely caused by the hourly expansion of the 6-hourly GFS background. For offsets 1–3 h, the RMSE of GFS increases from 1.3442 to 1.4838 m/s, whereas the RMSE of SwiftWind only slightly increases from 0.8655 to 0.8950 m/s. This much smaller degradation suggests that SwiftWind remains robust at off-cycle hours and provides useful temporal filling under a 6-hourly background-field setting.

4.2. Real-World Observational Experiments

In this section, we reconstruct spatially continuous sea surface wind speed fields using two complementary sources of real-world observations: the ASCAT-A/B/C satellite measurements and the ICOADS dataset.

In the experimental design, a crucial step is the downsampling of ASCAT wind observations. This process is motivated by three main considerations. First, it allows us to construct sparse-observation scenarios similar to those in the idealized experiments. Second, the number of ASCAT measurements at each time step is much larger than that of ICOADS, which could dominate the training process and reduce the contribution of ICOADS data. Third, the long revisit period of ASCAT causes significant variability in its spatial coverage across the study region, potentially leading to instability during model training. Specifically, the downsampling procedure is implemented by defining a downsampling ratio hyperparameter and then randomly sampling the corresponding fraction of observations from the original satellite measurements in a spatially uniform manner. In the main experiments, we set the downsampling ratio to 1/40. A sensitivity analysis of this hyperparameter is provided in the Sensitivity to Downsampling Ratio section. The downsampled ASCAT-A/B/C observations are then combined with ICOADS to form the final model inputs.

Because the number and spatial distribution of real observations vary substantially over time, we design four experimental settings to investigate how fluctuations in observation amount and observation error influence reconstruction performance. Following the findings from the OSSEs, time steps with 500–1000 available observations are categorized as the “Selected” cases, representing relatively data-rich conditions. To further assess the impact of observation quality, we additionally introduce an “Ideal” setting, in which ERA5 values are interpolated to the actual observation locations for comparison.

Accordingly, four experimental configurations are defined:

(1)

Ideal-Selected, representing ERA5-interpolated (zero-error) observations within the selected range of 500–1000 samples.

(2)

Real-Selected, representing real (noisy) observations within the same range.

(3)

Ideal-All, using ERA5-interpolated observations within the training time steps.

(4)

Real-All, using real observations within the training time steps.

Figure 6 presents an example of the reconstruction results for the Ideal-Selected and Real-Selected configurations. SwiftWind outperforms the two baseline models under both conditions, demonstrating its robustness to variations in the number and spatial distribution of observations. However, the performance in the Real case is slightly lower than that in the Ideal case, indicating that the quality of observational data can influence the accuracy of wind speed field reconstruction, which is also consistent with physical intuition.

Using an evaluation procedure consistent with the OSSEs, the model performance is examined through statistical indicators, time-series analysis, spatial error distributions, and RAPSD.

Figure 7 compares three models and GFS-6h against ERA5 under the four configurations. Compared with the initial GFS-6h background field, all three models achieve obvious improvements, demonstrating that incorporating sparse observational data through AI models can effectively improve the background field. Among them, SwiftWind consistently outperforms the other two models, with the best performance in the Ideal-Selected case, where the mean L2 loss, RMSE, and MAE reach 0.1614, 1.0384 m/s, and 0.7548 m/s, respectively, representing improvements of 30.25%, 30.26%, and 30.87% relative to GFS. More results are shown in

Table 5. Quantitative comparison of SwiftWind and two baseline models (FNO and ViT) across four configurations in real-world observational experiments.

Experiments	Model	Mean L2 Loss		RMSE (m/s)		MAE (m/s)
		Value	Improv.	Value	Improv.	Value	Improv.
Ideal-Selected	FNO	0.1741	24.76%	1.1205	24.74%	0.8057	26.21%
	ViT	0.1768	23.60%	1.1376	23.59%	0.8017	26.58%
	SwiftWind	0.1614	30.25%	1.0384	30.26%	0.7548	30.87%
Ideal-All	FNO	0.1845	19.68%	1.1905	19.69%	0.8758	19.30%
	ViT	0.1848	19.55%	1.1924	19.56%	0.8570	21.04%
	SwiftWind	0.1743	24.12%	1.1247	24.12%	0.8313	23.40%
Real-Selected	FNO	0.1854	19.88%	1.1929	19.88%	0.8889	18.59%
	ViT	0.1900	17.89%	1.2228	17.87%	0.8941	18.12%
	SwiftWind	0.1774	23.34%	1.1418	23.31%	0.8493	22.22%
Real-All	FNO	0.1893	17.59%	1.2215	17.59%	0.9155	15.65%
	ViT	0.1930	15.98%	1.2455	15.98%	0.9163	15.57%
	SwiftWind	0.1822	20.68%	1.1758	20.68%	0.8786	19.05%
–	GFS-Selected	0.2314	–	1.4889	–	1.0919	–
	GFS-All	0.2297	–	1.4823	–	1.0853	–

The table reports the mean L2 loss, RMSE, and MAE values together with their relative improvements over the GFS background field. The bold values indicate the best results.

. The Ideal configurations produce better results than the Real ones, probably because the accuracy of observations at key locations has a strong influence on reconstruction quality. Meanwhile, the Selected cases perform better than the All cases, suggesting that large variations in observation count across time can negatively affect the reconstruction performance. This result further highlights the influence of data-availability fluctuations and indicates that a more consistent number of observations is favorable for achieving stable and accurate reconstructions.

Figure 8 shows the spatial patterns of MAE for the three models. SwiftWind exhibits smaller errors than the other two models and produces smoother and more spatially coherent error patterns, whereas ViT still displays a grid-like structure like OSSEs. Consistent with the previous results, the Ideal configurations outperform the Real ones, and the Selected cases perform better than the All cases. In addition, errors over open-ocean regions are lower than those near coastal areas, probably because coastal winds are more complex and affected by local terrain and external forcing. These findings suggest that integrating coastal meteorological stations with marine observations could be a promising direction for improving wind speed field reconstruction in coastal transition zones.

Figure 9 shows the radially averaged power spectral density (RAPSD) of wind speed fields. All models reproduce the large-scale spectral characteristics reasonably well, with curves close to that of ERA5, indicating that the dominant large-scale wind field structures are successfully recovered. At higher spatial frequencies, corresponding to smaller spatial scales, SwiftWind agrees more closely with ERA5 than the other models. This result suggests that SwiftWind better captures small-scale variability and preserves more realistic fine-scale structures.

In addition, we performe temporal-offset analysis for the Real-All case. As shown in

Table 6. Temporal-offset analysis of SwiftWind, two baseline models (FNO and ViT), and the GFS background field in the Real-All case.

Offset (h)	Model	Mean L2 Loss	RMSE (m/s)	MAE (m/s)
0	FNO	0.1714	1.1053	0.8309
	ViT	0.1767	1.1390	0.8364
	SwiftWind	0.1668	1.0752	0.8041
	GFS-6h	0.2055	1.3248	0.9656
1	FNO	0.1740	1.1267	0.8483
	ViT	0.1778	1.1511	0.8462
	SwiftWind	0.1694	1.0970	0.8201
	GFS-6h	0.2076	1.3442	0.9819
2	FNO	0.1817	1.1797	0.8899
	ViT	0.1849	1.2004	0.8859
	SwiftWind	0.1768	1.1481	0.8605
	GFS-6h	0.2159	1.4023	1.0281
3	FNO	0.1900	1.2361	0.9318
	ViT	0.1938	1.2608	0.9331
	SwiftWind	0.1829	1.1902	0.8930
	GFS-6h	0.2280	1.4838	1.0919
All	FNO	0.1893	1.2215	0.9155
	ViT	0.1930	1.2455	0.9163
	SwiftWind	0.1822	1.1758	0.8786
	GFS-6h	0.2297	1.4823	1.0853

Note: Offset denotes the temporal difference between each hourly target field and the native 6-hourly GFS background field used as input. Offset 0 h corresponds to the native GFS cycles, while offsets 1–3 h correspond to off-cycle target hours. The bold values indicate the best results.

, SwiftWind consistently achieves the lowest errors across all temporal offsets. At the native GFS cycles, SwiftWind reduces the RMSE from 1.3248 m/s for GFS-6h to 1.0752 m/s, indicating that the model still provides effective correction when the original GFS background is available. As the offset increases from 1 to 3 h, the RMSE of GFS-6h increases from 1.3442 to 1.4838 m/s, whereas SwiftWind increases more moderately from 1.0970 to 1.1902 m/s. This result confirms that, even with realistic ASCAT and ICOADS sampling, SwiftWind is less sensitive to the temporal offset of the 6-hourly background field and maintains better reconstruction accuracy at off-cycle hours.

To complement the ERA5-based evaluation, we further assess the models using a withheld buoy subset constructed from ICOADS, as described in Section 2.2. This additional experiment is motivated by the fact that, although ERA5 is a practical reference field, agreement with ERA5 alone is not sufficient to demonstrate improved agreement with the real atmosphere-ocean state. In this experiment, the Real-Selected and Real-All configurations are compared against the withheld buoy observations, and the model outputs are bilinearly interpolated to the buoy locations for quantitative comparison.

Table 7. Quantitative comparison of different models against withheld buoy observations in real-world experiments.

Experiments	Model	RMSE (m/s)	MAE (m/s)	MBE (m/s)	r
Real-Selected	FNO	1.2811	0.9911	-0.1105	0.9151
	ViT	1.3315	1.0295	−0.0136	0.9072
	SwiftWind	1.3451	1.0487	0.0479	0.9048
Real-All	FNO	1.2809	0.9858	−0.1055	0.9159
	ViT	1.3411	1.0310	0.0584	0.9074
	SwiftWind	1.3257	1.0312	0.0932	0.9091
−−	ERA5	1.0701	0.9134	0.0227	0.9422
	GFS−6h	1.5926	1.2009	0.3333	0.8923

Note: The bold values indicate the best results.

presents the detailed quantitative results against the withheld buoy observations. Among the three deep learning models, FNO achieves the best performance on this buoy-based benchmark, while SwiftWind remains competitive and is comparable to ViT. This is likely because the withheld buoys are concentrated in a relatively localized region, whereas both FNO and ViT take gridded fields interpolated from the observations as inputs, which can be advantageous for matching localized station measurements. In contrast, SwiftWind directly ingests irregular discrete observations. Nevertheless, SwiftWind still clearly outperforms the GFS-6h background, achieving lower RMSE and MAE together with higher correlation. Overall, the buoy-based experiment serves as a complementary observational validation and further supports the effectiveness and robustness of SwiftWind under real observational conditions.

4.3. Arbitrary-Location Inference Experiments

SwiftWind reconstructs wind speed fields by modeling the spatial correlations among observations at different locations. Because it explicitly encodes geographic coordinates and supports variable-length inputs, the model inherently possesses the capability to query wind speeds at arbitrary positions.

To verify this property, we design an experiment that extends the training query locations by including ASCAT observation coordinates, in addition to the ERA5 uniform-grid points. Specifically, the ASCAT query locations are chosen from the remaining ASCAT observation positions after excluding the downsampled ASCAT observations that are already used as model inputs. This design avoids querying wind speed values at locations that have already been provided to the model as input observations. The ASCAT dataset is selected because its observations are irregularly distributed, while its accuracy is comparable to that of ERA5. During testing, these remaining ASCAT locations are used as input queries, and the corresponding wind speed estimates are generated directly by SwiftWind.

For the training strategy, we fine-tune SwiftWind from the Real-Selected configuration using only a few additional epochs, thus following a pretraining and fine-tuning approach that ensures stable convergence. Importantly, both the training and validation data used in the Real-Selected pretraining stage are strictly restricted to the 2017–2022 period. The subsequent fine-tuning stage also uses only ASCAT observations from 2017 to 2022. The 2023 data are reserved exclusively for final testing after fine-tuning. This protocol ensures a strict temporal separation, thereby preventing any data leakage.

The testing results at ASCAT locations are shown in Figure 10. Compared with ASCAT, SwiftWind and ERA5 exhibit strong linear agreement, while GFS shows a clear overestimation at high wind speeds. In terms of statistical metrics, SwiftWind achieves RMSE, MAE, MBE, and r of 1.299, 0.962 m/s, −0.037 m/s, and 0.903, respectively, outperforming GFS. Although the numerical gains in RMSE and MAE appear moderate, they are physically meaningful given the sparse and noisy real-world conditions. These results demonstrate that SwiftWind can accurately infer wind speeds at arbitrary query locations by leveraging learned spatial relationships among observations. Moreover, SwiftWind shows strong potential for integrating multi-source observational data, with improved data quality and quantity expected to enhance its accuracy at arbitrary locations. In addition, SwiftWind reconstructs hourly wind speed fields from the coarse 6 h GFS background and a limited number of observations across all experimental configurations.

Overall, SwiftWind can integrate irregular observations from multiple sources to generate spatially continuous sea surface wind speed fields at arbitrary locations. This capability demonstrates the model’s strong adaptability to real-world observation systems and its practical potential for rapid wind field reconstruction to support marine forecasting and ship routing.

5. Discussion

5.1. Ablation Study

5.1.1. Different Data Sources’ Design

To investigate the contribution of multi-source observations to SwiftWind and to quantify the benefits of observational data fusion for sea surface wind reconstruction, we conduct an ablation study using different combinations of observational data, as summarized in

Table 8. Ablation study on the impact of different observational data combinations for Real-All Case.

Ablation Experiments	Mean L2 Loss		RMSE (m/s)		MAE (m/s)
	Value	Improv.	Value	Improv.	Value	Improv.
ICOADS Only	0.1988	13.45%	1.2826	13.47%	0.9662	10.97%
ASCAT-B + ICOADS	0.1861	18.98%	1.2006	19.00%	0.9001	17.06%
ASCAT-A/B + ICOADS	0.1863	18.89%	1.2018	18.92%	0.9002	17.06%
ASCAT-A/B/C + ICOADS	0.1822	20.68%	1.1758	20.68%	0.8786	19.05%
GFS-All	0.2297	–	1.4823	–	1.0853	–

The table reports the mean L2 loss, RMSE, and MAE values together with their relative improvements over the GFS background field. The bold values indicate the best results.

. In all experiments, ICOADS serves as the fundamental observational source to ensure model operability since it provides observations at nearly all time steps for latent aggregation in the encoder. Additional observations from different ASCAT measurements are progressively incorporated to examine the impact of increasing observation density.

All experiments are conducted under the Real-All case in the real-world experiments, which best reflects realistic maritime operational scenarios. As shown in Table 8, incorporating observational data leads to consistent performance improvements over the GFS background field. Even when only sparse ICOADS observations are available, the model achieves 13.47% reduction in RMSE and 10.97% reduction in MAE, demonstrating the robustness of SwiftWind under limited observation conditions. As additional ASCAT observations are introduced, the reconstruction accuracy improves steadily. These results demonstrate that SwiftWind effectively utilizes sparse observations and consistently benefits from denser multi-source data through observational fusion.

5.1.2. Coordinate Encoding Design

To evaluate the effectiveness of the latitude–longitude coordinate encoding module in representing spatial locations, we conduct an ablation experiment using two different coordinate representations. Specifically, under identical model architectures and hyperparameter settings, latitude and longitude are represented either through the proposed coordinate encoding scheme or as direct input channels, referred to as raw lat–lon input channels. All experiments are also under the Real-All case to ensure consistency.

The quantitative results are shown in

Table 9. Ablation study on the impact of latitude–longitude representations for the Real-All case.

Ablation Experiments	Mean L2 Loss		RMSE (m/s)		MAE (m/s)
	Value	Improv.	Value	Improv.	Value	Improv.
Lat–Lon coordinate encoding	0.1822	20.68%	1.1758	20.68%	0.8786	19.05%
Raw Lat–Lon as input channels	0.2000	12.93%	1.2902	12.96%	0.9707	10.56%
GFS-All	0.2297	–	1.4823	–	1.0853	–

The table reports the mean L2 loss, RMSE, and MAE values together with their relative improvements over the GFS background field. The bold values indicate the best results.

. The latitude–longitude coordinate encoding achieves lower reconstruction errors than the raw coordinate input across all evaluation metrics. These results indicate that the coordinate encoding scheme enables the model to effectively capture spatial positional information. This advantage is particularly important for handling irregularly distributed and non-gridded observations.

5.2. Sensitivity Analysis

Sensitivity to Downsampling Ratio

Because the downsampling ratio directly controls the sparsity level of the satellite observations used as model input, we further conduct a sensitivity analysis of this hyperparameter. The downsampling step is introduced mainly to simulate sparse-observation conditions in realistic applications while also reducing the computational cost of model training. Specifically, for a given downsampling ratio, the corresponding fraction of observations is randomly sampled from the original satellite measurements.

To examine its influence, we additionally tested four downsampling levels, namely 1/100, 1/40, 1/20, and 1/10. All experiments were conducted under the Real-All configuration. The quantitative results are summarized in

Table 10. Sensitivity analysis of the downsampling ratio for the Real-All case.

Downsampling Ratio	Mean L2 Loss		RMSE (m/s)		MAE (m/s)
	Value	Improv.	Value	Improv.	Value	Improv.
1/100	0.1850	19.46%	1.1939	19.46%	0.8935	17.67%
1/40	0.1822	20.68%	1.1758	20.68%	0.8786	19.05%
1/20	0.1822	20.68%	1.1759	20.68%	0.8783	19.07%
1/10	0.1843	19.76%	1.1895	19.75%	0.8899	18.00%
GFS-All	0.2297	–	1.4823	–	1.0853	–

The table reports the mean L2 loss, RMSE, and MAE values together with their relative improvements over the GFS background field. The bold values indicate the best results.

. Overall, the model performance changes only slightly across the tested downsampling levels, indicating that the main conclusions of this study are not strongly affected by the specific choice of the downsampling ratio. The best overall performance is obtained at 1/40 and 1/20, and all tested ratios show clear improvements over the GFS background.

These results indicate that the proposed framework is stable under moderate changes in observational sparsity. When the downsampling ratio is too small, less satellite information is retained, which may weaken the benefit of the ASCAT observations. In contrast, using a larger retained fraction does not bring further improvement, suggesting that simply adding more satellite observations does not necessarily lead to better reconstruction in this setting. Considering both performance and computational cost, the adopted ratio of 1/40 is a practical and well-balanced choice in this study.

5.3. Limitations and Future Work

Despite the promising results of SwiftWind, several limitations and directions for future work deserve further investigation.

(1) From an architectural perspective, introducing a learnable weighting matrix for both observational and background inputs could help account for the varying confidence levels of different data sources. This may enable more adaptive data fusion and reduce the impact of noisy observations on the reconstruction results.

(2) The current implementation focuses solely on two-dimensional surface wind speed. Although ASCAT and ICOADS provide wind vector information, the present study uses only wind speed. Future work could extend the framework toward wind vector reconstruction, together with multi-variable learning and physics-informed loss functions to improve physical consistency.

(3) The evaluation still relies primarily on ERA5-based validation. However, improved agreement with ERA5 does not necessarily imply improved agreement with the real wind field. Because the training inputs are assimilated into ERA5, SwiftWind may partially align with ERA5 assimilation patterns, meaning the improvement over the GFS-6h may be systematically overestimated to some extent. Although a complementary buoy-based validation is included, future studies should further incorporate more independent observational benchmarks, such as additional buoy networks, field campaign measurements, or other observation sources that are less tightly coupled to the reanalysis assimilation system.

6. Conclusions

Sea surface wind speed is a key variable in numerical weather prediction and is essential for ocean navigation, route planning, and wind energy assessment. However, constrained by communication conditions during ship operations, there is an urgent need for a reconstruction approach capable of handling sparse observations. We propose SwiftWind, a flexible deep learning framework for a fast and accurate reconstruction of wind speed fields by combining limited heterogeneous observations with background forecasts. SwiftWind supports variable-length observation inputs, incorporates latitude–longitude positional encoding, and enables wind speed inference at arbitrary locations, making it well suited for real-world scenarios with irregular and moving observations. By integrating attention mechanisms and learnable latent representations, SwiftWind effectively captures global spatial dependencies and refines large-scale background structures.

The effectiveness of SwiftWind is validated through a series of OSSEs with varying observation densities, real-world evaluations using downsampled ASCAT-A/B/C and ICOADS data, as well as arbitrary-location inference experiments. The results from multiple perspectives, including overall statistical metrics, temporal evolution, spatial error distribution, radially averaged power spectral density and temporal-offset analysis, show that SwiftWind delivers high reconstruction accuracy, maintains stable performance over time, and produces spatially smooth and coherent error patterns. Under ERA5-based evaluation, SwiftWind performs robustly under varying numbers, qualities, and spatial distributions of observations, surpassing representative deep learning baselines such as FNO and ViT. Moreover, the model uniquely supports accurate arbitrary-location wind speed queries, which holds great practical significance. However, in independent buoy validation, SwiftWind performs comparably to ViT and slightly worse than FNO. This is likely due to the scattered-point-processing mechanism and the concentrated distribution of buoys. Future work should incorporate more diverse independent observations to enhance single-point validation, which we will continue to improve.

Overall, SwiftWind demonstrates strong scalability and robustness in both sparse reconstruction and multi-source data fusion, indicating its potential for near-real-time onboard wind speed reconstruction. Moreover, this framework provides new insights for data assimilation. By sparsifying and optimally utilizing heterogeneous observations, it offers an efficient pathway to reduce computational cost and alleviate high-dimensional challenges. This paradigm suggests that a small number of high-quality observations can effectively refine coarse background fields. In the future, such AI-assisted reconstruction frameworks could play an important role in accelerating analysis generation and improving forecasting accuracy in operational marine and atmospheric systems.