Leveraging satellite observations and machine learning for underwater sound speed estimation

For a comprehensive understanding of our methodology, including the data sources, ML models, evaluation metrics, and detailed model comparisons, refer to the Materials and Methods section in the supplementary materials. We employed two advanced models—Deep Neural Network (DNN) and K-nearest Neighbor (KNN)—to predict underwater sound speed based on surface data. Standard evaluation metrics, specifically Root Mean Squared Error (RMSE) and R-squared (R²) scores, were used to assess the performance of these models. Our analysis revealed that the KNN model outperformed the DNN model, leading us to select KNN for subsequent analyzes.

Table 1 provides an overview of the datasets used for both training and prediction. Our analysis utilized three primary datasets: (1) the World Ocean Circulation Experiment (WOCE) dataset, which includes ~29 million data instances collected from 1992 to 1998 (see Fig. 3A)³⁰; (2) WOA dataset, which offers monthly averaged data from 2004 to 2023 with a 1° × 1° horizontal resolution down to 2000 m depth³¹; and (3) the Physical Oceanography Distributed Active Archive Center (PODAAC), which provides daily updates on satellite-observed SST³² and salinity³³.

In addition to predictions based on satellite data (Table 1), other predictions incorporated temperature and salinity at zero depth from the CTD data within the datasets as surface inputs to train and forecast sound speed fields. These predictions were then compared with sound speed calculated from CTD data at various depths within the datasets (See the “Methods” section for details about the calculation).

Insights into model performance

We start from interpreting the physics behind the effectiveness of our model in predicting underwater sound speed based on sea surface data. To do this, we analyzed the correlation between surface sound speed and sound speed at various depths using CTD data from the 2015 WOA³¹. This analysis evaluated correlation values from the surface to depths of up to 2000 m for both March and September (Fig. 2), representing summer and winter seasons, respectively.

The high correlation values observed in the upper 500 m (Fig. 2) indicate a strong influence of surface parameters on sound speed in this region. This finding predicts our model’s ability to accurately capture the vertical SSP based on surface conditions, which is crucial given that temperature and salinity, both of which vary at the surface, predominantly influence sound speed in the upper ocean. The results demonstrate the model’s proficiency in leveraging surface data for accurate sound speed predictions in these upper layers.

As depth increases, correlation values decrease (Fig. 2), suggesting that surface conditions have a diminished influence on sound speed. In deeper regions, pressure becomes the dominant factor affecting sound speed. Here, the model relies on historical data patterns to predict sound speed, effectively managing the complexities associated with deeper ocean profiles. By integrating historical data, the model should maintain robust predictive accuracy even in deeper regions where surface parameters are less relevant.

With these results, our model should effectively use surface parameters for sound speed predictions in the upper ocean while adapting to the stable pressure influences in deeper waters, ensuring comprehensive prediction capabilities across varying ocean depths.

Prediction within the training time window

We trained our model using 80% of the WOCE dataset³⁰ and ensure robust performance evaluation by employing a 5-fold cross-validation (see Supplementary). Figure 3A shows a map of the CTD data collection locations for the WOCE dataset. We then predicted sound speed values for 5 million data instances from the remaining 20% of the data reserved for testing. Figure 3B shows an illustrative example of one predicted SSP, which closely aligns with the CTD-calculated values, demonstrating the model’s potential applicability.

To further evaluate the model’s efficacy, we conducted a detailed error analysis by comparing the predicted sound speed values with those calculated using CTD data. We categorized prediction errors into bins across different depth ranges. The symmetry in the heatmap (Fig. 3C) suggests an equal likelihood of positive and negative errors, with a sharp peak indicating consistent model performance and minimal significant outliers. The error distribution heatmap (Fig. 3C) reveals the greatest dispersion near the surface (0–1000 m), where the ocean exhibits significant variability, with error magnitudes ranging from −12 to 12 m/s, and over 99% of errors within  ±0.5 m/s. The mean absolute error (Fig. 3D) shows a depth-dependent variation, peaking at 0.16 m/s around 100 m and then stabilizing at greater depths, consistent with the heatmap analysis.

Overall, the results show a trend of improving prediction accuracy with depth. The model faces challenges in the upper ocean, where wind and ocean interactions introduce greater variability, but it performs better in the deep ocean, where pressure predominantly influences sound speed. However, those large-magnitude errors predominantly found at shallow depths are infrequent, highlighting the model’s overall effectiveness in sound speed prediction, at least within the training time window.

Prediction beyond the training time window

Our model was trained using in-situ CTD data from the WOCE dataset, collected between 1990 and 1998³⁰. A key question is whether this model, trained on historical data, can accurately predict SSPs beyond this period. To investigate this, we applied our model to predict sound speed using the WOA dataset³¹, which provides monthly averaged data on temperature and salinity for specific depths, latitudes, and longitudes. We compared these predictions with SSPs derived from CTD data within the WOA dataset in 2015.

We examined SSPs at various latitudes along 150° West longitude in January to assess the model’s ability to replicate latitude-dependent underwater sound speed variations. The model’s predictions (dashed lines) closely align with SSPs calculated from CTD data in the WOA (solid lines) (Fig. 4A). The model effectively captured key relationships, such as higher sound speed values at lower latitudes corresponding to warmer surface temperatures and lower sound speed values at higher latitudes associated with cooler temperatures. It also accurately predicted minimal variations in sound speed across different latitudes in deep ocean regions. These results demonstrate the model’s capability to reproduce the dependence of sound speed on latitude, validating its predictive accuracy and its ability to generalize beyond the training data.

We analyzed predictions for March and September 2015, representing winter and summer in the northern hemisphere (and vice versa in the southern hemisphere), to evaluate the model’s ability to capture seasonal variations in sound speed. We focused on the North Atlantic, a region known for significant seasonal fluctuations. Comparison of calculated profiles using monthly averaged CTD data from the WOA dataset with our model’s predictions (Fig. 4B) showed strong agreement. The model accurately reflected expected seasonal patterns, demonstrating lower surface sound speeds in March (winter) and higher values in September (summer), consistent with typical temperature variations. The predictions also maintained consistency in deeper ocean regions across seasons, underscoring the model’s reliability in capturing surface variability and deep-water stability.

Expanding our analysis to the southern hemisphere, we tested the model’s predictions for the Indian Ocean, focusing on inverse seasonal trends compared to the northern hemisphere. The model predictions successfully mirrored established seasonal trends of sound speed in the southern hemisphere (Fig. 4C). Results accurately reflected higher sound speed values associated with warmer surface temperatures in March (summer) and lower values due to colder temperatures in September (winter), demonstrating the model’s consistency across different global regions.

These comprehensive analyzes (Fig. 4A–C) validate our model’s predictive capabilities across different latitudes and seasons beyond the training period. Figure 4D further compares our model’s forecast with the CTD-derived sound speed field along a meridional cross-section at 150°W longitude for January 2015. The results underscore our model’s precision and reliability in predicting global sound speed distributions, highlighting its significant potential for practical applications in ocean acoustics.

The model’s predictive accuracy is bolstered by its ability to interpret the relationships between sound speed and key environmental parameters, such as temperature, salinity, and pressure. The variation of these environmental parameters over the years or decades within the same seasons is not as profound as the seasonal variation within a year. The seasonal variations are pronounced enough to significantly change sound speed. By effectively capturing these seasonal fluctuations, the model adeptly manages smaller interannual changes, enabling it to make accurate predictions even beyond its initial training period. In other words, given the model’s ability to capture the strong seasonal variations in sound speed, it appears not surprising that the ML model demonstrates proficiency in predicting ocean sound speed beyond its training period. By integrating robust historical datasets like WOCE, the model incorporates these parameters into its framework, allowing it to leverage long-term temperature trends for informed predictions. Its adaptability is crucial, as it identifies recurring patterns and integrates both seasonal and long-term climate trends for effective generalization. This integration ensures the model’s relevance and accuracy, providing reliable predictions even in scenarios beyond its primary training scope.

Global predictions

We evaluated our model’s global performance using the WOA³¹ datasets for March and September 2015, representing winter and summer in the northern hemisphere. This analysis compared model-predicted sound speeds with those derived from CTD data across ~19 million data points at a 1° × 1° resolution, as defined by the WOA dataset. This global assessment provides a broad view of the model’s accuracy across diverse ocean conditions and locations.

Depth-based heatmaps of prediction errors for March and September 2015 (Fig. 5A, B) reveal that the model maintains accuracy throughout the water column, with more pronounced errors near the surface (0–500 m) due to complex dynamics in the upper ocean. Despite some increased error dispersion at shallower depths, there is no significant rise in error with depth, reflecting reliable performance even in deeper waters. The symmetric distribution and peak near zero indicate consistent model performance with few significant outliers. These results for predictions beyond the training periods align with those in Fig. 3C for predictions within the training period, further validating the model’s performance across different datasets and temporal scales.

In the heatmaps (Fig. 5A, B), over 95% of errors fall within  ±20 m/s, with error magnitudes ranging from −60 to 60 m/s. The MAE distribution across depths (Fig. 5C) peaks at around 8 m/s between 0 and 200 m and decreases with depth, consistent with the depth-based heatmaps. Compared to predictions within the training period (Fig. 3C), these global predictions beyond the training period show a larger error range due to expanded data coverage and temporal extrapolation. Despite these challenges, the model’s performance in capturing seasonal variations over all depths validates its robustness across diverse oceanographic conditions throughout the year.

To evaluate the model’s global performance, we calculated the MAE for each location and averaged it across all depths. Contour plots for March (Fig. 6A) and September (Fig. 6B) show MAE distribution across latitudes and longitudes, with most of the world’s oceans exhibiting low errors within 8 m/s (as indicated by the blue shading). The plots also highlight regions with notably higher errors (marked by red squares), reflecting the model’s challenges in dynamic regions or areas with limited data. These are regions:

1. (I)

   The Arctic region near Greenland and Iceland (area 1 in Fig. 6) shows errors as high as 38 m/s. This large error is due to variable temperature and salinity profiles resulting from seasonal sea ice dynamics and limited training data³⁴. Climate change impacts, such as accelerated ice melt and shifting ocean currents–factors not fully captured by historical data³⁵—further exacerbate prediction errors. These complexities contribute to an unpredictable environment, challenging the model’s accuracy in this region.

2. (II)

   The North Atlantic near the United States and Canada (area 2 in Fig. 6) exhibits significant errors influenced by the Gulf Stream’s warm water transport and strong currents³⁶. Coastal regions generally show higher errors due to rapidly changing environments.

3. (III)

   The Mediterranean Sea (area 3 in Fig. 6) shows increased errors due to its complex water masses, seasonal variations, and high evaporation rates³⁷.

4. (IV)

   A small area in the South Pacific Ocean (area 4 in Fig. 6) displays high errors, potentially due to localized oceanographic phenomena and insufficient training data.

5. (V)

   The Japan Sea (area 5 in Fig. 6) shows errors up to 51 m/s, influenced by the Kuroshio current and complex oceanographic features³⁸.

These factors, including encountering unfamiliar oceanic conditions and long-term changes, highlight the model’s limitations and the need for ongoing refinement and potential region-specific adjustments.

Regional model

Our examination of the global model’s performance across various marine environments identified certain limitations in specific oceanic regions. For example, in the Arctic region near Greenland and Iceland (area 1 in Fig. 6), insufficient training data (Fig. 7A) likely contributed to a significant increase in error, with a maximum MAE of 35 m/s (Fig. 7B).

To address the challenges posed by data scarcity in specific areas, we developed a regional model. This model, trained with inputs similar to the global model, uses CTD data to calculate sound speed as its target while incorporating surface data. For training, we utilized the 2004 World Ocean Atlas (WOA) dataset, focusing exclusively on the Arctic region with a horizontal resolution of 1° × 1°, and comprising ~380,000 data instances (Fig. 7C).

The regional model significantly improved performance, reducing the maximum prediction error from 35  m/s to 13 m/s in the Arctic region (Fig. 7D). This result highlights the advantages of using regional models with more focused datasets to tackle specific environmental challenges, particularly in regions where global models may fail to capture intricate local oceanographic details.

However, while the reduction from 35 m/s to 13 m/s is notable, the remaining maximum error of 13 m/s is still somewhat higher than the average MAE of 5 m/s achieved with the global model. This residual error underscores the ongoing challenge posed by the Arctic’s complex ocean dynamics for achieving precise sound speed predictions.

Influence of prediction error on underwater sound propagation

To evaluate the impact of sound speed prediction errors on underwater sound propagation, we used the Bellhop ray tracing module in Python, a well-established tool for ocean acoustic modeling³⁹. Our analysis focused on transmission loss (TL), which measures the reduction in acoustic signal strength over distance and provides insights into sound propagation in the ocean¹¹. We examined TL at 200 Hz and 15 kHz to represent low- and middle-frequency underwater sound waves. Low-frequency waves (200 Hz) generally travel longer distances with less attenuation, while middle-frequency waves (15 kHz) experience greater attenuation and, consequently, more TL. Therefore, we used a 50 km range for the low-frequency scenario, while for the mid-frequency scenario, a 20 km range was selected.

We selected a location in the South Atlantic (6°E longitude, 11°S latitude) where the prediction error was close to the depth-averaged MAE (Fig. 5E), providing a representative scenario. Our analysis involved a sound source at 840 m depth (where sound speed is minimal) in March 2015. We used the SSP predicted by our ML model (Fig. 8A) to simulate TL for both a 200 Hz source (Fig. 8B) and a 15  kHz source (Fig. 8C). For comparison, we also used the SSP derived from CTD data in the WOA (Fig. 8D) for TL simulations (low-frequency in Fig. 8E, mid-frequency in Fig. 8F). The TL results illustrate how acoustic energy is distributed over distance and depth, revealing areas of high and low TL due to interference patterns.

Discrepancies between predicted and actual SSPs (Fig. 8G), ranging from −2 to 10 m/s, can affect propagation paths and TL patterns. Differences in TL simulations based on predicted versus actual SSPs for both low-frequency (Fig. 8H) and mid-frequency (Fig. 8I) show that TL differences generally fall within  ±3 dB (light green color). Only a few areas exhibit larger TL variations, indicated by reddish or blue colors. These larger differences are typically observed near ray caustics or regions with path interference, where TL is highly sensitive to input parameters.

The model’s consistent performance across frequencies, with TL discrepancies generally within  ±3 dB, suggests its effectiveness for various acoustic applications, including naval assessments, oceanographic surveys, and studies of anthropogenic noise impacts, particularly for low to mid-frequency sources. However, it may not be suitable for applications requiring TL accuracy beyond  ±3 dB, high-frequency acoustics (above 1000 kHz) without further validation, or complex environments with rapid oceanographic changes or intricate bathymetry. For such critical applications, it is advisable to use this model in conjunction with advanced propagation tools or in-situ measurements to improve accuracy.

Satellite data-based predictions

Our ML approach leverages near real-time SST and sea surface salinity (SSS) data from remote sensing satellites to predict underwater sound speed. This methodology overcomes the limitations of traditional in-situ measurements, which are often expensive and geographically constrained, by providing high-resolution, three-dimensional sound speed predictions for any location and time. Such real-time capabilities are not available with traditional in-situ data, which is typically limited to specific years.

To illustrate the high-resolution mapping capabilities of our model, we utilized sea surface parameters from the PODAAC, which provides daily updates on satellite-observed surface conditions. For example, we used SST³² (Fig. 9A) and SSS³³ (Fig. 9B) data for November 8, 2023, as inputs to our model to predict sound speed variations at a depth of 50 m globally (Fig. 9C). The results show higher sound speeds near the equator and lower sound speeds in polar regions as expected, demonstrating the correctness of the model.

Unlike traditional 3D ocean circulation models, which face challenges with real-time data delivery due to high computational demands, our ML approach offers rapid predictions for specific coordinates and depths. While 3D ocean circulation models provide valuable insights, our ML-based model has significant potential to enhance sound speed predictions, especially for applications requiring timely data.