Modeling Ocean Circulation with Machine Learning

Understanding ocean circulation is key to predicting weather, climate patterns, and managing resources related to the ocean. One way to assess this circulation is by observing Sea Surface Height (SSH), which is how high the surface of the ocean is in different areas. However, to get a clear picture, we need to separate SSH into two parts: balanced motions (BMs), which change slowly over time, and unbalanced motions (UBMs), which change rapidly.

Currently, satellites like the recently launched Surface Water and Ocean Topography (SWOT) satellite are able to measure SSH with exceptional detail. This new satellite can capture data with a resolution of 5-10 km, where both BMs and UBMs are roughly equal in size. However, SWOT only passes over each area once every 21 days, which makes it challenging to use standard methods that require more frequent data. Therefore, we need new ways to handle SSH measurements that can work with just one snapshot at a time.

#The Challenge with Current Methods

Recent attempts to use machine learning, particularly deep learning (DL), have shown promise in separating BMs and UBMs. Some studies have framed the problem as translating one type of image (the total SSH) into another (the separated BMs and UBMs). While these attempts have been somewhat successful, they often struggle with the wide range of scales in ocean data and also require a lot of training data, which is in short supply.

One major issue with current methods is that the accuracy of predictions tends to vary between different scales. The patterns in the ocean data can show significant differences, meaning that some methods may miss important details. For example, when using pixel-wise mean squared error (MSE) loss to evaluate the predictions, the model often focuses on the larger patterns while ignoring smaller, yet significant, details.

To overcome some of these challenges, researchers are looking at techniques such as zero-phase component analysis (ZCA) whitening, which aims to improve the separation of BMs and UBMs across different scales.

#Importance of Ocean Dynamics

The ocean plays an essential role in our planet's climate and weather systems. It holds and moves large amounts of heat, carbon, and other important substances. The movement of water in the ocean consists of various processes that happen at different speeds and scales. By analyzing how these processes work together, we can gain insights into climate changes and manage resources like shipping, fishing, and renewable ocean energy.

Currently, the primary method to estimate global ocean flow is satellite altimetry. These observations help measure the height of the ocean surface, which is linked to the underlying water movement. However, simply measuring SSH is not enough; we need to break this down into BMs and UBMs to understand the flow better.

Traditionally, BMs and UBMs can be separated using various filtering techniques. These filters usually require data recorded over short intervals - from minutes to a few hours. Since standard satellites only collect data every 10 days or so, this can create issues for separating the two types of motions accurately.

With the SWOT satellite now providing higher resolution data, we need to develop methods that can operate with just a single snapshot of SSH.

#Machine Learning Approaches

With the rise of machine learning techniques, there's potential to treat the SSH separation task as an image transformation challenge. Some models, like convolutional neural networks (CNNs), have been applied with varying success. However, the multi-scale nature of ocean data still poses challenges. The amount of signal at different scales can vary greatly, making it difficult for the models to capture all the necessary details.

Using a typical loss function that focuses on pixel-wise accuracy often leads to overlooking important information in smaller scales. To address this, some researchers have tried adding gradients to their loss functions to account for smaller details; however, this introduces new complexities, such as the need for fine-tuning and risks of overfitting.

To combat these issues, the application of ZCA whitening is proposed as a way to preprocess the data. This technique can help balance information across scales, reduce the risks of overfitting, and stabilize the training process by minimizing correlations between data samples.

#Proposed Methodology

Our methodology involves breaking down the total SSH into its components: BMs and UBMs. We train a machine learning model to predict the UBM for given SSH input and derive the BM from that. Our training data comes from high-resolution global ocean simulations focusing on a particular ocean region known as the Agulhas retroflection area.

To improve the training process, we employ two data augmentation techniques: rotating the data images to help the model learn better with different orientations and creating synthetic samples to boost the available training data. Following this, we apply ZCA whitening to further enhance the model's ability to recognize both large-scale and small-scale features.

#Evaluating Model Performance

To understand how well our machine learning techniques are working, we compare different models, such as traditional Gaussian filters and various UNet configurations, which are designed for image analysis. We look at two main performance indicators: the pixel-wise absolute error distribution and the Power Spectral Density (PSD) of the predictions. This helps us see how accurately the models are predicting the components and how well they capture information across different scales.

Initial results indicate that all machine learning models perform better than traditional Gaussian filters, showing they can effectively reduce fine-scale UBM features required for accurate flow assessments. Among these, the AugZCA-UNet model stands out, consistently outperforming the others while maintaining a lower error rate.

#Challenges Ahead

Although our approach marks progress in using machine learning for this task, several challenges still remain. One major issue is that the ZCA process requires images to fit a specific size, which can create problems when handling datasets of different dimensions.

Additionally, applying ZCA to larger images can consume a lot of memory, necessitating adjustments to make the process more efficient. We also need to assess the model's performance in areas where there are gaps in data, especially given the coverage limitations of the SWOT satellite.

Finally, we should explore how well the model generalizes across different setups and conditions, particularly when compared to more traditional methods.

#Conclusion

The AugZCA-UNet model shows great promise in effectively separating SSH into BMs and UBMs, improving our ability to analyze ocean dynamics at finer scales. Its capacity to handle data scarcity and capture fine-scale variations without heavy tuning might prove vital for advancing research in oceanography and climate science.

As we continue to refine these models and techniques, we hope to address existing challenges and apply them to real-world SSH data from missions like SWOT, ultimately enhancing our understanding of ocean behaviors and their impact on our planet.