Abstract:Abstract. The reconstruction of sea surface currents from satellite altimeter data is a key challenge in spatial oceanography, especially with the upcoming wide-swath SWOT (Surface Ocean and Water Topography) altimeter mission. Operational systems however generally fail to retrieve mesoscale dynamics for horizontal scales below 100 km and time-scale below 10 days. Here, we address this challenge through the 4DVarnet framework, an end-to-end neural scheme backed on a variational data assimilation formulation. W… Show more
“…where x ⋆ is the 4DVarNet reconstruction, x s,i is a nonconditional simulation of the underlying process with similar statistical properties than x and x ⋆,s,i is the 4DVarNet reconstruction of x s,i using as sparse observations a subsampling of the simulation with same mask Ω than true observations. In absence of observations errors, and because it is backboned on variational DA, we proved, see Beauchamp et al (2022b), that 4DVarNet applied to the GP Optimal Interpolation with:…”
Section: Toward a Stochastic Formulationmentioning
confidence: 75%
“…Such behaviors are typical for smoothers like 4DVarNet which cannot retrieve smaller energy areas without any additional observations. On this point, the future SWOT mission will surely help to solve for such problems (Gaultier et al, 2015; Metref et al, 2020; Beauchamp et al, 2022a; Febvre et al, 2022). Figure 5. Ensemble-based 4DVarNet standard deviations over the test period (January 2017): the full standard deviation map is given for and only the highest uncertainties levels are given along z -axis for the other dates.…”
Section: Resultsmentioning
confidence: 99%
“…In practice, this is not an easy task when no model is available, see Section 2.3 for a practical solution. When not possible, future works may consider the DL problem of joint learning for both the reconstruction and prior emulation based on neural or differentiable formulations of the latter, see, for example, differentiable physical quasi-geostrophic model (Frezat et al, 2022) or SPDE-based linear approximations (Beauchamp et al, 2022b). Such additional developments would enable to incorporate the ensemble statistics into the 4DVarNet outer training loss, in order to comply with maximum likelihood criteria w.r.t to the Ground Truth (supervised setting) or the observations (unsupervised setting).…”
Section: Toward a Stochastic Formulationmentioning
confidence: 99%
“…Recently, we proposed an end-to-end deep learning (DL) scheme called 4DVarNet drawing from variational DA to learn jointly priors and solvers. This approach was successfully applied on the reconstruction of sea surface state based on altimetric datasets (Beauchamp et al, 2022a) in the context of both traditional nadir altimeters and the upcoming SWOT mission. Though, 4DVarNet currently only provides a reconstruction of the state space without quantifying the related uncertainties.…”
Uncertainty quantification (UQ) plays a crucial role in data assimilation (DA) since it impacts both the quality of the reconstruction and near-future forecast. However, traditional UQ approaches are often limited in their ability to handle complex datasets and may have a large computational cost. In this paper, we present a new ensemble-based approach to extend the 4DVarNet framework, an end-to-end deep learning scheme backboned on variational DA used to estimate the mean of the state along a given DA window. We use conditional 4DVarNet simulations compliant with the available observations to estimate the 4DVarNet probability density function. Our approach enables to combine both the efficiency of 4DVarNet in terms of computational cost and validation performance with a fast and memory-saving Monte-Carlo based post-processing of the reconstruction, leading to the so-called En4DVarNet estimation of the state pdf. We demonstrate our approach in a case study involving the sea surface height: 4DVarNet is pretrained on an idealized Observation System Simulation Experiment (OSSE), then used on real-world dataset (OSE). The sampling of independent realizations of the state is made among the catalogue of model-based data used during training. To illustrate our approach, we use a nadir altimeter constellation in January 2017 and show how the uncertainties retrieved by combining 4DVarNet with the statistical properties of the training dataset lead to a relevant information providing in most cases a confidence interval compliant with the Cryosat-2 nadir alongtrack dataset kept for validation.
“…where x ⋆ is the 4DVarNet reconstruction, x s,i is a nonconditional simulation of the underlying process with similar statistical properties than x and x ⋆,s,i is the 4DVarNet reconstruction of x s,i using as sparse observations a subsampling of the simulation with same mask Ω than true observations. In absence of observations errors, and because it is backboned on variational DA, we proved, see Beauchamp et al (2022b), that 4DVarNet applied to the GP Optimal Interpolation with:…”
Section: Toward a Stochastic Formulationmentioning
confidence: 75%
“…Such behaviors are typical for smoothers like 4DVarNet which cannot retrieve smaller energy areas without any additional observations. On this point, the future SWOT mission will surely help to solve for such problems (Gaultier et al, 2015; Metref et al, 2020; Beauchamp et al, 2022a; Febvre et al, 2022). Figure 5. Ensemble-based 4DVarNet standard deviations over the test period (January 2017): the full standard deviation map is given for and only the highest uncertainties levels are given along z -axis for the other dates.…”
Section: Resultsmentioning
confidence: 99%
“…In practice, this is not an easy task when no model is available, see Section 2.3 for a practical solution. When not possible, future works may consider the DL problem of joint learning for both the reconstruction and prior emulation based on neural or differentiable formulations of the latter, see, for example, differentiable physical quasi-geostrophic model (Frezat et al, 2022) or SPDE-based linear approximations (Beauchamp et al, 2022b). Such additional developments would enable to incorporate the ensemble statistics into the 4DVarNet outer training loss, in order to comply with maximum likelihood criteria w.r.t to the Ground Truth (supervised setting) or the observations (unsupervised setting).…”
Section: Toward a Stochastic Formulationmentioning
confidence: 99%
“…Recently, we proposed an end-to-end deep learning (DL) scheme called 4DVarNet drawing from variational DA to learn jointly priors and solvers. This approach was successfully applied on the reconstruction of sea surface state based on altimetric datasets (Beauchamp et al, 2022a) in the context of both traditional nadir altimeters and the upcoming SWOT mission. Though, 4DVarNet currently only provides a reconstruction of the state space without quantifying the related uncertainties.…”
Uncertainty quantification (UQ) plays a crucial role in data assimilation (DA) since it impacts both the quality of the reconstruction and near-future forecast. However, traditional UQ approaches are often limited in their ability to handle complex datasets and may have a large computational cost. In this paper, we present a new ensemble-based approach to extend the 4DVarNet framework, an end-to-end deep learning scheme backboned on variational DA used to estimate the mean of the state along a given DA window. We use conditional 4DVarNet simulations compliant with the available observations to estimate the 4DVarNet probability density function. Our approach enables to combine both the efficiency of 4DVarNet in terms of computational cost and validation performance with a fast and memory-saving Monte-Carlo based post-processing of the reconstruction, leading to the so-called En4DVarNet estimation of the state pdf. We demonstrate our approach in a case study involving the sea surface height: 4DVarNet is pretrained on an idealized Observation System Simulation Experiment (OSSE), then used on real-world dataset (OSE). The sampling of independent realizations of the state is made among the catalogue of model-based data used during training. To illustrate our approach, we use a nadir altimeter constellation in January 2017 and show how the uncertainties retrieved by combining 4DVarNet with the statistical properties of the training dataset lead to a relevant information providing in most cases a confidence interval compliant with the Cryosat-2 nadir alongtrack dataset kept for validation.
“…This method is based on a trainable adaptation of the 4DVAR [24] variational data assimilation method, and out-performs concurrent approaches in the considered OSSE setup [9]. We consider two 4DVarNet interpolation configurations, one using only nadir altimetry data [25], one using jointly nadir altimetry and sea surface temperature data [26]. We also include the latter as it significantly improves the reconstruction of the SSH at finer scales.…”
<p>Satellite radar altimeters are a key source of observation of ocean surface dynamics. However, current sensor technology and mapping techniques do not yet allow to systematically resolve scales smaller than 100km. With their new sensors, upcoming wide-swath altimeter missions such as SWOT should help resolve finer scales. Current mapping techniques rely on the quality of the input data, which is why the raw data go through multiple preprocessing stages before being used. Those calibration stages are improved and refined over many years and represent a challenge when a new type of sensor start acquiring data.</p><p>We show how a data-driven variational data assimilation framework could be used to jointly learn a calibration operator and an interpolator from non-calibrated data . The proposed framework significantly outperforms the operational state-of-the-art mapping pipeline and truly benefits from wide-swath data to resolve finer scales on the global map as well as in the SWOT sensor geometry.</p><p>&#160;</p>
Deep learning has recently gained attention in the atmospheric and oceanic sciences for its potential to improve the accuracy of numerical simulations or to reduce computational costs. Super‐resolution is one such technique for high‐resolution inference from low‐resolution data. This paper proposes a new scheme, called four‐dimensional super‐resolution data assimilation (4D‐SRDA). This framework calculates the time evolution of a system from low‐resolution simulations using a physics‐based model, while a trained neural network simultaneously performs data assimilation and spatio‐temporal super‐resolution. The use of low‐resolution simulations without ensemble members reduces the computational cost of obtaining inferences at high spatio‐temporal resolution. In 4D‐SRDA, physics‐based simulations and neural‐network inferences are performed alternately, possibly causing a domain shift, that is, a statistical difference between the training and test data, especially in offline training. Domain shifts can reduce the accuracy of inference. To mitigate this risk, we developed super‐resolution mixup (SR‐mixup)–a data augmentation method for domain generalization. SR‐mixup creates a linear combination of randomly sampled inputs, resulting in synthetic data with a different distribution from the original data. The proposed methods were validated using an idealized barotropic ocean jet with supervised learning. The results suggest that the combination of 4D‐SRDA and SR‐mixup is effective for robust inference cycles. This study highlights the potential of super‐resolution and domain‐generalization techniques, in the field of data assimilation, especially for the integration of physics‐based and data‐driven models.
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