Tag: barthélémy

Improving Ocean Reanalysis with the Offline Ensemble Kalman Smoother

Wang, Y., Counillon, F., Ying, Y., Barthélémy, S., Evensen, G. 2025: Improving Ocean Reanalysis with the Offline Ensemble Kalman Smoother. Tellus A. https://doi.org/10.16993/tellusa.4087

Summary: The Ensemble Kalman Smoother (EnKS), an extension of the Ensemble Kalman Filter, can improve the accuracy of the state estimate by assimilating ‘future’ observations. We propose to use the EnKS algorithm to enhance the accuracy and reliability of preexisting reanalyses produced with a fully coupled Earth system model. The offline EnKS is applied to two reanalyses of the Norwegian Climate Prediction Model (NorCPM) to update sea surface height, mixed layer depth, and temperature and salinity for all depth levels of the reanalyses. In an idealized framework, we tune temporal localization parameters and reveal that the optimal temporal localization parameter is 0.1, corresponding to a time delay of about 13 days. In a real framework, we find that observation error variance has to be inflated by a factor of four to account for the autocorrelation of the gridded observational product and avoid overfitting. In both frameworks, the offline EnKS improves the accuracy for the top 300 m temperature, sea surface height, and mixed layer depth, but yields limited improvements in the top 300 m salinity and the water properties below 300 m. Also, it enhances the reliability of the reanalysis. The improvement is notably lower in a real framework than in an idealized framework; this is mostly due to the lack of high quality and independent datasets for proper validation. Overall, this study demonstrates that the offline EnKS has the potential for efficiently improving pre-existing reanalyses.

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Hybrid covariance super-resolution data assimilation

Barthélémy, S., Counillon, F., Brajard, J., Bertino, L. 2024: Hybrid covariance super-resolution data assimilation. Ocean Dynamics. https://doi.org/10.1007/s10236-024-01643-6

Summary: The super-resolution data assimilation (SRDA) enhances a low-resolution (LR) model with a Neural Network (NN) that has learned the differences between high and low-resolution models offline and performs data assimilation in high-resolution (HR). The method enhances the accuracy of the EnKF-LR system for a minor computational overhead. However, performance quickly saturates when the ensemble size is increased due to the error introduced by the NN. We therefore combine the SRDA with the mixed-resolution data assimilation method (MRDA) into a method called “Hybrid covariance super-resolution data assimilation” (Hybrid SRDA). The forecast step runs an ensemble at two resolutions (high and low). The assimilation is done in the HR space by performing super-resolution on the LR members with the NN. The assimilation uses the hybrid covariance that combines the emulated and dynamical HR members. The scheme is extensively tested with a quasi-geostrophic model in twin experiments, with the LR grid being twice coarser than the HR. The Hybrid SRDA outperforms the SRDA, the MRDA, and the EnKF-HR at a given computational cost. The benefit is the largest compared to the EnKF-HR for small ensembles. However, even with larger computational resources, using a mix of high and low-resolution members is worth it. Besides, the Hybrid SRDA, the EnKF-HR, and the SRDA, unlike the MRDA, prevent the smoothing of dynamical structures of the background error covariance matrix. The Hybrid SRDA method is also attractive because it is customizable to available resources.

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Adaptive Covariance Hybridization for the Assimilation of SST Observations Within a Coupled Earth System Reanalysis

Barthélémy, S., Counillon, F., Wang, Y. 2024: Adaptive Covariance Hybridization for the Assimilation of SST Observations Within a Coupled Earth System Reanalysis. JAMES. https://doi.org/10.1029/2023MS003888

Summary: Data assimilation is a statistical method that reduces uncertainty in a model, based on observations. Because of their ease of implementation, the ensemble data assimilation methods, that rely on the statistics of a finite ensemble of realizations of the model, are popular for climate reanalysis and prediction. However, observations are sparse—mostly near the surface—and the sampling error from data assimilation method introduces a deterioration in the deep ocean. We use a method that complements this ensemble with a pre-existing database of model states to reduce sampling error. We show that the approach substantially reduces error at the intermediate and deep ocean. The method typically requires the tunning of a parameter, but we show that it can be estimated online, achieving the best performance.

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Benefit of vertical localization for sea surface temperature assimilation in isopycnal coordinate model

Wang, Y., Counillon, F., Barthélémy, S., Barth, A. 2022: Benefit of vertical localization for sea surface temperature assimilation in isopycnal coordinate model. Front Clim. https://doi.org/10.3389/fclim.2022.918572

Summary: Sea surface temperature (SST) observations are a critical data set for long-term climate reconstruction. However, their assimilation with an ensemble-based data assimilation method can degrade performance in the ocean interior due to spurious covariances. Assimilation in isopycnal coordinates can delay the degradation, but it remains problematic for long reanalysis. We introduce vertical localization for SST assimilation in the isopycnal coordinate. The tapering functions are formulated empirically from a large pre-industrial ensemble. We propose three schemes: 1) a step function with a small localization radius that updates layers from the surface down to the first layer for which insignificant correlation with SST is found, 2) a step function with a large localization radius that updates layers down to the last layer for which significant correlation with SST is found, and 3) a flattop smooth tapering function. These tapering functions vary spatially and with the calendar month and are applied to isopycnal temperature and salinity. The impact of vertical localization on reanalysis performance is tested in identical twin experiments within the Norwegian Climate Prediction Model (NorCPM) with SST assimilation over the period 1980–2010. The SST assimilation without vertical localization greatly enhances performance in the whole water column but introduces a weak degradation at intermediate depths (e.g., 2,000–4,000 m). Vertical localization greatly reduces the degradation and improves the overall accuracy of the reanalysis, in particular in the North Pacific and the North Atlantic. A weak degradation remains in some regions below 2,000 m in the Southern Ocean. Among the three schemes, scheme 2) outperforms schemes 1) and 3) for temperature and salinity.

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Super-resolution data assimilation

Barthélémy, S., Brajard, J., Bertino, L., Counillon, F. 2022: Super-resolution data assimilation. Ocean Dyn. https://doi.org/10.1007/s10236-022-01523-x

Summary: Increasing model resolution can improve the performance of a data assimilation system because it reduces model error, the system can more optimally use high-resolution observations, and with an ensemble data assimilation method the forecast error covariances are improved. However, increasing the resolution scales with a cubical increase of the computational costs. A method that can more effectively improve performance is introduced here. The novel approach called “Super-resolution data assimilation” (SRDA) is inspired from super-resolution image processing techniques and brought to the data assimilation context. Starting from a low-resolution forecast, a neural network (NN) emulates the fields to high-resolution, assimilates high-resolution observations, and scales it back up to the original resolution for running the next model step. The SRDA is tested with a quasi-geostrophic model in an idealized twin experiment for configurations where the model resolution is twice and four times lower than the reference solution from which pseudo-observations are extracted. The assimilation is performed with an Ensemble Kalman Filter. We show that SRDA outperforms both the low-resolution data assimilation approach and a version of SRDA with cubic spline interpolation instead of NN. The NN’s ability to anticipate the systematic differences between low- and high-resolution model dynamics explains the enhanced performance, in particular by correcting the difference of propagation speed of eddies. With a 25-member ensemble at low resolution, the SRDA computational overhead is 55 percent and the errors reduce by 40 percent, making the performance very close to that of the high-resolution system (52 percent of error reduction) that increases the cost by 800 percent. The reliability of the ensemble system is not degraded by SRDA.

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