Empirical determination of the covariance of forecast errors: An empirical justification and reformulation of hybrid covariance models

Carrió, Diego S.; Bishop, Craig H.; Kotsuki, Shunji

doi:10.1002/qj.4008

Cited by 4 publications

(4 citation statements)

References 32 publications

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“…This improvement is likely because the hybrid covariance model has a higher rank, allowing it to fit more observations, and that it also has more accurate background error covariances between widely separated locations as empirically demonstrated with SPEEDY (cf. Figure 9 of Carrió et al 2021). As the localization scale increased, the optimal hybrid parameter α shifted to smaller values to mitigate the impacts of sampling noise from the ensemble-based error covariance for observations that were distant from the analysis grid points.…”

Section: Hybrid Letkf For Da Cycle Experimentsmentioning

confidence: 99%

“…Therefore, the improvement in Figure 11d would be mainly owing to improved background error covariance rather than the increased rank. Hybrid background error covariance provides more accurate estimates than does ensemble-based error covariance (Carrió et al 2021).…”

Section: Impacts Of Applying Different Localization Scalesmentioning

confidence: 99%

“…This approach was first investigated by Hamill and Snyder (2000) and Lorenc (2003), who estimated the error covariance through the linear combination of climatological and flow-dependent error covariance. Carrió et al (2021) compared true forecast error covariance and static/flow-dependent error covariance using an intermediate atmospheric global circulation model and found that the hybrid approach provided better estimates on forecast error covariance than both static and flow-dependent methods. The hybrid approach has been used mainly in variational DA systems to incorporate flow-dependent error covariances in addition to static error covariance.…”

Section: Introductionmentioning

confidence: 99%

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Implementing Hybrid Background Error Covariance into the LETKF with Attenuation-Based Localization: Experiments with a Simplified AGCM

Kotsuki

Bishop

2022

Monthly Weather Review

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Recent numerical weather prediction systems have significantly improved medium-range forecasts by implementing hybrid background error covariance, for which climatological (static) and ensemble-based (flow-dependent) error covariance are combined. While the hybrid approach has been investigated mainly in variational systems, this study aims at exploring methods for implementing the hybrid approach for the local ensemble transform Kalman filter (LETKF). Following Kretchmer et al. (2015), the present study constructed hybrid background error covariance by adding collections of climatological perturbations to the forecast ensemble. In addition, this study proposes a new localization method that attenuates the ensemble perturbation (Z-localization) instead of inflating observation error variance (R-localization). A series of experiments with a simplified global atmospheric model revealed that the hybrid LETKF resulted in smaller forecast errors than the LETKF, especially in sparsely observed regions. Due to the larger ensemble enabled by the hybrid approach, optimal localization length scales for the hybrid LETKF were larger than those for the LETKF. With the LETKF, the Z-localization resulted in similar forecast errors as the R-localization. However, Z-localization has an advantage in enabling to apply different localization scales for flow-dependent perturbation and climatological static perturbations with the hybrid LETKF. The optimal localization for climatological perturbations was slightly larger than that for flow-dependent perturbations. This study proposes Optimal EigenDecomposition (OED) ETKF formulation to reduce computational costs. The computational expense of the OED ETKF formulation became significantly smaller than that of standard ETKF formulations as the number of climatological perturbations was increased beyond a few hundred.

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Section: Hybrid Letkf For Da Cycle Experimentsmentioning

confidence: 99%

Section: Impacts Of Applying Different Localization Scalesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Implementing Hybrid Background Error Covariance into the LETKF with Attenuation-Based Localization: Experiments with a Simplified AGCM

Kotsuki

Bishop

2022

Monthly Weather Review

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“…Covariance hybridization (Hamill & Snyder, 2000) linearly combines the flow‐dependent covariance computed from a finite Monte‐Carlo ensemble with another covariance matrix that is less prone to sampling error. The static matrix can be parameterized (Hamill & Snyder, 2000; Weaver & Courtier, 2001), computed from a long model simulation (Counillon et al., 2009), computed as the average of the background error covariance matrices from a previous data assimilation run (Carrió et al., 2021) or computed from a dynamical ensemble at a lower resolution (Rainwater & Hunt, 2013). The hybrid covariance method achieves better performance than the standalone EnKF, particularly for small ensembles, and performance converges to that of the EnKF for large ensembles (Counillon et al., 2009; Raboudi et al., 2019; X. Wang et al., 2007).…”

Section: Introductionmentioning

confidence: 99%

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

Barthélémy,

Counillon,

Wang

2024

J Adv Model Earth Syst

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Ensemble data assimilation methods, such as the Ensemble Kalman Filter (EnKF), are well suited for climate reanalysis because they feature flow‐dependent covariance. However, because Earth System Models are heavy computationally, the method uses a few tens of members. Sampling error in the covariance matrix can introduce biases in the deep ocean, which may cause a drift in the reanalysis and in the predictions. Here, we assess the potential of the hybrid covariance approach (EnKF‐OI) to counteract sampling error. The EnKF‐OI combines the flow‐dependent covariance computed from a dynamical ensemble with another covariance matrix that is static but less prone to sampling error. We test the method within the Norwegian Climate Prediction Model, which combines the Norwegian Earth System Model and the EnKF. We test the performance of the reanalyzes in an idealized twin experiment, where we assimilate synthetic sea surface temperature observations monthly over 1980–2010. The dynamical and static ensembles consist respectively of 30 members and 315 seasonal members sampled from a pre‐industrial run. We compare the performance of the EnKF to an EnKF‐OI with a global hybrid coefficient, referred to as standard hybrid, and an EnKF‐OI with adaptive hybrid coefficients estimated in space and time. Both hybrid covariance methods cure the bias introduced by the EnKF at intermediate and deep water. The adaptive EnKF‐OI performs best overall by addressing sampling noise and rank deficiencies issues and can sustain low analysis errors by doing smaller updates than the standard hybrid version.

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High-Resolution Data Assimilation for Two Maritime Extreme Weather Events: A Comparison between 3dvar and Enkf

Carrió Carrió,

Mazzarella,

Ferretti

2024

Preprint

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Empirical determination of the covariance of forecast errors: An empirical justification and reformulation of hybrid covariance models

Cited by 4 publications

References 32 publications

Implementing Hybrid Background Error Covariance into the LETKF with Attenuation-Based Localization: Experiments with a Simplified AGCM

Implementing Hybrid Background Error Covariance into the LETKF with Attenuation-Based Localization: Experiments with a Simplified AGCM

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

High-Resolution Data Assimilation for Two Maritime Extreme Weather Events: A Comparison between 3dvar and Enkf

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