Ensemble-variational sea ice data assimilation

Anna Shlyaeva, Mark Buehner, Alain Caya,Data Assimilation and Satellite Meteorology Research

Jean-Francois Lemieux, Gregory Smith, Francois Roy, Environmental Numerical Prediction Research

Tom Carrieres Canadian Ice Service

Environment Canada

Page 2 – April 19, 2023

Regional Ice Prediction System (RIPS)

• Four 3DVar analyses per day of ice concentration at 5 km resolution on rotated lat-lon grid

• Observations assimilated:– SSMI and SSMIS NT2 retrievals– ASCAT observations– Canadian Ice Service ice charts

• Four 48hr CICE v.4.0 forecasts per day on CREG12 (subset of ORCA12) domain

• Atmospheric forcings from GEM, ocean forcings and initial fields from GIOPS

Page 3 – April 19, 2023

• state-dependent variances

• anisotropic covariances

Motivation to use ensembles

• Provide an estimate of the uncertainty in the analysis and background states

• Provide initial conditions for ensemble forecasts

• Improve how observations are assimilated by using improved background-error covariances obtained from ensembles:

Higher variances in marginal ice zone

Lower variances in open water and inside packed ice

Ensemble covariances Static covariances Currently used in 3DVar:

• constant variances

• constant correlation lengthscale

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Ensemble assimilation (with perturbed observations)

Forecast step

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Observations,

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Deterministic assimilation Ensemble of assimilations usingensemble covariances

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Page 5 – April 19, 2023

First step: Ensemble of 3DVars (static B)

Ensemble forecasts

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Experiments for evaluating ensemble spread and tuning model error simulation

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Simulation of uncertainties in forcings and initial fields

• Using ensemble atmospheric forecasts (Global Ensemble Prediction System) to force CICE

• Perturbing sea surface temperature (SST) and mixed layer depth (MLD) with differences between forecasts valid at the same time (NMC-like approach)

• Multiplying ocean current speed by a random number ~N(1,0.05)

• Initial spread generated by horizontally correlated ice concentration perturbations only near the marginal ice zone

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Model biases

• Problem 1: model doesn’t represent fast ice

• Problem 2: model bias introduced through biases in atmospheric and ocean forcings

Ensemble meanStrong winds incorrectly cause the ice to move in all ensemble members

Ensemble spreadEnsemble spread is very low, butmean error is very high

Canadian Arctic Archipelago, July 2011, fast ice case

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Extreme sea ice model error parametrization

• 21 ensemble member:– 7 members: full CICE model– 7 members: CICE dynamics only– 7 members: CICE thermodynamics only

• Motivation– Dynamics: 1/3 of ensemble members don’t move: increased

ensemble spread in the ‘ice shouldn’t move, but it’s moving’ case

– Thermodynamics: 1/3 of ensemble members don’t melt/freeze: increased ensemble spread in the ‘error in the forcings causing biases due to incorrect melt/freeze’ case

Page 9 – April 19, 2023

Ensemble of 3DVars experiment

• Experiment June 8, 2011 – September 30, 2011– Summer is the hardest period both for the analyses and for the

forecasts

• Observations perturbed with correlated errors (approach similar to initial ice concentration perturbations)

• Assimilated observations:– SSMI NT2 retrievals– SSMI/S NT2 retrievals– ASCAT observations– Canadian Ice Service ice charts

• Verification based on Canadian Ice Service daily ice charts (available for different regions)

Page 10 – April 19, 2023

• Statistics averaged over Foxe Basin ice charts for ice points with 10%-90% ice concentration (dashed for ensemble spread, solid for RMSE of ensemble mean)

Full ensemble vs 7 members using full model

Background ensemble spread and RMSE of ensemble mean time series

RMSEspread

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• Statistics averaged over Foxe Basin ice charts for ice points with 10%-90% ice concentration (dashed for ensemble spread, solid for RMSE of ensemble mean)

Full ensemble vs 7 members using full model

Background ensemble spread and RMSE of ensemble mean time series

Extreme model error parametrization:

• Improves consistency between ensemble spread and error of ensemble mean (similar growth rates during forecast)

• Results in improved ensemble mean (smaller RMSE)

RMSEspread

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Average observed ice concentration (in daily ice charts)Bottom:RMSE of ensemble mean & ensemble spread

Time-averaged ensemblespread and RMSE maps

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Page 13 – April 19, 2023

Second step: First EnVar experiments

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Using ensemble covariances from the ‘ensemble of 3DVars’ experiment in the EnVar data assimilation

Page 14 – April 19, 2023

EnVar: Single observation experiment

Observation=55%; Background=30%

Left: Background ice concentration

Using static covariances(10 km lengthscale)

Using ensemble covariances(50 km localization distance)

Page 15 – April 19, 2023

EnVar ice concentration analysis increment example (July 18, 2011)

Using static covariances (10 km lengthscale)

Using ensemble covariances(50 km localization distance)

Sharper and stronger increments (close to the ice edge, where there is a strong gradient in variances) in the ensemble covariances case

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EnVar ice concentration analysis example (July 18, 2011)

Using static covariances Using ensemble covariances

Less negative ice concentration artefacts in analysis in the ensemble covariances case

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EnVar analysis example: updating unobserved variables

Background ice concentration field Ice concentration increment

SST increment, degreesIce thickness increment, meters

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Conclusions

• Ensemble of 3DVars strategy:– Appears to give reasonable relationship between ensemble

spread and error in ensemble mean with current approach for simulating model error

– Also plan to compare ‘extreme model error parametrization’ with less extreme approach of perturbing several model parameters (ice-ocean, ice-atmosphere drags, ice rigidity, ice albedo)

• First experiments using EnVar for assimilation:– Sharper and more detailed analysis increments close to the ice

edge due to anisotropic ensemble covariances and strong gradients in ensemble variance

– Ensembles can be used to update other variables, e.g. ice thickness (distribution)

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Page 20 – April 19, 2023

EnVar: using ensemble covariances in 3DVar

• 3DVar cost function:

• Using static B:

• Using ensemble covariances:

where L is localization operator (we use diffusion operator) and

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Ice concentration perturbations

• Generate random field (white noise)• Multiply it by a factor dependent on the ice concentration at the current point

• Apply diffusion operator• Multiply by sigma

Goal: perturb mostly close to the marginal ice zone