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 – September 14, 2015 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 – September 14, 2015 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 covariancesStatic covariances Currently used in 3DVar: constant variances constant correlation lengthscale

Page 4 – September 14, 2015 Ensemble assimilation (with perturbed observations) Forecast step Background, Observations, Static B R Analysis, Analysis step Deterministic assimilationEnsemble of assimilations using ensemble covariances Analyses Ensemble forecast step Backgrounds Ensemble analysis step Ensemble B Perturbed observations R Obs,

Page 5 – September 14, 2015 First step: Ensemble of 3DVars (static B) Ensemble forecasts Analyses Backgrounds Ensemble analyses Static B Perturbed observations R Obs, Ensemble B Experiments for evaluating ensemble spread and tuning model error simulation

Page 6 – September 14, 2015 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

Page 7 – September 14, 2015 Model biases Problem 1: model doesn’t represent fast ice Problem 2: model bias introduced through biases in atmospheric and ocean forcings Ensemble mean Strong winds incorrectly cause the ice to move in all ensemble members Ensemble spread Ensemble spread is very low, but mean error is very high Canadian Arctic Archipelago, July 2011, fast ice case

Page 8 – September 14, 2015 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 – September 14, 2015 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 – September 14, 2015 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 RMSE spread

Page 11 – September 14, 2015 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) RMSE spread

Page 12 – September 14, 2015 Average observed ice concentration (in daily ice charts) Bottom: RMSE of ensemble mean & ensemble spread Time-averaged ensemble spread and RMSE maps

Page 13 – September 14, 2015 Second step: First EnVar experiments Background Analysis Forecast step Backgrounds Analysis step Ensemble B R Obs, Using ensemble covariances from the ‘ensemble of 3DVars’ experiment in the EnVar data assimilation

Page 14 – September 14, 2015 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 – September 14, 2015 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 60% 50% 40% 30% 20% 10% 0% -10% -20% -30% -40% -50% -60% 60% 50% 40% 30% 20% 10% 0% -10% -20% -30% -40% -50% -60%

Page 16 – September 14, 2015 EnVar ice concentration analysis example (July 18, 2011) Using static covariancesUsing ensemble covariances Less negative ice concentration artefacts in analysis in the ensemble covariances case 100% 80% 60% 40% 20% 0% -20% -40% 100% 80% 60% 40% 20% 0% -20% -40%

Page 17 – September 14, 2015 EnVar analysis example: updating unobserved variables Background ice concentration field Ice concentration increment SST increment, degrees Ice thickness increment, meters 60% 50% 40% 30% 20% 10% 0% -10% -20% -30% -40% -50% -60%

Page 18 – September 14, 2015 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 – September 14, 2015 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

Page 21 – September 14, 2015 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