Effects of model error on ensemble forecast using the EnKF Hiroshi Koyama 1 and Masahiro Watanabe 2 1 : Center for Climate System Research, University of Tokyo / Environmental Science, Hokkaido University 2 : Center for Climate System Research, University of Tokyo UAW 2008, 1 July 2008

Introduction  The ensemble forecast error of numerical weather prediction is caused not only by inaccurate initial conditions but also by model deficiencies.  The model deficiencies can have an impact on the forecast error in the one-month forecast. Model deficiencies  The method to improve measures against the model deficiencies  There is little method with theoretical proof for effectiveness Model ensemble

 The feature of the prediction scores in the one-month ensemble forecast with model error  The effectiveness of model ensemble methods Purpose Method  The prediction scores on imperfect model with model errors are compared to those on perfect model  Initial ensemble members are generated by EnKF  Introduce model ensembles  Models : 1. Lorenz’96 model (low-order) 2. AGCM (high-order) Purpose and Method

The EnKF ( Ensemble Kalman Filter; Evensen 1994 ) is the technique for uniting ensemble forecast and data assimilation. Observation Analysis (Data assimilation) Ensemble forecast ＋ Initial perturbations for next forecast Ensemble Kalman Filter True By repeated the cycle of ensemble forecast and data assimilation, the best analysis and initial perturbation will be obtained. ＋ Ensemble forecast

x : large-scale, y : small-scale y fluctuate more rapidly than x x : forecast variables, directly computable y : sub-grid scale processes, unresolved M = 8, N = 4 F=10, h=1, c=10, b = 10 (Smith2000, Orrell2002) Periodic boundary Loenz’96 model (Lorenz 1996) Time evolution of x and y Lorenz96-EnKF : Model AGCM x y

( Smith2000,Orrel2003,Wilks2005 ) Imperfect model with model error The term of y is approximated by the linear regression of x. y is not calculated. (Parameterization of y) Perfect model without model error y term in the equation of x Imperfect model Perfect model Lorenz96-EnKF : Model Good as primary approximation

EnKF  Serial EnSRF （ Whitaker and Hamill 2002 ）  Number of initial members ： 50  S.D. of observation error ： x = 0.2, y = 0.02  Assimilated interval ： 0.05 （≒ 6 hours on real atmosphere ）  Online estimation of covariance inflation （ Miyoshi and Kalnay 2005 ）  Localization of covariance matrix （ Gaspari and Cohn 1999 ） True and Observation  True ： Control run in perfect model  Observation ： True + Gaussian random noise Lorenz96-EnKF : Experimental design

= （ RMSE in imperfect model ）－（ RMSE in perfect model ） Perfect model Model error is the maximum at about day 8 forecast Lorenz96-EnKF : Result Imperfect model Model error  Predictability limit is about 20 days.  Spread is almost equal to RMSE  Predictability limit is about 15 days.  Spread is considerably smaller than RMSE Forecast day RMSE (Climatology) RMSE (Climatology) RMSE(Control run) RMSE Spread RMSE Spread imperfect perfect

 Random coefficient is multiplied by parameterization term  This coefficient is different in every member and every step (Buizza et al.1999) 1. Stochastic physics method (STC) 2. Multi parameter method (MLT) Model ensembles Lorenz96-EnKF : Model ensembles  Multiple parameter set are created by adding parameter perturbations to control parameters  Initial ensemble forecast run independently for each parameter set  (Total member) = (Initial member) x (Parameter member) : Gaussian noise k : k th member w k : amplitude Parameter set : : parameterization term

NON STC MLT NON STC MLT Both model ensemble methods are effective on reducing model error and optimizing spread.  By introducing model ensemble, model error is reduced after day 7 forecast.  By introducing model ensemble, Spread / RMSE is close to 1. Model error Spread / RMSE Lorenz96-EnKF : Result Forecast day NON : without model ensemble MLT : multi-parameter STC : stochastic physics

 CCSR/NIES/FRCGC AGCM 5.7b  T21L11 global spectral model  Forecast variables ： u, v, t, ps, q EnKF The same package used in the Lorenz 96 model  Ensemble members : 32  Assimilated interval : 6 hours  Simultaneous estimation of covariance inflation and observation errors (Li et al.) Type of experiment Scenario nameModelTrueObservation Perfect AGCM Control run of AGCM True ＋ Gaussian random noise Imperfect JRA-25 re-analysis data （ Nov2007, 6houly ） AGCM AGCM-EnKF : Experimental design

 RMSE is smaller than S.D. of observation error.  Spread is equal to RMSE  Stability for 3 months Perfect RMSE Spread T 500 Z 500 RMSE Spread  Predictability limit is about 20 days.  Similar to the result of Lorenz’96 model AGCM-EnKF : Result  Assimilated spread is considerably smaller than RMSE  Forecast spread is also so geography ? Land surface variables ? Imperfect T 500 assimilation forecast assimilationforecast Spread RMSE Spread Forecast day Date

Conclusion and Perspectives By using Lorez’96 model with model error, the one-month forecasts are started from initial perturbation created by EnKF.  Model error is the maximum at about day 8 forecast.  Model ensemble methods are effective on reducing model error and optimizing spread  To continue the experiment using AGCM.  To find systematic relationship between model deficiency and model error.  To find and evaluate more effective model ensemble methods Conclusion Perspectives