1. Towards Improving Coupled Climate Model Using EnKF Parameter Optimization Towards Improving Coupled Climate Model Using EnKF Parameter Optimization Zhengyu Liu 1, Shaoqing Zhang 2, Yun Liu 1 R. Jacob 3, Xinrong Wu 4, Xuefeng Zhang 4, Feiyu Lu 1 1. Univ. Wisconsin-Madison 2. GFDL/NOAA, USA 3. ANL/DOE 4. NMDIS/SOA, China

2. Motivation: Coupled Model Biases SST (shading), Rainfall (contour) Prep Latitude Lin, 2007, JC

3. Improve a complex climate model directly in the coupled mode? (after the tuning of each component model) Objective Model biases Structure biasesParameter biases Parameter Estimation using Data Assimilation: 4D Var: adjoint in CGCM EnKF: forward modeling, practical for a complex system

4. Meso-scale weather model Objective: improve forecasting error, Approach: time-marching EnKF on synoptic obs (Anderson, 2001) Aksoy et al., 2006a (perfect model) Aksoy et al, 2006b (perfect model) Tong and Xue, 2007 (perfect model) Hu et al., 2010 (real data) ……. Climate model Objective: reduce climatology bias for projection Approach: Iterative EnKF on climatological obs (Annan et al., 2004) Annan et al., 2005: AGCM (reanalysis atmosphere) Edwards and March, 2005: OGCM (perfect model, ocean obs) Ridgewell et al., 2007: Marine BGC model (real data, ocean obs) EnKF Parameter Optimization Anderson, J., 2001: Lorenz Model: Variable Augmentation and prediction

5. EnKF Parameter Optimization for Coupled Models Potential Issues Different time scales: fast processes, slow processes, coupled processes Biases in climatology, climate variability, “climate noise” e.g: tropical bias, ENSO, NAO,.. atmos. synoptics Biases in single component (before coupling) vs. coupled system Atmosphere obs + Ocean obs + (other system component obs) Great spatial variation: low vs high lat? ocean vs land? …. …..

6. EnKF Parameter Optimization for Coupled Models Outline A conceptual coupled model study (perfect model) Zhang S., Liu, Z., A. Rosati and T. Delworthy, 2012. A study of enhancive parameter correction with coupled data assimilation for climate simulation and prediction using a simple coupled model. Tellus, A first try! A CGCM study (perfect model) Liu Y., Z. Liu, S. Zhang, X. Rong, R. Jacob, S. Wu and F. Lu, 2014: Ensemble-based parameter estimation in a coupled GCM using the adaptive spatial average method. J. Climate (in press) First Success in CGCM! A intermediate coupled model study (“biased physics”) Zhang X., S. Zhang, Z. Liu, X. Wu and G. Han, 2014: Parameter optimization in an intermediate coupled climate model with biased physics. J. Climate (in rev) Further challenges… All use EAKF (Anderson, J., 2001)

7. A Conceptual Model Study (“Perfect Model”) Obs Frq: different in A (1 day) and O (4 day) N=20 Initial para error ~10% Fixed low threshold of para ensemble spread (as in Askoy et al. 2006) Correlation cut-off Atmos Ocean (O m =10) Step 1: State estimation to quasi-equilibrium Step 2: Simultaneous state-para estimation Zhang S. et al., 2011, Tellus Spin-up

8. Multi-parameter Estimation Zhang S. et al., 2011, Tellus

9. Fast Ocean Atmosphere Model (FOAM) (Jacob, 2007) Atmosphere: CCM2 R15 +CCM3 Physics Ocean: POP-like 2.4 o x1.2 o x24-levels Obs. Err = 10% Std(CTRL) SST Obs: 1 monthly (gridded) Atmosphere Obs: T, U, V, 12 hrly (gridded) N=30 members Ocean/Atmosphere coupling covariance not used Localization: atmos: 1000 km, ocn:500 km Parameters: Solar Penetration Depth (SPD) + Other parameters A CGCM Study (“Perfect Model”) Liu Y., PH.D thesis Liu Y. et al., 2014a,b, J. Clim

10. Parameter Sensitivity a) SST: ann. climatology sensitivity c) SST: 1 month sensitivity (Dec) b) SST: 1 month sensitivity (June) a) SST: ann. climatology sensitivity c) SST: 1 month sensitivity (Dec) b) SST: 1 month sensitivity (June) a) SST: ann. climatology sensitivity c) SST: 1 month sensitivity (Dec) b) SST: 1 month sensitivity (June) a) SST: ann. climatology sensitivity a) D SST: ann. SPD 20m - 17m b) c) Liu Y. et al., 2014, J. Clim 1 month sensitivity Ensemble spread: June Climatology sensitivity 1 month sensitivity, Ensemble spread Dec

11. Estimation of SPD Liu Y. et al., 2014, J. Clim Year Assimilation of monthly SST obs only

12. Adaptive Spatial Average Scheme (ASA) Liu Y. et al., 2014, J. Clim For a global uniform parameter Spatial updating (localization): GPO (Wu et al. 2012) SA (Spatial Average): Askoy et al., 2006 ASA (Adaptive Spatial Average): Liu Y. et al., 2014

13. Spatial Variation of Parameter Sensitivity a) SST: ann. climatology sensitivity c) SST: 1 month sensitivity (Dec) b) SST: 1 month sensitivity (June) a) SST: ann. climatology sensitivity c) SST: 1 month sensitivity (Dec) b) SST: 1 month sensitivity (June) a) SST: ann. climatology sensitivity c) SST: 1 month sensitivity (Dec) b) SST: 1 month sensitivity (June) a) SST: ann. climatology sensitivity a) D SST: ann. SPD 20m - 17m b) c) Liu Y. et al., 2014, J. Clim 1 month sensitivity Ensemble spread: June Climatology sensitivity 1 month sensitivity, Ensemble spread Dec

14. ASA: Quality of Estimation and Ensemble Spread ASA (Adaptive Spatial Average): A good estimate ~ small posterior ensemble spread σ(β) β=SPD x=SST Liu Y. et al., 2014, J. Clim σ(SPD) rmse(SPD) Obs = truthObs = truth + error rmse(SPD) σ(SPD) SPD % average grids

15. Summary Different time scales…? Spatial and temporal (stochastic) variation ? Preliminary results encouraging Parameter optimization seems feasible for CGCMs, but Real world parameter optimization most challenging! Flux adjustment? Physical mechanism ? (breeding mode?) Earth system model?