Towards Improving Coupled Climate ModelUsing EnKF Parameter Optimization

Towards Improving Coupled Climate ModelUsing EnKF Parameter Optimization

Zhengyu Liu1, Shaoqing Zhang2, Yun Liu1

R. Jacob3, Xinrong Wu4, Xuefeng Zhang4, Feiyu Lu1

1. Univ. Wisconsin-Madison2. GFDL/NOAA, USA3. ANL/DOE4. NMDIS/SOA, China

Motivation: Motivation: CoupledCoupled Model Biases Model Biases

SST (shading), Rainfall (contour)

Pre

p

Latitude

Lin, 2007, JC

Improve a complex climate model directly in the coupled mode?(after the tuning of each component model)

ObjectiveObjective

Model biases

Structure biases Parameter biases

Parameter Estimation using Data Assimilation:

4D Var: adjoint in CGCM

EnKF: forward modeling, practical for a complex system

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 OptimizationEnKF Parameter Optimization

Anderson, J., 2001: Lorenz Model: Variable Augmentation

and prediction

EnKF Parameter Optimization for Coupled ModelsEnKF 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? ….

…..

EnKF Parameter Optimization for Coupled ModelsEnKF 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)

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(Om=10)

Step 1: State estimation to quasi-equilibriumStep 2: Simultaneous state-para estimationZhang S. et al., 2011, Tellus

Sp

in-u

p

Multi-parameter Estimation

Zhang S. et al., 2011, Tellus

Fast Ocean Atmosphere Model (FOAM) (Jacob, 2007)Atmosphere: CCM2 R15 +CCM3 PhysicsOcean: POP-like 2.4ox1.2ox24-levels

Obs. Err = 10% Std(CTRL)SST Obs: 1 monthly (gridded)Atmosphere Obs: T, U, V, 12 hrly (gridded)

N=30 membersOcean/Atmosphere coupling covariance not usedLocalization: atmos: 1000 km, ocn:500 kmParameters: Solar Penetration Depth (SPD) + Other parameters

A CGCM Study (“Perfect Model”)

Liu Y., PH.D thesisLiu Y. et al., 2014a,b, J. Clim

Parameter Sensitivity

a) SST: ann. climatology sensitivity

c) SST: 1 month sensitivity (Dec)

b) SST: 1 month sensitivity (June)

a) SST: ann. climatology sensitivitya) D SST: ann. SPD 20m - 17m

b) <SST, SST>

c) <SST, SST>

Liu Y. et al., 2014, J. Clim

1 month sensitivityEnsemble spread: June

Climatology sensitivity

1 month sensitivity,Ensemble spreadDec

Estimation of SPD

Liu Y. et al., 2014, J. Clim

Year

Assimilation of monthly SST obs only

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

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 sensitivitya) D SST: ann. SPD 20m - 17m

b) <SST, SST>

c) <SST, SST>

Liu Y. et al., 2014, J. Clim

1 month sensitivityEnsemble spread: June

Climatology sensitivity

1 month sensitivity,Ensemble spreadDec

ASA: Quality of Estimation and Ensemble Spread

ASA (Adaptive Spatial Average):

A good estimate~ small posterior ensemble spread σ(β)

β=SPDx=SST

Liu Y. et al., 2014, J. Clim

σ(SPD)

rmse(SPD)

Obs = truth Obs = truth + error

rmse

(SP

D)

rmse

(SP

D)

σ(SPD) σ(SPD)

SP

D

SP

D

% average grids % average grids

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?