Optimum initialization of South Asian seasonal forecast using

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Optimum initialization of South Asian seasonal forecast using climatological relevant singular vectors Siraj Ul

Optimum initialization of South Asian seasonal forecast using climatological relevant singular vectors Siraj Ul Islam and Youmin Tang Environmental Science and Engineering, University of Northern British Columbia, Prince George, BC, Canada NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Forecast Errors • Forecast errors comes from model imperfection and poor initial conditions. To

Forecast Errors • Forecast errors comes from model imperfection and poor initial conditions. To improve initialization: – Knowledge about initial error distribution? – Infinite ensemble members? • Model improvements and good initialization process is essential to achieve skillful forecast. Kang et al, 2007 2 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Forecast Initialization Methods • Random Perturbations – Random perturbation are generated without any consideration

Forecast Initialization Methods • Random Perturbations – Random perturbation are generated without any consideration of model dynamics. • Time Lag Ensemble – Ensemble forecast initialized from different IC with time lag (6 hour, 3 hour etc. ). • Optimized perturbations – Maximize the benefit of ensemble prediction with a finite number of ensembles. 3 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Optimum Perturbations • Initial error grows in the forecasts can be explained by a

Optimum Perturbations • Initial error grows in the forecasts can be explained by a set of ensemble with perturbed forecasts. • Two widely used dynamically constrained methods are – Breeding vectors – Singular vectors (SV) • The goal is to generate few ensemble members to efficiently describe forecast uncertainty -> Fast growing perturbations 4 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Breeding method Breeding takes a pair of forecast perturbations and periodically rescales them down

Breeding method Breeding takes a pair of forecast perturbations and periodically rescales them down and adds them to the new analysis state. Perturbations only grossly reflect analysis errors. (Toth and Kalnay, 1993, 1997; Cai et al. , 2003; Tang and Deng, 2010, 2011). BD (+) perturbation Breeding breeding interval : 1 day, 3 days, 5 days BD (-) perturbation NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017 3(breeding intervals) × 2(mirror images) = 6 ensemble members Rescaling factor (percentage) : 10%

Singular vector (SV) SV method (Palmer et al. , 1994 etc. ) measure the

Singular vector (SV) SV method (Palmer et al. , 1994 etc. ) measure the optimal error growth of nonlinear dynamic systems. – perturbations which grow most rapidly • computationally very expensive for seasonal prediction – requires a linearized version of a real model. • major difficulty in separating the SVs from the unwanted growing modes – SV in GCMs (coupled or uncoupled) • This methods has been implemented mainly on ensemble weather forecast. Tang et al. , 2006 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017 6

Climatically-relevant SV (CSV) • Its is modified SV method where the fast error growth

Climatically-relevant SV (CSV) • Its is modified SV method where the fast error growth is due to climatically relevant instabilities – running a large ensemble of integrations to average out the weather noise. • CSV is cost efficient since – it does not demand tangent linear and adjoint models. • This method derive SVs with an ensemble of 10– 30 members in a reduced space based using empirical orthogonal function (EOF) modes. 7 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

CSV Application • While the correlation skill of ENSO forecasts have improved remarkably, seasonal

CSV Application • While the correlation skill of ENSO forecasts have improved remarkably, seasonal prediction of climatic features such as the South Asian Monsoon (SAM) still needs substantial efforts. • So far most of the optimized initialization methods are applied for ENSO forecast only. § We have therefore tried to investigate “Can we improve the SAM forecast skill using optimum perturbation? ” 8 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

South Asian Monsoon (SAM) Monsoon systems are caused by the seasonal reversal of winds

South Asian Monsoon (SAM) Monsoon systems are caused by the seasonal reversal of winds due to differential heating between land ocean 9 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

SAM Teleconnections Weak Monsoon Strong Monsoon SAM -ve IOD +ve IOD Indian Ocean ENSO

SAM Teleconnections Weak Monsoon Strong Monsoon SAM -ve IOD +ve IOD Indian Ocean ENSO El-Nino La-Nina IOD and ENSO plays an important role in modulating the SAM depending on the sign and amplitude of these two phenomena. Both influence SAM and interfere constructively or destructively (increase or decrease). 10 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Simulation Tools Model CCSM 3 CCSM 4 CESM 1 Atmosphere CAM 3 (L 26)

Simulation Tools Model CCSM 3 CCSM 4 CESM 1 Atmosphere CAM 3 (L 26) CAM 4 (L 26) CAM 5 (L 30) Dynamics Spectral Finite Volume Ocean POP 2 (L 40) POP 2. 2(L 60) POP 2. 2 (L 60) Land CLM 3 CLM 4 Sea Ice CSIM 4 CICE Coupled Atmosphere Only CCSM 4 CAM 4 (L 26) CAM 5 (L 30) 11 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Model Validation Research Framework CAM 4/CCSM 4 Acquired from National Center for Atmospheric Research

Model Validation Research Framework CAM 4/CCSM 4 Acquired from National Center for Atmospheric Research (NCAR) Control Runs Ensemble Runs Sensitivity Runs Analysis, mean climatology, ENSO teleconnections, air-sea interactions etc. Forecast Seasonal Forecast & Input data preparation Control Forecast Time Lag Forecast Analysis of forecast basic skill, spread etc. Ensemble Runs CSV Runs Sensitivity Runs CSV Forecast Comparison Analysis 12 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Validations Experiments 13 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19

Validations Experiments 13 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

CAM 4/5 and CCSM 4 Validation less overestimation 14 NONLINEAR AND STOCHASTIC PROBLEMS IN

CAM 4/5 and CCSM 4 Validation less overestimation 14 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

June–September (JJAS) anomaly precipitation composites of and monsoon years weak (1982, 1984, 1986, 1987,

June–September (JJAS) anomaly precipitation composites of and monsoon years weak (1982, 1984, 1986, 1987, 1989 and 2002) strong (1980, 1981, 1983, 1988, 1994, 1996, 1998, 2007) 15 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

SAM-ENSO Relationship Predictability spring barrier SST simulations in CCSM 4 are consistent with atmospheric

SAM-ENSO Relationship Predictability spring barrier SST simulations in CCSM 4 are consistent with atmospheric model in coupled mode. NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017 16

Sensitivity Simulations Is consistent SST simulated by CCSM 4 is responding to less precipitation

Sensitivity Simulations Is consistent SST simulated by CCSM 4 is responding to less precipitation or air-sea coupling? 17 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Model Validation Research Framework CAM 4/CCSM 4 Acquired from National Center for Atmospheric Research

Model Validation Research Framework CAM 4/CCSM 4 Acquired from National Center for Atmospheric Research (NCAR) Control Runs Ensemble Runs Sensitivity Runs Analysis, mean climatology, ENSO teleconnections, air-sea interactions etc. Forecast Seasonal Forecast & Input data preparation Control Forecast Time Lag Forecast Analysis of forecast basic skill, spread etc. Ensemble Runs CSV Runs Sensitivity Runs CSV Forecast Comparison Analysis 18 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Experiments for CSV Implementation Exp. Name Description Perturbation Domain Time Span Initial Conditions (IC)

Experiments for CSV Implementation Exp. Name Description Perturbation Domain Time Span Initial Conditions (IC) No of EOFs used Ensemble Members for each EOF IO 30 years perturb run using EOFs as perturbations Indian Ocean 1980 -2009 Control run IC created with prescribed SST 3 10 IO 10 10 years perturb run using EOFs as perturbations Indian Ocean 2000 -2009 Observed IC from NCAR’s DART system 3 and 10 10 and 20 PO 10 30 years perturb run using EOFs as perturbations Pacific Ocean 2000 -2009 Observed IC from NCAR’s DART system 3 10 IO_CCSM 4 4 years coupled run using EOFs as perturbations Indian Ocean 2000, 2004, 2008 and 2009 Observed IC from NCAR’s DART system + 100 Year control run SST 3 10 TLE Time Lag Ensemble forecast - 2000 -2009 6 hours lag observed IC from NCAR’s DART system - 6 CSVp Ensemble forecast using +ve CSV as perturbations Indian Ocean 2000 -2009 Observed IC from NCAR’s DART system - 10 CSVn Ensemble forecast using –ve CSV as perturbations Indian Ocean 2000 -2009 Observed IC from NCAR’s DART system - 10 30 CSVp Ensemble forecast using +ve CSV as perturbations Indian Ocean 1980 -2009 Control run IC created with prescribed SST - 10 Control Forecast Ensemble forecast without CSV perturbation - 2000 -2009 and 1980 -2009 Observed IC from NCAR’s DART system - 10 All experiments start from Jun 1 st of every year with lead time of 4 months (June, July, August and September, JJAS). In CAM 4 experiments, persistence SST is used as boundary conditions (BC) whereas in CCSM 4, SST is used from the multiyear control run of ocean model. NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017 19

Time Lag Ensemble (TLE) We initialized SAM forecast at previous times as well as

Time Lag Ensemble (TLE) We initialized SAM forecast at previous times as well as at the current time. Initialization Prediction 6 ensemble members (6 hr lag) However, this method do not capture optimal perturbation, which represents the maximum portion of forecast errors with a limited ensemble size. 20 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

CSV Perturbation and Target Variables Models = CAM 4 Climate System = Monsoon Season

CSV Perturbation and Target Variables Models = CAM 4 Climate System = Monsoon Season = JJAS Initial Perturbation Variable = SST Target Variable = OLR Time Period = 2000 -2009 and 1980 -2010 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

SST EOFs Patterns Used for Perturbation Indian Ocean Pacific Ocean NONLINEAR AND STOCHASTIC PROBLEMS

SST EOFs Patterns Used for Perturbation Indian Ocean Pacific Ocean NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017 22

CSV Theory Perturbed Ensemble Mean Control Ensemble Mean EOF Patterns SVD analysis of operator

CSV Theory Perturbed Ensemble Mean Control Ensemble Mean EOF Patterns SVD analysis of operator R yield SVs, Singular values and Final Patterns (FP) 23 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Why only OLR? Mean climatology of June, July, August and September for Outgoing Longwave

Why only OLR? Mean climatology of June, July, August and September for Outgoing Longwave Radiation (OLR). Much better climatology than precipitation 24 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Why only OLR? Singular values grows fro more than two months. 25 NONLINEAR AND

Why only OLR? Singular values grows fro more than two months. 25 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Number of EOFs Vs Ensemble Members The convergence of the leading singular values with

Number of EOFs Vs Ensemble Members The convergence of the leading singular values with increasing number of ensemble members, optimized for 4 month time interval. Each color line represent individual year. In each year, 20 singular values are calculated by increasing the ensemble size from 1 to 20 in the CSV method. 26 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

The first leading EOF patterns of the CSVs (left) and FPs (right) computed over

The first leading EOF patterns of the CSVs (left) and FPs (right) computed over 10 individual CSV patterns for all the four lead times. CSVs are extracted over Indian Ocean. 27 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Leading EOF of OLR FPs, at lead time 3 (a) calculated using CSV as

Leading EOF of OLR FPs, at lead time 3 (a) calculated using CSV as perturbation (b) estimated by applying linear propagator R to CSV 28 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

SAM Ensemble Forecast using CSVs as perturbation (a) RMSE calculated over 10 years (2000

SAM Ensemble Forecast using CSVs as perturbation (a) RMSE calculated over 10 years (2000 -2009 using observed initial conditions) (b) RMSE is for 30 years forecast (1980 -2009 using CAM 4 control initial conditions). 29 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

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Future Work Using CCSM 4 The leading SST CSVs and OLR FPs for lead

Future Work Using CCSM 4 The leading SST CSVs and OLR FPs for lead time 0, 1, 2 and 3 obtained using CCSM 4 model. (Line) Lead time variation of CCSM 4 singular values over Indian Ocean 31 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Summary • The structure of monsoon are well reproduced in CCSM 4 and CAM

Summary • The structure of monsoon are well reproduced in CCSM 4 and CAM 4 along with biases (mostly overestimation). • Forcing CAM 4 with coupled model SST clarified the impact of the air-sea coupling in the interannual variability of the SAM precipitation. • CSV resembles a dipole-like structure over the Indian Oceans. When the CSVs are extracted over the Indian Ocean, their growth rates are found to be more consistent with the increase of lead time. • Ensemble forecast generated by CSV perturbations has a more reliable ensemble mean compared to both the TLE mean and the control forecast. • Methods such as CSV have potential for long term climate prediction. For example, Hawkins and Sutton (2011) applied this method to decadal predictions of the Atlantic Ocean. 32 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

A simple forecast model 33 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION,

A simple forecast model 33 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

Extra 34 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24,

Extra 34 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

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Influence of SST bias (Sensitivity Runs) 36 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND

Influence of SST bias (Sensitivity Runs) 36 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

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2004 El Nino 2007 La Nina 2008 La Nina 2009 El Nino 2003 and

2004 El Nino 2007 La Nina 2008 La Nina 2009 El Nino 2003 and 2007 IOD 38 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

CAM Evolution Model CCSM 3 ( 2004 ) CCSM 3. 5 ( 2007 )

CAM Evolution Model CCSM 3 ( 2004 ) CCSM 3. 5 ( 2007 ) CCSM 4 ( Apr 2010 ) CESM 1 ( Jun 2010 ) Atmosphere CAM 3 (L 26) CAM 3. 5 (L 26) CAM 4 (L 26) CAM 5 (L 30) Boundary Layer Turbulence Holtslag-Boville(93) Shallow Convection Deep Convection Holtslag-Boville Dry Turbulence Hack (94) Bretherton Park(09) UW Moist Turbulence Hack Park-Bretherton (09) UW Shallow Convection Zhang-Mc. Farlane (95) Zhang-Mc. Farlane Neale et al. (08) Richter-Rasch(08) Zhang et al. Park-Bretherton Rasch (10) with Park & Vavrus’ mods. Revised Cloud Macrophysics Zhang et al. (03) Stratiform Microphysics Rasch-Kristjansson (98) Rasch-Kristian. Morrison and Gettelman (08) Single Moment Double Moment Radiation / Optics CAMRT (01) CAMRT RRTMG Aerosols Bulk Aerosol Model (BAM) BAM Dynamics Spectral Finite Volume (96, 04) Finite Volume Ocean POP 2 (L 40) POP 2. 1 (L 60) POP 2. 2 -BGC POP 2. 2 Land CLM 3. 5 CLM 4 -CN CLM 4 Sea Ice CSIM 4 CICE Iaconoet al. (08) / Mitchell (08) BAM Modal Aerosol Model (MAM) Liu& Ghan(2009) 39 Slide taken from NCAR CCSM 4 tutorials (modified) NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

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Indian Ocean Dipole (IOD) 41 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION,

Indian Ocean Dipole (IOD) 41 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

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Singular Vector 43 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19

Singular Vector 43 NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017

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2 -tier Climate prediction system 1 -tier Climate prediction system Atmosphere Prescribe SST as

2 -tier Climate prediction system 1 -tier Climate prediction system Atmosphere Prescribe SST as boundary condition Ocean SST Prediction SST prediction skill Coupling of atmosphere and ocean process NONLINEAR AND STOCHASTIC PROBLEMS IN ATMOSPHERIC AND OCEANIC PREDICTION, NOV. 19 -24, 2017