Internal Atmospheric Dynamics and Climate Variability

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Internal Atmospheric Dynamics and Climate
Variability

• Ben Kirtman
• George Mason University
• Center for Ocean-Land-Atmosphere Studies

Acknowledgements R. Wu, S.-W. Yeh, D. Min, K.
Pegion and S. Kinter
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• How Does Internal Atmospheric Dynamics Impact
  Climate Variability?
• One-Way Air-Sea Interactions (Atmospheric
  Stochastic Forcing or Noise)
• Ocean as Thermodynamic Red Filter
• Ocean-Dynamics Preferred Time scale
• Two-Way Air-Sea Interactions
• Coupled Feedbacks (stable) Noise
• Coupled Feedbacks (stable) Noise Ocean
  Dynamics
• Unstable Coupled Feedbacks

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• ENSO (Two-way Air-Sea Interactions)
• Self Sustained (Unstable) or Damped ( Noise)
• Damped Linear Dynamics Non-linearity ? Noise
• Noise Amplitude Unrelated to Signal
• Loss of Predictability due to Noise
• Non-normality and Spatial Structure of Noise
• Variations in Predictability Random
• Unstable Non-linear Control of Growth
• Loss of Predictability Chaos vs. Noise
• Details of Noise Not Important
• Signal and Noise Amplitude Dependence
• Variations in Predictability Fundamental
• Testing Generally Requires Ad-Hoc Assumptions
  About the Stochastic Forcing and Simplified
  Theoretically Motivated Models

Null-Hypothesis gt
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Outline

• Motivation and Definitions
• Defining the Noise
• The Interactive Ensemble Impact of Noise in a
  CGCM
• Impact of the Noise
• Global ENSO Teleconnections
• Analysis of Variance (Damped vs. Unstable)
• Ensemble Spread and Mean Predictability
  Implications
• Low Frequency Variability in the Tropical Pacific
• Stochastically Forced Variability
• Decadal Variability of ENSO
• Evidence for Important Non-linearities Properties

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Defining the Noise Due to Internal Atmospheric
Dynamics

• Atmospheric Ensemble Realizations

With Finite Ensembles Can Only Estimate Signal
and Noise
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Using AGCM Ensembles to Isolated the Forced
Seasonal- to-Interannual Signal in Long Climate
Simulations
1 Ensemble Member
2 Ensemble Member
3 Ensemble Member
4,5,6 Ensemble Members
NCEP Analysis
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Coupled GCM Ensemble Realizations
How to Separate Signal and Noise? Assumptions
about the Statistics of the Noise
72 Months
12 Months
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Simple Coupled Model Perspective
? Atmos
Standard Coupled Model
? Ocean
? Atmos
Interactive Ensemble Coupled Model
? Ocean
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Simple Coupled Model Perspective
? Atmos
Standard Coupled Model
? Ocean
Coupled Feedbacks
? Atmos
Interactive Ensemble Coupled Model
? Ocean
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Simple Coupled Model Perspective
? Atmos
Standard Coupled Model
? Ocean
Lag-1 Auto-Correlation
? Atmos
Interactive Ensemble Coupled Model
? Ocean
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Simple Coupled Model Perspective
? Atmos
Standard Coupled Model
? Ocean
Prescribed External Noise
? Atmos
Interactive Ensemble Coupled Model
? Ocean
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CGCM Perspective
? Atmos
Standard Coupled Model
? Ocean
Noise is Internal to the System
? Atmos
Interactive Ensemble Coupled Model
? Ocean
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Anomaly Coupled (i.e., correct climatology)
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The tropical SST variability Standard Coupled
Interactive Ensemble Model
- The NINO3.4 (5?N-5?S,170?E-240?E) SST
variability
The Standard Coupled Model 200 yrs
The Interactive Ensemble Model 500 yrs
Self Sustained, but More Regular and More
Biennial
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Stronger Tropical-Extratropical Telenconnections
Removing Too Much Noise?
Broader Meridional Scale
Reduced Heatflux Noise
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Analysis of Variance
Atmospheric Noise
Ignoring Lag-1 Auto-Correlation
Standard
Ocean Noise
Ocean Variance
Interactive
Ensemble Averaging
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Large Ensemble Limit
M ? 8
If Oceanic Noise Comparable to Atmospheric Noise
Only Relatively Modest Reduction in Variance
Independent of Ensemble Size
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Small Ocean Noise
If Small Ocean Noise and the Null Hypothesis is
Correct
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Weak Coupling
Moderate Coupling
Variance Ratio
Strong Coupling
Ocean Noise/Atmos Noise
Null Hypthesis Ratio1/6
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Including the Lag-1 Auto-Correlation
Weak Coupling
Moderate Coupling
Variance Ratio
Strong Coupling
1/6
Ocean Noise/Atmos Noise
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What to Expect

• If Ratio 1/M
• Stochastically Forced System with Stable Coupled
  Feedbacks and Small Ocean Noise
• If ½ lt Ratio lt 1
• Relatively Large Internal Oceanic Noise?
• Perhaps Unstable Coupled Feedbacks?
• Simple Model Fails Important Non-Linearity?
• If 1 lt Ratio
• Unstable Coupled Feedbacks?
• Simple Model Fails Important Non-Linearity?

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s2 SSTA Standard Coupled
Variance Ratio Standard/Interactive
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Are the Noise and Signal Related?

• Stochastic Climate Model
• Uncertainty and Signal are Independent
• Uncertainty and Signal are Related
• Non-Linearity?
• Signal Measured by Ensemble Mean
• Wind Stress in Nino4
• Uncertainty Measured by Ensemble Spread
• Wind Stress in Nino4

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What to Expect
Interactive Ensemble Stochastic Coupled Model
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Does the SST Depend on the Uncertainty in the
Atmosphere?
Unconditional Distribution Of Ocean Y
Distribution of Ensemble Spread X Of Atmosphere
Conditional Distribution Of Ocean Y
Does the Uncertainty in the Atmosphere Depend on
the SST?
Unconditional Distribution of Ensemble Spread X
Of Atmosphere
Unconditional Distribution of Ensemble Spread X
Of Atmosphere
Unconditional Distribution Of Ocean Y
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What We Get From the Interactive Ensemble CGCM
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Does the Uncertainty Depend on the Signal?
U-Stress (Nino4) Ensemble Spread (Distribution of
Uncertainty)
Conditional Distribution of Spread with an
Easterly Anomaly Small Spread
Unconditional U-Stress (Distribution of Signal)
Does the Uncertainty Depend on the Signal?
Conditional Distribution of Spread with an
Westerly Anomaly Large Spread
Gaussian
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Does the Signal Depend on the Uncertainty?
U-Stress Ensemble Spread
SSTA Distribution Assuming Small Spread
(Uncertainty)
Unconditional SSTA
Does the Signal Depend on the Uncertainty?
U-Stress Ensemble Spread
SSTA Distribution Assuming Large Spread
(Uncertainty)
Unconditional SSTA
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Composite 95-ile SST
Composite 5-ile SST
More Uncertainty in tx for Warm Events Compared
to Cold Events
Composite Zonal Wind Stress Spread
Based on 95-ile SST
Based on 5-ile SST
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Predictability Implications

• Cold Events More Predictable then Warm Events?

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warm
Normal
cold
6 Months Lead
6 Months Lead
Reduced Noise
Standard Model
Nino3.4 ROC Curves
9 Months Lead
9 Months Lead
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Testing The Null Hypothesis

• Variance Ratios Regions of Tropical Indo-Pacific
  Variability that cannot be Explained by the Null
  Hypothesis (i.e. Ratio Larger than one)
• Potential Importance of Ocean Noise
• Uncertainty and Signal Strongly Related,
  Contradicting the Null Hypothesis
• Cold Events more Predictable than Warm Events
• Low Frequency Variations in ENSO Amplitude
  (Predictability)
• Null Hypothesis Determined by Noise and
  Independent of Mean State Changes

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Low Frequency Variability in the Tropical Pacific

• Evidence for Stochastically Forced Modes
• No Impact on ENSO
• Evidence for Non-Linear Processes
• ENSO Residual or Modulator?
• Chicken and Egg Problem

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Tropical decadal variability (10 year running
means) Standard Coupled Model
EOF1 46.4
EOF2 11.7
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Time Series EOF1
10-Year Running Nino3 Variance
Time Series EOF2
10-Year Running Nino3 Variance
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Warm Composite SSTA
Standard Coupled Model
COLD Composite SSTA
Difference in SSTA Variability
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Interactive Ensemble Dominant Mode of Tropical
Pacific Variability
EOF1 41.6
EOF1 28.1
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Interactive Ensemble Six Members
Time Series EOF1
10-year Running Nino3 Variance
Interactive Ensemble Twelve Members
Time Series EOF1
10-year Running Nino3 Variance
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Warm Composite SSTA
Interactive Ensemble (6) Coupled Model
COLD Composite SSTA
Difference in SSTA Variability
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Interactive Ensemble Six Members
10-year Running Nino3 Variance
Do the Changes in the Variance Relate to Any Mean
State Changes?
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High ENSO Variance SSTA Composite
Interactive Ensemble (6) Coupled Model
Low ENSO Variance SSTA Composite
Difference in SSTA Variability
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Interactive Ensemble Six Members
EOF2 10.6
Interactive Ensemble Twelve Members
EOF2 22.8
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Interactive Ensemble Six Members
EOF2 Time Series
10-year Running NINO3 Variance
Interactive Ensemble Twelve Members
EOF2 Time Series
10-year Running NINO3 Variance
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EOF Amplitudes
EOF1
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EOF1
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Amplitude
EOF1
30
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EOF2
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Difficult to Detect
EOF2
IE-12
SC
IE-6
Decreasing Noise ?
? EOF1 Stochastically Forced Mode ? Independent
of ENSO ? EOF2 Non-Markovian ? Residual? or
Modulator?
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Markov Model Derived From Interactive Ensemble
(6) Output EOF1-EOF10
10-Year Running NINO3 Variance
Regression with SSTA
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Concluding Remarks

• Interactive Ensemble Mechanism for Controlling
  the Stochastic Forcing at the Air-Sea Interface
• No Assumptions Regarding the Statistics of the
  Noise Required
• Preserves the Internal Dynamics of the Component
  Models
• SSTA Variance Ratios
• Indo-Pacific Regions Where there Appears to be
  Unstable Coupled Interactions
• Ensemble Mean and Ensemble Spread
• More Wind Stress Uncertainty During Warm Events
• Cold Events More Predictable
• Non-Linear Processes
• Low Frequency Variability in the Tropical Pacific
• Dominant Mode of Variability Stochastically
  Forced
• ENSO Variance Mode
• Non-Linear Process
• Residual? or Modulator?