# Presentation: 302225

## 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

## 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

- 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

**Notes:**
1-way: Hasselmann (1976); Ocean response to stochastic forcing may give some preferred time scales, general used as a null-hypothesis for mid-latitude ocean variability.

2-Way: Coupled feedbacks matter need noise

ENSO: Coupled feedbacks important; debate is whether damped or unstable. 
	Damped Feedbacks + Noise -> Linear Dynamics, non-linearity is just noise and its amplitude is unrelated to signal.

## 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

- 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” =>

**Notes:**
1-way: Hasselmann (1976); Ocean response to stochastic forcing may give some preferred time scales, general used as a null-hypothesis for mid-latitude ocean variability.

2-Way: Coupled feedbacks matter need noise

ENSO: Coupled feedbacks important; debate is whether damped or unstable. 
	Damped Feedbacks + Noise -> Linear Dynamics, non-linearity is just noise and its amplitude is unrelated to signal.

## 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

**Notes:**
Already covered some aspects of the motivation, but will show one additional figure. Need to define what I mean by the noise and how the interactive ensemble coupling works.
 Show how this coupling approach addresses some aspects of the basic questions: i.e., self-sustained? Irregularity? Periodicity? Noise in what component of the surface fluxes matters?
 Look at how co-variability in the ENSO-monsoon system in the presence of much reduced noise, want to understand the dynamical and physical mechanisms associated with ENSO-monsoon interactions. Most interesting aspect of this analysis is that we are able to isolate where coupling matters – it turns out that coupling in the Pacific doesn’t matter, but there is a subtly here in that anomalies are required (only need forced response). In the Indian Ocean coupling is critical.
 Extend this approach to models that are not anomaly coupled and to more than one model. The question here is why are two coupled models (that use the same ocean component and coupling strategy so very different)? Are the differences due to heat flux or momentum flux? Use this strategy to try to answer this question. 

## Defining the Noise Due to Internal Atmospheric Dynamics

- • Atmospheric Ensemble Realizations:

- With Finite Ensembles Can Only Estimate Signal and Noise

**Notes:**
Some kind of filtering required, with auto-regressive models assume noise Gaussian and white, which implies that the noise amplitude in independent of the signal (it is important to emphasize noise amplitude).
 In terms of observations we only have one realization, but we can use ensemble of atmospheric realizations to try to estimate the noise. With this strategy noise and signal only defined in the limit of infinite ensembles, but no additional assumptions required about the relationship between the noise and the signal or the statistics of the noise.

## Using AGCM Ensembles to 

- 4,5,6 Ensemble Members

- 1 Ensemble Member

- 2 Ensemble Member

- 3 Ensemble Member

- NCEP Analysis

- Using AGCM Ensembles to
- Isolated the Forced Seasonal-
- to-Interannual Signal in Long
- Climate Simulations

**Notes:**
Slow down, Slow down.
 Identify the Pacific domain
 Identify NCEP analysis
Identify One Ensemble member: Note AGCM forced by observed SST, monthly means, Think of this as the level of variability of the atmospheric component a standard coupled model.
 Point out that the interactive ensemble approach is to couple the blue curves with the ocean component.
 Problems with the structure of the signal, despite the fact that we don’t have ensemble of realizations for observations.

## Coupled GCM Ensemble Realizations

- 72 Months

- 12 Months

- How to Separate Signal and Noise?
- 	Assumptions about the Statistics of the Noise

## Simple Coupled Model Perspective

- Interactive Ensemble
- Coupled Model

-  Atmos

-  Ocean

-  Atmos

-  Ocean

**Notes:**
Slow Down: Make sure to indicate that this is a conceptual model, Note that linear dynamics is not modified

## Simple Coupled Model Perspective

- Interactive Ensemble
- Coupled Model

-  Atmos

-  Ocean

-  Atmos

-  Ocean

**Coupled Feedbacks**

**Notes:**
Slow Down: Make sure to indicate that this is a conceptual model, Note that linear dynamics is not modified

## Simple Coupled Model Perspective

- Interactive Ensemble
- Coupled Model

-  Atmos

-  Ocean

-  Atmos

-  Ocean

**Lag-1 Auto-Correlation**

**Notes:**
Slow Down: Make sure to indicate that this is a conceptual model, Note that linear dynamics is not modified

## Simple Coupled Model Perspective

- Interactive Ensemble
- Coupled Model

-  Atmos

-  Ocean

-  Atmos

-  Ocean

**Prescribed External Noise**

**Notes:**
Slow Down: Make sure to indicate that this is a conceptual model, Note that linear dynamics is not modified

## CGCM Perspective

- Interactive Ensemble
- Coupled Model

-  Atmos

-  Ocean

-  Atmos

-  Ocean

**Noise is Internal to the System**

**Notes:**
Slow Down: Make sure to indicate that this is a conceptual model, Note that linear dynamics is not modified

## Anomaly Coupled (i.e., “correct climatology”)

## Self Sustained, but More 

***- 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

## Slide 15

## Slide 16

## Removing

- Too Much
- Noise?

- Stronger
- Tropical-Extratropical
- Telenconnections

- Reduced Heatflux
- Noise

- Broader
- Meridional
- Scale

## Slide 18

## Analysis of Variance  

- Standard:

- Interactive:

- Atmospheric
- Noise

**Ocean**
- Noise

- Ensemble
- Averaging

- Ocean
- Variance

**Ignoring Lag-1 Auto-Correlation**

## Large Ensemble Limit

- M → ∞

- If Oceanic Noise Comparable to Atmospheric
- Noise Only Relatively Modest Reduction in Variance Independent of Ensemble Size

## Small Ocean Noise

- If Small Ocean Noise and the “Null Hypothesis” is Correct

## Variance Ratio

- Weak Coupling

- Moderate Coupling

- Strong Coupling

- Ocean Noise/Atmos Noise

- Null Hypthesis
- Ratio=1/6

**Notes:**
Go Slow: Mention specific example of 6 ensemble members; Strong coupling much slower asymptote; 

## Variance Ratio

- Strong Coupling

- Moderate Coupling

- Weak Coupling

- Ocean Noise/Atmos Noise

- 1/6

**Including the Lag-1 Auto-Correlation**

## What to Expect

- If Ratio ≈ 1/M
- Stochastically Forced System with Stable Coupled Feedbacks and Small Ocean Noise
- If 1⁄2 < Ratio < 1
- Relatively Large Internal Oceanic Noise?
- Perhaps Unstable Coupled Feedbacks?
- Simple Model Fails –  Important Non-Linearity?
- If 1 < Ratio
- Unstable Coupled Feedbacks?
- Simple Model Fails – Important Non-Linearity?

**Notes:**
Number of possible reasons why the simple model will fail: (i) non-local coupling, (ii) non-linearity, (iii) 

## σ2 SSTA Standard Coupled

**σ****2**** SSTA Standard Coupled**

**Variance Ratio Standard/Interactive**

**Notes:**
Variance plots here

## 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

## What to Expect

- Stochastic Coupled Model

## Does the “SST” Depend on the Uncertainty in the Atmosphere?

- Distribution of Ensemble
- Spread X Of Atmosphere

- Unconditional Distribution
- Of Ocean Y

- 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

## What We Get From the Interactive Ensemble CGCM

## Does the Uncertainty Depend on the Signal?

- U-Stress (Nino4) Ensemble Spread
- (Distribution of _Uncertainty_)

- Unconditional U-Stress
- (Distribution of _Signal_)

- Conditional Distribution of Spread
- with an Easterly Anomaly: Small Spread

- Conditional Distribution of
- Spread with an Westerly
- Anomaly: Large Spread

- Gaussian

## U-Stress Ensemble Spread

- U-Stress Ensemble Spread

- U-Stress Ensemble Spread

- Unconditional SSTA

- SSTA Distribution Assuming
- Small Spread (Uncertainty)

- Unconditional SSTA

- Does the Signal Depend on the Uncertainty?

- Does the Signal Depend on the Uncertainty?

- SSTA Distribution Assuming
- Large Spread (Uncertainty)

## Composite 95%-ile SST

- Composite 5%-ile SST

- Composite Zonal Wind Stress Spread

- Based on 95%-ile SST

- Based on 5%-ile SST

- More Uncertainty in τx for Warm Events Compared to Cold Events

## Predictability Implications

- Cold Events More Predictable then Warm Events?

## Reduced Noise

- Standard Model

- 6 Months Lead

- 6 Months Lead

- 9 Months Lead

- 9 Months Lead

- cold

- Normal

- warm

- Nino3.4 ROC Curves

## 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

## 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

## Tropical decadal variability (10 year running means):

**Tropical decadal variability (10 year running means):**
**Standard Coupled Model**

**EOF1**
**46.4%**

**EOF2**
**11.7%**

## 10-Year Running Nino3 Variance

- Time Series EOF1

- Time Series EOF2

## “Warm” Composite SSTA

- “Warm” Composite SSTA

- “COLD” Composite SSTA

**Difference in SSTA Variability**

**Standard **
**Coupled **
**Model**

## EOF1: 41.6%

**EOF1: 41.6%**

**EOF1: 28.1%**

**Interactive Ensemble: Dominant Mode of Tropical Pacific Variability**

## Interactive Ensemble: Six Members

- Interactive Ensemble: **Six Members**

- 10-year Running Nino3 Variance

- Time Series EOF1

- Interactive Ensemble: **Twelve Members**

- 10-year Running Nino3 Variance

- Time Series EOF1

## “Warm” Composite SSTA

- “Warm” Composite SSTA

- “COLD” Composite SSTA

**Difference in SSTA Variability**

**Interactive**
**Ensemble (6) **
**Coupled **
**Model**

## Do the Changes in the Variance Relate to Any Mean State Changes?

**Do the Changes in the Variance Relate to Any Mean State Changes?**

- Interactive Ensemble: **Six Members**

- 10-year Running Nino3 Variance

## Slide 44

## High ENSO Variance SSTA Composite

- Low ENSO Variance SSTA Composite

**Difference in SSTA Variability**

**Interactive**
**Ensemble (6) **
**Coupled **
**Model**

## EOF2 10.6%

**EOF2 10.6%**

**EOF2 22.8%**

**Interactive Ensemble: Six Members**

**Interactive Ensemble: Twelve Members**

## Interactive Ensemble: Six Members

- 10-year Running NINO3 Variance

- EOF2 Time Series

- 10-year Running NINO3 Variance

- EOF2 Time Series

- Interactive Ensemble: Twelve Members

## EOF Amplitudes

**Amplitude**

**SC**

**IE-6**

**IE-12**

**10%**

**20%**

**30%**

**40%**

**50%**

**EOF1**

**EOF1**

**EOF1**

**Decreasing Noise ******

**EOF2**

**EOF2**

**► ****EOF1: Stochastically Forced Mode ******** Independent of ENSO**
**► ****EOF2: “Non-Markovian” ******** Residual? or Modulator?**

- Difficult to Detect

## Slide 49

**Notes:**
One possible explanation of why the decadal model is so large scale is that noise occurs on the largest spatial scales

## Markov Model Derived From Interactive Ensemble (6) Output: EOF1-EOF10

- 10-Year Running NINO3 Variance

- Regression with SSTA

## 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?