# Presentation: 759114

## Tropical and Stratospheric Influences on Extratropical Variability and Forecast Skill

- Matt Newman and Prashant Sardeshmukh
- ESRL PSD/CIRES CDC

## Motivation

- Consider the dynamical system describing the variable x,
- 	dx/dt = N(x) + F     (N is a nonlinear operator and F is external forcing)
- This can always be rewritten as
- 	dx/dt = slow nonlinearity + fast nonlinearity
- If:
- we are only interested in the slowly evolving portion of x
- and there is a big difference between “fast” and “slow”
- this may be usefully approximated as
- 	dx/dt = Lx + white noise

** **

**Linear inverse model (LIM)**

- “Optimal” growth :   Eigenvectors of **GDG**T

- Then -lag and zero-lag covariance related as

- So we can solve the above for L.

## Our LIM studies

- Winkler et al (2001)
- Established LIM  (using tropospheric streamfunction and Tropical heating) as a useful model
- Newman et al (2003)
- Showed LIM skill comparable to Reforecast MRF skill
- Estimated predictability (“forecast the forecast skill”)
- Today
- Add sea level pressure and stratospheric streamfunction to LIM and evaluate statistics

## DATA

- 7-day running mean anomalies computed from 4x daily NCEP Reanalysis (DJF 1968/69-2002/03) with annual cycle removed
- Streamfunction (**** ): 250 mb and 750 mb
- Streamfunction (S): 30 mb and 100 mb
- Sea level pressure (slp)
- Diabatic heating (H): Chi-corrected, column-integrated between 300N and 300S
- Truncation in EOF space: retain about 90% of slp and **** variance, and about 55% of H and S variance

## Leading two eofs for each field

**Leading two eofs for each field**

**x(t) = 85-component vector whose components are **
**the time-varying**
**coefficients of the leading slp, ******H, and S**
**PCs.**
**L is thus a **
**85x85 matrix**
**Trained on 5-day lag**

** **

**Linear inverse model (LIM)**

- “Optimal” growth :   Eigenvectors of **GDG**T

- Then -lag and zero-lag covariance related as

- So we can solve the above for L.

## Forecast Skill

**Note that Tropical heating notably enhances slp skill everywhere except the NAO region.**

## LIM reproduces the observed 21-day lag covariance(except)

## What are the effects of the Tropics and the Stratosphere on extratropical tropospheric variability?

## Turn “off” coupling

*d***x**    *d  *| **x****N** |    | **L****NN**** L****NT** | | **x****N** |
- --- = --  |     | = |              |  |    |   + **noise**
*dt*    *dt*  | **x****T** |    | **L****TN**** L****TT** |  | **x****T** |
- So we can set submatrices **L****NT** and **L****TN** to zero and examine effects on variance, lagged covariability, and anomaly growth.

**Turn “off” coupling**

## Tropospheric variance can be substantially reproduced without “external forcing” terms Top:Observed varianceMiddle:LIM varianceBottom: LIM variance from “free” tropospheric terms only

## Most tropospheric persistent variance can be reproduced only by including “external forcing”,primarily heatingTop:LIM varianceMiddle:LIM variance when effects of H are removedBottom: LIM variance when effects of S are removed

## Peak ‘optimal’ anomaly growth is later for upper levelsMaximum amplification (MA) curves for different targets of anomaly growth

## Strongest mid-tropospheric anomaly growth is associated with initial tropical heatingLeading singular vector for amplification of PSI EOF 1 over 21 daysLeft panels CI = 1/2 right panels CI

## Strongest surface anomaly growth is associated with initial extratropical anomalies including in the stratosphereLeading singular vector for amplification of slp EOF 1 over 21 daysLeft panels CI = 1/2 right panels CI

## Tropical impact on tropospheric forecast skill Stratosphereimpact on surface forecast skillForecast skill of leading slp and streamfunction PCs for full LIM and LIM without either Tropics or Stratosphere initial conditions

## Conclusions

- Linear inverse model reproduces major features of observed covariability
- External forcing acts more to increase *persistent* variability than to increase overall variability
- Tropics greatly enhances persistent variability throughout the Pacific sector and over North America
- Stratosphere enhances persistent variability primarily in the polar region and over Europe
- Difference in norms is important
- Tropics affects deeper atmosphere (including stratosphere)
- Stratosphere affects surface more than mid troposphere

## Slide 19

## Variance budget