Tropical and Stratospheric Tropical and Stratospheric Influences on Extratropical Influences on Extratropical

Variability and Forecast Variability and Forecast SkillSkill

Matt Newman and Prashant SardeshmukhMatt Newman and Prashant Sardeshmukh

ESRL PSD/CIRES CDCESRL PSD/CIRES CDC

MotivationMotivationConsider the dynamical system describing the variable Consider the dynamical system describing the variable x,,

dx/dt = N(x) + F (N is a nonlinear operator and F is external forcing) (N is a nonlinear operator and F is external forcing)

This can always be rewritten asThis can always be rewritten as

dx/dt = slow nonlinearity + fast nonlinearitydx/dt = slow nonlinearity + fast nonlinearity

If:If: we are only interested in the slowly evolving portion of xwe are only interested in the slowly evolving portion of x and there is a big difference between “fast” and “slow” and there is a big difference between “fast” and “slow”

this may be usefully approximated asthis may be usefully approximated as

dx/dt = Lx + white noisedx/dt = Lx + white noise

Linear inverse model (LIM)Linear inverse model (LIM)

“Optimal” growth : Eigenvectors of GDGT

Then -lag and zero-lag covariance related as

So we can solve the above for L.

“Best” forecasts of x are:

Our LIM studiesOur LIM studies

Winkler et al (2001)Winkler et al (2001) Established LIM (using tropospheric streamfunction Established LIM (using tropospheric streamfunction

and Tropical heating) as a useful modeland Tropical heating) as a useful model Newman et al (2003)Newman et al (2003)

Showed LIM skill comparable to Reforecast MRF skill Showed LIM skill comparable to Reforecast MRF skill Estimated predictability (“forecast the forecast skill”)Estimated predictability (“forecast the forecast skill”)

TodayToday Add sea level pressure and stratospheric Add sea level pressure and stratospheric

streamfunction to LIM and evaluate statisticsstreamfunction to LIM and evaluate statistics

DATADATA

• 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 Leading two eofs two eofs for each for each

fieldfield

x(t) = 85-component vector whose components are the time-varyingcoefficients of the leading slp, H, and SPCs.

L is thus a 85x85 matrix

Trained on 5-day lag

Linear inverse model (LIM)Linear inverse model (LIM)

“Optimal” growth : Eigenvectors of GDGT

Then -lag and zero-lag covariance related as

So we can solve the above for L.

“Best” forecasts of x are:

Forecast Forecast SkillSkill

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

LIM LIM reproduces reproduces

the the observed observed 21-day lag 21-day lag covariancecovariance

(except)(except)

What are the effects of the What are the effects of the Tropics and the Stratosphere Tropics and the Stratosphere on extratropical tropospheric on extratropical tropospheric

variability?variability?

LIM can be written in its components parts as:

dx d | xN | | LNN LNT | | xN |--- = -- | | = | | | | + noisedt dt | xT | | LTN LTT | | xT |

So we can set submatrices LNT and LTN to zero and examine effects on variance, lagged covariability, and anomaly growth.

Turn “off” couplingTurn “off” coupling

Tropospheric Tropospheric variance can be variance can be substantially substantially reproduced without reproduced without “external forcing” “external forcing” termsterms

Top:Top:Observed varianceObserved variance

Middle:Middle:LIM varianceLIM variance

Bottom: Bottom: LIM variance from “free” LIM variance from “free” tropospheric terms onlytropospheric terms only

Most tropospheric Most tropospheric persistentpersistent variance variance can be reproduced can be reproduced only by only by includingincluding “external forcing”,“external forcing”,primarily heatingprimarily heating

Top:Top:LIM varianceLIM variance

Middle:Middle:LIM variance when effects LIM variance when effects of H are removedof H are removed

Bottom: Bottom: LIM variance when effects LIM variance when effects of S are removedof S are removed

Peak Peak ‘optimal’ ‘optimal’ anomaly anomaly growth is growth is later for later for upper levelsupper levels

Maximum Maximum amplification (MA) amplification (MA) curves for different curves for different targets of anomaly targets of anomaly growthgrowth

Strongest mid-Strongest mid-tropospheric tropospheric anomaly growth is anomaly growth is associated with associated with initial tropical initial tropical heatingheating

Leading singular vector for Leading singular vector for amplification of PSI EOF 1 amplification of PSI EOF 1 over 21 daysover 21 days

Left panels CI = 1/2 right panels CILeft panels CI = 1/2 right panels CI

Strongest surface Strongest surface anomaly growth is anomaly growth is associated with associated with initial extratropical initial extratropical anomalies including anomalies including in the stratospherein the stratosphere

Leading singular vector for Leading singular vector for amplification of slp EOF 1 amplification of slp EOF 1 over 21 daysover 21 days

Left panels CI = 1/2 right panels CILeft panels CI = 1/2 right panels CI

Tropical impact Tropical impact on tropospheric on tropospheric forecast skill forecast skill

StratosphereStratosphereimpact on impact on surface forecast surface forecast skillskill

Forecast skill of leading slp Forecast skill of leading slp and streamfunction PCs for and streamfunction PCs for full LIM and LIM without either full LIM and LIM without either Tropics or Stratosphere initial Tropics or Stratosphere initial conditionsconditions

ConclusionsConclusions Linear inverse model reproduces major features of Linear inverse model reproduces major features of

observed covariabilityobserved covariability External forcing acts more to increase External forcing acts more to increase persistentpersistent

variability than to increase overall variabilityvariability than to increase overall variability Tropics greatly enhances persistent variability throughout Tropics greatly enhances persistent variability throughout

the Pacific sector and over North Americathe Pacific sector and over North America Stratosphere enhances persistent variability primarily in Stratosphere enhances persistent variability primarily in

the polar region and over Europethe polar region and over Europe Difference in norms is important Difference in norms is important

Tropics affects deeper atmosphere (including Tropics affects deeper atmosphere (including stratosphere)stratosphere)

Stratosphere affects surface more than mid troposphereStratosphere affects surface more than mid troposphere

Variance Variance budgetbudget