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