Time scales and spatial patterns of passive ocean-atmosphere decay modes

Time scales and spatial patterns of passive ocean-atmosphere decay modes

• Analysis of simulated coupled ocean-atmosphere decay characteristics– Atmosphere: intermediate level complexity model– Ocean: uniform 50m thermodynamic mixed layer (no ocean dynamics = “passive”)

• Focus on tropical decay structures– e.g., convecting versus nonconvecting regions

• Approaches– Temporal autocorrelation persistence– Eigenvalue analysis– Simple prototypes

• Analysis of simulated coupled ocean-atmosphere decay characteristics– Atmosphere: intermediate level complexity model– Ocean: uniform 50m thermodynamic mixed layer (no ocean dynamics = “passive”)

• Focus on tropical decay structures– e.g., convecting versus nonconvecting regions

• Approaches– Temporal autocorrelation persistence– Eigenvalue analysis– Simple prototypes

Benjamin R. Lintner1 and J. David Neelin1

1Dept. of Atmospheric and Oceanic Sciences and Institute of

Geophysics and Planetary Physics, University of California Los Angeles

ben@atmos.ucla.edu

AGU 2007 Fall Meeting San Francisco, CASession A22B (December 11th, 2007)

Observed autocorrelation persistenceObserved autocorrelation persistence

e-folding time of gridpoint temporal autocorrelation ( p) estimated from the

ERSST data set (1950-2000) Mostly low values (< 100

days), except over the central/eastern Pacific, parts of the Atlantic and Indian Ocean basins Long persistence associated

with El Niño/Southern Oscillation

e-folding time of gridpoint temporal autocorrelation ( p) estimated from the

ERSST data set (1950-2000) Mostly low values (< 100

days), except over the central/eastern Pacific, parts of the Atlantic and Indian Ocean basins Long persistence associated

with El Niño/Southern Oscillation

DaysTotal Variability

ENSO Regressed

Quasi-equilibrim Tropical Circulation Model (QTCM)Quasi-equilibrim Tropical

Circulation Model (QTCM)

• Approximate analytic solutions for tropical convecting regions

Convection constrains Tvertical structure of baroclinic P gradients vertical structure of v vertical structure of

• Implement analytic solutions for projection of primitive equations in a Galerkin-like expansion in the vertical

• QTCM includes a full complement of GCM-like parameterizations (e.g., radiative transfer, surface turbulent exchange, Betts-Miller convection); is computationally efficient; and has been applied to multiple problems in tropical climate dynamics (e.g., ENSO teleconnections, monsoons, global warming,…)

• Approximate analytic solutions for tropical convecting regions

Convection constrains Tvertical structure of baroclinic P gradients vertical structure of v vertical structure of

• Implement analytic solutions for projection of primitive equations in a Galerkin-like expansion in the vertical

• QTCM includes a full complement of GCM-like parameterizations (e.g., radiative transfer, surface turbulent exchange, Betts-Miller convection); is computationally efficient; and has been applied to multiple problems in tropical climate dynamics (e.g., ENSO teleconnections, monsoons, global warming,…)

(Note: the version here has K =1.)

See Neelin and Zeng, 2000; Zeng et al., 2000

QTCM EquationsQTCM Equations

Simulated pSimulated p

Large spread in values (~50 days to > 300 days)

Relationship between mean precipitation (line contours) and persistence Long persistence in SE tropical

Pacific/Atlantic (weak convection)

Long persistence in ENSO source region Implications for ENSO variability

and/or characteristics?

Statistically significant spatial pattern correlation between models (r = 0.54)

Large spread in values (~50 days to > 300 days)

Relationship between mean precipitation (line contours) and persistence Long persistence in SE tropical

Pacific/Atlantic (weak convection)

Long persistence in ENSO source region Implications for ENSO variability

and/or characteristics?

Statistically significant spatial pattern correlation between models (r = 0.54)

DaysQTCM

CCM3

Eigenvalue analysisEigenvalue analysis

• Interpretation of autocorrelation persistence ambiguous (e.g., single timescale only; local versus nonlocal influences?)

• Eigenvalue analysis offers a simple way to estimate the modal nature of (slow) ocean-atmosphere decay

• Approach: Partition the oceanic domain into N regions that form a N-dimensional subspace of SST anomalies. An SST perturbation (Ts) is applied to the jth region, and the anomalous surface heat flux in the ith region is computed (Fi). Thus, the time-evolution is:

• Interpretation of autocorrelation persistence ambiguous (e.g., single timescale only; local versus nonlocal influences?)

• Eigenvalue analysis offers a simple way to estimate the modal nature of (slow) ocean-atmosphere decay

• Approach: Partition the oceanic domain into N regions that form a N-dimensional subspace of SST anomalies. An SST perturbation (Ts) is applied to the jth region, and the anomalous surface heat flux in the ith region is computed (Fi). Thus, the time-evolution is:

€

cm ik∂tΔTsk = Gi

jΔTs j ; Gij =

ΔFi

ΔTs j

€

Ts(t) = VDV−1ΔTs(0)

€

cm

€

V

€

D

: Diagonal matrix of mixed layer depths (assumed equal)

: Eigenvector matrix of cm-1G

: Diagonal matrix with elements e-it, with i the eigenvalues of cm-1G

Eigenvalue exampleEigenvalue example

35 basis regions (33 tropical; 2 extratropical)

Only ~3 modes have decay times substantially larger than the local decay times, estimated from the diagonal elements of G

Leading mode has most uniform spatial structure (as expected), but nonnegligible regional structure

35 basis regions (33 tropical; 2 extratropical)

Only ~3 modes have decay times substantially larger than the local decay times, estimated from the diagonal elements of G

Leading mode has most uniform spatial structure (as expected), but nonnegligible regional structure

Decay Time i-1

Local Decay Estimate Gii-1

Days

Mode #

Eigenvalues/Decay Times

Mode 1 Loading

Decay time scalingDecay time scaling• Approach: In 1D, assuming a homogeneous basic state and diagnostic

frictional momentum balance (rxT = uuu), solve the thermodynamic

equations and obtain a dispersion relationship of the form:

• Approach: In 1D, assuming a homogeneous basic state and diagnostic frictional momentum balance (rxT = u

uu), solve the thermodynamic equations and obtain a dispersion relationship of the form:

k0 = 0 (WTG limit: T uniform)k0 = 1k0 = 2k0 = 3

Characteristic length scale:

Mode #

Days For typical QTCM parameters, k0 1.5 Relatively rapid timescales

dominate tropical decay

Inclusion of cloud-radiative feedback (CRF) lowers local decay times by half, but has less impact on broader modes CRF effect associated with

shielding of the surface to incoming shortwave

For typical QTCM parameters, k0 1.5 Relatively rapid timescales

dominate tropical decay

Inclusion of cloud-radiative feedback (CRF) lowers local decay times by half, but has less impact on broader modes CRF effect associated with

shielding of the surface to incoming shortwavew/ CRF

w/o CRF

Convecting-nonconvecting separationConvecting-nonconvecting separation

(Inverse) decay time of LC/G modes insensitive/weakly sensitive to c, which indicates the frequency of convection in Nc

PC modes remain close to one another, esp. for large/small c

Relative insensitivity to areal extent of the nonconvecting region SST

Inverse decay time approaching G mode in nonconvecting limit (c = 0)

(Inverse) decay time of LC/G modes insensitive/weakly sensitive to c, which indicates the frequency of convection in Nc

PC modes remain close to one another, esp. for large/small c

Relative insensitivity to areal extent of the nonconvecting region SST

Inverse decay time approaching G mode in nonconvecting limit (c = 0)

• Approach: Discretize equations subject to approximations (e.g., WTG limit) into N regions, with variable convection within a subset Nc and fully convecting in the rest, and perform eigenvalue analysis 1 (slow) Global, “G”; N-(Nc+1) (degenerate fast) Local Convecting, “LC”, and Nc (almost degenerate) Partially Convecting, “PC”, modes

• Approach: Discretize equations subject to approximations (e.g., WTG limit) into N regions, with variable convection within a subset Nc and fully convecting in the rest, and perform eigenvalue analysis 1 (slow) Global, “G”; N-(Nc+1) (degenerate fast) Local Convecting, “LC”, and Nc (almost degenerate) Partially Convecting, “PC”, modes

Day-1

c

LC

PC

G

Nc ( = 2) boxes nonconvecting

N ( = 8) boxes fully convecting

2-box analogue2-box analogue

Facilitates straightforward analytic study of PC and G modes

A simplifying assumption in the 2-box case as shown is the strict QE limit (vanishing convective adjustment timescale), which accounts for the offset between N-box and 2-box solutions

Facilitates straightforward analytic study of PC and G modes

A simplifying assumption in the 2-box case as shown is the strict QE limit (vanishing convective adjustment timescale), which accounts for the offset between N-box and 2-box solutions

G

PC

f1 = 0.75

f1 = 0.50

f1 = 0.33

• Approach: Replace N boxes by two: one fully convecting (of size fraction f1), the other partially convecting (of size fraction f2 = 1 - f1). The elements of G are:

and the eigenvalues are given by:

• Approach: Replace N boxes by two: one fully convecting (of size fraction f1), the other partially convecting (of size fraction f2 = 1 - f1). The elements of G are:

and the eigenvalues are given by:

Notation: e.g.,

is T associated with 1K SST anom in box 1; 0K SST

anom in box 2

Day-1

c

PC

G

f1 = 0.75

Why nonconvecting regions decay slowlyWhy nonconvecting regions decay slowly In the fully convecting limit (c =

1), excitation of convective heating generates wave response Strong horizontal spreading of the

effect of the SST perturbation Also, tight coupling of T and q

In the nonconvecting limit (c = 0), T and q largely decoupled, with little change in T Weak spreading away from

perturbation

Also in nonconvecting regions, evaporation balances moisture divergence (associated with large-scale descent)

In the fully convecting limit (c = 1), excitation of convective heating generates wave response Strong horizontal spreading of the

effect of the SST perturbation Also, tight coupling of T and q

In the nonconvecting limit (c = 0), T and q largely decoupled, with little change in T Weak spreading away from

perturbation

Also in nonconvecting regions, evaporation balances moisture divergence (associated with large-scale descent)

c = 1

c = 0.25

c = 0

Temperature

Box 2 Humidity

K

f1

Eigenmode “blending”Eigenmode “blending”

Increasing the horizontal damping/transport, such as through enhanced heat/moisture export of from the tropics through eddies, decreases G and PC mode decay times

Blending of eigenvector loadings occurs as the two eigenvalues approach one another in the limit of strong export Plausible explanation for spatial

nonuniformity seen in slowest decay mode(s)

Increasing the horizontal damping/transport, such as through enhanced heat/moisture export of from the tropics through eddies, decreases G and PC mode decay times

Blending of eigenvector loadings occurs as the two eigenvalues approach one another in the limit of strong export Plausible explanation for spatial

nonuniformity seen in slowest decay mode(s)

Day-1

unitless

Horizontal damping/transport (Wm-2K-1)

Eigenvalues

Eigenvectors

Thank you for listening!Thank you for listening!

Acknowledgements: We thank J.C.H. Chiang for providing access to the CCM3 mixed layer simulation. This work was supported by NOAA grants NA04OAR4310013 and NA05)AR4311134 and NSF grant ATM-0082529. BRL further acknowledges partial financial support by J.C.H. Chiang and NOAA grant NA03OAR4310066.

Acknowledgements: We thank J.C.H. Chiang for providing access to the CCM3 mixed layer simulation. This work was supported by NOAA grants NA04OAR4310013 and NA05)AR4311134 and NSF grant ATM-0082529. BRL further acknowledges partial financial support by J.C.H. Chiang and NOAA grant NA03OAR4310066.

In press, Journal of Climate

preprint available at: http://www.atmos.ucla.edu/~csi/