1. 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. Lintner 1 and J. David Neelin 1 1 Dept. 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, CA Session A22B (December 11 th, 2007)

2. Observed 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 Ni ñ o/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 Ni ñ o/Southern Oscillation DaysTotal Variability ENSO Regressed

3. Quasi-equilibrim Tropical Circulation Model (QTCM) Approximate analytic solutions for tropical convecting regions Convection constrains T  vertical 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 T  vertical 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

4. QTCM Equations

5. Simulated  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) Days QTCM CCM3

6. Eigenvalue 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 (  T s ) is applied to the j th region, and the anomalous surface heat flux in the i th region is computed (  F i ). 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 (  T s ) is applied to the j th region, and the anomalous surface heat flux in the i th region is computed (  F i ). Thus, the time-evolution is: : Diagonal matrix of mixed layer depths (assumed equal) : Eigenvector matrix of c m -1 G : Diagonal matrix with elements e - i t, with i the eigenvalues of c m -1 G

7. Eigenvalue 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  G i i -1 Days Mode # Eigenvalues/ Decay Times Mode 1 Loading

8. Decay time scaling Approach: In 1D, assuming a homogeneous basic state and diagnostic frictional momentum balance (r  x T =  u u u), solve the thermodynamic equations and obtain a dispersion relationship of the form: k 0 = 0 (WTG limit: T uniform) k 0 = 1 k 0 = 2 k 0 = 3 Characteristic length scale: Mode # Days  For typical QTCM parameters, k 0  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, k 0  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 w/ CRF w/o CRF

9. Convecting-nonconvecting separation  (Inverse) decay time of LC/G modes insensitive/weakly sensitive to  c, which indicates the frequency of convection in N c  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 N c  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 N c 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c LC PC G N c ( = 2) boxes nonconvecting N ( = 8) boxes fully convecting

10. 2-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 f 1 = 0.75 f 1 = 0.50 f 1 = 0.33 Approach: Replace N boxes by two: one fully convecting (of size fraction f 1 ), the other partially convecting (of size fraction f 2 = 1 - f 1 ). The elements of G are: and the eigenvalues are given by: Approach: Replace N boxes by two: one fully convecting (of size fraction f 1 ), the other partially convecting (of size fraction f 2 = 1 - f 1 ). 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c PC G f 1 = 0.75

11. Why 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 f1f1

12. 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 -2 K -1 ) Eigenvalues Eigenvectors

13. 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. In press, Journal of Climate preprint available at: http://www.atmos.ucla.edu/~csi/