1. Ocean Mixed Layer Dynamics and its Impact on SST & Climate Variability
Michael Alexander
Earth System Research Lab
michael.alexander/presentations

2. Ocean Mixed layer T s ρ ∆T=Tb-Tm
Turbulence creates a well mixed surface layer where temperature (T), salinity (S) and density (ρ) are nearly uniform with depth
Primarily driven by vertical processes (assumed here) but can interact with 3-D circulation
Density jump usually controlled by temperature but sometimes by salinity (especially in high latitudes)
Often “ measured” by the depth at which T is some value less than SST (e.g. ∆T = 0.5)
Under goes large seasonal cycle
This impacts the evolution of ocean temperature anomalies and has important biological consequences
surface T s ρ ∆T
∆T=Tb-Tm

3. Vertical Flux: Entrainment and MLD (h)
Entrainment “To pull or draw along after itself”
MLD – Mixed Layer Depth or h
When deepening:
dh/dt = we
we = M + B – D / (Dr - S)
Where
M - Mechanical Turbulence (wind stirring)
B - Buoyancy Forcing
Net surface heating/cooling (Qnet)
Precipitation – Evaporation (P-E)
D - Dissipation (eh)
Δρ - Density jump at base of the ML
S - Shear across ML (not in all models)
When Shoaling:
we = 0 (no detrainment, h reforms closer to the surface)
h = M /(B – D)

4. Seasonal Cycle of Temp & MLD Northeast Pacific (50ºN, 145ºW)
MLD (h)

5. Climatological Mixed Layer Depth (m)

6. SST Tendency Equation Integrated heat budget over the mixed layer:
Variables
v – velocity (current in ML)
Tm – mixed layer temp (SST)
Tb – temp just beneath ML
h – mixed layer depth
w – mean vertical velocity
we – entrainment velocity
Qnet – net surface heat flux
Qswh – penetrating shortwave radiation
A – horizontal eddy viscosity coefficient
ρ – density of sea water
C – Specific heat of sea water
Qnet
Tm = SST

7. Temperature change due to the surface heat flux
Over March through August a location in the North Pacific typically receives 150 Wm-2 flux through the surface. Assuming a constant mixed layer depth of 50 m, and no other changes in the ocean how much will the SST change over that time?
dTm/dt = d(SST)/dt = Qnet/ρch
ΔSST = (Qnet/ρch) x Δt
ρ = 1025 kg/m3; c = Joules/(kg °C)
ΔSST = (150 Wm-2 / (1025 kg m-3 x 3850 Joules kg-1 °C-1 x 50 m)) * (184 days * s day-1)
SST = 12.1°C
=> Check units (W = J s-1)
=> reasonable value for winter to summer change in SST

8. Zonal Average Mean Standard Deviation Surface Heat Flux
Entrainment Flux
Zonal Average Mean
The four terms net surface heat flux (Qnet), and heat flux through the base of the
mixed layer due to entrainemnt (Qwe) and pentrating solar radiation at the base of the mixed layer Qswh) are obtained from an atmospheric general circulation model coupled to a mixed layer ocean model. The EkmEntrainment terms were multiplied by ch to get units of W m-2. The terms have been averaged over the North Pacific and Atlantic oceans
For the 12 calendar months between 10 and 70N
Standard
Deviation

9. Observed Standard Deviation of SST Anomalies (°C)
March
August

10. Processes for Generating SST Anomalies

11. Simple model for generating SST variability “stochastic model”
Heat fluxes associated
with weather events,
“random forcing”
Ocean response to flux back heat
which slowly damps SST anomalies
SST anomalies form
-λTm F
Air-sea interface
Fixed depth ocean
No currents
Bottom
dTm/dt = Qnet
ρch
dTm/dt = F – λTm
ρch

12. Stochastic SST Anomaly model II idealized forcing and time series
Null Hypothesis for midlatitude SST variability

13. Stochastic Model: correspondence to the real world
Stochastic Model: correspondence to the real world? Observed and Theoretical Spectra for SST anomalies (SSTA) at a location in the North Pacific Ocean
Theoretical spectra (white line) of stochastic model
Observed
Spread (5%-95%)
Period
1yr
10 yr
No damping
SSTA Variance
1 mo
Temperature Variance
Atm forcing
Observed SST variance spectra (black line) in a 5°x5° box centered on 50°N, 145°W using 134 years of month anomalies from an SST data set. The gray and white cures are based on a stochastic model fit to the SST data (estimate F’ and lamda in stochastic model equation. The gray shading represents the 5th and 95th percentile bounds for yr simulated spectra; the white line is the average of simulated spectra and overlays the theoretical spectra on an AR(1) model, the discrete form of Equation 4.
Atmospheric forcing and ocean feedback can be estimated from data. Then can then develop stochastic model and generate multiple time series to look at spread

14. Patterns of Surface Fluxes and SSTs: example North Atlantic Oscillation
Anomaly patterns associated with a +1 standard deviation departure of the North Atlantic Oscillation (NAO) Index during winter (December–March) defined using the station index of Hurrell et al. (2003). (a) Sea surface temperature (SST) (shading), sea-level pressure (SLP) (contours), and surface wind (arrows). (b) Sensible plus latent energy flux (Qsh + Qlh) (shading), SLP (contours), and surface wind (arrows). The SLP contour interval is 1 hPa, with negative values dashed.
Contours are sea level pressure (SLP); vectors - winds
Shading left is SST anomalies, on right is the Flux anomalies
NAO north-south SLP anomaly pattern over the Atlantic

15. The Reemergence Mechanism
Qnet’
MLD
Winter Surface flux anomalies
Create SST anomalies which spread over ML
ML reforms close to surface in spring
Summer SST anomalies strongly damped by air-sea interaction
Temperature anomalies persist in summer thermocline
Re-entrained into the ML in the following fall and winter
Namias and Born 1970, 1974;
Alexander and Deser (1995, JPO); Alexander et al

16. Reemergence in three North Pacific regions
Regression between SST anomalies in April-May with monthly temperature anomalies as a function of depth.
Regions
Alexander et al. (1999, J. Climate)

17. Reemergence in the North Atlantic
Reg 2 - Northeast Atlantic (47%)
Reg 1 - Subtropical Atlantic (48%)
Timlin, Alexander, Deser,
2002, J.Climate

18. Reemergence of SST Tripole
Auto-correlation of EOF PC time series
Level of
significance
Degrees Celsius
Reemergence of the
SST North Atlantic tripole
Leading EOF of March SST
ERSSTv2 Datasets [ ]
Watanabe and Kimoto (2000); Timlin et al. 2002, Deser et al 2003,
De Coetlogon and Frankignoul 2003 : all in J. Climate

19. Impact of reemergence on SST Persistence: Augmenting the Stochastic SST model
Deser et al. 2003
Heat content (EM)
Obs (dashed)
Entraining
Model (EM)
SST (EM)
SST (OBS)
Fig. 1. Conceptual ocean紡tmosphere systems considered in this study. (left) The original simple stochastic climate model of Frankignoul and Hasselmann (1977) and (right) the proposed extension. In both systems, temperature anomalies (T′) in the ocean mixed layer are assumed to result from atmospheric forcing (F′) only and damp back to the atmosphere at a rate λT′. In the original model, the mixed layer depth (H) is constant; in the extended model, H undergoes a strong seasonal cycle, with largest extent in winter and smallest in summer. In this configuration, T′ created in winter can persist beneath the summer mixed layer and become reentrained into the mixed layer the following winter, as indicated schematically by the thick black arrows. The effective thermal capacity of this system depends upon the depth of the winter mixed layer (Heff)

20. Deser et al. 2003
Heat content (EM)
Obs (dashed)
Entraining
Model (EM)
SST (EM)
SST (OBS)
North Atlantic
Left. Correlation of February SST anomalies with monthly SST anomalies from the previous January through the following September for a region in the far North Atlantic (50｡N-65｡N, 60｡W-10｡W). Values are plotted for the obser- vations(solid circles) and the MLM(open circles). The other curves are computed using Eq.5: with =15, 17.5, and 20 Wm-2C and h in February from observations(456m; dashed line) and from the MLM (240m; solid line); with =17.5 and h=50 m (squares); and with =17.5 and monthly values of averaged over the domain from the MLM (triangles).
Right: Mean seasonal cycle of mixed layer depth (m) for NPAC from observations (dashed) and that used in the entraining stochastic climate model (solid). (bottom) Monthly lag autocorrelation curves from Mar for heat content (solid step function like curve) and SST (solid) from the entraining model. The observed SST autocorrelation curve is dashed. The theoretical autocorrelation function for heat content based upon the extended simple stochastic climate model is shaded
Heff = winter MLD for interannual variability in a stochastic model

21. Main Concepts Mechanisms for the behavior of SST anomalies Questions?
Mixed Layers
Processes that control its depth
Wind stirring buoyancy forcing, density jump at base of ML
Processes that control its temperature (SST)
Surface heat flux
Entrainment heat flux
Mechanisms for the behavior of SST anomalies
Stochastic model
Reemergence
Large scale patterns of atmospheric forcing organizes fluxes, shapes SST Anomaly and reemergence patterns
Questions?

22. Reemergence of the late
1. What is the oceanic reemergence?
2. Surface signature of reemergence in the Labrador Sea
e-folding = ~ 36 mths
e-folding = ~ 4 mths
Auto-correlation of the Labrador SST time series
(Starting from March), e.g. for lag=1, March and April
time series are correlated, for lag =2 March and May etc.
Sea Surface
Temperature
Reemergence of the late
winter SST anomalies
a year after
Deser et al (J.Clim)
e-folding = ~ 4 mths
Auto-correlation of the Labrador SST time series
(all months considered), e.g. for lag=1, Jan50/Feb50/…/Dec00
values are correlated with Feb50/Mar50/…/Jan01 values
Level of
significance
ERSSTv2 Datasets [ ]
Degrees Celcius

23. Atmosphere forcing the ocean in winter: NAO & the Atlantic SST tripole
March SST EOF1 (shade)
Regressed JFM SLP (contour)
PC time series: March SST (bars),
JFM MSLP (line)
Correlation=0.63
NCEP MSLP [ ]
e.g. Deser and Timlin (1997), J.Clim.

24. Summary Forcing of SST (mixed layer temperature
Net heat flux key term, Ekman transport & entrainment also important
SST anomalies larger in summer than winer due to shallow MLD
Processes that impact extratropical SST variability
Stochastic atmospheric forcing
Reemergence
Atmospheric Bridge
Tropical Pacific => Global SSTs
Impacts in both winter and summer
Influence of air-sea feedback on extratropical atmosphere complex
Other Processes that influence SST variability
Cloud - SST feedbacks
Ocean currents & Rossby waves in western N. Pacific
Changes in the Thermohaline Circulation

25. Additional Topics The flux components and their variability
Schematic of the mixed layer model
Pattern of atmospheric circulation (SLP) and the underlying fluxes)
Basin-wide reemergence
The Pacific Decadal Oscillation
Wind generated Rossby waves and its relation to SSTs
The Latif and Barnett mechanism for the PDO and “problems” with this mechanism

26. Atmosphere-Ocean Ice Model
Atmospheric GCM
NCAR CAM2–T42 resolution
Ice
Thermodynamic portion of NCAR CSIMv4
Ocean
Mixed layer Model (MLM)
An individual column model with a uniform mixed layer
Atop a layered model that represents conditions in the pycnocline
Prognostic ML depth
Same grids as the atmosphere (128 lon x 64 lat)
36 vertical levels (from 0m to 1500m depth)
higher resolution close to surface and a realistic bathymetry
Flux correction needed to get reasonable climate
Cassou et al J Clim; Alexander et al JGR, Alexander et al 2002 – J.Clim ; Gaspar 1988 – JPO

27. Mixed Layer Ocean Model
Qnet
Qcor h
(MLD)
Qwe
Tm1
Tb1
Qswh CA

28. Mean ML Budget terms (Wm-2) in January From an AGCM couple to a mixed layer ocean model
Surface Flux
Qnet
Ekman
Qek =
cvek(Tm)
Entrainment
Qwe =
cwe(Tb-Tm)

29. Mean Mixed Layer Budget terms (Wm-2) in August

30. Standard Deviation of the Mixed Layer Budget Terms (Wm-2) in January
Standard deviation is a frequently used measure of variability about the mean.

31. Standard Deviation of Fluxes in August Results from an AGCM- Ocean MLM
Qnet
W m-2
Qwe =
cwe(Tb-Tm)
W m-2
Qwe /
Qnet

32. Fig11 JGR 2000
Fig.11. Composite of the six leading components (˚Cmon-1) of the SST tendency equation(3) as a function of calendar month. The composites are constructed at each MLM grid point based on when the local monthly SST tendency exceeds one standard deviation, the resulting values are then averaged between 20˚N-70˚N.

33. Wind Generated Rossby WavesL
Atmosphere
Ocean ML
Rossby
Waves
Thermocline
Wind sterss curl
West
East
After waves pass ocean currents adjust
Waves change thermocline depth, if mixed layer reaches that depth, cold water can be mixed to the surface

34. Observed Rossby Waves & SST
Correlation Obs SST hindcast
With thermocline depth anomaly
KE Region: 40°N, 140°-170°E
SSTOBS
T400
SSTfcst
March
Forecast equation for SST based on integrating wind stress
(curl) forcing and constant propagation speed of the
(1st Baroclinic) Rossby wave
Schneider and Miller 2001 (J. Climate)

35. Forecast Skill: Correlation with Obs SST Wave Model & Reemergence
years
Schneider and Miller 2001 (J. Climate)

38. Climatological heat fluxes August

39. Zonal Average of the standard deviation of the mixed layer budget terms

40. Observed SST (C) / SLP (mb) Warm-Cold (50-03)
DJF
JAS

41. Evolution of the leading pattern of SST variability as indicated by extended EOF analyses
No ENSO;
Reemergence
ENSO;
No Reemergence
Alexander et al. 2001, Prog. Ocean.

42. Upper Ocean: Temperature and mixed layer depth
El Niño – La Niña model composite: Central North Pacific
Alexander et al. 2002, J. Climate

43. ENSO SST & MLD in Western N. Pacific Region
Niño – Niña: NCEP Ocean Temp & White MLD ( )
La Niña MLD °C
20-30% increase in MLD in the Western North region Pacific
As large as 50% in some locations during late summer-early fall
El Niño MLD