Recent observations and modelling studies of physical variability

along Line-P

Howard Freelandand

Patrick Cummins

Dept. of Fisheries and OceansInstitute of Ocean Sciences

Sidney, BC Canada

A brief reminder, the duty cycle of an Argo float

Density = (# of floats in an area) / (# of floats targetted in that area)

30°N

40°N

50°N

60°NArgo float density (14th June 2006)

180° 160°W 140°W 120°W

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.5

2

4

This is a recent picture of local coverage

The annual cycle of surface salinity at OSP:

32.4

32.5

32.6

32.7

J F M A M J J A S O N D

< Tabata and Peart1956-81

32.4

32.5

32.6

32.7

J F M A M J J A S O N D

< Marie Robert1956-91

32.4

32.5

32.6

32.7

J F M A M J J A S O N D

< Argo 2001-present

This change in the annual cycle was pointed out to me by Jim Gower and poses problems in the estimation of anomaly fields.

The annual cycle of surface salinity at OSP:

1960 1970 1980 1990 200032.2

32.4

32.6

32.8

33

Mon

thly

mea

n sa

linity

(psu

) The weather ship era Research vessel era Argo era

Freeland, H.J. K.L. Denman, C.S. Wong, F. Whitney and R. Jacques (1997), using rather less data than shown here, reported a freshening trend of 0.43 psu/century.

The effect on Mixed Layer Depth:-Year

Mid

-win

ter m

ixed

-laye

r dep

th

Regression line is 58 m/century

1960 1970 1980 1990 20000

50

100

150 Freeland, H.J. K.L. Denman, C.S. Wong, F. Whitney and R. Jacques (1997), using rather less data than shown here, reported a shallowing trend of 63 m/century.

Slightly more of the series was simulated by Cummins and Lagerloef (2002) with a stochastic climate model.

What does the structure of salinity variability in the upper ocean look like?

Jan-’02 >

Jan-’03 >

Jan-’04 >

Jan-’05 >

Jan-’06 >

And how does it propagate...

-400 -300 -200 -100 0 100 200 300 400

Displacement along Line-P (km)

-400

-300

-200

-100

0

100

200

300

400

Dis

plac

emen

t in

time

(day

s)

0.89 k

m/day

-5 -4 -3 -2 -1 0 1 2 3 4 5

n of wave number kn = 2πn/L

-5

-4

-3

-2

-1

0

1

2

3

4

5

m o

f fre

quen

cy ω

m =

2πm

/ T0

0.89 km/day

710 km.

810 d.

What was the nature of the changes in 2002?

Using the methods described in Freeland and Cummins, Argo: a new tool for environmental assessment and monitoring of the world’s oceans. Progress in Oceanog. 64(1), 31-44, 2005.

1) Compute dynamic height relative to 1000 dbars at every float location.

2) Compute and subtract mean dynamic height and compute variance.

3) Project these onto 20 EOFs of the stream function field derived from a quasi-geostrophic model of the N.E. Pacific and compute weights.

4) Sum mean and the weighted EOFs.

5) Typically this accounts of 87-93% of the total variance.

We saw massive changes in the latitude of the NPC

40°N

44°N

48°N

52°N

2002 2003 2004 2005 2006

←Strongest flow at 150°W

←Dividing streamline at 145°W

Here are a few specimen maps

Current strengths (Delta-dynamic height) are also variable.

Principal Component Analysis on the time series of

ΔDNPC, ΔDGAk and ΔDCCurr

On average: ΔDNPC, ΔDGAk and ΔDCCurr

61% of NPC water flows into the Gulf of Alaska

39% of NPC water flows into the California Current

Fluctuations: ΔD’NPC, ΔD’GAk and ΔD’CCurr

EOF #1 – 82% of variance associated with vector (.807, .307, .505)

EOF #2 – 18% of variance associated with vector (.113, -.759, .642)

NPC

NPC

GAk

GAk

CCurr

CCurrHow well are these things represented in Patrick’s model?

A survey of recent modelling of NE Pacific physical time series

Physical variables of interest: anomalies of– SST – SSS– SSH and upper layer thickness – Volume transport of North Pacific Current

Models of ocean variability:– Stochastic climate models– Reduced-gravity quasi-geostrophic models – Ocean general circulation models

Linear Stochastic Climate Models• Advanced by Hasselmann (1976). Simplest climate model (null

hypothesis for more complicated models). Most likely to apply inregions of relatively weak currents and mesoscale eddies. Of the form:

• Spectrum of the ocean response is a low-pass filtered version of the atmospheric forcing which often has a white noise spectrum,

• Feedback processes parameterized in terms of a linear damping with a time scale given by

.d qdtθ λθ= −

22

2 2

| ( ) || ( ) | Q ωωω λ

Θ =+

1.λ −

• Hall and Manabe (1997) examined how well linear stochastic theory applied to SST and SSS data from four weather stations:

• Compared SST and SSS spectra from observations and from an OGCM.

• Only internal oceanic processes (turbulent diffusion) damp SSS anomalies.

• Negative feedbacks for SST included latent and sensible heat transfers to the atmosphere, as well as turbulent diffusion. So shorter damping time scale is expected for SST: a means to test the theory.

Hall & Manabe, 1997. Can local linear stochastic theory explain sea surface temperature and salinity variability? Climate Dynamics. 13, 767-780.

1

1

Station P observationsSST : 4.3 monthsSSS : 11.6months

λ

λ

−

−

=

=

1

1

OGCM results at PapaSST : 28.2 monthsSSS : 5.7 months

λ

λ

−

−

=

=

Upper layer thickness and SSH variability

h = anomaly in pycnocline depth (positive upward)hs = sea surface height (SSH) anomalyH1 = mean layer depth

, reduced gravity parameter

Typically,

( ) oog ρρρ 1−=′

.500

1≈

hhs

hgghs′

−=

Freeland, Denman, Wong Whitney & Jacques, 1997. Evidence of change in the winter mixed layer in the northeast Pacific Ocean. Deep Sea Res. 44, 2117-2129.

Upper layer thickness variability and two-layer fit from an Alace float drifting

near OWS P

Reduced-gravity QG model

• Governing equation:

• - the potential vorticity.

• - Rossby radius of deformation.

• Linear damping with time scale given by λ–1.

• Ekman pumping velocity, we, determined from monthly mean NCEP reanalysis wind stress anomalies,

1R g H f′=

λζφθ

βζ−−=

∂∂

+∂∂

2cos Rwh

ate

( )2 2R hζ −= ∇ −

.ˆ1 f

zwe ρτ

×∇⋅=

Local Ekman Pumping Model• Neglecting the beta effect (and Rossby waves) along with

the minor contribution of the relative vorticity the QG model dynamics reduce to

• This has the form of the stochastic climate model of Hasselman (1976) driven by Ekman pumping. In discrete form it can be written in the form of a first-order auto-regressive (Markov) process.

• Lagerloef (1995) modelled 0-450 db dynamic heights inferred from XBT data and T-S relation for Gulf of Alaska.

( ),22 hRh −<<∇

.hwdtdh

e λ−=

Local Ekman model simulation of upper layer thickness anomalies at OWS P

Cummins & Lagerloef, 2002. Low frequency pycnocline depth variability at Ocean Weather Station P in the northeast Pacific. J. Phys. Oceanog. 32, 3207-3215.

Cummins & Lagerloef, 2004. Wind-driven interannual variability over the northeast Pacific Ocean. Deep Sea Res. 51, 2105 -2121.

How representative is variability at OWS P?

SSH correlation map

(Based on 1993-2003 satellite altimeter data)

Modelling SSH variability

• The models are evaluated in terms of hindcast skill

where and the angle brackets denote a time average. Single optimal value of g’ is:

with r the local correlation coefficient between interface displacement and the SSH data. the ratio of the interface displacement to the SSH variance. Overbar denotes spatial average over the NE Pacific.

2,o

rg g γγ

′ = −

( ) 2 21 o oS h h hα= − −

g gα ′= −

2γ

Cummins & Lagerloef, 2004. Wind-driven interannual variability over the northeast Pacific Ocean. Deep Sea Res. 51, 2105 -2121.

Fields contoured where .3.0≥S

Skill: QG model

Skill: local Ekman model

yrs 31 =−λ

1 2 yrsλ − =

-20.018 msog′ =

-20.017 msog′ =

S at OWS P 0.72=

S at OWS P 0.57=

An optimized hindcast with the local Ekman model

• Local value of g′ to optimize local fit to data:

• Initial conditions estimated from data:

• Single value of λ–1, but easily generalized to variable λ–1

to further optimize skill.

.0,00,

≥=′<−=′

rgrgrg γ

( ) ( ) ( )-2

, 0 , 0 ,

with 0.02 m s .oh t h t g g

g

′= = − =

′ =

x x

Cummins & Lagerloef, 2004. Wind-driven interannual variability over the northeast Pacific Ocean. Deep Sea Res. 51, 2105 -2121.

Skill of optimized local Ekman model with

Map of optimal .g′

1 2 yrs.λ − =

S at OWS P 0.82=

T/P-Jason data Optimized Ekman modelEOF 1

PC 1

EOF2

PC 2

Optimized Ekman modelT/P-Jason data

Capotondi, Alexander, Deser & Miller, 2005. Low frequency pycnocline variability in the northeast Pacific. J. Phys. Oceanog. 35, 1403-1419.

OGCM Results

• NCAR Ocean Model • global, non-eddy resolving• NCEP forcing • 40 year simulation ’58-’97 (Doney et al., 2003)

How well does the local Ekman model explain pycnocline variability in the OGCM?

Capotondi, Alexander, Deser & Miller, 2005. Low frequency pycnocline variability in the northeast Pacific. J. Phys. Oceanog. 35, 1403-1419.

1Optimal (months)λ −

Correlation coefficient

Capotondi, Alexander, Deser & Miller, 2005. Low frequency pycnocline variability in the northeast Pacific. J. Phys. Oceanog. 35, 1403-1419.

Pycnocline depth variability in the OGCM vs. local Ekman and Rossby wave models

Variability along 49 No

1970s 'regime shift'

Capotondi, Alexander, Deser & Miller, 2005. Low frequency pycnocline variability in the northeast Pacific. J. Phys. Oceanog. 35, 1403-1419.

Variability along 40.5 No

1970s 'regime shift'

Co-variability of the Alaska and California Currents

• 0-1000 db dynamics heights from Argo show that correlated in-phase variations of the Alaska and California Currents (the ‘breathing mode’) dominated over the anticorrelated variations (the ‘bifurcation mode’).

• Douglass et al. (2006) found evidence for the bifurcation mode in XBT sections for the period 1993-2002.

• Here we examine gyre transports from the reduced-gravity QG model in an integration with NCEP forcing for the period 1948 - 2003 and consider the statistical properties of the response.

QG model: mean streamlines AC and CC transport anomalies

AC

CC

Variance NPC AC CCMode 1: 69% 0.81 0.33 0.48Mode 2: 31% 0.09 0.75 -0.66

NPC=AC+CC

EOF decomposition of anomalies

-‘Breathing’ mode is dominant here-consistent with Argo observations

Summary

• Long time series data from the Line P program, and more recent data from satellite altimetry and Argo have proven essential in understanding nature of the physical variability of the NE Pacific Ocean.

• A hierarchy of models from the simplest stochastic climate models (Hasselmann, 1976) to complex OGCMsconstitutes a valuable set of tools to investigate the data.

• There is now compelling evidence for regarding large scale upper ocean variability over the interior of the NE Pacific as a response to direct atmospheric forcing.

• Only the product g′ H1 must be specified for the interface displacement. However, g′ is required for SSH.

• g′ H1 = 7.5 m2/s2 gives a reasonable fit to observed values the first mode deformation radii (Chelton et al., 1998).

Zonally-averaged long Rossby wave speed

QG Model Parameters

Ekman pumpingspectrum

Implications for forecastingBased on these studies, assume that anomalies of upper ocean mass field (vertically integrated heat content) are governed by a noise driven AR(1) process, viz.,

An appropriate forecast may be constructed from

where is the range of the forecast, hc is the (known) seasonal climatology, ha(t) are the anomalies observed at time t. w(m) is a weighting function.

For a noise-driven process, the best possible choice is weighted persistence of anomalies. Setting w(m) = γ m minimizes the mean square error. As expected, less weight is given to observed anomalies as the range increases, and the forecast reverts to climatology.

1,211 <+= ++ γεγ nnna hh

,,2,1,0),()()()( K=++=+ mthmwthth ac ττ

tmΔ=τ