Damping of Tropical Instability Waves caused by the action of surface currents on stress

R. Justin Small1, Kelvin Richards2,

Shang-Ping Xie3, Pierre Dutrieux2, Toru Miyama4

School of Ocean and Earth Science and Technology, University of Hawaii

2. Department of Oceanography3. Department of Meteorology

4. Frontier/JAMSTEC, Yokohama, Japan1. Now at NRL, Stennis Space Center

Surface stress, bulk flux form.

ooDWINDNO

ooDCURRENTWIND

DCURRENTNO

UUC

UUUUC

UUC

1010&

1010

where U10 is 10m wind, UO is surface current, is air density and CD the drag coefficientPreviously considered by:•Bye (1986) -understress•Dewar and Flierl (1987) –’top drag’•Paconowski (1987) – OGCM, damping of equatorial currents•Luo et al (2005) CGCM, heat budget•and others

Our Aim: to investigate how ‘understress’ impacts Tropical Instability Waves in model and observations .

Methods• 1. IPRC Regional ocean-atmosphere Model

(IROAM).– IPRC Regional Atmospheric Model (Wang et al 2003)– MOM2 (Pacanowski and Griffies 2000)– Ocean current included in surface stress

• 2. Analysis: – data is filtered by removing 12° longitude running mean

(to highlight TIWs).– EKE budget– Modified EKE budget stress term

IPRC Regional Ocean-Atmosphere Model (iROAM) on ES

Atmosphere: IPRC-RAM0.5°×0.5°, L 28

GFDL Modular Ocean Model 20.5°×0.5°, L 30

InteractiveForced by

NCEP reanalysis

Ocean spin-up Coupled

‘91 – ‘95 96 – 03

Xie et al (2007), J. Climate

Methods (2)

Model Sensitivity Experiments:

Exp. 1. Fully coupled and with current in stress ‘Understress’.

Exp. 2 Coupled but no current in stress ‘No understress’

Exp. 3 Atmosphere-only

Eddy Kinetic Energy

Figure 1. EKE (kgm-1s-2), depth averaged from the surface to 100m. a): Experiment 1. b): Experiment 2.

Figure 2. EKE (kgm-1s-2), depth averaged to 100m then averaged between longitudes 140W to 110W. Thick solid line: experiment 1, Dashed line: experiment 2, Thin solid line: Experiment 1-Experiment 2.

The EKE is given by 1/20(u2+v2), and is computed from one year of data, May 1st 2000 to April 30th 2001, which includes one full TIW ‘season’. A depth average of the EKE is then performed to a depth of 95 m.

With understress No understress

Eddy Kinetic Energy Budget

Figure 4. Budget terms (Top) experiment 1 (Bottom) experiment 2 (no understress): barotropic (thick solid), baroclinic (thick dash), stress-current feedback (thin solid) modified stress-current feedback (thin dash). (10-5kgms-3)

y

Uu

x

UuuBT ,0

wgBC

h

uS

c

.

where BC is the baroclinic conversion, BT is the barotropic conversion and S is the stress-feedback damping term due to the interaction of the part of the stress modified by the TIWs with the TIW surface current field, the term of interest here. Here the angled brackets denote a depth average to depth h, uc

is the ocean surface velocity, u and U are the depth dependent ocean eddy and large scale current respectively, and is the surface stress.

Fully coupled

Eddy Kinetic Energy Budget (2)

Figure 4. Budget terms (Top) experiment 1 (Bottom) experiment 2 (no understress): barotropic (thick solid), baroclinic (thick dash), stress-current feedback (thin solid) modified stress-current feedback (thin dash). (10-5kgms-3)

.

The modified stress-current feedback is the effect on Exp. 2 (no understress) if understress was suddenly switched on:

1010

1010

UU

UUUU CCWm

h

uS

mc

m

No understress

understress

E-folding damping timescales at 3N are 30 days (unmodified), 12 days (modified).

Let’s identify the mechanism by which the eddies are damped – Ekman pumping

Surface stress curl is being modified by the surface currents

Figure 7c) Curl of the anomalous relative motion Us, (10-5s-1 per m) from Exp 1 with the ocean vorticity (10-5s-1 per m) regression is overlaid as contours. d) Exp 2. as c).

Therefore the eddies are damped via Ekman pumping

Figure 8. Ekman pumping (color, 10-6 ms-1cm-1) and SSHA (contours), both regressed onto SSHA at 120W, 4.5N. a) using observations of sea surface height anomalies (SSHA) from TOPEX/POSEIDON altimeters and stress derived from 10 m neutral wind from QuiKSCAT. b) Exp 1. c) as b) but with estimated Ekman pumping derived from Exp. 1 vorticity (contours, 10-6 ms-

1cm-1).

c)

fxwE

0

1

Ekman pumping same sign as the SSH anomalies – leads to decay, e-folding timescale ~115 days

Effect on cold tongue/Equatorial Front

Figure B. Heat flux (top ocean model level), due to horizontal advection. Left: mean flow. Right: eddy heat flux. Units are C/day. Averaged from 130 W to 100 W. From fall of 2000 (4 months of data).

 

Figure A. Annual cycle of the difference in monthly mean SST (°C), Exp. 1 minus Exp. 2, as a function of latitude. The data is averaged between 120W and 100 W. 10 m wind differences are also shown, northward pointing up and eastward pointing right, with a 0.7ms-1 scale arrow shown. From IROAM 8-year climatology.

 Heat flux by eddies and upwelling is affected by understress

SST Understress - standard

In the absence of generation and conversion terms, the understress would cause the EKE to decay on an e-folding timescale of just 30 days, comparable to the time period of the TIWs.

Summary

The Ekman pumping anomalies compares well with a rough estimate which assumes that only the understress is modifying the stress. The consequent dissipation has an e-folding timescale of 115 days.

Mean SST at Equatorial Front is affected by undestress, with a reduction of up to 0.4°C occurring in Fall.

Part 2. How to detect currents from stress: a method

• Satellite scatterometers measure the stress at the surface due to wind relative to surface current. Can we somehow use this to measure surface current? We need some knowledge or assumption about the winds.

• First attempt is to filter scatterometry to show oceanic mesoscale which is smaller than atmospheric mesoscale. Near equator:– Atmospheric Rossby radius 6-12 degrees latitude. – Oceanic Rossby radius 1-3 degrees latitude.

• Then show the rotational part of the stress which should be strongly affected by the rotational part of the ocean eddies. ( Divergent part of stress may be affected by SST gradients.)

Equatorial currents Kelly et al, GRL, 28, 2469-2472, 2001.

IROAM: Snapshots

1 Sep 1999

20 Sep 1999

10 Oct 1999

Ocean Surface Vorticity Curl of 10 m neutral wind x (-1)

Filter by removing 10°longitude running mean

IROAM: Hovmöller diagrams

Ocean surface vorticity Curl of neutral wind (*-1)

Linear regression onto vorticity (IROAM)

a) Surface ocean vorticity (color) and currents (vector.) Both are regressed onto vorticity at 4. N, 120 W.

b) Minus curl of 10 m neutral winds regressed onto same vorticity index as in a). Vectors show the rotational part of the neutral winds, and vector units are same as in a).

Linear regression onto vorticity (observed)

a) From altimetry: geostrophic vorticity (color) and geostrophic currents (vector.) Both are regressed onto vorticity at 4.5 N, 120 W.

b) From QuiKSCAT: minus curl of 10 m neutral winds regressed onto same vorticity index as in a). Vectors show the rotational part of the neutral winds, and vector units are same as in a).

How to improve method• The curl of the small-scale stress (or neutral wind)

is not just dependent on ocean current.• Other factors include:

– curl associated with small scale atmospheric features such as fronts.

– Curl associated with SST gradients

• Small scale atmospheric curl may be estimated (?) from NWP products. Alternatively, may be removed by time averaging. (Cornillon and Park 2001).

• Curl associated with SST gradients has been related to the strength of the SST gradient perpendicular to the wind.(Chelton et al 2001).

Applications to other regions

Central Pacific ~ Hawaii Indian Ocean SEC – IT Eddies

Observed SSH (contour) and 10 m neutral wind curl (color) regressed onto SSH at a fixed point. From 3 years of data.

Summary Part 2

A potential method to identify currents from surface stress is identified.Fully removing the atmospheric influence on stress is difficult without some kind of time averaging.

SchematicNo current

Some stress

Wind with equal current

No stress

No shear at interface

Shear above interface

Wind against current

More stress

Wind

Sea Surface

Current

High shear across interface

Wind

Sea Surface

Wind speeds increase over warmer SST due to pressure gradient effects and momentum mixing Small et al 2003, J. Climate

Surface stress curl is being modified by the surface currents

Figure 7. a, b) Curl of the anomalous stress (color) regressed onto SSHA at 120W, 4.5N. Units 10-6Nm-3 per m of SSH. a) Exp 1. The SSH regression is overlaid as contours. b) Exp 2. The SSH regression is overlaid as contours.

Sea Surface Height Anomaly

Fig. 3. SSH standard deviation due to TIW variability (color, cm). Top left) IROAM Exp. 1, with understress Top right) IROAM Exp. 2, no understress. Bottom) Observations from altimetry. In top row the mean SSH (cm) is added as contours.

With understress No understress

Observations

From Chelton et al (2001, JCLI.)

Tropical Instability Waves modify surface stress in two main ways:1. By modifying the overlying wind

Results from a regional coupled model, Xie et al (2007)

Ocean surface currents will modify the stress (relative motion effect)