Interactions between Surface Waves and Nonlinear Ekman Currents in

Gulf Stream Fronts as shown by SAR Images

Interactions between Surface Waves and Nonlinear Ekman Currents in

Gulf Stream Fronts as shown by SAR Images

Guoqiang LiuWith William Perrie Bedford Institute of Oceanography, Canada

Vladimir Kudryavtsev Satellite Oceanographic Laboratory (SOLab)

https://sites.google.com/site/guoqiangliu13/

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Physical Interpretation of SAR Imagery for Low Backscatter on Warm Side of the Thermal Frontal

Jet

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The average SST measured by TMI over the 3-day time period 11–13 Dec 2001. The vectors overlaid on the SST field are the QuikSCAT wind

stresses on 12 December 2001.

Chelton 2004 JC and Science

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A schematic summary of the SST influence on low-level winds

Chelton 2004 JC

Recently, it has been suggested that thermal fronts can be observed by SAR images [Xie et al., 2010; Chris J. 2012; Kuang et al., 2012].

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SeaSAR 2012, 18 June 2012 Chris Jones

However, some SAR image patterns violate this theory, Low Backscatter appear in the warm side of the

thermal front

RADARSAT-2 SAR image at UTC 22:28 on 30 January 2012 of the Gulf Stream region (enhanced processed)

Sea surface temperature acquired by NOAA-16 at UTC 00:11 31 January 2012

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What can cause the low backscatter in the SAR images?Is the damping films? Such as phytoplankton, rain band

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Is the wind shear?

Windsat 20120130 21:36 UTC (wind speed and direction)

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How about the wave-current interaction ?

Alpers and Hennings [1984]

NRCS Δσ/σ0 is proportional to the horizontal surface current gradient.

r is the coordinate in the look direction of the SAR antenna. A is a positive constant that depends on radar parameters and wind vector.

Lower Backscatter, We need a negative current gradient in the SAR looking direction.

So, is there a strong surface current gradient close to the thermal front?

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Surface ocean current is very complicated

Total surface current=Tidal current + geostrophic current + wave-driven current + Langmuir circulation + Ekman current + …

Which one contribute to the surface current gradient near the strong current jet??

Mechanism of the SAR imagery of nonlinear Ekman upwelling

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The theory of the Ekman layer is central to geophysical fluid dynamics and its applications to general circulation (Pedlosky 1987). Net Ekman transport is

The above theory is linear and the current divergence is typically small.

Current divergence at the sea surface

Wind never blow on the uniform current field, especially in dynamic Gulf Stream !!!

Wind stress coupling with the mesoscale vortex

DAVID S. TROSSMAN 2009 JPO

Ekman Transport

Ekman Suction

Upper oceanic Ekman dynamics become complicated

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The Nonlinear Ekman dynamics depends on the relative voricity ξ generated by mesoscale eddiesBut for mesosacle eddies, ξ is still small ~0.1f

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In the upper ocean, submesoscale dynamics often has big relative vorticity ~f

Sea surface Temperature from MODIS Ferrari 2011 SCIENCE Relative vorticity from ROMS model

Patrice et al 2010 JPO

Mixed layer instability and frontogenesis theory

A direct estimate of the large relative vorticity ξ is that the wind forced horizontal Ekman mass transport,

ME =-τ/ρ(f + ξ)

depends on the net vorticity of the flow field f + ξ

Mahadevan, A. et al., SCIENCE 2008

Nonlinear Ekman upwelling cause ~10 times of Normal Ekman upwelling

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Ocean Model current=geostrophic current + Ekman current + … 14

At the ocean surface, the Ekman current vector can be written as

u = τ/ρ[Aw (f + ξ)]1/2

Aw is the vertical viscosity coefficient. We use this equation to estimate surface nonlinear Ekman current

NRL Layered Ocean Model (NLOM) global ocean nowcast as the a priori existing current field in the Gulf Stream frontal region.

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Navy Layered Ocean Model (NLOM) model results

(a)Relative vorticity field calculated from the NLOM current field captured at 00:00 30 Jan 2012

(b) Surface current speed (m/s)

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(a) Distribution of current divergence from NLOM model results (1/s)

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(a) Schematic of negative and positive relative vorticity ξ on both sides of the Gulf Stream frontal jet. The blue dashed line indicates the north wall of Gulf Stream.

(b) Schematic of the generation of nonlinear Ekman upwelling and the surface current gradient.

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Schematic illustrating the generation of the SAR radar signature of the current gradient owing to the nonlinear Ekman dynamics

(a)surface Ekman current divergence in the frontal jet region(b) variation of the small scale sea surface roughness(c) variation in the radar image intensity; the relative dark band shows up in the current divergence region (‘delta-like ‘NRCS variation).

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(b) Section of SAR image (normalized on the mean value) taken along across the front direction by averaging in the yellow rectangular in (a). (c) Modeled NRCS over the yellow rectangular region (normalized on mean NRCS, VV component [dB])

As argued, the impact of the mesoscale ocean current on integral properties of the wind waves (like MSS and wave breaking parameters) is mainly governed by divergence of the sea surface current field.

Radar Imaging Model transfer function

The modeled result confirms the strong divergence induced by Nonlinear Ekman currents

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Bragg scattering: NRCS Bragg wave intensity;relation depends on incidence angle

Longer waves modulate the NRCS Tilt modulation affects incidence angle Hydrodynamic modulation affects Bragg wave

energy

Surface current affect the large waves, then modulate Bragg waves

Tilt and hydrodynamic modulationTilt and hydrodynamic modulation

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The Combination of RIM and COAWST The Combination of RIM and COAWST RIM Structure

Future study (the case is sunning for explaining this phenomena)

Surface wave spectrum with the effect of the ocean surface currents

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Roll Vortices from SAR

Submesoscale eddies

1. Liu, G., Perrie W., Vladimir. Kudryavtsev, Shen H., Zhang B., He Y. and Hu H., Physical Interpretation of SAR Imagery for Low Backscatter on Warm Side of the Thermal Frontal Jet. Submitted to Geophysical Research Letters.

2. Pedlosky, Joseph, 2008: On the Weakly Nonlinear Ekman Layer: Thickness and Flux. J. Phys. Oceanogr., 38, 1334–1339.

3. Mahadevan, A., L. Thomas and A. Tandon, 2008. Comment on "Eddy/Wind

Interactions Stimulate Extraordinary Mid-Ocean Plankton Blooms," Science,

320, 448b.

4. Chelton, D. B., S. K. Esbensen, M. G. Schlax, N. Thum, and M. Freilich (2001),

Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical Pacific, J. Clim., 14, 1479–1498.

5. Chelton, D. B., M. G. Schlax, M. Freilich, and R. F. Milliff (2004), Satellite measurements reveal persistent small‐scale features in ocean winds, Science, 303, 978–983.

Key references

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Call for Papers: Special Issue 

Ocean Modelling Special Issue on Ocean Surface Waves

•Wind input to waves, wave dissipation, wave-wave interactions, wave-current interactions; wave-ice interactions; coupled atmosphere-wave-ocean interactions, shallow water and nearshore effects, wave-mud interactions, propagation schemes, adaptive grids

•Theoretical, numerical, laboratory, and observational field studies (including in situ and remotely sensed data), in coastal or global oceans, in support of innovative new approaches to ocean wave modelling, and the evaluation of new approaches

•Operational forecasting, data assimilation and fusion methods in numerical wave models, wind fields for wave hindcasting or forecasting, simulation of case studies for dedicated field experiments, or storm events

•Application of wave models in the interpretation of climatic characteristics of waves and storms, climate change impacts on wave climate, extremal analysis, wave reanalyses/hindcasts, impacts of waves on ocean climate, and on the coupled atmosphere-ocean climate system.

Deadline for submissions is December 31, 2014. 

Thank you !

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