air-sea exchange : 1 soee3410 : lecture 4 ian brooks

Air-Sea Exchange : 1

SOEE3410 : Lecture 4Ian Brooks

SOEE3410 :Atmosphere & Ocean Climate Change 2

Interaction with the Ocean Surface

• Unlike land surfaces, the ocean surface roughness changes with wind speed.– Higher winds larger waves

rougher surface

• The wave height that can be supported by a given wind speed is limited by gravity & the weight of water in the wave, and the loss of energy to the ocean mixed layer via turbulent mixing.


Charnock’s Relation

• A simple parameterization of ocean surface roughness as a function of the wind stress was formulated by Henry Charnock (1955).

where a is a constant (~0.015), and g is gravitational acceleration (9.8 ms-2).

g

uaz

2*

0


We have seen that the surface wind stress can be parameterized in terms of a drag coefficient and wind speed at a given height:

this can be related to the sea-surface roughness by Charnock’s relation

g

uaz

2*

0

22* UCu D

The problem of parameterizing the wind stress over the ocean thus becomes one of determining the drag coefficient as a function of variables that are easily measured or modelled.

CD has most often been parameterized as a simple function of wind speed with the assumption that wind and waves are in equilibrium.

– Waves fully developed

– Wind constant and with long ‘fetch’


Mean annual wind stress magnitude (N m-2) derived from satellite radar scatterometer measurements.


Wind-Wave Interaction

• The ocean surface roughness depends on the wind stress over it. A feedback process exists between wind speed, stress, and wave height

wind speed wind stress wave height

Energy transferto ocean

-

+

+

+

+


• The assumption of a steady state is an oversimplification

• The rapid motion of synoptic weather systems means winds are constantly changing speed and direction

• Fetch is often limited: e.g. in flow off-coast

• Time required to achieve steady state depends on wind speed– At low winds (~5 ms-s) steady

state is reached in about 2 to 3 hours.

– At high winds (~15 ms-1) it may take 24 hours

• Waves generated in one location propagate to areas with different wind conditions– Waves not all generated by

local wind

– Wind and wave directions NOT necessarily the same

– Direction of mean wind and wind stress not necessarily the same!

– Waves of different wavelengths may have different orientations and directions of travel.


Significant wave height (contoured), wave direction at spectral peak (arrows), wind speed (barbs)(NOAA OceanModelling Branch)


• Waves of different wavelengths interact in a non-linear fashion, transferring energy to wavelengths both higher and lower then the initial waves.– Short wavelength (high

frequency) waves break easily, dissipating energy in white-capping

– Long wavelength (low frequency) waves dissipate very little energy, and thus can travel far from their point of origin; known as swell

• One approach is to parameterize CD as a function of ‘wave age’.

• The wave age is the ratio between the friction velocity and phase-speed of the waves at the peak in the wave spectrum.Transfer of energy to longer wavelengths shifts the dominant wavelength with time. Longer waves travel faster than short, so that propagating waves disperse, becoming separated by wavelength.


9.5

20

37

52

80

0.10 0.2 0.3 0.4 0.5 0.6 0.7

0.1

0

0.2

0.3

0.4

0.5

0.6

Wave frequency (Hz)

Wav

e E

nerg

y (m

2 Hz-1

)

Evolution of wave spectrum with fetch (km)

Afte

r H

asse

lman

n et

al.,

197

3.


• The motion of water associated with waves and swell on the ocean surface is felt down to a depth approximately equal to the wavelength of the wave. If the water depth is much greater than this the waves are known as deep water waves. Wind driven waves on the open ocean are deep water waves.

• Shallow water waves occur when the water depth is less than the wavelength. In this case the waves feel the effect of the sea bed, and different physics apply.

• Shallow water waves occur over the continental shelves (depths ≤50 m) and near coasts.

• Wind stress–wave relationship is different for shallow water waves.


LOW WINDS

• Most measurements of fluxes on the atmospheric side of air-sea interface made in wind speeds of 2-15 ms-1.

• As mean wind zero, parameterizations based on mean wind speed will fail.

• Zero mean wind does not necessarily mean no air motion: localised gusts organised around individual convective cells (primarily in tropics).– Local airflow towards base of rising convection cell– Spatial/temporal average of gusts zero mean wind

• A gustiness factor needs adding to flux parameterization for convective conditions.


HIGH WINDS

• At high winds (>~15 ms-1) measurement becomes increasing difficult: motion of ships or buoys is severe; spray wetting of instruments; instruments on fixed towers risk damage from waves.

• Significant quantities of spray droplets in near-surface air– Increases drag on wind: Spray droplets accelerate to local wind

speed extracting momentum from near-surface wind. As they fall back into ocean they transfer this momentum to the ocean surface layer

– Surface heat flux modified: Evaporation of droplets removes heat from air above the surface

– Moisture flux modified: Evaporation adds water vapour to air above surface


Very recent measurements have shown that wave height and surface roughness (and hence CD and u*) do not continue to increase with ever higher wind speeds, but level off at about 30-40 m s-1 and may start to decrease again at higher winds. Several explanations for the physical processes involved have been proposed, but there is not yet full explanation.

Powell, M. D., P. J. Vickery, and T. A. Reinhold, 2003: Reduced drag coefficient for high wind speeds in tropical cyclones. Nature, 422, 279-283. doi:10.1038/nature01481.


A small digression…

• Wind-driven wave of 27.7m (91ft) measured during hurricane Ivan in 2004.

• Measured by US Navy Research Lab* via pressure sensors on sea bed – hydrostatic equation relates pressure to depth of water above.

• Computer models of Hurricane Ivan suggest the largest waves in region of strongest wind near eye-wall may have been up to 40m (132ft)!

• Measured waves larger than expected we still don’t fully understand wind-wave processes.

Image ©BBC

*Wang, D. W., D. A. Mitchell, W. J. Teague, E. Jarosz, M. S. Hubert. 2005: Extreme waves under Hurricane Ivan. Science, vol. 309, issue 5736, 896. DOI: 10.1126/science.1112509

http://www.sciencemag.org/cgi/content/full/309/5736/896


RRS Discovery

SHIPPING FORECAST ISSUED 0505 THURSDAY 30 NOV 2006

BAILEYSOUTHERLY STORM 10 TO HURRICANE FORCE 12. PHENOMENAL. RAIN OR SQUALLY SHOWERS. MODERATE, OCCASIONALLY POOR

RSS Discovery cruise D313

Maximum wave height : 17 m


February 2000, the largest waves ever recorded in the open ocean were measured by the UK Research Ship RRS Discovery : 29.1m

Sustained 10m winds speeds of 21 m s-1

Significant wave height Hs = 18.5 m(Hs = 4standard deviation of wave heights)

Again, wave models under-predicted the maximum wave heights.

Holliday, N. P., M. J. Yelland,R. Pascal, V. R. Swail, P. K. Taylor, C. R. Griffiths, and E. Kent (2006), Were extreme waves in the Rockall Trough the largest ever recorded?, Geophys. Res. Lett., 33, L05613, doi:10.1029/2005GL025238.


Surfactants modify the wave field because they change the surface tension of the ocean surface. The surfactant film damps the wave-field – particularly the shortest wavelengths – reducing the surface roughness.


Top-Down Turbulence

• Low-level, stratiform clouds (stratus and stratocumulus) absorbs both shortwave solar and longwave infra-red radiation, and emits longwave radiation.

• Over the ocean cloud base temperature is usually close to the sea-surface temperature Up- and down-welling

IR are almost equal below cloud

Up-welling IR is ~constant day & night. No down-welling IR at night.

Strong solar radiation daytime only


Longwave radiative cooling of cloud top causes cloud-top air to become more dense, and to sink downwards, generating turbulence convection driven by cooling at top of BL instead of heating at bottom.

Over large areas of ocean, when wind speed is low, this is the dominant processes generating turbulence. It is an important source of turbulence even for moderate windspeeds.


During the day, strong solar heating of the cloud offsets the longwave cooling. The cloud deck may become warmer than the air below, thus stable, and the cloud and sub-cloud layers become decoupled.

The cloud is then cut off from the source of water vapour, and may this or break up.

Turbulence is maintained in-cloud by radiative forcing – the peak of shortwave heating is below the peak for longwave cooling, thus destabilizing the upper part of the cloud and generating turbulence.

Below cloud turbulence is maintained via mechanical (wind driven) mixing.


Sensible Heat Flux

• The heat flux depends upon the difference in temperature between the air and sea surface.

• The relevant water temperature is the skin temperature, not the bulk water temperature.

• Skin temperature is maintained very close to bulk temperature by turbulent mixing within the ocean surface mixed layer except when the wind speed approaches zero.

• Water surface provides a uniform source of water vapour.

• The viscous sub-layer of air adjacent to water surface can be assumed to be saturated, and at the temperature of the water surface.

• Evaporation from surface requires input of latent heat from water – cools water surface slightly. The large heat capacity of water and turbulent mixing within ocean mixed layer limit the temperature drop.

Latent Heat Flux


Cool skin

Warm layer

residualmixed layer

Thermocline

Surface temperature

Solar radiationEvaporation

~1

-10

cm

~ m

etr

es

< 1 mm

ocea

n

~

~

• When wind-driven mixing is very low, solar radiation warms a thin layer of water near the surface. This increases local stability and further suppresses mixing.

• Evaporation of water at the surface causes evaporative cooling, producing a cooler ‘skin’ layer at the top of the warm layer. This is convectively unstable, promoting mixing within the warm layer, and limiting the extent of the cooling in the skin layer.


Additional Reading: Air-Sea Fluxes

• SOLAS (Surface Ocean Lower Atmosphere Study) Science plan:

http://www.uea.ac.uk/env/solas/aboutsolas/organisationaandstructure/sciplanimpstrategy/sciplanis.html

– Focus 2: Exchange processes at the air-sea interface

– Focus 3: Air-sea flux of CO2 and other long-lived radiatively active gases



air-sea exchange : 1 soee3410 : lecture 4 ian brooks

Documents

local wind wind

ocean slide

surface wind stress

given wind speed

simple function of wind

direction of mean wind

developed wind constant

annual wind stress magnitude