Flux Model Comparisons Note: There is a lot of detail slides that will be skipped.

Flux Model ComparisonsFlux Model Comparisons

Note: There is a lot of detail slides that will be skipped.

Modeled Mean of Fluxes (1997-2004)Modeled Mean of Fluxes (1997-2004)

SW IndianSW Indian SW PacificSW Pacific Drake PassDrake Pass Cold TongueCold Tongue KuroshioKuroshio Gulf StreamGulf Stream GlobalGlobal



Stress (N mStress (N m-2-2))

Sensible Heat Flux (W mSensible Heat Flux (W m-2-2))

Latent Heat Flux (W mLatent Heat Flux (W m-2-2))

SummerSummer

WinterWinter

W m

W m

-2-2W

mW

m-2-2

N m

N m

-2-2

Datasets (Datasets (January 30, 1997 January 30, 1997 → → December 31, 2004December 31, 2004))

• Coordinated Ocean Reference Experiment (CORE) version 1:Coordinated Ocean Reference Experiment (CORE) version 1:

o Combined satellite and NCEP reanalysis data.Combined satellite and NCEP reanalysis data.o 10 m Air Temperature, 10 m winds, 10 m specific humidity, and SLP.10 m Air Temperature, 10 m winds, 10 m specific humidity, and SLP.o Provided at 4 Times/DayProvided at 4 Times/Dayo dx=1.875dx=1.875°°, dy~1.875, dy~1.875°°

• Reynolds (2006) OI SST:Reynolds (2006) OI SST:

o Enhanced with Pathfinder AVHRR DataEnhanced with Pathfinder AVHRR Datao Provided DailyProvided Dailyo dx=0.25dx=0.25°, dy=0.25°; re-gridded to 1.875°.°, dy=0.25°; re-gridded to 1.875°.

• NOAA Wavewatch 3 (NWW3) Modeled Global Wave Data (Tolman, 2002):NOAA Wavewatch 3 (NWW3) Modeled Global Wave Data (Tolman, 2002):

o Utilizing the following data types: significant wave height (m), dominant wave Utilizing the following data types: significant wave height (m), dominant wave period (s), and wave direction (degrees).period (s), and wave direction (degrees).

o Provided 6 Times/DayProvided 6 Times/Dayo dx=1.25dx=1.25°, dy=1°; re-gridded to 1.875°°, dy=1°; re-gridded to 1.875°

• Two commonly applied approaches are:Two commonly applied approaches are:

1.1. with a drag coefficient (with a drag coefficient (CCDD) and wind speed ) and wind speed (U):(U):

2.2. with a roughness length, with a roughness length, zz00, solve the log wind equation for , solve the log wind equation for uu**::

Estimating StressEstimating Stress

κκ == 0.4 0.4 →→ von Karman constant von Karman constant

z z == 10 m 10 m →→ reference height reference height

LL →→ Monin-Obukhov stability length Monin-Obukhov stability length

U(z)U(z) →→ wind at height wind at height zz

ϕϕ →→ stability parameterstability parameterzz00 → → roughness lengthroughness length

Effect of Stability on Transfer CoefficientsEffect of Stability on Transfer Coefficients

• This particular example is using the stress parameterization of Smith (1988).

o Lines are isopleths of Tair-Tskin

StableStable

UnstableUnstable

Drag Coefficient vs. Wind SpeedDrag Coefficient vs. Wind Speed Heat Transfer Coeff. vs. Wind SpeedHeat Transfer Coeff. vs. Wind Speed

UnstableUnstable

StableStable

UU1010(m/s)(m/s) UU1010(m/s(m/s)

CCDD (

x10

(x1

0-4-4))

CCHH (

x10

(x1

0-4-4))

Global Near-Surface Stability DistributionGlobal Near-Surface Stability Distribution

sfc

sfc

v vb 2

v 10

gz( T )Ri

T U

Near-Neutral RiNear-Neutral Ribb Stability (1997-2004) Stability (1997-2004)

* Expressed as a percentage of the ‘Local’ Ri* Expressed as a percentage of the ‘Local’ Ribb distribution. distribution.

Drake Drake PassagePassage

Gulf StreamGulf Stream

KuroshioKuroshio

Other WBCsOther WBCs

~70% Near-Neutral ~70% Near-Neutral 24.4 % Moderately Unstable24.4 % Moderately Unstable

Atmospheric Stability ParameterizationsAtmospheric Stability Parameterizations

• “ “Neutral Assumption”:Neutral Assumption”:

o Stability functions for momentum, temperature, and moisture are set to zero.Stability functions for momentum, temperature, and moisture are set to zero.

• “ “Old”: Businger-Dyer relationsOld”: Businger-Dyer relations

o Stable stratification (Businger et al. 1971 and Dyer 1974):Stable stratification (Businger et al. 1971 and Dyer 1974): linear relationshiplinear relationship

o Unstable stratification (Businger 1966 and Dyer 1967):Unstable stratification (Businger 1966 and Dyer 1967): non-linear relationship (more complex than previous)non-linear relationship (more complex than previous)

• “ “New”: (more recent and complex than Businger-Dyer)New”: (more recent and complex than Businger-Dyer)

o Stable stratification (Beljaars and Holtslag 1991):Stable stratification (Beljaars and Holtslag 1991): non-linear relationship non-linear relationship

o Unstable stratification (Benoit 1977):Unstable stratification (Benoit 1977): modified and more complex form of Businger-Dyermodified and more complex form of Businger-Dyer

• Large and Pond (1981):Large and Pond (1981):o Neutral Drag coefficientNeutral Drag coefficient::

o DiscontinuousDiscontinuous at 10 m s at 10 m s-1-1

o Produces a neutral stress (i.e. Produces a neutral stress (i.e. stability has no impact on stressstability has no impact on stress))

• Large et al. (1994):Large et al. (1994):o Neutral DragNeutral Drag coefficient: coefficient:o Difference from Large and Pond:Difference from Large and Pond:

ContinuousContinuous at all wind speeds at all wind speeds

• Smith (1988):Smith (1988):

o Charnock (1955) based Charnock (1955) based roughness lengthroughness length, , αα=0.011.=0.011.o Dependent upon changes in uDependent upon changes in u**

o Differences from previous:Differences from previous: Stress is determined by roughnessStress is determined by roughness Stress is influenced by stabilityStress is influenced by stability

Sea-state Independent ParameterizationsSea-state Independent Parameterizations

Sea-state Dependent ParameterizationsSea-state Dependent Parameterizations

• HEXOS (Smith et al. 1992, 1996)HEXOS (Smith et al. 1992, 1996)o Similar to Smith (1988), but Similar to Smith (1988), but roughness is now a function of inverse wave ageroughness is now a function of inverse wave age ( (CCpp//uu**))--11::o Generally producesGenerally produces

Greater stress for rising seas (steeper waves),Greater stress for rising seas (steeper waves), Smaller stress for falling seas (swell).Smaller stress for falling seas (swell). Doesn’t apply for swell.Doesn’t apply for swell.

• Taylor and Yelland (2001)Taylor and Yelland (2001)o An alternative to HEXOS, where An alternative to HEXOS, where roughness length is a function of wave heightroughness length is a function of wave height ( (HHss) and ) and

wave-slopewave-slope ( (HHss//LL).).o Differences from HEXOS:Differences from HEXOS:

No dependency on friction velocity.No dependency on friction velocity. Open-ocean wind stresses are less likely to be overestimated.Open-ocean wind stresses are less likely to be overestimated.

• Bourassa (2006):Bourassa (2006):o Adds a surface componentAdds a surface component to the log-wind profile, U to the log-wind profile, Uorborb= = ππ(H(Hss/T/Tpp))

Shear is decreased when swell and wind are directionally alignedShear is decreased when swell and wind are directionally aligned (i.e. a majority of (i.e. a majority of cases). cases).

Shear is increased when swell and wind are directionally opposedShear is increased when swell and wind are directionally opposed (i.e. outflow (i.e. outflow boundaries and fast-moving cold fronts). boundaries and fast-moving cold fronts).

Enhanced shear produces higher stressesEnhanced shear produces higher stresses, which is further enhanced by a Charnock-, which is further enhanced by a Charnock-based roughness length, with an empirically derived Charnock parameter, based roughness length, with an empirically derived Charnock parameter, αα=0.035.=0.035.

Observed (x) and Modeled (y) Friction Observed (x) and Modeled (y) Friction Velocity (Velocity (uu**))

Large and Pond (1981) Smith (1988)

Taylor and Yelland (2001)

Bourassa (2006)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.0 0.2 0.4 0.6 0.8 1.0 1.20.0 0.2 0.4 0.6 0.8 1.0 1.2

1.2

1.0

0.8

0.6

0.4

0.2

0.0

1.2

1.0

0.8

0.6

0.4

0.2

0.0

1.2

1.0

0.8

0.6

0.4

0.2

0.0

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Results of Bourassa (2006) Results of Bourassa (2006) Compared to SWS2 ObservationsCompared to SWS2 Observations

•This variation has a non-zero Newtonian frame of references and displacement height.

•Displacement height is a fraction of the significant wave height.

10

0.80.8 log s

EN current orbitalv o

z HuU u U

k z

0.52 22

2

0.0190.035o

uz

u g

• Charnock’s constant

is actually constant.

Wildly Different Models & Wildly Different Models & ObservationsObservations

•Courtesy Will Drennan

Consistency CheckConsistency Check

• An eighteen member ensemble of flux ‘models’ is used to check for consistency.

o Six drag coefficient or roughness length parameterizationso Three stability parameterizations (including neutral stability)o Results in eighteen (six times three) combinations

• Extremes at the high and low ends are inconsistent.

o This consistency check focuses on more typical valueso The inter-quartile range (IQR) is calculated for each grid cell for each season and

each flux modelo The diagnostic we use for consistency is the standard deviation of the IQR

Note that this diagnostic focuses more on a difference in range of values than in a shift of the mean.

Latent Heat Flux InconsistenciesLatent Heat Flux Inconsistencies

Standard DeviationStandard Deviation from Mean IQR (1997-2004)

Stress InconsistenciesStress Inconsistencies

Standard DeviationStandard Deviation from Mean IQR (1997-2004)

Stand-Alone Flux AlgorithmsStand-Alone Flux Algorithms

• COAREv3.0 (Fairall et al. 2003): Most COAREv3.0 (Fairall et al. 2003): Most state-of-the-artstate-of-the-art flux algorithm to date. flux algorithm to date.

o Many additional considerations, but only the following are utilized:Many additional considerations, but only the following are utilized: Taylor and Yelland (2001) Roughness Length. Taylor and Yelland (2001) Roughness Length. Businger-Dyer Relations blended with Businger-Dyer Relations blended with Grachev et al.Grachev et al. (2000) for Unstable (2000) for Unstable

conditions.conditions. Beljaars and Holtslag (1991) for Stable conditions.Beljaars and Holtslag (1991) for Stable conditions. RiRibb to to reduce # of iterations for stability down to 3reduce # of iterations for stability down to 3 (previous version required 20). (previous version required 20). Webb et al. (1980) correctionWebb et al. (1980) correction to improve the accuracy of Latent Heat Flux to improve the accuracy of Latent Heat Flux

estimates.estimates. A A more up-to-date temperature and moisture roughness lengthmore up-to-date temperature and moisture roughness length

parameterization, relative to what is utilized by the previous stress-related parameterization, relative to what is utilized by the previous stress-related parameterizations.parameterizations.

• Kara et al. (2005): A Kara et al. (2005): A Polynomial Curve Fit to COAREv3.0Polynomial Curve Fit to COAREv3.0..

o 0 Stability iterations.0 Stability iterations.o No sea-state dependency.No sea-state dependency.o Polynomial expressions are supplemented by a look-up table to calculate heat, Polynomial expressions are supplemented by a look-up table to calculate heat,

moisture, and momentum transfer coefficients. moisture, and momentum transfer coefficients.o Stability and wind speed variations are implicitly accounted for.Stability and wind speed variations are implicitly accounted for.o Advertises reasonable agreement with COAREv3.0 at Advertises reasonable agreement with COAREv3.0 at 5X greater efficiency5X greater efficiency..

Stress-Related ComparisonStress-Related Comparison

• Examined at the Gulf Stream and Drake Passage.Examined at the Gulf Stream and Drake Passage.

• Stability parameterizations held constant, allowing for direct comparison of stress-Stability parameterizations held constant, allowing for direct comparison of stress-related parameterizations.related parameterizations.

• Only results from the ‘New’ stability parameterizations are shown. Results from Only results from the ‘New’ stability parameterizations are shown. Results from remaining parameterizations are qualitatively similar.remaining parameterizations are qualitatively similar.

• A seasonal comparison is included: Summer vs. Winter.A seasonal comparison is included: Summer vs. Winter.

o Seasons are hemisphere-relative.Seasons are hemisphere-relative.

• Key Features to Notice:Key Features to Notice:

o The tails of the distributions are the episodic events.The tails of the distributions are the episodic events.o Distinctions between sea state independent-dependent parameterizations.Distinctions between sea state independent-dependent parameterizations.o Seasonal changes in the strength of episodic events, as determined by the Seasonal changes in the strength of episodic events, as determined by the

estimated flux magnitudes.estimated flux magnitudes.o Seasonal changes in parameterized consistency.Seasonal changes in parameterized consistency.

Gulf Stream: Latent Heat FluxGulf Stream: Latent Heat Flux

Summer: July - SeptemberSummer: July - September Winter: January - MarchWinter: January - March

Gulf Stream Region: Gulf Stream Region:

IQR InconsistenciesIQR Inconsistencies

RMS Diff. from Mean:RMS Diff. from Mean:

≤ ≤ 5% 5% 9.21 % 9.21 %

≤ ≤ 5 W m5 W m-2-2 19.13 % 19.13 %


≤ ≤ 5% 5% 3.70 % 3.70 %

≤ ≤ 5 W m5 W m-2-2 10.09 % 10.09 %

← ← Fractional Fractional →→

← ← Absolute Absolute →→

ModerateModerate

IntenseIntense

Extreme!Extreme!

Drake Passage: Latent Heat FluxDrake Passage: Latent Heat Flux

Summer: January - MarchSummer: January - March Winter: July - SeptemberWinter: July - September

Drake Passage: Drake Passage:

IQRIQR InconsistenciesInconsistencies


≤ ≤ 5% 5% 8.42 % 8.42 %

≤ ≤ 5 W m5 W m-2-2 74.03 % 74.03 %


≤ ≤ 5% 5% 7.59 % 7.59 %

≤ ≤ 5 W m5 W m-2-2 58.80 % 58.80 %



ModerateModerate

IntenseIntense

Extreme!Extreme!

Gulf Stream: Sensible Heat FluxGulf Stream: Sensible Heat Flux





≤ ≤ 5% 5% 4.02 % 4.02 %

≤ ≤ 5 W m5 W m-2-2 76.34 % 76.34 %


≤ ≤ 5% 5% 3.56 % 3.56 %

≤ ≤ 5 W m5 W m-2-2 28.24 % 28.24 %



ModerateModerate

IntenseIntense

Extreme!Extreme!

Drake Passage: Sensible Heat FluxDrake Passage: Sensible Heat Flux





≤ ≤ 5% 5% 8.46 % 8.46 %

≤ ≤ 5 W m5 W m-2-2 65.49 % 65.49 %


≤ ≤ 5% 5% 10.79 % 10.79 %

≤ ≤ 5 W m5 W m-2-2 46.64 % 46.64 %



ModerateModerate

IntenseIntense

Extreme!Extreme!

Gulf Stream: StressGulf Stream: Stress





≤ ≤ 5% 5% 0.89 % 0.89 %

≤ ≤ .05 N m.05 N m-2-2 71.95 % 71.95 %


≤ ≤ 5% 5% 4.02 % 4.02 %

≤ ≤ .05 N m.05 N m-2-2 97.28 % 97.28 %



ModerateModerate

IntenseIntense

Extreme!Extreme!

Drake Passage: StressDrake Passage: Stress





≤ ≤ 5% 5% 2.58 % 2.58 %

≤ ≤ .05 N m.05 N m-2-2 83.17 % 83.17 %


≤ ≤ 5% 5% 1.72 % 1.72 %

≤ ≤ .05 N m.05 N m-2-2 73.20 % 73.20 %



ModerateModerate

IntenseIntense

Extreme!Extreme!

Gulf Stream: Curl of the StressGulf Stream: Curl of the Stress





≤ ≤ 5% 5% 1.60 % 1.60 %

≤ ≤ 5x105x10-8-8 N m N m-3-3 74.87 % 74.87 %


≤ ≤ 5% 5% 0.36 % 0.36 %

≤ ≤ 5x105x10-8-8 N m N m-3-3 35.58 % 35.58 %



ModerateModerate

IntenseIntense

Extreme!Extreme!

Drake Passage: Curl of the StressDrake Passage: Curl of the Stress





≤ ≤ 5% 5% 0.59 % 0.59 %

≤ ≤ 5x105x10-8-8 N m N m-3-3 42.61 % 42.61 %


≤ ≤ 5% 5% 0.46 % 0.46 %

≤ ≤ 5x105x10-8-8 N m N m-3-3 31.52 % 31.52 %



ModerateModerate

IntenseIntense

Extreme!Extreme!

Result SummaryResult Summary

•Parameterization consistency tends to deteriorate in response to the Parameterization consistency tends to deteriorate in response to the strength of the forcing.strength of the forcing.

o There is relatively large amount of strong forcing in high latitudesThere is relatively large amount of strong forcing in high latitudeso More common in the Southern OceanMore common in the Southern Oceano Stronger events in the NH mid to high latitudesStronger events in the NH mid to high latitudes

• Inconsistencies are ‘primarily’ due to various sea-state dependencies.Inconsistencies are ‘primarily’ due to various sea-state dependencies.

o More pronounced in the Gulf Stream than in Drake Passage.More pronounced in the Gulf Stream than in Drake Passage. Indicates that sea-state in Drake Passage is more swell dominant, Indicates that sea-state in Drake Passage is more swell dominant,

where the Gulf Stream is more wind-wave dominant.where the Gulf Stream is more wind-wave dominant.Wind-waves provide greater roughness than swell, which translates to Wind-waves provide greater roughness than swell, which translates to

greater stress and heat flux estimates.greater stress and heat flux estimates.

o Non-neutral stability provides relatively ‘minor’ inconsistencies with Non-neutral stability provides relatively ‘minor’ inconsistencies with regard to the COAREv3 and Kara et al. (2005) algorithms.regard to the COAREv3 and Kara et al. (2005) algorithms.

ConclusionsConclusions

• How Practical Is the Assumption of Sea-state Independence?How Practical Is the Assumption of Sea-state Independence?

o Depends on the region .Depends on the region .Tropical, open-ocean regions (i.e. where episodic wind-stress and wind-Tropical, open-ocean regions (i.e. where episodic wind-stress and wind-

waves are minimal) provide the best consistency.waves are minimal) provide the best consistency.WBC and ice-edge regions contain a higher probability of episodically WBC and ice-edge regions contain a higher probability of episodically

induced wind stress and sea-state conditions, where associated induced wind stress and sea-state conditions, where associated inconsistencies are physically significant.inconsistencies are physically significant.

o Depends on the time of year.Depends on the time of year.Summer months contain relatively mild episodic events over most Summer months contain relatively mild episodic events over most

regions (exception: tropical storms and monsoons).regions (exception: tropical storms and monsoons).Winter months are prone to fast moving cold-air outbreaks, which result Winter months are prone to fast moving cold-air outbreaks, which result

in substantially younger seas with higher wind-wave heights, in substantially younger seas with higher wind-wave heights, contributing to higher roughness lengths, which finally produces greater contributing to higher roughness lengths, which finally produces greater heat flux and stress estimates. Consistency diminishes as flux heat flux and stress estimates. Consistency diminishes as flux magnitude increases.magnitude increases.

Conclusions - ContinuedConclusions - Continued

• How Good is the Assumption of Neutral Stratification?How Good is the Assumption of Neutral Stratification?

o Depends on the region.Depends on the region.Higher wind speeds result in a higher probability of ‘near-neutral’ Higher wind speeds result in a higher probability of ‘near-neutral’

events, which is why open-ocean regions (i.e. Southern Oceans) tend to events, which is why open-ocean regions (i.e. Southern Oceans) tend to be dominated by ‘near-neutral’ events.be dominated by ‘near-neutral’ events.

Cold-air outbreaks are fairly common in WBC and ice edge regions, Cold-air outbreaks are fairly common in WBC and ice edge regions, resulting in highly unstable conditions, due to the contrast of warm resulting in highly unstable conditions, due to the contrast of warm SSTs with a cold and dry air mass.SSTs with a cold and dry air mass.

o Depends on the flux diagnostic being examined.Depends on the flux diagnostic being examined.Latent and Sensible heat fluxes are the Latent and Sensible heat fluxes are the MostMost sensitive to changes in sensitive to changes in

atmospheric stability, and therefore the estimates are most adversely atmospheric stability, and therefore the estimates are most adversely affected by non-neutral conditions.affected by non-neutral conditions.

If a modeler is mainly concerned with estimating stress, he/she could If a modeler is mainly concerned with estimating stress, he/she could use the ‘Neutral’ assumption for a greater variety of atmospheric use the ‘Neutral’ assumption for a greater variety of atmospheric conditions.conditions.

ReferencesReferences

• Beljaars, A. C. M., and A. A. M. Holtslag, 1991: Flux parameterization over land surfaces for atmospheric models, Beljaars, A. C. M., and A. A. M. Holtslag, 1991: Flux parameterization over land surfaces for atmospheric models, JJ.. Appl Appl.. Meteor Meteor..,, 3030, , 327-341. 327-341.

• Benoit, R., 1977: On the integral of the surface layer profile-gradient functions.Benoit, R., 1977: On the integral of the surface layer profile-gradient functions. J J.. Appl Appl.. Meteor. Meteor., , 1616, 859-560., 859-560.

• Bourassa, M. A., 2006: Bourassa, M. A., 2006: Satellite-based observations of surface turbulent stress during severe weatherSatellite-based observations of surface turbulent stress during severe weather, , Atmosphere - ocean interactionsAtmosphere - ocean interactions, , Vol. 2., W. Perrie, Ed., Wessex Institute of Technology Press, 35 – 52 pp.Vol. 2., W. Perrie, Ed., Wessex Institute of Technology Press, 35 – 52 pp.

• Businger, J. A., 1966: Transfer of heat and momentum in the atmospheric boundary layer. Businger, J. A., 1966: Transfer of heat and momentum in the atmospheric boundary layer. Proc. Arctic Heat Budget and Atmospheric Proc. Arctic Heat Budget and Atmospheric CirculationCirculation, Santa Monica, CA, RAND Corporation, 305-332., Santa Monica, CA, RAND Corporation, 305-332.

• ______, J. C. Wyngaard, Y. Izumi, and E. F. Bradley, 1971: Flux profile relationships in the atmospheric surface layer. ______, J. C. Wyngaard, Y. Izumi, and E. F. Bradley, 1971: Flux profile relationships in the atmospheric surface layer. JJ.. Atmos Atmos.. Sci Sci., ., 2828, , 181-189.181-189.

• Charnock, H., 1955: Wind stress on a water surface. Charnock, H., 1955: Wind stress on a water surface. QuartQuart.. J J.. Roy Roy.. Meteor Meteor.. Soc Soc., ., 8181, 639-640., 639-640.

• Dyer, A. J., 1967: The turbulent transport of heat and water vapour in an unstable atmosphere. Dyer, A. J., 1967: The turbulent transport of heat and water vapour in an unstable atmosphere. QuartQuart.. J J.. Roy Roy.. Meteor Meteor.. Soc Soc., ., 9393, 501-508., 501-508.

• ______, 1974: A review of flux-profile relationships. ______, 1974: A review of flux-profile relationships. BoundBound..-Layer Meteor-Layer Meteor., ., 77, 363-372., 363-372.

• Fairall, C. W., E. F. Bradley, J. E. Hare, A. A. Grachev, and J. B. Edson, 2003: Bulk parameterizations of air-sea fluxes: updates and Fairall, C. W., E. F. Bradley, J. E. Hare, A. A. Grachev, and J. B. Edson, 2003: Bulk parameterizations of air-sea fluxes: updates and verification for the COARE algorithm. verification for the COARE algorithm. JJ.. Climate Climate., ., 1616, 571-591., 571-591.

• Kara, A. B., H. E. Hurlburt, and A. J. Wallcraft, 2005: Stability-dependent exchange coefficients for air-sea fluxes.Kara, A. B., H. E. Hurlburt, and A. J. Wallcraft, 2005: Stability-dependent exchange coefficients for air-sea fluxes. J J.. Atmos Atmos.. and Oceanic and Oceanic TechnolTechnol.., , 2222, 1080-1094. , 1080-1094.

• Large, W. G., and S. Pond, 1981: Open ocean momentum flux measurements in moderate to strong winds. Large, W. G., and S. Pond, 1981: Open ocean momentum flux measurements in moderate to strong winds. JJ.. Phys Phys.. Oceanogr Oceanogr., ., 1111, 324-, 324-336.336.

• ______, J. C. McWilliams, and S. C. Doney, 1994: Oceanic vertical mixing: a review and a model with a nonlocal boundary layer ______, J. C. McWilliams, and S. C. Doney, 1994: Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization. parameterization. RevRev.. Geophys Geophys..,, 3232. 363-403.. 363-403.

• ______, and S. G. Yeager, 2004: Diurnal to decadal global forcing for ocean and sea-ice models: The data sets and flux climatologies. ______, and S. G. Yeager, 2004: Diurnal to decadal global forcing for ocean and sea-ice models: The data sets and flux climatologies. NCAR Technical Note, NCAR/TN-460†STR, 105pp.NCAR Technical Note, NCAR/TN-460†STR, 105pp.

• Reynolds, R. W., 2006: Personal communication.Reynolds, R. W., 2006: Personal communication.

• Smith, S. D., 1988: Coefficients for sea surface wind stress, heat flux, and wind profiles as a function of wind speed and temperature. Smith, S. D., 1988: Coefficients for sea surface wind stress, heat flux, and wind profiles as a function of wind speed and temperature. JJ.. GeophysGeophys.. Res Res..,, 9393, 15,467-15,472., 15,467-15,472.

• ______, R. J. Anderson, W. A. Oost, C. Kraan, N. Maat, J. DeCosmo, K. B. Katsaros, K. L. Davidson, K. Bumke, L. Hasse, and H. M. ______, R. J. Anderson, W. A. Oost, C. Kraan, N. Maat, J. DeCosmo, K. B. Katsaros, K. L. Davidson, K. Bumke, L. Hasse, and H. M. Chadwick, 1992: Sea surface wind stress and drag coefficients: the HEXOS results. Chadwick, 1992: Sea surface wind stress and drag coefficients: the HEXOS results. BoundBound..-Layer-Layer.. Meteoro Meteoro., ., 6060, 109-142., 109-142.

• Taylor, P. K., and M. J. Yelland, 2001: The Dependence of sea surface roughness on the height and steepness of the waves. Taylor, P. K., and M. J. Yelland, 2001: The Dependence of sea surface roughness on the height and steepness of the waves. JJ.. Phys Phys.. OceanogrOceanogr., ., 3131, 572-590. , 572-590.

• Tolman, H. L., 2002: Validation of WAVEWATCH III version 1.15 for a global domain. Tolman, H. L., 2002: Validation of WAVEWATCH III version 1.15 for a global domain. Technical Note.Technical Note. Environmental Modeling Center, Environmental Modeling Center, Ocean Modeling Branch, NOAA.Ocean Modeling Branch, NOAA.

Atmospheric Stability Atmospheric Stability ParameterizationsParameterizations

• “ “Neutral Assumption”:Neutral Assumption”:

oStability parameters for momentum, temperature, and moisture are set to zero.Stability parameters for momentum, temperature, and moisture are set to zero.

• “ “Old”: Businger-Dyer relationsOld”: Businger-Dyer relations

ostable stratification (Businger et al. 1971 and Dyer 1974):stable stratification (Businger et al. 1971 and Dyer 1974):

ounstable stratification (Businger 1966 and Dyer 1967):unstable stratification (Businger 1966 and Dyer 1967):

• “ “New”:New”:

ostable stratification (Beljaars and Holtslag 1991):stable stratification (Beljaars and Holtslag 1991):

ounstable stratification (Benoit 1977):unstable stratification (Benoit 1977):

5( / )m t q z L

2 1/ 42ln (1 ) / 2 , (1 16 / )t q x x z L

2 12ln (1 ) / 2 ln (1 ) / 2 2 tan ( ) / 2m x x x

ϕϕmm -> -> stability parameter for momentumstability parameter for momentum

ϕϕtt -> -> stability parameter for temperature and stability parameter for temperature and

moisturemoisture

LL -> Monin-Obukhov Stability Length -> Monin-Obukhov Stability Length

aamm = 0.7= 0.7, , bbmm = 0.75= 0.75, c , c = 5.0= 5.0, d , d = 0.35= 0.35

aat,qt,q = 1.0= 1.0, , bbt,qt,q = 0.667= 0.667

1/ 4(1 15 / )z L 1/ 4

0 0(1 15 / )z L

/( / ) ( / / ) /dz Lm m m ma z L b z L c d e b c d

3/ 2 /, , ,

2(1 / ) *( / / )* / 1

3dz L

t q t q t q t qa z L b z L c d e b c d

2 21 10 0

02 2

( 1)*( 1)ln 2(tan tan )

( 1)*( 1)m

0,

12*ln

1t q

(1 9* / )z L

,0 0(1 9* / )t q

z L

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