Inferring the Skin Temperature Inferring the Skin Temperature from its Distribution Measured from its Distribution Measured

with an Infrared Camerawith an Infrared CameraA.T. JESSUP A.T. JESSUP 11, W.E. ASHER, W.E. ASHER11, M.A. ATMANE, M.A. ATMANE22, , K.R. PHADNISK.R. PHADNIS11, C.J. ZAPPA, C.J. ZAPPA33, M.R. LOEWEN, M.R. LOEWEN22

11Applied Physics Laboratory, University of Washington, USAApplied Physics Laboratory, University of Washington, USA22Civil and Environmental Engineering ,University of Alberta, Civil and Environmental Engineering ,University of Alberta, CanadaCanada33Lamont-Doherty Earth Observatory, Columbia University, USALamont-Doherty Earth Observatory, Columbia University, USA

AcknowledgementsS.R. Long, NASA, Wallops Flight Facility, Wallops Island, VA

National Science Foundation

2011 NASA SST Science Team Meeting

Jessup, A. T., et al. Geophys. Res. Let., 2009.

Thermal Signature of Boundary Layer Thermal Signature of Boundary Layer DisruptionDisruption

Random Eddy Penetration• Not all eddies fully disrupt BL• BL thickness varies• Skin temperature varies

Seek to determine:1. Does complete disruption of TBL occur?2. If so, how often?3. Implications

• Surface Renewal Theory• Can T be inferred from distribution?

Boun

dary

Lay

er T

hick

ness

Skin

Tem

pera

ture

Zappa et al [1998] (adapted from Harriott [1962] and Gulliver [1991])

mm

AIRWATER SURFACE

THERMAL BOUNDARY LAYER

Heat loss due to evaporationCauses surface to cool

TbulkTskin

Temperature Profile

Cool Skin Effect at an Air-Water Interface

IR Optical Depth is 10 m, so IR measures TskinT 0.1 to 0.5 C

Bulk-skin temperature difference

Tbulk also referred to as Tsubskin

Wire Wake Disruptions: FLIP Wire Wake Disruptions: FLIP 19921992

• Measured T • IR radiometer• Thermistor at 0.1 m

• Compared with Twakes = Tin wake – Toutside wake• Results –

• Low wind• T = 0.55 K• Twakes = 0.45 K

• High wind• T = 0.2 K• Twakes = 0.1 K

• Within measurement uncertainty

• Complications• Accuracy of IR: no external calibration• Tbulk measurement depth• Skin temperature recovery

Zappa et al [1998]

Wire Mesh Surface Disrupter: Wire Mesh Surface Disrupter: FLIP: COPE 1995 & FAIRS 2000FLIP: COPE 1995 & FAIRS 2000

Schiff [2006]

Branch [2006]

[Garbe et al., 2004]

T from TT from Tsurfsurf Distribution DistributionSurface Renewal with constant Q

bulkosurf TttQtT )(

[Soloviev and Schlϋssel., 2004]

bulkTmtt

p

2

2 )'(lnexp'

1)(

21)(2

PC

combined with lognormal PDF for

2

2

2

ln12

*4

exp)(

)(

QTTmerfc

mQTT

Tp

bulksurf

bulksurfsurf

Tbulk

Tskin

PDF for Tsurf

[Garbe et al., 2004]Then fit to PDF is given by

• Tskin = mean of PDF• Tbulk = intercept of T-axis

Tprofile

Tbulk28 mm72 mm

150 mm

Tairqairu

CO2 laserIR camerakH via ACFT

Tbulk via PDF

LabRad IR radiometerTskin (calibrated)

FLUXESQsensibleQlatentu*

76 cm

45 cmWind

Flux Exchange Dynamics Study (FEDS) 4Flux Exchange Dynamics Study (FEDS) 4NASA Air-Sea Interaction Research Facility, Wallops Island, Virginia

Instrumentation MeasurementIR Camera kH via ACFT, p(Tsurf) IR Radiometer Tskin, calibrated “LabRad”: Accuracy ± 0.05 K

Air: U, T, q profiles Qnet, u*SeaBird T sensors Tbulk, calibrated: Accuracy 0.001 KFast T sensor Twater, sub-skin profilesGas Chromatograph Bulk kG

Experimental ConditionsExperimental Conditions

• Winds Speed: Winds Speed: 4.1 to 9.3 m s4.1 to 9.3 m s-1-1

• Friction Velocity:Friction Velocity: 0.09 to 0.55 m s0.09 to 0.55 m s-1-1

• Heat Flux (up):Heat Flux (up): 20 to 442 W m20 to 442 W m-2-2

• Air-water Air-water T:T: -6 to 3.9 K-6 to 3.9 K• Relative Humidity:Relative Humidity: 70 to 81 %70 to 81 %• Bulk-skin Bulk-skin T:T: 0.10 to 0.24 K 0.10 to 0.24 K

Data Set: 22 runs of 5-min duration

Correction to Tb vs Tb-Ts

Sub-skin Temperature Sub-skin Temperature ProfileProfile

Tb: T from sensor at 28 mmTp(z): Profile TTs: Skin T from LabRad

-250

-200

-150

-100

-50

0

Dep

th (m

m)

21.821.721.621.5Temperature (°C)

Tp(z) Tb Ts

Profile, Bulk, and Skin Temperature

-0.04

-0.02

0.00

0.02

0.04

T b -

T p(z

min

) (°C

)0.250.200.150.100.050.00-0.05

Tb- Ts (°C)

Tb - Tp(zmin) < 0.04 KWell mixed

Surface Temperature PDFSurface Temperature PDF• Long tails typicalLong tails typical

• TTss from LabRad from LabRad• Assign to meanAssign to mean

• TTbb from profile from profile• Mean Percentile Mean Percentile

99.9099.90• 99.80 or above for 99.80 or above for

19 of 22 runs19 of 22 runs

0.20

0.15

0.10

0.05

0.00

p(T sk

in)

21.821.621.421.2

Temperature (°C)

Tsubskin

Tskin

Occurrence of Tb in PDF implies complete surface renewal

Can T be inferred from distribution?

R/V Kilo Moana6-16 Dec

Samoa to Hawaii

LTAIRS – Lighter-than-Air Remote Sensing

SSPSurface Salinity ProfilerISAR

M-AERI Mk II

IR Camera

• Compare IR PDF with Tskin and Tbulk• Investigate Spatial Variability

ConclusionConclusion• Laboratory investigation of surface disruptionLaboratory investigation of surface disruption

• TTskinskin measured using calibrated IR radiometer measured using calibrated IR radiometer• TTbulkbulk measured & occurred at 99.90 %-ile in p(T measured & occurred at 99.90 %-ile in p(Tsurfsurf))

• Demonstrated that:Demonstrated that:• Complete renewal occursComplete renewal occurs• Partial renewal is a common occurrencePartial renewal is a common occurrence

• TTbulkbulk given by T given by Tmaxmax in PDF from IR image in PDF from IR image• Estimate of Saunders’ Estimate of Saunders’ consistent with others consistent with others

Implication of High Percentile Implication of High Percentile of Tof Tbb in PDF in PDF

Very rapid cooling if all renewals completeVery rapid cooling if all renewals completeOROR

Partial renewal also occursPartial renewal also occurs

Compare T to cooling expected in mean

• Comparable: Most events complete• Significantly less: partial renewal common

Surface Renewal Time Scale Surface Renewal Time Scale from Active Controlled Flux from Active Controlled Flux

TechniqueTechnique1.0

0.8

0.6

0.4

0.2

0.0

(s

)

0.60.40.20.0u*(m s-1)

1.0

0.8

0.6

0.4

0.2

0.0 l

(mm

)

0.50.40.30.20.1u* (m s-1)

c (Ward and Donelan [2006])

l

Measurement l : thermal diffusivity

TT Recovery in time Recovery in time

oqttT 2112)(

po cQq

Soloviev and Schlüssel [1994]

Q: net heat flux: density of watercp: specific heat

Change in time : T = 0.06 ± 0.03K

Measured bulk-skin difference: T = 0.16 ± 0.04 KOn average, a water parcel renewing the surface

does not have enough time to cool down to mean Ts

Degree of Partial RenewalDegree of Partial Renewal

12

4

102

4

1002

4

t * /

5004003002001000Q ( W m-2)

Consider t*• Time for complete renewal based on T• Compare to

Ratio t/ • >>1 for low Q• approaches 1 for large Q

Behaves like surface renewal only when strongly forced

Saunders’ Constant Saunders’ Constant

*kuqT 10

8

6

4

2

0La

mbd

a

0.60.40.20.0u* (m s-1)

wu*

Tkq

Conduction Eq.

Dimensional AnalysisSaunders predicted =6

Measured: = 5.9 ± 1.9

Compare to Compare to Ward and Donelan [2006]Ward and Donelan [2006]

• Measured c

• Found =2.4 ± 0.5

6.221

c

wwa u*

21)(

but

via

So =6.3