Inferring the Skin Temperature from its Distribution Measured with an Infrared Camera A.T. JESSUP 1, W.E. ASHER1, M.A. ATMANE2, K.R. PHADNIS1, C.J. ZAPPA3, M.R. LOEWEN2 1Applied Physics Laboratory, University of Washington, USA 2Civil and Environmental Engineering ,University of Alberta, Canada 3Lamont-Doherty Earth Observatory, Columbia University, USA Acknowledgements S.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 Disruption Boundary Layer Thickness Skin Temperature Random Eddy Penetration Not all eddies fully disrupt BL BL thickness varies Skin temperature varies Seek to determine: Does complete disruption of TBL occur? If so, how often? Implications Surface Renewal Theory Can DT be inferred from distribution? Zappa et al [1998] (adapted from Harriott [1962] and Gulliver [1991])

Heat loss due to evaporation Cool Skin Effect at an Air-Water Interface Heat loss due to evaporation Causes surface to cool AIR WATER SURFACE d  1 mm THERMAL BOUNDARY LAYER Tbulk IR Optical Depth is 10 mm, so IR measures Tskin Tskin DT  0.1 to 0.5 C Temperature Profile For those who may not be familiar with the cool skin effect, I will take a moment to explain its significance to infrared remote sensing of a water surface. At any air-water interface where there is a net heat flux from the water to the air, a thermal boundary layer develops that is on the order of a millimeter thick under low wind conditions. Because turbulent motions are suppressed close to the air-water interface, heat transfer across the thermal boundary layer is primarily by conduction, which results in a temperature difference between the bulk water below and the temperature at the surface of a few tenths of a degree. Since the optical depth of the infrared radiation we detect is about 10 microns, the temperature we measure corresponds to the surface or skin temperature at the very top of the thermal boundary layer. If this boundary layer is disrupted from below, the bulk water will be brought to the surface and result in an infrared signature that corresponds to the temperature of the bulk water. For the unstratified conditions illustrated here, disruption of the surface will result in a warm signature. But if the sub-surface temperature profile is not uniform but stratified, then we can anticipate that the temperature signature of a surface disruption may depend on the degree of stratification. Bulk-skin temperature difference Tbulk also referred to as Tsubskin

Wire Wake Disruptions: FLIP 1992 Measured DT IR radiometer Thermistor at 0.1 m Compared with DTwakes = Tin wake – Toutside wake Results – Low wind DT = 0.55 K DTwakes = 0.45 K High wind DT = 0.2 K DTwakes = 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: FLIP: COPE 1995 & FAIRS 2000 Schiff [2006] Branch [2006]

DT from Tsurf Distribution PDF for Tsurf Surface Renewal with constant Q Tskin combined with lognormal PDF for t Tbulk [Soloviev and Schlϋssel., 2004] Then fit to PDF is given by [Garbe et al., 2004] Tskin = mean of PDF Tbulk = intercept of T-axis [Garbe et al., 2004]

Flux Exchange Dynamics Study (FEDS) 4 NASA Air-Sea Interaction Research Facility, Wallops Island, Virginia Instrumentation Measurement IR 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 K Fast T sensor Twater, sub-skin profiles Gas Chromatograph Bulk kG LabRad IR radiometer Tskin (calibrated) IR camera kH via ACFT Tbulk via PDF CO2 laser FLUXES Qsensible Qlatent u* Tair qair u Wind 45 cm Tprofile Tbulk 28 mm 72 mm 150 mm 76 cm

Experimental Conditions Data Set: 22 runs of 5-min duration Winds Speed: 4.1 to 9.3 m s-1 Friction Velocity: 0.09 to 0.55 m s-1 Heat Flux (up): 20 to 442 W m-2 Air-water DT: -6 to 3.9 K Relative Humidity: 70 to 81 % Bulk-skin DT: 0.10 to 0.24 K

Sub-skin Temperature Profile Profile, Bulk, and Skin Temperature Correction to Tb vs Tb-Ts Tb - Tp(zmin) < 0.04 K Well mixed Tb: T from sensor at 28 mm Tp(z): Profile T Ts: Skin T from LabRad

Surface Temperature PDF Long tails typical Ts from LabRad Assign to mean Tb from profile Mean Percentile 99.90 99.80 or above for 19 of 22 runs Occurrence of Tb in PDF implies complete surface renewal Can DT be inferred from distribution?

Surface Salinity Profiler R/V Kilo Moana 6-16 Dec Samoa to Hawaii IR Camera LTAIRS – Lighter-than-Air Remote Sensing M-AERI Mk II Compare IR PDF with Tskin and Tbulk Investigate Spatial Variability SSP Surface Salinity Profiler ISAR

Conclusion Laboratory investigation of surface disruption Tskin measured using calibrated IR radiometer Tbulk measured & occurred at 99.90 %-ile in p(Tsurf) Demonstrated that: Complete renewal occurs Partial renewal is a common occurrence Tbulk given by Tmax in PDF from IR image Estimate of Saunders’ l consistent with others

Implication of High Percentile of Tb in PDF Very rapid cooling if all renewals complete OR Partial renewal also occurs Compare DT to cooling expected in mean t Comparable: Most events complete Significantly less: partial renewal common

Surface Renewal Time Scale from Active Controlled Flux Technique Measurement k: thermal diffusivity

DT Recovery in time t Change in time t: DTt = 0.06 ± 0.03K Soloviev and Schlüssel [1994] Q: net heat flux r: density of water cp: specific heat Change in time t: DTt = 0.06 ± 0.03K Measured bulk-skin difference: DT = 0.16 ± 0.04 K On average, a water parcel renewing the surface does not have enough time to cool down to mean Ts

Degree of Partial Renewal Consider t* Time for complete renewal based on DT Compare to t Ratio t/ t >>1 for low Q approaches 1 for large Q Behaves like surface renewal only when strongly forced

Saunders’ Constant l Conduction Eq. Dimensional Analysis Measured: l= 5.9 ± 1.9 Dimensional Analysis Saunders predicted l=6

Compare to Ward and Donelan [2006] Measured dc Found l=2.4 ± 0.5 via but So l=6.3