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Convective Transport Theory for Surface Fluxes Tested over the Western Pacific Warm Pool. Greischar, Lawrence; Stull, Roland B. 1999-07-31

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1JULY 1999 2201GREISCHAR AND STULLq 1999 American Meteorological SocietyConvective Transport Theory for Surface Fluxes Tested over the Western PacificWarm PoolLAWRENCE GREISCHARDepartment of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, WisconsinROLAND STULLAtmospheric Science Programme, Department of Geography, University of British Columbia,Vancouver, British Columbia, Canada(Manuscript received 21 July 1997, in final form 9 July 1998)ABSTRACTTurbulent flux measurements from five flights of the National Center for Atmospheric Research Electra aircraftduring the Tropical Oceans and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGACOARE) are used to test convective transport theory (CTT) for a marine boundary layer. Flights during lightto moderate winds and under the clearest sky conditions available were chosen. Fluxes of heat, moisture, andmomentum were observed by the eddy-correlation method. Mean kinematic values for the observed sensibleand latent heat fluxes and momentum flux were 0.0061 K m s21, 0.0313 g kg21ms21, and 0.0195 m2s22,respectively.For the range of mixed-layer wind speeds (0.8–8.4 m s21) studied here, the version of CTT that includes themixed effects of buoyant and shear-driven transport give a better fit to the observations than either the COAREbulk algorithm or the pure free-convection version of CTT. This is to be expected because both of those latterparameterizations were designed for light winds (,5ms21approximately).The CTT empirical coefficients listed in Table 3 exhibited slight sensitivity to the COARE light flux conditions,compared to their previous estimates during larger fluxes over land. For example, COARE heat fluxes wereroughly 10 times smaller than previous land-based flux measurements used to calculate CTT coefficients, butthe corresponding empirical mixed-layer transport coefficients were only 3% smaller. COARE momentum fluxeswere also roughly 10 times smaller, but the CTT coefficients were about four times smaller. The greater variationin momentum coefficient may be due, in part, to insufficient flight-leg length used to compute momentum fluxes,to uncertainties in the effects of the ocean surface current and waves, or perhaps to roughness differences.1. IntroductionThe western Pacific warm pool was identified duringthe Tropical Oceans and Global Atmosphere (TOGA)program as an important contributor to global climatevariability. A Coupled Ocean–Atmosphere ResponseExperiment (COARE) was therefore designed, whichincluded measurement of interfacial fluxes as one of thekey elements. Webster and Lukas (1992) emphasizedthe importance of flux parameterizations especially forlow-wind regimes.The convective transport theory (CTT) proposed byStull (1994) is just such a parameterization. This theoryparameterizes surface fluxes of heat, moisture, and mo-mentum as the product of an empirical transport coef-Corresponding author address: Prof. Roland Stull, AtmosphericScience Programme, Department of Geography, 1984 West Mall, Uni-versity of British Columbia, Vancouver, BC V6T 1Z2, Canada.E-mail: rstull@geog.ubc.caficient, a ‘‘buoyancy velocity scale,’’ and the differencebetween mean surface and interior of mixed-layer valuesof the respective property.The COARE observations made within the intensiveflux array (IFA) in conjunction with extensive surfacemeasurements by ships and buoys contain the infor-mation necessary to test CTT under marine conditions.Thirty-two flights of the National Center for Atmo-spheric Research (NCAR) Electra aircraft were madeduring the intensive operations period (IOP) of Novem-ber 1992 and February 1993, many of which had low-level boundary layer legs in the area of concurrent sur-face measurements made by ships and at the improvedmeteorological instrumentation (IMET) buoy at 18459S,1568E.The published values of the empirical transport co-efficients for CTT were originally estimated using air-borne flux measurements from the Boundary LayerField Experiment 1983 (BLX83) in Oklahoma (rough-ness length: 0.05 m; latitude: 358N; vegetation: mixed2202 VOLUME 56JOURNAL OF THE ATMOSPHERIC SCIENCESpasture and crops; season: boreal spring). Data fromanother land-based experiment (Koorin) conducted un-der somewhat different conditions in Australia (rough-ness length: 0.4 m; latitude: 168S; vegetation: uniformsparse trees; season: austral winter) were used to confirmthe theory and the values of the coefficients.The objective of this paper is to test this theory andits limits under the marine conditions of the westernPacific warm pool (roughness length: 3 3 1025m; lat-itude: 28S; marine conditions; season: austral summer)using the Electra aircraft data obtained during theCOARE IOP. An overview of CTT is given in section2. The Electra aircraft data and ancillary observationsare described in section 3. Section 4 describes the dataprocessing steps, and CTT is tested against the Electradata in section 5. Concluding remarks are made in sec-tion 6.2. Model descriptionDuring conditions of free convection and calm orlight winds, turbulence is generated by buoyant ther-mals, rather than mechanically by surface-layer windshear (Stull 1997). Convective thermals efficientlytransport heat, moisture, and momentum between thesurface and the mid–mixed layer, with a rate of verticaltransport proportional to the Deardorff velocity w*5[(g/y)zi]1/3, where g is gravitational acceleration,Tw9u9y sis the mean absolute virtual temperature, ziis theTymixed-layer (ML) depth, and w9 is the surface ki-u9ysnematic vertical flux of virtual potential temperature,which is proportional to a buoyancy flux. While tradi-tional drag laws fail in the limit of zero mean wind,surface fluxes during free convection nonetheless canbe described by CTT (Stull 1994) over a range of calmto light winds:2u 5 CwM (1)D ML***w9u95CwDu (2)sH**w9r95CwDr, (3)sE**where , w9 , and w9 , are the surface kinematic2u u9 r9ss*fluxes of momentum, heat, and water vapor, respec-tively, and u*is also known as the friction velocity. Thelast factor in each equation above is a difference be-tween the surface skin condition and the mid-mixed-layer value: Du 5 uskin2 uML, Dr 5 rskin2 rML, andDM 5 MML2 Mskin5 MML, where Mskin5 0 by defi-nition. By using skin and mid-mixed-layer values in theabove formulations, it was proposed by Stull (1994) thatthe CTT parameterization should be independent of sur-face aerodynamic roughness length zo. This assumptionwill be tested here.The empirical mixed-layer transport coefficients formomentum, moisture, and heat were found (Stull 1994)to be C*D5 0.023 6 0.007 and C*Eł C*H5 0.00636 0.0016, respectively, based on measurements overland (United States and Australia), where the error tol-erance is given as a standard deviation. Stull had in-sufficient data to calculate C*Ebut hypothesized that itmight be equal to C*H. We will test that hypothesis here.Kustas et al. (1996) has demonstrated that surfaces withcomplex geometry, such as forests, require correctionsto the above coefficients to compensate for shading re-lated to solar illumination versus viewing angles. Equa-tions (1)–(3) are in implicit form, because the fluxes onthe left side of Eqs. (2) and (3) depend on w*, whichitself is a function of heat and moisture fluxes viaw9 ł w9 (1 1 0.61r) 1 0.61uw9 .u9 u9 r9yss sHowever, (1)–(3) can be rearranged into explicit form(Stull 1994):2u 5 bwM (4)DB ML*w9u95bwDu (5)sHBw9r95bwDr, (6)sEBwhere convective transport coefficients (bD, bH, bE) arerelated to the mixed-layer coefficients by bD5C*D, bH5 , and bE5 C*E. The buoyancy1/2 3/2 1/2CCHH H** *velocity scale is1/2gw [ z Du . (7)BiB12TyThe buoyancy temperature difference is DuB[ bDu,for b [ w9 /w9 , which can be approximated in ex-u9 u9yssplicit form asDuBł Du(1 1 0.61rs) 1 0.61usDr. (8)For convection over land (Oklahoma and Australia) itwas shown (Stull 1994) both theoretically and empiri-cally thatDuBł Duy, (9)where Duyequals the difference of virtual potential tem-peratures between the surface skin and middle mixedlayer. Equation (9) will be tested here for a maritimetropical atmosphere. This buoyancy velocity can alsobe used to parameterize the surface flux of virtual po-tential temperature:w9 5 bHwBDuB.u9ys(10)A mixed-layer Richardson number was defined asR*[ [wB/MML]2, (11)where Stull (1994) suggested that even in noncalm con-ditions, turbulence is in quasi–free convection wheneverR*. 3. This free convection condition will also beexamined here for tropical maritime boundary layers.Another prediction of CTT is that a diagnostic ex-pression for mixed-layer depth is possible:21 w9u9sz 5 . (12)i12(g/T )Du b Duy BHThis, too, will be tested.1JULY 1999 2203GREISCHAR AND STULLTABLE 1. Boundary layer and surface-flux data from five flights of the NCAR Electra aircraft during the TOGA COARE IOP. Variablesinclude start time (Local 5 UTC 1 11 h) of beginning of the approximately 15-min low-level horizontal flight leg; flight ID, flight identificationof Electra aircraft; leg ID, identification for each near-surface horizontal flight leg; z leg, mean altitude of the flight leg above sea level; zi,depth of mixed layer; MML, uML, and rML, wind speed, mean potential temperature (relative to 100 kPa), and mixing ratio in the interior ofthe mixed layer; Psurf, Tskin, and uskin, surface pressure, temperature, and potential temperature (relative to 100 kPa) of the surface radiometricskin temperature; rsat(Tskin), saturated mixing ratio at the surface skin temperature; Du 5 uskin2 uML; Dr 5 rsat(Tskin) 2 rML; Here, ^w9&,u9s^w9&, ^w9&, and u* are the leg-averaged surface kinematic vertical fluxes of heat, virtual temperature, moisture, and momentum, re-2u9 r9vs sspectively. Means and standard deviations of all numbers in each column are shown at the bottom. Symbol t represents u.Finally, for those conditions where mechanical gen-eration of turbulence by wind shear is great enough tobe comparable to convective turbulence, a ‘‘mixed’’ me-chanical-buoyant version of CTT was also proposed:2u 5 (CM1 bw)M (13)DML ML DML B ML*w9u95(CM1 bw)Du (14)sHML ML HML Bw9r95(CM1 bw)Dr, (15)sBML ML BML Bwhere Stull (1994) empirically found the drag coeffi-cient values for momentum and heat to be CDML50.0035 and CHML5 0.001, respectively, with the con-vective transport coefficients for this mixed-convectioncase of bDML5 0.0007 and bHML5 0.000 25, respec-tively.Based on (7), (11), and (14), the buoyancy velocityand Deardorff velocity scales are related byw*5 (bHML1 ,21/2 1/3CR) wHML B*(16)which will be tested here.3. ObservationsThirty low-level flight segments (Table 1) from fiveflights of the Electra aircraft flown during the COAREIOP, between November 1992 and February 1993, wereused in this study to estimate surface fluxes of heat,2204 VOLUME 56JOURNAL OF THE ATMOSPHERIC SCIENCESFIG. 1. Low-level flight paths show locations of flight legs andvertical profiles (slant ascent and descent flights, shown by letter Vwith subscript indicating number of profiles at each approximate lo-cation) used in this study. The position of the IMET buoy and theapproximate locations of the ship R/V Franklin (ship symbol) duringthe times of flights RF04, RF05, RF06, and RF25 are shown. Ap-proximate wind direction during each flight is indicated by an arrownear the flight label. The boundary of the IFA is indicated by a dashedline.moisture, and momentum. These data also provided es-timates of the surface and middle boundary layer pa-rameters needed to test the theory. The flight segmentswere chosen to avoid precipitating conditions, gust-frontboundaries, and to be as cloud free as possible. Anattempt was made to use flight data over a variety ofwind speeds in order to test the CTT over a range fromnear-calm free-convective conditions to conditions inwhich mechanically generated turbulence transport as-sociated with mean wind shear contributes significantlyto the still-dominant buoyant transport. Surface datafrom the IMET buoy (Release 1.0b of WHOI buoy datafrom Dr. Robert Weller, Woods Hole Oceanographic In-stitute) were useful for choosing appropriate flight daysas were satellite and radar images and surface and upper-air analyses (TCIPO 1993; Asencio et al. 1993; Bondand Alexander 1994). A corrected version of theElectra’s radiometric surface temperatures was obtained(Y. Serra 1997, personal communication). COARE ship-based current data obtained from the archive at the Uni-versity of Hawaii were used to estimate the effects ofsurface currents on the model.Flight conditions varied from clear with light windsto partly cloudy with winds up to 8 m s21. Flights RF04,RF05, RF06, and RF25 were class 0 (described in theTOGA COARE Operations Plan as having clouds andvery small, short-lived showers with areas less than 10km2covering not more than 5% of the flight area; TCI-PO 1992) and flight RF16 was class 1 (indication ofconvective cores less than 25 km2and lasting less than30 min and no mesoscale organization greater than 50km or long-lived stratiform rain areas greater than 2500km2within the target domain). Rainfall data (15 minaverages) from the R/V Franklin (Release 1.0 fromBradley and Coppin, CSIRO Centre for EnvironmentalMechanics, Canberra, Australia), which was in the vi-cinity of flights RF04, RF05, RF06, and RF25, indicatedno precipitation at its location during these flights. Sur-face radar data were available for flights RF04 andRF16, which roughly delineated cloudy areas. Sensorson the Electra detected some liquid water content onlyduring short sections of leg 2 of flight RF06. Thesesections were excluded from the analysis.Fast-rate measurements of the global positioning sys-tem (GPS)–corrected wind components, potential tem-perature, and mixing ratio were used to compute theeddy-correlation surface fluxes of heat, moisture, andmomentum. These variables are described in detail inMiller and Friesen (1989). Slow-rate measurements ofaircraft position and time, surface skin temperature, andan estimate of surface pressure were used to map low-level flight legs and determine the pressure and tem-perature conditions at the surface. Estimates of mixed-layer properties were made where the aircraft descendedto or ascended from low-altitude flight legs, resultingin several vertical profiles through the mixed layer dur-ing each day’s flight pattern. Some flight patterns alsohad legs at higher levels within the mixed layer.4. Data processingProcessing of the flight data began by producing two-and three-dimensional plots of the aircraft’s flight pathin order to identify suitable low-level flight legs. Figure1 shows the locations of the low-level legs studied fromthe five separate flights. The IMET buoy is shown, asare the approximate locations of the R/V Franklin dur-ing flights RF04, RF05, RF06, and RF25. An elevationversus time plot of the on-station part of a flight wasalso used to define the start and finish times of eachflight leg, and of the slant ascent or descent soundingthat often occurred between the low-level flight legs.Fast-rate values for the three wind components, mix-ing ratio, and potential temperature were extracted foreach leg and plotted (as in Fig. 2). The following re-strictions (Sun et al. 1996) were placed on the data: 1)differences of flight levels between adjacent samplingpoints were required to be less than 5 m; and 2) rolland pitch angles were restricted to 248 to 148 and 08to 38, respectively. Also as in Sun et al. (1996), pointsin the fast-rate data that differed by more than fourstandard deviations from the mean along 1 km of flightwere replaced by using a linear interpolation betweengood data values. Fluxes calculated using this ‘‘de-spiked’’ data were mostly changed by less than 1% witha maximum difference of 5%.The fast rate data are sampled at 20 Hz, which givenan aircraft speed of approximately 100 m s21results ina short wavelength sampling limit of approximately 10m. In order to remove mesoscale effects of diameterslarger than 2500 m and corresponding to wavelengths1JULY 1999 2205GREISCHAR AND STULLFIG. 2. Times series plots of (a) potential temperature, (b) mixingratio, (c) wind speed, and (d) wind direction for leg 1 of flight RF16.Time (in s) from 0000 UTC on 16 December 1992. Every fifth pointof the 20-Hz data is plotted.greater than 5 km, a 50-s moving linear average andtrend was subtracted from the fast-rate data in a mannersimilar to Otles and Young (1996). Eddy fluxes of heat,moisture, and momentum were then computed from 18km or longer sections of these filtered flight legs usinga program that first removed any remaining trend.Thicknesses of the mixed layer were estimated fromvertical profiles of virtual potential temperature, mixingratio, and winds measured during aircraft slant ascentand descent soundings at the ends of the low-level flightlegs. One-second averages of the fast data were plottedin these vertical profiles. Radar altitudes were used upto their limit of about 750 m, with pressure altitudesapproximately adjusted to match the radar data, usedabove this level. Only one mixed-layer thickness esti-mate was greater than 750 m for the cases studied here.Generally, the vertical profile of virtual potential tem-perature gave the best indication of mixed-layer thick-ness, with a nearly constant value of uyup to the mixed-layer depth zi. The locations of these slant soundingsare shown in Fig. 1.Surface values of temperature, pressure, and mois-ture were estimated as follows. A corrected version ofthe Electra radiometric surface temperatures (Y. Serra1997, personal communication) includes correctionsfor emissivity, reflectivity, transient trends, and offsetwere averaged to obtain an initial estimate of Tskin.Anapproximate correction for absorption due to moisturecontent between the aircraft and surface was estimatedfrom the rate of change of the radiometric surface tem-perature with height during slant ascent and descentsoundings (Fig. 1). This rate appeared to be fairly linearover the lowest several hundred meters of elevationand varied from 10.06 K to 10.14 K per 100-m de-crease in elevation. A mean value of 10.1 K per 100m was used, resulting in corrections for this effect ofless than 0.1 K for the 32–66-m flight elevations. Arough comparison of these corrected sea surface tem-peratures with concurrent ship values from the R/VFranklin showed occasional agreement but with a ten-dency for the ship observations to be slightly cooler.If real, such a bias would tend to make the free-con-vective coefficients for heat and moisture somewhatlarger. Surface pressure was obtained from a data chan-nel that estimates the surface pressure from aircraftvalues of pressure, virtual temperature, and elevation.Since the aircraft potential temperatures were definedwith respect to a reference pressure of 100 kPa, Tskinwas also converted to a potential temperature at thisreference pressure using the surface pressure estimate.Saturation mixing ratio at the surface was obtainedfrom Tskinand surface pressure using Teten’s formula(Stull 1988). As in Fairall et al. (1996) this saturationmixing ratio is multiplied by 0.98 to account for thereduction of vapor pressure caused by a typical salinityof 34 parts per thousand.Mean mixed-layer values of wind speed, potentialtemperature, and mixing ratio were estimated from meanvalues at the flight elevation. The aircraft offset tablefrom the TOGA COARE Flux Group (1996) was usedto correct observational offsets of the Electra aircraftinstrumentation. GPS–corrected winds (D. Raymond1997, personal communication) were used to estimatewind speeds. Several pairs of collinear flight lines flownwithin approximately a 0.6-h time period at differentelevations from three of the flights showed that potentialtemperature and mixing ratio remained nearly constantbetween approximately 35- and 95-m elevation, al-though wind speed generally increased slightly with al-titude. The vertical profiles used to estimate mixed-layerthicknesses also indicated fairly constant values of theseparameters through the mixed layer.Table 1 lists the observed surface values of temper-ature Tskin, potential temperature uskin, pressure Psurf, andmixing ratio rsat. Also listed are mixed-layer values ofthickness zi, wind speed MML, potential temperature uML,and mixing ratio rML, determined for each flight-leg seg-ment. Also in Table 1 are the surface fluxes of heat,moisture, and momentum. Surface fluxes of heat, mois-ture, and momentum were assumed to be reasonablyrepresented by their respective values measured from2206 VOLUME 56JOURNAL OF THE ATMOSPHERIC SCIENCESTABLE 2. Mixed-layer and buoyancy scales. Variables are b, ratio of virtual temperature flux to heat flux, both at the surface; DuB, buoyancytemperature difference; Duy, virtual potential temperature difference between the surface skin and the mixed layer; w*, Deardorff velocity;wB, buoyancy velocity; R*, mixed-layer Richardson number; C*D, mixed-layer transport coefficient for momentum; C*H, mixed-layer transportcoefficient for heat; C*E, mixed-layer transport coefficient for moisture. Asterisks in the column labeled ‘‘Free conv.’’ indicate those datafor which R* . 3.0, which were used to calculate the boldface mean values at the bottom of the table. Convective transport coefficients formomentum, heat, and moisture are indicated by bD,bH, and bE, respectively.the lowest aircraft flight level, because flux profileslopes were expected to be relatively small in theCOARE region. The momentum flux components werecombined to yield the square of the friction velocity[ 5 (u9w921 y9w92)1/2]. The surface virtual temper-2u*ature flux w9 was computed from the heat and mois-u9ysture fluxes (Stull 1994), and this in turn was used tocompute the Deardorff convective velocity w*5[(g/Ty)ziw9 ]1/3. Table 2 shows the following mixed-u9yslayer and buoyancy scales: ratio of kinematic virtualtemperature flux to heat flux b; buoyancy temperaturedifference DuB[Eq. (8)]; virtual temperature differencebetween the surface skin and the mixed layer Duy; buoy-ancy velocity scale wB[Eq. (7)]; mixed-layer Richard-son number R*[Eq. (11)]; and the mixed-layer transportcoefficients for momentum C*D, heat C*H, and moistureC*E, and the corresponding convective transport coef-ficients (bD, bH, bE).5. ResultsFigure 2 shows the recorded potential temperature,mixing ratio, wind speed, and direction (vs time in sec-onds from 0000 UTC on 16 December 1992) for leg 11JULY 1999 2207GREISCHAR AND STULLFIG. 3. Variation of mixed-layer transport coefficients for (a) heatC*H, (b) moisture C*E, and (c) momentum C*D, with mixed-layerRichardson number R*. Values for the 30 COARE flight segmentsstudied are plotted as black squares, and for comparison the BLX83land-based data are shown by diamonds. Approximate free convectionoccurs for R*. 3.0, as indicated by the relatively constant valuesof mixed-layer transport coefficients for moisture and momentum.Thin horizontal lines (dashed for BLX83) show mean values for thetransport coefficients: C*H5 0.0061 (0.0063) and C*E5 0.0044(0.0063) for heat and moisture, respectively; and C*D5 0.0053(0.0230) for momentum. (a) Shows linear fits to the semilog graphsfor the COARE data (solid) and BLX83 data (dashed). (b) and (c)Thicker curves show second-order polynomial fits [in terms oflog(R*)] to the semilog graphs of the COARE data.of flight RF16. A cool gust front similar to one seen inship data (Tsukamoto and Ishida 1995) occurs near95 200 sec. It is very evident in the temperature andwind data, and appears as an increase in variance of themixing ratio observations. The liquid water channel onthe Electra aircraft did not indicate any precipitationduring this flight leg. The flight segments evaluated fromthis leg were chosen to avoid the discontinuities at theboundary of the gust front. Table 1 shows the changesin fluxes associated with this event (between RF16 1Aand 1B on the warm side and 1C on the cool side).Consistent with the theory, heat, moisture, and mo-mentum fluxes increased by approximately 100%, 23%and 50%, respectively, with the cooling, drying, andincreased winds of the mixed layer.Figure 3 shows the variation of mixed-layer transportcoefficients for heat, moisture, and momentum with themixed-layer Richardson number. The land-based valuesfrom BLX83 are also plotted for comparison. As in Stull(1994) R*. 3.0 was the criterion adopted for free con-vection, indicating that buoyant production of turbu-lence kinetic energy is at least three times greater thanshear production. As can be seen from both the BLX83and the COARE data in Fig. 3, the choice of R*. 3to define free convection is somewhat arbitrary, withthe empirical coefficients becoming even more uniformas R*increases to 10 and beyond. Also plotted (Figs.3b and 3c) are second-order polynomial fits [in termsof log(R*)], showing that the coefficients for moistureand momentum become approximately steady for freeconvection. The variation of C*Hwith R*shows a nearlylinear variation (Fig. 3a) over the range of the semilogplot. This was also found over land (Stull 1994), whichsuggests that vertical heat transport continues to becomemore efficient as winds become lighter, perhaps causedby better organization of the coherent thermal structures.Figure 3a shows the remarkably similar linear trendsfor the COARE and BLX83 data with a fit to the com-bined datasets yielding the relation C*H5 0.0091 20.0020 log(R*).Table 2 shows the results of averaging the 12 free-convective cases for the proposed empirical values C*D5 0.0053 (60.0023), C*H(heat) 5 0.0061 (60.0024),and C*E(moisture) 5 0.0044 (60.0010). These valuesare plotted as horizontal solid lines in Fig. 3 and canbe compared to the land-based BLX83 values (dashedlines). The very good agreement between the COAREand BLX83 values for C*His evident in Fig. 3a. Figure3b also has plotted the BLX83 values of C*Hin orderto test Stull’s (1994) assumption that C*Eł C*H. Al-though C*Eis smaller than the BLX83 (and COARE)values of C*H, it is still within error limits. However,C*D(Fig. 3c) is only about 25% of the published valuefor nonmarine conditions. There is considerable scatterin the momentum data, which may have several causes.Some might be related to mesoscale heterogeneitycaused by precipitation-induced intrusions of cool airmasses (Williams et al. 1996). In addition, some maybe due to insufficient leg length used to compute themomentum fluxes, to uncertainties in the mean mixed-layer wind speed and surface currents; but the differenceis large enough to suggest that roughness-length effectsor other factors may need to be incorporated into theCTT.The free and mixed formulations of CTT were tested.Figure 4 shows plots of predicted versus observed fluxes2208 VOLUME 56JOURNAL OF THE ATMOSPHERIC SCIENCES←Correlation coefficients (Rfand Rmfor the free and mixed cases)between predicted and observed values are shown. The root-mean-square error for the mixed case (rmsm) is shown. The diagonal linerepresenting a 1:1 perfect fit is shown for reference.FIG. 4. Predicted and observed fluxes are compared for (a) heat,(b) moisture, and (c) momentum. Two predictions are presented: onebased on free convection [(1)–(3)] with only free-convective casesplotted, and the other based on mixed convection [(13)–(15)] withall cases plotted. Coefficients determined in this study were used.of heat, moisture, and momentum. Two predictions arepresented: one based on free convection [(1)–(3)] forobservations with R*. 3.0, and the other based onmixed convection [(13)–(15)] for all observations. Cor-relation coefficients and root-mean-square differences(mixed case) between the predicted and observed valuesshown in Fig. 4 give an estimate of performance. Theroot-mean-square error differences for the sensible andlatent fluxes correspond to 2 W m22and 16 W m22,compared to typical magnitudes of those fluxes of 7.5Wm22and 94.3 W m22, respectively.Transport coefficients for the free-convective casehave already been presented. The least squares best-fitcoefficients for the mixed-convective case based on allthe data in Tables 1 and 2 are for momentum fluxesCDML5 0.000 38 (60.000 12), bDML5 0.000 41(60.000 09); for sensible heat fluxes CHML5 0.000 44(60.000 05), bHML5 0.000 30 (60.000 04); and for la-tent heat fluxes CEML5 0.000 62 (60.000 19), bEML50.000 18 (60.000 03). The error estimates were ob-tained by a Monte Carlo simulation (Press et al. 1986)and allowed for random errors in observed values of upto 20% of their respective means. When compared tothe previously published values of CDML5 0.003 50,bDML0.000 70, and CHML5 0.001 00, bHML5 0.000 25there are considerable differences between most of thecorresponding coefficients. The marine values for themixed momentum coefficients are similar to those formixed heat and moisture, which is consistent with theresult for the convective case with C*Dbeing more near-ly equal to C*Hand C*Efor these marine data.Acoustic Doppler current profiler (ADCP) data fromseveral of the ships in the IFA during the flights studiedwere used in an attempt to correct for the effects ofsurface currents on wind speed difference between themiddle mixed layer and surface. These data give 0.5-hbin-averaged values centered at approximately 20-mdepth and generally indicated eastward-moving currentswith speeds up to 0.6 m s21but with considerable var-iability in space and time. These speeds and the generaldirection are born out by the many surface buoy tra-jectories plotted for December 1992 (TCIPO 1993) withthe January 1993 trajectories showing more of a south-ward component. Since it was not possible to get anaccurate estimate of the surface currents beneath eachflight segment the transfer coefficients were recomputedfor a 60.6 m s21adjustment to the wind speed.Table 3 shows the results of these calculations. Themomentum coefficient C*Dfor the free-convective caseis affected most since its computation involved the low-1JULY 1999 2209GREISCHAR AND STULLTABLE 3. Variation of CTT coefficients for a 60.6ms21range of ocean surface currents, which could have affected the wind-speeddifference between the mid-ML and the surface.Free convectiveCurrent speed C*DC*HC*EbDbHbE10.6ms21020.6ms210.00390.00530.01080.00590.00610.00650.00430.00440.00470.000290.000410.000810.000470.000500.000540.000330.000350.00038Mixed convectiveCurrent speed CDMLCHMLCEMLbDMLbHMLbEML10.6ms21020.6ms210.000430.000380.000280.000440.000440.000430.000610.000620.000620.000260.000410.000600.000260.000300.000330.000130.000180.00023est wind speeds from 0.8–3.1 m s21. The small changesin the heat and moisture coefficients are due to feweror more points falling into the free-convective range.All the mixed convective case coefficients are affectedsince they involve wind speed, though again the mo-mentum coefficients are most affected.A comparison with the latest (version 2.0f) COAREbulk parameterization (Fairall et al. 1996), which wasdesigned for light wind conditions, was also made. Fig-ure 5 shows the comparison with correlations and rmsdifferences between the bulk and covariance (eddy cor-relation) fluxes for the 25 flight segments flown at el-evations of less than one-tenth of the mixed-layer thick-ness. At larger flux values the bulk estimates are some-what greater than the measured covariance values. The10-m wind speeds for these data range from 0.8 to 7.8ms21, so they represent a fair range of values for thisregion. The correlation coefficients are slightly betterthan those for CTT shown in Fig. 4 though the rmserrors are larger. Confining the sample to cases withwind speeds of 5 m s21or less lowered the rms errorsto 0.0017 K m s21, 0.0055 g kg21ms21, and 0.0033 ms21, respectively, for the heat, moisture, and momentumfluxes, values comparable to CTT. This is a fairly crudecomparison since the aircraft was measuring at heightsfrom 30–66 m and there is the possibility of some de-viation from the surface values.Using completely independent data (eddy correla-tion flux observations from the R/V Moana Wave),Chang and Grossman (1999) compared CTT with bulksurface flux algorithms. For their calculations ziwasassumed to be comparable to the lifting condensationlevel (LCL), and mid-mixed-layer values of other var-iables were estimated by adjustment from observationlevel to the top of the surface layer (;0.1zi) usingMonin–Obukhov similarity theory and a linear ad-justment from there to the middle of the mixed layer(0.5zi). Based on the Moana Wave flux observationsthey determined an ‘‘ocean’’ set of CTT coefficientsand concluded that CTT was the best algorithm forcalculating latent heat, sensible heat, and momentumfluxes.The relationship between Deardorff velocity andbuoyancy velocity scales given in (16) was tested. Fig-ure 6 is a scatterplot of the two velocity scales showingthe strong relationship of their magnitudes as evidencedby the least squares line passing through the origin witha slope of 1.0033. The corresponding correlation co-efficient is 0.41 with an rms error of approximately 12%of the mean. The low correlation coefficient reflects thelimited range of w*values for these TOGA COAREflights.Figure 7 shows a plot of buoyant versus virtual-tem-perature differences, which were shown to be approx-imately equal for convection over land. The leastsquares line through the origin has a slope of 0.954, acorresponding correlation coefficient of 0.82, and an rmserror of approximately 14% of the mean. Thus, the ap-proximation in (9) is also good for these more humidmarine conditions.A test of the prediction of zigiven in (12) was madewith the limited number of flight legs adjacent to slantvertical profiles. The predicted versus observed valuesof zishowed considerable scatter. Since the predictedvalue of ziin (12) depends on the square of the observedheat flux and on Du22, and Du under marine conditionsis generally quite small, there is a strong dependenceon the observed heat flux and on accurate temperaturemeasurements both at the surface and mid–mixed layer.We do not recommend use of this relationship in theCOARE region. The large impact of measurement errorson reducing skill to diagnose mixed-layer depths wasanticipated by Stull (1994).6. ConclusionsTurbulent flux measurements made from five flightsof the Electra aircraft during the TOGA COARE IOPconfirmed the CTT free-convective coefficient for sen-sible heat flux. Averaging 12 estimates of the dimen-sionless mixed-layer transport coefficients gave valuesfor C*Hand C*Efor heat and moisture fluxes that werenot significantly different from each other and from thepreviously published value. However, the estimate ofC*Dfrom momentum fluxes is less than one-quarter ofthe published land-based value. There is considerable2210 VOLUME 56JOURNAL OF THE ATMOSPHERIC SCIENCESFIG. 5. Comparison of fluxes predicted by the COARE bulk pa-rameterization vs those observed by the Electra aircraft for (a) sen-sible heat, (b) moisture, and (c) momentum. Correlation coefficientsbetween predicted and observed values are shown. The root-mean-square errors are listed with the value for the cases with wind speedless than 5 m s21shown in parentheses. The diagonal line representinga 1:1 perfect fit is shown for reference.FIG. 6. Comparison of Deardorff velocity and buoyancy velocityscales described in (16). Slope of the least squares line passingthrough the origin, the corresponding correlation coefficient, and theroot-mean-square error are shown. The diagonal line representing a1:1 perfect fit is shown for reference.FIG. 7. Comparison of DuBand DuVdescribed in (10). Slope of theleast squares line passing through the origin, the corresponding cor-relation coefficient, and the root-mean-square error are shown. Thediagonal line representing a 1:1 perfect fit is shown for reference.scatter in the momentum data that may be due to in-sufficient flight-leg length used to compute the mo-mentum fluxes, and to uncertainties in the mean mixed-layer wind speed and surface currents; but the differenceis large enough to suggest that roughness-length effectsor other factors need to be incorporated into the CTT.1JULY 1999 2211GREISCHAR AND STULLThe mixed formulations of CTT, which include a windspeed factor, gave good results for heat, moisture, andmomentum fluxes even under moderate wind conditionsof 5–8 m s21; however, the best-fit coefficients wereconsiderably different than the published land-basedvalues.A comparison of the observed fluxes with estimatescomputed from the COARE bulk algorithm was made.Heat, moisture, and momentum fluxes computed usingthis bulk algorithm, which was designed for light windconditions, tended to be larger than the observed fluxesfor wind speeds greater than5ms21. At wind speedsless than 5 m s21the agreement improved considerably,with rms errors comparable to those of the mixed CTTmodel.Various relations resulting from the CTT were testedfor marine conditions. The theoretical value of the ratioof the Deardorff velocity and buoyancy velocity scaleswas confirmed. The approximate equality of the buoy-ancy and virtual temperature differences was found tohold even in the high-humidity conditions of the equa-torial Pacific. Estimation of the mixed-layer thicknessfrom surface heat flux and temperature difference be-tween surface and mixed-layer showed considerablescatter, thus limiting its usefulness in the tropical marinecontext of the COARE region.The feasibility of extending CTT to marine conditionsusing the mixed formulation with adjusted coefficientshas been demonstrated. Root-mean-square errors ofroughly 22% (2 W m22and 16 W m22for sensible andlatent heat fluxes, respectively) were obtained for thismixed-convective CTT model tuned for marine condi-tions. More marine studies are needed to reveal theroughness and possibly other effects on CTT, and wheth-er this model can be used in other areas of the ocean.Acknowledgments. This work was supported mostlyby National Science Foundation Grant ATM-9411467,with partial support from Canadian grants from the At-mospheric Environment Service and the Natural Sci-ences and Engineering Research Council. The TOGACOARE International Project Office was very helpfulin providing the Electra data (processed at the NCARATD) and necessary documentation. Discussions withJohn Young, Bob Grossman, and Yolande Serra (whoprovided corrected radiometric SST data) are greatlyappreciated. Comments from three anonymous review-ers greatly improved the manuscript.REFERENCESAsencio, N., J. P. Lafore, P. Pires, and J. L. Redelsperger, 1993:Analyses quotidiennes du Cepmmt durant la perioded’observations intensives de l’experience TOGA/COARE. ME-TEO FRANCE Groupe de Meteorologie a Moyenne EchelleNote de Travail 12, 243 pp. [Available from La Librairie deMeteo-France, 2 Avenue Rapp, 75340 Paris Cedex 07 France.]Bond, G., and D. Alexander, 1994: TOGA COARE Meteorology Atlas.TOGA COARE International Project Office, 366 pp.Chang, H.-R., and R. L. Grossman, 1999: Evaluation of bulk surfaceflux algorithms for light wind conditions using data from theCoupled Atmosphere-Ocean Response Experiment (COARE).Quart. J. Roy. Meteor. Soc., in press.Fairall, C. W., E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S.Young, 1996: Bulk parameterization of air-sea fluxes for TropicalOcean-Global Atmosphere Coupled Ocean–Atmosphere Re-sponse Experiment. J. Geophys. Res., 101, 3747–3764.Kustas, W. P., T. J. Schmugge, and L. E. Hipps, 1996: On using mixed-layer transport parameterizations with radiometric surface skintemperature for computing regional scale sensible heat flux.Bound.-Layer Meteor., 80, 205–221.Miller, E. R., and R. B. Friesen, 1989: Standard output products fromthe NCAR Research Aviation Facility. NCAR Research AviationFacility Bulletin 9, 70 pp.Otles, Z., and J. A. Young, 1996: Influence of shallow cumuli onsubcloud turbulence fluxes analyzed from aircraft data. J. Atmos.Sci., 53, 665–676.Press, W., B. Flannery, S. Teukolsky, and W. Vetterling, 1986: Nu-merical Recipes. Cambridge University Press, 818 pp.Stull, R., 1988: An Introduction to Boundary Layer Meteorology.Kluwer Academic Publishers, 666 pp., 1994: A convective transport theory for surface fluxes. J. At-mos. Sci., 51, 3–22., 1997: Reply. J. Atmos. Sci., 54, 579.Sun, J., J. F. Howell, S. K. Esbensen, L. Mahrt, C. M. Greb, R.Grossman, and M. A. LeMone, 1996: Scale dependence of air–sea fluxes over the western equatorial Pacific. J. Atmos. Sci., 53,2997–3012.TCIPO, 1992: TOGA COARE Operations Plan. TOGA COARE In-ternational Project Office, 391 pp. [Available from TCIPOUCAR, P.O. Box 3000, Boulder, CO 80307.], 1993: TOGA COARE Intensive Operations Period OperationsSummary. TOGA COARE International Project Office, 506 pp.[Available from TCIPO UCAR, P.O. Box 3000, Boulder, CO80307.]TOGA COARE Flux Group, cited 1996: TOGA COARE AircraftOffset Table. [Available online at http://www.wave.eng.uci.edu/Projects/TogapCepex/togacoare.html.]Tsukamoto, O., and H. Ishida, 1995: Turbulent flux measurementsand energy budget analysis over the eqauatorial Pacific duringTOGA-COARE IOP. J. Meteor. Soc. Japan, 73, 557–568.Webster, P. J., and R. Lukas, 1992: TOGA COARE: The CoupledOcean–Atmosphere Response Experiment. Bull. Amer. Meteor.Soc., 73, 1377–1416.Williams, A. G., H. Kraus, and J. M. Hacker, 1996: Transport pro-cesses in the tropical warm pool boundary layer. Part I: Spectralcomposition of fluxes. J. Atmos. Sci., 53, 1187–1202.

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