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  • View in gallery

    The domain of TOGA COARE in 1992–93. The perimeter of the IFA is shown by the solid black line. Surface moorings deployed during COARE included the WHOI IMET mooring and the ATLAS moorings of the TAO array. Inside the IFA, the approximate coverage of the Doppler radars mounted on the RV Vickers and Xiangyanghong 5 is shown by the two overlapping circles. The RV Moana Wave operated near the IMET mooring, while the RV Wecoma carried out repeat “bow tie” surveys that passed near the IMET mooring. The RV Franklin operated within the IFA, approaching the IMET buoy and the RV Moana Wave for intercomparison studies

  • View in gallery

    (a) Time series of the surface meteorology observed at the IMET mooring site. The periods of the flux intercomparisons are indicated by the dashed vertical lines. Rain rate is shown at the top as a daily average. The wind speed components, Vnorth and Veast, are positive toward the east and the north, respectively; and, top to bottom, the panels show rain rate, the wind speed components, barometric pressure, q (specific humidity), LW (incoming longwave), SW (incoming shortwave radiation), air temperature, and SST. (b) Time series of surface fluxes observed at the IMET mooring site. The periods of the flux intercomparisons are indicated by dashed vertical lines. Top to bottom, the panels show the daily averaged net heat flux, north and east components of the wind stress, the latent heat flux, the sensible heat flux, the net shortwave radiation, and the net longwave radiation, with the fluxes determined using version 3.0 of the COARE bulk formulas

  • View in gallery

    Timelines summarizing the periods when different ships participated in COARE, including the RVs Wecoma, RV Moana Wave, RV Franklin; the MV Alis; the Hakuho Maru; and the RVs Keifu Maru, Vickers, Natsuchima, and Xianyanghong 5. Time on station is indicated by a heavy black line for each vessel, and the intercomparison periods are identified by dashed vertical lines. While the ships with the most time in the COARE IFA all worked to be on station by conducting three cruises or legs, different exact dates on station lead to different definitions of legs 1, 2, and 3. Three of the definitions of the legs used to date are indicated by shading and the O, M, and P labels

  • View in gallery

    Time series of surface meteorology from the RV Franklin obtained during two different small-scale convective systems, illustrating the time scales of variability associated with these events: (a) 24 h of data from 26 to 27 Nov 1992 and (b) 16 h of data from 9 Dec 1992. Air temperature, bulk SST (BSST), radiometric skin SST (SSST), rain rate, wind speed, and specific humidity (Qair) are shown

  • View in gallery

    A scan by the shipboard Doppler radars from 1001 UTC 11 Feb 1993, showing the presence of rainbands associated with a convective system passing through the IFA. Note the strong band northeast of the RV Vickers, located in the center of the right-hand circle. The two ships were approximately 145 km apart, and the range rings are every 50 km. (Provided by P. Kucera, University of Iowa)

  • View in gallery

    Radiometric SST and wind speed measured from a low-flying (approximately 60 m above the sea surface) aircraft during two occasions during COARE. On 28 Nov 1992 (top two panels), the wind speeds were low and west-southwesterly, and considerable spatial variability in SST was observed. On 1 Feb 1993, the west-northwesterly winds were higher, and the resultant mixing reduced the spatial variability in SST. (Provided by C. Friehe and S. Burns, University of California, Irvine)

  • View in gallery

    Evaporative flux, specific humidity, vertical velocity, sensible heat flux, and potential temperature observed at an elevation of approximately 30 m above the sea surface as measured by J. Hacker (Flinders University) from the Cessna while flying within the IFA. This flight encountered different air masses, which is reflected in changing mean values of temperature and humidity and in the spatial variability in the fluxes. The aircraft covered 600 m in 10 s. (Provided by J. Hacker, Airborne Research Australia, Flinders University)

  • View in gallery

    (a) Composite plot of the time series of accumulated rainfall from select shipboard rain gauges (ORG is an optical rain gauge; sip is an R. M. Young self-siphoning rain gauge; PRC5 is the gauge of the RV Xiangyanghong 5), and ATLAS is the TAO buoy at 2°S, 156°W. The noncontinuous records at the site from the ships have been plotted so the accumulated rainfall at the beginning of the subsequent leg starts at the value from the end of the previous leg. (b) Select in situ accumulated rainfall records together with time series extracted at the site of the IMET and TAO buoys from the radar dataset

  • View in gallery

    Temperature, salinity, and potential density profiles in the upper 10 m of the ocean obtained during 1 day, 4 Dec 1992, of the low wind period shown in Fig. 10. Note that at the time of the last profile (2028 local time) rain had just fallen and deposited relatively cool water near the surface

  • View in gallery

    Near-surface air temperature, bulk SST (BSST), radiometric skin SST (SSST), and skin SST determined from the bulk SST time series using the COARE 2.5b algorithm (SST 2.5b). Data were obtained from the RV Franklin during a period that initially had very light winds and later had moderate winds with occasional rainshowers as evidenced by the cool spikes in radiometric skin temperature coincident with the recorded rainfall

  • View in gallery

    Comparison plots of measured incoming shortwave radiation (a) before and (b) after corrections based on the sensor intercomparison studies. The data comes from 28 Nov 1992 during IC1

  • View in gallery

    Comparison plots of measured incoming longwave radiation (a) before and (b) after corrections based on the sensor intercomparison studies. To show the effect of solar heating, the observed incoming shortwave radiation is plotted and labeled solar. The data come from IC1

  • View in gallery

    Comparison of the winds (adjusted to a common height) from four ships and the IMET buoy during IC2: (a) the uncorrected data and (b) the corrected winds. In both panels the average is plotted

  • View in gallery

    Intercomparison of the transfer coefficients from COARE 2.5b, Large and Pond (1981, 1982), and COARE 2.6a for (a) stress, (b) latent heat flux, and (c) sensible heat flux at 10 m under neutral conditions

  • View in gallery

    Plots of the differences between (a) wind stress, (b) latent heat flux, and (c) sensible heat flux computed using hourly data from the IMET buoy from 19 to 27 Dec 1992 and the COARE 2.5b, Large and Pond (1981, 1982), and COARE 2.6a bulk formulas. The 10-m wind speed is also shown in (c) to indicate the range of wind speeds encountered during this period

  • View in gallery

    Comparison of the temperature at 2 m simulated with the PWP 1D ocean model (Price et al. 1986) driven by the bulk formula's air–sea fluxes observed at the WHOI IMET mooring with the (top) temperature observed at that mooring at 2 m and of (bottom) predicted sea salinity at 2 m with the salinity observed at 2 m; after Anderson et al. (1996)

  • View in gallery

    The flux group timeline, simplified to illustrate the concept and to highlight important issues. Details of the numbered workshops are given below. Solid circles indicate the focus of particular workshops [and the release of corrected soundings by NCAR/Atmospheric Technology Division (ATD)]. Open circles are published outcomes. The release dates of the various versions of the bulk flux algorithm are shown. The COARE98 volume (26) contains nine review papers and 133 extended abstracts of research across all aspects of COARE science. Horizontal lines indicate ongoing programs that relate directly to the work of the flux group, and their workshops are indicated by open squares. The flux group workshop numbers identify the following meetings: 1) COARE planning meeting, Apr 1992, Townsville, Australia; 2) flux group, 13–16 Sep 1993, UCAR, Boulder, CO; 3) flux group, Feb 1994, Scripps Institution, La Jolla, CA; 4) COARE data workshop, 2–11 Aug 1994, Météo-France, Toulouse, France; 5) joint flux–mesoscale workshop, 11–13 Jul 1995, NCAR, Boulder, CO; 6) flux group, 2–4 Aug 1995, University of Hawaii, Honolulu, HI; 7) joint flux–mesoscale workshop, 9–11 Oct 1996, Woods Hole, MA; 8) joint flux–mesoscale–oceans workshop, 14–16 May 1997, NCAR, Boulder, CO; and 9) COARE98 conference–workshop, 7–14 Jul 1998, NOAA/NIST, Boulder, CO. The numbers under the publications line refer to key publications: 1) Anderson and Baumgartner (1998); 2) Bradley et al. (2000); 3) Bradley et al. (2001); 4) Burns et al. (1999); 5) Burns et al. (2000); 6) Clayson and Curry (1996); 7) Clayson et al. (1996); 8) Curry et al. (1999); 9) Fairall et al. (1996b); 10) Fairall et al. (1996a); 11) Fairall et al. (1998); 12) Fairall et al. (2003); 13) Feng et al. (1998); 14) Feng et al. (2000); 15) Grachev et al. (2000); 16) Jabouille et al. (1996); 17) Johnson and Ciesielski (2000); 18) Lin and Johnson (1996); 19) Mlawer et al. (1997); 20) Wang et al. (2002); 21) Moncrieff and Klinker (1997); 22) Montmerle et al. (2000); 23) Redelsperger et al. (2000a); 24) Short et al. (1997); 25) Smyth et al. (1996); 26) WCRP (1999); 27) Xie and Arkin (1997); 28) Zeng et al. (1998); 29) Zeng et al. (1999); and 30) Zipser and Johnson (1998).

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The Interface or Air–Sea Flux Component of the TOGA Coupled Ocean–Atmosphere Response Experiment and Its Impact on Subsequent Air–Sea Interaction Studies

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  • 1 Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
  • | 2 CSIRO Land and Water, Canberra, Australia
  • | 3 Department of Oceanography, University of Hawaii at Manoa, Honolulu, Hawaii
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Abstract

The interface or air–sea flux component of the Coupled Ocean–Atmosphere Response Experiment (COARE) of the Tropical Ocean Global Atmosphere (TOGA) research program and its subsequent impact on studies of air–sea interaction are described. The field work specific to the interface component was planned to improve understanding of air–sea interaction in the Tropics by improving the methodology of flux measurements and by collecting a comprehensive set of observations with coverage of a broad range of time and space scales. The strategies adopted for COARE, particularly the on-site intercomparisons, postexperiment studies of instrument performance, and bulk flux algorithm development, ensured the compilation of very high quality data for the basic near-surface meteorological variables and air–sea fluxes. The success in meeting the goals of improved air–sea heat and freshwater fluxes was verified by closure of the ocean heat and freshwater budgets to within 10 W m−2 and 20%, respectively. These results confirm that accurate in situ observations of air–sea fluxes can be obtained during extensive measurement campaigns, and have established the foundation for current plans for global, long-term oceanic observations of surface meteorology and air–sea fluxes. At the same time, some uncertainties remained after COARE, which must be addressed in future studies of air–sea interaction.

Corresponding author address: Robert A. Weller, WHOI, Clark 204a, MS 29, Woods Hole, MA 02543. Email: rweller@whoi.edu

Abstract

The interface or air–sea flux component of the Coupled Ocean–Atmosphere Response Experiment (COARE) of the Tropical Ocean Global Atmosphere (TOGA) research program and its subsequent impact on studies of air–sea interaction are described. The field work specific to the interface component was planned to improve understanding of air–sea interaction in the Tropics by improving the methodology of flux measurements and by collecting a comprehensive set of observations with coverage of a broad range of time and space scales. The strategies adopted for COARE, particularly the on-site intercomparisons, postexperiment studies of instrument performance, and bulk flux algorithm development, ensured the compilation of very high quality data for the basic near-surface meteorological variables and air–sea fluxes. The success in meeting the goals of improved air–sea heat and freshwater fluxes was verified by closure of the ocean heat and freshwater budgets to within 10 W m−2 and 20%, respectively. These results confirm that accurate in situ observations of air–sea fluxes can be obtained during extensive measurement campaigns, and have established the foundation for current plans for global, long-term oceanic observations of surface meteorology and air–sea fluxes. At the same time, some uncertainties remained after COARE, which must be addressed in future studies of air–sea interaction.

Corresponding author address: Robert A. Weller, WHOI, Clark 204a, MS 29, Woods Hole, MA 02543. Email: rweller@whoi.edu

1. Introduction

In this article we describe the interface or air–sea flux component of the Coupled Ocean–Atmosphere Response Experiment (COARE) of the Tropical Ocean Global Atmosphere (TOGA) research program. The background for and overall objectives of COARE are reviewed by Webster and Lukas (1992, hereafter WL92). COARE was organized around six components: the interface or air–sea flux component, large-scale atmospheric circulation and waves, atmospheric convection, large-scale ocean circulation and waves, ocean mixing, and modeling. The fieldwork of COARE was carried out in a domain centered near the equator, northeast of Papua New Guinea (Fig. 1). The bulk of the observations were collected during the 4-month intensive observation period (IOP) of November 1992–February 1993. The scientific objectives specific to the air–sea flux component (WL92) were “1) to provide a high-quality data set of heat, moisture, and momentum fluxes in the warm-pool region; 2) to understand the physics and thermodynamics of interfacial exchange processes that have particular behavior in this region of low wind speeds and strong atmospheric convection; 3) to improve various empirical formulae used to estimate net surface heat flux for use in warm-pool regions; 4) to determine the magnitude (and significance for longer-term models) of short time-scale variability of the fluxes of heat, moisture, and momentum—hourly, diurnal, and episodal, and; 5) to understand the impact of the full range of wind structures, from the ambient trade-wind regime through episodic westerly bursts, on the ocean–atmosphere fluxes of heat, moisture, radiation, and momentum.”

The warm pool region of the western equatorial Pacific, with its low mean wind speeds, high tropical insolation, and intermittent, energetic forcing associated with convective systems, presented a formidable observational challenge to air–sea flux studies during COARE. Before COARE, estimates of the net annual heat flux in the warm pool in five existing climatologies ranged from 20 to 100 W m−2 (WL92). The uncertainty was ascribed partly to the difficulty of making accurate and adequately sampled measurements of the surface meteorological variables (i.e., air temperature and humidity, precipitation, incoming shortwave and longwave radiation) in the low wind, convective conditions, and partly to the inadequacy of existing bulk formulas for wind stress and heat fluxes in these conditions. The latter had mostly been developed during windy, midlatitude field experiments, and the applicability of the bulk transfer coefficients and parameterizations to tropical conditions was in some doubt. Additionally, there was potential for large uncertainty and large interannual variability in the annual rainfall estimates. Spencer (1993) pointed to differences of up to 0.7 m yr−1 in the COARE region among the Janowiak and Arkin (1991) satellite infrared estimates, an in situ dataset based on Legates and Wilmott (1990) and Jaeger (1983), and his own satellite microwave datasets and further showed interannual variability in the region of over 2 m yr−1.

Planning for COARE recognized the need to improve the measurements and to develop appropriate bulk flux algorithms. The TOGA goal of determining the net air–sea heat flux to an accuracy of 10 W m−2 on monthly to seasonal time scales was adopted (WL92; Godfrey et al. 1999b). Accurate rainfall measurements were also a goal, because of the large annual precipitation, greater than 4 m yr−1 according to Dorman and Bourke (1979), and its probable role in stabilizing the surface layer of the ocean (Lukas and Lindstrom 1991). To help achieve these goals, results and experiences from pilot air–sea flux field studies in the warm pool region (Bradley et al. 1991, 1993; Chertock et al. 1993; Young et al. 1992) were used to help formulate an experimental strategy and improve the methodology for measurements. Part of the challenge was the variability of the region, which spanned a wide range of scales in space and time. Episodic westerly wind bursts, lasting up to 2 weeks in duration and with scales of many hundreds to a thousand or more kilometers, were recognized as an energetic component of the coupled air–sea system and a possible important factor in the onset of the ENSO phenomenon. At the same time, however, the air–sea fluxes were influenced by smaller scales, including squalls and small convective systems down to individual elements a few kilometers in size, and by processes whose temporal variability ranged over periods from months to hours.

Our purpose here is to describe the fieldwork in COARE associated with the interface component, to document the steps taken to ensure the accuracy and compatibility of the diverse surface meteorological and air–sea flux measurements, and to summarize how these data were used to refine the bulk formulas. In addition, we document the accuracies that can now be achieved in surface meteorological and air–sea flux measurements made at sea. It is our belief that the effort invested in the COARE air–sea flux component has paid large dividends, a notion reinforced by many contributions to the recent COARE98 conference (WCRP 1999), by the adoption of the COARE bulk formulas by many researchers, and by the interest in the COARE interface component shown by analysts and modelers alike, as we show in sections 4 and 5. COARE contributions to the state of the art were also discussed at the workshop organized by the World Climate Research Programme/Scientific Committee for Oceanographic Research (WCRP/SCOR) Working Group on Air–Sea Fluxes (WCRP 2001). We assess the impacts of this effort on the planning and execution of subsequent field programs where accurate surface measurements and air–sea fluxes have been needed and on the thrusts now developing to further extend our understanding to very low wind and to high wind regimes. We submit that the successes of the COARE air–sea flux effort have created a foundation upon which to build strategies for sustained flux observations on a global basis.

2. Observational approach during COARE

During the planning for COARE, an air–sea interaction (flux) working group was established. The flux group recognized that success in addressing the objectives of the flux component of COARE would require the coordinated use of multiple measurement platforms, an emphasis on comparison and intercalibration, and a concentrated effort following the field work to identify and resolve data quality problems and to improve bulk flux estimates. The flux group strategy included appropriate sampling, better measurement methods, and direct eddy correlation measurement of energy and momentum fluxes to calibrate the exchange coefficients in appropriate bulk flux formulas. Sampling of the broad range of space and time scales and collection of data over the 4-month IOP were accomplished by fielding and maintaining many flux-measuring platforms, including land stations and moorings in place for the duration, and by staggering the deployment within the region of ships and aircraft. At select sites, accurate point measurements of the fluxes were collected to support the development of improved bulk algorithms, which would then be used with high quality bulk meteorological observations to cover larger space and longer time scales.

The most intensive measurement programs were conducted in the intensive flux array (IFA; Fig. 1). Land-based meteorological stations at Kavieng and at Kapingamarangi Atoll defined the western and northern corners of the perimeter of the IFA, while the research vessels (RVs) Kexue 1 and Shiyan 3 were stationed at the eastern and southern corners. Two vessels, the RVs Vickers and Xiangyanghong 5, operated stabilized, Doppler radars from fixed locations within the IFA for much of the IOP to measure and map rainfall (Rutledge et al. 1993; Short et al. 1997). The RV Keifu Maru also operated a Doppler radar during November 1992. The TOGA Tropical Atmosphere and Ocean (TAO) (Hayes et al. 1991) array of surface buoys provided a large-scale and longer-term context and was locally augmented during COARE to improve its zonal resolution and to measure shortwave radiation and rainfall. Shipboard, ground-based, aircraft, and satellite sampling in the COARE large-scale domain (LSD) and outer sounding array (OSA) also provided large-scale coverage for the air–sea interface work.

Three surface moorings provided time series from within the IFA. The TAO mooring at 0°, 156°E measured wind velocity, sea (1-m depth) and air temperature, humidity, rainfall, and shortwave radiation. TAO moorings at 2°S, 156°E and at 0°, 154°E measured wind velocity, air temperature and humidity, incoming rainfall, and sea temperature. The Woods Hole Oceanographic Institution (WHOI) surface mooring, identified as the Improved Meteorological (IMET) mooring, at 1.75°S, 156°E, measured wind velocity, downwelling radiation (both shortwave and longwave), air temperature and relative humidity, barometric pressure, and ocean temperature near the sea surface (0.45 m). Time series from the IMET mooring (Fig. 2a) provide an overview of the temporal variability of the surface meteorology within the IFA [for more detail see Weller and Anderson (1996), and for the large-scale ocean–atmosphere context during COARE, see Lukas et al. (1995)]. From late October to early November 1992 a series of 3- to 7-day-long southwesterly wind events with speeds between 3 and 8 m s−1 was observed. Low wind speeds, typically 2 m s−1, persisted from 14 November through 12 December. The following period until about 4 January 1993 was marked by a sequence of moderately strong wind events, with flow toward the southeast associated with the now-celebrated December westerly wind burst (WWB). Instantaneous winds greater than 30 m s−1 were observed on board the RV Wecoma, and a peak wind of 17.2 m s−1 was recorded by the IMET mooring on 23 December. The WWB was followed by another period of very low wind speeds from 4 to 15 January, and then a period of sustained westerlies and squalls.

These time series can be interpreted as a record of three cycles of the intraseasonal oscillation (ISO; Madden and Julian 1972) that passed through the IFA (Kiladis et al. 1994). The active phases of these ISOs passed the site of the mooring in the first week of November 1992, around 20 December 1992, and at the end of January into early February 1993. The periods characterized by low winds and clear skies indicate the suppressed phase of the ISO. According to Chen et al. (1996) the phase of the second ISO, where convection is suppressed, lasts from 13 November to 8 December 1992 in the IFA; the active phase is from 9 December 1992 through early January 1993, though there is a break in the convective activity during 17–19 December. The suppressed phase of the third ISO lasts from 6 to 26 January and as with ISO2 was marked by very little high cloud cover. During the active phase of ISO3, which continued through the end of the IOP, moderate winds with short-lived (several hours to 1 day in duration), higher-speed westerly wind events were seen in the IFA rather than sustained westerlies. The ISO during the COARE IOP was unusually strong, related to the resurgence of ENSO warm event conditions that had started during 1991, but which had relaxed to near normal prior to the IOP (Lukas et al. 1995).

The research vessels Alis, Franklin, Hakuho Maru, Malaita, Moana Wave, Natsushima, Noroit, and Wecoma worked within the IFA for various periods during the IOP (Fig. 3). The three periods when the Moana Wave and Wecoma worked simultaneously at the center of the IFA are called legs 1-O, 2-O, and 3-O. The RV Wecoma steamed a repeat butterfly or bow-tie pattern centered on the IMET mooring, nominally at 4 m s−1, for each of its three legs throughout the IOP (see Fig. 1). The RV Moana Wave operated within a few miles of IMET, moving slowly upwind (about 1.5 m s−1) then repositioning. The RV Franklin steamed triangles at 4 m s−1 around a drogued buoy, which drifted with the surface current on various tracks through the IFA. The shipboard observations (Table 1) included direct turbulent flux measurements and surface meteorology. Ships that made near-surface oceanographic measurements provided information on both the local forcing and oceanic response. For example, Fig. 4 shows time series obtained aboard the RV Franklin during the passage of two small convective systems with accompanying changes in air temperature, wind, and rain. The shipboard sampling program also provided information about spatial variability across the IFA. Figure 5 shows one rainfall map observed by the two Doppler radar&ndash=uipped ships, the Vickers and the Xiangyanghong 5. The two radar ships were both on station for three periods: legs 1-M, 2-M, and 3-M.

Five of the research aircraft carried out “boundary layer” flights at between 30 and 100 m above the sea surface (Table 2). They were the Electra from the National Center for Atmospheric Research (NCAR), two P-3s from the National Oceanic and Atmospheric Administration (NOAA), the C-130 from the Met Office, and the Cessna (C340) from Flinders University, Adelaide, South Australia. During these flights, the aircraft measured bulk meteorological parameters and turbulent fluxes, and frequently overflew ships and moorings to make comparisons with surface observations. On some occasions they flew side by side to intercompare their own sensors. These intercomparisons are discussed in Burns et al. (1999, 2000). The aircraft data complement other datasets by providing “snapshots” of spatial variability over hundreds of kilometers. Figure 6, for example, shows the contrast between the considerable spatial variability of the SST on a low-wind day and that when the SST was substantially more uniform due to strong wind mixing. Figure 7 is an example of the mesoscale variability in the marine atmospheric surface layer observed during a Cessna flight. Different air masses were encountered, distinguished by different mean temperature and humidity, and quite dissimilar behavior of the turbulent fluxes. At higher altitudes, the National Aeronautic and Space Administration (NASA) DC-8 and ER-2 collected information about clouds, lightning, radiation fields, and atmospheric temperature and humidity, and also tested methods for remote sensing of rain.

During the IOP, surface meteorological and flux fields from satellites and from the analysis cycle of the operational numerical weather prediction models were collected and archived to provide coverage of the large scales. Geostationary Meteorological Satellite (GMS), NOAA, Defense Meteorological Satellite Program (DMSP), European Remote Sensing Satellite-1 (ERS-1), and TOPEX/Poseidon satellites provided data, including sea surface temperature, sea surface topography, radiation, wind speed, and rainfall. Model output was also obtained from the Bureau of Meteorology Research Centre (BMRC, Melbourne, Australia), the National Centers for Environmental Prediction (NCEP, Washington, D.C.), the European Centre for Medium-Range Weather Forecasts (ECMWF, Reading, United Kingdom), and the Japan Meteorological Agency (JMA, Tokyo, Japan).

3. Intercomparison of basic observations

With the rather severe accuracy requirements implied by the goal of reducing the uncertainty in net air–sea heat flux to 10 W m−2 or less, dedicated intercalibrations were planned as part of the air–sea interaction component of COARE. This was an unprecedented opportunity for the groups making eddy correlation flux measurements from ships under way, which requires correction to wind measurement for the ship motion, to compare their technique and results. To obtain adequate turbulence statistics for the eddy fluxes, and to test individual meteorological and radiation sensors during both day and night conditions, each intercomparison needed to run over a full diurnal cycle. This time requirement was substantial, but all aircraft and shipboard groups participated.

According to plan, the RVs Alis, Franklin, Hakuho Maru, Moana Wave, and Natsushima assembled near the IMET mooring for two dedicated meteorology and flux intercomparisons on 27–28 November 1992 (IC1) and on 3–4 February 1993 (IC2). The ships steamed upwind from the buoy on parallel tracks separated by approximately 1 km for 3 h at 1.5 m s−1, returning in 1 h at 6 m s−1 and repeating the process. Up to six upwind legs were completed during each 24-h intercomparison period; fortunately, weather conditions were ideal on both occasions. During the comparisons the RV Wecoma continued on its butterfly pattern, passing the buoy twice. On 28 November the three turboprop aircraft scheduled a combined boundary layer mission to participate in IC1.

In addition to the dedicated intercomparisons, additional opportunities were sought for close intercomparison of surface and aircraft platforms. The RV Moana Wave operated during legs 1-O and 2-O in the vicinity of the IMET mooring, and near the equatorial TAO mooring in leg 3-O. The RV Wecoma maintained its sampling pattern around the IMET mooring for much of the IOP. The Flinders C340 anchored many of its low-level missions to the Franklin's position, and similarly the turboprops (Electra, P-3s) flew frequently over the IMET mooring and the Moana Wave. Burns et al. (1999, 2000) identified a total of 267 occasions, including IC1 and IC2, when individual aircraft were sufficiently close to a surface platform to enable comparisons to be made.

Immediately following the field program, analysis of the data from these intercomparisons became a priority activity, leading to a series of flux group workshops. Further calibrations and comparisons of sensors were initiated as needed to resolve issues arising from the field intercomparisons and achieve the COARE 10 W m−2 goal. In terms of the bulk estimates of the energy fluxes, assuming that measurement errors in the quantities used in the bulk calculation are independent, this implies required accuracies in the air–sea temperature difference of 0.2°C, in the humidity difference of 0.2 g kg−1, and in the wind speed of 0.2 m s−1 (Fairall et al. 1996b). Special sensors, more precise but less rugged than the ship's regular instrumentation, had been installed to this end. Despite this care, none of the platforms was free from error in all of its measurements. These errors would have gone undetected without the collaborative intercomparisons.

Correction of the errors has been an incremental process, reviewed and guided by COARE flux group workshops (e.g., Bradley and Weller 1997; Bradley et al. 1997) and the COARE International Data Workshop (Chinman et al. 1995). Discrepancies have been traced to calibration errors, instrument malfunction or exposure problems, and also sometimes to genuine small-scale variability. When comparing a particular variable measured by perhaps five platforms, our strategy has been to select one instrument, perhaps the most consistent, or a superior instrument, or the best exposed, to use as a reference to identify errors and remove biases from the others. Descriptions of this process as applied to each of the key variables are given below to illustrate the magnitude of the errors and our success in correcting them. The focus here is on the surface observations. For the aircraft observations detailed results of intercomparisons appear in Burns et al. (1999, 2000). Reconciling discrepancies between rainfall observations has proved to be the most challenging. Because of the particular importance of precipitation for COARE and the climatology of the region, we performed substantial analyses, which yielded new information about the COARE rainfall observations and which we discuss first and at some length.

a. Precipitation

The precipitation measurements made during COARE have received considerable attention in an effort to determine the accuracy of the various methods. Point rainfall measurements were made on the ships and buoys using volumetric gauges, such as the self-siphoning R. M. Young funnel gauge, and optical rain gauges (ORGs, Scientific Technologies). Satellites and shipboard radars provided remotely sensed spatial coverage. Stabilized C-band Doppler radars were deployed simultaneously on the Vickers and Xiangyanghong 5 (PRC5). Atmospheric thermodynamic budgets also provided precipitation estimates over the IFA. At the 1994 COARE data workshop in Toulouse, France, serious disagreement was discovered between the various methods (Chinman et al. 1995, p. 26). Leaving aside a broad range of satellite estimates, these results formed two groups: the radars, atmospheric budgets, and siphon gauges supported an IOP-average rainfall of 5–6 mm day−1 and the ORGs indicated about twice that value. Being relatively new and untried instruments, the ORGs were suspected of overestimating relative to the more traditional systems. Possible problems were errors in calibration, sensitivity to ship and mooring vibration, and inappropriate responses to the intensity and drop size distribution (DSD) of tropical rainstorms.

All of these possibilities were studied on three of the COARE ORGs, using an artificial rain facility (or rain tower) in which a uniform distribution of raindrops fell to terminal velocity, and the rain rate could be varied over the range 20–200 mm h−1 (F. Bradley and C. Paulson 2002, personal communication). The vibration effect reported by Short et al. (1997) was not evident, nor was there any apparent dependence on DSD, supporting the conclusions of Nystuen et al. (1996). However, while the calibration slopes of all three ORGs agreed with the factory specification, two of the three had a constant offset of a few millimeters per hour, which could lead to large percentage errors at low rain rates. The only other defect found was imperfect cosine response, leading to overestimation of the vertical component of rain through the ORG beam. This can be a significant effect on board ship, where the ship's forward speed and rolling accentuate relative rainfall angles, and could also lead to a net bias on a mooring tilted by the wind. In the new rainfall analysis described below, corrections for this effect based on relative wind and direction time series have been applied to the Moana Wave, Wecoma, and Franklin ORG data, typically lowering rain rates by 15%.

Bradley and Paulson also explored the underestimation of siphon gauges due to wind deflection of raindrops away from the funnel opening. This phenomenon is well known in funnel gauges used over land; the World Meteorological Organization (WMO) Commission for Instruments and Methods of Observation (CIMO) initiated a series of workshops and a monitoring program designed inter alia to investigate the problem for operational gauges (WMO 1985, 1989). Koschmeider (1934) proposed an empirical wind speed–dependent correction. Folland (1988) developed a theory for loss of catch based on aerodynamics, droplet size, and rain rate, which agrees fairly well with field observations over land, where corrections are generally less than 10%. However, the problem is much more severe at sea where winds are stronger, often enhanced by the ship's speed, and by flow distortion over the entire vessel, not just the gauge itself.

The COARE radar rainfall data have also undergone close scrutiny (Rutledge et al. 1993; Short et al. 1997; Petersen et al. 1999). Several sources of error were discovered, and improvements were made to the signal processing and data analysis. These included careful recalibration of the two systems, corrections for range attenuation and gain, and separate ZR relationships for convective and stratiform rainfall. The relationship between radar reflectivity, Z, and rain rate, R, is customarily based on “rain-gauge adjustment” (Steiner and Houze 1997), which is fairly straightforward over land but problematical for ocean platforms. Tokay and Short (1996) found that, for the same reflectivity, stratiform rain rates are about half those of convective precipitation. However, Steiner and Houze (1997), using extensive datasets from two tropical coastal sites, found that correlations between radar rainfall estimates and rain gauge accumulations were too poor to justify using separate relationships. Short et al. (1997) give reflectivity Z = 323R1.43 for stratiform and Z = 120R1.43 for convective rainfall, and have developed 2 km × 2 km resolution, 10-min rain-rate maps by merging data from the two radars (e.g., Fig. 5).

Ciesielski et al. (1997; see also Bradley and Weller 1997, p. 17; Bradley et al. 1996) sought an independent estimate of average rainfall for the IOP through analysis of atmospheric heat and moisture budgets. This technique, described by Yanai et al. (1973), makes use of atmospheric soundings of temperature and humidity obtained over space and time, to determine the “apparent heat source” (known as Q1) and the “apparent moisture sink” (Q2) of a volume of the atmosphere. An extensive array of sounding sites was distributed over the COARE domain, within which the budgets for specific regions were determined using the interpolation technique of Nuss and Titley (1994).

A novel use of Doppler wind profilers for precipitation profile measurements was also introduced during COARE. The UHF profilers, originally intended for the measurement of lower-tropospheric winds in the Tropics (Carter et al. 1995), are sensitive to hydrometeors and have now been applied to precipitation research (Gage et al. 1994, 1996; Ecklund et al. 1995; Williams et al. 1995, 1999). A unique precipitation dataset was collected using UHF profilers at Integrated Sounder System (ISS) sites during COARE. Preliminary studies show reasonable agreement between profiler and scanning radars in the statistical partitioning of tropical precipitation. The profiler uses the vertical structure of hydrometeor echoes, their Doppler velocity, and spectral width, as well as their temporal continuity in determining precipitation type (Williams et al. 1995).

After all instrumental corrections, the results were presented to a flux group workshop at WHOI (Bradley and Weller 1997). As shown in the “early results” columns of Table 3, disagreement between ORGs and the radars remained large. The discrepancy was largely explained by Johnson and Ciesielski (2000) who, using the moisture budget technique, determined the IFA-averaged rainfall rate for the IOP to be 8.2 mm day−1 compared to a revised radar estimate of 5.4 mm day−1. However, when they computed budgets just over the radar area (which covers about one-third of the IFA) and for the same 101 days that the radars were operational, their rainfall was only 6.8 mm day−1. For these same 101 days but over the entire IFA, the estimate was 7.4 mm day−1. These results indicate that the radars were situated in a relatively drier region of the IFA, and that the 101 days of radar exposure were during relatively drier periods of the IOP.

To obtain better insight into the accuracy of the in situ rain gauges on ships and moorings during COARE, in their intended role as validation for the remotely sensed rainfall estimates, we have reanalyzed and compared the rainfall time series from the original archives. Figure 8a shows the accumulating rainfall as measured on several platforms. Because of the considerable variability found by Johnson and Ciesielski (2000), we have been particularly careful to include only data that are comparable in space and time. Data from the survey ships (Moana Wave, Franklin, and Wecoma) were restricted to the same area (1°–3°S, 153°–157°E) specified by Johnson and Ciesielski (2000), under radar coverage (see Fig. 1), and excluding transits to and from ports. Data from ORGs on the radar ships (Vickers and Xiangyanghong 5) were only included when the ships were on station. The TAO mooring with an ORG was at 2°S, 156°E. Because ships entered the box at different times and followed different cruise patterns, there is no common origin for time series, although most begin around 10 November 1992 (day 315). After a data gap, caused by a port call or instrument failure, each time trace resumes at its previous value, thus offset from other traces during this interval.

Rainstorms, particularly those associated with tropical convection, are perhaps the “patchiest” of all meteorological phenomena. The rainfall accumulation is dominated by individual storms, of a scale of a few tens of kilometers at most, even when part of mesoscale convective processes; the intensity recorded by a particular gauge will depend on its location within the storm, and indeed whether the storm encounters the platform at all. Over the entire period shown in Fig. 8, any single location recorded less than 20 significant rainfall events, which, statistically, imposes a limit on the accuracy with which observations at a single point can determine the IOP average. [Silverman et al. (1981), Gabriel (1981), Bell (1987), and Bell et al. (1990) discuss the stochastic characteristics of rainfall.] Average rainfall estimates (mm day−1) from the present data analysis are included in Table 3 and differ from the earlier values mainly because measurements made outside the selected area have been excluded, as have periods when instruments were not working (e.g., the Wecoma's ORGs did not come on line until several days after the siphon gauges at the beginning of each leg; the Franklin's siphon gauge failed on day 344).

We draw attention to some features of the data in Fig. 8a and Table 3. Both the Franklin and the Moana Wave recorded at least one intense rainfall event (days 344 and 355, respectively) not experienced by other platforms, which contributed to their higher day-average rainfall. The second ORG deployed on the Wecoma on day 392 appears to be more sensitive than the first; however, it was mounted on the bow and was clearly observed [by one of the authors (RL)] to be subject to spray coming over the bow in rough weather. The original ORG, mounted amidships, does appear to be more consistent with other instruments. The Wecoma also carried two siphon gauges, which generally agreed with one another, so for clarity only their average is displayed. The Franklin deployed an ORG and a siphon gauge. As expected, on both ships the siphon gauges were underestimated relative to the ORGs because of the wind effect already discussed, but more seriously on the Franklin. This is thought to be due to the location of the Franklin's gauge, high on the masthead and subject to more severe wind flow distortion. The Xiangyanghong 5 carried two ORGs that differed in sensitivity by about 10%; their average is shown in Fig. 8a.

The period between days 355 and 375 included the strong westerly wind event, which Weller and Anderson (1996) describe as occurring in three bursts. It triggered widespread storm activity so that, despite being in different locations, the ORG rain accumulations on the Moana Wave, Wecoma, and Xiangyanghong 5 over this period are quite similar (about 300 mm in 20 days). Note that the slopes of the ORG traces from both the Vickers and the TAO buoy agree quite well with those of the other three ships when the rain rates, as retrieved from the archive, are halved. We can only speculate on the reasons for this. The Vickers deployed two ORGs simultaneously, which often responded differently storm to storm, although both recorded close to 1400 mm of rainfall overall; the time series shown is their average, halved. The TAO ORG time series does not indicate any features suggesting malfunction, or which could not be explained by natural variability of rainfall intensity. The discrepancy in either case may be an errant factor of 2 in calibration or in data processing, but at this stage it is impossible to verify.

Some of the above rainfall time traces are repeated in Fig. 8b, together with time series obtained from the NASA/Tropical Rainfall Measuring Mission (TRMM) merged radar datasets (Short et al. 1997) at 2-km altitude above the IMET and TAO mooring locations. These are separated by only 30 km, but the traces diverge significantly due to different response to a few rain events. Direct comparison with the TAO ORG data is not valid because of the uncertainty discussed above, and also not with the IMET because substantial gaps in its rainfall record were filled with data from the Moana Wave and TAO. However, compared with the Moana Wave and the Xiangyanghong 5 accumulations during leg 2, the radar estimates are considerably less. The intensity of some rain events seems to be missed by the radar, for example, the storms around days 358 and 369. The difference cannot be entirely ascribed to overestimation by ORGs, because the Wecoma's siphon gauges also recorded these storms. Other comparisons of the radar data with surface observations were made by Bradley et al. (1996; see also Bradley and Weller 1997, p. 18), who “navigated” the Franklin through the radar rainfall grid and, allowing 5 min for the rain to fall from 2-km altitude, obtained ORG rain rates around 30% higher than the radar. Computing radar rain rates at only 1-km altitude decreased the discrepancy to about 25%. Short et al. (1997) did a similar exercise with the Moana Wave over a 42-day period, and found that the ratio of ORG to radar rainfall was about 2.5; the respective time series during leg 2 in Fig. 8b confirm this. At the same time, the ORG data from the Xiangyanghong 5 (which carried one of the radars) on this leg agree well with the Moana Wave data, as might be expected with such widespread storm activity. Statistically, Short et al. (1997) show excellent agreement between the rainfall rate distributions from the radars and from the Xiangyanghong 5 ORGs, averaging over 8 min to allow for the fall time, and excluding rain rates below 0.5 mm h−1 or when the ship was under way to avoid suspected vibration effects.

It is clear from the above that much of the discrepancy between different rainfall estimates can be explained in terms of spatial and temporal variability. The “IOP-average rainfall” reported by the various measuring platforms depended very much on their period of deployment and their location within the IFA. The C-band radar observations showed these to be a very powerful tool providing great insight into the behavior of storm patterns in convective regimes. However, despite skillful deployment, careful data analysis, and consideration of all possible sources of error, the evidence presented above points to the fact that overall they underestimated the rainfall during COARE. The ORGs proved to be generally robust in the marine environment, but subject to instrumental sources of error, which may not be readily detected. Steps taken by the planners of COARE and by the NASA TRMM office to deploy many and varied precipitation sensors have enabled us to identify defective instruments with a fair degree of certainty. Previous experience tells us that funnel gauges on ships are likely to severely underestimate rainfall, for well-known reasons, and the results from COARE bear this out.

Using the atmospheric moisture budget technique, Johnson and Ciesielski (2000) show that the radar ships were on station during relatively drier periods of the IOP and that the TOGA radar, aboard the Xiangyanghong 5, was stationed in a precipitation minimum. Their east–west decrease of IOP-average rain rate from about 11 mm day−1 at 157°E to 7 mm day−1 at 153°E (their Fig. 8a) corresponds almost exactly with the difference in ORG estimates by the three survey ships that operated in the vicinity of IMET (average 11.03 mm day−1) and by the Xiangyanghong 5 (average 7.02 mm day−1). This is almost certainly fortuitous, but supports their IOP/IFA average of 8.2 mm day−1 rather than the most recent radar revision of 5.4 mm day−1. Furthermore, ocean freshwater budget calculations by Feng et al. (2000) over the Wecoma COARE cruise area implied average precipitation of 8.0 mm day−1 compared with the ORG measurement of 9.0 mm day−1 (the difference from Table 3 is because times were different). Rain rates from the same ORG instruments have also been used to obtain acceptable closures of the freshwater budget in the tropical Indian Ocean by Godfrey et al. (1999a).

For the Algorithm Intercomparison Project (AIP-3), 57 satellite rainfall algorithms were compared against the COARE radar rainfall observations (Ebert 1996; Ebert and Manton 1998). This work showed that on average the algorithms overestimated precipitation by about 30% relative to the radars. The radar dataset used was the version represented in the early results column in Table 3; about half the discrepancy would be accounted for with the subsequent correction for range dependence. It is interesting to note that the three independent satellite rainfall estimates for the COARE IOP concur with a value in the range 8–10 mm day−1. Agreement between the radar and satellite estimates based on outgoing longwave radiation (OLR) improves as the averaging area is increased; daily, 1.25° estimates have a correlation of over 0.7 with radar.

b. Sea surface temperature

Sea surface temperature is the basic variable that, along with surface wind, couples the ocean and atmosphere, by influencing the magnitude of the surface turbulent fluxes and the net flux of longwave radiation. More than for any previous experiment, TOGA COARE analysis highlighted the need to be precise about the definition of sea surface temperature, particularly to distinguish between the water temperature at some depth (the bulk value) and that at the actual interface. The latter is the temperature that physically determines the surface heat fluxes. Cooling due to the fluxes of sensible and latent heat and the emission of longwave radiation occurs at the interface, whereas the shortwave radiative heating is distributed over depth (Fairall et al. 1996a). Under conditions of light wind and strong sun, a diurnal warm layer can form in the near surface producing vertical gradients as much as 3°C in the upper meter (Price et al. 1986). Thus, the common nomenclature “SST” is ambiguous generally, and particularly unhelpful in the context of the domain and rationale for COARE, that is, the sensitivity of coupled models to interface temperature and fluxes, which lead to the flux accuracy goal of 10 W m−2 with implications for the performance of bulk flux algorithms.

The true interface temperature cannot be measured with current technology (Donlon et al. 2002). Ocean “skin” temperature measurements from ships, aircraft, and satellites using infrared (IR) radiometers, usually in the wavelength band 8–11 μm, penetrate the water to a depth of a few hundredths of a millimeter depending on wavelength. Donlon et al. (2002) illustrate schematically typical temperature profiles in the upper few meters of the ocean, and adopt SST with subscripts to define the various layers produced by the cool skin and diurnal warm processes. While this facilitates the development of their analysis, we feel that their terminology is too complicated for practical purposes, and may well add to the present confusion. Here we reserve the abbreviation SST for an IR radiometrically determined, or modeled, skin temperature, recognizing that this carries a small depth uncertainty associated with the wavelength and specify “bulk” near-surface temperature measured at depth z as NST(z). However, the increasing role of microwave instruments, with penetration depths of some millimeters, may require some reassessment of this strategy.

Figure 9 shows temperature, salinity, and density profiles in the upper 10 m of the ocean, measured with a precision thermosalinograph mounted on top of the SeaSoar towed by the Franklin. To avoid disturbance to the ocean structure, the SeaSoar was fitted with a rudder, which deflected it clear of the ship's wake; other techniques to obtain undisturbed high-resolution, near-surface ocean measurements during COARE are described by Soloviev et al. (1998, 1999). This was a fairly typical day that began with low winds and strong insolation but became stormy with periods of rain. Rainfall fell at a temperature close to the wet-bulb temperature (Gosnell et al. 1995; Anderson et al. 1998), cooler than the sea surface temperature prior to the rain, and produced a near-surface layer of cool, freshwater. The penetrating solar radiation resulted in diurnal restratification in low winds.

In COARE, SST was measured radiometrically from one or two ships and by all the aircraft, using IR radiometers with varying degrees of accuracy, but the majority of the sea temperature measurements were made at various depths from ships and moorings. The COARE bulk algorithm (Fairall et al. 1996b) uses transfer coefficients derived from surface renewal theory, for which skin temperature is the appropriate value, and incorporates models of both the cool skin and warm layer, to estimate SST from a bulk measurement at a known depth. The TOGA program specified an accuracy of ±0.3°C for SST over a 2° × 2° region (WCRP 1985) as a target for validation of spaceborne radiometers. An error of 0.3°C changes sensible and latent heat fluxes calculated with the bulk algorithm by 2 and 10 W m−2, respectively, for typical climatic conditions in the Tropics. Averaged over 70 days during COARE, inclusion of the cool skin in the sea surface temperature value used in the bulk formula increased heat input to the ocean by about 11 W m−2, while adding the warm layer decreased it by about 4 W m−2 (although the effect can be up to 50 W m−2 at midday).

During IC1, the observed water temperature at sensor depth on the Moana Wave, the Franklin, and the IMET buoy agreed to within 0.2°C at night and 0.5°C during the day, which was clear with light winds and an associated strong near-surface temperature profile. During IC2, a cloudier day with stronger winds, agreement of 0.1°C was seen during the night and day. This indicated that calibration of the SST sensors was satisfactory, and no corrections were justified or attempted. On the basis of wingtip-to-wingtip comparisons, Burns et al. (2000) found that aircraft IR measurements differed by 0.7° ± 0.4°C and made empirical corrections to remove systematic offsets. These improved the comparison accuracy to 0.1° ± 0.3°C. Burns et al. (2000) then compared these corrected aircraft IR measurements with those from surface platforms (the TAO and IMET moorings, and the RVs Franklin, Moana Wave, and Wecoma), adjusted to the surface (SST) value using the models in the COARE bulk algorithm, and found overall agreement to be 0.3° ± 0.5°C, with the aircraft SST observations exceeding surface values systematically by about 0.3°C. The comparison does depend on the validity of the bulk algorithm models of cool skin and warm layer, although this is well supported by the Franklin radiometric SST measurements. Figure 10 illustrates the agreement achieved between the radiometric and calculated skin temperatures at the Franklin. In some cases, the spatial variability of SST combined with the different sampling strategies of aircraft and ships may also be a factor, as there is an indication of a persistent spatial structure in SST under low winds as shown in Fig. 6 and discussed by Walsh et al. (1998) and also under high winds (Soloviev and Lukas 1996).

c. Shortwave and longwave radiation

Consistent differences in incoming shortwave and longwave radiation were discovered when comparing raw data from IC1 and IC2. After the IOP, shortwave and longwave sensors from a number of the platforms were assembled together on the roof of a building at WHOI; these comparisons reproduced the differences seen during COARE. As a result, many of the shortwave sensors were sent to the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Canberra, Australia, where they were intercompared. The Wecoma pyranometer was then recalibrated against a pyroheliometer by the Australian Bureau of Meteorology. Since its calibration factor was found to be identical to that provided by the manufacturer before COARE, this instrument was selected as the reference. Corrections to other shortwave radiometers range from 0% to 12% as indicated in Fig. 11, which shows the raw and corrected shortwave comparisons in IC1.

A similar technique was used to reconcile differences in the aircraft shortwave measurements, as described by Burns et al. (2000). Correction for the aircraft's attitude is necessary, using data from the inertial navigation system (INS), and decreased the measurements by 25%–30%. The comparison flights then revealed that the N308D (Electra) pyranometer overestimated by about 6%, so its data were reduced by this amount. The final estimate of data accuracy for aircraft shortwave irradiance was 3 ± 16 W m−2 and agreement with the surface platforms 3 ± 37 W m−2 (Burns et al. 2000). The quite different sampling methods between aircraft and fixed surface platforms makes shortwave comparison especially difficult unless the sky is completely clear. In the context of the 10 W m−2 goal therefore, the regular calibration of aircraft radiation instruments becomes particularly important.

Intercomparison of the incoming longwave radiometers (pyrgeometers) revealed a number of errors, and led to reexamination of the fundamental theory of the instruments. During IC1, discrepancies of 12 W m−2 during the night and up to 50 W m−2 during the day were discovered (Fig. 12a). Downwelling radiation in this region is dominated by the very high water vapor content in the atmospheric mixed layer, and varies little with either high cloud or diurnally. The fairly constant signal of the Moana Wave sensor is therefore considered the most reasonable. Its better performance was because that instrument alone recorded all temperature signals (thermopile output, base and dome temperatures) required to satisfy its theoretical response (Albrecht and Cox 1977). The Moana Wave instrument was therefore adopted as the reference, and all others were corrected for the nighttime bias and daytime overestimate due to radiative heating of the body and silicon dome of the sensor. These radiative heating effects were largely removed using a form of the algorithm developed by Alados-Arboledas et al. (1988). Figure 12b shows the comparison after all instruments were corrected, where the maximum instantaneous disagreement is now only 10 W m−2.

Subsequent estimates of the surface emissivity based on several radiation sensors aboard the RV Franklin seemed to indicate that the calibration constant for the Moana Wave pyrgeometer was incorrect, thus bringing into question the absolute values of all measurements referenced to it (the much-used IMET data, for example). In fact, reexamination of the pyrgeometer theory revealed an inconsistency in the original derivation (Fairall et al. 1998), which causes the instrument to underestimate downwelling longwave radiation by about 9 W m−2. This was confirmed by comparing the original Moana Wave pyrgeometer data with the radiative transfer model RRTM (Mlawer et al. 1997), using COARE atmospheric soundings as input, which indicated a 7 W m−2 underestimate. It was therefore decided to adopt Rapid Radiative Transfer Model (RRTM) as the downwelling longwave reference and to adjust all other measurements to it.

This work by the COARE flux group, reported in Bradley and Weller (1997), also impacted on the analysis of the aircraft pyrgeometer data. Measurements of global longwave radiation are not as seriously affected by aircraft attitude changes as are those of solar radiation, but Burns et al. (2000) discovered that some data had to be rejected when the pyrgeometer was out of thermal equilibrium, after rapid descent from high altitude to the surface for example, and devised objective criteria to detect this condition. They also found a need to correct errors in measurement of the instrument dome temperature, possibly caused by dynamic heating of the dome, which significantly affected the longwave value. As with the SST and shortwave measurements, the comparisons revealed a need for small (1%–2%) corrections to several of the aircraft pyrgeometers to achieve overall agreement of 2 ± 3 W m−2, which is within the accuracy specification of the instrument. After all corrections, agreement with surface platforms was 3 ± 6 W m−2. The various uncertainties in the performance of conventional pyrgeometers, highlighted by the extreme demand for accuracy in COARE, has led to the development of a more suitable pyrgeometer design (Payne and Anderson 1999).

d. Wind speed and direction

There are many reasons why accurate measurement of wind speed over the ocean is important. The ocean roughness, and thus the drag coefficient, increases with wind speed, so that ocean wind stress increases more rapidly than the square of the wind speed. Furthermore, the scalar fluxes calculated using a bulk flux algorithm are directly proportional to wind speed, and the wind stress is an important factor in determining the atmospheric stability, which in turn modulates exchange coefficients. Thus any error in wind speed will result in significant errors in the sensible and latent heat fluxes. In order to satisfy the 10 W m−2 “goal” for the net surface heat flux in COARE, Fairall et al. (1996b) estimated that wind speed accuracy to 0.2 m s−1 was needed. In Table 1 of Burns et al. (1999), investigators responsible for wind measurement on ships and moorings indicate that their data are within, or close to, this accuracy. However, in most cases this has been achieved through careful post facto analysis by the COARE Flux Group, in particular for the data from the two dedicated intercomparison days.

IC1 and IC2 were quite similar days, revealed most clearly in the wind speed records. Each took place in the aftermath of a stormy period with winds around 8 m s−1 steadily declining throughout the day, in IC1 becoming almost calm and in IC2 settling at around 4 m s−1. This provided a representative range of wind speed over which to compare wind observations on the participating ships and the IMET mooring. Initial comparison of the wind speed time series showed that all instruments followed the prevailing trend, with individual short-term differences due to gustiness and the separation of platforms. Longer-term differences became more obvious when a 1-h running mean was applied, as in Fig. 13a, with a spread across all platforms of at least 1 m s−1. This was mostly systematic, suggesting measurement bias, but it also included random differences not easily explained by platform separation. Variance analysis around an average time series gave a standard deviation over platforms and time of 0.60 and 0.46 m s−1 for IC1 and IC2, respectively.

Examination of the individual measurements revealed a need for corrections to almost all instruments, some quite subtle, such as the need to adjust wind speed from instrument level to the standard 10-m height. The anemometers on the Franklin and Moana Wave were corrected approximately for flow distortion by the ship, following wind tunnel tests on a model of the Franklin. A fundamental rather than instrumental problem surfaced in the way that different platforms reference the wind. From a moving ship, true ambient wind speed is obtained by combining the vectors of the ship speed over the ground and the relative wind as measured by the wind speed–direction sensors. The Franklin and Wecoma estimated ship speed from the acoustic speed log/gyro system; the Moana Wave computed it from GPS. The first method gives the wind relative to water at the effective depth of the acoustic log, while the second gives wind relative to the earth. Strictly speaking, the appropriate wind with which to compute air–sea exchange via bulk algorithms is that relative to the water surface, so that in the presence of significant currents the former method is preferable. During COARE, the Moana Wave and IMET data were able to be corrected with the vector current measured at 5-m depth on the mooring. After all corrections were applied, agreement between platforms was much improved as shown in Fig. 13b; the overall standard deviation was reduced to 0.41 and 0.24 m s−1 for the two intercomparison periods. The corrections were assumed to apply throughout the COARE deployment.

Two of the above uncertainties in wind speed measurement, flow distortion and current correction, warrant further discussion because, while we have acknowledged and tried to account for them in a crude way for COARE, they are generally disregarded. Yet they can be very significant, and have important consequences for our calculation of air–sea fluxes by bulk methods and for our more general understanding of air–sea interaction (Blanc 1986).

The wind tunnel flow distortion corrections referred to above were determined for the specific positions of anemometers on board the Franklin and Moana Wave, for wind directions straight ahead and at one or two angles to port and starboard. Over the bow, they showed deceleration of wind at the end of the Franklin's bow boom by 3%, and acceleration of 3% on the foremast and 5% on the main mast; fortuitously, the position of the sonic anemometer above the bow on the Moana Wave's instrument gantry proved to be at the transition between deceleration and acceleration, so no correction was applied. Yelland et al. (1998) have studied flow distortion in more detail, using computational fluid dynamics (CFD) software to model the wind flow around two U.K. research ships, validating their computations against the wind tunnel results of Thiebaux (1990) on two Canadian vessels. Their main concern was the effect of flow distortion on open-ocean neutral drag coefficients CD10N. Four anemometers mounted across the foremast platform of the RRS Charles Darwin initially differed by 20% in CD10N, but agreed to 5% or better when corrected for the computed distortion to wind speed. The CFD results showed that the instruments underestimated wind speed between 3.5% and 13.5% depending on position and blockage, and that the wind was displaced upward by at least 1 m, corresponding to flow tilt angles between 6° and 9°. CFD corrections on ships of different shape, the Darwin with its bluff profile and the more streamlined RRS Discovery, reduced a 40% difference between the two ships in estimates of CD10N to only 10%. The computations show that the impact of flow distortion on CD10N was both large and sensitive to the relative wind direction; elevation of the flow by only 1 m and deceleration by less than 1% act in the same sense to overestimate CD10N by about 6%. One important (and no doubt controversial) outcome of this work by Yelland et al. (1998) is that, when their extensive datasets on open-ocean drag coefficients are corrected for flow distortion, there is no evidence of any sea state or wave age dependence. Apparent sea state dependence reported previously may be explained by variations in wind flow distortion. Also, much of the scatter in CD10N diagrams could be caused by changes in the relative wind direction.

The question of vector addition of measured wind, ship speed, and ocean current to obtain true wind relative to the water surface also has an impact on the accurate measurement of bulk fluxes. In the first place, ship speed can be comparable with the wind speed in the tropical oceans, putting the same demand on the accuracy of the ship's log as on the wind sensor. During COARE the Franklin's log/gyro system was calibrated against other estimates of ship speed through the water, including GPS observations, but this is not common practice. Second, currents are usually measured from these platforms at some depth, 5 m in the case of IMET and even deeper for a ship's Doppler log. However, it is worth noting that under light wind conditions and strong upper-ocean stratification, such as are frequently encountered in the COARE region, there may exist strong shear in the upper few meters and indeed at the surface itself (Kudryavtsev and Soloviev 1990). Thus correcting with the current measured at even a few meters depth may be inadequate. In situations requiring the highest wind speed accuracy, deployment of a shallow current meter on a mooring may be necessary to obtain near-surface currents, to be combined with ship speed calculated from high-precision GPS. Alternatively, a deployment of a surface drifter or use of radar to measure the surface current could provide surface currents. Until these corrections to true wind speed for flow distortion and surface current are resolved, there will remain some uncertainty in flux determination by the bulk method, no matter how refined the bulk algorithms become in terms of their physics.

On the aircraft, there are several alternative sensors available for wind measurement and various ways of processing the data for the most accurate result. Burns et al. (1999) examined these for each aircraft, and concluded that horizontal wind speeds and directions did not require additional corrections beyond those performed by the respective data processing facilities. Taking data from what seemed to be the most consistent and reliable sensors, they quote the comparisons between aircraft as 0.1 ± 0.3 m s−1 and 2.0° ± 8.2° for wind speed and direction, respectively. For comparison with the surface platforms, all measurements were standardized to 10-m height by Burns et al. (1999) using the flux-profile routines available within the COARE bulk flux algorithm (Fairall et al. 1996b). The wind speed comparison was remarkably good, 0.0 ± 1.0 m s−1 with the ships and −0.2 ± 0.8 m s−1 with the moorings, while the direction bias was also small, of order 5° in each case. Considering the number of steps involved in the data processing for aircraft winds and projecting them to the surface, this is remarkable agreement.

e. Air temperature and humidity

Sensors protected by nonventilated, multiplate shields (Gill 1983) on the RV Moana Wave and the IMET buoy measured air temperatures that were too high during sunny, low-wind conditions. During the night of IC1, agreement with the Franklin's aspirated psychrometers was within 0.1°–0.2°C for air temperature, indicating that calibration factors were correct. During the day, however, the unaspirated buoy sensor read at least 1°C too high. Empirical algorithms were developed (Weller and Anderson 1996; Tsukamoto and Ishida 1995; Anderson and Baumgartner 1998) to minimize the error; with this correction, daytime agreement improved to 0.1°–0.5°C. Since conversion of specific humidity from the relative humidity measured by some sensors requires air temperature, these radiative heating errors carry over. Without corrections to air temperature, specific humidities across the three platforms disagreed at times by up to 1 g kg−1; with corrections, typical instantaneous agreement was 0.3–0.5 g kg−1.

Burns et al. (1999) carefully examined, and made empirical corrections to, all the aircraft temperature and humidity measurements. The comparisons revealed ambient temperature differences of up to 0.6°C between aircraft, but these were mostly constant biases and the correction reduced overall differences to within 0.1°C. Agreement with the surface platforms at standard 10-m height was generally within 0.2°–0.4°C, depending on the aircraft–surface pair being compared. For example, the large number of occasions when the Cessna flew very low and slowly over the Franklin led to good comparison statistics and to agreement in ambient temperature of −0.1 ± 0.15°C and humidity of 0.0 ± 0.1 g kg−1.

All the aircraft used chilled-mirror hygrometers to measure dewpoint temperature from which ambient specific humidity could be calculated. These are often regarded as reference instruments against which data from other humidity sensors may be verified, but the intercomparison work showed that these instruments could not always be relied upon. Burns et al. (1999) found that both dewpoint instruments on the N42RF were biased high, and the ship comparisons revealed problems with the Wecoma's dewpoint hygrometer system. Removal of constant biases reduced the aircraft–aircraft disagreements from about 0.8 to 0.2 g kg−1 and, again depending on the particular aircraft–surface pair, improved agreement there also. Humidity comparisons between the aircraft and the Wecoma and IMET are scattered, the former perhaps due to the dewpoint problem, and the latter because of solar heating of the sensor unit.

f. General comments

Detailed description of the performance of the sensors for the basic state variables, as revealed by the intercomparisons during COARE, is provided in the two papers by Burns et al. (1999, 2000). A few examples to illustrate how the improvements in accuracy that were incorporated in the final versions of the COARE datasets were achieved, through the planned comparisons in the field and subsequent studies, have been given above. They show that, without this collaborative work by the COARE flux group, the accuracy in the mean observations of these variables needed to meet the goal of 10 W m−2 for net flux into the ocean could not have been achieved. This conclusion, set against a background of the combined experience of the many COARE investigators and their technical staff in work on air–sea interaction is disturbing. Operating alone, investigators responsible for any one of the aircraft, ships, or moorings specially developed to deliver “high quality” flux data may have returned unaware of serious errors in the measurements.

One lesson to be learned from this is that frequent calibration of sensor systems is essential and, furthermore, that close scrutiny of calibration facilities and procedures may be called for. Another is that duplication of sensors or provision of measurement redundancy is not profligate, whether it be on ships, moorings, or aircraft. Burns et al. (2000) emphasize that the use of empirical corrections, through intercomparison, is not the preferred method to compensate for inaccurate measurements. This is true, and the COARE experience has already led to improvements in instrumentation and experimental procedures, many of which are cited in the above paragraphs (see also Fairall et al. 1999). However, the disparity between the laboratory and marine environments means that instruments will not always perform as expected, despite best care, and if more than one platform is involved in a measurement campaign, dedicated (and properly planned) intercomparison work should be integral with the experiment plan.

4. Development of the COARE bulk formula and intercomparison of the fluxes

Of equal importance to the success of the COARE interface effort was the development of formulas to improve bulk estimates of air–sea fluxes in the warm pool. The TOGA COARE bulk flux algorithm was developed early in the postexperiment analysis, by Fairall et al. (1996b), to provide a common code for use by the COARE research community. It was based on the model of Liu et al. (1979, hereafter LKB), to take account of the light wind, strongly convective conditions commonly found over tropical oceans, and depended on the simultaneous observations on the Moana Wave of direct (covariance) fluxes and the required meteorological quantities. Improvements to the accuracy of the observations as described in the previous section and revisions to the transfer coefficients and parameterizations in the bulk formula thus proceeded in parallel and iteratively.

Version 1.0 was released in November 1993 and included various modifications to the LKB code. Following Smith (1988) the momentum roughness length, zo, was specified as the sum of the Charnock (1955) formula and a smooth flow limit, with the Charnock constant (α = 0.011) evaluated from the Moana Wave direct flux measurements in COARE. Specific humidity at the air–sea interface was calculated from the saturated vapor pressure at the SST, reduced relative to the freshwater value by 2% to allow for average 34-psu salinity (Kraus and Businger 1994). The dimensionless profile functions were given a form that asymptotically approached the proper convective limit as wind speed goes to zero (Panofsky and Dutton 1984). In this “free convection” regime, these functions are expected to follow a (z/L)−1/3 dependence, where z/L is the dimensionless Monin–Obukhov stability parameter. Approaching neutral stability, the functions were blended to a standard Kansas form (Businger et al. 1971) and the Kansas forms were also used for stable conditions. Following Godfrey and Beljaars (1991), the wind speed in the bulk expression was augmented by a gustiness velocity proportional to the convective scaling velocity, W∗ (Deardorff 1970), with the proportionality constant (β = 1.2) adopted on the basis of the direct flux measurements. The so-called Webb correction to latent heat flux, which arises from the requirement that the net dry mass flux be zero (Webb et al. 1980), was also calculated in the algorithm.

The major modification for version 2.0 (August 1994) was the inclusion of optional models for the cool skin effect and the diurnal thermocline, to correct bulk water temperatures to SST. The cool skin model was based on Saunders (1967) with a modification to include the effects of buoyancy flux. The cool skin effect is typically about 0.3°C during the night. During the day the cool skin may be reduced or eliminated entirely by solar heating in the upper layer of the ocean (Soloviev and Schluessel 1994). Thus a warm layer model, a simplified scaling version of the Price et al. (1986) mixed layer model, was added to extrapolate bulk water temperature measurements made at some known depth to the surface. The depth of the warming is determined by a critical Richardson number and the profile of the solar energy absorption in the water (Paulson and Simpson 1981). The physics of both the cool skin and warm layer models are described by Fairall et al. (1996a). Calculation of fluxes of momentum (Caldwell and Elliott 1971) and sensible heat due to rainfall were included, with raindrops assumed to be close to the surface wet-bulb temperature (Gosnell et al. 1995; Anderson et al. 1998).

The next modifications to the algorithm were made in August 1995, when transfer coefficients were reduced by 6% to give better average agreement with covariance latent heat fluxes from several COARE ships. At the Woods Hole workshop, 9–11 October 1996 (Bradley and Weller 1997), it was agreed that no further development would be attempted to the community version of the COARE bulk flux algorithm, and that a version 2.5b bulk algorithm “package” would be made available, consisting of the FORTRAN source code and a test dataset. This was released at a meeting of the flux group at NCAR, 14–16 May 1997 (Bradley et al. 1997), and is now available online (at http://www.coaps.fsu.edu/COARE/flux_algor/). The formalism of the COARE version 2.5b algorithm is described in Fairall et al. (1996a). It has been used with success in subsequent field observations from ships and aircraft, both in equatorial and midlatitude regions; a list of publications in which the COARE algorithm has been used appears in Bradley et al. (1997), and there are more than 200 citations at this time. Its major limitation was that it had not been verified above about 12 m s−1 wind speed or for regions outside the Tropics. There were also features that could impede its implementation in numerical models, for example, a fixed 20-loop iteration around exchange coefficients, stability, and fluxes. In 1998 the authors released an interim version 2.6a (Bradley et al. 2000), which partially addressed these limitations, and they have since consolidated other recent analytical and observational developments, together with some new features, into a version 3.0. All versions, with documentation and the test datasets, are available online (at ftp://ftp.etl.noaa.gov/et7/users/cfairall/bulkalg/).

Version 3.0 is fully described by Fairall et al. (2003). The NOAA Environmental Technology Laboratory (ETL) has built on experience during the COARE cruises, to assemble a greatly expanded air–sea interaction database (Fairall et al. 2001) with over 7000 h of covariance flux measurements including 800 h in wind speeds exceeding 10 m s−1 and 2200 h outside the Tropics. These data indicated that the Charnock parameter increased at higher wind speeds and also showed that a simple analytic relationship could be used in place of the Liu et al. (1979) lookup tables to specify scalar roughness lengths. These two changes affect the momentum and scalar transfer coefficients directly. Both the convective and stable profile functions have been revised in light of recent publications. The latent heat flux has been reformulated in terms of mixing ratio instead of water vapor density, because this is the fundamentally conserved quantity and also because it eliminates the need for a Webb et al. (1980) correction. However, the small vertical Webb velocity is still calculated for use with trace gas eddy fluxes. The stability iteration has been reduced from 20 to 3 loops, using bulk Richardson number parameterization for an improved first guess (Grachev and Fairall 1997), which enhances its suitability for numerical models. Optional code has been added to account for the effects of surface gravity waves on the fluxes, using the wave age parameterization of Oost et al. (2002) or the model of Taylor and Yelland (2001), which parameterizes surface roughness in terms of the significant wave height and peak wavelength. This feature would allow the algorithm to be applied in coastal/shallow water areas, and is partly in response to requests from some users. It has not been evaluated by the authors, but has been included as an incentive for researchers who have wave measurements available to contribute to the study of wind–wave relationships. The COARE 3.0 algorithm is valid for wind speeds to about 20 m s−1, and for both tropical and higher-latitude regions.

The differences between fluxes and transfer coefficients computed with both versions 2.5b and 3.0 of the COARE algorithm, and an earlier widely used scheme (Large and Pond 1981, 1982, hereafter LP) are shown in Figs. 14 and 15. This is a 9-day period during COARE (19–27 December) selected for its wide range of wind speeds. Hourly basic measurements are from the IMET buoy as shown in Fig. 2b (Weller and Anderson 1996). Blanc (1985) describes the essential features of 10 algorithms developed between 1973 and 1982, as more validating data became available. The LP algorithm, in common with others including LKB and the COARE algorithms, incorporates the effects of atmospheric stability on wind, temperature, and humidity profiles in the surface layer using the dimensionless profile functions referred to above. Large and Pond based their transfer coefficients on about 1600 h of data obtained mainly using the dissipation method (e.g., Fairall and Larsen 1986), verified against a small amount of covariance data. Their drag coefficient is constant below a wind speed of 11 m s−1 then increases linearly; scalar transfer coefficients are also constant in the unstable regime. The algorithm was not claimed to be valid below a wind speed of 4 m s−1, but for this comparison we extrapolate it to 1 m s−1. We also take care to use identical values in the three algorithms for the various physical properties such as specific heat capacity.

In Fig. 14, the drag coefficients for both COARE algorithms follow from adoption of the Smith (1988) “smooth plus Charnock” laws, with the latter modified above 10 m s−1 wind speed in version 3.0. A central element of the LKB model is the determination of the heat transfer through the interfacial sublayers, and the form of velocity and scalar profiles within them. Matching these exponential profiles to the outer turbulent logarithmic profiles leads to relationships between the scalar roughness lengths (zot, zbq) and the momentum roughness length via the roughness Reynolds number Rr = (zou∗)/υ. LKB parameterize these relationships as power laws, presenting a table of the coefficients, which are used in COARE algorithms up to version COARE 2.5b. The corresponding neutral exchange coefficients for sensible and latent heat increase at very low wind speeds, and show a maximum where the profiles match. This is more pronounced on the very expanded scale of Fig. 14 than in the original LKB paper. Fairall et al. (1996b, Fig. 2b) show moisture transfer coefficients derived from the Moana Wave covariance latent heat flux measurements during COARE. They are reproduced in Fig. 14 and suggest a somewhat smoother transition from smooth flow through the profile matching region. This is confirmed by the large covariance flux database (Fairall et al. 2001), which was used to revise the exchange coefficients for COARE version 3.0.

Figure 15 illustrates the differences between fluxes calculated with the three bulk algorithms, referred to as COARE 2.5b. The wind speed is shown at the bottom. General correspondence with the exchange coefficients is obvious, although it should be borne in mind that other differences between the algorithms (e.g., different convective profile functions) will also affect the comparison. The only significant difference in stress between the two versions of the COARE algorithm appears when the variable Charnock constant in COARE 3.0 causes a sharp spike whenever the hourly wind speed exceeds 10 m s−1. With wind speeds often higher than the crossing point of the LP and COARE 2.5b drag coefficients (Fig. 14a), the former seriously underestimates stress during this period. On the other hand, LP frequently overestimates the total turbulent heat flux by at least 25 W m−2 relative to COARE 2.5b. Plotting absolute rather than percentage differences sets the heat fluxes in the context of the 10 W m−2 goal for COARE. Below wind speeds of 5 m s−1 and above 11 m s−1, latent heat flux is slightly increased with the revised COARE algorithm as we would expect from Figs. 14b and 14c. Between these wind speeds we expect lower fluxes; according to Fig. 15 the reduction averages about 10 W m−2. Sensible heat flux is generally increased in COARE 3.0, due to the fact that it uses identical Rr relations for zoq and zot whereas in LKB (and hence COARE 2.5b) they are slightly different.

5. Confirmation of the fluxes—Ocean and atmosphere heat and freshwater budgets

Comparisons of the fluxes have been made across the various platforms—ship, buoy, and aircraft. Initial differences between turbulent fluxes measured on the Moana Wave and on other platforms led to the revision of the algorithm to version 2.5, and subsequent issues were addressed in version 3.0. Table 4 illustrates good agreement in leg-averaged basic variables and fluxes measured on three platforms. During periods when spatial variability across the IFA was small, averaging across platforms brought agreement in the net heat flux to better than 10 W m−2. This results, in part, from the choice of a “best” sensor for a given variable and subsequent adjustment of other data as described above. Furthermore, all platforms computed bulk fluxes with the same algorithm, which had been tuned to a consensus of transfer coefficients derived from covariance flux measurements. Independent estimates were required to verify that during this process the air–sea fluxes had converged toward their true values. Such confirmation came from the results of budget studies over volumes of the ocean and atmosphere.

Ocean heat budgets were calculated at several platforms within the IFA, over periods within the IOP from a few weeks to 4 months. The upper-ocean heat budget was shown to be essentially one-dimensional, sea surface and upper-ocean temperature variability at the IMET mooring being well represented by the one-dimensional Price–Weller–Pinkel model (PWP; Price et al. 1986) forced by the observed heat, freshwater, and momentum fluxes over the duration of the IOP (Anderson et al. 1996). However, such simple ocean budget studies also pointed to transient departures from the one-dimensional balance and the need to examine the way in which penetrating solar energy heats the upper ocean. The comparison of observed and modeled 2-m temperature in Fig. 16 shows that much of the high-frequency variability (diurnal to several day) and most of the lower-frequency variability is reproduced in the model. But there are periods, at the beginning of the record and during leg 2-O, when the temperatures do not track one another. The ocean mixed layer depth was so shallow that the mean radiative heat flux emerging from its base was of similar magnitude to the mean net heat flux at the sea surface. Siegel et al. (1995) made direct measurements of the solar spectrum at various depths using a spectroradiometer lowered from the Vickers. They found that approximately 20 W m−2 penetrates beyond 30 m and also that a phytoplankton bloom decreased the radiation at that depth by 6 W m−2, thus increasing the heating of the upper 30 m by 0.11°C month−1. PWP was used with a fixed, double-exponential parameterization of solar absorption and did not simulate the impact of the bloom. Nor did it include advection.

Table 5a is based on the work of Feng et al. (2000) and summarizes the contributions to the upper-ocean heat budget, the surface net heat flux inferred from the ocean budget, and that observed on the Wecoma and the IMET during legs 1-O, 2-O, and 3-O. Table 5b presents the corresponding summary for salinity. Closure of upper-ocean heat budgets was made easier because, on average, horizontal temperature gradients were small so that, even in the presence of large zonal currents, the advective heat flux was also relatively small. Leg 2-O had the largest advective contribution, which was associated with a Yoshida jet, inertial motion, and a submesoscale eddy that passed through the IFA (Feng et al. 2001). At the beginning of leg 3-O, the thermocline depth quickly dropped from above 50 m to below 50 m, which is mostly an adiabatic process. This process would bring in a vertical advection in the ocean budgets from a fixed depth to sea surface, but may not significantly affect the ocean budget following the mixed layer depth. With the additional sources of temperature variability included in Feng et al.'s (2000) ocean budget, the difference between the observed surface heat flux and that inferred from the ocean budget was within 6 W m−2 for each leg. Smyth et al. (1996) also examined the heat budget in the IFA, using data obtained from the Wecoma on leg 2-O and concluded that they could close the one-dimensional heat budget within 10 W m−2. These two ocean budget studies verify that the flux group intercomparison strategy, subsequent correction procedures, and bulk flux algorithm development have enabled leg averages of the surface heat forcing to be determined within 5–10 W m−2 accuracy.

The comparison of model and observed near-surface salinities in Fig. 16 suggests that the upper-ocean salinity budget is more complex. The model freshens in leg 2-O in contrast to the observations and has a dramatic decrease in salinity in early January not seen in the data. The rainfall time series used by Anderson et al. (1996) is based largely on ORG data from the Moana Wave, Wecoma, and the TAO buoy at 2°S. Satellite rainfall maps show significant spatial gradients across the IFA and one possible failing of this one-dimensional calculation is its lack of horizontal advection of freshwater. Feng et al. (2000) show that the advective terms are very important (Table 5b) and illustrate a dramatic improvement in the agreement with observation when three-dimensional rather than one-dimensional budgets are calculated (their Fig. 11). They estimated rain rates from their upper-ocean salinity budgets to be within approximately 20% of the rain-rate observations, falling within the range of instrumental measurements.

As pointed out in section 3, resolution of the various precipitation estimates has been particularly troublesome due to large spatial and temporal variability, and with uncertainties in both in situ instrument and radar performance. Our analysis leading to Fig. 8 revealed various instrumental failings, including the discovery that the Wecoma ORG1 was inoperative for a few days at the beginning of each of the three periods specified by Feng et al. (2000). This gap in the ORG1 data was not known by Feng et al. (2000), but the Wecoma ORG numbers in Table 5b take account of such missing observation periods in calculating cruise-average rainfall. The inferred precipitation (P) can be combined with the number of days specified to obtain the total rainfall for each leg (35, 280, and 82 mm respectively). The ORG rainfall measurements for the identical periods, with the small amount of missing data filled with the average from the two siphon gauges, are 33, 338, and 65 mm (from ORG1; 77 mm from the bow ORG2) for the three legs. The differences are +6%, −15%, and +26% (+6%), confirming the assessment of Feng et al. (2000). Combining the three legs the overall difference is only 8%. Agreement of the freshwater budget closure to such a margin is very satisfactory. The analysis involved has also exposed the complexity of the situation, the magnitude and importance of all the uncertainties involved, and provides a benchmark for similar studies in the future.

Atmospheric heat and moisture budget studies by Lin and Johnson (1996) and Johnson and Ciesielski (2000) were central to our ability to reconcile disagreements between in situ rainfall observations. During the process, significant humidity biases were found in the sondes and correction procedures developed (Zipser and Johnson 1998; Lucas and Zipser 2000; Wang et al. 2002). The resulting precipitation maps of Johnson and Ciesielski (2000) showed clearly how sensitive leg-averaged and IOP-averaged precipitation estimates could be to both the location of the observing platform and the time interval used in the averaging. They provided independent estimates of rainfall as listed in Table 3, and reproduced exactly the east–west gradient in rainfall observed by the in situ ORGs.

The success of the heat and freshwater budget closure during the COARE IOP indicates that such joint observational campaigns in the upper ocean and atmospheric boundary layer enable independent estimates of the air–sea fluxes of heat and moisture. A key factor in comparing point time series with areal estimates is the averaging period. This is particularly critical for the freshwater budget, when significant spatial gradients in rainfall may exist. The agreement achieved in COARE among the oceanic, atmospheric, and direct determinations of the net heat and freshwater fluxes vindicates the space–time sampling strategy of the Wecoma repeat surveys. These and the associated oceanic measurements identified and quantified the processes most important to the determination of SST in the warm pool and of the net air–sea heat flux.

On approximately biweekly time scales and under three very different forcing regimes, with the advective and turbulent flux terms accounted for, the heat budget in the surface layer of the warm pool during the COARE IOP balances the air–sea heat flux to within 10 W m−2 and the freshwater to within 20%. This remarkable degree of agreement between direct and indirect flux estimates is a testimonial to the high quality of the basic observations, and to the efforts of the flux group in adding value and precision to the COARE air–sea flux dataset.

6. Assessment—Spatial variability and comparison with model and satellite products

Meeting the objectives of the COARE air–sea flux component, listed in the introduction, proved to be a significant challenge for the flux group. To maintain focus and define collaborations, a timeline for the various objectives was established early in the process and updated as work progressed. Figure 17 illustrates the concept and shows how the work of the flux group continued many years beyond the end of the field program. This period was punctuated by workshops as required, and achievements were marked by steady publication in the literature. Though considerable success was realized in many areas, we must now also acknowledge particular challenges that emerged along the way and could not be resolved.

The initial objective for the flux group was to assemble a high quality in situ dataset of heat, moisture, and momentum fluxes in the warm pool region. This was achieved and, on weekly and longer time scales, met the required accuracy goals. New, and subsequently updated, bulk formulas were developed, which have become widely used beyond COARE. This effort, and the work done to obtain ocean and atmospheric budget-based estimates of the fluxes, resulted in improved understanding of the physics and thermodynamics of the interfacial exchange processes, including those that create the diurnal warm layer and the cool skin. The fundamental lesson of the need for careful calibration was relearned. Empirical corrections were developed. For a number of the sensors, such as the pyrgeometers, the analysis and study led to a better understanding of sensor performance. The most comprehensive analysis to date of the viability of in situ rainfall measurements was conducted and gave us new confidence in our ability to rate the performance of different sensors. The rainfall time series, together with extensive salinity measurements in the upper ocean, allowed COARE investigators to show how the freshwater component of the air–sea buoyancy flux was critical to warm-layer maintenance.

Good temporal resolution of surface meteorology and the air–sea fluxes was achieved at a number of sites, most importantly at the IMET buoy and the Moana Wave near the center of the Wecoma survey pattern. However, as the flux group work proceeded, the goal of producing spatial maps became ever more important, especially as work turned toward addressing the science objective of understanding the impact of systems with various spatial scales. Beyond the intercomparison of collocated sensors, mapping added the necessity of integrating observational systems that had greatly different spatial sampling characteristics (e.g., ships, radars, aircraft), which, as we have seen, was a particular problem in the case of rainfall estimates.

When planning COARE, it was not anticipated that leg-averaged surface meteorological and air–sea flux fields would show strong trends across the IFA that would vary greatly between the three legs. It was important to know about the time and space scales of the structures that characterized the IFA and forced the warm pool; but in most cases, the spatial variability only became evident well into the analysis of COARE data, for example the gradients in precipitation found by Johnson and Ciesielksi (2000). It is most likely that gradients in the surface fluxes were also present, but mapping of the fluxes with spatial resolution that would resolve these gradients, and could be produced at a regular time interval, was not possible from the in situ observations alone. Because of their application in the computation of wind stress and the magnitude of the surface currents relative to the wind, knowledge of surface currents across the IFA would be needed in computing the fluxes. The flux group looked to the oceanographic participants in COARE for maps of surface currents, but they found the spatial variability present in the IFA too great to allow maps of the surface currents to be produced from the available observations. The flux group also looked to the meteorological participants in COARE for spatial coverage. Interesting spatial patterns of surface mean square slope and SST were observed from the aircraft under low wind conditions (Walsh et al. 1998) but the aircraft boundary layer missions produced spatial maps of air–sea fluxes on only two occasions, one of which was outside the IFA (Geldmeier and Barnes 1997).

Two other sources of spatial fields were available, the gridded fields produced by numerical models and the fields captured by satellite remote sensing, and have been used in efforts to map the fluxes across the warm pool. Two types of atmospheric model products were examined. The first were the traditional numerical weather prediction products. The European Centre for Medium-Range Weather Forecasts (ECMWF) model analysis fields provide gridded values of surface meteorological parameters while the model forecast fields provide surface fluxes. The ECMWF TOGA COARE special dataset was generated with the operational model run on the operational initialized analysis fields. The only differences in the special runs were that a lower resolution of T106 was used and the forecast fields were for 3 and 6 h. When the surface analysis and 6-h forecasts were averaged over the legs of the COARE ships, differences were found between the model and observations. The model winds were often 0.5–1 m s−1 lower, 0.4 m s−1 lower in the mean over the IOP, and were directed 13°–22° to the left of the observed winds during the three legs. The model and the observed shortwave radiation differed considerably, by 30–60 W m−2. Table 6 compares the means of the IMET data and the ECMWF model during the December westerly wind burst, during a period of low winds in January, and during short-lived, squall-like wind events in late January and early February. The ECMWF model overestimated the net heat loss by 17% during the westerly wind bursts, indicated a net heat gain as opposed to the observed loss during the squalls, and underestimated the neat heat gain by 59% during the low wind period. During the westerly wind burst the model latent heat loss was 64 W m−2 greater than that observed, but this error was largely offset by the model net shortwave radiation, which was 57 W m−2 too large. Similar overestimation by the model of the mean shortwave radiation (89 W m−2 too high) was seen during the squalls, but in this case was not compensated by error in the latent heat flux. Similar results came from comparisons between time series from the IFA and NCEP model products.

Because the coarse spatial and temporal resolution of the numerical weather prediction models is potentially a major source of difficulty in replicating the observed surface meteorology and air–sea fluxes, it was of interest to determine if the higher-resolution, cloud-resolving models (CRM) could do better. Fortunately, the Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) had independently selected COARE as the focus for case studies comparing CRMs, single-column models (SCMs), and the COARE observations (Moncrieff et al. 1997). Redelsperger et al. (2000a), for example, examined how well CRMs simulated a squall line observed during COARE. The CRMs captured the mesoscale variability associated with the deep convection that the NWP models missed. The resulting enhanced surface fluxes were larger than the simple gustiness parameterization of Godfrey and Beljaars (1991) predicted, and much closer to the observed fluxes (Redelsperger et al. 2000b). Jabouille et al. (1996) suggested that the mesoscale flux enhancements should be parameterized in terms of GCM precipitation activity, and Redelsperger et al. (2000b) have developed such a parameterization that improves CRM surface flux comparisons with COARE observations. When such improved parameterizations are eventually included in atmospheric and coupled GCMs, it is expected that the improvements will accumulate on larger scales as well.

Satellite remote sensing offered the other means to map the surface meteorological and air–sea flux fields. Work by Clayson et al. (1996) on the COARE IOP suggested that satellite retrievals of fluxes with useful accuracy may be possible at time scales of 1–3 h and space scales of 30–100 km. Chou et al. (1997) and Schultz et al. (1997) developed satellite-based fields of the sensible and latent heat fluxes. Curry et al. (1999) document production of such a dataset for the COARE IOP with 3-h and 50-km time and space resolution. Progress has resulted from improved physical models for determining flux components from the quantities sensed by the satellite, the use of data from more than one sensor to determine a given quantity, models of the atmosphere and upper ocean to determine parametric relationships, and the high quality in situ validation data provided during COARE. Curry et al. (1999) compared their satellite-based time series from the grid point closest to the Moana Wave with the fluxes measured on the ship. The 3-hourly values had the following (ship minus satellite) biases: −26 W m−2 for net shortwave, −8 W m−2 for net longwave, 19 W m−2 for latent heat flux, −4 W m−2 for sensible heat flux, −0.014 N m−2 for momentum flux, and 0.06 mm h−1 for precipitation. The respective means for the satellite-based fluxes at the Moana Wave were 209 W m−2, −45 W m−2, −127 W m−2, −6 W m−2, 0.070 N m−2, and 0.39 mm h−1.

With most of the in situ flux-measuring platforms located near the center of the IFA, the best way to map the flux fields has come from using NWP model fields, satellite-based fields, or combinations of these. Curry et al.'s (1999) map of the average net surface heat flux for the COARE IOP shows 50–60 W m−2 at the western end of the IFA compared to 40–50 W m−2 in the eastern half of the IFA. Even so, the combined space and time variability of the surface meteorological and air–sea flux fields over the IFA provided perhaps the greatest challenge to COARE. For example, one aim was to understand the space–time variability of the ocean mixed layer in response to atmospheric forcing over the IFA. To achieve this, the large diurnal signal in heating, in precipitation, and in mesoscale enhancement of the fluxes indicated the need for maps of the surface fluxes at high space (∼10 km) and time (∼3 h) resolution. As discussed above, preparation of surface flux fields requires that the surface currents as well as the surface meteorological and surface radiation fields be at that same resolution, and such fields could not be prepared for COARE.

7. Impacts of the TOGA COARE air–sea interface effort

Demonstration of the ability to make accurate observations of surface meteorology and air–sea fluxes of heat, freshwater, and momentum in TOGA COARE has had impacts on modeling and on how we will proceed in the future to make maps of the air–sea fluxes. These are not unrelated. Numerical weather prediction models produce gridded fields of surface meteorology and fluxes that are often used to develop maps of the surface fluxes. Establishing definitively the accuracy of the in situ surface meteorological quantities and air–sea fluxes in COARE has indicated a means to assess the accuracy of atmospheric models.

In October 1995 a WCRP workshop was held at ECMWF to discuss air–sea flux fields for forcing ocean models and the validation of atmospheric general circulation models (WCRP 1996). Several COARE flux investigators participated, and the issues associated with subgrid-scale variability in the NWP models were discussed. It is anticipated that the analysis of that variability in COARE will help to improve parameterization of the fluxes on the grid scale of the atmospheric general circulation models. Higher-resolution model runs may be performed in the future, and both NCEP and ECMWF have expressed interest in collaborating with COARE investigators in making use of the COARE data, investigating the use of the COARE bulk flux algorithm in the models, and developing a better understanding of the surface fluxes in COARE.

The large-scale models do not at present have the space and time resolution required, for example, to force ocean models for studies of local response to diurnal heating, or to an isolated convective system. However, mesoscale atmospheric models are able to do so, producing surface flux fields with gridding down to 1 km. Cloud-resolving models coupled to ocean mixed layer models may provide a basis for improved parameterizations of convection, cloud microphysics, radiation transfer, and the atmospheric boundary layer. Such improved mesoscale models could then improve the analyses of surface fluxes. In the near future research will focus on simulations of case studies with cloud-resolving models and other mesoscale models and on 4D data assimilation using mesoscale models. Priority will be placed on the development of model parameterizations that correctly simulate physical processes. With these high-resolution models, it will be possible to study the mesoscale enhancement of monthly averaged fluxes, the effect of deep convection on fluxes, and the three-dimensionality of convection and the associated downdrafts.

The well-documented accuracy and temporal resolution embodied in the air–sea fluxes obtained during TOGA COARE enables modeling studies to substitute these for previous forcing, with its known large uncertainties. It also forms the basis for other model studies to develop forcing fields for the warm pool that are tuned to agree with the COARE observations in the IFA. Some studies have targeted specific air–sea interaction processes in the warm pool. For example, Anderson et al. (1996) examined the ocean response to the combination of rain, winds, and heating that marked the COARE IOP. Other studies have used the data from COARE as a basis for extending analyses in both space and time. Shinoda and Hendon (1998), for example, use the IMET flux time series from COARE as a control when developing gridded flux products for the tropical western Pacific and Indian Oceans. They looked at both the warm pool response during COARE and the intraseasonal variability of the upper ocean of the broader region between 1986 and 1993.

Investigators are increasingly using the COARE bulk flux algorithm. This is partly because of recognition that it was based on a very carefully evaluated dataset, but also because it is continuously updated as new data and relevant results become available. In the original version, exchange coefficients were tuned to the limited amount of direct latent heat flux data obtained during COARE, that is, specific to a tropical environment characterized by light winds and strong convection. Subsequently, the NOAA/ETL group has compiled an order of magnitude more direct flux data, including measurements at higher latitudes and in winds up to 20 m s−1 (Fairall et al. 2001). This, together with improved internal physics, has enabled revision of the exchange coefficients and validation of the algorithm over a much broader range of conditions (Bradley et al. 2000; Fairall et al. 2003).

The successful combination of carefully calibrated, unattended surface meteorological instrumentation on a buoy, and of the COARE bulk flux algorithm, has had a major impact on strategies to observe and improve global fields of air–sea fluxes. From experience during COARE, we know that a well-instrumented surface mooring can be deployed for months and provide time series of surface meteorology accurate enough to be used with the COARE bulk formulas to provide mean net heat flux with error of less than 10 W m−2. Since COARE, such moorings have been deployed to improve determination of air–sea flux fields in a particular region, as in the Arabian Sea in 1994–95 (Weller et al. 1998) where large biases were found in NWP model air–sea fluxes. Such moorings are now called surface flux reference sites (SFRSs). When their data are withheld rather than used in NWP model initialization, the SFRSs provide independent data to examine the performance of the models. At present several SFRSs exist, and in a pilot project known as Surface Flux Analysis (SURFA), their data are being shared with the Atmospheric Model Intercomparison Project (AMIP) for comparison with the surface meteorology and air–sea fluxes output by some of the NWP models. In addition, data from IMET and TAO moorings deployed in the Atlantic, and from IMET-equipped research ships, are being used to develop daily, 1° × 1° gridded flux fields in the Atlantic Ocean (Sun et al. 2003).

The buoy data also provide the means to calibrate and validate both the fields of primary variables produced by remote sensing methods and the derived air–sea fluxes. COARE data and the bulk flux algorithm are included in the parallel datasets from satellite and in situ sources currently being assembled by the SeaFlux from Space project (Curry et al. 2004). This is a GEWEX initiative to validate satellite-derived air–sea flux fields. Shinoda et al. (1998) and others have developed gridded flux fields in the tropical western Pacific and Indian Oceans, validated through comparison with the IMET surface flux time series collected during COARE. It is planned to deploy and maintain similar surface moorings on a long-term basis, so as to continuously provide the high quality time series needed to anchor the flux fields.

The WCRP program on Climate Variability (CLIVAR) has developed a strategy for improved global air–sea flux fields, using SFRSs to anchor the fluxes at perhaps 10 locations in each ocean basin. In addition, spatial variability in the surface meteorological and air–sea flux fields will be obtained from volunteer observing ships (VOSs; i.e., merchant ships equipped with the same sensors as those used on the SFRSs), which make regular, repeat, cross-basin transits. COARE highlighted issues that require particular attention in very low winds: radiative heating of sensors, accurate measurements of surface-referenced wind velocity, and uncertainties in the behavior of bulk transfer coefficients. Winds above 10 m s−1 were rare in COARE, but the configuration of the bulk flux algorithm has readily enabled its extension and applicability to much higher winds as more observations became available.

The TOGA COARE campaign and subsequent work by the flux group has highlighted the importance of continuing air–sea interaction studies and the benefits of closer collaboration between those working on either side of the air–sea interface. The WCRP/SCOR Working Group on Air–Sea Fluxes (WGASF) concluded their evaluation of the state of the art with a report (WCRP 2000) and a workshop (WCRP 2001). Both forums affirmed the value of and need for the following:

  • high quality in situ observations from long-term moorings (surface flux reference sites) and from ships;
  • continuing intercomparison and evaluation of flux products from different sources;
  • ongoing interaction between the NWP centers and these sources of high quality surface observations both to improve and validate the models;
  • field work on the ocean and atmospheric boundary layers, especially in regimes (low wind and high wind) not yet well sampled; and
  • continued support for compilation of flux datasets and for efforts to identify and correct biases.

COARE provided a paradigm for many of these recommendations, by demonstrating how good in situ fluxes could be, the value of accurate in situ time series, and the contributions made by in situ datasets when using model and remotely sensed fields to develop maps. More recently a workshop on high-resolution marine meteorology, sponsored by NOAA/Office of Global Programs (OGP) and held at the Florida State University, considered ways to ensure that future observations from ships and moorings achieve the quality demanded of these applications. The report of this meeting (Smith et al. 2003) recommended a suite of practical measures, which were strongly influenced by the work and experiences of the COARE flux group.

8. Summary

For the TOGA COARE program, a primary goal was to obtain high quality measurements of the air–sea fluxes of heat, freshwater, and momentum in the warm pool region. This was successfully accomplished by a strategy that included predeployment instrument calibrations; dedicated instrument comparisons across platforms during the fieldwork; direct measurement of the turbulent fluxes and improvement of the bulk algorithm for computing fluxes from mean measurements, postdeployment calibrations, and comparisons; and the attention of a dedicated group of participants that persisted for more than 5 yr beyond the end of the field campaign. Emphasis following the fieldwork was on assuring the accuracy of the mean and turbulence measurements, on developing the COARE bulk algorithm, and on the use of the air–sea flux data at specific platforms within the IFA. Considerable progress has been made toward the air–sea interface goals of providing a high quality flux dataset, understanding, the physics and thermodynamics of the interfacial exchange processes in low wind speeds, improving the formulas used to estimate net heat flux in the warm pool, and determining the magnitude of short time-scale variability of the fluxes. The efforts of the COARE air–sea interface working group and the principal investigators involved were sustained over a number of years beyond the field experiment (Fig. 17), with the result that there was significant progress toward these goals. For temporal averages over weeks to months the goal of reducing the uncertainty to 10 W m−2 or less was met. Independent confirmation of the accuracy of the surface fluxes was provided by budget calculations in the upper ocean and in the atmosphere. The COARE bulk flux algorithm has continued to evolve to accommodate conditions commonly found away from the Tropics, particularly very high winds and stable atmospheric boundary layers.

The availability of accurate observations of surface fluxes in the warm pool has allowed the performance of numerical models and flux estimates from remote sensing to be evaluated during COARE. More generally, the results of the observational campaign in COARE show that when accurate in situ observations are available, they can be used to identify errors in model and remotely sensed surface meteorological and air–sea flux fields. This finding now guides strategies to develop global air–sea flux fields.

Acknowledgments

This paper summarizes the work by members of the Flux Working Group of TOGA COARE. The authors have acted as raporteurs for this enthusiastic and energetic group, which includes in addition to the authors: Steve Anderson, Gary Barnes, Sean Burns, Carol Ann Clayson, Peter Coppin, Meghan Cronin, Judy Curry, Lynn DeWitt, Chris Fairall, Carl Friehe, Alan Grant, Jorg Hacker, Denise Hagan, Phil Hignett, Hiroshi Ishida, Dick Johnson, Djamal Khelif, Paul Kucera, David Legler, Peggy LeMone, Guosheng Liu, Tetsuo Nakazawa, Carter Ohlmann, Clayton Paulson, David Rogers, Steve Rutledge, Yolande Serra, Dave Short, Xilong Song, Osamu Tsukamoto, Ed Walsh, Gary Wick, and Alastair Williams. Members of the Ocean Working Group and the Mesoscale Atmospheric Working Group have participated in meetings and contributed to the effort, including Paul Ciesielski, Peter Hacker, Dick Johnson, Mitch Moncrieff, Serge Planton, Jean-Luc Redelsperger, Libe Washburn, Ed Zipser, and others. The TOGA COARE International Project Office (Director Richard Chinman) provided essential computer and logistical assistance for the Flux Working Group and is gratefully acknowledged. Sharon DeCarlo at the University of Hawaii carried out analyses of the precipitation data. The National Oceanic and Atmospheric Administration through the Office of Global Programs, the ocean and atmospheric sciences divisions of the National Science Foundation, the Office of Naval Research, and the National Aeronautics and Space Administration contributed support for elements of the flux measurements made during COARE and the analyses. The authors gratefully acknowledge the support of NSF Grant ATM 95-25844 (RAW) and NSF Grants OCE-9216891 and OCE-9525986 (RL) in preparing this manuscript.

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