Uncertainties in sea surface turbulent flux algorithms and data sets

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. C10, 3141, doi:10.1029/2001JC000992, 2002

Uncertainties in sea surface turbulent flux algorithms and data sets Michael A. Brunke and Xubin Zeng Institute of Atmospheric Physics, The University of Arizona, Tucson, Arizona, USA

Steven Anderson Horizon Marine, Marion, Massachusetts, USA Received 23 May 2001; revised 9 January 2002; accepted 18 January 2002; published 4 October 2002.

[1] An intercomparison of eight bulk sea surface turbulent flux algorithms used in data

set generation as well as weather and climate prediction is performed for the tropical Pacific and midlatitude Atlantic. The results show some significant differences in fluxes due to differences in the way the algorithms consider wave spectrum, convective gustiness, and salinity as well as the way the algorithms parameterize roughness lengths and turbulent exchange coefficients. For instance, for sea surface temperature between 27.75
C and 28.25
C, the maximum differences in monthly latent heat flux and wind stress among algorithms over the tropical Pacific are about 23 W m
2 (or 16% relative to the algorithm-averaged flux) and 0.013 N m
2 (or 19% relative to the algorithm-averaged value) respectively. Evaluation of these algorithms using 270 hourly samples of observed turbulent flux data over the midlatitude Pacific shows that algorithms are largely consistent with observations. However, some algorithms show significant deviations from observations under certain conditions (e.g., weak wind conditions). Insights from the above intercomparison are then used to evaluate ocean surface turbulent fluxes from two global data sets, one is derived from satellite remote sensing while the other is a reanalysis. Over two buoy sites in the eastern and western tropical Pacific, the mean heat flux differences between the two data sets are primarily caused by differences in bulk variables (e.g., wind speed) rather than by differences in bulk algorithms. However, bulk algorithm differences could contribute up to 17 W m
2 to the long-term averaged latent heat flux over the tropical Pacific if different algorithms were used. This suggests that both bulk algorithms and the deviation of environmental variables need to be further improved in order to produce ocean surface turbulent fluxes with an accuracy of 10 W INDEX TERMS: 3339 Meteorology and Atmospheric Dynamics: Ocean/atmosphere interactions m
2. (0312, 4504); 3394 Meteorology and Atmospheric Dynamics: Instruments and techniques; KEYWORDS: sea surface turbulent fluxes, bulk aerodynamic algorithms, hourly fluxes, monthly fluxes, global flux data sets Citation: Brunke, M. A., X. Zeng, and S. Anderson, Uncertainties in sea surface turbulent flux algorithms and data sets, J. Geophys. Res., 107(C10), 3141, doi:10.1029/2001JC000992, 2002.

1. Introduction [2] In recent years, various bulk aerodynamic algorithms have been developed to calculate ocean surface turbulent fluxes from near-surface temperature, humidity, and wind speed as well as sea surface temperature. These algorithms were developed by different groups based upon data from various oceanic regimes. Several studies [Zeng et al., 1998; Chang and Grossman, 1999] have shown that fluxes calculated by different algorithms can vary significantly under very weak or strong wind conditions. These uncertainties have been shown to be important for weather forecasting and climate studies [Webster and Lukas, 1992; Miller et al., 1992; Wang et al., 1996].

Copyright 2002 by the American Geophysical Union. 0148-0227/02/2001JC000992$09.00

[3] Previously, regional and global data sets of sea surface turbulent fluxes have been derived based upon surface observations from buoys and ships. Recently, such data sets have also been developed using satellite data like the Hamburg Ocean Atmosphere Parameters from Satellite Data (HOAPS) (http://sop.dkrz.de/HOAPS), the Goddard Satellite-Based Surface Turbulent Fluxes (GSSTF) [Chou et al., 2001], and that by Curry et al. [1999]. These data sets are recognized to be useful in fully understanding the transfer of heat and freshwater between the atmosphere and ocean, in evaluating model surface fluxes, and in improving weather forecasting and climate models (e.g., http://paos.colorado.edu/curryja/ocean/home.html). To understand the differences among these data sets and to aid in the further development of global sea surface turbulent fluxes, uncertainties produced by differences in parameterization schemes need to be addressed. In particular, these differences include how light and strong wind

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Table 1. A Summary of Differences in the Eight Algorithms Used in This Studya Consideration of wave spectrum Gravity waves Capillary waves Roughness length Convective gustiness Effect of salinity on sea surface saturated humidity Transfer coefficients a

UA

COARE

Smith

BVW

CFC

CCM3

ECMWF

GEOS

Y N See Table 2. Y Y See text.

Y N

Y N

Y Y

Y Y

Y N

Y N

Y N

Y Y

N Y

Y Y

N Y

N Y

Y N

N N

Y, yes; N, no.

speeds, the stable regime, and mesoscale gustiness are handled. [4] The primary intent of this study is to evaluate and understand bulk algorithm uncertainties. The intercomparison includes five of the six algorithms used in the Zeng et al. [1998] study: version 2.5 of the algorithm developed out of the Coupled Ocean-Atmosphere Response Experiment (COARE) [Fairall et al., 1996]; the UA algorithm [Zeng et al., 1998] (hereafter referred to as UA); and those used in the National Center for Atmospheric Research (NCAR) Community Climate Model version 3 (CCM3), the European Center for Medium-Range Weather Forecasting (ECMWF) model, and version 1 of the Goddard Space Flight Center’s Earth Observing System reanalysis (GEOS-1) (hereafter referred to as GEOS). The algorithm used in the medium-range forecast (MRF) model of the National Center for Environmental Prediction (NCEP), which was included in the 1998 study, is eliminated from this study. NCEP has since adopted the UA algorithm. In addition, three other algorithms commonly used for research and data set production have been included: the Smith [1988] algorithm (hereafter referred to as Smith) currently in use to produce the HOAPS data set, the Bourassa et al. [1999] algorithm (hereafter referred to as BVW), and the Clayson et al. [1996] algorithm (hereafter referred to as CFC). Other algorithms such as those using convective transport theory [Stull, 1994; Greischar and Stull, 1999] were not included in this study, since they were designed to be used under a small number of conditions (e.g., calm to light winds and free convection for convective transport theory). Another purpose here is to assess the differences between global flux data sets due to uncertainties in the algorithms and bulk variables. To this end, a comparison of two data sets, the HOAPS data set derived from satellite remote sensing and the GEOS-1 reanalysis, is compared to their respective algorithms (Smith and GEOS respectively) forced by buoy observations. [5] Section 2 gives a general description of bulk aerodynamic algorithms and explains the variations in algorithms that result in the differences between calculated fluxes. Section 3 describes the observational data, while section 4 compares and evaluates algorithms using buoy observations from the tropical Pacific and midlatitudes. Section 5 presents a comparison of direct turbulent fluxes observed from a midlatitude platform with fluxes calculated from the algorithms. The comparison of the two data sets is presented in section 6. Finally, conclusions are given in section 7.

2. Bulk Aerodynamic Algorithms [6] Bulk aerodynamic algorithms derive the turbulent fluxes, i.e., wind stress t, latent heat flux LH, and sensible heat flux SH, using the mean values of the bulk variables,

near-surface wind speed U, air temperature Ta, and air specific humidity qa as well as the sea surface temperature (SST) Ts and specific humidity qs: t ¼ rCD ðS
Us ÞðU
Us Þ;

ð1Þ

LH ¼
rLv CE ðS
Us Þðqa
qs Þ;

ð2Þ

SH ¼
rCp CH ðS
Us Þðqa
qs Þ;

ð3Þ

where r is the density of air, Lv is the latent heat of vaporization, Cp is the heat capacity of air, S is the nearsurface wind speed with convective gustiness included if it is considered, Us is the surface current which is neglected in most algorithms, and CD, CE, and CH are the exchange coefficients for momentum, mositure, and heat respectively. [7] While all algorithms calculate the fluxes using equations (1) – (3), they differ in various ways due to the range of oceanic regimes that each algorithm was originally based on and to differences in the relevant physical parameterizations that each algorithm considers. Table 1 highlights the five physical parameterizations that contribute significantly to differences in calculated heat and momentum fluxes: surface wave spectrums, roughness length formulation, consideration of convective gustiness, consideration of the salinity effect on ocean surface saturated humidity, and turbulent exchange coefficient formulation. [8] Regarding wave spectrums, for instance, of the eight algorithms considered here BVW and CFC explicitly include the effects of both capillary and gravity waves, while the other six algorithms only include the effects of gravity waves. These differences in wave parameterizations lead to variations in how the surface roughness length for momentum, zo, is defined (see Table 2). UA, COARE, Smith, and ECMWF compute zo as the sum of the roughness lengths for gravity waves based upon Charnock’s [1955] formulation and that of a smooth surface. BVW and CFC have slightly different formulations for zo due to their explicit inclusion of capillary waves. CFC separates the formulation of zo into a smooth regime with zo = 0.11v/ u* and a rough regime where zo is computed as the sum of the roughness lengths for capillary and gravity waves. BVW’s formulation adds the ‘‘weighted’’ roughness length for smooth flow to the weighted root-mean square sum of the roughness lengths for capillary and gravity waves. These ‘‘weights’’ (the b0 coefficients in Table 2) are 0 or 1 depending on whether the roughness element is deemed to contribute to the total roughness. This formulation allows for the use of wave direction and state information that are not available in the data sets that we used. To be consistent with the other algorithms, we assumed that the wind and

BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

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Table 2. Equations for Roughness Lengths of the Eight Algorithms in This Studya Algorithm UA

Equations for the Roughness Lengths 2

0:013u* 0:11n þ zo ¼ u g

* zo zo 1=4 ln ¼ ln ¼ 2:67Re*
2:57 zot zoq

COARE

0:011u2* 0:11n þ u* g

zo ¼ zot u

Smith

n

* ¼ a1 Reb1 ; zoq u* ¼ a2 Reb2 where a1, a2, b1, b2 are coefficients that depend upon the range of Re * * n *

0:011u2* 0:11n þ u* g

zo ¼

CHN ¼

k2     ¼ 1:0  10
3 ln zzo ln zzot

CE ¼ 1:2CH BVW

20

12 0   12 31=2    ˆ u e u     7 i * * 0:0488s C @ 0 0:48 i i 6 B 0 0:11n 0 A 5 A þ bg zoi ¼ bn   þ 4@bc bci    wai g rw u*i u*i eˆ i  u*i  where bv0 , bc0 , and bg0 are coefficients that are 0 or 1 depending on whether the surface is contributing to the total roughness, bci is a weight for the capillary wave roughness length, u*i is the friction velocity vector in the direction of i, eˆ i is the unit vector in the direction of i, wai is the wave age in the direction of i, and i = 1 or 2 where 1 represents the direction of wave propagation and 2 represents the direction perpendicular to that of 1.

zot ¼ CFC

zo ¼

0:40n 0:62n ; zoq ¼ u* u*

2 0:019s 0:48n u* 0:11n þ for u* wa > cpmin ; zo ¼ for u* wa < cpmin uz* rw wa g u*

where cpmin is the minimum phase speed for waves to exist.


zot ¼ zo exp k 5



zoq ¼ zo exp k 5


1 Prt Sto



1 Sct Dao



where Prt is the turbulent Prandtl number, Sto is the interfacial Stanton number, Sct is the turbulent Schmidt number, and Dao is the interfacial Dalton number. ECMWF

CCM3

zo ¼

0:018u2* 1:65  10
6 þ u* g

zot ¼

6  10
6 9:3  10
6 ; zoq ¼ u* u*

k2 0:0027 CDN ¼  þ 0:000142 þ 0:0000764U10N 2 ¼ U10N 10 ln zo where U10N is the 10-m neutral wind speed. zot = 2.2  10
9 m for z > 0, zot = 4.9  10
5 m for z < 0 zoq = 9.5  10
5 m

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BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

Table 2. (continued) Algorithm GEOS

Equations for the Roughness Lengths

zo ¼ uA1 þ A2 þ A3 u* þ A4 u2* þ A5 u3* , where A1, A2, A3, A4, A5 are constant coefficients. *

  1=2 zo zo ¼ ln ¼ 0:72 Re*
0:135 ln zot zoq

a

Here zo, zot, and zoq are the roughness lengths for momentum, heat, and moisture respectively, CDN and CHN are the neutral exchange coefficients for momentum and heat respectively at 10 m, CH and CE are the exchange coefficients for heat and moisture respectively, u* is friction velocity, g is gravitational acceleration, n is the kinematic viscosity of air, rw is the density of water, s is the surface tension of water, Re* is the roughness Reynolds number, wa is wave age, and z = z/L, where z is the height above the surface and L is the Monin-Obukhov length.

waves were moving always in the same direction and were in local equilibrium. CCM3 derives zo from an empirical formulation of the neutral drag coefficient at a height of 10 m, and GEOS calculates zo empirically based on an interpolation of the moderate to high wind speed data from Large and Pond [1981] and weak wind speed data from Kondo [1975]. [9] The computation of the roughness lengths for heat and moisture, zot and zoq, respectively, also varies among the algorithms (see Table 2). While zot and zoq are assumed to be the same in three algorithms (UA, CCM3, and GEOS), they are different in the other five algorithms. In CCM3, zot and zoq are constant based on the data from Large and Pond [1982], while in CFC they are functions of zo, the turbulent Prandtl and Schmidt numbers, and the interfacial Stanton and Dalton numbers as prescribed by surface renewal theory. [10] At low wind speeds, previous studies have found that heat fluxes do not approach zero. Bradley et al. [1991], for

instance, observed latent heat flux to be 25 W m
2 under calm wind conditions. This is due to the fact that at low wind speeds atmospheric boundary layer large eddies become important in the transfer of heat and moisture under unstable conditions. Some algorithms take this into account by adding a convective gustiness parameter bw* such that the surface wind U¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 u2 þ v2 þ bw* ;

ð4Þ

where u and v are the zonal and meridional components of the wind, respectively, b is an empirical coefficient, and w* is the convective velocity scale, also known as the Deardorff velocity, defined as w* ¼


1=3 g
qv u* zi ; qv *

Figure 1. The sea surface temperature (Ts) of three buoys of the Tropical Atmosphere-Ocean (TAO) array (5
S, 110
W; 0
N, 155
W; 0
N, 156
E) (dots) and of the Coastal Mixing and Optics (CMO) array (40
2903200N, 70
3001000W) (plus signs) plotted as a function of the air-surface temperature difference (
T = Ta
Ts).

ð5Þ

BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

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Figure 2. Hourly (a) latent heat (LH) fluxes, (b) sensible heat (SH) fluxes, and (c) wind stresses averaged over the TAO array plus the two Pan-American Climate Study (PACS)/Woods Hole Oceanographic Institution (WHOI) buoys plotted as a function of the air-surface potential temperature difference
q in 0.5 K bins. Each line represents the calculated fluxes of each of the eight algorithms used: UA (solid line), Smith (solid line with crosses), COARE (dotted line), BVW (dash-triple dotted line), CFC (solid line with plus signs), CCM3 (short dashed line), ECMWF (dash-dot line), and GEOS (long dashed line). (d– f ) present the relative differences of each of the other seven algorithms (same lines) from UA for the fluxes shown in (a – c) respectively. Note that potentially very large relative differences when fluxes are close to zero are not shown in this and other similar figures.

where g is the acceleration due to gravity, qv is the virtual potential temperature of the air, qv* is the temperature scaling parameter, u* is friction velocity, and zi is the height of the convective boundary layer. Of the eight algorithms used in this intercomparison (see Table 1), UA, COARE, BVW, and ECMWF include this convective gustiness parameterization. CCM3 and GEOS limit the wind speeds to no less than 1 m s
1. Smith imposes a limit of 0.1 m s
1, but the HOAPS group only uses the algorithm for wind speeds greater than or equal to 1 m s
1 (J. Schulz, personal communication, 2001). In contrast, CFC does not limit wind speeds and as a result may not converge occasionally. [11] The algorithms also differ in their consideration of the effect of salinity on the surface saturated humidity. The ratio of surface saturated specific humidity over saline water

qs to that over freshwater qsat at the same sea surface temperature Ts [Kraus and Businger, 1994] can be approximated by qs ðs; Ts Þ

1
0:527s; qsat ðTs Þ

ð6Þ

where s is the salinity. Considering the average salinity value of 35 parts per thousand, the saturated specific humidity over ocean water is depressed by 2%. Among the eight algorithms, ECMWF and GEOS do not consider this effect, while the other six schemes do (see Table 1). [12] The final difference among these algorithms is variations in the formulation of the turbulent exchange coefficients for momentum, heat, and moisture, i.e., CD, CH, and CE respectively. Although all formulations are based upon Monin-Obukhov similarity theory, they choose

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Figure 3. The number of hourly observations for the TAO array and the PACS/WHOI buoys made in each of the 0.5 m s
1 wind speed (U) bins between 0.5 and 15 m s
1, 0.5
C sea surface temperature (Ts) bins between 18
and 32
C, and 0.5 K
q bins from
6 to +3 K. slightly different coefficients and have different treatments under very unstable or stable conditions. A comparison of the neutral exchange coefficients at a height of 10 m from the previous five algorithms (UA, COARE, CCM3, ECMWF, and GEOS) was performed by Zeng et al. [1998]. Of the three algorithms added to this study, Smith sets CHN to a constant (1  10
3). BVW and CFC have consistently larger CDN values than most of the other algorithms with the highest difference being at low wind speeds. For instance, BVW’s CDN is 84% relative to the average of UA, Smith, COARE, CCM3, and GEOS at U10N = 3 m s
1. Also, at moderate to high wind speeds, CFC produces the lowest CEN: 1.03  10
3 for U10N 10 m s
1 compared to the average CEN of the other seven algorithms, 1.17  10
3.

3. Observational Data [13] Four different observational data sets are used in our comparison of these eight algorithms: those of the Tropical Atmosphere-Ocean (TAO) buoy array, two Pan-American Climate Study (PACS) buoys, the Coastal Mixing and Optics (CMO) buoy array, and the San Clemente Ocean Probing Experiment (SCOPE). The 69 buoys of TAO are located in the tropical Pacific from 137
E to 95
W and from 9
N to 8
S. Measurements for wind speed are taken at 4 m above the surface and for relative humidity and air temperature at 3 m above the surface [Hayes et al., 1991]. The nearly 2 million hourly samples used were standard quality data from May 1990 to January 1999 as used by Zeng et al. [1998]. [14] Also in the tropical Pacific are the two buoys operated by Woods Hole Oceanographic Institution for

PACS (hereafter referred to as PACS/WHOI) at 10
N and 3
S along 125
W (referred to as PACS/WHOI-N and PACS/WHOI-S respectively) [Anderson et al., 2000]. The buoys were separated into two deployments: one from April to December 1997 and the other from December 1997 to September 1998. Two different meteorological instrumentation packages were used. For the time series of about 24,000 hourly samples used here, during the first deployment, wind speed and air temperature were measured at 3.25 m and 2 m above the surface respectively at both locations, while relative humidity was measured at 2.50 and 2.65 m at the north and south locations, respectively. During the second deployment, wind speed was measured at 3.30 and 3.25 m for the north and south locations respectively, relative humidity at 2.55 and 2.65 m for north and south respectively, and air temperature at 2.15 m at both. [15] In addition to the tropical data, we have used data from a midlatitude site, the CMO array, also operated by Woods Hole. The array of four buoys was operational between August 1996 and June 1997 centered at 40
2903200N, 70
3001000W on the continental shelf 100 km south of Cape Cod, Massachusetts [Galbraith et al., 1999]. For the meteorological time series of over 30,000 hourly samples used, only measurements from the central site with an ocean depth of 70 m were considered at which wind speed, relative humidity, and air temperature were measured at 3.3, 2.7, and 2.6 m above the surface, respectively. The intercomparison has been extended to include this midlatitude site in order to investigate how the eight algorithms perform in a different regime in parameter space. Figure 1 shows surface temperature versus the

BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS Table 3. Mean Wind Stresses (t), Latent Heat Flux (LH), and Sensible Heat Flux (SH) Produced by Each of the Eight Algorithms as Well as the Eight-Algorithm Average for the TAO Array and the PACS/WHOI Buoys Algorithm

t, N m
2

LH, W m
2

SH, W m
2

UA Smith BVW CFC COARE CCM3 ECMWF GEOS Average

0.062 0.059 0.069 0.070 0.065 0.061 0.071 0.062 0.065

104.0 104.4 106.1 102.7 103.4 103.7 118.9 102.9 105.8

5.1 4.6 4.5 5.2 4.9 5.0 4.9 4.6 4.8

air-surface temperature difference (
T = Ta
Ts) for all samples from CMO and samples from three TAO buoys (5
S, 110
W; 0
N, 155
W; and 0
N, 156
E). The tropical temperatures are greater than 20
C while the midlatitude temperatures are mostly less than 20
C. Also, the stability of the tropical samples is mainly unstable (
T < 0) or weakly stable while some of the midlatitude samples are quite stable. Therefore the CMO site allows us to explore how these algorithms would perform in varying climate regimes. Note that though roughness length parameterizations were developed for open ocean conditions in some of the algorithms, the same bulk algorithms are used for both open ocean and coastal waters in practice in global modeling and data set development. Therefore a comparison of these algorithms using data from CMO would still be useful despite the buoy’s location in shallow water.

5-7

[16] Previously, in the work of Zeng et al. [1998], five of the eight algorithms (UA, COARE, CCM3, ECMWF, and GEOS) have been evaluated using the TOGA COARE flux data over the tropical western Pacific with wind speed ranging from 1 to 10 m s
1. It was found that CCM3 overestimates SH and LH under weak wind conditions, and ECMWF overestimates LH for wind speeds greater than 6 m s
1. To further evaluate the bulk algorithms over a different climate regime, here we use the measurements made by R/P FLIP located at 33
N, 118
W off the coast of Southern California from 17 September 1993 to 28 September 1993 during SCOPE (provided by C. W. Fairall, personal communication, 2000). The 305 h of measurements of wind speed, air temperature, and specific humidity were gathered at 10 m above the surface. Fluxes were measured using the inertial-dissipation and covariance methods. As in the work of Zeng et al. [1998], the LH and SH fluxes determined by the covariance method and the wind stresses by the inertial-dissipation method were used as originally suggested by Fairall et al. [1996]. Potentially corrupted data at winds 60
to 100
relative to the bow and during contamination by sea salt or sun glint were eliminated. In total, 242 points were used.

4. Algorithm Intercomparison 4.1. Comparison of Hourly Fluxes [17] In this section, the fluxes computed from hourly observations from the eight algorithms are compared. Figure 2 shows the hourly heat fluxes and wind stresses binned into 0.5 K bins of the air-surface potential temperature difference
q based on TAO and PACS/WHOI data.

Figure 4. Hourly (a) LH fluxes, (b) SH fluxes, and (c) wind stresses averaged for TAO, PACS/WHOI, and CMO plotted as a function of Ts in 0.5
C bins.

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Figure 5. Monthly averages of hourly (a) LH flux, (b) SH flux, and (c) wind stress for the TAO array as a function of monthly wind speed U in 0.5 m s
1 bins. (d – f ) present the relative differences of each of the other seven algorithms (same lines) from UA for the fluxes shown in (a – c) respectively.

Positive and negative
q values represent stable and unstable atmospheric stratifications respectively. The latent heat flux (LH) values for ECMWF are systematically higher than those from the other seven algorithms under all stability conditions, while CFC and GEOS give the lowest LH values under unstable conditions. The maximum LH difference under unstable conditions among algorithms is 30 W m
2 (Figure 2a) and the relative differences from UA of the other seven algorithms are within +15% and
10% (Figure 2d). Other studies have made similar comparisons of relative differences between algorithms. Blanc [1985], for example, compared the relative differences of each of 10 schemes to all others and found typical relative differences for LH of 15– 31%. Under stable conditions, five algorithms (UA, COARE, BVW, CCM3, and Smith) give similar LH values while the other three give significantly higher results. For sensible heat flux (SH) (Figures 2b and 2e) Smith gives the lowest values under unstable conditions while CCM3 gives the highest values under stable conditions. Figures 2c and 2f shows that the wind stress differences are nearly independent of
q and the relative differences from UA

of the other seven algorithms are typically within +20% and
10%. [18] Hourly flux differences among algorithms have also been evaluated as a function of wind speed. The results are consistent with those of Zeng et al. [1998]; the algorithms show remarkable differences in the computed fluxes and wind stresses for high and low wind speeds. For instance, for wind speeds between 10.75 and 11.25 m s
1 the maximum difference between algorithms is 57.42 W m
2 for LH, 2.6 W m
2 for SH, and 0.065 N m
2 for wind stress compared to the algorithm-averaged values: 204.6, 16.1, and 0.25 N m
2 respectively. Similarly, large differences between algorithms are also found at high and low Ts in agreement with Zeng et al. [1998]. For Ts between 30.25
C and 30.75
C, LH ranges from 108.5 W m
2 (BVW) to 87.5 W m
2 (CFC). Also, as reported by Zeng et al. [1998], the maximum difference in algorithm LH fluxes and wind stresses is quite large at moderate Ts. This is due to the significant overestimation by ECMWF for LH flux and by BVW, CFC, and ECMWF for wind stress. For example, at Ts = 27
C ± 0.25
C, ECMWF’s LH flux is over 17 W m
2 higher than the average of the other seven

BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

5-9

Figure 6. Same as in Figure 5 except as a function of monthly Ts in 0.5
C bins.

algorithms (108.1 W m
2 ), while CFC, BVW, and ECMWF produce wind stresses that are higher than the average of the other five algorithms. [19] Figure 3 shows the number of observations made for all of the TAO array plus the two PACS/WHOI buoys. The greatest numbers of observations are made around U = 6.25 m s
1, Ts = 28.75
C, and
q =
0.5 K. Wind speeds greater than 11.75 m s
1, Ts greater than 31.25
C and less than 19.25
C, and
q greater than +1.25 K and less than
4.25 K occur infrequently. Thus results at high Ts, high U, or very stable
q would not contribute much to the mean LH, SH, and stresses over the whole array. Additionally, some of the stable
q cases (
q > 0 K) may also be erroneously caused by radiative heating of naturally ventilated sensors as is used in TAO [Anderson and Baumgartner, 1998]. Table 3 presents these mean wind stresses and heat fluxes for TAO and PACS/WHOI. The maximum difference for LH and SH is 17.6 and 0.72 W m
2 (or 16 and 14% relative to the algorithm-averaged fluxes) respectively, while for wind stress it is 0.014 N m
2 (or 22% relative to the algorithm-averaged wind stress). Some of the large differences in the binned data contribute to the differences in Table 3. For example, the highest LH mean (120.3 W m
2) from ECMWF is contributed primarily by its consistently

higher LH fluxes for neutral and unstable
q, moderate Ts, and, to a lesser degree, high wind speed due to a smaller number of observations. Higher wind stresses at low and moderate wind speeds for BVW and CFC are reflected in their higher means in Table 3. The highest SH mean is from CFC (5.2 W m
2) rather than from CCM3 as we might expect from the
q-binned data in Figure 2, because of the large number of unstable cases where CFC had higher SH fluxes (Figure 2). [20] As is the case for the TAO and PACS/WHOI buoys, large hourly flux differences among algorithms also exist in the CMO data for high and low wind speeds. CCM3 consistently has the highest SH fluxes over most wind speeds and sea surface temperatures at CMO. Under very stable conditions, CCM3 still produces a much larger SH than the other algorithms. For instance, for
q = 2 ± 0.25 K, CCM3 calculates a mean SH of
36.2 W m
2 in contrast to the algorithm average of
55.8 W m
2. [21] Figure 4 shows the hourly heat fluxes and wind stresses from the TAO, PACS/WHOI, and CMO buoys binned together across the entire spectrum of Ts in 0.5
C bins. LH is considerably different between algorithms for Ts > 25
C (Figure 4a), and SH is appreciably different for Ts > 30
C (Figure 4b). For Ts < 17
C (characteristic of

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BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

Figure 7. Same as in Figure 5 except as a function of monthly
q in 0.5 K bins.

the midlatitude ocean at CMO), CCM3 produces significantly higher SH fluxes than the other algorithms. Wind stresses differ considerably among algorithms for Ts < 13
C and for 22
C < Ts < 28
C (Figure 4c). These results are consistent with earlier discussions in this subsection. 4.2. Comparison of Monthly Fluxes [22] To explore the climatological implications of the hourly flux differences previously discussed, Figures 5 –7 show the monthly averages of hourly LH, SH, and wind stress versus the monthly averages of hourly wind speed, Ts, and
q over the TAO array. The monthly LH and wind stress divergences among algorithms increase with wind speed (Figures 5a and 5c), but the relative differences from UA (Figures 5d and 5f) are nearly constant except under weak and strong wind conditions. ECMWF gives a consistently higher LH than other schemes, while BVW gives the highest wind stress under weak wind conditions. The monthly LH flux and wind stress are widely scattered even at moderate Ts (Figures 6a and 6c) as was the case for the hourly data (e.g., Figure 4 of Zeng et al. [1998]). However, because the monthly SH is quite small (Figures 5b and 6b), the maximum difference among algorithms is within 2 W m
2. The maximum divergence in wind stress is nearly independent of the

stability (Figures 7c and 7f), and the LH divergence is also nearly independent of stability for
q < 0 (Figures 7a and 7d). Under stable conditions, CCM3 produces significantly higher SH fluxes than other algorithms (Figures 7b and 7e) as was the case for the hourly data (Figures 2b and 2e). [23] Figures 8 – 10 show the time series of monthly fluxes and wind stresses using the PACS/WHOI and CMO data. The observed net shortwave and net longwave fluxes are shown, because they enable us to compute the net surface heat flux Fnet, which is one of the driving forces of oceanic processes. Note that energy fluxes into the ocean are defined as positive in these figures. The minimum Fnet during February 1998 at WHOI-N (Figure 8f ) and during July 1997 at WHOI-S (Figure 9f ) are primarily caused by the maximum of LH in magnitude (Figures 8a and 9a). In contrast to these two tropical sites, the midlatitude CMO site has a larger annual range of monthly Fnet (Figure 10f ). The negative Fnet in winter at CMO is caused by both the increase of LH (in magnitude) (Figure 10a) and the decrease of net shortwave radiation (Figure 10d). The average maximum differences for LH flux, SH flux, and Fnet are 26.4, 2.1, and 28.0 W m
2 respectively at WHOI-N while the corresponding values at WHOI-S are slightly smaller. These flux differences are much larger than 10 W m
2, the

BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

5 - 11

Figure 8. Monthly averages of (a) LH flux, (b) SH flux, (c) wind stress, (d) observed net shortwave (SW) radiation, (e) observed net longwave (LW) radiation, and (f ) net flux using the buoy data at PACS/ WHOI-N (10
N, 125
W) from May 1997 to September 1998. accuracy required for climate research, and are principally due to the flux differences between ECMWF and CFC. ECMWF consistently has the highest LH in magnitude (Figures 8a and 9a), and hence the lowest net heat flux into the ocean (Figures 8f and 9f ) at both WHOI sites. In contrast, CFC produces noticeably lower LH and SH fluxes in magnitude from November 1997 to June 1998 at WHOIN (Figures 8a and 8b) and from April to December 1997 at WHOI-S (Figures 9a and 9b). These are translated to the highest net heat fluxes during these periods (Figures 8f and 9f ). At CMO the scatter for LH and Fnet (Figures 10a and 10f ) is tighter than at both PACS/WHOI sites with mean maximum differences among algorithms of 7.6 and 10.8 W m
2, respectively. However, the mean maximum difference for SH flux is higher (6.3 W m
2) (Figure 10b) due to consistently higher SH in magnitude from CCM3 especially from February 1997 onward when the air temperature Ta was warmer than Ts, a situation of stable stratification. For wind stress the average maximum difference over each site is 20% relative to the algorithm average wind stress for the whole period (Figures 8c, 9c, and 10c). CFC and BVW usually produce the highest wind stress while CCM3 typically gives the lowest stress.

[24] Figures 5 – 10 use monthly means of hourly stresses and heat fluxes, a method referred to as the sampling method [Esbensen and Reynolds, 1981]. In contrast, the classical method uses monthly means of wind speed, air and surface temperature, and relative humidity in calculating monthly fluxes from the algorithms. This method has been previously used to produce global climatological data sets [e.g., Hsiung, 1986] and satellite-derived data sets (e.g., HOAPS and Liu [1988]). Table 4 compares monthly fluxes from these two methods. For TAO and PACS/ WHOI the small biases in LH and SH for all algorithms except for CCM3, BVW, and GEOS in LH suggest that the classical method can produce reasonable monthly heat fluxes in the tropics on average as discussed by Esbensen and Reynolds [1981], Zhang [1995], and Esbensen and McPhaden [1996]. The root-mean-square deviation (RMSD) of the monthly LH difference using the two methods is small, generally less than 2.5% relative to the mean flux (e.g., Table 3), while the corresponding value is 8 to 10% for SH. At CMO the monthly biases remain low for LH flux for most algorithms (except Smith, CFC, and COARE), while they are significantly higher for SH flux. Monthly wind stress from the sampling method is on

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BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

Figure 9. Same as in Figure 8 except for the buoy data at PACS/WHOI-S (3
S, 125
W) from April 1997 to September 1998.

average always greater than that from the classical method for TAO and PACS/WHOI. At CMO the underestimation by the classical method is even greater. The relatively larger bias in wind stress than in LH or SH is consistent with previous studies [Esbensen and Reynolds, 1981; Zhang, 1995]. This is likely due to small timescale variations in the wind speed within each month [Khalsa and Businger, 1977]. 4.3. Interpretation of Results [25] The results show that ocean surface heat and momentum fluxes differ appreciably among algorithms even for monthly averaged fluxes. These differences are entirely caused by the different treatments of various processes in each of the bulk algorithms as discussed in section 2. For instance, BVW and CFC consistently have higher hourly and monthly wind stresses than most of the other algorithms (e.g., Figures 2c, 5c, 6c, and 7c) likely due to their explicit inclusion of capillary waves. Another factor that could increase wind stress is the choice for the Charnock constant in the formulation of the roughness length for momentum (zo). For instance, ECMWF’s Charnock constant is higher (0.018) than those used by some of the other algorithms

(0.013 or 0.011) (see Table 2). This causes the wind stress from ECMWF to be consistently higher than that from most other algorithms (except BVW and CFC) for most conditions at TAO and PACS/WHOI. [26] ECMWF also has higher LH fluxes (e.g., Figures 2a, 5a, 6a, and 7a), which are primarily caused by the higher Charnock constant as well as the exclusion of the effect of salinity on the sea surface saturated humidity (see Table 1). GEOS-1 also excludes the effect of salinity (see Table 1), and its LH fluxes, which are normally close to or below those of most other algorithms also increase dramatically at high wind speeds and stable conditions. [27] Several of the significant differences in calculated heat fluxes can be attributed to differences in the formulation of the roughness lengths for momentum, heat, and moisture, zo, zot, and zoq, respectively. For instance, CFC’s formulation of zoq based on surface renewal theory (see Table 2) contributes to its lower LH fluxes than most other algorithms at unstable conditions (
q < 0 K) (Figures 2a and 7a), while its zo with the inclusion of capillary waves is responsible for its higher LH fluxes than most other algorithms for stable conditions (Figures 2a and 7a). At stable conditions, CCM3’s SH fluxes were significantly

BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

5 - 13

Figure 10. Same as in Figure 8 except for the CMO buoy data (40
2903200N, 70
3001000W) from August 1996 to June 1997. higher than those of the other algorithms (Figures 2b and 7b). This was also consistently the case at CMO (e.g., Figure 10b). This is due to the algorithm’s use of a considerably smaller zot for stable conditions than that for unstable conditions. Similarly, Smith’s formulation for zot based upon a constant CHN of 1  10
3 is the primary cause for its lowest SH fluxes for unstable conditions (Figures 2b and 7b).

5. Evaluation Using Platform Data [28] In this section, direct turbulent measurements of airsea fluxes are compared with fluxes computed by the eight algorithms. Table 5 presents the biases, RMSDs, and correlations of the algorithms to the observed fluxes from SCOPE. The algorithm fluxes are correlated very well with the observed fluxes, which is similar to what Zeng et al. [1998] found for the COARE data. The highest correlation coefficients are for wind stresses, while the lowest correlation is in SH flux. For LH flux most algorithms produce means above the observed value. Three of the eight algorithms (Smith, BVW, and GEOS) generate SH flux means lower than observation. For wind stress most of the algorithms (except BVW and CFC) have means lower than

observation. The maximum RMSD is 0.01 N m
2 for wind stress (for CFC), 11.7 W m
2 for LH (for Smith), and 5 W m
2 for SH (for COARE). [29] To evaluate the statistical significance of the biases in Table 5, the Student’s t test [Wilks, 1995] is used. For wind stress and SH flux, no biases are shown to be statistically significant at the 95% level. For LH fluxes, however, biases from all algorithms except CFC and GEOS are significant at the 95% level. To evaluate the statistical significance of the correlations in Table 5, the Fisher transform [Wilks, 1995] is used in calculating a Z statistic. Using this method, all correlations in Table 5 are found to be significant at the 99% level. [30] In addition to the overall statistics in Table 5, algorithm biases can be further evaluated in terms of the environmental conditions. Figures 11 – 13 show the results of the algorithms compared with the observed covariance LH and SH fluxes and inertial-dissipation stresses from SCOPE (solid line with triangles) as a function of wind speed (Figure 11), Ts (Figure 12), and
q (Figure 13) along with the relative differences of each of the algorithms from observed. Figures 11c and 11f show that the positive bias in wind stress from CFC in Table 5 is caused by the overestimate of wind stress for U  5 m s
1, while

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BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

Table 4. Comparison of the Monthly Average Wind Stress (t), Latent Heat Flux (LH), and Sensible Heat Flux (SH) Derived From Hourly Data for TAO With PACS/WHOI and CMO (i.e., the Sampling Method) With the Monthly t, LH, and SH Computed Using Monthly Bulk Variables in the Algorithms (i.e., the Classical Method)a UA t LH SH

t LH SH

Smith

Bias, 10
3 N m
2 RMSD, 10
3 N m
2 Bias, W m
2 RMSD, W m
2 Bias, W m
2 RMSD, W m
2

7.90 3.85 0.51 1.61
0.15 0.44

8.41 3.74
0.41 5.30
0.13 1.30

Bias, 10
3 N m
2 RMSD, 10
3 N m
2 Bias, W m
2 RMSD, W m
2 Bias, W m
2 RMSD, W m
2

34.3 11.3
0.88 4.08 2.05 2.51

30.3 9.9 3.01 3.55 1.70 1.92

BVW

CFC

TAO, PACS/WHOI 9.31 8.45 4.79 4.21 2.06 0.08 1.84 2.26
0.04
0.05 0.39 0.72 CMO 38.6 13.3 0.05 3.34 1.97 2.50

54.7 22.4 3.16 4.15 5.75 2.13

COARE

CCM3

ECMWF

GEOS

7.50 3.78
1.76 2.52
0.28 0.43

8.26 3.47 4.74 1.94 0.16 0.46

9.07 4.65 0.66 1.64
0.13 0.42

4.17 3.23
3.59 2.06
0.36 0.40

33.3 10.6
1.97 3.90 1.60 1.71

32.5 11.4 0.73 3.65 4.91 3.89

37.4 12.5
0.32 3.49 1.97 2.52

28.9 11.2
0.45 3.23 2.03 2.67

a Shown are the biases, i.e., the mean differences in wind stresses and heat fluxes between the sampling and classical methods, and the root-mean square deviation (RMSD) of the results from the two methods.

the negative biases in wind stress from most of the other algorithms are primarily caused by the underestimate of wind stress for wind speeds less than 6 m s
1. The latter could be due to turbulent distortion produced by the platform that would affect the bulk aerodynamic measurements. The highest LH values are given by CCM3 for U < 3 m s
1 and by Smith for 3 m s
1 < U < 9 m s
1 (Figures 11a and 11d), which contribute to their larger LH biases compared to the other algorithms in Table 5. The highest SH values are given by CCM3 for U < 4 m s
1 and by UA for U > 4 m s
1 (Figures 11b and 11e), which lead to their larger SH biases in Table 5. The overestimate of LH and SH under weak wind conditions by CCM3 agrees with results using the TOGA COARE flux data of Zeng et al. [1998]. Figure 12 shows that the divergence of fluxes among the algorithms is nearly independent of the surface temperature. CCM3 overall gives the highest LH and SH fluxes (Figures 12a, 12b, 12d, and 12e) while Smith gives the lowest wind stress (Figures 12c and 12f ). CCM3 gives consistently high LH values in Figures 13a and 13d, contributing to its highest LH bias among algorithms in Table 5. The divergence of SH fluxes among algorithms increases with the decrease of
q in Figure 13b, while the divergence of wind stress reaches its maximum for
q

between
3 and
2 K (Figure 13c). Five algorithms consistently underestimate wind stress while two algorithms (BVW and CFC) overestimate wind stress most of the time (Figure 13f ). [31] Note that only 242 hourly samples were used in Table 5 and Figures 11– 13. Additionally, like with CMO, the samples were taken nearshore, so that the flux divergences among the algorithms are not necessarily consistent with Figures 2 and 4 – 10. As with the bulk measurements, turbulent distortion could also affect the covariance heat fluxes. If the observed LH values based on the inertialdissipation method (rather than the covariance method data) are used, all algorithms except CCM3 give negative LH biases (rather than positive biases in Table 5). If the average of the inertial-dissipation and covariance LH data is used, the bias is
3.7 and
4.8 W m
2 for GEOS and CFC, respectively, and between 0.4 and 4.8 W m
2 for the other six algorithms. Similarly, if the average is used for observed SH fluxes, the average bias is
0.8 and
1.0 W m
2 for Smith and BVW and between
0.9 and 0.7 W m
2 for the other six algorithms. For the observed wind stress, if covariance data instead of inertial-dissipation data are used, the bias is further increased for BVW and CFC (compared with Table 5) but decreased by as much as 69% for the other

Table 5. Evaluation of the Wind Stresses (t), Latent Heat Flux (LH), And Sensible Heat Flux (SH) of the Eight Algorithms Using the 242 Hourly Samples From the SCOPE Observationsa t LH SH

Bias, 10
3 N m
2 RMSD, 10
3 N m
2 r Bias, W m
2 RMSD, W m
2 r Bias, W m
2 RMSD, W m
2 r

UA

Smith

BVW

CFC

COARE

CCM3

ECMWF

GEOS


2.03 7.79 0.98 6.12 11.47 0.94 1.33 4.56 0.87


3.40 6.73 0.98 8.40 11.68 0.94
0.07 4.59 0.86

2.49 8.82 0.98 7.96 10.09 0.95
0.39 4.03 0.90

3.02 10.80 0.98
0.04 10.17 0.95 0.80 4.35 0.87


2.39 7.06 0.98 5.16 11.55 0.94 0.49 4.96 0.84


2.21 5.58 0.98 9.49 10.39 0.95 1.39 3.99 0.89


1.17 9.28 0.98 5.98 10.69 0.95 0.64 4.20 0.88


2.76 5.98 0.98 1.03 10.80 0.94
0.21 4.65 0.86

a Shown are the biases, i.e., the differences between computed and observed means; the root-mean square deviation (RMSD) between computed and observed values; and correlation coefficients (r). The SCOPE mean values are 3.05  10
2 N m
2, 46.11 W m
2, and 13.85 W m
2 for wind stress, LH flux, and SH flux, respectively.

BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

5 - 15

Figure 11. Hourly (a) LH fluxes, (b) SH fluxes, and (c) wind stresses averaged for SCOPE plotted as a function of wind speed U in 0.5 m s
1 bins. The solid line with triangles represents the observed fluxes. (d – f ) present the relative differences of the eight algorithms from observed. algorithms. These analyses suggest that BVW and CFC probably overestimate wind stress particularly at moderate and high wind speeds, while wind stress values from the other algorithms and SH and LH values from all of the algorithms are fairly consistent on average with observations. [32] Obviously, there are difficulties and limits in collecting turbulence measurements used to make direct covariance and turbulent dissipation flux calculations. Direct covariance measurements are often corrupted with ship motion and flow distortion, while turbulent dissipation measurements assume turbulent distortion can be neglected and that the wave boundary layer is obeying the law of the wall. These factors and others can make the interpretation of turbulent measurements uncertain. However, all bulk formulae are basically empirical while the turbulent observations, in spite of some uncertainties, are direct observations. It is encouraging that these results show a high correlation between turbulent and bulk fluxes. However, it is clear that more turbulent flux and wave data, including long time series over various climate regimes, are still needed to resolve the large discrepancies in wind stress and heat fluxes among the various bulk algorithms and further refine

the physical parameterization of surface waves, roughness length, and transfer coefficients.

6. Comparison of Global Flux Data Sets Over the TAO Array [33] Various global ocean surface flux data sets have been developed based on in situ (buoy and ship) data, remote sensing data, and reanalysis. Comparisons and evaluations of these data sets have also been reported [Wang and McPhaden, 2001]. Here insights gained from our algorithm intercomparison in the previous sections will be used to evaluate and understand the differences between two commonly used global monthly gridded flux data sets: the HOAPS data set (2
latitude  2
longitude grid) and the GEOS-1 reanalysis (2
latitude  2.5
longitude grid). [34] The two data sets derive the bulk variables using different methods. HOAPS derives its bulk variables (nearsurface wind speed, temperature, and humidity along with surface saturated humidity and temperature) from observations made by the polar-orbiting Advanced Very High Resolution Radiometer (AVHRR) and the Special Sensor Microwave/Imager (SSM/I) (http://sop.dkrz.de/HOAPS).

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BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

Figure 12. Same as in Figure 11 except as a function of Ts in 0.5
C bins.

The near-surface humidity qa is obtained using the brightness temperatures at 19, 22, and 37 GHz [Schlu¨ssel, 1996]. Air temperature Ta is thus obtained by assuming that the relative humidity is a constant 80%. The AVHRR Pathfinder sea surface temperature products were used to obtain sea surface temperature Ts. Thus the surface saturated humidity qs is derived by assuming that it is 2% lower than the saturated humidity qsat at Ts (J. Schulz, personal communication, 2001). Finally, the 10-m wind speed U10 is obtained based on the method of Schlu¨ssel and Luthardt [1991], which uses the brightness temperature difference between vertically and horizontally polarized components at 19 and 37 GHz as well as the brightness temperatures of the vertically polarized components at 19, 22, and 37 GHz. GEOS-1 produces bulk variables and surface fluxes based on the assimilation of data from rawindsondes, dropwindsondes, and temperature soundings from the Tiros Operational Vertical Sounder (TOVS) as described by Schubert et al. [1993]. Other data sources included surface synoptic reports, ships, buoys, rocketsondes, aircraft measurement of winds, and cloudmotion winds derived from satellite. [35] With the bulk variables thus obtained, bulk algorithms (Smith for HOAPS and GEOS for GEOS-1) are used

to obtain CH and CE, the bulk transfer coefficients for heat and moisture respectively. Sensible heat flux (SH) and latent heat flux (LH) can then be computed using equations (2) and (3). Thus SH or LH differences among algorithms are caused by differences in both bulk algorithms (as represented by CH and CE) and bulk variables (U,
q, and
q). Table 3 shows that the LH and SH differences between GEOS and Smith algorithms averaged over the whole multiyear period for all TAO buoys are rather small (3.1 and 0.18 W m
2 respectively). However, they may be significantly larger when comparing data sets using other algorithms. For instance, the maximum LH and SH differences among algorithms in Table 3 (due to CE and CH alone) are as large as 17.6 and 0.72 W m
2, respectively. [36] To evaluate the relative contributions of bulk algorithms versus bulk variables to flux differences, Figure 14 compares the HOAPS and GEOS-1 flux data sets with those computed based on the Smith and GEOS algorithms using the bulk variables from all TAO buoys. Neither the SCOPE nor CMO data are used here because they are either too short or do not overlap with the GEOS-1 data set. At times the two data sets produce fluxes fairly close to what their algorithms produce using the buoy data. However, both data sets greatly underestimate LH flux from January 1992

BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

5 - 17

Figure 13. Same as in Figure 11 except as a function of
q in 0.5 K bins. onward, while HOAPS significantly underestimates SH flux during that period. To evaluate the role of different bulk algorithms and different bulk variables in these differences, the flux difference between the two data sets
FHOAPS, GEOS-1 can be decomposed into three terms:
FHOAPS; GEOS-1 ¼ðFHOAPS
FSmith Þ þ ðFSmith
FGEOS Þ
ðFGEOS-1
FGEOS Þ;

ð7Þ

where F could be LH or SH. The terms (FHOAPS
FSmith) and (FGEOS-1
FGEOS) represent the flux difference caused by the difference of bulk variables in HOAPS and GEOS-1 respectively with those from TAO buoy observations, while the term (FSmith
FGEOS) represents the flux difference caused by bulk algorithm differences. Table 6 presents these four terms averaged over all of the TAO array.
FHOAPS,
2 with the (FHOAPS
FSmith) term GEOS-1 is
16 W m contributing the most. Similarly, for SH flux the highest contribution to the difference between the two data sets is also from (FHOAPS
FSmith). Consistent with these results, (FHOAPS
FSmith) has a higher correlation (0.69 for LH and 0.87 for SH) with
FHOAPS, GEOS-1 than the other two terms in equation (7). Also shown in Table 6 are the four terms averaged over all TAO buoys in the eastern (95
to 125
W),

central (140
to 180
W), and western (137
to 165
E) Pacific. For LH flux the magnitude of
FHOAPS, GEOS-1 is lowest in the eastern Pacific and increases westward, largely due to the steady increase of the (FHOAPS
FSmith) term from east to west. For SH flux the
FHOAPS, GEOS-1 term is primarily contributed by the (FGEOS-1
FGEOS) term over the eastern Pacific and by the (FHOAPS
FSmith) term over the western Pacific. For these two data sets, flux differences caused by bulk algorithm differences (i.e., the (FSmith
FGEOS) term) are much smaller than those due to bulk variable differences (i.e., the (FHOAPS
FSmith) or (FGEOS-1
FGEOS) terms) in magnitude. However, as mentioned earlier, bulk algorithm differences could contribute up to 17.6 W m
2 on average over all TAO buoys to LH flux difference if other algorithms were used. [37] To further understand the significant impact of bulk variable differences on flux differences, Figure 15 presents the time series of monthly 10-m wind speed (U10) and air surface temperature and humidity differences (
T and
q respectively) averaged over all of the TAO array. Both GEOS-1 and HOAPS produce generally slightly smaller wind speeds than buoy measurements.
T from HOAPS is much (4
C) smaller than those from buoy measurements while those from GEOS-1 are very close to buoy observations.
q from HOAPS is generally smaller in magnitude

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BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

Figure 14. Monthly (a) LH fluxes and (b) SH fluxes averaged over all of the TAO array from May 1990 to November 1993. Results from the HOAPS and GEOS-1 data sets are denoted by the solid and short dashed lines respectively, while fluxes computed using the corresponding bulk algorithms (i.e., the Smith and GEOS algorithms) with the colocated TAO buoy bulk variables are denoted by the solid line with crosses and the long-dashed line respectively. than buoy observations while those from GEOS-1 are greater. Similar to equation (7), the difference between the bulk variables of the two data sets
XHOAPS, GEOS-1 can be broken down thus    
XHOAPS; GEOS-1 ¼ XHOAPS
Xbuoy
XGEOS-1
Xbuoy ; ð8Þ

where X represents U10,
T, or
q. (XHOAPS
Xbuoy) and (XGEOS-1
Xbuoy) therefore are the differences between the bulk variables used by HOAPS and GEOS-1 respectively and buoy observations. Table 7 presents these three terms averaged for all of the TAO array as well as for the eastern, central, and western Pacific. HOAPS’ values for wind

speed and
T are lower than the buoy observations increasing in magnitude from west to east. This explains why the SH flux from HOAPS is generally considerably lower than those of the Smith algorithm using buoy observations. The difference between HOAPS’
q and buoy observations is large in the western Pacific (1.6 g kg
1) so that the (FHOAPS
FSmith) term is considerably smaller than zero (
42 W m
2) for LH flux (see Table 6) in agreement with Schulz et al. [1997]. Further data analysis reveals that the large bias of
q in the HOAPS data set in this region is primarily caused by the overestimate of qa. Note that the biases in qa are also reflected in
T as the air temperature Ta is calculated assuming that the relative humidity is a constant 80%. The error in CH using this

Table 6. Statistics for All Terms in Equation (7) Using All of the TAO Array as Well as Using the Buoys in the Eastern (95
to 125
W), Central (140
to 180
W), and Western (137
to 165
E) Pacific
FHOAPS,

GEOS-1

= (FHOAPS
FSmith) + (FSmith
FGEOS)
(FGEOS-1
FGEOS)

East Central West All

0.76
20.54
32.86
16.34

LH Flux, W m
2
3.71
1.11
15.17 0.05
41.85 1.32
15.52
0.06


5.58 5.42
7.67 0.76

East Central West All


3.00
1.83
5.47
2.39

SH Flux, W m
2 1.19 0.32
2.45 0.06
8.78
0.23
2.45 0.08

4.51
0.56
3.54 0.03

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BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

Figure 15. Buoy observations (solid line with diamonds) of (a) wind speed, (b) air-surface temperature difference
T, and (c) air-surface specific humidity difference
q plotted along with the values used by HOAPS (solid line) and GEOS-1 (short dashed line) averaged over all of the TAO array. assumption can be as high as 50% at low wind speeds and stable conditions to 2% at high wind speeds and highly unstable conditions [Schulz et al., 1997]. [38] It is important to note that the difference in bulk variables between the HOAPS or GEOS-1 data set and buoy observations is partially caused by the inherent difference between point values from buoys and gridded values. It is also partially caused by errors in satellite retrieval (HOAPS) and in data assimilation (GEOS-1). For instance, the global mean standard error for satellite-retrieved monthly air specific humidity qa in HOAPS is 0.8 g kg
1 (J. Schulz, personal communication, 2001). In situ data from midlatitude oceans are also needed to further evaluate these global flux data sets.

the calculation of surface saturated humidity, and how the transfer coefficients are parameterized. Subsequently, these algorithm differences result in uncertainties in ocean surface fluxes. Table 7. Statistics for All Terms in Equation (8) Using All of the TAO Array as Well as Using the Buoys in the Eastern (95
to 125
W), Central (140
to 180
W), and Western (137
to 165
E) Pacific
XHOAPS,

GEOS-1

= (XHOAPS
Xbuoy) + (XGEOS-1
Xbuoy) U, m s
1

East Central West All

0.23
0.58 0.15
0.28

East Central West All


3.06
3.56
2.65
3.33

East Central West All

0.42 0.78 2.14 0.87

7. Conclusions [39] While all bulk algorithms utilize Monin-Obukhov similarity theory to calculate sea surface turbulent energy and momentum fluxes, there are slight variations between algorithms developed by different groups. These differences include those in the wave spectrums explicitly considered, in the roughness lengths parameterizations, whether or not convective gustiness is considered, whether or not the effect of salinity is taken into consideration in


0.88
0.81
0.52
0.76


1.1
0.23
0.67
0.49


3.51
3.31
2.07
3.17


0.44 0.25 0.58 0.15


0.16 0.14 1.55 0.26


0.58
0.64
0.59
0.61


T,
C


q, g kg
1

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BRUNKE ET AL.: SEA SURFACE TURBULENT FLUX ALGORITHMS

[40] In evaluating these uncertainties, an intercomparison of eight algorithms used in data set generation as well as weather and climate prediction (i.e., the UA, COARE, Smith, BVW, and CFC algorithms plus those used in the NCAR CCM3, ECMWF forecast model, and GEOS-1 reanalysis) reveals considerable flux differences among algorithms over the tropical Pacific and midlatitude Atlantic. For hourly fluxes, notably large differences in LH and SH fluxes and wind stresses occur at weak and strong wind speeds and in LH and wind stress at moderate tropical sea surface temperatures, as also reported previously by Zeng et al. [1998]. Additionally, significant differences in hourly LH fluxes occur for very unstable conditions. Similar results also appear in the monthly average of the hourly fluxes. For instance, at Ts = 28
± 0.25
C, the maximum difference in monthly LH and wind stress over the TAO buoys are 23 W m
2 (or 16% relative to the algorithm-averaged flux) and 0.013 N m
2 (or 19% relative to the algorithm-averaged value), respectively. [41] Of the eight algorithms, some algorithms regularly produce appreciably different fluxes from the others. For example, under stable conditions and at low wind speeds, CCM3 consistently produces SH values above the other seven algorithms. CCM3’s zot for stable conditions is responsible for its higher SH values for stable conditions, and its constant zot along with the specification of a minimum wind speed of 1 m s
1 contributes to its highest SH fluxes at low wind speeds. LH values from ECMWF are consistently higher most of the time primarily because of its use of a relatively high Charnock constant (0.018) and the exclusion of the salinity effect in computing the surface saturated humidity. The wind stresses produced by BVW and CFC are considerably higher than those of the other algorithms because of their explicit inclusion of capillary waves. [42] A comparison of the computed fluxes from the eight algorithms with the observed direct covariance LH and SH data and inertial-dissipation wind stress data from SCOPE over the midlatitude Pacific shows that the correlations between each of the algorithms and SCOPE data is significant at the 99% level with the highest (lowest) correlations for wind stress (SH fluxes). The maximum wind stress bias is
3.4  10
3 N m
2 from Smith primarily due to its underestimate for wind speeds less than 6 m s
1. The maximum LH and SH flux biases are 9.5 and 1.4 W m
2 respectively (both from CCM3) principally due to its overestimate of these fluxes for wind speeds below 3 m s
1. However, none of the algorithm biases in wind stress or SH fluxes is significant at the 95% level. While LH flux biases from six algorithms are significant at the 95% level, the biases become insignificant if the average of observed covariance and inertial-dissipation data is used. Therefore to resolve the large flux discrepancies among algorithms as revealed in this paper, more observational data over various climate regimes are still needed. [43] Finally, the monthly LH and SH fluxes of the HOAPS data set based upon satellite observations and the GEOS-1 reanalysis are compared with those computed using their corresponding algorithms (i.e., the Smith and GEOS algorithms) forced by bulk variables from all TAO buoys. The mean LH flux difference between HOAPS and GEOS-1 is
16 W m
2 primarily due to differences in the bulk variables. A comparison of the wind speed and the air-

surface differences in temperature and specific humidity used by the two data sets with buoy observations further shows that GEOS-1 consistently produces better
T than HOAPS, while neither of them is consistently better than the other in
q or wind speed estimates over the eastern, central, and western Pacific. The bulk variables from HOAPS and GEOS-1 can be considerably different in some months that contribute to the significant flux differences between the data sets. Although the contribution to the flux differences by algorithm differences is quite small, the maximum average difference of LH fluxes over the tropical Pacific can be as high as 17.6 W m
2 if other algorithms were used. Therefore to produce global ocean surface fluxes with an accuracy of 10 W m
2, both bulk algorithms and the derivation of bulk variables need to be further improved. [44] Acknowledgments. This work was supported by the NOAA OGP under grants NA16G91619, NA96GP0388, NA66GP0130, and NA96GP0428 and by the ONR under grant N0014-95-1-0339. A. Beljaars, M. A. Bourassa, C. A. Clayson, C. W. Fairall, A. Molod, and J. Schulz are thanked for providing their subroutines or algorithms. We are thankful to J. Schulz, M. Bourassa, N. Renno´, and S. Mullen, as well as C. Hammond and the reviewers for their helpful comments. C. W. Fairall is thanked for providing the observed flux data over the midlatitude Pacific. We also thank the TOGA TAO Office of the Pacific Marine Environmental Laboratory for the TAO buoy data and the HOAPS group for their flux and bulk variable data.

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S. Anderson, Horizon Marine, Marion, MA 02738, USA. M. A. Brunke and X. Zeng, Department of Atmospheric Sciences, The University of Arizona, Physics-Atmospheric Sciences Building, P.O. Box 210081, Tucson, AZ 85721, USA. ([email protected])