The Importance of Relative Wind Speed in Estimating Air–Sea Turbulent Heat Fluxes in Bulk Formulas: Examples in the Bohai Sea

Xiangzhou Song College of Oceanography, and Key Laboratory of Coastal Disaster and Protection, Ministry of Education, Hohai University, Nanjing, Jiangsu, China

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Abstract

Sea surface currents are commonly neglected when estimating the air–sea turbulent heat fluxes in bulk formulas. Using buoy observations in the Bohai Sea, this paper investigated the effects of near-coast multiscale currents on the quantification of turbulent heat fluxes, namely, latent heat flux (LH) and sensible heat flux (SH). The maximum current reached 1 m s−1 in magnitude, and a steady northeastward current of 0.16 m s−1 appeared in the southern Bohai Strait. The predominant tidal signal was the semidiurnal current, followed by diurnal components. The mean absolute surface wind was from the northeast with a speed of approximately 3 m s−1. The surface winds at a height of 11 m were dominated by the East Asian monsoon. As a result of upwind flow, the monthly mean differences in LH and SH between the estimates with and without surface currents ranged from 1 to 2 W m−2 in July (stable boundary layer) and November (unstable boundary layer). The hourly differences were on average 10 W m−2 and ranged from 0 to 24 W m−2 due to changes in the relative wind speed by high-frequency rotating surface tidal currents. The diurnal variability in LH/SH was demonstrated under stable and unstable boundary conditions. Observations provided an accurate benchmark for flux comparisons. The newly updated atmospheric reanalysis products MERRA-2 and ERA5 were superior to the 1° OAFlux data at this buoy location. However, future efforts in heat flux computation are still needed to, for example, consider surface currents and resolve diurnal variations.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xiangzhou Song, song@ouc.edu.cn

Abstract

Sea surface currents are commonly neglected when estimating the air–sea turbulent heat fluxes in bulk formulas. Using buoy observations in the Bohai Sea, this paper investigated the effects of near-coast multiscale currents on the quantification of turbulent heat fluxes, namely, latent heat flux (LH) and sensible heat flux (SH). The maximum current reached 1 m s−1 in magnitude, and a steady northeastward current of 0.16 m s−1 appeared in the southern Bohai Strait. The predominant tidal signal was the semidiurnal current, followed by diurnal components. The mean absolute surface wind was from the northeast with a speed of approximately 3 m s−1. The surface winds at a height of 11 m were dominated by the East Asian monsoon. As a result of upwind flow, the monthly mean differences in LH and SH between the estimates with and without surface currents ranged from 1 to 2 W m−2 in July (stable boundary layer) and November (unstable boundary layer). The hourly differences were on average 10 W m−2 and ranged from 0 to 24 W m−2 due to changes in the relative wind speed by high-frequency rotating surface tidal currents. The diurnal variability in LH/SH was demonstrated under stable and unstable boundary conditions. Observations provided an accurate benchmark for flux comparisons. The newly updated atmospheric reanalysis products MERRA-2 and ERA5 were superior to the 1° OAFlux data at this buoy location. However, future efforts in heat flux computation are still needed to, for example, consider surface currents and resolve diurnal variations.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xiangzhou Song, song@ouc.edu.cn

1. Introduction

Air–sea turbulent heat fluxes (THFs) include the latent heat flux (LH) and the sensible heat flux (SH), which are associated with evaporative and convective processes, respectively. THFs strongly influence the ocean mixed layer depth and the stability and convection within the atmospheric boundary layer (e.g., Cayan 1992). THFs also constitute the key components that balance the surface radiative processes to obtain the net air–sea heat fluxes. Following the Monin–Obukhov similarity theory (Monin and Obukhov 1954), THFs are conventionally estimated by bulk formulas (Liu et al. 1979; Large and Pond 1981; Fairall et al. 1996, 2003; Edson et al. 2013). However, the errors in THFs at global to regional scales suffer from uncertainties arising primarily from the observational physical variables in the air–sea boundary layers and empirical estimates of parameters (Weare 1989; Gleckler and Weare 1997; Grist and Josey 2003; Brunke et al. 2011; Yu et al. 2013; Song and Yu 2013; Weller et al. 2016; Song and Yu 2017). Errors have been identified either by direct intercomparisons between point-to-point observations and flux products (Gleckler and Weare 1997; Josey 2001; Brunke et al. 2011) or by physical constraints based on the heat budget balance in a specified control region (Song and Yu 2013, 2017).

The heat flux community has made great efforts to reduce the large biases and uncertainties in the air–sea THFs to achieve globally balanced products, including adjusting the air–sea flux climatology using ocean heat transport constraints (Grist and Josey 2003), reducing the solar radiation by 5% to obtain a balanced system (Large and Yeager 2009) and increasing LH + SH by a mean magnitude of 8 W m−2 in the global ice-free ocean based on a newly updated bulk algorithm (L. Yu, 2019, personal communication). For objectively analyzed THF estimates, the bulk scalar wind speed relative to Earth, namely, the absolute wind (AW), is solely used (Yu and Weller 2007; Berry and Kent 2009), whereas sea surface currents (SFC) are usually neglected based on the assumption that the currents have less impact than the surface winds. However, previous studies (Duhaut and Straub 2006; Dawe and Thompson 2006; Wu et al. 2017) have shown that the wind stress, including the currents, is reduced by a few percent over most of the basin. Furthermore, coupling the SFC is vital for improving our ability to predict the sea surface temperature (SST) because the air–sea THFs will be calculated better physically. For instance, Luo et al. (2005) found that the warm-pool/cold-tongue thermal structure in the equatorial Pacific is simulated better with coupled SFC than without, which has also been confirmed by the simulations performed by Deng et al. (2009) and Zhao et al. (2011).

Thus, the heat flux community has proposed that the wind relative to the sea surface might not be negligible when estimating the THFs, but this hypothesis has not been evaluated by full buoy observations and likely represents a missing physical theory in the estimation and study of air–sea THFs. One may expect that the inclusion of SFC in the bulk formulas would reduce the heat flux magnitude, as currents tend to flow parallel to the mean wind and the relative wind (RW) speed is typically smaller than the AW speed. Nevertheless, this hypothesis might not hold true when the surface current is upwind or rotating at different frequencies. In coastal seas, where current magnitudes of 10%–20% of the wind speed are common, the difference between the RW and AW can be quite pronounced (Plagge et al. 2012). Typically, the maximum full current speed in a tide-dominated coastal region can reach 1 m s−1. Multiscale currents with magnitudes ranging from 0 to 1 ms−1 can contribute to an RW speed between the ocean and the atmosphere in the bulk formulas, which may further affect the accurate estimation of THFs. In this paper, the author aims to revisit the effect of currents on estimating the high-frequency THFs in the coastal ocean, where the high spatial–temporal resolution of heat flux products tends to achieve a better regional heat budget balance (Song and Yu 2017).

The marginal seas adjacent to China experience significant tidal currents (Guo and Yanagi 1998; Niwa and Hibiya 2004; Song et al. 2019) with magnitudes of approximately 1 m s−1. In such a region with strong tidal currents, neglecting the currents when estimating the THFs may render the results invalid because the high-frequency rotation of the tidal currents and other multiscale ocean dynamics can modify the RW speed. In addition to tidal currents, the mean current in the marginal seas of China is characterized by upwind flows, for example, the Taiwan Warm Current in the East China Sea (Su 1998; Yang 2007; Isobe 2008) and the Yellow Sea Warm Current in the Yellow Sea (Uda 1934; Ichikawa and Beardsley 2002; Lin et al. 2011), which extends to the strait of the Bohai Sea. The magnitude of the RW can be higher than that of the AW due to these upwind flows. In this situation, if only the AW speed is used in the bulk formulas, the THFs might be lower than those using RW. Thus, the main goal of this paper is to evaluate the differences in the THFs that might be generated by multiscale SFC.

The observed air–sea boundary variables and SFC from an operational 10-m foam buoy are used to identify these differences. Utilizing the in situ measurements acquired by this buoy, the differences under stable and unstable atmospheric stability conditions are discussed. The high-resolution LH and SH estimates are then compared with the satellite-based analyzed heat flux and newly released atmospheric reanalysis to help assess the uncertainties in the heat flux products. The remainder of this paper is organized as follows: section 2 introduces the observed air–sea variables in the Bohai Sea, the gridded heat flux products, and the bulk formulas used in this paper; section 3 presents the characteristics of the general observational winds and SFC and the analysis of the differences between the THF estimates with and without SFC; section 4 shows the discrepancies in LH + SH under different air–sea boundary stability conditions in warm and cold seasons and highlights the diurnal variability in THFs; section 5 discusses the use of the hourly and daily results of the THFs with and without SFC to diagnose the objectively analyzed product and new atmospheric reanalysis; and finally, section 6 presents a summary and discussion.

2. Data and method

a. Data description

1) Buoy observations

An air–sea 10-m buoy is deployed in the southern strait of the Bohai Sea (Fig. 1) and is maintained by the North China Sea Branch of the State Oceanic Administration (SOA). This buoy provides high-resolution observations of standard meteorological variables, including surface wind speed, wind direction, surface air temperature (SAT), SST, sea surface salinity, relative humidity, sea level pressure, and surface current data. The observational heights for wind, air temperature and relative humidity are 11 m above the sea surface (Fig. 2), while the sensor for detecting the temperature and salinity at the sea surface is located at a depth of −0.5 m (i.e., 0.5 m beneath the sea surface). A downward-looking RDI 300 K acoustic Doppler current profiler (ADCP) was anchored under the buoy, and the vertical bin size was set to 2 m. The effective depth for the SFC was −4 m. The surface velocity observations lasted from 1 April to 30 November in 2016. Current data were not available in October because of maintenance. The mean state in this paper was the result of an 8-month average based on buoy observations. All the instruments and sensors were calibrated by the National Center of Ocean Standards and Metrology.

Fig. 1.
Fig. 1.

Location of the 10-m buoy in the Bohai Sea (black triangle). The colored background field is the annual (12 month) mean LH in 2016 (W m−2) from the ECMWF ERA5 project. The squares and dashed lines are the grids of OAFlux with a spatial resolution of 1° × 1°. The solid circles with dashed lines are the grids of ERA5 with a resolution of 0.25° × 0.25°. The diamonds with dashed lines are the grids of MERRA-2 with a resolution of 0.625° (zonal) × 0.5° (meridional). The nearest points from the OAFlux and new atmospheric reanalysis grids to the observing buoy location were used for the analysis. The incorporated frame (red) represents the study area of the Bohai Sea.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

Fig. 2.
Fig. 2.

The in situ observations by the 10-m buoy. The instruments are marked in red. The observation height of the meteorological variables is approximately 11 m.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

Observations of the air–sea variables collected over eight months were used to investigate the effect of currents on the air–sea THFs in the coastal sea. In boreal summer, SH can be transferred from the atmosphere to the ocean because the air temperature is higher than the SST and the atmospheric boundary layer tends to be stable. However, in boreal wintertime, the transfers of both LH and SH are relatively large due to the strong wind speeds and air–sea temperature/humidity differences in the convectively unstable boundary layer. Thus, two typical seasons—summer and winter—were chosen for analysis. The observational data from July and November 2016 were used to represent the summer and winter seasons, respectively. Negative THF values in this paper denote heat loss by the ocean, while positive values indicate heat gain. The negative (positive) difference under unstable (stable) atmospheric boundary conditions indicates higher estimates of THFs based on RW than those based on AW.

2) Objectively analyzed air–sea fluxes

The objectively analyzed air–sea fluxes (OAFlux) project for the global oceans (Yu and Weller 2007) provides a multidecadal analysis of air–sea heat and momentum fluxes for research on the global energy budget and climate change. Synthesized measurements/estimates from various sources, including satellite observations and reanalysis, were used to reduce the errors, and a best estimate with minimum error variance was produced. The Coupled Ocean–Atmosphere Response Experiment (COARE) bulk flux algorithm, version 3.0, of the OAFlux project was used (Fairall et al. 1996, 2003). OAFlux outputs daily estimates of LH and SH and the associated parameters, namely, SST, SAT, specific humidity and wind speed. It is widely regarded as an important benchmark for air–sea flux intercomparisons and the global surface heat budget (e.g., Cronin et al. 2019; Yu 2019). The third version of OAFlux with temporal and spatial resolutions of daily and 1° was used in this paper.

3) Newly released atmospheric reanalysis

The Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2; Gelaro et al. 2017), using the Goddard Earth Observing System Model, version 5 (GEOS-5), released by NASA’s Global Modeling and Assimilation Office provides data beginning in 1980 and continuing to the present. This new global reanalysis replaces and extends the original MERRA dataset (Rienecker et al. 2011). The European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 project provides hourly estimates of a large number of atmospheric, land and oceanic climate variables (Hersbach et al. 2019). ERA5 replaces the ERA-Interim (Dee et al. 2011) reanalysis, which stopped being produced on 31 August 2019. Both ERA5 and MERRA-2 combine large historical observation datasets into global reanalysis datasets using advanced modeling and data assimilation systems. MERRA-2 and ERA5 output hourly oceanic LH and SH and the associated SST, SAT, specific humidity, and wind speed (WS) variables. The related heat flux datasets have been described in detail in previous publications (Song and Yu 2013, 2017).

b. Method of estimating THFs

THFs are computed by the following bulk formulas:
QLH=ρLecE|UzUsfc|(Δq),
QSH=ρcpcH|UzUsfc|(ΔT),
where QLH represents the LH, QSH represents the SH, ρ is the density of air, Le is the latent heat of evaporation, cp is the specific heat capacity of air, Uz is the wind vector at a height z, namely, the AW speed, and Usfc is the SSC. |UzUsfc| represents the wind speed relative to the current. The turbulent exchange coefficients for the LH and SH are denoted by cE and cH, respectively, and Δq and ΔT represent the sea–air humidity and temperature difference, respectively.
The wind speed relative to the surface current is calculated as follows:
|UzUsfc|=[(uzuSSC)2+(υzυSSC)2]1/2,
while the AW relative to Earth is calculated by
|Uz|=[(uz)2+(υz)2]1/2,
where uz and uSSC are the zonal AW vector and surface current, respectively, and υz and υSSC represent the corresponding meridional components. In this paper, the COARE bulk flux algorithm, version 3.0 (Fairall et al. 1996, 2003; Edson et al. 2013), of the OAFlux project was used (Yu and Weller 2007).

3. Observational results and THF discrepancies: A general analysis

a. Statistical characteristics of the SFC and AW speed

The current directional occurrence Gn with a certain direction is calculated as follows:
Gn=fnη+n=136fn,
where η represents the number of missing observational samples and fn represents the number of observational samples in a certain current direction range. The directions were divided into 36 bins of 10° each, and the velocity magnitudes ranging from 0 to 1 m s−1 were classified into 10 grades at intervals of 0.1 m s−1. Figure 3 shows a rose plot of the SFC. Two significant structures can be found. One is a structure consisting of rotating tidal currents oriented from northwest to southeast. The maximum speed of the rotating currents is approximately 1 m s−1. The other structure is a significant eastward current with an occurrence frequency of 13%. The total sum of occurrences from east to northeast with a 30° rotation exceeds 15%, and the maximum speed of the current is approximately 1 m s−1. Therefore, a dominant, steady northeastward current flows through the southern channel of the Bohai Strait, which is traditionally considered to have a southern outflowing current and a northern inflowing current. These findings are similar to previous observations (e.g., Guan 1994; Zhang et al. 2018) and model simulations (e.g., Fang et al. 2000; Wang et al. 2010; Zhou et al. 2017).
Fig. 3.
Fig. 3.

Rose plot of the SFC (unit: m s−1). The hourly observational current samples range from 1 Apr to 30 Nov 2016. The directions were divided into 36 bins of 10° each. The directional frequency was calculated by Eq. (5). The velocity magnitudes were colored into 10 grades with a resolution of 0.1 m s−1.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

Harmonic analysis was used to decompose the full velocity into velocities at different frequencies. The surface velocity u can be separated into two main parts: the tidal and inertial flows uj and the mean residual current u¯:
i=1Nu(i)=i=1Nu¯+i=1Nj=19uj(i),
i=1Nj=19uj(i)=i=1Nj=19Ajcos[ωjt(i)φj].

The high-frequency currents conventionally include the diurnal components of K1, O1, P1, and Q1, the semidiurnal tides of M2, S2, N2, and K2, and the inertial dynamics f. Aj, ωj, and φj represent the amplitudes, frequencies, and phases, respectively, of the above nine components. The term t(i) represents the time with an interval i. The least squares method is used to obtain the periodic tidal currents and the residual mean flow. Hourly observations of currents during the 8-month period are included for the harmonic analysis.

Figure 4 shows the northeastward residual mean current, the diurnal and semidiurnal rotating tidal ellipses and the near-inertial oscillations. The mean steady current is approximately 0.16 m s−1. The predominant tidal ellipse is the semidiurnal M2 current, followed by the diurnal components of K1, O1, and P1, while the other tidal components and near-inertial dynamics are weak. The tidal ellipses stretch across the topography, which is different from the circular rotation in the open shelf of the Yellow Sea and East China Sea (e.g., Lee and Jung 1999; Kang et al. 2002; Lozovatsky et al. 2008; Song et al. 2019). The ellipses of M2, K1, and O1 show significant rotating tidal currents from northwest to southeast. These have also been identified in the rose plot of SFC illustrated in Fig. 3.

Fig. 4.
Fig. 4.

The mean residual mean current (black, unit: cm s−1) and tidal ellipses of the diurnal, semidiurnal, and near-inertial current constitutes based on harmonic analysis (Song et al. 2019). The hourly observational current data from 1 Apr to 30 Nov 2016 are included. The diurnal ellipses include the K1, O1, P1, and Q1 components, while the semidiurnal ellipses include the M2, S2, N2, and K2 components (see the legend). The inertial oscillations are represented by f (green ellipse).

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

Similar to Fig. 3, Fig. 5 shows a rose plot of the surface winds at a height of 11 m over the sea surface based on Eq. (5). In contrast to the current directions, the winds originated from nearly all directions during the eight months. The percentages of wind directions range evenly from 2% to approximately 5%. However, the dominant directions of the East Asian monsoon (EAM; e.g., Chang 2004) switch from northeast in winter to southwest in summer. The 8-month mean wind blew from the northeast at a speed of approximately 3 m s−1. Strong winds appeared mainly in winter as a result of storms and reached speeds of approximately 17 m s−1. The above results indicate that both the winds and the SFC show significant directional variations.

Fig. 5.
Fig. 5.

Rose plot of the sea surface wind vectors at 11 m (unit: m s−1). The hourly observational wind samples from 1 Apr to 30 Nov 2016 are included. Note that the vectors represent the direction of origin, which is different from the ocean currents. The figure configuration is the same as in Fig. 3.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

b. Discrepancy analysis with SFC corrections

In this section, the difference in THFs between the schemes using the RW speeds [Eq. (3)] and AW speeds [Eq. (4)] in the bulk formulas is analyzed. Figure 6a shows the estimated hourly LH and SH in July. The monthly mean LH and SH were 23 and 11 W m−2, respectively, which indicates that heat was transferred from the atmosphere to the ocean due to the higher temperature and air humidity in summer. Figure 6b shows the corresponding results in November. The monthly mean LH and SH were −178.8 and −93.9 W m−2, respectively. The maximum mean LH and SH were approximately −600 and −500 W m−2, respectively, indicating a large loss of heat from the sea due to the cold air in winter. The statistics of the heat flux difference (QDIFF) between the RW and AW are summarized in Table 1.

Fig. 6.
Fig. 6.

The estimated hourly air–sea LH (red, unit: W m−2) and SH (blue, unit: W m−2) in (a) July and (b) November from the buoy observations based on the COARE 3.0 bulk algorithm.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

Table 1.

The monthly mean LH and SH (unit: W m−2) based on buoy observations and the mean, maximum, minimum, and standard deviation (STD) of the LH and SH differences (QDIFF) (unit: W m−2) between the relative wind (RW) and absolute wind (AW) schemes.

Table 1.

In July, the monthly mean QDIFF values between the RW and AW (RW − AW) were 1.4 and 0.6 W m−2 for LH and SH, respectively, which account for 6.1% and 5.5% of the mean values (Fig. 7). This discrepancy indicates that the THFs are lower in magnitude if the AW is used. The magnitudes of the hourly QDIFF for LH and SH in July are larger when the values of LH and SH are higher. The maximum QDIFF values for LH and SH were 14 and 6 W m−2, respectively, while the minimum values were −6 and −1 W m−2, respectively. The standard deviations of QDIFF for LH and SH were 2 and 1 W m−2, respectively.

Fig. 7.
Fig. 7.

The hourly differences (unit: W m−2) of (left) LH(RW) − LH(AW) and (right) SH(RW) − SH(AW) in (a),(b) July and (c),(d) November. The bars and colors indicate the magnitudes of the heat flux differences (unit: W m−2). The black curves are the daily running mean plots. Note the different color bars and y-axis ranges between subplots.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

In November, the mean QDIFF values for LH and SH were −1.1 and −0.7 W m−2, respectively, with magnitudes comparable to those in July. The maximum, minimum, and standard deviation of QDIFF in November were 21, −24, and 4 W m−2, respectively, for LH and 10, −15, and 2 W m−2, respectively, for SH. These results indicate that the monthly mean LH and SH values are 1 W m−2 lower in July and November if the RW speed is not included in the bulk formulas. However, the hourly QDIFF values for LH and SH had a mean value of 10 W m−2 and ranged from 0 to 24 W m−2. Thus, it is necessary to consider the effect of the SFC on the RW speeds when estimating the surface heat fluxes in studies on the diurnal cycles (see section 5) of the upper-ocean dynamics.

Figures 8a and 8b show the mean wind and surface current at the buoy location. It is evident that the current constitutes an upwind flow. Thus, in the 8-month mean state, the magnitude of the air–sea turbulent heat flux will be enlarged as a result of an increased RW speed. Figure 8c shows the magnitude differences (scatterplots) between the RW and AW (RW − AW) with axes of the current magnitude (x axis) and the vector angle difference between the wind and current (y axis). The RW speed is enhanced when the surface current magnitude rises, and the angular difference between the wind and current increases from π/2 to π. In general, the differences in the heat flux with and without SFC are higher with larger wind speeds [Eqs. (1) and (2)]. However, the pattern of this heat flux difference is not identical to that of the wind speed difference because the heat flux depends on the nonlinear interactions between the wind speeds and sea–air humidity/temperature gradients. In contrast, the air–sea turbulent heat flux is reduced with a relatively small vector angle difference ranging from 0 to π/2. In this situation, the SFC tends to be parallel to the wind, thereby reducing the RW speed and air–sea THFs.

Fig. 8.
Fig. 8.

Mean (a) wind (black vector) and (b) surface current (black vector) at the buoy location in the southern Bohai Strait. The purple circles are the velocity contours. The numbers of the circles are marked. Note the different units for the mean wind (unit: m s−1) and surface current (unit: cm s−1). (c) The RW − AW magnitudes (unit: m s−1) with changing vector angles ([0, π]) and current magnitudes ([0, 1]). (d) As in (c), but for the air–sea turbulent heat flux differences THF(RW) − THF(AW) between the schemes with and without SFC.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

4. THF difference analysis related to atmospheric stability and diurnal variability

In mid-July 2016, the direction of the THFs was from the ocean to the upper atmosphere (Fig. 6a) because of the changes in the air–sea gradients of water vapor and temperature. This section discusses the THF differences with and without SFC under the conditions of unstable, near-neutral and stable atmospheric boundary layers. Stability is determined by the Monin–Obukhov stability parameter (z/L), where z is the height of the turbulent transfer coefficient and L is the Obukhov length scale:
L=u*2κgT¯T*,
where κ ≈ 0.4 is the von Kármán constant, g is the constant of gravitational acceleration, u* is the friction velocity, T¯ is the mean temperature in the boundary layer, and T*=wT¯/u*. wT¯ is the Reynolds stress term, where T and w represent the temperature and vertical motion, respectively, and the prime symbol denotes a fluctuation. The Obukhov length scale represents the ratio of the work performed by the Reynolds stress to that performed by buoyancy forces. By convention, unstable, near-neutral and stable conditions are defined as z/L < −0.4, −0.4 < z/L < 0.1, and z/L > 0.1, respectively, in this paper. The SFC can contribute to the modification of the atmospheric boundary layer by modifying the wind friction velocity (e.g., Vandemark et al. 1997; Plagge et al. 2012).

The observations in July indicate dominantly stable boundary conditions, with the SAT being higher than the SST in the warm season. However, in November, the atmospheric boundary layer became convectively unstable due to a strong air–sea temperature gradient. Fewer near-neutral conditions (|L| → ∞) were observed in July. Only two samples were found to have transferred from a stable condition to a near-neutral state as a result of the SFC-modified friction velocity. Thus, only the stable and unstable conditions are discussed here. Figure 9 shows the hourly observations of LH and SH averaged in July and November under stable and unstable boundary conditions. Two significant features can be found: an evident difference in the heat fluxes including and excluding SFC and the strong diurnal variability in LH and SH.

Fig. 9.
Fig. 9.

Comparisons of the diurnal variability of LH and SH under (a),(b) stable (July, z/L > 0.1) and (c),(d) unstable (November, z/L < −0.4) atmospheric boundary layer conditions among the buoy estimates (red and blue), OAFlux (dark yellow), and newly released atmospheric reanalysis products ERA5 (purple) and MERRA-2 (green). Note that OAFlux provides only daily results, and thus, no diurnal variability is shown. The mean results are incorporated to the right of the panels using the same colors.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

In July, with a predominantly stable atmospheric boundary layer, the LH and SH estimates including SFC are 2 and 1 W m−2 higher than those excluding SFC, respectively (Fig. 9). Larger differences can be found from 1700 to 0800 LT of the next day. In November, the boundary layer conditions continue to be unstable due to the cold SAT in winter (Fig. 6). Thus, the differences in the THFs with and without SFC are the same as the monthly mean results in section 3b. The magnitudes of LH and SH based on RW are both 1 W m−2 higher than those without SFC. Relatively large discrepancies exist in the afternoon from 1500 LT to midnight.

Figure 9 also shows the significant diurnal variability in both LH and SH in July and November under stable and unstable boundary layer conditions. In July, both LH and SH decrease from 0100 to 1300 LT. In November, the atmospheric boundary layer is strongly unstable due to convection when the SST is much higher than the SAT. The evaporative LH gradually increases when solar radiation warms the sea surface from 0600 to 1800 LT. SH also increases from the early morning to the afternoon but subsequently decreases. The largest SH under unstable conditions (approximately −110 W m−2) occurs at 1300 LT.

5. Heat flux comparisons

Knowing the extent of THF uncertainties in objectively analyzed products and atmospheric reanalysis is crucial for understanding the global heat energy budget (Yu 2019). Traditional point-to-point comparisons between observations and gridded products are powerful methods for diagnosing heat flux uncertainties (Gleckler and Weare 1997; Josey 2001; Brunke et al. 2011). Utilizing the calculations of LH and SH with and without SFC in the Bohai Strait, this section presents a comparison among the THFs estimated from the buoy observations and the OAFlux, MERRA-2, and ERA5 datasets. Two comparisons are performed: a comparison of the diurnal THF variations and a comparison of the daily mean values from April to November 2016.

a. Hourly resolution (diurnal) comparison

OAFlux, MERRA-2, and ERA5 assimilate the high-resolution daily 1/4° Optimum Interpolation Sea Surface Temperature (OISST) products provided by NOAA (Reynolds et al. 2007) as the boundary conditions. OAFlux outputs daily variables without diurnal variations, whereas MERRA-2 and ERA5 output the diurnal LH and SH with modeled atmospheric variables but a constant daily SST. Figure 9 shows the diurnal variations in LH and SH from the buoy estimates OAFlux, MERRA-2, and ERA5 under stable and unstable boundary layer conditions. The atmospheric stability was determined by the parameter z/L using the buoy observations. The OAFlux assimilation was computed when the hourly samples of stability conditions in a day exceeded 18 (2/3 of the day).

In July, under stable conditions, MERRA-2 and ERA5 deviate from the buoy estimates with and without SFC in terms of both the diurnal variations and the magnitudes (Table 2). This indicates the poor ability of reanalysis data to reproduce the LH and SH under stable boundary conditions. In November, under unstable atmospheric boundary layer conditions, the predicted diurnal variations in LH and SH of MERRA-2 and ERA5 compared with the buoy computations are better than those in July. The simulated diurnal variations during the daytime are much better than those during the nighttime. The LH and SH magnitudes in the reanalysis data are approximately 30 W m−2 lower than those of the buoy estimates. OAFlux shows consistency with the buoy measurements in terms of the magnitudes (Fig. 9 and Table 2), possibly due to the use of the same algorithm, namely, COARE 3.0.

Table 2.

The statistics of the monthly mean LH and SH (unit: W m−2) under stable and unstable atmospheric boundary conditions.

Table 2.

Large deviations can be found in the hourly scatterplots of LH and SH between the buoy estimates and the atmospheric reanalysis results of MERRA-2 and ERA5 (Figs. 10 and 11). The difference in LH (SH) between the buoy observations and reanalysis results [THF(Re) − THF(Obs)] ranges from −500 (−200) to 500 (300) W m−2, with large root-mean-squares (RMSs). This indicates a poor ability to reproduce high-resolution coastal air–sea THFs and thus a limited ability to obtain an in-depth understanding of local air–sea interactions and upper-ocean dynamics. As MERRA-2 and ERA5 take only the SST as the bottom forcing boundary and do not consider the upper-ocean dynamics, the THFs tend to be slightly closer to the buoy estimates without SFC (NO SFC). MERRA-2 and ERA5 have lower LH and SH magnitudes, and thus, the slopes of the linear regression are less than 1. ERA5 has lower RMSs (by 1–6 W m−2), higher regression slopes (by approximately 0.1) and lower deviations than MERRA-2. For SH, the value obtained by ERA5 is approximately 70% of that retrieved from the buoy estimates.

Fig. 10.
Fig. 10.

The hourly intercomparisons of (a),(b) LH and (c),(d) SH between the buoy estimates including SFC and the newly released atmospheric reanalysis products (a),(c) MERRA-2 and (b),(d) ERA5. The linear regression relations (purple lines) and RMS results are incorporated into the panels.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

Fig. 11.
Fig. 11.

As in Fig. 10, but for the results of the buoy estimates of LH and SH excluding SFC.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

b. Comparisons of the daily THFs

The hourly LH and SH with the inclusion of SFC from April to December 2016 were averaged into the daily heat flux. The THFs were not estimated in October, as the ADCP data were absent because of equipment maintenance. Figure 12 shows the daily THFs of the buoy estimates, OAFlux, MERRA-2, and ERA5. The daily buoy-based THFs from April to September and in November were compared directly with those of the OAFlux, MERRA-2, and ERA5 over the same time periods. The correlations between the buoy estimates, OAFlux, and reanalysis all exceed 0.8 at the 95% confidence level by the Student’s t test. ERA5 has the highest correlation coefficients, which reach 0.9 at the 95% confidence level (Fig. 13). Based on the COARE 3.0 algorithm, the high-resolution buoy estimates show more significant peaks than the other products in both summer and winter. In winter, cold and dry northeasterly winds blew over the relatively warm sea surface, and the strong wind speeds and large air–sea contrasts in temperature and humidity induced high THFs (e.g., Yu 2007; Song and Yu 2012). OAFlux, MERRA-2, and ERA5 can capture the cold air outbreaks and high LH + SH values in winter. However, the extreme values of LH and SH are 200 and 100 W m−2 less than the buoy measurements, respectively.

Fig. 12.
Fig. 12.

Time series of the daily mean (a),(c) LH and (b),(d) SH in 2016 from the buoy estimates (purple denotes those including SFC and blue denotes those excluding SFC) and OAFlux (green), MERRA-2 (red), and ERA5 (black). The daily THFs of OAFlux in 2016 were directly used. The daily mean LH and SH based on buoy observations and high-resolution atmospheric reanalysis were obtained from hourly products. The buoy observations (current observations) extended from 27 Apr to 15 Dec 2016, and observations were missing in October.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

Fig. 13.
Fig. 13.

Taylor diagrams showing three statistical properties of the (a),(c) LH and (b),(d) SH comparison: the standard deviations (STDs), root-mean-squares (RMSs), and correlation coefficients (CCs) of the differences between the three products and buoy observations. A total of 202 samples of daily collocations in 2016 were used from the buoy observations, OAFlux, MERRA-2, and ERA5.

Citation: Journal of Atmospheric and Oceanic Technology 37, 4; 10.1175/JTECH-D-19-0091.1

During the buoy observational period, the mean buoy-based LH and SH values including (excluding) SFC were −57 (−56) and −15 (−14) W m−2, respectively, while they were −67 and −16 W m−2 for OAFlux, −62 and −11 W m−2 for MERRA-2, and −61 and −11 W m−2 for ERA5, respectively. In the 8-month mean state, the LH and SH based on RW are higher than those without SFC by approximately 1 W m−2. The buoy estimates of LH and SH show higher magnitudes in summer and winter with different heat flux directions; however, the 8-month mean magnitudes of LH and SH in the buoy estimates are lower than those in the OAFlux and reanalysis due to the averaging processes. The mean LH in OAFlux is the highest, approximately 10 W m−2 higher than the corresponding buoy estimate; in contrast, the 8-month mean SH in OAFlux is relatively closer to that of the buoy estimates. The 8-month mean LH + SH in the atmospheric reanalysis products show better agreement with the buoy estimates than do those from OAFlux at this buoy location. However, the reanalyzed LH is approximately 5 W m−2 higher than the buoy-estimated LH, while the SH is approximately 5 W m−2 lower. The main biases among the different models come from the different algorithms employed, as demonstrated in a recent review by Yu (2019).

In general, the mean differences in LH and SH arise primarily from sampling issues, empirical estimates of parameters, and changes related to the observational systems (e.g., Yu et al. 2013). The uncertainties in atmospheric variables can accumulate and have significant impacts on the accuracy of the flux products, which can lead to large discrepancies in the different heat flux products. To summarize the comparisons of the statistics among OAFlux, MERRA-2, and ERA5 with respect to the buoy observations, Taylor diagrams displaying the correlation coefficients (CCs), standard deviations (STDs), and RMS differences between the three products and buoy observations are shown in Fig. 13. As shown, ERA5 has the smallest RMSs and highest CCs, followed by MERRA-2. MERRA-2 exhibits the smallest STDs for the differences compared to the buoy estimates both with and without SFC. OAFlux is less accurate with regard to the buoy computations with and without SFC. This indicates significant improvements in the newly updated flux reanalysis. A new high-resolution version of OAFlux (0.25° × 0.25°) with the COARE 4.0 algorithm has recently become available (e.g., Yu 2019); this version performs better at achieving a global heat budget in the global ice-free ocean (L. Yu, 2019, personal communication). After the new version of OAFlux is finalized and published, further comparisons will be performed to help determine the uncertainties in the fluxes.

6. Summary and discussion

This paper illustrates the importance of the RW speed on air–sea THFs. The THFs based on RW were estimated to be 2 W m−2 higher than those without SFC because the mean surface current in the southern Bohai Strait was an upwind flow. Nevertheless, although the mean discrepancy of the THFs was only 2 W m−2, the hourly difference in the heat flux between the use of RW and AW averaged 10 W m−2 in magnitude and ranged from 0 to 24 W m−2 as a result of rotating tidal currents in the marginal seas of China. Thus, it is important to include the SFC for the calculation of air–sea THFs and the study of upper-ocean dynamics, particularly in coastal seas with strong rotating tidal currents.

This paper also discusses the THF differences under stable and unstable atmospheric boundary conditions. In November, as the boundary layer is strongly convectively unstable, the differences are the same as the monthly results. However, in July, when the atmospheric boundary layer is stable, the LH (SH) including SFC is approximately 2 (1) W m−2 higher than that excluding SFC.

It should be noted that the buoy-based air–sea observations can provide only the fundamental air–sea variables for the calculation of THFs using bulk formulas. That is, there are no direct air–sea THF observations in terms of the eddy covariance method at the buoy location, and thus, it was not possible to provide independent estimates of THFs to determine whether the variability in the THFs is determined by the AW or RW. These high-resolution THFs are helpful in assessing the heat flux differences between observations and objectively analyzed/reanalysis products through comparisons. The newly released MERRA-2 and ERA5 produce excellent 8-month mean LH + SH estimates compared to the buoy estimates. In the mean state, compared with the buoy observations, OAFlux “overestimated” LH by approximately 10 W m−2. All three products exhibit good correlations (>0.8 at the 95% confidence level) with the LH + SH time series from the buoy observations. Furthermore, the daily THFs of ERA5 and MERRA-2 have superior STDs, CCs, and RMSs than OAFlux with respect to the buoy measurements. The effects of improving these products must still be determined, namely, with regard to their improved abilities to 1) describe the diurnal variations, especially at night, 2) reduce the errors in hourly/daily air–sea variables, 3) resolve extreme atmosphere events (e.g., cold air outbreaks), and, of course, 4) incorporate SFC in better bulk algorithms. The study by Song and Yu (2017) found that high-resolution models that resolve complex coastlines can provide net air–sea heat fluxes that are more physically reasonable than those provided by low-resolution models. It is supposed that the air–sea heat fluxes along a coastline with complex geographical and air–sea interaction processes should have significant effects on the regional and global energy balances. In the future, the coastal buoy station discussed in this work will be operated to calibrate atmospheric variables for long-term heat flux intercomparisons.

The global mean net air–sea heat flux [QNET; Eq. (9)] in the ice-free ocean is an important indicator of the global heat budget balance:
QNET=Qsw+Qlw+QTHF,
where Qsw, Qlw, and QTHF represent solar radiation, longwave radiation and THF, respectively. The value of QNET = 4 W m−2 is required to approximately balance the interior ocean heat budget over a controlled volume defined by isotherms (Walin 1982; Niiler and Stevenson 1982; Toole et al. 2004; Song 2012; Song and Yu 2013). However, the current atmospheric reanalysis and analyzed products show global mean QNET values ranging from approximately 5 to 30 W m−2 (Song and Yu 2013; Yu 2019), which are higher than the value actually required by the ocean heat budget balance. The dynamic mechanism for such great differences is the lack of energy constraints at the global air–sea boundary in the models. The higher estimates (2–3 W m−2) of THFs based on RW in this paper may help find solutions to balancing the global heat budget, in addition to the ways summarized in the introduction. In addition to the mean differences, the THFs still exhibit larger hourly biases associated with tidal fluctuations, diurnal variations and atmospheric stability.

SFC may be aligned with the surface wind according to the wind-driven ocean dynamics. However, over the global ocean, mesoscale eddies and western boundary currents are dominant dynamics and are not determined by local wind stress. Thus, the RW, namely, the synoptic winds relative to the multiscale SFC, should be carefully considered when calculating the air–sea THFs in different regions (e.g., equatorial regions and the western boundary current and its extensions). Modern altimetry observations (e.g., AVISO) provide the opportunity to assimilate SFC into bulk formulas for heat flux products. This paper took only a buoy in the Bohai Sea as an example to determine the importance of the RW in estimating the THFs. A global framework involving the combination of high-resolution wind vectors and SFC will be proposed in future studies.

As shown in this paper, the tidal dynamics contributed to the multiscale SFC and the RW speed. Tidal processes are some of the most significant factors in the marginal seas of China. In addition to the direct contribution of the SFC to the RW, tidal advection can modify the local temperature, and the salinity changes with the tidal frequency (Song et al. 2019). Tidal mixing affects the temperature and salinity in the upper-ocean mixed layer (e.g., Xia et al. 2006). Consequently, these are important parameters for the estimation of the THFs. Changes in the sea surface thermal and humidity state associated with tides can affect the calculation of the THFs, but the assessment of these changes is beyond the current scope of this paper.

Acknowledgments

The author extends his thanks to all the crew of the North Sea Branch of the SOA. This manuscript could not have been completed without their long-term fundamental observation work. The author appreciates the constructive comments and suggestions from the three anonymous reviewers.

Data availability statement: The OAFlux (version 3), MERRA-2 and ERA5 data were downloaded from http://www.oaflux.whoi.edu/, https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/and https://www.ecmwf.int/, respectively.

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  • Fig. 1.

    Location of the 10-m buoy in the Bohai Sea (black triangle). The colored background field is the annual (12 month) mean LH in 2016 (W m−2) from the ECMWF ERA5 project. The squares and dashed lines are the grids of OAFlux with a spatial resolution of 1° × 1°. The solid circles with dashed lines are the grids of ERA5 with a resolution of 0.25° × 0.25°. The diamonds with dashed lines are the grids of MERRA-2 with a resolution of 0.625° (zonal) × 0.5° (meridional). The nearest points from the OAFlux and new atmospheric reanalysis grids to the observing buoy location were used for the analysis. The incorporated frame (red) represents the study area of the Bohai Sea.