Observed Subdaily Variations in Air–Sea Turbulent Heat Fluxes under Different Marine Atmospheric Boundary Layer Stability Conditions in the Gulf Stream

Xiangzhou Song aKey Laboratory of Marine Hazards Forecasting, Ministry of Natural Resources, Hohai University, Nanjing, China

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Xuehan Xie aKey Laboratory of Marine Hazards Forecasting, Ministry of Natural Resources, Hohai University, Nanjing, China

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Yunwei Yan aKey Laboratory of Marine Hazards Forecasting, Ministry of Natural Resources, Hohai University, Nanjing, China

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Shang-Ping Xie bScripps Institution of Oceanography, University of California, San Diego, La Jolla, California

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Abstract

Based on data collected from 14 buoys in the Gulf Stream, this study examines how hourly air–sea turbulent heat fluxes vary on subdaily time scales under different boundary layer stability conditions. The annual mean magnitudes of the subdaily variations in latent and sensible heat fluxes at all stations are 40 and 15 W m−2, respectively. Under near-neutral conditions, hourly fluctuations in air–sea humidity and temperature differences are the major drivers of subdaily variations in latent and sensible heat fluxes, respectively. When the boundary layer is stable, on the other hand, wind anomalies play a dominant role in shaping the subdaily variations in latent and sensible heat fluxes. In the context of a convectively unstable boundary layer, wind anomalies exert a strong controlling influence on subdaily variations in latent heat fluxes, whereas subdaily variations in sensible heat fluxes are equally determined by air–sea temperature difference and wind anomalies. The relative contributions by all physical quantities that affect subdaily variations in turbulent heat fluxes are further documented. For near-neutral and unstable boundary layers, the subdaily contributions are O(2) and O(1) W m−2 for latent and sensible heat fluxes, respectively, and they are less than O(1) W m−2 for turbulent heat fluxes under stable conditions.

Significance Statement

High-resolution buoy observations of air–sea variables in the Gulf Stream provide the opportunity to investigate the physical factors that determine subdaily variations in air–sea turbulent heat fluxes. This study addresses two key points. First, the observed subdaily amplitudes of heat fluxes are related to various processes, including wind fields and air–sea thermal effect differences. Second, the global sea surface heat budget is known to not be in near-zero balance and it ranges from several to tens of watts per square meter. Therefore, consideration of the relatively strong influence of subdaily variability in air–sea turbulent heat fluxes could provide a new strategy for solving the global heat budget balance problem.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xiangzhou Song, xzsong@hhu.edu.cn

Abstract

Based on data collected from 14 buoys in the Gulf Stream, this study examines how hourly air–sea turbulent heat fluxes vary on subdaily time scales under different boundary layer stability conditions. The annual mean magnitudes of the subdaily variations in latent and sensible heat fluxes at all stations are 40 and 15 W m−2, respectively. Under near-neutral conditions, hourly fluctuations in air–sea humidity and temperature differences are the major drivers of subdaily variations in latent and sensible heat fluxes, respectively. When the boundary layer is stable, on the other hand, wind anomalies play a dominant role in shaping the subdaily variations in latent and sensible heat fluxes. In the context of a convectively unstable boundary layer, wind anomalies exert a strong controlling influence on subdaily variations in latent heat fluxes, whereas subdaily variations in sensible heat fluxes are equally determined by air–sea temperature difference and wind anomalies. The relative contributions by all physical quantities that affect subdaily variations in turbulent heat fluxes are further documented. For near-neutral and unstable boundary layers, the subdaily contributions are O(2) and O(1) W m−2 for latent and sensible heat fluxes, respectively, and they are less than O(1) W m−2 for turbulent heat fluxes under stable conditions.

Significance Statement

High-resolution buoy observations of air–sea variables in the Gulf Stream provide the opportunity to investigate the physical factors that determine subdaily variations in air–sea turbulent heat fluxes. This study addresses two key points. First, the observed subdaily amplitudes of heat fluxes are related to various processes, including wind fields and air–sea thermal effect differences. Second, the global sea surface heat budget is known to not be in near-zero balance and it ranges from several to tens of watts per square meter. Therefore, consideration of the relatively strong influence of subdaily variability in air–sea turbulent heat fluxes could provide a new strategy for solving the global heat budget balance problem.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xiangzhou Song, xzsong@hhu.edu.cn

1. Introduction

In the context of turbulent fluctuations and Reynolds stresses, air–sea turbulent heat fluxes, including evaporative surface latent heat flux and conductive sensible heat flux, play a central role in air–sea interactions (Cronin et al. 2019; Yu 2019). Due to the greater air–sea differences in humidity and temperature (Renfrew and Moore 1999; Kelly et al. 2010), air–sea turbulent heat fluxes are greater in the midlatitude western boundary current systems of the Northern Hemisphere than in other areas. Air–sea turbulent heat fluxes balance the surface heat budget against incoming solar radiation at the air–sea interface (Trenberth et al. 2009). Anomalies in turbulent heat fluxes are strongly correlated with variations in air–sea variables, particularly the sea surface temperature (SST). Additionally, air–sea turbulent heat fluxes tend to damp SST anomalies via air–sea feedback (Frankignoul 1985; Frankignoul et al. 1998; Frankignoul and Kestenare 2002; Park et al. 2005; Hausmann et al. 2016).

The surface turbulent heat flux can indirectly affect the surface wind by modulating the horizontal SST gradient due to the SST–wind coupling relationship at the air–sea interface. SST–wind couplings have been investigated throughout the global ocean (Chelton et al. 2001, 2004; Xie 2004; O’Neill et al. 2005, 2010; Samelson et al. 2006, 2020; Small et al. 2008; Perlin et al. 2004; Schneider and Qiu 2015). The SST–wind coupling is closely associated with the atmospheric boundary layer stability-induced modulation of the vertical penetration of surface-generated turbulence and the vertical mixing of momentum. In the context of SST–wind relationships, surface fluxes play a central role in determining atmospheric boundary layer winds in response to mesoscale SST perturbations or SST gradients (Lindzen and Nigam 1987; Song et al. 2009; Koseki and Watanabe 2010; Perlin et al. 2004; Samelson et al. 2020). For example, higher surface heat fluxes can lead to deeper penetration of momentum fluxes, while relatively low upward heat fluxes can help trap momentum fluxes near the surface (Samelson et al. 2020). Thus, understanding air–sea turbulent heat flux variations is vital for research on air–sea interactions.

Many studies have documented decadal to interannual variations (Cayan 1992; Yu 2007; Song and Yu 2012) and synoptic weather-scale variations (Lin et al. 2009; Song et al. 2021) in air–sea turbulent heat fluxes. Herein, we focus on subdaily air–sea turbulent heat fluxes. Previous studies have indicated that resolving the subdaily variations in the turbulent heat fluxes in coupled air–sea processes can enhance simulations and predictions from the convective scale (Webster et al. 1996; Slingo et al. 2003) to the intraseasonal scale (Shinoda 2005; Seo et al. 2014) to interannual patterns, including ENSO (Bernie et al. 2008). Several studies have quantified heat flux changes induced by subdaily SST variability. Schiller and Godfrey (2005) estimated an average increase in net heat flux of 10 W m−2 based on a one-dimensional coupled ocean–atmosphere model at a mooring in the tropical Pacific. Ward (2006) used profilers deployed in the Gulf of California to estimate net heat fluxes using bulk SST and skin temperature, and the difference was found to be close to 60 W m−2. Clayson and Bogdanoff (2013) used parameterized datasets to determine that the global mean climatological heat flux variability induced by subdaily SST changes is approximately 4.45 W m−2, while the average heat flux variability in tropical oceans reaches 10 W m−2. In addition, Masson et al. (2012) suggested that the ENSO amplitude decreases by 15% when subdaily SST variations are not accounted for. Subdaily variations in SST are confirmed to be a key factor in surface heat fluxes and their balance.

Considering the existence of coupled SST–wind relationships, the contribution of subdaily wind variations to the air–sea heat flux also needs to be investigated. First, wind gustiness is one of the strongest contributors to surface heat fluxes (Fairall et al. 2003), particularly when convection is active. Atmospheric cold pools generated by convection over the ocean have several direct effects on surface fluxes (Barnes and Garstang 1982; Young et al. 1995; Jabouille et al. 1996; Saxen and Rutledge 1998; de Szoeke et al. 2017). Surface winds increase in cold pools when moving toward the warm pools where convection occurs, thereby enhancing surface heat fluxes (Yokoi et al. 2014). In addition, the surface latent heat flux increases in response to both increases in surface winds over cold pools and peaks over warm pools induced by an enhancement of the surface wind gustiness (Wofsy and Kuang 2012). Second, high-frequency wind variability strongly contributes to climatological air–sea turbulent heat fluxes by increasing the surface daily mean wind speed (Ogawa and Spengler 2019; Wu et al. 2020a,b). For example, Ogawa and Spengler (2019) reported that the global climatological latent heat flux is dominated by submonthly vector wind variations, as these variations nonlinearly enhance the midlatitude surface wind speed. Additionally, Wu et al. (2020b) demonstrated the importance of weather-scale vector wind variability for climatological latent heat flux in tropical oceans. Therefore, focusing on subdaily wind variations can further advance the understanding of SST–wind coupling. We choose one of the strongest regions of SST fronts, namely, the western boundary current, to begin our study.

To date, most studies of the subdaily variability have been conducted based on model simulations, which introduce additionally uncertainty into the estimation process. The inclusion of in situ observations, such as buoys, can improve the estimation accuracy to some extent (Bentamy et al. 2017; Cronin et al. 2019; Yu 2019). However, only a few studies have investigated turbulent heat flux changes caused by subdaily variations using in situ observations due to the lack of high-resolution measurements. For example, evident subdaily air–sea turbulent heat flux variations have recently been reported in western boundary current systems (Clayson and Edson 2019), coastal seas (Song 2020), and tropical oceans (Yan et al. 2021). Using high-resolution (hourly) air–sea measurements from the global tropical moored buoy array, Yan et al. (2021) found significant subdaily variations in the tropical surface latent heat flux, with a maximum magnitude exceeding 20 W m−2. Additionally, they noted that subdaily variations in SST are the primary contributors in the majority of tropical oceans, whereas subdaily variations in wind speed or air humidity are more important in other regions. Based on a 3-h satellite air–sea flux product (SeaFlux-CDR version 2), Clayson and Edson (2019) estimated the global subdaily variations in air–sea turbulent fluxes and demonstrated a regional maximum in the winter over the western boundary current regions. These authors suggested that further work is necessary to fully establish the statistics and drivers of the processes involved. Following their footsteps, we further examine the subdaily variations in air–sea turbulent heat fluxes over the Gulf Stream.

This paper explores the drivers of subdaily air–sea turbulent heat flux variations under different boundary layer states in the Gulf Stream. The approach includes the use of available hourly or 30-min observations of air–sea variables from various buoys: operational buoys provided by the National Data Buoy Center (NDBC) and an air–sea observing buoy provided by the Climate and Ocean: Variability, Predictability and Change (CLIVAR) Mode Water Dynamic Experiment. Specifically, 14 buoys with measurements spanning nearly one whole year were selected to broadly cover the Gulf Stream region (Fig. 1 and information in the appendix) and to depict the subdaily air–sea turbulent heat flux variations.

Fig. 1.
Fig. 1.

Locations of the air–sea buoys (yellow dots; Table 1) within the Gulf Stream region used in this study. The buoys are numbered (green markers) according to their latitude from north to south. The colored background is the 2011 annual mean (W m−2) standard deviation of hourly latent heat flux, where the 45-W m−2 contour is highlighted by the white line based on the fifth major global reanalysis produced by European Centre for Medium-Range Weather Forecasts (ECMWF) (ERA5). The ERA5 annual mean SST is incorporated as black curves.

Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-24-0003.1

Despite the significant progress made over the past three decades in quantifying and estimating surface fluxes (Cronin et al. 2019; Yu 2019), the use of flux products to close the surface heat budget globally remains challenging. Yu (2019) integrated the mean heat fluxes across ocean basins worldwide and revealed a large imbalance with a typical value of ∼O(10–20) W m−2. In addition, both the mean turbulent heat fluxes and their uncertainties in parameterization-based flux estimates are greatest in the western boundary current regions. One of the main reasons for these uncertainties is a lack of information about subdaily variations in air–sea variables (Cronin et al. 2019). Another question thus arises: Similar to our findings in a recent study on tropical oceans (Yan et al. 2021), can the estimation of the mean latent heat flux in the western boundary currents be improved by considering the subdaily influences of air–sea variables? If so, this work might provide insight into the balance between regional and global surface heat budgets, given the influence of latent heat flux in western boundary current regions and tropical oceans.

This study has three aims: 1) to provide a basic quantitative estimate of the variations in air–sea turbulent heat fluxes in the Gulf Stream, 2) to investigate the physical drivers of these variations under different boundary layer stability regimes, and 3) to determine the contribution of subdaily variations to mean estimates of the air–sea turbulent heat fluxes in a certain period. The remainder of this paper is organized as follows. Section 2 introduces the algorithms and data used in this study. The buoy-based quantitative heat flux variations are analyzed in section 3. Section 4 presents physical explanations of the subdaily variations in the air–sea turbulent heat fluxes in the Gulf Stream region. Section 5 addresses the magnitude of subdaily variations in the mean air–sea turbulent heat fluxes under the same marine atmospheric boundary layer stability conditions. Finally, the study is summarized and discussed in section 6.

2. Methods and data

a. Heat flux calculation with a bulk algorithm

According to Monin–Obukhov similarity theory (Monin and Obukhov 1954), latent and sensible heat fluxes can be conventionally estimated using air–sea variables in bulk formulas (Liu et al. 1979; Fairall et al. 2003; Edson et al. 2013):
QLH=ρaLecE|uz|(qsqa),
QSH=ρacpch|uz|(TsTa),
where QLH and QSH represent the latent and sensible heat fluxes, respectively; ρa is the air density; Le is the latent heat flux of evaporation; cp is the specific heat capacity at a constant pressure; cE and ch are the turbulent exchange coefficients for latent heat flux (Dalton number) and sensible heat flux (Stanton number), which are calculated based on semiempirical mixing-length theory and are not constant; |uz| is the vector wind speed; and Δq = qsqa and ΔT = TsTa represent the differences in the specific humidity and temperature between sea surface and near-surface air, respectively, for latent and sensible heat fluxes. The qs = 0.98 × qsat(SST, SLP), where qsat denotes the specific humidity at saturation (Buck 1981) and SLP represents the sea level pressure. In this study, a bulk algorithm called Coupled Ocean–Atmosphere Response Experiment version 3.5 (COARE 3.5) was used to compute the heat flux (Fairall et al. 1996, 2003; Edson et al. 2013).
The marine atmospheric boundary layer stability can be estimated by ζ = z/L, where z is the height of the turbulent exchange coefficient and L is the Obukhov length scale (Monin and Obukhov 1954):
L=u*2κgT¯T*,
where κ is the von Kármán constant, which is set to 0.4 in this study (Dyer 1974; Högström 1988; Fairall et al. 1996, 2003); u*=κz(u¯/z) denotes the frictional velocity; g is the gravitational constant of acceleration; T¯ is the mean temperature in the boundary layer; and T*=(ωθ¯/u*) (ω′ and θ′ are the fluctuations in the vertical velocity and temperature). The L represents the ratio of the work done by the Reynolds stress to that done by buoyancy forces. The boundary layer stability is classified into three regimes: stable (ζ > 0.1), near-neutral (−0.4 ≤ ζ ≤ 0.1), and unstable (ζ < −0.4) (Large and Pond 1981, 1982; Plagge et al. 2012; Song 2020).

b. Buoy observations

The observations from buoy maintained by the NDBC provide data for the air–sea variables that can be used to estimate the air–sea turbulent heat fluxes based on the above bulk formulas. The SST and meteorological parameters such as the surface air temperature, dewpoint, SLP, and wind speed at a specified observational height can be directly obtained. A detailed technical description can be found in Table 1 and Fig. A1. In this study, the absolute wind speed relative to Earth is used to calculate the heat fluxes in the Gulf Stream without considering the surface current, which may give rise to uncertainties in latent and sensible heat fluxes ranging from −18 to 20 and −4 to 4 W m−2, respectively (Song 2021). However, surface currents are assumed to not strongly affect our investigation of subdaily variations because of the dominance of the geostrophic current in the Gulf Stream region.

Table 1.

Information on the buoys in the Gulf Stream region used for this work shown in Fig. 1. The buoys listed in this paper are organized by both their World Meteorological Organization (WMO) number and their latitudes from north to south. The numbers in parentheses following the variables are the observational height with reference to the sea surface. Negative values represent an underwater depth for the SST, and a value of zero denotes the sea surface. The whole calendar year was chosen for each buoy, with the percentage of measurements in the year listed in column 6. The water depths for the buoys range from 16 m (11-41008) to 4500 m (4-CLIMODE); 1 n mi = 1.852 km.

Table 1.

3. Amplitudes of the subdaily air–sea turbulent heat flux variations and marine atmospheric boundary layer stability

a. Amplitudes of the subdaily air–sea turbulent heat flux variations and their seasonality

The amplitude of the subdaily variations is defined by their standard deviation, in which the daily standard deviations of the subdaily variations (Qamp) in the hourly air–sea turbulent heat fluxes are estimated based on the following relationship:
Qamp=1N1i=1N|Q(i)μ|2,
where μ=(1/N)i=1NQ(i) is the mean value of the heat fluxes for hourly observational samples on a given day.

Figure 2 shows the annual mean amplitudes of these subdaily variations at 14 buoy stations in the North Atlantic, and Fig. 3 shows their monthly mean amplitudes. Three major features can be identified. First, the observed subdaily amplitudes for latent heat fluxes are greater than those for sensible heat fluxes. The annual mean observed amplitude of the subdaily variations in latent heat fluxes at all stations is 40 W m−2, compared to 15 W m−2 for sensible heat fluxes. Second, larger subdaily variation amplitudes are detected at 35°N, where the Gulf Stream is deflected northeast off the East Coast of the United States. Among the 14 stations, the maximum monthly mean amplitude of the subdaily variations in latent heat flux is 79 W m−2 at Station 4 in December, while that in sensible heat flux is 47 W m−2 at Station 2 in February. Third, the amplitudes of the subdaily variations in latent and sensible heat fluxes exhibit apparent seasonal cycles (Figs. 3a,b). The mean amplitudes of the latent and sensible heat fluxes are 52 and 25 W m−2, respectively, in boreal winter from November to February, while those in boreal summer from May to August are only 27 and 6 W m−2, respectively. This phenomenon is attributed to the enhanced wind speed and air–sea humidity and temperature differences in winter, as even small changes in the wind speed or air–sea humidity or temperature difference can induce large-amplitude subdaily variations.

Fig. 2.
Fig. 2.

Annual mean amplitudes (Qamp) of the subdaily variations in (a) latent heat fluxes and (b) sensible heat fluxes in the Gulf Stream based on the buoy observations. Note the different color scales and dot sizes for latent and sensible heat fluxes.

Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-24-0003.1

Fig. 3.
Fig. 3.

Monthly mean amplitudes (Qamp) of the subdaily variations in (a) latent heat fluxes (W m−2) and (b) sensible heat fluxes (W m−2) over one calendar year. The results for months with observations on fewer than 10 days are not shown. The 14-buoy monthly mean values of Qamp for the latent and sensible heat fluxes are shown in (c) and (d), respectively.

Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-24-0003.1

b. Marine atmospheric boundary layer stability determined from buoy observations

The observed marine atmospheric boundary layer stability (ζ = z/L) is determined by Eq. (3). Figure 4 shows the proportions of the three regimes based on the hourly observations from all 14 buoys over 1 year. Near-neutral stability (−0.4 ≤ ζ ≤ 0.1) is predominant, accounting for 79% of all observational samples, followed by unstable (14%) and stable (7%) conditions. Stable boundary conditions are frequently observed at Stations 1 and 2, with percentages exceeding 20%. However, stable boundary conditions are relatively scarce south of Stations 1 and 2, where large air–sea temperature differences favor convective instability. Accordingly, the proportion of stations recording an unstable boundary layer increases from 4% at Station 1 to a mean of 15% south of Stations 1 and 2.

Fig. 4.
Fig. 4.

Percentages of different boundary layer stability regimes estimated based on Eq. (3): stable (ζ > 0.1; blue), near-neutral (−0.4 ≤ ζ ≤ 0.1; orange), and unstable (ζ < −0.4; yellow).

Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-24-0003.1

The boundary layer stability estimated from hourly and 10-min data often varies among different regimes within a given day, making quantification of the processes that contribute to the subdaily air–sea turbulent heat flux variations difficult. Thus, the first and most important step is to investigate the drivers of subdaily air–sea turbulent heat flux variations under the same continuous boundary layer stability conditions. Accordingly, this study focuses on the contributions of the wind speed and air–sea humidity and temperature differences to the high-frequency variations in air–sea turbulent heat fluxes for all three boundary layer stability regimes. To accomplish this task, observational durations under constant ζ = z/L are chosen. Given the dominance of near-neutral conditions in the Gulf Stream, for which the percentage is approximately 4 times that of the other conditions (Fig. 4), stations with continuous observations for more than 96 h are selected for the near-neutral regime, whereas stations with continuous observations for more than 24 h are chosen for stable and unstable boundary conditions. Furthermore, to better investigate the subdaily variations, we screen samples with a duration of exactly 24 h in the above selected samples using a 24-h sliding method.

Figure 5 shows the number of segments identified for each of the three different stability regimes at each of the 14 buoy locations. Only six buoys contain segments satisfying the above criterion for stable boundary layer conditions across 1 year, for which Stations 1 and 2 are representative. In contrast, 13 of all 14 buoys exhibit long continuous periods of near-neutral and unstable boundary layer conditions. In total, the numbers of 24-h segments chosen for stable, near-neutral, and unstable boundary conditions are 1164, 13 157, and 459, respectively. Table 2 shows the buoy stations with the longest duration cases, which have the largest number of 24-h samples with the same boundary layer stability regime, and their basic observations. Under stable boundary conditions, the latent and sensible heat fluxes are negative, which indicates heat transfer from the atmosphere to the ocean. At Station 1, this process persists for the dates from 1 to 7 July 2008, with mean latent and sensible heat fluxes of −11 and −5.7 W m−2, respectively. The longest durations of the near-neutral (Station 10-41002) and unstable (Station 13-41010) boundary conditions are also summarized in Table 2.

Fig. 5.
Fig. 5.

Numbers of 24-h segments from the observations at each station spanning 1 year with the same continuous boundary layer stability regime: stable (ζ > 0.1; blue), near-neutral (−0.4 ≤ ζ ≤ 0.1; orange), and unstable (ζ < −0.4; yellow).

Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-24-0003.1

Table 2.

Summary of the 24-h mean estimated air–sea heat fluxes and associated meteorological variables during the longest durations of the three boundary layer stability regimes at Stations 1 (stable), 10 (near-neutral), and 13 (unstable). The station number, date, latent heat flux (W m−2), sensible heat flux (W m−2), air–sea temperature difference (°C), and wind speed (m s−1) are listed for each regime.

Table 2.

4. Determining the factors that control subdaily air–sea turbulent heat flux variations

We apply the following linearized formulas to study the physical drivers of subdaily air–sea turbulent flux anomalies under different stability regimes (Tanimoto et al. 2003; Song and Yu 2012):
QLH=C1{|uz|(Δq)¯+|uz|¯(Δq)+[|uz|(Δq)|uz|(Δq)¯]},
QSH=C2{|uz|(ΔT)¯+|uz|¯(ΔT)+[|uz|(ΔT)|uz|(ΔT)¯]},
where the overbar and prime symbols denote the 24-h average and the subdaily variable anomalies, respectively, under the same boundary layer stability regime. The first two decomposed terms on the right-hand side (rhs) of Eqs. (5) and (6) represent the effects of wind anomalies and thermal anomalies (humidity and temperature), respectively, and the last two terms represent the effects of nonlinearities. The |uz|¯ is the 24-h scalar average of the horizontal wind speed. In addition, C1 and C2 are set to the 24-h averages of ρaLecE and ρacpch, respectively. This approximation is made in order to isolate the contributions by thermal versus wind anomalies.

a. Special case studies of the longest durations of the three boundary layer stability regimes

Figure 6 shows the hourly and half-hourly precision air–sea turbulent heat flux anomalies and their contributing terms based on Eqs. (5) and (6) under the longest durations of the three continuous stability regimes at the three stations. The mean correlation coefficients over all 24-h samples—for example, r[QLH,C1|uz|(Δq)¯]—between the air–sea turbulent heat flux anomalies and contributing terms are summarized in Table 3. The boundary layer is strongly stable at Station 1-44011 at the beginning of July, with a mean air–sea temperature difference of −2.1°C. Wind turbulence tends to overcome the buoyancy effect in the boundary layer and contributes to high-frequency variations in latent and sensible heat fluxes. The subdaily variations in latent and sensible heat fluxes show better consistency with those in the wind speed anomaly term (Figs. 6a,d). Hence, the wind speed plays a dominant role in the subdaily variations in latent and sensible heat fluxes (r ≈ 0.9; Table 3). This correlation coefficient is greater than that for the air–sea differences (r ≈ 0.6), and the nonlinear terms are much smaller and can be neglected, as they are not statistically significant.

Fig. 6.
Fig. 6.

Hourly anomalies in latent and sensible heat fluxes (black) and three contributing factors from the rhs of Eqs. (5) and (6), namely, the wind speed anomalies (red), thermal anomalies (blue), and nonlinearities (green). The longest durations of the analyzed stability regimes listed in Table 2 are chosen as representative case studies for (top) stable, (middle) near-neutral, (bottom) and unstable boundary conditions. The time series are the mean results of the individual flux anomaly terms over all 24-h samples at the same time, and the colored shading represents the corresponding standard deviation.

Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-24-0003.1

Table 3.

Mean correlation coefficients r between the hourly air–sea turbulent heat flux anomalies and the hourly anomalies in the wind speed, air–sea differences, and nonlinearities. The numbers outside the parentheses are the mean results based on all 24-h samples obtained from the three stations for the longest duration of the three continuous stability regimes, as shown in Fig. 6, and the numbers in parentheses are the average of the correlation coefficients from all 14 buoys under the same continuous stability regimes.

Table 3.

The situation is quite different for the near-neutral boundary layer condition (−0.4 ≤ ζ ≤ 0.1). In this case, the air–sea temperature difference is typically weaker than those in the stable and unstable cases. For example, the mean air–sea temperature difference is only 0.8°C at Station 10-41001 during the period from 1 to 17 May 2015. The role of the wind speed anomaly is weakened when the air–sea temperature and humidity differences are suppressed, with smaller correlation coefficients r of 0.71 and 0.59 for the latent and sensible heat fluxes, respectively (Figs. 6b,e). However, the thermal effect anomalies more strongly control the subdaily sensible heat flux variations than the subdaily latent heat flux variations. The r value between the latent heat flux anomaly term and the air–sea humidity difference anomaly term is only 0.76 (Fig. 6b), while that between the sensible heat flux anomaly term and the air–sea temperature difference anomaly term reaches 0.92 (Fig. 6e). The nonlinear effects play a minor role in the hourly latent and sensible heat flux anomalies.

When the boundary layer is unstable with an air–sea temperature difference of 1.3°C (14–18 June 2015, Station 13-41010), the wind speed anomalies dominate the subdaily variations in latent heat fluxes, similar to the situation under a continuously stable boundary layer. Wind speed anomalies play a central role in large air–sea humidity differences, with high-frequency wind variations serving to blow away local water vapor and remove heat, which helps establish a new vapor balance at the sea surface. A high correlation coefficient (r = 0.83) is observed, confirming the consistent variations shown in Fig. 6c. However, the situation for the sensible heat flux is different from that for the latent heat flux. Under a continuously unstable convective boundary layer, the subdaily variations in the air–sea temperature difference dominate the subdaily variations in sensible heat fluxes, with a correlation coefficient of 0.85, while the role of the wind speed anomalies is much weaker. The nonlinear effects on latent and sensible heat fluxes are also negligible and not statistically significant under a continuously unstable boundary layer.

b. Mean results based on all the selected samples from the 14 buoys in the Gulf Stream

In addition to the above special case studies of the longest continuous observations under the same boundary layer stability regime, the mean results based on all the selected segments from the 14 buoys shown in section 3 are explored in this section. In general, for all stability regimes, the scatterplots of the correlation coefficients for the latent and sensible heat flux anomalies and the overall mean correlation coefficients listed in Table 3 indicate that the results of the preceding physical analyses of these three special cases are significant. First, the dominant role of wind speed anomalies in the subdaily variations in latent and sensible heat fluxes is evident, given the high correlation coefficient of 0.9 under stable boundary layer conditions. In contrast, the contributions of the hourly anomalies in the air–sea temperature and humidity differences are not only secondary but also important (r > 0.6). Second, the situations under near-neutral boundary conditions are different from those under stable boundary conditions. The high-frequency anomalies of the air–sea temperature and humidity differences are the major drivers (r ≈ 0.8) of the subdaily variations in latent and sensible heat fluxes under near-neutral boundary conditions, respectively. The wind speed term plays an equivalent but slightly weaker role than the air–sea temperature and humidity differences. Third, under convective instability, the wind speed anomalies control the subdaily variations in latent heat fluxes with r > 0.8, whereas the subdaily variations in sensible heat fluxes are dominated by a combination of high-frequency anomalies in the wind speed and air–sea temperature difference, with both correlation coefficients close to 0.8. Overall, the special case studies and the mean results yield similar conclusions regarding the physical drivers controlling hourly latent and sensible heat flux anomalies, which means that the reliability of the conclusions is confirmed by combining extreme and mean values.

5. Physical processes that influence the subdaily variation amplitudes and mean magnitudes under the same boundary layer stability regime

a. Subdaily variation amplitudes associated with the wind speed and air–sea humidity and temperature differences

The physical processes controlling the subdaily variation amplitudes of air–sea turbulent heat fluxes under the same continuous boundary layer stability regime are investigated in this section. The original amplitudes of the latent and sensible heat fluxes can be estimated using Eq. (4). The 24-h mean |uz|, Δq, and ΔT are used to examine the roles of the wind speed, air–sea humidity difference, and air–sea and temperature difference, respectively, in the amplitudes of the latent and sensible heat flux variations. The latent heat flux amplitudes are estimated using the following relationships:
QLH(Δq¯)=ρaLecE|uz|(Δq¯),
QLH(|uz|¯)=ρaLecE|uz|¯(Δq),
where the parameters are the same as those in Eqs. (1) and (2) and the overbars over the air–sea humidity difference and wind speed indicate the 24-h means when calculating the latent heat flux. Similarly, the sensible heat flux amplitudes can be estimated by substituting the corresponding turbulent coefficients and air–sea temperature difference. The actual subdaily variation amplitudes are estimated based on Eq. (4).

Figure 7 shows all the subdaily variation amplitudes for the latent and sensible heat fluxes. The most significant feature is the evident suppression of the subdaily amplitude variations with constant wind speed and air–sea humidity and temperature differences compared to the full amplitudes using the original latent and sensible heat fluxes. This occurs in all the cases. However, the reduction in the amplitudes differs under different stability regimes, which is closely associated with the dominant physical driver, as shown in Table 3. Under near-neutral boundary layer stability, the air–sea humidity and temperature differences dominate the subdaily variations in latent and sensible heat fluxes, respectively. If Δq or ΔT is set to the 24-h mean value, then the subdaily variation amplitudes are greatly reduced. On average, the latent and sensible heat flux amplitudes are reduced by 38% and 71%, respectively, based on all the results from the 14 buoys. Under a stable boundary layer, where wind speed anomalies are the major driver of subdaily air–sea turbulent heat flux variations, the latent and sensible heat flux amplitudes are reduced by 59% and 68% when using the 24-h mean wind speed, respectively. Similar results can be found for the special case studies using the longest observation durations with the same continuous boundary layer stability regime at Stations 1-44011, 10-41001, and 13-41010. These results for all boundary stability regimes confirm the findings listed in Table 3.

Fig. 7.
Fig. 7.

Amplitudes (Qamp) of subdaily variations in (a) latent (W m−2) and (b) sensible (W m−2) heat fluxes calculated using Eq. (4), which are the 24-h mean results based on the observations from all 14 buoys and for all boundary stability regimes. The blue bars indicate the originally estimated amplitudes. The orange and yellow bars represent the amplitudes of subdaily variations in latent and sensible heat fluxes calculated using the 24-h mean air–sea humidity or temperature difference and wind speed, respectively. The percentages marked above the bars indicate the reduction in the amplitude when using the mean Δq, ΔT, and |uz| compared to the original amplitude.

Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-24-0003.1

b. Role of subdaily air–sea variable variations in subdaily air–sea turbulent heat flux variations

To study the contributions of subdaily variations in wind speeds and thermal effects (temperature and humidity) to subdaily air–sea turbulent heat flux variations under the same boundary layer stability regime, the air–sea variables are divided into two components, as described by Yan et al. (2021):
{uz=(uz)subdaily+(uz)meanTs=(Ts)subdaily+(Ts)meanqa=(qa)subdaily+(qa)meanTa=(Ta)subdaily+(Ta)mean,
where (uz)subdaily, (Ts)subdaily, (qa)subdaily, and (Ta)subdaily are the subdaily variations in the wind speed, SST, air-specific humidity, and surface air temperature, respectively, and (uz)mean, (Ts)mean, (qa)mean, and (Ta)mean are the 24-h mean wind scalar, SST, air-specific humidity, and surface air temperature, respectively. The air–sea turbulent heat fluxes associated with the subdaily variations in the relevant variables are calculated as follows (Tanimoto et al. 2003; Song and Yu 2012; Yan et al. 2021):
{(QLH)ALLsubdaily=(QLH)ρaLecE|(uz)mean|{qs[(Ts)mean](qa)mean}(QLH)uzsubdaily=(QLH)ρaLecE|(uz)mean|(qsqa)(QLH)Δqsubdaily=(QLH)ρaLecE|uz|{qs[(Ts)mean](qa)mean}(QLH)Tssubdaily=(QLH)ρaLecE|uz|{qs[(Ts)mean]qa}(QLH)qasubdaily=(QLH)ρaLecE|uz|[qs(qa)mean],
{(QSH)ALLsubdaily=(QSH)ρacpch|(uz)mean|[(Ts)mean(Ta)mean](QSH)uzsubdaily=(QSH)ρacpch|(uz)mean|(TsTa)(QSH)ΔTsubdaily=(QSH)ρacpch|uz|[(Ts)mean(Ta)mean](QSH)Tssubdaily=(QSH)ρacpch|uz|[(Ts)meanTa](QSH)Tasubdaily=(QSH)ρacpch|uz|[Ts(Ta)mean],
where the variables in Eqs. (10) and (11) have the same meanings as those in Eqs. (1) and (2), respectively. The variables (QLH)ALLsubdaily and (QSH)ALLsubdaily are the latent and sensible heat fluxes induced by the variability in all the subdaily air–sea variables, respectively. The other variables are the latent or sensible heat fluxes influenced by the variability in the subdaily individual variables, including those induced by wind (uzsubdaily), specific humidity (Δqsubdaily, Δqasubdaily), and temperature (ΔTsubdaily, Tssubdaily, and Tasubdaily).

The mean results of Eqs. (10) and (11) are estimated and shown in Figs. 8 and 9. In terms of the air–sea interface regime in the Gulf Stream, a stable boundary layer characterized by heat transfer from the atmosphere to the ocean is rare, and its latent and sensible heat fluxes induced by subdaily variable variations are obviously lower than those in the other stability cases. The contributions to latent and sensible heat fluxes induced by subdaily variations in all the variables for all buoy stations are −0.8–0.2 and −0.7–0.1 W m−2 (Figs. 8a and 9a), and their mean contributions, defined as the average absolute values, are 0.4 and 0.3 W m−2, respectively. Negative values are due to the background SST field being lower than the air temperature field in the stable boundary layer, while positive average results are due to the presence of critical boundary conditions. The latent heat flux induced by subdaily variations in all the variables under near-neutral boundary stability presents the largest spatial variability compared to that under the other conditions, from approximately −4.3 to 3.1 W m−2 (Fig. 8b), with an average absolute value of 2.0 W m−2. This result may be due to the large spatial variability in the subdaily wind speed and air-specific humidity variability, with both of their standard deviations exceeding 4 W m−2 (Fig. 8e). The sensible heat flux contributions from all the subdaily variable variations are from approximately −0.9 to 1.1 W m−2 (Fig. 9b), and the average absolute value is 0.5 W m−2. The magnitude of the flux contributions from subdaily variable variations in the unstable case is comparable to that in the near-neutral case, with corresponding latent and sensible heat flux changes ranging from −3.0 to 1.0 W m−2 and from −1.0 to 3.0 W m−2 (Figs. 8c and 9c) and mean absolute values of 1.1 and 0.6 W m−2, respectively.

Fig. 8.
Fig. 8.

(a) Mean subdaily latent heat flux variations (W m−2) induced by subdaily variations in all the variables over all 24-h samples for individual buoy stations and (d) mean subdaily latent heat flux variations (W m−2) for all buoy stations caused by subdaily variations in all the variables (ALL; green) and individual variables, including wind speed (uz; blue), air–sea specific humidity difference (Δq; orange), SST (Ts; yellow), and air-specific humidity (qa; purple). (b),(e) and (c),(f) As in [(a) and (d)], but for near-neutral and unstable boundary layer conditions, respectively. The numbers near the colored dots in (a)–(c) represent the buoy station numbers. The values near the bars in (d)–(f) indicate the standard deviation of the subdaily variations in latent heat flux from all the buoy stations (W m−2), reflecting the magnitude of the spatial difference in the subdaily contributions.

Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-24-0003.1

Fig. 9.
Fig. 9.

As in Fig. 8, but for the sensible heat flux. Note that the humidity terms for the latent heat fluxes are replaced by temperature terms for the sensible heat fluxes.

Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-24-0003.1

The choices of the segments in this study depend on the boundary layer regime, which avoids the effects of seasonal cycles, as indicated in Fig. 3. However, note that seasonal signals may introduce additional errors into the mean values (standard deviations in Figs. 8 and 9). In addition, the 14 buoy observations from north to south cover a large Gulf Stream region, with different structures of multiscale ocean dynamics and air–sea interactions, which may also potentially contribute to the total statistical errors. Even with errors associated with seasonal variations and geographical locations, the total contributions of the subdaily variations, as listed above, indicate similar error magnitudes to those estimated by Tomita et al. (2010). These authors showed an average latent heat flux error of 1 W m−2 for subdaily variables relative to the daily average variables based on the wind scalar averaging method in the northwestern Pacific.

6. Conclusions

In this paper, data from 14 air–sea buoys maintained by the NDBC are used to address three scientific issues. First, the mean amplitudes of the subdaily variations in latent and sensible heat fluxes at all stations are 40 and 15 W m−2, respectively, as defined by the standard deviation of the hourly observations, which is closely associated with seasonal cycles. For example, in winter, the air–sea humidity and temperature differences are stronger than those in the other seasons, which provides an enhanced background for the mean estimates of the latent and sensible heat fluxes and their subdaily amplitudes.

Second, the physical drivers of the subdaily variations in latent and sensible heat fluxes under the same continuous boundary layer conditions are quantitatively examined. Both the overall results and the specific case studies indicate that thermal effect anomalies (r ≈ 0.8) and wind anomalies (r < 0.8) are the major drivers of subdaily turbulent heat flux variations under near-neutral boundary conditions. With a stable boundary layer, wind anomalies play a dominant role in the subdaily variations in latent and sensible heat fluxes (r ≈ 0.9). Under a convectively unstable boundary layer, the wind anomalies control the subdaily latent heat flux variations (r > 0.8), whereas the subdaily sensible heat flux variations are dominated by the air–sea temperature difference and wind anomalies, with r close to 0.8. The basic driver is the counterbalance between the buoyancy effects and wind turbulence at the air–sea interface. When the boundary layer is stable or near-neutral, wind anomalies or turbulence disturbs and overcomes the buoyancy effects. Thus, the wind effects are dominant. However, when the boundary is convectively unstable, the buoyancy effects strongly influence the boundary processes and the associated air–sea heat fluxes.

Third, unresolved subdaily influences result in underestimation of the mean latent and sensible heat fluxes in the Gulf Stream, which may account for the nonzero global mean surface heat budget balance (Yu 2019). Under near-neutral and unstable boundary layer conditions, the mean subdaily total contributions to the latent heat flux are 2.0 and 1.1 W m−2 and those to the sensible heat flux are 0.5 and 0.6 W m−2, respectively. Even under the rarely observed stable conditions in the Gulf Stream, the underestimations are 0.4 and 0.3 W m−2 for the latent and sensible heat fluxes, respectively. The results associated with this issue are extensions of our recent findings (Yan et al. 2021) in tropical oceans based on buoy arrays.

This study only provides results for periods of the same continuous boundary layer stability conditions, which provides a relatively idealized understanding of subdaily variations in latent and sensible heat fluxes. How hourly air–sea turbulent heat fluxes vary with rapidly switching boundary layer stability has not been addressed and is left for further investigation. For example, how do air–sea turbulent heat fluxes change with rapidly switching boundary layer stability regimes, and what are the controlling processes in such situations? Further comparisons can be made between the subdaily variability magnitudes under rapidly switching stability conditions and under the same continuous boundary layer conditions. The subdaily variability magnitude under rapidly switching boundary layer conditions is expected to be slightly less than that under near-neutral or unstable condition due to the negative contribution of stable conditions.

In addition, the 14 buoys chosen in the Gulf Stream are spatially limited compared to the large expanse of the strong western boundary current, but the study area is sufficiently representative considering our current observational ability. Note that one whole calendar year of observations for each buoy is used to investigate the physical drivers of subdaily variations, which cannot capture the effects of climate on subdaily variations, as long-term climate signals (e.g., the North Atlantic Oscillation or El Niño) may result in large-scale variations in the air–sea thermal difference and wind (Song and Yu 2012), which undoubtedly contribute to subdaily variations. Therefore, more complex patterns of seasonal climatological changes will be further explored in the future. The subdaily heat flux variations are tentatively inferred to be more drastic in winter than in other seasons due to enhanced winds and greater air–sea thermal contrast.

Finally, the bulk algorithm used in this study to estimate air–sea turbulent heat fluxes only considers the cool skin effect and does not address the warm-layer effect when parameterizing the foundation SST at a certain measurement depth to the skin temperature. This is because solar radiation observations are not directly incorporated by the NDBC buoys. However, diurnal warm-layer processes can be included in buoy observations by analyzing the turbulent heat flux contribution induced by the subdaily SST variations. In addition, warm-layer effects are more important in open ocean studies than in the Gulf Stream because diurnal warming may be disrupted by fronts with strong horizontal SST gradients and high-frequency ocean currents. Based on our recent work on the warm-layer effect in the tropics (Yan et al. 2024), we will conduct new studies on the warm-layer effect of the western boundary current. Although there are several limitations regarding the quantitative estimates provided in this study, the analyses presented demonstrate that the conclusions in this paper are robust.

Acknowledgments.

This study is funded by the National Natural Science Foundation of China (42122040 and 42076016) and the Fundamental Research Funds for the Central Universities (B220201016). The authors appreciate the constructive comments from the anonymous reviewers.

Data availability statement.

The buoy observations in this study are openly available from the historical NDBC data website (https://www.ndbc.noaa.gov/historical_data.shtml#stdmet) and the CLIVAR Mode Water Dynamic Experiment (CLIMODE) website of the Woods Hole Oceanographic Institution (http://uop.whoi.edu/projects/CLIMODE/climode.html). The reanalysis product ERA5 can be downloaded at https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels?tab=form. The MATLAB source code for the COARE algorithm (version 3.5) can be found at the FTP server (ftp://ftp1.esrl.noaa.gov/BLO/Air-Sea/bulkalg/cor3_5/).

APPENDIX

Observed Air–Sea Variables and Estimated Turbulent Heat Fluxes

This section introduces the measurements at the air–sea interface in the Gulf Stream and the analytical processes adopted to estimate the latent and sensible heat fluxes. Except for the representative CLIMODE station, all the operational buoys provide satisfactory observational coverage (>90%) in 1 year. Detailed information on these buoys is available in Table 1 and Fig. A1. High-temporal-resolution measurements can be used to investigate subdaily variations in latent and sensible heat fluxes. The high-resolution data are averaged to calculate the hourly heat fluxes. As shown in another study (Song 2021), operational buoys do not provide observations of relative humidity. However, the dewpoint at a specified height is complementarily measured along with the air temperature. Thus, the water vapor can be estimated based on the Tetens empirical equation (Murray 1967):
eT=E0×10aT(b+T),
where E0 = 6.11, a = 7.5, and b = 237.3 are the constants and T is the dewpoint. Similarly, the saturated water vapor can also be calculated using the air temperature, and the relative humidity can be estimated using the vapor associated with the dewpoint and saturated water vapor.
Fig. A1.
Fig. A1.

Timeline of the daily mean air–sea observations from all 14 operational buoys (Fig. 1) included in this study.

Citation: Monthly Weather Review 152, 5; 10.1175/MWR-D-24-0003.1

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