Dropsonde-Based Heat Fluxes and Mixed Layer Height over the Sea Surface near the Korean Peninsula

Abstract

Dropsonde-based sensible heat flux, latent heat flux, and buoyancy flux were estimated over the sea around the Korean Peninsula in 2021. During a preceding severe weather (SW) mission, a total of 243 dropsondes were released from a National Institute of Meteorological Sciences (NIMS) Atmospheric Research Aircraft (NARA). The heat fluxes were indirectly validated by comparison with model-based heat fluxes. The sensible heat flux calculated by the bulk transfer method depended entirely on the temperature difference between the sea level and atmosphere, whereas the latent heat flux was mainly affected by wind speed. Boundary layer heights above 800 m are closely related to buoyancy flux, which is greater in regions with higher sea surface temperatures. Furthermore, the utility of the dropsonde was confirmed in the marine atmospheric boundary layer (MABL) growth, which is difficult to observe in situ and, a relationship was proposed for estimating MABL based on mean meteorological data over the sea level.

1. Introduction

Korea is located in the eastern part of the Eurasian continent, between China and Japan and is protected from the Pacific Ocean by Japan. The three-sided seas of Korea are distinctly affected by regional natural conditions including dynamic oceanographic settings and active mixing by cold and warm currents [1]. The sea is characterized by the Kuroshio currents which transport moisture and heat from the tropics. Oceanic mesoscale such as eddies which act like a biological pump and coastal upwelling are transporting heat budget and water mass and interacting with the atmosphere in the MABL [2,3].

Surface fluxes over the ocean are required to evaluate coupled ocean-atmosphere and weather forecasting models and to provide surface forcing for ocean models. This is useful in understanding the temporal and regional variations in the exchange of heat between the atmosphere and ocean, and provides a large-scale context for field experiments [4]. Ocean-atmosphere heat fluxes are important components of the climate system through which the atmosphere and ocean exchange energy and contribute to maintaining the Earth’s climate system in a state of climate equilibrium. [5]. Ocean heat flux parameters linked to the sea surface temperature (SST) are critical for simulating typhoon structure and intensity [6,7]. Before a typhoon passes through a certain area, the latent and sensible heat fluxes from the warm ocean to the atmosphere supply moisture to the atmosphere [8,9]. The exchange of vapor and heat, consequently caused by the SST, affect heat fluxes and atmospheric boundary layer stability owing to changes in atmospheric fields such as temperature, atmospheric pressure, and wind within the ocean-atmospheric boundary layer [10,11]. For example, a sea heat flux is the amount of heat that evaporates water from the sea surface that results in SST cooling, which is then released to warm the atmosphere when water vapor condenses to form clouds [5]. Sea surface wind can be modified by SST, sea surface currents, and changes in MABL stability.

The heat fluxes can be calculated using the eddy covariance system, which directly estimates the turbulence that exchanges energy and physical quantities between the atmosphere and sea level [12]. However, direct observation of heat flux at sea is limited in space and time because it is performed only at specific points, such as at ships or ocean observation stations [13]. Previous studies have been conducted in which heat fluxes have been calculated by using ship or buoy observation data to the bulk transfer method [14,15,16,17]. Petersen and Renfrew [18] compared the direct heat fluxes (eddy heat fluxes) to the model heat fluxes based on the Coupled Ocean-Atmosphere Response Experiment (COARE) 3.0 algorithm using neutral heat transfer coefficients for moisture and heat. The model-induced heat fluxes were consistently less than the eddy heat fluxes, with a difference of up to 50 W m⁻² at times. Bharti et al. [19] reported that heat transfer coefficients over mid-latitudes and strong-wind regimes are still being improved. However, these bulk heat fluxes are not without bias. The model’s input parameters were progressively corrected. They also reported a difference in the buoy-and ship-based heat transfer coefficients. Petersen and Renfrew [20] reported an evident requirement for ocean-atmosphere flux observations. The authors emphasized the importance of eddy heat fluxes over the sea because a lack of direct observations may result in an underestimation of the bulk transfer coefficients and, thus, of model heat fluxes. Fairall et al. [21] stated that sea spray droplet effects are expected to become significant at wind speeds exceeding 15–20 m s⁻¹ and have ignored sea spray droplet effects on the bulk transfer coefficient.

The marine atmospheric boundary layer (MABL) development is strongly related to surface heat fluxes; however identifying MABL over the sea is challenging. Unlike on land where the atmospheric boundary layer height is confirmed by a wind profiler or lidar as well as a radiosonde, MABL has been verified by a radiosonde released from a ship. Aircraft-based observations have some advantages over ship-based observations such as being independent of the sea surface and having more information flow distortion effects for any given run. With the recent development of aircraft-based weather observation technology, data collection by dropsondes, which can determine the vertical profile and height of MABL, is increasing. Zhang et al. [7] estimated the surface flux by applying 2242 Global Positioning System dropsonde observation data to the bulk transfer method. They suggested that sea surface heat fluxes play an important role in strengthening or weakening hurricanes and emphasized the important role of heat flux-based boundary layer recovery in adjusting low-level thermodynamic structures. Bharti et al. [19] calculated bulk heat fluxes using the COARE 3.5 bulk algorithm with in situ data from a ship and used the bulk heat fluxes as in situ heat flux observations to validate model heat fluxes such as Australian Integrated Marine Observing System (IMOS) fluxes, European Centre for Medium-Range Weather Forecasts ReAnalysis-Interim (ERA-Interim) fluxes, and Objectively Analyzed Air-Sea Heat Fluxes (OAFlux).

There remains a lack of a platform capable of directly measuring heat fluxes or estimating MABL over the sea around the Korean Peninsula. The Korea Meteorological Administration (KMA)/NIMS initiated the annual operation of NARA over the sea with the aim of reducing the uncertainty of atmospheric observations as of January 2018 [22]. This study aims to present a method for calculating bulk heat fluxes using a dropsonde and determining the MABL height. We discussed the relationship between SST and heat fluxes. Section 1 describes the development of the MABL based on the dropsonde-based buoyancy flux (BFD) and proposes a method for estimating the MABL height using only simpler measured mean quantities (SST, air temperature, humidity, and wind speed). Section 2 describes the data and a method for estimating the heat fluxes using the bulk transfer method. Section 3 shows dropsonde-based estimates of heat fluxes and verifies the dropsonde-based estimates of heat fluxes with the satellite and model-based heat fluxes. We also suggest a relationship between dropsonde-based estimates of heat fluxes and dropsonde-observed MABL height in Section 4. The conclusions made from these evaluations are given in Section 5.

2. Materials and Method

2.1. Dropsonde

Since 2017, the KMA/NIMS has employed the NARA with the objective of observing for more than 300 h [23]. The NARA used is the Kingair350 from Beechcraft Corporation of the United States, with a maximum operating altitude of approximately 9 km and a maximum operating time of approximately five hours. The NARA observations were conducted in the West Sea (WS), East Sea (ES), and South Seas (SS) of the Korea Air Defense Identification Zone from Gimpo Airport base (Figure 1). The WS is part of the East Asian Marginal Sea, bordering Korea and Japan (north), Taiwan (south), China (west), and the Ryukyu Islands (east). The WS acts as a large reservoir as well as a source and sink of heat energy for transferring the sea to the atmosphere and vice versa [24]. The ES is a semi-enclosed marginal sea that is bounded by the Asian continent, Sakhalin Island, and Japanese islands [25]. Enhancing severe weather (SW) predictability requires aircraft dropsonde data assimilation. The SW predicting mission had four sub-missions: SW-01 (a heavy rain pre-observation mission), SW-02 (a typhoon pre-observation mission), SW-03 (a heavy snow pre-observation mission), and SW-04 (a basic meteorological element comparison of satellite output). The observations for the SW missions were conducted in the areas of WS, ES, and SS. The SW-03 mission was mainly carried out over the ES in the winter, with additional submissions carried out in the WS and the SS. Dropsondes are sensors that measure air temperature (°C), humidity (%), barometric pressure (hPa), and GPS signals to analyze horizontal wind speed (ms⁻¹), wind direction (°). The dropsondes descend at a rate of 11 m s⁻¹ from meteorological aircraft to sea level, thereby providing the aforementioned measurements along the way. Data from Vaisala’s dropsonde (RD-94) data were collected on a NARA using Advanced Vertical Atmospheric Profiling System (UCAR/NCAR, 1993), which receives radio signals transmitted from in-flight dropsondes. The raw data were processed using the Atmospheric Sounding Processing Environment (ASPEN), version 3.3-668, which provides sounding data where provided after applying standard quality control algorithms and corrections [26]. We also compared the dropsonde vertical profile with NARA atmospheric instrument (e.g., AIMMS-20) and confirmed good agreement [22].

Dropsondes were launched from NARA at altitudes ranging from 4 to 9 km in each sea area. In 2021, a total of 49 single day flights were completed, and 243 vertical profiles were obtained (

Table 1. List of dropsondes launched in 2021.

Date	Time (KST)	Site	Available Profile	Date	Time (LST)	Site	Available Profile	Date	Time (LST)	Site	Available Profile
21 January	15	WS	1	27 May	13–14	WS	5	2 August	13–14	WS	4
22 January	13–14	ES	4	8 June	13–14	WS	6	7 August	13–14	WS	3
27 January	13–14	WS	2	10 June	13–14	WS	6	9 August	13–14	WS	3
29 January	13	ES	2	18 June	14–15	SS	7	12 August	13–14	WS	6
1 February	14	WS	2	22 June	13–14	WS	6	20 August	09–10	WS	6
3 February	14	WS	4	23 June	13–14	WS	6	21 August	08–09	WS	4
4 February	13	ES	2	25 June	13–14	WS	6	23 August	08–09	WS	6
25 February	13–14	WS	4	28 June	13–14	WS	6	24 August	08–09	WS	5
2 March	14	ES	4	29 June	13–14	WS	6	31 August	08–10	WS	6
6 March	13–14	ES	6	1 July	13–15	SS	8	1 September	08–09	WS	6
9 March	13	WS	2	3 July	13–14	SS	4	6 September	09–10	WS	6
17 March	13–14	WS	4	5 July	13–15	SS	7	12 September	09–10	SS	10
26 March	13–14	WS	4	7 July	13–14	SS	8	13 September	09–10	WS	6
30 March	13–14	WS	3	9 July	13–14	SS	8	14 September	09–10	WS	6
23 April	13–14	WS	6	27 July	13–14	WS	6	18 November	15	WS	2
11 May	13–14	WS	5	29 July	13–14	WS	5
20 May	13–14	WS	6	30 July	13–14	WS	3

). Out of which, 115 dropsondes were released from 21 flights during the cyclone period, and 128 dropsondes were released from 28 flights during the anticyclone period. The primary scientific goal of this SW predicting mission was to investigate the atmosphere-ocean interaction for SW [22].

2.2. Sea Surface Temperature

The National Oceanic and Atmospheric Administration (NOAA) provided Optimum Interpolation (OI) SST (v2.1) with a spatial resolution of 0.25° and a temporal resolution of 1 day. The daily mean OISST (from here forward, OISST) was established using a methodology that included bias correction of in situ (ship and buoy) and satellite observations [27,28]. The OISST is based on the combination of both satellite observations from the Advanced Very High Resolution Radiometer (AVHRR), an infrared sensor mounted on NOAA satellite, and in situ observations from ships and buoys. The OISST was compared with the hourly SST measured by 15 KMA marine atmospheric buoys positioned around the Korean Peninsula. Since the KMA buoy data observed by unmanned operating systems may include some anomalous observations, we used in situ measurements obtained after the quality control process [29]. The closest OISST grid data within 0.25° were selected spatially at each buoy point, and the closest buoy SST data were used when the dropsonde observation was performed. The total number of data points used for the comparison was 3810, with a RMSE accuracy of 1.4 °C, a mean bias of −0.3 °C, and a correlation coefficient of 1.0 (Figure 2). When compared with dependent Argo float observations [30], the final v2.1′s mean bias and root mean square error (RMSE) were −0.04 °C and 0.24 °C, respectively [31,32,33]. The mean bias and RMSE are larger than in previous studies due to the different characteristics of the seas around the Korean Peninsula, such as water depth and currents [24,25] and the use of observation data for all four seasons. We assumed that the magnitude of the diurnal fluctuation in sea surface temperature is small and used this as input data for the heat flux calculation alongside dropsonde data.

2.3. Model-Based Heat Fluxes

The model-based sensible heat flux (SHFN) and latent heat flux (LHFN) were provided by the SeaFlux-Climate Data Record (CDR) version 2, which is an ocean surface flux developed with near-surface meteorology derived from passive microwave satellite observations. SeaFlux-CDR version 2 is a significant improvement over SeaFlux-CDR version 1. A novel model-based interpolation approach was used to generate the turbulent heat fluxes and associated values at temporal resolutions of 3-h (01:30, 04:30, 07:30, 10:30, 13:30, 16:30, 19:30, and 22:30 KST, which is the mid-timepoint of each 3-h period in the elapsed-time format from 1988 to the present) and spatial resolution of 0.25°. The dataset is available from the NOAA Climate Data Records repository (https://www.ncei.noaa.gov/products/climate-data-records/ocean-heat-fluxes, accessed on 18 December 2022), which has been widely used in surface energy budget analyses and water cycle research [13,34,35]. We referred to the satellite and model-based sensible heat flux (SHFN) and latent heat flux (LHFN) at the time closest to the launch of each dropsonde (Table 1).

2.4. Bulk Transfer Method

The bulk transfer method was used to calculate the heat fluxes over the sea around the Korean Peninsula. In practical applications, the sensible heat flux and the latent heat flux were estimated directly from the data obtained using eddy covariance equipment using left Equations (1) and (2). The buoyancy flux was estimated using Equation (3) [36]. In addition, it is often related to the mean atmospheric variables via bulk transfer parameterization using right Equations (1) and (2):

$$\mathrm{SHF}={\mathrm{c}}_{\mathrm{p}}{\mathsf{\rho }}_{\mathrm{a}}\overline{ \mathsf{\theta }\prime \mathrm{w}\prime } \simeq {\mathrm{c}}_{\mathrm{p}}{\mathsf{\rho }}_{\mathrm{a}}{\mathrm{C}}_{\mathrm{h}}{\mathrm{u}}_{10}\left({\mathsf{\theta }}_0-{\mathsf{\theta }}_{10}\right)$$

(1)

$$\mathrm{LHF}={\mathrm{L}}_{\mathrm{v}}{\mathsf{\rho }}_{\mathrm{a}}\overline{ \mathsf{\theta }\prime \mathrm{w}\prime } \simeq {\mathrm{L}}_{\mathrm{v}}{\mathsf{\rho }}_{\mathrm{a}}{\mathrm{C}}_{\mathrm{q}}{\mathrm{u}}_{10}\left({\mathrm{Q}}_0-{\mathrm{Q}}_{10}\right)$$

(2)

$$\mathrm{BF}=\mathrm{SHF}+0.07\mathrm{LHF}$$

(3)

where c_p (1004 J K⁻¹ kg⁻¹) is the constant pressure-specific heat, ${\mathrm{L}}_{\mathrm{v}}$ (2.44 × 10⁶ J kg⁻¹) is the latent heat of vaporization [5,20], and C_h, C_q are the sensible and latent heat transfer coefficients, respectively. ${\mathsf{\rho }}_{\mathrm{a}}$ is the atmospheric density of air (1.25 kg m⁻³), $\mathsf{\theta }\prime$ is the fluctuation in air temperature, $\mathrm{w}\prime$ is the fluctuation in vertical wind speed, and the overbar indicates the time-averaged property. ${\mathsf{\theta }}_0$ is the virtual potential temperature (K) at the sea surface and ${\mathsf{\theta }}_{10}$ is the virtual potential temperature (K) at a reference height (approximately 10 m). ${\mathrm{Q}}_0$ is the dropsonde-based saturation mixing ratio (g kg⁻¹) closest to sea level using the OISST, and ${\mathrm{Q}}_{10}$ is the dropsonde-based mixing ratio (g kg⁻¹) at a reference height (approximately 10 m). ${\mathrm{u}}_{10}$ is the dropsonde-based wind speed (m s⁻¹) at the reference height (near 10 m).

The C_h, C_q should be modified regarding the stability of atmospheric conditions to consider the effects of atmospheric stability on the SHF and LHF. This can be achieved by applying dimensionless stability functions [37]. Stability functions ($\mathsf{\psi }$) for stable and unstable atmospheric conditions were used in this study. All stability functions for momentum $\left({\mathsf{\psi }}_{\mathrm{m}}\right)$, heat (${\mathsf{\psi }}_{\mathrm{h}}$), and moisture (${\mathsf{\psi }}_{\mathrm{e}}$) were assumed to be equal under stable conditions and can be expressed by Equation (4):

$$0<\frac{{\mathrm{z}}_{\mathrm{r}}}{\mathrm{L}},{ \mathsf{\psi }}_{\mathrm{m}}={ \mathsf{\psi }}_{\mathrm{h}}={ \mathsf{\psi }}_{\mathrm{e}}=-\frac{5{\mathrm{z}}_{\mathrm{r}}}{\mathrm{L}}$$

(4)

The stability functions for momentum $\left({\mathsf{\psi }}_{\mathrm{m}}\right)$, heat (${\mathsf{\psi }}_{\mathrm{h}}$), and moisture (${\mathsf{\psi }}_e$) were used under unstable conditions and were expressed as Equation (5):

$$\begin{gathered} \frac{{\mathrm{z}}_{\mathrm{r}}}{\mathrm{L}}<0,{ \mathsf{\psi }}_{\mathrm{m}}=\ln \left[\left(\frac{1+{\mathrm{x}}^2}{2}\right){\left(\frac{1+\mathrm{x}}{2}\right)}^2\right]-2{\tan }^{-1}\mathrm{x}+\frac{\mathsf{\pi }}{2} \\ \frac{{\mathrm{z}}_{\mathrm{r}}}{\mathrm{L}}<0,{ \mathsf{\psi }}_{\mathrm{h}}={ \mathsf{\psi }}_{\mathrm{e}}=2\ln \left(\frac{1+{\mathrm{x}}^2}{2}\right) \end{gathered}$$

(5)

where x = (1–15 ($\frac{{\mathrm{z}}_{\mathrm{r}}}{\mathrm{L}}$))^0.25 [37,38]. C_h, represented by Equation (6), was generally determined before the SHF and LHF can be estimated using Equations (1b) and (2b). The bulk transfer coefficients C_h and C_q for heat and moisture were assumed to be the same [19]. The well-known Monin–Obukhov similarity theory is mostly used to close the bulk transfer parameterization [39,40,41,42]:

$${\mathrm{C}}_{\mathrm{h}}={\mathrm{k}}^2{\left[\ln \left(\frac{{\mathrm{z}}_{\mathrm{r}}}{{\mathrm{z}}_{0\mathrm{m}}}\right)-{\mathsf{\psi }}_{\mathrm{m}}\left(\frac{{\mathrm{z}}_{\mathrm{r}}}{\mathrm{L}}\right)\right]}^{-1}{\left[\ln \left(\frac{{\mathrm{z}}_{\mathrm{r}}}{{\mathrm{z}}_{0\mathrm{m}}}\right)-{\mathsf{\psi }}_{\mathrm{h}}\left(\frac{{\mathrm{z}}_{\mathrm{r}}}{\mathrm{L}}\right)\right]}^{-1}$$

(6)

$${\mathrm{C}}_{\mathrm{h}}={\mathrm{C}}_{\mathrm{q}}$$

(7)

where k is the von Karman constant (0.4), z_r is the observation reference height (m), and z_0m is the roughness length (m). Geernaert et al. [43] used a roughness length of 2.0 × 10⁻⁵ m to calculate the SHF and LHF. Hussein [44] used a roughness length of 7.3 × 10⁻⁴ m to calculate the SHF and LHF. Therefore, according to the surface conditions, we used 1.0 × 10⁻⁴ m as the roughness length over the WS, ES, and SS within the range classified by Stull [43].

$${\mathrm{u}}_{*}=\frac{{\mathrm{ku}}_{10}}{\ln \left(\frac{{\mathrm{z}}_{\mathrm{r}}}{{\mathrm{z}}_{0\mathrm{m}}}\right)-{\mathsf{\psi }}_{\mathrm{m}}\left(\frac{{\mathrm{z}}_{\mathrm{r}}}{\mathrm{L}}\right)}$$

(8)

The Monin–Obukhov length L can be expressed as Equation (8).

$$\mathrm{L}=\frac{-{\mathrm{u}}_{*}^3{\mathsf{\rho }}_{\mathrm{a}}{\mathrm{T}}_{\mathrm{av}}}{\mathrm{kg}\left[\frac{\mathrm{SHF}}{{\mathrm{c}}_{\mathrm{p}}}+0.61\frac{\left({\mathrm{T}}_{\mathrm{a}}+273.16\right)\mathrm{LHF}}{{\mathrm{L}}_{\mathrm{v}}}\right]}$$

(9)

where g is the gravitational acceleration (=9.8 m s⁻²), ${\mathrm{T}}_{\mathrm{av}}$ is the virtual air temperature (K) at approximately 10 m, ${\mathrm{T}}_{\mathrm{a}}$ is the air temperature (°C) at approximately 10 m, and ${\mathrm{u}}_{*}$ is the friction speed (m s⁻¹) [38,45].

The ${\mathrm{u}}_{*}$, SHF, and LHF must be estimated to determine L and vice versa. Therefore, L was calculated using an iterative method. When the initial value of L is assumed to be neutral atmospheric stability (=10¹⁵), ${\mathsf{\psi }}_{\mathrm{m}}$ and ${\mathsf{\psi }}_{\mathrm{h}}$ are equal to zero. Based on these variables, ${\mathrm{u}}_{*}$, C_h, SHF, and LHF can be calculated iteratively using Equations (1)–(8) and substituted into Equation (9) to obtain a new value of L under the condition that the ratio (L_n − L_n−1)/L_n−1 is less than 1% [46,47].

3. Results

3.1. Sea Surface Temperature Field

The bulk transfer coefficient, C_h, is influenced by atmospheric stability conditions over the water surface and, as a result, may be affected by the temperature and humidity gradients [20]. Figure 3a,b shows the SST distribution on 3 February (Case 1) and 2 August (Case 2), respectively. Each dropsonde (black triangle) was launched on 37.18°N, 124.43°E and 37.18°N, 124.41°E respectively at an altitude of approximately 4 km in the West Sea (WS). The gradient of SST distribution in winter was greater than the gradient of SST distribution in summer. For each case, the closest SST to where the dropsonde was launched was 7.3 °C and 26.4 °C, respectively.

Figure 4a,b shows the SST and dropsonde-based air temperature near 10 m at the point where the dropsonde was launched. In Case 1, both SST and air temperature increased from the initial launch A to the final point B, with SST and air temperature gradients (slope of linear regression) of 0.01 °C km⁻¹. In Case 2, the SST decreased from A to 150 km south and then increased, whereas the air temperature increased and then decreased. This is because the spatial change in water temperature in the shallow West Sea (WS) of the Korea Air Defense Identification Zone was small during summer, hence the SST gradient was not discernible, thus the air temperature gradient could not be obtained.

Figure 4c shows the scatter plot between SST and air temperature gradients in 48 cases (Table 1), except for the 21 January case (because there was only one dropsonde data). The values of SST and air temperature gradient mean the slopes of the linear regression of SST and air temperature in each case. When SST increased, air temperature increased in 29 cases, and when SST decreased, air temperature decreased. When the SST gradient (°C km⁻¹) increased, the air temperature gradient (°C km⁻¹) decreased in four cases, while when it decreased, the temperature gradient increased in 15 cases. In the WS in May, June, and September, the direction of increase and decrease in SST and air temperature did not coincide. This is because the atmosphere was affected by the change in the synoptic scale caused by the approaching cyclone but not by the local sea surface temperature. Kwon et al. [48] reported that during the cyclone period, the MABL structure was primarily affected by synoptic effects, whereas during the anticyclone period, the MABL structure was predominantly affected by local effects. The response of the MABL to mesoscale SST is often characterized by a link between downwind SST gradients [49] and wind stress divergence.

3.2. Sensible and Latent Heat Fluxes

The bulk transfer coefficient C_h, was calculated indirectly using the bulk transfer method [47]. The C_h clearly varies in response to temporal changes in atmospheric stability (Figure 5). The C_h varied depending on atmospheric stability, as can be seen from Equation (6). The atmospheric stability was mostly unstable, probably because most dropsonde observations were made around 1:00 PM, when SST was higher than the air temperature. The C_h varied from 0.84 × 10⁻³ to 0.94 × 10⁻³, which was not significantly different from the values proposed in previous studies over the sea [5,7,50,51,52].

The dropsonde-based SHF (SHFD) and dropsonde-based LHF (LHFD) were estimated using C_h and compared with SHFN and LHFN, respectively. Figure 6 shows a linear relationship between the SHFD and the SHFN, with a correlation coefficient of 0.6, a mean bias of −3.9 W m⁻², and a RMSE of 19.3 W m⁻², which is less than approximately 10% of the maximum SHFN. In the presence of high sensible heat flux, the difference increased, and SHFD exceeded 100 W m⁻². The comparison of the LHFD and LHFN shows good agreement, with a correlation coefficient of 0.7, a mean bias of 5.0 W m⁻², and a RMSE of 36.1 W m⁻², which is less than approximately 10% of the maximum LHFN. We confirmed that the bulk transfer method is useful for estimating SHFD and LHFD. Petersen and Renfrew [16] reported that model-based heat fluxes were over 100 W m⁻² less than the aircraft-based direct flux measurements (i.e., eddy covariance method). Furthermore, they suggested that the lack of direct observations in extreme situations (i.e., in conditions of high wind speed, at high latitudes, and in a region where there are frequently large ocean-atmosphere temperature and humidity gradients) may result in an underestimation of the transfer coefficients in such situations, and thus an underestimation of model-based heat fluxes. They also suggested that flux parameterization schemes are based on large observational datasets, mostly ship-based observations, and that many of these observations are from the less direct inertial dissipation method. Bharti et al. [19] reported that reanalysis flux products perform poorly, with biases as high as 100 W m⁻² over the Southern Ocean. The biases in model-based heat flux can be attributed to a higher bias in air temperature (10 m) and wind speed (10 m) at lower latitudes and in SST at higher latitudes. According to Bae et al. [53], the lack of ocean observation platforms contributes to uncertainty in calculating the heat transfer coefficient based on the heat flux parameterization. Given that the systematic limit, such as coarse spatial resolution and interpolation smoothing is the cause of model-based heat flux underestimation, SHFD and LHFD can be regarded as in situ observations obtained using the direct eddy covariance method [19].

Figure 7a shows the sensible heat flux depending on the difference (△$\mathsf{\theta }$) between the OISST-based virtual potential temperature ${\theta }_0$ (K) and dropsonde-based virtual potential temperature ${\theta }_{10}$ (K) based on 243 dropsonde profiles. The SHFD tended to increase when △$\mathsf{\theta }$ was increased and decrease when it was decreased. A negative SHFD indicates that heat is transferred to the sea from the atmosphere. In spring and summer, when △$\mathsf{\theta }$ is small, there is almost no heat exchange via SHFD, whereas the heat inflow from the ocean to the atmosphere significantly increases in late autumn and winter when the △$\mathsf{\theta }$ is relatively large, and the wind speed is high. In particular, the magnitudes of SHFD and LHFD in winter were nearly twice as large as those estimated in summer. Figure 7b shows a scatter plot of seasonal LHFD and the difference (ΔQ) between the dropsonde-based saturation mixing ratio ${\mathrm{Q}}_0$ (g kg⁻¹) closest to the sea level using OISST and the dropsonde-based mixing ratio ${\mathrm{Q}}_{10}$ (g kg⁻¹) at a reference height (approximately 10 m). In general, as ΔQ increases, so does the LHFD. The △Q remained low in the spring but increased from summer to autumn and winter when the atmosphere was dry. The amount of evaporation in the ocean due to the difference in humidity between the ocean and the atmosphere greatly affects the LHFD during the season when ΔQ is high. Unlike the SHFD, the wind speed difference (Figure 7c) contributed proportionally to the LHFD. Ritcher et al. [54] stated that they found no statistically significant trend, of the bulk transfer coefficient C_h with wind speeds up to roughly 20 m s⁻¹. They also hypothesize that the influence spray is nonexistent in some way to yield unchanged flux coefficient. Fairall et al. [21] reported that spray droplet effects on the order of 10 W m⁻² for the Humidity Exchange Over the Sea program-type conditions where direct evaporation is about 250 W m⁻² and stated that bulk heat fluxes to be accurate within 5% for wind speeds of 0–10 m s⁻¹ and 10% for wind speeds of between 10 and 20 m s⁻¹. It was assumed that the dropsonde wind speed at the altitude of 10 m used in this study was less than 20 m s⁻¹ and that the sea-spray effect could be ignored. From spring to autumn, the SHFD in all sea areas is less than 20 W m⁻². In particular, a negative SHFD partially appears in the southern ES and WS during the summer. A negative SHFD indicates that heat flows from the atmosphere into the ocean. From autumn, the SHFD gradually increased from high latitudes, and it can be seen that the largest SHFD appeared in winter. Considering the characteristics of the LHFD shown in Figure 6 similar to the SHFD, it shows a low value in spring and summer but increases from autumn, showing the highest value of 160–360 W m⁻² in winter. Sobel et al. [55] suggest that stronger (weaker) wind speeds over the off-equatorial regions increase (reduce) the LHFD and increase (decrease) SST. High (low) LHFD over the warm pool can be sustained because the incoming solar radiation is partially offset by ocean heat flux convergence (divergence) [55,56].

We also evaluated the contribution of spatial bulk parameters, variation of C_h, wind speed (dynamic term), △$\mathsf{\theta }$ = ${\theta }_0-{\theta }_{10}$ and △Q = ${\mathrm{Q}}_0–{\mathrm{Q}}_{10}$ (thermodynamic term) to the heat flux variation. These terms were derived from Equations (1) and (2) with respect to the horizontal distance (Figure 8). The spatial variation of SHFD and LHFD was investigated using 193 dropsonde observations (Table 1). Since the bulk transfer coefficients are a function of stability (see Figure 5), the first term on the right side indicates the variation in stability. This stability term is negligible in the heat flux along the flight axis (Figure 8a). Figure 8b shows the variation in heat fluxes based on the wind force. Heat fluxes increase as the wind speed increases. The heat flux, in particular, appears to decrease as the wind weakens. Figure 8c shows the variation of sensible heat flux based on the variation of △T and the variation of latent heat flux based on △Q. Notably, as the vertical difference of thermodynamic parameters increased, so did the variation of heat fluxes. Kwon et al. [48] reported that the dynamic and thermodynamic terms can operate in the same or opposite sense and that the heat fluxes during the low-pressure period were completely dependent on the thermodynamic characteristics of the incoming air mass during the low-pressure period. In this study, the thermodynamic term prevailed and resulted from the southward flight trajectories from the cold to warm zone. The increase in the thermodynamic term was associated with an increase in SST across the SST gradient. The air temperature increased in relatively quickly where the SST is higher and △$\mathsf{\theta }$ increases. When the air temperature increases, the saturated vapor pressure and △Q increase. SST horizontal gradients cause surface turbulent heat fluxes to have horizontal gradients [57].

$$\frac{\mathrm{dSHFD}}{\mathrm{dx}}={ \mathsf{\rho }\mathrm{C}}_{\mathrm{p}}\left\{\frac{{\mathrm{dC}}_{\mathrm{h}}}{\mathrm{dx}}\left[{ \mathrm{u}}_{10}\left({\mathsf{\theta }}_0-{\mathsf{\theta }}_{10}\right)\right]+{\mathrm{C}}_{\mathrm{h}}\frac{{\mathrm{du}}_{10}}{\mathrm{dx}}\left({\mathsf{\theta }}_0-{\mathsf{\theta }}_{10}\right)+{ \mathrm{C}}_{\mathrm{h}}{\mathrm{u}}_{10}\frac{\mathrm{d}}{\mathrm{dx}}\left({\mathsf{\theta }}_0-{\mathsf{\theta }}_{10}\right)\right\}$$

(10)

$$\frac{\mathrm{dLHFD}}{\mathrm{dx}}={ \mathsf{\rho }\mathrm{L}}_{\mathrm{v}}\left\{\frac{{\mathrm{dC}}_{\mathrm{q}}}{\mathrm{dx}}\left[{ \mathrm{u}}_{10}\left({\mathrm{Q}}_0-{\mathrm{Q}}_{10}\right)\right]+{\mathrm{C}}_{\mathrm{q}}\frac{{\mathrm{du}}_{10}}{\mathrm{dx}}\left({\mathrm{Q}}_0-{\mathrm{Q}}_{10}\right)+{ \mathrm{C}}_{\mathrm{q}}{\mathrm{u}}_{10}\frac{\mathrm{d}}{\mathrm{dx}}\left({\mathrm{Q}}_0-{\mathrm{Q}}_{10}\right)\right\}$$

(11)

3.3. Marine Atmospheric Boundary Layer

Figure 9 shows the dropsonde-based virtual potential temperature (red solid) and mixing ratio (blue dotted) profiles launched from the NARA at 13:51:41 KST in Case 1 and 14:16:59 KST in Case 2, respectively, and the dropsonde-induced MABL height was 1250 m and 250 m, respectively. The MABL in Case 1 was greater than that in Case 2 because both SHFD and LHFD were greater. The SHFD of Case 1 and Case 2 was 41.5 W m⁻² and 0.3 W m⁻², respectively, and the LHFD was 94.6 W m⁻² and 28.9 W m⁻², respectively. The SHFD and LHFD in Case 1 were higher than those in Case 2; △$\mathsf{\theta }$ and △Q during winter were larger than △$\mathsf{\theta }$ and △Q in summer. The dropsonde-based buoyancy flux (BFD) in Case 1 (42.2 W m⁻²) was also greater than that in Case 2 (0.5 W m⁻²). The △$\mathsf{\theta }$ in winter and summer was approximately 4.2 °C and 0.2 °C, respectively, and the △Q was approximately 4 g kg⁻¹ and 3 g kg⁻¹, respectively. The wind speeds at approximately 10 m were approximately 8.9 m s⁻¹ and 3.1 m s⁻¹ in winter and summer, respectively.

4. Discussion

The BFD was estimated using SHFD and LHFD from Equation (3). The dependence of the MABL height on the BFD is illustrated in Figure 10a. As BFD increased, the MABL height also increased. The BFD ranged from 0 W m⁻² to 300 W m⁻² with the MABL height increasing up to 2 km. Because △$\mathsf{\theta }$, △Q, and wind speed were higher in the ES than in the WS, MABL height and BFD were mainly higher in the ES in winter (Figure 10a). In summer, BFD reached 57.5 W m⁻², with a mean MABL height of 358.3 m (Figure 10a). The lower the latitude in summer, the smaller the BFD, owing to the smaller ΔT. In autumn, the BFD ranged from 0.3–70.0 W m⁻² with the mean BFD being 20.6 W m⁻², and the mean MABL height being 300.0 m. Summer and autumn MABL heights were generally lower than spring MABL heights. In winter, the BFD values were 0.1–303.6 W m⁻², the mean BFD was 65.1 W m^−2, and the mean MABL height was 826.3 m. When the BFD increased, the MABL height also tended to increase. In particular, when △$\mathsf{\theta }$, △Q, and wind speed were larger in the ES in winter, the MABL depth also increased owing to the transfer of much heat from the sea level to the atmosphere. In winter, the value of BFD, such as in spring, was higher in the ES than in the WS. The summer had the lowest mean BFD, while the winter had the highest. Especially during spring and summer, the BFD values were often negative, indicating heat transfer from the atmosphere to sea level. It was confirmed that most MABL heights were also high during the season when BFD was high. Kim et al. [58] reported that the buoyancy flux can be erroneously underestimated due to an underestimation of SST, especially in summer when the temperature difference between the atmosphere and the ocean is small.

The BFD is assumed to decrease with height and reach zero at the top of the MABL. The vertical profiles of the BFD normalized by the maximum BFD, according to the MABL height normalized by the maximum MABL height, using 80 vertical profiles that can determine the MABL height, are shown in Figure 10b. The slope is close to −1 at 120 W m⁻² or more, which is 0.4 times the maximum value of BFD, and at 800 m or more, which is 0.4 times the maximum value of the MABL height. Therefore, it is possible to estimate the MABL height if the BFD is greater than 120 W m⁻² (green lines). Specifically, if the bulk transfer method is used without directly measuring the turbulence, the MABL height can be determined using only the more easily measured mean quantities (sea surface temperature, air temperature, humidity, and wind speed). However, future studies should focus on the relationship between BFD and MABL height using more dropsonde observation cases. Although the comparison of the dropsonde and NARA atmospheric instrument (e.g., AIMMS-20) showed good agreement [22], it is not easy to obtain an accurate SST to determine heat fluxes based on the Monin-Obukhov similarity. This is a limitation of estimating dropsonde-based heat fluxes. Possible solutions could include using the gradient method [37] or the profile method [58] which does not require SST, and using dropsonde with infrared sensor to estimate SST [7,47].

5. Conclusions

The seas serve as a large source/sink and reservoir of heat energy, transferring it from the sea to the atmosphere and vice versa. For the first time in Korea, the dropsonde-based sensible heat flux (SHFD) and latent heat flux (LHFD) were estimated using dropsonde observation data from the NARA in this study. The SHFD and LHFD over the seas were estimated using the bulk transfer method, and they were compared and analyzed with model-based sensible heat flux (SHFN) and latent heat flux (LHFN). The SHFD and LHFD were found to be overestimated when compared with SHFN and LHFN. When the sensible heat flux is high, the difference grows, and SHFD exceeds up to 100 W m⁻². We can consider SHFD and LHFD as in situ observations obtained by the direct eddy covariance method by considering that the cause of the underestimation of model-based heat fluxes is the systematic limit, such as coarse spatial resolution and smoothing by interpolation. The SHFD showed a tendency to increase when △$\mathsf{\theta }$ increased and to decrease when it decreased. The LHFD and △Q showed the same tendency to increase/decrease and were relatively more sensitive to wind speed than SHFD. We also evaluated the contribution of the spatial bulk parameters, variation in stability, dynamic term, and thermodynamic term to the heat flux variation. The increase in the thermodynamic term is linked to an increase in SST across the SST gradient. The air temperature increases relatively quickly when the SST is higher and △$\mathsf{\theta }$ increases. When the air temperature increases, the saturated vapor pressure and △Q increase. In addition, a method for estimating MABL height using dropsonde-based buoyancy flux data was proposed. The slope was close to −1 at 120 W m⁻² or more, which was 0.4 times the maximum value of BFD, and at 800 m or more, which was 0.4 times the maximum value of the MABL height. This study proposes a relationship between the heat flux estimates derived from dropsondes and the MABL height observed by dropsondes as guides for estimating MABL height using only more easily measured mean quantities. Since dropsondes data have been accumulated, it will be possible to determine the threshold of buoyancy flux to estimate the MABL height in future studies. This study could contribute to enhancing the scientific understanding of heat fluxes and MABL over the sea around the Korean.

This study also calls for further analyses of the uncertainty in the mean measurements such as dropsonde and SST, heat transfer coefficients, and heat fluxes. We plan to investigate the further analyses of the sensitivity experiments by using eddy covariance heat fluxes and SST observation data from the Ieodo Ocean Research Station (32.12°N, 125.18°E) and also perform a seasonal analysis.