The cool skin F96 model, also known as the COARE model, was proposed on the basis of the physics described by Saunders (1967). The net heat flux Q_net of the sea surface cool skin is given by:

where Q_l and Q_s represent the latent heat flux and sensible heat flux, respectively, and Q_nlw is the net longwave radiance. The temperature difference ΔT, also referred to as the magnitude of the cool skin effect, can be described as:

where δ is the thickness of the cool skin and k is the thermal conductivity of the sea surface. Details can be found in Saunders (1967) and Fairall et al. (1996). Note that in this paper, ΔT equals SST_skin minus SST_depth and positive values of fluxes refer to heat flux transfer from the air to the sea. The COARE model has been updated to the latest version 3.6 since November 1993. Significant modifications to the COARE 3.0 model included extending the range of wind speed to about 20 m s^-1, which was validated using field measurements at high wind speeds and high latitudes (Fairall et al., 2003). COARE 3.5 was based on buoy data and was trained using a larger dataset of observations (Edson et al., 2013). Zhang et al. (2021) compared latent heat fluxes computed by the COARE 3.0 and 3.5 models according to different factors and reported that COARE 3.5 produced a mean percentage error of 2.0% compared to COARE 3.0 when using SST_skin as input. The mean percentage error increased to 18% when SST_skin was replaced by SST_depth as the input for COARE 3.0. The COARE 3.6 model improved the effects of waves on fluxes, including the influence of surface roughness and whitecap fraction on wave parameters. In this study, we simulated the F96 model using COARE 3.6 and used SST_skin measurements as the inputs for the flux computations.

Donlon et al. (2002) first obtained an empirical parameterization for the relationship between cool skin ΔT and wind speed at a height of 10 meters (U₁₀). The function is as follows:

The function contains three coefficients (a, b and c). A number of studies have assumed similar relationships and derived their own parameterizations (Minnett et al., 2011; Alappattu et al., 2017; Zhang et al., 2020; Luo et al., 2022). The details of the coefficients from previous studies can be found in Table 1 of Luo et al., 2022. In this study, our newly derived parameterization was compared to other existing models.

We used a dataset comprising measurements from 11 cruises by the research vessel Dong Fang Hong II of the Ocean University of China to compute the cool skin effect and validate the models. The dataset included measurements from 263 days, from 17 August 2015 to 31 October 2018. The cruises were named according to the starting year and month, e.g., “201508”. The cruise information and measurement ranges are listed in Table 1 and the cruise tracks are shown in Figure 1. All of the cruises took place in the Northwest Pacific: eight (“201508”, “201510”, “201601”, “201612”, “201703”, “201712”, “201807” and “201809”) were conducted in the China Seas and their adjacent waters; two (“201603” and “201805”) went east to areas with longitudes of 142°E to 153°E and latitudes of 32°N to 39°N; and one (“201702”) went southeast to around 143°E, 22°N and then headed south to the equator.

The SST_skin measurements were obtained using the Infrared Sea Surface Temperature Autonomous Radiometer (ISAR), which is a self-calibrating radiometer with a spectral bandpass of 9.6-11.5 μm and a nominal accuracy of ±0.1 K (Donlon et al., 2008). ISAR is capable of continuous autonomous operation for up to about 3 months, under the protection of a storm shutter. An ISAR 5C was deployed on the Dong Fang Hong II and has been operating continuously since 2009. The ISAR 5C was installed on the port side of the vessel at a height of 13 meters above the waterline, which had a nadir sea view angle of 45° to avoid being affected by the ship’s wake and a zenith sky view angle of 45°. Radiance observed from sea view mainly consists of two parts: the SST_skin emitted radiance at the spectral bandpass and the reflected downwelling sky radiance (Donlon et al., 2008). The ISAR 5C obtained SST_skin measurements at time intervals of approximately 4 to 5 minutes. As shown in Table 1, the minimum SST_skin observed by the ISAR occurred during the cruise “201601”, with a measurement of 271.11 K, and the maximum value was observed during the cruise “201807”, with a measurement of 307 K. The largest temperature range was observed during the cruise “201702”, which was measured as being from 277.66 K to 303.81 K.

Many sources have contributed to the uncertainty of SST_skin measurements collected by ISAR while operating on the sea (Donlon et al., 2008; Wimmer and Robinson, 2016). To improve confidence in the performance of ISAR and evaluate the accuracy of the measurements, the ISAR 5C used in this study was calibrated before and after each cruise using an external BB-ASSIST II blackbody, manufactured by LR TECH, Canada. BB-ASSIST II have a 70 mm aperture and an effective emissivity greater than 0.9998. Its absolute temperature accuracy is ±5 mK and the operating temperature ranges from ambient to 65°C because it only has a heating system. The temperature differences between the ISAR 5C and the BB-ASSIST II blackbody of both pre- and post-calibration showed good agreement with the ±0.1 K accuracy. Maintenance was carried out after each cruise, including changing the hardened gold front surface mirror on the scan drum inside the ISAR (Donlon et al., 2008). SST_skin measurements need to be calibrated and traced to SI units when used for the validation of satellite SST measurements and other research objectives, including the evaluation of the oceanic thermal effects discussed in this paper (Minnett and Corlett, 2012). The ISAR 5C radiometer and BB-ASSIST II blackbody used in this study both participated in an international comparison project conducted by the National Physical Laboratory (NPL), UK, in June 2016, which was called Fiducial Reference Measurements for Surface Temperatures derived by Satellite (FRM4STS) (Theocharous et al., 2019). The comparison results from both the ISAR 5C and the BB-ASSIST II showed good agreement with the NPL traceable radiometric standards. Note that ISAR SST_skin measurements from 7 out of 11 cruises in this study were used to validate the Level 2P SST product of the Visible Infrared Imaging Radiometer Suite (VIIRS) onboard Suomi National Polar-orbiting Partnership (S-NPP) satellite. The comparison results showed positive bias of 0.14 K and standard deviation of 0.30 K in total number of 853 matchups (Yang et al., 2018).

A Sea Bird SBE 48 hull contact temperature sensor was used for the SST_depth measurements at a depth of approximately 4 m. It was installed on the port side of the vessel, as with the ISAR 5C. The SBE 48 was attached to the inside of the ship’s hull below the waterline using magnets and was then covered with insulating sponge material. The initial accuracy of SBE 48 is ±0.002 K, with a typical stability of 0.0002 K per month. SBE 48 temperature sensors have been deployed on several vessels and have proved to be capable of measuring SST with similar accuracy as that measured by water injection temperature sensors, such as the SBE 3 and SBE 38 (Beggs et al., 2012). The SBE 48 SST_depth data were sampled every second and averaged every 10 samples.

The downwelling shortwave and longwave radiation were measured by a Kipp & Zonen CMP21 pyranometer and a CGR4 pyrgeometer, respectively. CMP21 pyranometer has a spectral range of 285–2800 nm and a response time of 5 s. CGR4 pyrgeometer has a spectral range of 4500–42000 nm and a response time of 18 s. Both instruments were installed on top of a small plane platform, which was at a height of approximately 15 m above the waterline with a 180° field of view. The solar radiation measurements were averaged every minute. As shown in Table 1, the shortwave radiance measured by the CMP21 had a maximum value of 1332.11 W m^-2 in cruise “201805”. The nighttime measurements from the CMP21 were slightly less than zero due to the zero offsets of the instrument. The longwave radiance ranged from 182.15 W m^-2 to 522.69 W m^-2 across the 11 cruises.

The vessel management system (VMS) on the Dong Fang Hong II provided meteorological observation data at 1-minute intervals, including wind speed, air temperature, air pressure, relative humidity, etc. Wind sensors on the VMS weather station were installed at a height of 19 m and the other sensors were installed 18 m above the sea surface. Using the real heights of the observations as inputs, the COARE 3.6 model was capable of computing reference heights for the wind speed, air temperature and relative humidity profiles (Fairall et al., 2003). The wind speeds adjusted to 10 m (U₁₀) ranged from 0 to 21.64 m s^-1 and the maximum wind speed occurred during cruise “201603”, as shown in Table 1. Strong winds often lead to large uncertainties of the shipboard measurements, especially the ISAR SST_skin used in this study. The roll and pitch of the vessel contributed to uncertainty of the view angle dependent sea surface emissivity which is crucial to the sky radiance correction (Wimmer and Robinson, 2016). Hence, datasets under strong winds (U₁₀ >15 m s^-1) are eliminated to further ensure the quality of the measurements. The last column in Table 1 shows the ranges of the relative humidity adjusted to 10 m (RH₁₀) measurements. The most humid air conditions occurred during the summer cruise “201805” and “201807”, with maximum RH₁₀ values of 99.6% and 99.5%, respectively.

The sea skin layer is cooler than the layer just below it due to air–sea heat transfer throughout the whole day (Fairall et al., 1996; Minnett et al., 2011). Previous researches on the cool skin effect have mostly used nighttime measurements to avoid the diurnal warming effect (DW) during daytime (Donlon et al., 2002; Zhang et al., 2020; Zhang et al., 2021; Luo et al., 2022). Zhang et al. (2020) reported a new approach that uses the maximum diurnal warming effect (DW_max) during the daytime as a constraint to eliminate DW residuals at nighttime. Strong DW events can lead to the warming of the sea surface skin at the whole night (Zhang et al., 2020). Note that in this study, we separated day and night using the solar zenith angle of 110° to consider less solar heat contamination at night. Due to the large number of measurements (63108), we first examined the appropriate DW_max threshold for the dataset. We only used daytime and nighttime data that had DW amplitudes that were less than the DW_max for our analysis. The statistics for the temperature differences ΔT (SST_skin minus SST_depth) under different DW_max thresholds from 1.0 K to 0.0 K are shown in Figure 2. The mean ΔT decreased slightly as the DW_max decreased from 1.0 K to 0.3 K and then dropped from -0.22 K to -0.36 K when the DW_max decreased to 0.0 K. The total number of ΔT measurements reduced from 39909 to 29086, i.e., from 63.2% to 46.1% of the 63108 measurements, as the DW_max changed from 0.3 K to 0.2 K. The differences between the daytime and nighttime ΔT measurements and the standard deviation reduced as the DW_max decreased because DW events were removing. As shown in Figure 2, DW_max values of 0.2 K or smaller were quite strict as the majority of the ΔT measurements were eliminated. In addition, for the cases of the warm skin phenomenon discussed in this study, we selected 0.3 K for the DW_max threshold.

For the dataset with the 0.3 K DW_max threshold, the statistics for the ΔT results from the F96 model and the observed data are shown in Table 2. The distributions of the nighttime and daytime ΔT measurements and the ΔT measurements from the F96 model and the field observations are shown in Figure 3. The total number of ΔT measurements was 39909, with 14693 (36.8%) collected at nighttime and 25216 (63.2%) collected during daytime. As shown in Figure 3A, the observed nighttime and daytime ΔT measurements had similar quasi-Gaussian distributions to those presented in previous studies (Zhang et al., 2020; Luo et al., 2022). The mean and median ΔT values were smaller at nighttime compared to daytime. The mean and standard deviation of all observed ΔT measurements were -0.22 K and 0.20 K, respectively. The ΔT measurements from the F96 model had lower mean and median values, as well as smaller STD and RSD values, in comparison to those from the field observations. The distribution of the ΔT measurements from the F96 model had a peak value around -0.20 K, as shown in Figure 3B. Note that in contrast to previous studies, we measured more positive ΔT values, especially in nighttime, with a proportion of 1251 (8.5%) out of the 14693 ΔT measurements.

The relationship between ΔT and local time is shown in Figure 4. The observed ΔT measurements changed little at midnight, with the minimum bin-averaged ΔT of -0.25 K occurring between 6 a.m. and 7 a.m. The ΔT reduced by a quite small amplitude from midnight to dawn, which was similar to the findings of Zhang et al. (2020). Even though strong DW events were eliminated using the 0.3 K DW_max threshold, the observed ΔT measurements still increased after sunrise and reached a peak of the bin-averaged value of -0.17 K between 11 a.m. and 12 a.m. due to solar heat compensation. The measurements from the F96 model did not increase in the daytime and instead remained relatively stable throughout the whole day because the cool skin effect in the model was independent from the warm layer estimation and was corrected using an improved solar transmission model (Fairall et al., 2003; Wick et al., 2005).

The coefficients in Eq. (3) from the empirical model of Donlon et al. (2002) were derived using observed ΔT and U₁₀ measurements, as follows:

Figure 5 shows five previous parameterization functions and the new parameterization that we derived in this study. The parameterizations of Donlon et al. (2002); Minnett et al. (2011) and Alappattu et al. (2017) were given under 2 m s^-1< U₁₀< 15 m s^-1, considering the relatively minor role of wind shear-driven mixing on thermal skin heat transfer when U₁₀< 2 m s^-1 and also with the small number of measurements. Based on our large number of measurements, we extended U₁₀ to 0 m s^-1, which was similar to the study by Zhang et al. (2020) and Luo et al. (2022). The results from our dataset fit well with those of Luo et al. (2022) within the entire U₁₀ range and were also in good agreement with those of Donlon et al. (2002) at 2 m s^-1< U₁₀< 6 m s^-1. The magnitude of ΔT in this study was slightly smaller than that in the study by Zhang et al. (2020) at 2 m s^-1< U₁₀< 6 m s^-1. Minnett et al. (2011) overestimated ΔT at low wind speeds when U₁₀ was< 6 m s^-1, possibly due to their relatively small dataset. At moderate to high wind speeds (U₁₀ > 6 m s^-1), all of the results produced similar patterns, which were less dependent on U₁₀. Alappattu et al. (2017) overestimated the magnitudes of ΔT at all U₁₀ values in comparison with other parameterizations. Note that Minnett et al. (2011) and Alappattu et al. (2017) also included both daytime and nighttime observations, whereas the others only included nighttime measurements. The newly derived parameterization showed a good performance compared to those of the previous models.

The cool skin effect is described as the loss of heat from the sea surface. Zhang et al. (2020) introduced the idea of the reverse process of air–sea heat flux transfer, which can be considered as the “warm skin”. Direct physical evidence of the warm skin under the conditions of heat flux transfer from the air to the sea has been observed when the air is extremely humid and the air temperature is higher than the SST (Zhang et al., 2020). In this study, 8.5% of the observed nighttime ΔT measurements were positive, which motivated us to investigate the warm skin phenomenon. We first checked the relationship between ΔT and RH₁₀ and the temperature difference between T_{air_10} and SST_skin (Figure 6). There was a strong positive correlation between the ΔT measurements from both the field observations and the F96 model and the RH₁₀, as well as the temperature difference between T_{air_10} and SST_skin. As shown in Figure 6A, the F96 model overestimated the ΔT measurements of the cool skin at around 30%–60% humidity in comparison to the observed ΔT measurements and the average values of the observed ΔT measurements were almost equal within the range. The ΔT results fit well when humidity increased from 60% to 100% and the maximum mean value of the observed ΔT measurements was 0.01 K at 95%–100% humidity. The temperature difference between T_{air_10} and SST_skin mainly ranged from -10 K to 3 K and the majority of the observed positive ΔT values were distributed at temperature differences of -1 K to 3 K, as shown in Figure 6B. The observed cases of the warm skin phenomenon with positive ΔT values occurred under the conditions of very humid air and an air temperature that was equivalent to or warmer than the temperature of the sea surface. In this study, measurements were taken in the Northwest Pacific, which often has high atmospheric moisture levels and temperatures in the summer. Therefore, we further investigated seasonal variations in ΔT. As shown in Figure 7, the magnitudes of ΔT in May, June and July were smaller than those in other months, which was mainly contributed by the measurements from the cruise “201805” and “201807”. The bin-averaged observed ΔT values were -0.09 K, -0.06 K and 0.02 K in these three months, respectively. The results from the other months were larger, with the minimum value occurring in November with 232 ΔT measurements.

Even though we used DW_max constraints to eliminate strong DW events from the dataset, we still needed to be careful when investigating the warm skin phenomenon considering solar contamination. Thus, we chose the observed nighttime ΔT measurements from the cruise “201805” and “201807” to conduct a further analysis. Figure 8 shows the locations of all observed nighttime ΔT measurements during the two cruises (121.00°E–153.14°E 31.10°N–39.22°N). The maximum positive ΔT value of 0.45 K was measured at 123.51°E 34.85°N, together with an RH₁₀ value of 96.6%.

Figure 9 illustrates the relationships between the RH₁₀ and air–sea temperature differences and the observed nighttime ΔT measurements from the cruise “201805” and “201807”. The ΔT measurements from the field observations and the F96 model increased as the air became more humid and the bin-averaged ΔT values were -0.02 K and 0.02 K at 96%–98% and 98%–100% RH₁₀, respectively, and the percentages of positive ΔT values were 51.8% and 63.5%, respectively. The warm skin phenomenon occurred when the air was much warmer than the sea surface. The proportions of positive ΔT values were 60.8%, 49.3% and 64.3% at RH₁₀ values of 76%–78% and 84%–88%. The presence of high proportions of positive ΔT values resulted from higher air–sea temperature differences of around 2–3 K. Positive ΔT values at extremely high RH₁₀ also came with warmer air temperatures. The physical processes of the warm skin phenomenon were interpreted as follows: high relative humidity contributed to a large positive (air to sea) latent heat flux Q_l; the large positive air–sea temperature difference resulted in a large positive (air to sea) sensible heat flux Q_s; Q_l, Q_s and the net longwave radiation Q_nlw (downward was positive) constituted the net heat flux Q_net of the sea surface (Fairall et al., 1996). In total, we observed 667 positive ΔT values out of the 1913 nighttime measurements during the cruise “201805” and “201807”. The magnitude of the observed warm skin phenomenon ranged from around 0 to 0.3 K, with a mean value of 0.08 K and a standard deviation of 0.06 K. More measurements are needed in future research, especially under very humid and warm atmospheric conditions, in order to conduct an accurate numerical analysis of the reverse heat transfer mechanism at the air–sea interface.