1. Introduction
Air–sea heat fluxes, including shortwave and longwave radiative fluxes and latent and sensible turbulent heat fluxes, are the primary conduits for the dynamic coupling between the ocean and atmosphere. Therefore, the accurate estimation of heat fluxes across the air–sea interface is important for the proper simulation and prediction of the multiscale air–sea interaction processes (e.g., Seo et al. 2014; Demott et al. 2016; Zhang et al. 2019; Ying et al. 2021). For the global, ice-free, open ocean the net surface heat flux into the ocean is estimated to be between 2 and 3 W m−2 (Yu 2019). However, most current heat flux products have net surface heat fluxes ranging from −16 to 25 W m−2 and therefore do not match the estimated heat balance (Yu 2019). This level of uncertainty is an obstacle to the accurate understanding of the upper-ocean heat budget and air–sea interactions.
In the heat balance, surface latent heat flux (LHF) is the primary component that balances the incoming solar radiation, especially for the tropical oceans (Carton and Zhou 1997). However, of the four components of global net surface heat flux, the estimate of LHF has the largest uncertainty (e.g., L’Ecuyer et al. 2015; Valdivieso et al. 2017). The root-mean-square errors of LHF products from buoy data vary between 21 and 51 W m−2 (Bentamy et al. 2017). In particular, an intercomparison of 12 air–sea heat flux products showed a large standard derivation in LHF (evaporation) over the tropical and subtropical oceans (40°S–40°N, Yu 2019). The LHF uncertainty likely results from many causes, such as the uncertainties in transfer coefficients used in bulk parameterization schemes, the uncertainties in the measurements of LHF-related variables (e.g., surface winds, sea surface skin temperature (SSTskin), and near-surface specific humidity), and the inadequate temporal sampling of diurnal variability of LHF-related variables (e.g., Fairall et al. 1996b; Brunke et al. 2003, 2011; Chou et al. 2004; Bourras 2006; Iwasaki et al. 2010; Clayson and Bogdanoff 2013; Weihs and Bourassa 2014; Bentamy et al. 2017; Brodeau et al. 2017; Cronin et al. 2019). The present study focuses on the last source of uncertainty: the effects of diurnal variations in LHF-related variables on the climatological mean LHF.
The climatological diurnal warming of SSTskin is on the order of 1/10 K in the tropical oceans (e.g., Clayson and Weitlich 2007; Kawai and Wada 2007; Kennedy et al. 2007; Bellenger and Duvel 2009). On calm, sunny days, diurnal SSTskin warming can reach or exceed 1 K (e.g., Fairall et al. 1996b; Ward 2006). The strong diurnal warming can induce an increase in the LHF of up to 50 W m−2 at midday (Fairall et al. 1996b; Ward 2006). Based on long-term reanalysis data, Clayson and Bogdanoff (2013) found that fully resolving diurnal SSTskin variability increases the climatological LHF by up to 10 W m−2 over the tropical oceans relative to employing only nighttime SSTskin to estimate LHF. However, up until now the contribution of the diurnal SSTskin to the climatological LHF has not been estimated quantitatively from field observations.
High-frequency variability in surface wind field can also make a significant contribution to the climatological mean LHF by increasing mean surface wind speed (e.g., Ogawa and Spengler 2019; Wu et al. 2020a,b). For example, the submonthly wind variability contributes a significant fraction of mean wind speed and therefore contributes to the climatological LHF over the midlatitudes (Ogawa and Spengler 2019). Taking into account the diurnal variability in surface winds generally induces an enhancement of the daily mean wind speed, which also may increase the daily mean LHF and its climatology. However, to our knowledge, the effect of diurnal variation in winds on the climatological LHF over the tropical oceans has not been previously reported.
Using 3-hourly satellite-based LHF, Clayson and Edson (2019) estimated the global diurnal LHF amplitude in boreal winter and found that it reaches maxima over the tropics and western boundary current (WBC) regions (i.e., the Gulf Stream and the Kuroshio Extension). They focused on the amplitude maxima in the WBC regions, which were verified by comparisons with buoys, but did not examine the LHF in the tropical oceans. The Global Tropical Moored Buoy Array (GTMBA) provides long-term high-frequency (hourly or 10-min) measurements of LHF-related variables over the tropical oceans, which are suitable for studying the diurnal variation in the LHF. Resolving the diurnal cycles of the LHF and SSTskin for air–sea coupling processes in the tropics could provide an improved physical understanding of the atmospheric moisture budget (Seo et al. 2014), which plays a central role in modulating the Madden–Julian oscillation (Madden and Julian 1971, 1972). Therefore, in the present study, we first examine the characteristics of and mechanisms behind the diurnal LHF variation in the tropical oceans using field observations from the GTMBA, and then evaluate the effect of diurnal variability on the climatological LHF.
2. Data and method
Comparison of estimated latent heat fluxes using the downwelling shortwave/longwave (DSWR/DLWR) radiation from the ERA5 and GTMBA.
3. Results
a. Characteristics and mechanisms of diurnal LHF variation
Figure 2a shows the spatial distribution of the timing of the daily maximum LHF in the tropical oceans. The daily maximum LHF occurs in the afternoon (1200–1600 local time) over the majority of the tropical oceans, except in the southeastern tropical Pacific Ocean (along 8°S) and northwestern and southwestern tropical Atlantic Ocean where it shifts to the early morning (0500–0700 local time) (see also line plot in Fig. S1a in the online supplemental material). The daily minimum LHF occurs roughly at local midnight (2200–0200 next day local time) over most of the tropical oceans (Figs. 2b and S1b). Its timing changes to the morning (0700–0900 local time) for some spots in the Indo-Pacific warm pool and in the eastern tropical Pacific Ocean (along 95°W) and to the late afternoon (1600–1800 local time) in the southwestern tropical Atlantic Ocean. This remarkable spatial pattern in the diurnal LHF phase suggests a significant diurnal variation in the LHF over the tropical oceans. The amplitude of the climatological diurnal LHF is illustrated in Fig. 2c. The diurnal variation in LHF is strongest in the center of the Indo-Pacific warm pool near the equator. The domain-averaged (2°S–2°N, 67°–156°E) diurnal amplitude of LHF is 15.8 W m−2 with a maximum value of 21.1 W m−2 located around (2°N, 137°E) (Fig. S1c). Another large diurnal LHF amplitude region is located over the equatorial cold tongues of the Pacific and Atlantic Oceans, with maximum amplitudes of 13.6 and 11.4 W m−2, respectively. We also notice relatively large diurnal amplitudes off the equator, such as in the central part of the Bay of Bengal (16.3 W m−2), northeastern corner of the tropical Pacific Ocean (20.1 W m−2), and southwestern tropical Atlantic Ocean (11.3 W m−2).
To investigate the mechanisms behind the diurnal LHF variation in the tropical oceans, the diurnal phase of the LHF is compared with those of the two factors driving it: surface wind speed and air–sea specific humidity difference. The daily minimum and maximum values in the LHF occur roughly at the same time as those in the air–sea humidity difference over most tropical oceans (Figs. 3a,b), suggesting that the diurnal phase of the LHF relies mainly on that of the air–sea humidity difference. The air–sea humidity difference is the difference between the SSTskin-associated saturation specific humidity and surface air specific humidity. A comparison between them shows that the timing of the daily maximum air–sea humidity difference mostly depends on the timing of the daily maximum SSTskin, while the timing of the daily minimum is mainly close to the timing of the daily maximum surface air specific humidity (Fig. 3c). For example, LHF reaches a maximum at 1500 LT, and reaches a minimum at 0100 LT around the buoy at 0°, 180° (Fig. 4). The phase of the LHF resembles that of air–sea humidity difference, due to much stronger diurnal variability in the air–sea humidity difference than in surface wind speed. The daily maximum and minimum air–sea humidity differences occur at 1500 and 0000 LT, respectively. Relative to surface specific humidity, SSTskin-associated saturation specific humidity has a stronger diurnal signal at 0°, 180°. As a result, the diurnal variability in air–sea humidity difference is determined primarily by SSTskin-associated saturation specific humidity. The timing of the daily maximum air–sea humidity difference is the same as that of the daily maximum SSTskin. However, during the period from midnight to morning when the surface saturation specific humidity is low, its change is smaller than that in surface specific humidity, which varies from its maximum to minimum. This results in the timing of the daily minimum air–sea humidity difference being close to that of the daily maximum surface specific humidity.
To quantitatively evaluate the relative importance of the diurnal variations in air–sea humidity difference and wind speed, their percentage contributions to the climatological diurnal LHF amplitude were calculated (see methods in section 2). Compared with the diurnal variation in wind speed, the diurnal variation in air–sea humidity difference makes a larger contribution to the diurnal LHF amplitude in all tropical ocean regions except in the southwestern tropical Atlantic Ocean (Figs. 5a,b, see also Fig. S2a). The contribution of the diurnal variation in air–sea humidity difference is primarily induced by the diurnal variation in SSTskin over most tropical oceans, with the diurnal variation in air specific humidity only playing a secondary role (Figs. 5c,d, see also Fig. S2b). However, in the southeastern tropical Pacific Ocean (along 8°S) and northwestern tropical Atlantic Ocean, the contribution from diurnal air specific humidity is more important than that from diurnal SSTskin. The contributions of the diurnal SSTskin, air specific humidity, and wind speed are 71%, 21%, and 10% on average over all buoy sites, respectively. Over the region where the contribution from the diurnal SSTskin variability dominates, its contribution reaches 87%, while the contributions from the diurnal variations in air specific humidity and wind speed decrease to 11% and 7%, respectively.
According to the bulk algorithm of LHF, the contribution of the diurnal variation in SSTskin is dependent not only on the diurnal SSTskin amplitude but also on the magnitude of surface wind speed. In the tropical Eastern Hemisphere, the diurnal amplitude in the SSTskin-associated saturation specific humidity is much larger than those in the air specific humidity and wind speed, resulting in the dominance of the contribution of the diurnal SSTskin variation (Fig. 6). While in the tropical Western Hemisphere, the diurnal SSTskin-dominated contribution results from both a larger diurnal saturation specific humidity amplitude and higher mean surface wind speed. The amplitude of the diurnal SSTskin variability depends primarily on the magnitudes of surface wind speed and solar radiation (e.g., Kawai and Wada 2007; Gentemann et al. 2003). Surface solar radiation is strong over the entire tropical oceans, with the annual mean value exceeding 180 W m−2 at all GTMBA sites (Fig. S3), so the spatial distribution of the diurnal SSTskin amplitude is determined by that of surface wind speed. Surface wind speed has a significant impact on SST by modulating both oceanic turbulent mixing and surface turbulent heat fluxes (e.g., Duvel and Vialard 2007; Wu et al. 2015). During the daytime, lower wind speeds favor the formation of a shallower oceanic surface mixed layer due to weaker turbulent mixing, and take less heat away from the ocean surface, both of which are helpful for maintaining larger diurnal warming (e.g., Kawai and Wada 2007; Gentemann et al. 2003). The spatial correlation coefficient between the surface wind speed and diurnal SST amplitude is −0.88 (Figs. 2d,e). This indicates that surface wind speed determines the spatial patterns of the diurnal SSTskin amplitude and therefore the diurnal LHF amplitude over the tropical oceans. The spatial correlation coefficient between the diurnal LHF amplitude and surface wind speed is −0.82 (Figs. 2c,e, see also blue and magenta curves in Fig. 6b). Over the core area of the Indo-Pacific warm pool and the equatorial Pacific and Atlantic cold tongues, the surface wind speed is relatively low, inducing large diurnal SSTskin warming that results in large diurnal LHF amplitudes (Figs. 2c–e).
For the central part of the Bay of Bengal (near 15°N, 90°E) and northeastern corner of the tropical Pacific Ocean (near 12°N, 95°W), surface wind speed has a similar diurnal phase and amplitude with the air–sea humidity difference and makes a significant contribution to the diurnal LHF amplitude (Figs. 7a–d). The combined effect of the diurnal variations in SSTskin and wind leads to a large diurnal LHF amplitude in these two regions. For the southwestern tropical Atlantic Ocean (near 14°S, 32°W), the diurnal amplitude of surface wind speed is twice that of air–sea humidity difference, inducing and dominating the large diurnal LHF amplitude there (Figs. 7e,f).
From the results above, we can see that there are strong relations between the diurnal variations in LHF and SSTskin over the tropical oceans. In the present study, SSTskin is calculated as the sum of the measured SSTbulk and the estimated skin-bulk SST difference using the F96 schemes. Thus, the accuracy of the F96 schemes is critical for the correct determination of the amplitude of the diurnal LHF variation. Using observed skin-bulk SST difference during nighttime (difference between shipborne infrared SST autonomous radiometer SSTskin and water intake SSTbulk at ~7.1–9.9-m depths), Zhang et al. (2020) validated several cool-skin schemes, and noted that the F96 scheme performs best and can capture most skin-effect trends and details. Alappattu et al. (2017) evaluated the performance of the F96 cool-skin and warm-layer schemes using both daytime and nighttime measurements, and found that the F96 schemes agreed fairly well under a moderate wind regime (between ~3 and ~7 m s−1). Over the GTMBA sites, surface mean wind speed varied between 4 and 8 m s−1, placing these sites mostly in the moderate wind regime. Therefore it is expected that the F96 schemes reproduce the skin-bulk SST difference very well at the GTMBA sites.
b. Effects of diurnal variations in LHF-related variables on the climatological LHF
Including the diurnal variability of SSTskin can improve the estimation of the climatological mean LHF by properly capturing the daytime SSTskin (e.g., Clayson and Bogdanoff 2013; Weihs and Bourassa 2014). Resolving diurnal variability captures the increase in SSTskin during the daytime arising from the shallowing of the mixed layer, but causes little change in the nighttime SSTskin (Shinoda 2005). As a result, the diurnal SSTskin warming increases daytime LHF and hence the climatological LHF (Seo et al. 2014). Including the diurnal variability of wind may also improve the climatological LHF estimate by rectifying the daily mean wind speed. Generally, daily (24-h) mean wind speed is higher than the modulus of daily (24-h) mean wind vector (
Figure 8a shows the total effect of diurnal variability on the climatology of LHF over the GTMBA sites. Taking into consideration the diurnal variations in LHF-related variables increases the climatological mean LHF by 3.7–16.6 W m−2 and on average by 9.1 W m−2 (see also black curve in Fig. S4). The increase of the climatological LHF mostly results from the inclusion of diurnal variabilities of the SSTskin and wind (Fig. S4), as mentioned above. The primary and secondary peaks in the contribution from the diurnal SSTskin variability are located over the core area of the warm pool (up to 6.6 W m−2) and equatorial cold tongues (up to 5.0 W m−2) where diurnal SSTskin warming is relatively large due to low wind speeds (Figs. 8b and 9a). Large values of the diurnal wind-associated contribution are found over the highly dynamic environment of the intertropical convergence zone (ITCZ, up to 11.4 W m−2), where the wind speed enhancement from resolving the diurnal variability is large (Figs. 8c and 9b). The opposite occurs over the southeastern Pacific and northern and southern Pacific Oceans, where the stable trade wind regime prevails. Compared with the diurnal SSTskin-associated contribution (2.5–6.6 W m−2), the magnitude associated with the diurnal winds exhibits a larger spatial difference (1.0–11.4 W m−2). This is due to the larger spatial difference in the wind speed enhancement than in the SSTskin-associated saturation specific humidity increase (Fig. 9). The spatial pattern in the diurnal wind-associated contribution dominates the total diurnal contribution (spatial correlation coefficient between them is 0.75; Figs. 8a, 8c, and S4). Thus, the total contribution from resolving the diurnal variability is significant over the ITCZ, especially in the core area of the ITCZ reaching a maximum value of 16.6 W m−2 (Fig. 8a).
We also quantitatively evaluate the relative importance of the diurnal variations in SSTskin and wind to the LHF climatology (Figs. 8d,e). It is clear that over the ITCZ, where the total effect of diurnal variability on the climatological LHF is large, the diurnal variation of wind makes a larger contribution to the LHF (61%) than does the SSTskin (41%). The opposite occurs over the trade wind regime regions, where the contributions of the diurnal variations in SSTskin and wind are 65% and 36%, respectively. It is worth noting that while the diurnal variation in wind makes an important contribution to the climatological mean LHF, it plays an only minor role in the diurnal LHF amplitude (see section 3a). The climatological LHF increase mainly arises from the mean value of the diurnal SSTskin/wind variation, while the diurnal LHF amplitude primarily depends on the diurnal amplitude of SSTskin/wind (see section 2). Compared with the diurnal SSTskin-associated saturation specific humidity, the diurnal winds show a comparable mean value (Fig. 9) but a smaller amplitude over most of the tropical oceans (Fig. 6), resulting in the different roles of the diurnal wind variability in the LHF climatology and the diurnal LHF amplitude.
In addition to the GTMBA observations, the effects of the diurnal variations in SSTskin and wind on the climatological LHF in the ERA5 reanalysis were also investigated. Compared with the GTMBA, the total contribution from diurnal variability is underestimated by about half (48%) in the ERA5, on average over the GTMBA sites (Fig. 11). For the diurnal SSTskin-associated and wind-associated contributions, their magnitudes are underestimated by 55% and 42%, respectively. This is due to the underestimation of the increases of mean SSTskin and wind speed by diurnal variability (53% and 51%, respectively). Despite this systematic underestimation in the ERA5 results, the spatial patterns strongly resemble those in the GTMBA and have spatial correlation coefficients greater than 0.94. Consistent with the GTMBA observations, the diurnal SSTskin-associated (wind-associated) contribution has a close power function (linear) relationship with surface mean wind speed (wind speed enhancement from diurnal variability) in the ERA5, and the total contribution from diurnal variability can be accurately estimated based on these relationships using a regression model (Figs. 12a–c). Note that the GTBMA observations were assimilated in the ERA5 results. The high performance of these relationships may be attributed to the use of data assimilation. To eliminate this possibility, these relationships were checked over the entire tropical ocean (20°S–20°N) using the ERA5 data. The results show a clear power function (linear) relationship between the diurnal SSTskin-associated (wind-associated) contribution and surface mean wind speed (wind speed enhancement from diurnal variability) over the tropics, and an accurate estimation of the total diurnal contribution based on these relationships (Figs. 12d–f). This suggests that the high performance in these relationships is a result of model dynamics, rather than data assimilation.
4. Summary and discussion
Inadequate sampling of diurnal variability is one of the sources for the uncertainty in the estimation of the LHF. Previously, the LHF uncertainty associated with diurnal variability over the global tropical oceans had not been investigated using field observations. The present study first examined the diurnal variation in LHF and then evaluated the effect of diurnal variability on the climatological LHF using observational data from the GTMBA. The results demonstrate that the diurnal LHF variation is robust in the tropical oceans, especially over the Indo-Pacific warm pool and equatorial cold tongues of the Pacific and Atlantic Oceans. The climatological amplitude maxima are 21.1, 13.6, and, 11.4 W m−2 in these three regions, respectively. Compared with diurnal variabilities of surface wind speed and air specific humidity, diurnal variability of SSTskin makes a primary contribution to the diurnal LHF amplitude. Over the regions where the diurnal SSTskin contribution is dominant, it accounts for 87% of the diurnal LHF amplitude. Because the diurnal SSTskin amplitude has an inverse relationship with surface wind speed over the tropics, the diurnal LHF amplitude exhibits an out of phase spatial pattern with surface wind speed. For instance, low wind speeds over the Indo-Pacific warm pool and equatorial Pacific and Atlantic cold tongues induce large diurnal SSTskin warming, and result in large diurnal LHF amplitude. The spatial correlation coefficient between them is −0.82. The diurnal variation in LHF over the tropics has obvious seasonality (Fig. 13). In the tropical Indian and Pacific Oceans, the diurnal LHF amplitude is larger (smaller) over the region south (north) of the equator in the boreal winter than in the boreal summer. In the tropical Atlantic Ocean, smaller (larger) diurnal LHF amplitude occurs near (off) the equator in the boreal winter. The reason for the seasonal difference in diurnal LHF variation needs to be investigated.
Resolving diurnal variations in SSTskin and wind can improve the estimation of the climatological LHF by properly capturing the daytime SSTskin and daily mean wind speed, respectively. The contribution to the climatological LHF from the diurnal SSTskin variability is large over the Indo-Pacific warm pool and the equatorial Pacific and Atlantic cold tongues, where low wind speeds induce a large diurnal SSTskin warming. Meanwhile, the contribution from the diurnal wind variability is large over the highly dynamic ITCZ and small over the stable trade wind regions. The diurnal SSTskin-associated and wind-associated contributions both reach maxima over the core area of ITCZ with the values of 6.6 and 11.4 W m−2, respectively. Compared with the diurnal SSTskin-associated contribution, the diurnal wind-associated contribution shows a larger spatial difference, and is larger (smaller) over the ITCZ (trade wind regions). The total contribution from diurnal variability exhibits a similar pattern with the diurnal wind-induced change, being large over the ITCZ. On average, the total contribution from diurnal variability to the climatological LHF is 9.1 W m−2 over the GTMBA sites. There exists a clear power function (linear) relationship between the diurnal SSTskin-associated (wind-associated) contribution and surface mean wind speed (wind speed enhancement from diurnal variability). The total contribution from diurnal variability can be estimated accurately using these relationships once long-term high-frequency (hourly) surface wind measurements are acquired. In addition to the GTMBA observations, similar power function and linear relationships can also be found over the entire tropical oceans in the ERA5 reanalysis, and the total diurnal contribution can also be estimated accurately based on these relationships.
This study focuses on the effect of diurnal variability on the climatological mean LHF. However, in some air–sea heat flux products, not only diurnal warming effect but also cool skin effect is not considered for SSTskin. Cool skin decreases LHF, having an opposing effect of diurnal warming (Fairall et al. 1996b; Bellenger and Duvel 2009). To quantify the combined effect of these two processes, the LHF induced by them (LHFDW&CS) was calculated based on the GTMBA measurements {
Over the past few decades, significant progresses have been made in estimating the global air–sea heat fluxes and their variations from the synoptic to decadal time scales. However, the global air–sea heat flux climatology has not yet reached a near zero balance with a residual warm bias (excessive heat flux implied on the sea surface, Song and Yu 2013; Yu 2019), which is an obstacle for our understanding of the upper-ocean heat budget and air–sea interactions. Many efforts have been made to achieve a balanced surface heat flux budget. For example, Large and Yeager (2009) applied a global reduction of 5% in solar radiation to achieve a balanced budget. While this is useful for balance, it appears to be beyond the physics. In this paper, it was found that the diurnal variations in air–sea variables make a significant positive contribution to the climatological mean LHF over the tropical oceans. Including the diurnal variations in air–sea variables will get a significant promotion in the global surface budget. This confirms the role of the high-resolution measurements in achieving a more accurate global heat budget balance in addition to the more accurate algorithms.
Acknowledgments
This study is supported by the National Natural Science Foundation of China (Grants 41976028, 42122040, and 41976003).
Data availability statement
The GTMBA observations are available at https://www.pmel.noaa.gov/gtmba, the ERA5 at https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5.
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