Four vessels' data records are used to obtain the air–sea interaction fluxes. The AJ, RM, MO, and CS research vessels are provided with meteorological and sea surface monitoring equipment, allowing them to measure the variables required to obtain the final flux products throughout their trajectories. The onboard measuring instrumentation is a Vaisala AWS430 unit, specifically designed to measure climatological variables within a marine environment. Information about the instruments used for the measurement of each magnitude is detailed in Table . The variables recorded during the period of 2011–2023 and stored within this data set are air temperature (DRYT), atmospheric pressure (ATMS), wind speed (WSPD), relative humidity (RELH), and total incident radiation (RDIN), recorded by the meteorological equipment, and sea temperature (TEMP), recorded using the TSG. The names of the variables and their descriptions follow the standards of the MedAtlas Parameter Usage Vocabulary from the British Oceanographic Data Centre (BODC), which can be further explored at https://vocab.seadatanet.org/search (last access: 15 October 2025).

Daily, both types of data, meteorological and TSG, are sent to the IEO Data Center on land and kept within archives for each month and vessel. Then, formatting and quality control (QC) procedures are applied for its permanent storage within MEDAR/MedAtlas format . MEDAR/MedAtlas is an ASCII auto-descriptive format available since the last decade of the 20th century, which merges to facilitate reading, recording, processing, and storing oceanographic data. Each file is provided with a heading where all metadata information is reflected alongside a flag column where the QC labels are specified. Data sampling has a different frequency for each type of data. In consequence, final flux products are calculated at an hourly frequency. Then, with all of the information above having been gathered, final MEDAR/MedAtlas formatted heat and momentum flux data archives are constructed (also following BODC vocabulary standards) for each month and vessel . The columns in these archives show the three air–sea interaction fluxes, SHFL, LHFL, and MOFL, along with the variables used in their calculation (which are shown in Table ). A flag column is also added based on the criteria specified in the QC section. Besides this, incident radiation (RDIN) is also included in order to bring about the possibility to determine the total heat storage (HS) in the ocean (Eq. ): 1HS=Qs+Qlw+SHFL+LHFL, where Qs is the shortwave incident radiation from the sun, and Qlw is the net longwave radiation. RDIN accounts for both shortwave and longwave incident radiation from the sun and atmosphere. The upward longwave radiation from the sea can be obtained with the Stefan–Boltzmann radiation law using the sea temperature (TEMP) through R=ϵσT4 , where ϵ is the emissivity ranging between 0.93 and 1 , and σ is the Stefan–Boltzmann constant. Thus, Qs and Qlw are addressed by the data set, and, alongside the air–sea interaction heat fluxes, both radiative and convective exchanges between the two media are determined.

In order to obtain reliable data products, it is important to elaborate on adequate validation and QC procedures. Both types of records (meteorological and TSG data, as well as subsequent flux products) are revised and checked by manual and automatic techniques. As was previously mentioned, all MEDAR/MedAtlas archives contain a flag column that specifies the QC of each variable and individual data sample. The flag criteria are based on SeaDataNet guidelines .

Firstly, meteorological and TSG data are validated by visual inspection, which is useful to check the reliability of the data set. This enables us to understand the noise of the time series while simultaneously identifying immediate anomalous or spike records. Thus, the time series of each year's data records for each data type is represented, allowing us to observe whether all measurements are within the temporal limits specified in the metadata heading. In addition, map plotting of the vessel's trajectories is a practical procedure to detect position errors. Additionally, other automatic processes are executed. A global range test for each variable is conducted by setting highly extreme thresholds, which would be impossible to exceed in real life: e.g. >100 % or negative values for relative humidity. Also, more restrictive limits are fixed, taking into account regional and seasonal climatological behaviours. The North Atlantic area does not reach such high sea surface and air temperature values as the western Mediterranean or Canary regions. Furthermore, additional QC tests are applied based on SeaDataNet recommendations . A gradient test (GT), represented by Eq. (), which evaluates if the gradient of a measurement and the previous and next values is too sharp, is applied for each variable: 2GT=|V2-V3+V1/2|, where V2  is the record being checked, and V1 and V3 are the previous and next measurements. If GT is higher than the values specified in Table , it is flagged as 4.

Temperature data are also tested under a spike test (ST) following Eq. (): 3ST=|V2-V3+V1/2|-|V3-V1/2|. SeaDataNet guidelines fix the ST at 6 °C (if ST > 6 °C, V2 fails the test). However, noticing the large threshold this quantities supposes, another fixed limit is implemented based on statistical analysis . This new threshold is calculated to be 3 times the interquartile range (IQR) parameter (3 × IQR); the IQR is defined based on the first (Q1) and third (Q3) quantiles of the monthly distribution: IQR = Q3-Q1. The most restrictive threshold, 6 °C or 3 × IQR, is the reference for each test. Lastly, additional QC procedures are applied: if a constant value is repeated notably during the record, it is flagged as 4, and, even if, under all of the tests applied, there exist notorious eye-catching spike values to remove, they are also flagged manually as 4 based on the expertise developed throughout the study. Regarding the final flux data set, if any of the meteorological or TSG variables involved in the calculation are flagged with a value other than 1, the air–sea interaction fluxes are automatically flagged in the same way. In addition, flux time series and map trajectories are newly checked in order to, firstly, confirm that all data are placed over the sea and, secondly, identify any prominent spikes which are then flagged manually.

The time period covered by this study is 2011–2023. However, the data record is not a continuous and uninterrupted time series. Data records are collected based on the availability of the ship's activities. Additionally, technical problems or preventative actions to maintain its good condition might turn the experimental equipment off, creating gaps in the record. This, along with the QC procedures, reduces the amount of valid data available (Fig. ).

Air–sea, heat, and momentum fluxes are transmitted to the surface layer (SL), the layer immediately closest to the interface between the atmosphere and ocean and the lowest layer in the ABL . Here, the turbulent exchange within both media, its dynamics, and its implications for the development of the ABL are ruled by Monin–Obukhov similarity theory , which ensures that these heat and momentum fluxes are constant with height. Mentioned fluxes are transported by the vertical wind component ω. Hence, sensible and latent heat fluxes can be considered to be temperature and humidity fluxes into the atmosphere, whereas the momentum flux appears as wind stress towards the surface. The experimental measurement of these quantities requires a temporal resolution that is enough to capture the turbulent fluctuations – or eddies – of the magnitudes immersed in these transports. Several experimental approaches exist to determine these quantities, e.g. the eddy correlation method or the dissipation method . However, the most useful methodology to calculate the mentioned turbulent fluxes, which is used in this study due to the experimental and technical constraints, is the bulk aerodynamic approximation (Eqs. –). Here, a relationship between air–sea fluxes and the gradient of temperature, specific humidity, and horizontal wind, respectively, is established between the sea surface and the corresponding measurement point in the atmosphere: 4SHFL=ρCpCTU(z)Ts-Ta(z),5LHFL=ρLCEU(z)qs-qa(z),6MOFL=ρCDU2(z), where the subindex “s” references the sea surface, whereas “a” references the atmosphere; ρ is the air density; Cp and L are the specific heat at constant pressure and the latent heat of evaporation, respectively; U is the wind speed; T and q are the temperature and the specific humidity of the media; and CT, CE, and CD are aerodynamic bulk coefficients. Following these criteria, SHFL to the atmosphere is positive if sea temperature is higher than air temperature, whilst LHFL is positive when there is evaporation. MOFL is always positive due to the wind stress from the atmosphere to the sea surface. In ideal conditions, U(z) is the wind speed relative to the sea surface current, which can be measured using specific equipment such as scatterometers . In this case, ultrasonic anemometers are used to measure wind speed and direction, unable to determine the sea current speed. Thus, U(z) is considered henceforth to be the absolute wind velocity, neglecting the effects of the surface ocean current. Previous studies have pointed to errors of between 10 %–20 % when neglecting ocean currents around 0.5 m s⁻¹ .

CT and CE are the aerodynamic heat and moisture coefficients, respectively. They depend on the stability of the SL, as well as the wind speed. Several researches have found values of CT between 1.1×10-3 for unstable stratification and 0.75×10-3 in a stable atmosphere . On the contrary, for CE, conclude that it depends more on wind speed than on stability. Hence, for this study, due to the limitation in obtaining the state of the stability of the ABL (it would be essential to calculate the characteristic turbulent scales of temperature, wind, and moisture according to Monin–Obukhov theory), the bulk aerodynamic coefficients are considered to be constants: 1×10-3 for CT and 1.3×10-3 for CE . Furthermore, for the drag coefficient CD, the wind dependency relation exposed in Large and Pond (1981) and implemented in the Python Air–Sea routines (https://github.com/pyoceans/python-airsea, last access: 15 October 2025) is used. The air density ρ is calculated using the ideal-gas equation . The specific humidity is derived from the pressure and relative humidity measurements. It is calculated using the specific humidity in saturated conditions based on the vapour pressure dependency on temperature as identified by , which is also addressed by the aforementioned Air–Sea routines, and the relation RH=q/qsaturated, with RH representing the relative humidity. The specific humidity of the sea surface qa is obtained analogously but considering saturation conditions. This is multiplied by a factor of 0.98 due to the reduction in saturated vapour pressure as a consequence of salt concentration . Specific heat at constant pressure Cp has a value of 1004.7 J kg⁻¹ K⁻¹, whereas the latent heat of evaporation amounts to 2.5×106 J kg⁻¹.

For these calculations, the availability of the meteorological and TSG variables measurements is needed. The absence of any variable involved in Eqs. ()–() makes it impossible to determine SHFL, LHFL, and MOFL. For the period from 2013 to 2016, there are no pressure measurements from the AJ, RM, and/or MO vessels (Fig. ). This also happens during the rest of the years for MO. Nonetheless, the data are still useful to determine the sign of the fluxes (difference in terms of temperature or humidity between ocean and atmosphere, as in Eqs. and ). Given that, despite the fact that the concrete value cannot be obtained, its tendency, proportionality, and behaviour can still be inferred.

Once the QC is applied and the data are in a well-suited MEDAR/MedAtlas format, results and analysis from AJ, RM, MO, and CS measurements can be obtained. During their oceanographic activities, the vessels cover a notorious area near the Spanish waters (Fig. a). The total sum of the entire data sampling between 2011 and 2023 is 211 713 rows of meteorological and TSG data and their subsequent air–sea flux products. However, the measurements flagged with 9 and 4 (meaning no data and error data, respectively) reduce the operative number of data available for each variable. In Table , the number (and percentage) flagged as “good value” (1) for each variable is shown, whereas, in Table , the flux products flagged as 4 for each marine region are specified. The atmospheric pressure is the variable with fewer good values (44.6 %) due to the lack of measurements during the period of 2013–2016 by the AJ, RM, and MO vessels, although this accounts for a significant number of 94 572 values. This is followed by the sea temperature (62.7 %), which directly affects the heat fluxes; this is the reason why there exists such a remarkable difference between the percentage of heat (14.1 %) and momentum (25.8 %) fluxes. The absence of good values of RELH stands out mainly during the CS's trajectories between 2011 and 2013, when values above 100 % and below 0 %, which prevent the correct determination of the air density, are recorded; however, its percentage of good values is a notorious 76.5 %. Also, some slightly disproportionate wind speed measurements recorded by CS are flagged as 4; nonetheless, it presents a high percentage of good values. Furthermore, DRYT exceeds these percentages, with 77.5 %, despite presenting occasional high values registered during the winter months in 2018 and 2019.

Figure b–d show an example of oceanographic visual products that can be represented with this data set using Ocean Data View (ODV) software , where air–sea fluxes calculated are plotted throughout the vessels' trajectories at the points where they are available. These plots give a visual idea of the spatial distribution and magnitude of each variable. Differences can be noticed between basins. The Mediterranean area exhibits higher evaporation amounts in comparison with the Atlantic facade. Sensible heat characteristics are less remarkable in these areas. Nevertheless, negative values in the Alboran Sea and along the Atlantic coast in the northwest of Spain stand out. In addition, the effect of the wind stress due to the trade winds is also noticeable in the Canary region for all air–sea interaction fluxes.

Further analysis processes can be carried out with these data sets. Annual cycles provide key information for understanding the mean behaviour and variability of a field at inter-annual frequencies. They also contribute to both validating the data and identifying key or eye-catching patterns to be analysed further. In this case, Table  shows the annual cycle for the sensible heat flux for each sea region considered. All regions manifest a similar behaviour, with the lowest values during the summer season (from June to August) and the highest results for November and December, showing a greater loss of heat by the ocean during winter months due to the contrast in terms of temperature between the sea surface and air. The annual mean is positive over the whole domain, with the highest quantities for the Canary (9.86 W m⁻²) and Levantine–Balearic (6.71 W m⁻²) regions, excluding the Alboran Sea, where several negative values are present and which conforms to an annual mean of -2.26 W m⁻². The special behaviour of this region, with an average annual cooling, compared to that of other basins is also detailed in the scientific literature . Some hypotheses to be considered to explain this behaviour are the income of colder North Atlantic waters or the upwelling processes of the Poniente wind regime and the two anticyclonic gyres in this basin . The standard deviation values, despite presenting amounts even higher than the mean result, are compatible with those of other studies.

Regarding latent heat flux (Table ), the annual cycle pattern is similar to that of the sensible heat but with greater values: lower quantities during the spring–summer transition and higher values during the winter season when wind stress is more intense. This confirms the greater loss of heat during winter months due to turbulent exchange. Higher annual mean values are found once again in the Canary (138.35 W m⁻²) and Levantine–Balearic (139.50 W m⁻²) regions. These behaviours are expected as the former is located in subtropical latitudes, commonly known to be areas with great levels of evaporation , whereas the latter belongs to the Mediterranean basin, where the evaporation regime is equally significant, even exceeding precipitation rates . The annual average within the Mediterranean area is slightly superior to that of the other model-based reconstructions ; nonetheless, their ranges of variability are compatible. More moderate values are found within the Cantabrian and Atlantic areas, where precipitation exceeds evaporation. However, there are significant quantities that must be validated by additional studies.

Momentum flux outcomes present expected values within the characteristic ranges of the specific location (Table ). The annual mean values for all regions are around 0.1 N m⁻². This quantity is exceeded in several regions during the months of November and December, enabling greater turbulent exchange between the ocean and the atmosphere. This is logical due to the atmospheric baroclinicity and the intensification of the wind regimes of these months. However, annual cycles are not satisfactorily defined for all regions. The Alboran–Strait area shows higher-than-expected values during July and August, in contrast with the inter-annual wind climatology of their regional winds, namely the Levante–Poniente regime . The Canary region also presents higher results during August, although this is already documented in the scientific literature .

The time series of heat and momentum fluxes are also plotted to analyse the evolution, tendencies, and gaps during the period considered. The western Mediterranean and the Cantabrian–Atlantic graphics are shown in Fig.  as they are the regions with more extension in this study. The data gap during the year 2020 and at the beginning of 2021, due to the difficult working context of the COVID pandemic, stands out. Uniquely, the AJ's data are available during this time frame, although with several problems in the temperature probe and the barometer which make it impossible to make a reliable calculation of the final products. These gaps are difficult to interpolate due to the high variability of the meteorological magnitudes implied in the flux calculation, creating a complicated context in which to study hypothetical tendencies or patterns, which are blurred by the intermittence of the time series. Thorough maintenance and care of the measuring equipment are fundamental in order to take advantage of the experimental measuring potential. However, several important conclusions can be drawn: the Mediterranean area exhibits greater latent heat fluxes due to the dominance of evaporation in its basin. Sensible heat is higher for the Cantabrian basin; the negative values from the Alboran Sea, aforementioned, decrease the mean value of the Mediterranean basin. Regarding momentum flux, the mean values for all of the basins are around 0.1 N m⁻², which is an expected quantity for these basins , with the highest value being for the Alboran Sea, presumably due to the influence of the Levante–Poniente wind regime .

The levels of 50 and 300 W m⁻² for sensible and latent heat, respectively, which are considered to be significant magnitudes for both variables, are marked by dashed red lines. The regions of the planet where the greatest turbulent heat exchange between the ocean and the atmosphere occurs are the western margins of the Atlantic and Pacific oceans, in the Gulf and Kuroshio currents, respectively, where these thresholds are exceeded . On the other hand, the 0.6 N m⁻² threshold is defined for momentum flux based on the results of other studies in open-ocean conditions . Regions with remarkable wind intensity regimes, such as the Southern Ocean, can reach values superior to 1 N m⁻² or even greater (2–8 N m⁻²) during tropical cyclones . The Alboran Sea expresses one of the highest frequencies (0.76 %) of momentum flux, exceeding this threshold, while it has the lowest ratio above the 50 W m⁻² sensible heat threshold – also expected because of its negative average value. In addition, the Levantine area shows the highest frequency (8.80 %) above the 300 W m⁻² barrier. On the contrary, the Cantabrian region has the lowest ratio for this variable (3.93 %), indicating a lower evaporation rate in comparison.

Furthermore, in order to address the issue of the lack of heat and momentum flux outcomes due to the absence of a necessary variable for their calculation, the evolution of key variables that significantly influence the final products (Eqs. –) can be examined separately (Fig. ). The temperature difference is directly proportional to the sensible heat flux, and it allows us to define the sign of this flux and to assess whether it implies a positive or negative heat contribution to ocean warming. Additionally, wind speed is proportional to all three air–sea interaction fluxes, and so its behaviour is crucial for inferring the magnitude of these products. Besides this, relative humidity is essential for determining the specific humidity of the air and, thus, the moisture difference compared to the ocean, which is proportional to latent heat flux. The higher the relative humidity, the less likely it is that water evaporation from the ocean will occur as the environment reaches saturation; in consequence, this potential energy remains stored in the ocean rather than being transferred to the atmosphere.

One additional application of the study of air–sea interaction fluxes is to obtain the net heat storage balance. The ocean heat budget is determined by both radiative (net shortwave and longwave radiation) and convective components. Sensible and latent heats account for the convective contribution, whereas the incident radiation is provided by the RDIN variable (Fig. c and f) measured by the meteorological measuring equipment. It accounts for the solar (shortwave) and atmospheric (longwave) radiation. The longwave emission by the ocean can be determined by the Stefan–Boltzmann law with the specific determination of the emissivity constant for ocean water . Beyond this, given that the ocean is not a fixed water mass, the advective-heat term might have an important magnitude to be considered in the heat balance . The Atlantic Meridional Overturning Circulation (AMOC) accounts for most of the northward transport of heat by the mid-latitude Northern Hemisphere . It reaches its peak heat transport around 26° N, where, consequently, the RAPID Climate Change Programme was established in 2004 to provide direct observational measurements of its flow and transport . Thus, this certainly has an important impact on the heat storage balance of the Canary region, which is close to this latitude, not to mention the impact on the rest of the Atlantic marine regions considered in this study. Regarding the Mediterranean Sea, mooring-based observations have established the net heat transport from the Atlantic through the Strait of Gibraltar to be 5.2 W m⁻² . Other authors have determined this flux to be between 8.5 W m⁻² and 5 W m⁻² based on measurements of the net water inflow and its temperature.

Figure  shows the annual cycles of the heat convective fluxes (Fig. a, d, b, and e) and the incident radiation (Fig. c and f) for two example regions, the western Mediterranean and the Cantabrian–Atlantic areas. Sensible and latent fluxes reach their minimum strength during the spring–summer transition, whereas they are more prominent during the colder seasons. On the contrary, the incident radiation presents a reverse pattern. During summer, less heat is lost by turbulent processes, and more is acquired by radiation, increasing the total heat budget. On the other hand, in winter, when there is a positive and marked contrast between the sea and air temperature, sufficient wind stress to trigger the convective fluxes, and less incident radiation, the ocean experiences a decrease in its heat storage.

Incident radiation is greater for the Mediterranean region than for the Cantabrian due to the differences in terms of their geographical location and cloud cover. However, in comparison to other studies in the former area , monthly mean radiation values might present some deficits, which contribute to underestimations of the heat income stored in the ocean, altering the total heat balance. Further comparisons and validation procedures must be done regarding incident radiation in order to obtain fairly reliable heat storage outcomes.