Input satellite SST is derived from the SEVIRI sensor on board the Meteosat Second Generation (Meteosat-11) satellite. SEVIRI has a repeat cycle of 15 min over the 60∘ S–60∘ N and 60∘ W–60∘ E domain, which is the Atlantic Ocean, European seas, and western Indian Ocean. The retrieval of SST from Meteosat-11/SEVIRI is managed by EUMETSAT OSI SAF, which provides subskin SST data as aggregated (L3C) hourly products remapped onto a 0.05∘ regular grid. Hourly products result from compositing the best SST measurements available in 1 h and are made available in near-real time with a timeliness of 3 h (see the OSI SAF product user manual; https://osi-saf.eumetsat.int/products/osi-206, last access: 30 August 2022). The file format follows the GHRSST Data Specification (GDS) version 2 from the Group for High Resolution Sea Surface Temperatures (GHRSST; https://podaac-tools.jpl.nasa.gov/drive/files/OceanTemperature/ghrsst/docs/GDS20r5.pdf, last access: 30 August 2022). The computation of SST in day and night conditions is based on a nonlinear split-window algorithm whose coefficients are determined from brightness temperature simulations on a radiosonde profile database, with an offset coefficient corrected relative to buoy measurements. A correction term derived from simulated brightness temperatures with an atmospheric radiative transfer model is then applied to the multispectral-derived SST (OSI SAF PUM; https://osi-saf.eumetsat.int/lml/doc/osisaf_cdop3_ss1_pum_geo_sst.pdf, last access: 30 August 2022). L3C data are provided with additional information, including quality level and cloud flags. Such quality flags are provided at pixel level, ranging over a scale of five levels with increasing reliability, i.e., from 1 (cloudy), 2 (bad), 3 (acceptable), and 4 (good) to 5 (excellent).

The accuracy of Meteosat-11 SST data has been assessed through comparison with co-located drifting buoys, for day and night data, separately, covering the period from February to June 2018 (see the OSI SAF scientific validation report; https://osi-saf.eumetsat.int/lml/doc/osisaf_cdop2_ss1_geo_sst_val_rep.pdf, last access: 30 August 2022). The mean bias and standard deviation (derived from the differences between SEVIRI SSTs and drifter measurements over a matchup database) during nighttime have been quantified in -0.1 and 0.53 K, respectively. During daytime, the bias remains practically unchanged (-0.09 K) and the standard deviation slightly higher (0.56 K). These statistics were derived by selecting SEVIRI SST with quality flags ≥3, and it is shown that the quality of SST improves when choosing higher quality levels. A similar validation procedure (Marullo et al., 2016), but performed over the Mediterranean Sea by using nighttime and daytime data selected with quality flags ≥4, shows that SEVIRI SST bias and the standard deviation are -0.03 and 0.47 K, respectively.

For our purposes, we selected L3C SST data with quality flag ≥3, as also indicated/suggested in the OSI SAF scientific validation report. A synthesis of the SEVIRI SST characteristics is reported in Table 1.

The model output fields of surface temperature are derived from the Mediterranean Forecasting System (MedFS), a numerical ocean prediction system that produces analyses, reanalyses, and short-term forecasts for the Mediterranean Sea and the eastern Atlantic ocean in the 18–6∘ W, 31–45∘ N box to better resolve the exchanges at the Strait of Gibraltar. MedFS is part of the Copernicus Marine Service and provides regular and systematic information about the physical state of the Mediterranean Sea (https://doi.org/10.25423/CMCC/MEDSEA_ANALYSISFORECAST_PHY_006_013_EAS6; Clementi et al., 2021). MedFS is a coupled hydrodynamic–wave model with a data assimilation component, with a horizontal grid resolution of 1/24∘ (∼4 km) and 141 unevenly spaced vertical levels (Clementi et al., 2017a, b; Pinardi et al., 2003). The Ocean general circulation model is based on the Nucleus for European Modelling of the Ocean (NEMO v3.6; Oddo et al., 2014, 2009), while the wave component is provided by WAVEWATCH III. The model solutions are corrected by a variational data assimilation scheme (3DVAR) of temperature and salinity vertical profiles and along-track satellite sea level anomaly observations (Dobricic and Pinardi, 2008). The Copernicus Mediterranean SST L4 product (CNR, 2015) is used for the correction of surface heat fluxes, with the relaxation constant of 110 Wm-2 K-1 centered at midnight since the product provides foundation SST (∼ SST at midnight).

The MedFS product is produced with two different cycles, namely a daily cycle for the production of forecasts (i.e., 10 d forecast on a daily basis) and a weekly cycle for the production of analyses. For our purposes, only hourly mean SST fields, which correspond to the first vertical level of the model centered at ∼1 m from the surface, are selected. The accuracy of SST data has been quantified via a root mean square difference (RMSD) of 0.57±0.11 and a bias of 0.14±0.09 ∘C obtained through a comparison with satellite-based L4 SST data (see https://catalogue.marine.copernicus.eu/documents/QUID/CMEMS-MED-QUID-006-013.pdf, last access: 30 August 2022). A synthesis of the MedFS SST characteristics is reported in Table 1.

Surface drifting buoys have been used for validation purposes (Sect. 4). Since there are no in situ instruments able to routinely measure skin/subskin SSTs, the commonly adopted validation procedure is to use drifters' data, also due to their high accuracy and closeness to the sea surface (their representative depth attains around ∼20 cm; Reverdin et al., 2010) and to their abundance compared to other in situ instruments, which allows us to achieve a more consistent and homogeneous temporal and spatial coverage. Of course, these observations are affected by a representativeness error when compared to subskin SSTs, which is typically quantified in terms of a bias between the two estimates.

Drifter data have been obtained from the Copernicus In Situ (INS) TAC (Thematic Assembly Centre; identified through 10.48670/moi-00044 (Mercator Ocean International, 2015a) for the Mediterranean Sea,and 10.48670/moi-00043 (Mercator Ocean International, 2015b) for the northeastern Atlantic ocean), which collects and distributes a variety of physical and biogeochemical seawater measurements, provided with the same homogeneous file format. Each in situ measurement, including drifters, undergoes automated quality controls before its distribution. The quality of the data is expressed by control flags indexed from 0 to 9, with the value of 1 indicating best quality. Drifter data have been used to compile an hourly matchup database (Sect. 4.1) over which validation statistics have been produced (Sect. 4.2). A synthesis of the drifter SST characteristics is reported in Table 1.

The OSTIA diurnal skin SST product (While et al., 2017) provides gap-free global maps of hourly mean skin SST at 0.25∘×0.25∘ horizontal resolution, obtained by combining in situ and infrared satellite data. This product is operationally produced by the Met Office within the Copernicus Marine Service (Meteorological Office UK, 2015a) and created using the OSTIA system (Good et al., 2020). The OSTIA system also produces a global daily average foundation SST L4 product (Meteorological Office UK, 2015b). Since the skin SST can be considered as the sum of three components, namely the foundation SST, the warm layer, and the cool skin, the OSTIA diurnal product is created by adjusting the OSTIA foundation SST analysis with a modeled diurnal warm layer analysis (which assimilates satellite observations) and a cool skin model, based, respectively, on the Takaya (Takaya et al., 2010) and Artale models (Artale et al., 2002). Assimilation into the warm layer model makes use of SEVIRI, GOES-West, and MTSAT-2 (Multifunctional Transport Satellite) geostationary infrared sensors, and of the polar orbiting Visible Infrared Imaging Radiometer Suite (VIIRS). Further details on the method can also be found in Copernicus PUM (https://catalogue.marine.copernicus.eu/documents/PUM/CMEMS-SST-PUM-010-014.pdf, last access: 30 August 2022). A synthesis of the OSTIA diurnal SST characteristics is reported in Table 1.

The Mediterranean diurnal optimally interpolated SST (hereafter referred to as MED DOISST) operational product consists of hourly mean gap-free (L4), satellite-based estimates of the subskin SST over the Mediterranean Sea (plus the adjacent eastern Atlantic box; see Sect. 2.2) at 0.0625∘×0.0625∘ grid resolution, from 1 January 2019 to near-real time. Specifically, the product is updated daily and provides 24 h mean data of the previous day, centered at 00:00, 01:00, 02:00, …, 23:00 UTC. The MED DOISST product is published on the Copernicus online catalogue and identified as SST_MED_PHY_SUBSKIN_L4_NRT_010_036 (product reference) and cmems_obs-sst_med_phy-sst_nrt_diurnal-oi-0.0625deg_PT1H-m (dataset reference). Further details on the product characteristics are provided in Table 2.

DOISST is the result of a blending of SEVIRI subskin SSTs and MedFS SSTs (as detailed in Sect. 3.2), where the former is representative of a depth of 1 mm and the latter of 1 m. Then, the DOISST effective depth does, in principle, vary between 1 mm up to 1 m, depending on how the relative amount of satellite observations used in the interpolation. However, diurnal warming is significantly reduced under cloudy conditions (when SEVIRI data are not available) so that, in those cases, the difference between the SST at 1 m and the subskin SST is small. Under clear-sky conditions, SEVIRI observations will dominate the retrieved SST, so the DOISST product can be safely defined as being representative of subskin values.

The reconstruction of gap-free hourly mean SST fields is based on a blending of SEVIRI (satellite) observations and MedFS (model) analyses (used as first guess/background) using optimal interpolation (OI), following the approach proposed by Marullo et al. (2014). The OI method determines the optimal solution to the interpolation of a spatially and temporally variable field with data voids, where “optimal” is intended in a least square sense (see, e.g., Bretherton et al., 1976). The optimally interpolated variable, or analysis (Fa), is obtained as follows: 1Fax,t=Fbx,t+∑i,j=1nWi,j(Fobs,ix,t-Fbx,t). In practice, the analysis Fax,t at a particular location in space and time x,t is obtained as a correction to a background field (Fbx,t). The correction is estimated as a linear combination of the observation anomalies (Fobs-Fb), where the coefficients Wi,j are obtained by minimizing the analysis error variance.

The choice of using MedFS SST as first-guess represents the best alternative to the use of climatologies or previous day analyses, as usually done by other schemes to produce daily SST L4 maps, since the model provides physically consistent estimates of hourly SSTs (Marullo et al., 2014). In fact, the model takes into account the effect of air–sea interactions by imposing external forcings that drive momentum and heat exchanges at the upper boundary. As such, it is able to reproduce at least part of the diurnal warming effects that are driven by the forcing diagnosed from atmospheric model analyses. Using MedFS SST as a first-guess means we are treating the hourly satellite data as corrections to the hourly model data. The observation anomalies are generally small and mostly drive corrections to the spatial patterns, while displaying a reduced diurnal cycle. Anomaly data from different times of the day can thus be more “safely” used to build the interpolated field at each reference time (with different weights). Unfortunately, the first MedFS model layer is at 1 m depth, which means that it will generally underestimate the diurnal cycle anyway. While 1D models could, in principle, be used to better reproduce subskin SST from model data, the approach presented here is focusing on providing estimates that are as close as possible to the original satellite data, avoiding the complications of setting up an additional preprocessing step just to improve the first guess.

The DOISST system ingests merged single-sensor (L3C) SEVIRI SST as the observation source and MedFS SST (first layer) as first guess.

The data subsampling strategy, inversion technique, and numerical implementation of the optimal interpolation scheme are based on the Copernicus NRT MED SST processing chain (Buongiorno Nardelli et al., 2013), which provides daily mean fields of foundation SST over the Mediterranean Sea (CNR, 2015). Here, the diurnal SST chain is organized in three main modules (Fig. 1).

Module M1 manages the external interfaces to obtain both upstream L3C and model data, where hourly mean L3C subskin SST data at 0.05∘ grid resolution are downloaded from OSI SAF while hourly MedFS SST data at 1.0182 m (first level) at 0.042∘ grid resolution from the Copernicus Marine Service.

Module M2 extracts and regrids (through bilinear interpolation) both SEVIRI L3C and MedFS SST data over the DOISST geographical domain at 1/16∘ grid resolution (see Table 2). A selection over SEVIRI is performed by flagging the pixels with quality flag <3.

Module M3 performs a space–time optimal interpolation (OI) algorithm. L4 data are obtained as a linear combination of the SST anomalies, weighted directly with their correlation to the interpolation point and inversely with their cross-correlation and error (Eq. 1). Correlations are typically expressed through analytical functions with predefined spatial and temporal decorrelation lengths. Here, the covariance function fr,Δt is the one defined in Marullo et al. (2014), and given as the product of a spatial and temporal component, as follows: 2fr,Δt=α⋅e-rR+1-α(1+r)c⋅e-ΔtTd, where r is the distance (km) between the observation and the interpolation point. Δt is the temporal difference (in hours) between the observation and the interpolation point, R=200 km is the decorrelation spatial length, T=36 h is the decorrelation time length, and the other parameters are set as follows: a=0.70, c=0.26, d=0.4. All these parameters have been derived in Marullo et al. (2014), deduced from a nonlinear least square fit between the estimated temporal and spatial correlations. In practice, the weights in expression (1) are computed directly from the analytical function (2).

The input data are selected only within a limited subdomain (within a given space–time interval, also called “influential” radius), with a temporal window of ±24 h (this the result of several trials over a large variety of environmental conditions; Marullo et al., 2014) and a spatial search radius of about 700 km (Buongiorno Nardelli et al., 2013). A check to avoid data propagation across the land is performed between each pixel within the subdomain and the given interpolation point (eventually discarded if there are land pixels between the straight line connecting the two points).

The interpolation error (analysis_error field in the L4 file; Table 2) is obtained from the formal definition of the error variance derived from optimal interpolation theory (e.g., Bretherton et al., 1976). This error ranges between 0 %–100 %, meaning that the error is almost zero when an optimal number of observations is present within the space–time influential radius, while only first-guess data are used (i.e., no observations are found within the search radius) when the error is 100 %.

The optimal interpolation algorithm is synthesized as follows. For clarity, in order to interpolate an SST map on a given day at 12:00 UTC, the following steps have to be done:

download ±24 hourly SEVIRI L3C and MedFS (first layer) SST fields (in their native spatial resolution) centered with respect to the interpolation time;

Obviously, the symmetric temporal window (±24 hourly) can be applied only for reprocessing. During near-real time DOISST processing, the input data are collected starting from 24 h before the interpolation time up to the last available SEVIRI hourly SST field.

Finally, the main difference with the original method is that all the input observations are interpolated, while in Marullo et al. (2014) valid SST observations are left unchanged (not interpolated).

The accuracy of the MED DOISST product has been assessed through comparison with independent co-located (in space and time) surface drifting buoy data (matchups). The relative and absolute validation framework is thus based on the compilation of a matchup database between DOISST, SEVIRI L3C, MedFS (all available at 1/16∘ as described in Sect. 3.3), and OSTIA diurnal (kept at its original 1/4∘ resolution), and drifters measurements covering the full years 2019 and 2020. The large number of drifters provides a rather homogeneous and continuous spatial and temporal coverage over the whole period (Fig. 2) allowing a robust statistical approach.

First, a preselection of high-quality drifter data is performed, retaining only temperatures with quality flag equal to 1 (good) or 2 (probably good; see Sect. 2.3). Then, the co-location is carried out on hourly basis, building a matchup database by collecting the closest (nearest neighbor) SST grid point to the in situ measurement within a symmetric temporal window of 30 min with respect to the beginning of each hour. A final quality outlier detection check is carried out by identifying drifter data for which the module of the difference with respect to satellite observations exceeds n times the standard deviation σ of the distribution of the differences (δ). At each step, n decreases, and data that fall out of the interval I=[mean(δ)-n⋅σmean(δ)+n⋅σ] are flagged as outliers and removed. For each n, the selected outliers are eliminated, and the process is repeated for the same value of n until no more outliers are detected. Then the system moves to n-1. The process starts for n=10 and stops at n=3, and removes ∼1% of the total original sampling (as expected from a Gaussian distribution) of drifter data that clearly revealed anomalous temperature values.

The main validation statistics are quantified in terms of mean bias and root mean square difference (RMSD) from matchup temperature differences (namely, SST minus drifter). Each statistical parameter is associated with a 95 % confidence interval computed through a bootstrap procedure (Efron and Tibshirani, 1994).