This paper focuses on the problem of generating sea surface temperature (SST) fields that resolve the diurnal cycle for modeling applications, using the tropical Atlantic Ocean as a test site. Our approach was to take advantage of geostationary satellite observations as the diurnal signal source to produce gap-free optimally interpolated (OI) SST fields. The OI schema merges microwave data from the Advanced Microwave Scanning Radiometer (AMSR) and infrared data from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) to produce diurnal optimally interpolated SST (DOISST) maps every 3 h on a 25 km grid combining the capability of AMSR to provide nearly bias-free daily SST estimates with the opportunity offered by SEVIRI to monitor the evolution of the SST over the day. Comparison of the SEVIRI data (distributed by the Ocean and Sea Ice Satellite Application Facility (SAF)) with in situ buoy measurements (Pilot Research Moored Array in the Tropical Atlantic) revealed a SAF spatial bias that was greater north of the equator than to the south. This was further confirmed using the Coriolis data set that showed a wide band of SAF high bias values (>0.6 K) which extended diagonally (NW → SE) across the tropical Atlantic. In contrast, the AMSR bias pattern was essentially flat (<0.2 K), justifying its use as a reference field to compute the SAF adjustment and to further investigate the spatial-temporal variability of the SAF bias. Analysis of the SAF-AMSR difference revealed strong similarities to ITCZ-related patterns observed in aerosol, columnar water vapor, and wind fields. Due to the bias dependence on atmospheric factors that have pronounced spatial variability and short time scales, the adjustment needs to be performed daily.
 Recent findings indicate that resolving the sea surface temperature (SST) diurnal cycle is important for better simulation of climate-related phenomena. Earth's movement externally forces the climate system on precessional, seasonal, and diurnal time scales, yet most climate models take into account only the first two [Bernie et al., 2007]. An effort to include the diurnal SST cycle in an ocean model of the Indo-Pacific resulted in an increase in the intraseasonal SST response to the Madden-Julian Oscillation by 20% and in the intensity of Ekman cells and equatorial upwelling by 10% [Bernie et al., 2007]. Moreover, when the coupling of this ocean model to an atmosphere model was changed from daily to 3-hourly, a more realistic spatial pattern of warming and precipitation in the tropical Pacific was produced [Bernie et al., 2008]. A similar improvement in the simulation of monsoonal phenomena was reported with the use of higher-frequency SST [Marullo et al., 2008; Klingaman et al., 2008]. Marullo et al.  found that the use of an SST boundary condition that explicitly includes the diurnal cycle improved the performance of a regional climate model (RegCM) in resolving physical components of the atmosphere dynamics such as African easterly waves. Thus, the modeling community could benefit from the use of gridded, diurnally resolved SST fields.
 Recent progress in understanding physical phenomena that occur in the upper ocean and the availability of more sophisticated numerical models require a more precise estimate of SST at all temporal and spatial scales, including the diurnal cycle [Xie et al., 2006; Bernie et al., 2007, 2008; Clayson and Weitlich, 2007]. In fact, numerical weather prediction, RegCM, and ocean models require SSTs with an accuracy of 0.1–0.3 K [Intergovernmental Oceanographic Commission, 1999]. This accuracy range is comparable to or lower than typical amplitudes of the diurnal cycle [e.g., Kennedy et al., 2007, Figure 2] and is well below that of diurnal warming, that is, excursions in excess of 3 K that have been often observed in the world oceans under low-wind and strong solar heating conditions [Stommel and Woodcock, 1951; Stommel, 1969; Minnett, 2003; Jessup and Branch, 2008; Gentemann et al., 2008; Merchant et al., 2008]. However, while in situ measurements of diurnal warming can provide information at high temporal resolution, they have limited spatial coverage and temporal duration. For the production of model-ready diurnal SST fields, satellite data offer a more practical starting point since they provide regular sampling and extensive areal coverage. However, the accuracy of satellite data has to be evaluated with in situ data, and the error has to be minimized if possible. In addition, an appropriate interpolation method would be needed to fill gaps. It is also important to recognize that a compromise between accuracy and spatial resolution has to be made. For climate modeling purposes, it is probably more critical to reproduce the large-scale daily rhythm of heating and cooling over large areas of the ocean rather than to simulate local diurnal warming events.
 Since the production of the desired SST diurnal fields will require combined use of in situ and remotely sensed data, the different definitions of SST need to be considered before merging heterogeneous information [Gentemann and Minnett, 2008]. Most in situ measurements can be considered bulk SSTs, that is, made at depths of 0.5–1.5 m below the surface. In contrast, infrared (IR) satellites measure SST of the skin layer (<1 μm from the surface), while microwave (MV) instruments provide a subskin (<1 mm) measurement. This makes it difficult to compare in situ observations with surface satellite data, as the skin layer responds more rapidly to changes in heat and momentum. This is true even when satellite SSTs are calibrated against subskin measurements since only a mean skin – subskin temperature difference is considered, leaving the diurnal oscillation of a specific day free to evolve differently at skin and subskin levels. Note that in simulations, the use of bulk SSTs, or even only nighttime SSTs, will likely produce an incorrect estimate of air-sea heat and gas fluxes in numerical models or physically based parameterizations for the gas transfer velocity [Webster et al., 1996; Woods et al., 1984; Schiller and Godfrey, 2005; D'Ortenzio et al., 2008; Kettle et al., 2009].
 An international effort, the Global High-Resolution Sea Surface Temperature (GHRSST) project, was made to develop gap-free multisensor products for model assimilation purposes [Donlon et al., 2007]. The GHRSST products, also referred to as level 4 products, are operationally produced by blending data from multiple sensors and also provide an estimate of the foundation temperature. The foundation SST is defined as the temperature of the water column free of diurnal temperature variability (daytime warming or nocturnal cooling) and is considered equivalent to the SST subskin in the absence of any diurnal signal (http://www.ghrsst-pp.org/SST-Definitions.html). These multisensor analyses provide subskin temperatures at different temporal scales (12-hourly, daily, monthly, annual) but do not resolve the diurnal cycle. Attempts have been made to introduce a diurnal cycle over the measured foundation temperature using meteorological forcing and simplified 1-D physical models or parameterizations developed from them (Buongiorno Nardelli et al., 2005; Gentemann et al., 2009; Stuart-Menteth et al., 2005; and references therein). This type of approach can be limited by the availability of realistic meteorological parameters and by validity of parameterization of the physical processes that occur in the upper ocean and at the air-sea interface (Pimentel et al., 2008a, 2008b).
 An alternative is to use SST measurements from geostationary satellites, which are currently the only source of repeated observations over the diurnal cycle. The existing geostationary platforms carry only IR-based instruments, which cannot see through clouds, and thus the data contain many gaps. Moreover, because of the fixed footprint, it would be necessary to combine data from the different geostationary sensors, each with their respective design and bias, to obtain global and basinwide coverage [e.g., Maturi et al., 2008].
 This study is focused on producing diurnal SST fields for the tropical Atlantic because of the availability of geostationary satellite data, as well as abundant in situ observations (see section 2). The Spinning Enhanced Visible and Infrared Imager (SEVIRI), carried on the Meteosat Second Generation (MSG) platform, has a footprint covering most of the Atlantic Ocean. The SEVIRI SST standard deviation is ∼0.5 K [Brisson et al., 2002] and can be expected to exhibit the biases associated with IR instruments. Merchant et al.  showed that Saharan dust occurrence within the SEVIRI field of view caused biases on of the order of 1 K. They developed an empirically derived dust correction algorithm that is applied according to a Saharan dust index, which is related to aerosol optical thickness. Although this correction removes an independent error of 0.2 K from the SEVIRI SSTs validated against buoys from all latitudes, a significant latitudinal bias still remains, especially in the 0°N–10°N region [Merchant et al., 2006]. Furthermore, Merchant et al.  noted the occurrence of a coherent negative bias of −0.2 to −0.4 K in the equatorial Atlantic Ocean when a nonlinear SST (NLSST) algorithm based on optimum coefficients derived from matches themselves is used. They argued that even though the linear regression used to derive the coefficients of the NLSST ensures zero bias and minimum variance for the domain spanned by the training data, this does not imply zero bias and minimum variance regionally. Merchant et al.  also investigated the sensitivity of the SST retrieval to water vapor w and to the true SST. They found that, in general, sensitivity of NLSST to w is modest but can reach values of −0.5 K for a 10% increase in w in some tropical regions where water vapor loading can be greatest, even though sensitivity is not simply proportional to the total columnar water vapor. They also noted that the sensitivity of the true SST to changes in the IR satellite-derived SST is less than 1:1. This effect is evident in the tropical Atlantic, where they found that IR SST retrievals can underestimate real temperatures changes by about 30%.
 Comparisons with MW-based satellite data offer a means to better understand the SEVIRI biases; MW-derived SSTs have been found to be more reliable in the tropical region [Gentemann et al., 2004]. MW-based satellite sensors include the Advanced Microwave Scanning Radiometer (AMSR), which provides one of the data sets used in this study. MW data can be retrieved through clouds and dust and thus have fewer cloud gaps on a daily basis. However, the MW retrievals have lower resolution than IR data and are sensitive to rain, sea-surface roughness, and land-water boundary transitions. Thus, MW and IR SST data sets are complementary and can be combined to obtain a reliable global data set. That is, IR and MW data can be merged once the infrared bias is corrected by adjusting to daily microwave values to produce fields with a better spatial coverage over a larger window of time scales.
 The tropical Atlantic Ocean is one of the most suitable regions of the world's oceans where merged (and interpolated) products can be tested during extreme conditions related to the frequent occurrence of high water vapor and aerosol loading and to the strong air-sea interaction that occurs in this area. The surface ocean temperature of this area plays an important role in the onset of the African monsoon [Hagos and Cook, 2007] and, in general, in many climate and ocean processes. Its variability is associated with the meridional displacement of the Intertropical Convergence Zone (ITCZ) and exhibits a marked seasonal signal whose amplitude can reach up to 7°C in the eastern part of the equatorial basin. This oscillation can cause a temperature gradient between the equatorial waters, influenced by the occurrence of the cold tongue, and the warmer water north of it, contributing to the onset of the African monsoon through the intensification of the southerly winds in the Gulf of Guinea [Okumura and Xie, 2004]. Okumura and Xie  also suggested that West African rainfall could be influenced significantly by SST through the advection of marine boundary layer temperature anomalies over Africa, which, in turn, cause the development of sea level pressure and surface wind convergence anomalies.
 The general aim of this paper is to generate SST fields over the diurnal cycle in the tropical Atlantic. In particular, we wanted to evaluate the extent to which geostationary satellite measurements are able to estimate the amplitude and variability of the SST diurnal cycle in the ocean, which is our basis for producing a level 4 time series of 3-hourly SST maps. The 3-hourly objective is consistent with the Global Climate Observing System requirements for SST as stated in a report by the World Meteorological Organization  on the adequacy of observational data for the United Nations Framework Convention of Climate Change. This work consists of four parts. Our first step is to compare SEVIRI and AMSR SST observations over the tropical Atlantic Ocean with corresponding in situ measurements provided by the Pilot Research Moored Array in the Tropical Atlantic (PIRATA) [Servain et al., 1998] and by the Coriolis operational oceanography system. Then we examine the difference between infrared (SEVIRI) and microwave (AMSR) SSTs and investigate the possible causes and analyze the spatial distribution of the SAF bias respect to in situ measurements. Based on the results of the first two steps, we propose a method that merges MW daily data with diurnal IR observations. Finally, we use optimal interpolation to produce gap-free SST fields every 3 h and evaluate their accuracy.
 Three satellite-derived SST data sets and two in situ data sets are examined in this study over a 2-year period (2006–2007), unless otherwise specified. All of the satellite data sets are remapped to the same grid resolution, and then interpolation is performed only within the study area, as detailed in section 3. The remapping was done over the AMSR 0.25° × 0.25° resolution grid for all the data sets, averaging all valid pixels falling into ±0.125° from the center of each AMSR pixel.
2.1. Ocean and Sea Ice Satellite Application Facility (SAF) Sea Surface Temperature (SST)
 A regional SST data set for the Atlantic Ocean is available at 0.1° spatial resolution from the Ocean and Sea Ice Satellite Application Facility (SAF). This study uses the Low and Mid Latitudes (LML) data set, which covers the area between 60°S and 60°N and between 100°W and 45°E. The MSG satellite carries the SEVIRI instrument that provides data over most of the study region, but west of 37.5°W, GOES-East data are used when available [Météo-France, 2006]. Thus, the majority of the data analyzed in this paper are SEVIRI data because only the westernmost edge of our study area contains GOES data. Products derived from the NOAA polar orbiters are added in order to cover the northernmost part of the Atlantic at latitudes greater than 50°N (out of our study area). The merging procedure starts from the single-satellite (GOES 12, MSG, or NOAA for the years of our investigation) SSTs averaged over the 0.1° SAF grid every 3 h. In common areas, where more than one single-satellite SST is available, one of the available SST values is chosen rather than averaging all the available values. The choice between satellites mainly depends on the quality index of the single-satellite products where SAF tries to select the best confidence level and to eliminate, as much as possible, sun glint, aerosol cases, and satellite zenith angles higher than limit values. GOES 12 SST data are retrieved in nighttime conditions only. MSG uses the same algorithm for day and night, but two additional general algorithms have been prepared to implement aerosol robust solutions. More details on algorithms, merging and remap procedures, are described elsewhere [Météo-France, 2006].
 The data examined in this study are primarily from SEVIRI. The accuracy of the entire Atlantic SST field is routinely checked at the hourly intervals against drifting buoy measurements (http://www.osi-saf.org/). An aerosol algorithm [Merchant et al., 2006] was implemented beginning 25 April 2006. The impact of this on the results is discussed where relevant.
 LML SST fields are available at 3 h intervals beginning at 0100 UTC. Although the IR instrument measures SST in the first few micrometers of the sea surface, the SAF retrieval algorithms are intended to produce subskin SSTs that generally differ from the skin by ∼0.2 K at night [Météo-France, 2006]. Thus, SAF SSTs can be validated with in situ (e.g., buoy) measurements at night, but in the daytime the subskin temperature is decoupled from a buoy measurement by the magnitude of the diurnal warming. SAF data quality flags were used to eliminate invalid data. The 0.1° SAF data are then binned using a weighted average to the 0.25° AMSR grid.
 The Advanced Microwave Scanning Radiometer-EOS (AMSR-E) on board the Aqua platform launched in 2002 measures SST and other geophysical parameters (e.g., wind speed, atmospheric water vapor) (http://www.ssmi.com/). Since only AMSR-E data are used in this paper, the data are here referred to only as AMSR. AMSR data are insensitive to clouds and thus provide relatively complete data fields. However, there may be missing SST data due to rain, proximity to land/ice, and high wind (>20 m/s). Ascending and descending (local overpass time at 0130 and 1330, respectively) daily global data are mapped to a 0.25° grid, with earlier data overwritten by later retrievals at high latitudes and at the daily seam. For our study, only the nighttime (descending) maps were used. Over our study period, there is only 1 day missing (18 November 2006).
2.3. Reynolds V1 Daily SSTs
 Reynolds optimum interpolation SST fields on a 0.25° grid are available from the National Climate Data Center (http://www.ncdc.noaa.gov) [Reynolds et al., 2007]. The daily Reynolds SST maps used in this study are based on advanced very high resolution radiometer (AVHRR) and in situ data. An alternate version that also uses AMSR data to produce optimally interpolated (OI) SST maps was not used since our bias adjustment schema is based on AMSR.
 It should be noted that the data selection procedure applied by the Reynolds optimal interpolation schema ignores the diurnal cycle that cannot be properly resolved using only one polar orbiting instrument. Thus Reynolds OI fields represent a daily average subskin SST that is bias adjusted using the spatially smoothed in situ SST average over a given time window [Reynolds et al., 2007]. More specifically, by incorporating daytime and nighttime satellite observations adjusted to the daily average of in situ data, the final result should be some temperature between the night and day extrema rather than the daily average. Thus the diurnal cycle should be considered as noise with respect to the Reynolds estimate.
 To describe atmospheric conditions, daily 1° resolution level 3 Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol products were used (http://ladsweb.nascom.nasa.gov/). Aerosol optical thickness (AOT) is provided for seven bands, and the Angstrom exponent (AExp) is estimated for two wavelength ranges. These visible band products are available during daytime only. In this paper, the AOT at 0.55 μm is used as an indicator of aerosol concentrations (i.e., the degree of light attenuation is proportional to the amount of aerosols present), and the AExp for 0.55–0.85 μm is used as an indicator of aerosol type since high AExp (>1) is indicative of pollution aerosols, while low Aexp (<0.5) over the Atlantic is typical of dust aerosols. Only MODIS data from the Aqua platform are used. Aerosol data at the coarser resolution of 1° are appropriate to describe the spatial scale of the atmospheric phenomena that can influence satellite SST estimates.
2.5. Pilot Research Moored Array in the Tropical Atlantic Mooring Array Temperatures
 Quality-screened in situ data from the PIRATA mooring array are distributed as 10 min averages (Figure 1) (http://www.pmel.noaa.gov/tao/data_deliv/deliv.html). Temperatures are available for various depths, but for this study, only the data at the shallowest depth (1 m) is used and is referred to as the buoy SST. The PIRATA data set also offers surface meteorological parameters (e.g., longwave radiation, shortwave radiation, wind, relative humidity, rain, air temperature, pressure). For this study, the buoy data are presented as 3 h averages centered at the SAF reporting time in order to match the satellite data. That is, a buoy value is computed for 0100, 0400, 0700, 1100, 1400, 1700, 2100, and 2300 UTC by averaging all valid measurements between ±1.5 h of the standard observing times.
2.6. Coriolis SST Data
 Coriolis (http://www.coriolis.eu.org/) is a French multiannual project devoted to the acquisition, validation, and dissemination of real-time and batch processed in situ data in the world's oceans. This project is part of the effort to develop automatic and permanent observation networks for operational oceanography. For our study period, all Coriolis SST data that pass quality control (“good” or code = 1) are used. This includes 15,698 Argo profiles, 4580 expendable bathythermograph or conductivity-temperature-depth profiles, and 10,976 buoys (Figure 1). Only surface data were used (depth <5 m). This limitation reduced the number of matchup points to 12,639, of which approximately half are obtained from a combination of drifting buoys and Argo floats. Although moored buoy array data are also part of the Coriolis data set, the PIRATA data are analyzed separately in this study. Thus, when referring to the Coriolis data, it is implicit that the PIRATA data are not included. From this section onward, when mentioning PIRATA we are referring to PIRATA buoys (the red boxes in Figure 1).
2.7. SST Matchups
 Five matchup data sets were developed to compare satellite estimates with in situ PIRATA and Coriolis data. For comparison with PIRATA, three matchup data sets were constructed: SAF, AMSR, and Reynolds versus PIRATA. For each SST data set, the colocated single-pixel value (after binning over the 0.25° AMSR grid) is extracted and compared with the PIRATA value at the corresponding local time. For SAF, matchups are made for each station at each SAF reporting time and are expressed in terms of local time to facilitate analyses over the diurnal cycle. For AMSR, matchups for both day and night passes are produced. Since the Reynolds fields are not associated with a specific sampling time, a daily buoy average is computed. Means are examined over different time intervals (e.g., daily, monthly, seasonal). SAF versus Coriolis and AMSR versus Coriolis matchups were produced selecting colocated single values from the interpolated SAF and AMSR fields (described below) at the closest time.
3. Validation and Analysis of the SST Field
3.1. Buoy-SAF-AMSR Comparisons
 The matchup SAF SSTs (before interpolation) showed spatially and temporally varying bias (in situ minus satellite) relative to the PIRATA buoy SSTs, particularly at the more northerly stations (Figure 2). At these locations, the monthly average SAF bias often ranged between 0.5 and 1.0 K, with the highest monthly bias of ∼1.8 K occurring at 12°N 23°W in June 2006. Single-day matchup biases sometimes exceeded 1.0–2.0 K (not shown). On the average, the annual bias north of the equator ranged between 0.4 and 0.8 K. In contrast, south of the equator, the bias was much smaller (−0.02 to 0.26 K). The exception was the 6°S 8°E station, where the mean bias was 0.46 K. This is still low if one compares the southern bias with the northern annual bias range. This pattern could be easily seen even though data were missing for many months at some stations. Another common trend in the northerly station biases was the seasonal fluctuation, although the lowest values did not occur at exactly the same month and the magnitude differed by station. This temporal trend was not observed in the southern stations. In contrast to the means, the standard deviations were relatively constant over space and time, on the order of 0.4 ± 0.1 K at the northern stations and 0.3 ± 0.1 K south of the equator.
 The north–south differences were less pronounced for buoy comparisons with AMSR and Reynolds SSTs (Figure 2). Over the entire 2 year period the mean bias was <0.05 K for AMSR and <0.2 K for Reynolds in most cases. The root-mean-square error (RMSE) was smaller for AMSR (0.2–0.4 K) than for Reynolds (0.2–0.5 K). Although the biases were much less, the northern stations still showed a slight temporal trend. The single exception was the 12°N 23°W station, where the bias and RMSE were larger compared to the rest of the stations, suggesting a possible problem with the buoy or a local phenomenon.
 The relation of the buoy-satellite biases to buoy meteorological observations was not consistent for each station and is dependent on data availability (not shown). However, combining all stations, the buoy-AMSR biases were found to have no significant dependence on wind and relative humidity. The analogous buoy-SAF comparison indicated a positive relation with relative humidity. In reality, IR sensors are sensitive to columnar water vapor content. Thus, this aspect is further investigated in section 3.4 using satellite measurements of environmental factors.
 In contrast to the latitudinal variations, the SAF SST fluctuations relative to the PIRATA stations were small (∼0.1 K) over the diurnal cycle (Figure 3). The average PIRATA-SAF bias was relatively stable, with an average bias of ∼0.4 K and a stable standard deviation of ∼0.4 K. This behavior is quite similar among stations (see Table 1) where the diurnal variability of the bias is between 0.05 and 0.2 K with a mean value of 0.13 K excluding the value at 1300 LT for the problematic 12°N 23°W station. This indicates that the main cause of the buoy-SAF difference is not at frequencies higher than the diurnal cycle. Clearly, this average cannot represent any single event, especially anomalous warming characterized by an extreme fluctuation in temperature. Reproduction of single events is beyond the scope of this study.
Table 1. Diurnal Pattern of Mean Difference Between Pilot Research Moored Array in the Tropical Atlantic and Ocean and Sea Ice Satellite Application Facility Sea Surface Temperatures
Mean Difference at Given Local Time
3.2. Coriolis-SAF-AMSR Comparisons
 Comparison with the Coriolis data set, which has a better spatial coverage than the PIRATA buoys (Figure 1), revealed a clear spatial pattern in SAF SST biases. Over the 2 year period, the mean SAF bias map showed a wide band of high values extending diagonally across the tropical Atlantic (Figure 4a). The maxima zone originates from about 0°N at 10°E and shifts northwestward to 20°N at 35°W. The area with high bias (>0.6 K) occurred between 0°N and 20°N. In this same region, Merchant et al.  found a significant residual bias of the same order of magnitude after application of their dust correction algorithm, which they suggested may be due to the presence of biomass-burning aerosols. In contrast, with respect to AMSR, the mean bias did not exceed 0.2 K in the entire study area (Figure 4b). Wentz et al.  obtained similar results, with the mean SST difference (AMSR-buoy) and standard deviation of −0.02 K and 0.34, respectively, confirming that AMSR provides reliable SSTs in the tropics. The respective bias trends for the two data sets (AMSR and SAF) relative to Coriolis data set were consistent with the buoy results (Figure 2), that is, that there is a coherent spatial pattern in the SAF bias. Moreover, the homogeneous AMSR bias distribution indicates that AMSR fields may be used as a reference field to adjust SAF SST maps in lieu of the sparser in situ data, as well as to analyze the SAF bias distribution and possible causes at different scales.
3.3. AMSR-SAF Comparisons
 The SAF comparison, shifted to AMSR rather than in situ data, produced analogous results. The mean difference between the nighttime AMSR and the 0400 SAF SST fields (Figure 4c) has a similar magnitude and spatial pattern as the Coriolis-SAF bias map based on single point matchups (Figure 4a). Minor local differences, for example, in the upwelling area of the northwest coast of Africa or the relative maxima present in the southern part of Figure 4a, could be due to the nonhomogeneous distribution of the Coriolis data points in contrast to the AMSR data that are regularly distributed in space and time. Thus, the spatial variability in the buoy-SAF bias is confirmed by the more extensive in situ matchup data set (but representing a less continuous time record than the buoys), as well as by comparison of the nighttime SAF with the AMSR reference. In the next section, the temporal pattern of these latitudinal biases is examined and related to environmental factors.
3.4. Latitudinal Patterns Over Time
 The averaged nighttime AMSR-SAF bias plotted versus latitude and time (Figure 5) showed that a latitudinal gradient was present year-round, with a zone of maximum values that shifted seasonally. For both years, the main band (often containing values >0.8 K) was centered just north of the equator in January and gradually migrated northward, reaching the northernmost extent in July (∼15°N). From July to September, the maxima location was stationary but diminished in magnitude (∼0.5–0.8 K). By October, a new nucleus of maximum values started to form near the equator, slowly intensifying until the cycle restarts in January. This general pattern was consistent for the 2 years, suggesting a regular forcing. However, superimposed on this seasonal trend were shorter-term variability features that differed between the 2 years. For example, the bias maximum at ∼15°N quickly dissipated after October 2007 but persisted several months after October 2006. Features that differ between the 2 years suggest a forcing component that has significant interannual variability. In January–February, the magnitude of the bias is greater in 2006 than in 2007, possibly due to the implementation of the SAF dust algorithm after April 2006. In spite of the algorithm change, however, the seasonal shift is the same for both years, indicating that the cause of this bias pattern has not been removed either because the aerosol correction is not sufficient or because there are other causes.
3.5. Wind, Water Vapor, and Aerosols
 To provide a comprehensive explanation of the observed seasonal bias and its latitudinal distribution, three environmental factors that can cause problems with IR retrievals or IR-MW coupling were examined: wind, total columnar water vapor, and aerosols [Reynolds, 1993; Arbelo et al., 2005; Merchant et al., 2009]. It is well known that the ITCZ migrates seasonally and affects the distribution of all three parameters. The position of the ITCZ, a zone of low pressure and calm winds (Doldrums), can be inferred from a plot of the average wind speed from AMSR plotted against latitude and time (Figure 6a). The observed seasonality in the AMSR-SAF bias (Figure 4) appears to be related to the position and shift of the Doldrums only in the general sense that there is a north–south migration, with both features reaching their northernmost extent at about the same time, around July. In many other aspects, the two patterns differ. The northernmost extent of the Doldrums is ∼10°N, a few degrees south of the maximum SAF bias. This is contrary to the hypothesis that the greatest decoupling between AMSR and SAF will occur in the low-wind region, especially in summertime, as a result of difference in penetration depth between MW and IR sensors. Another notable contrast with the AMSR-SAF bias pattern is that the Doldrums are at a southernmost location from January to May, while the AMSR-SAF bias maximum begins to shift northward in January. These timing mismatches suggest that the forcing of the seasonal pattern is dominated not by wind but another phenomenon controlled by the ITCZ, such as water vapor and aerosols. Still, there is some relation to winds in the shorter time scale since the smaller “cells” in the AMSR-SAF bias maxima belt appear to be on a comparable time scale.
 For columnar water vapor (WV), a wide band characterized by values above 50 mm can be easily identified in Figure 6b that corresponds to the low-wind region in Figure 6a and exhibits a seasonal excursion analogous to the ITCZ migration. If an envelope characterized by WV > 30 mm is traced in Figure 6b and overlaid over Figure 5, all the highest AMSR-SAF biases are contained within, but they do not coincide with the WV maxima (>50 mm) except in January, when the WV maximum is at the equator. The rest of the year, the maximum bias occurs just slightly north of the highest water vapor values. Thus, water vapor appears to be a contributing factor but cannot completely explain the AMSR-SAF bias pattern.
 Like water vapor and wind, aerosols show a seasonal variability in terms of AOT and AExp. For AOT (Figure 7a), a band of high values (>0.4) occurs right above the equator in January and starts migrating northward in March, reaching ∼20°N in August. From August until November, AOT values were generally lower, although event cells can still be recognized. In December, a band characterized by high AOT values can again be easily recognized near the equator, persisting until March, and the cycle repeats. In terms of position over time, the high-AOT band corresponds to the zone of maximum AMSR-SAF bias. The AOT band actually consists of a series of discrete cells of very high AOT (>1.0) interrupted by background values (<0.3), which would be consistent with the occurrence of discontinuous intense aerosol events. In the tropical Atlantic, low AExp values (<0.5) associated with high-AOT events may be attributed to dust aerosols [Kaufman et al., 2002]. Thus, the high-AOT features just described are probably dust based on low AExp (Figure 7b). In contrast, another high-AOT cell occurring at 10°S in August–September is characterized by higher AExp (∼0.8), suggesting the presence of biomass-burning aerosols. This high-AOT cell does not correspond to any maximum AMSR-SAF bias. The seasonality and location of dust and biomass-burning aerosol types are consistent with previous studies [Prospero et al., 2002]. This analysis suggests that aerosols may still have a significant contribution to the AMSR-SAF bias. Since MW SSTs are unaffected by aerosols [Castro et al., 2008], it follows that the SAF data set must still contain some dust-related bias that is not completely removed by existing algorithms. Until the SAF algorithms are improved to compensate with these spatially and temporally varying factors, the SAF data can be adjusted by computing daily bias maps at night relative to AMSR.
where r is the relative distance, Δt is the time lag, L is a form of “spatial” decorrelation length, and τ is a “temporal” decorrelation scale.
4.1.2. Residual Cloudy Pixel Flagging
 This test is performed on all selected images prior to initiating interpolation, to avoid contamination by unflagged cloudy pixels. First, cloud margins are eroded, flagging all values within a distance of m pixels to a pixel already flagged as cloudy. This test helps to identify pixels contaminated by proximity to cloud and permits inclusion of SAF data with a quality index of “acceptable” or better (code 3 or higher). The second step rejects SST values lower than a minimum threshold SST value (which can be changed seasonally). The third step is the comparison to the closest analysis available (in time) that is used as a reference only if the analysis error is lower than a fixed value. Data that differ from the reference field for more than a defined threshold (usually 2σ, where σ represents the average standard deviation between consecutive nighttime images) are not included in the analysis.
4.1.3. First-Guess Removal
 In the work of Marullo et al. , this step removed the corresponding decadal climatological field. In this work, daily Reynolds SST maps at 0.25° resolution were used.
4.1.4. Influential Data Selection
 The influential data selection is a balanced selection around the interpolation point in terms of spatial-temporal coverage. We used the approach described by Marullo et al.  to reduce the number of input observations and to remove most cross-correlated data following appropriate a priori considerations.
 For this study, the above schema was further modified to include a bias adjustment of SAF SSTs to overcome problems due to a cold bias observed in the tropical north Atlantic (see section 3). The AMSR-SAF bias is estimated during nighttime using two preliminary OI maps derived from AMSR night and SAF at 0400 UTC, respectively, and applied to all the SAF uninterpolated data within the same 24 h period.
4.2. Optimal Interpolation of Daily Nighttime SST Field
 The OI schema was applied to generate daily gap-free AMSR nighttime SST fields on a 0.25° grid over the Atlantic Ocean from 30°S to 30°N and from 50°W to 20°E. The covariance structure uses an exponentially decreasing function in the space and time domain described above with e-folding spatial and temporal decorrelation length and time scales of 180 km and 3 days respectively [Marullo et al., 2007; Reynolds et al., 2007]. The daily Reynolds SST field is used as a first guess for the OI computation.
 The SAF data at 0400 UTC provide the best match to the nighttime AMSR field. In fact, considering the longitudinal extent of the study area, the local time of this SAF data ranges from about 0040 to 0520, which are all at night and therefore can be considered approximately equivalent to the foundation temperature. An alternative would be to use SAF data at 0100 UTC, which means local times between 2140 of the previous day and 0220 of the same day. We excluded this second option to be as close as possible to the minimum SST of the day. The European Community–funded project called Medspiration used an analogous approach to compute the foundation temperature field [Robinson et al., 2007]. Before interpolation, the 0.1° SAF data are binned to produce a superobservation on the same grid as AMSR. These nighttime interpolated AMSR and SAF maps allow us to compute the bias at every grid point of our investigation domain.
4.3. Interpolation of 3-Hourly SAF SST
 The same interpolation scheme described above is applied to the 0.25° gridded SAF data to produce complete DOISST maps every 3 h. However, the SAF data could have a very large offset with respect to in situ measurements, while AMSR values are nearly unbiased (see section 4). Thus, the pixel-by-pixel daily difference between the AMSR and SAF is computed from the two interpolated nighttime fields (section 4.1), producing a spatially varying bias map. This bias map is then added to all the uninterpolated SAF data at 0.25° spatial resolution of the same day before entering in the OI process (Figure 8). The assumption that the bias could be assumed constant over the daily cycle is discussed in section 6.
 The OI input fields for each sampling period are the bias-adjusted SAF data acquired at the same time over the ±5 day window. This means that to produce the OI map for 0100 UTC, the input SAF data at 0100 UTC from the same day, the previous 5 days, and the next 5 days are used. Similarly, the 0400 UTC interpolated maps will use the 0400 data in the same time window, and so on for the different sampling times. For the interpolation at a certain hour, data from previous days at the same hour were used rather than using data from proximal hours. This choice is justified by a time correlation analysis performed on the SEVIRI SST data over our study period which showed that, on average, the data are less correlated to the same-day observations along the diurnal cycle and are more correlated with observations at the same time interval on subsequent days. Thus it can be assumed that the diurnal cycle generally has a greater effect on SSTs than the day-to-day variability, and therefore the observations at the same time of the previous day will provide a better indication of the SST at the same point in the diurnal cycle. It is important to underline that even if the output is at a fixed UTC time and covers a relatively large area, the interpolation function takes into account the local time of observation and is designed to exclude data pixels beyond a 180 km radius, which guarantees that the input data used in interpolation are acquired at nearly the same local time. Obviously the choice of the ±5 day search window of OI could, in principle, tend to reduce the impact of the diurnal cycle especially in case of isolated diurnal warming events. In practice the probability of selecting data more than 3 days from the interpolation time is small, considering the exponential form of the correlation function and the limited number of influential points used to interpolate. This tends to select data from the same day or ±1 day. When very persistent overcast conditions occur, the most distant (in both time and space) data could be selected, but in this case the absence of valid satellite information cannot be overcome by any interpolation technique or first guess. This OI procedure produces eight interpolated SST maps (every 3 h) daily from SAF data.
5. Reconstruction of the Diurnal Cycle
 A diagram of the DOISST scheme is shown in Figure 8 for 1 April 2006 to illustrate the different steps of our DOI approach. The process starts with the eight uninterpolated 3-hourly SAF maps (Figure 8a). It is difficult to distinguish the diurnal cycle in these input maps because of the wide temperature range over the tropical Atlantic (∼14.0 K) compared to the diurnal SST fluctuations (order of <1 K). However, the differences in cloud cover can be seen. An adjustment is applied to these eight maps based on the difference between the interpolated fields for nighttime AMSR and 0400 SAF OI map (Figure 8b). The two interpolated fields in Figure 8b are similar and are consistent with the typical SST distributions for April in the region, except that the SAF values are larger than AMSR (discussed in section 4). Note that the large gaps along the African coast in the 0400 uninterpolated SAF image are correctly filled by the OI, producing low SSTs at middle latitudes and high SSTs at low latitudes, a pattern also seen in the more complete AMSR field. The difference map shows the highly variable distribution of the SAF bias in space within a nighttime period (when the two data sets are expected to agree). In this example, biases exceed 1 K over a large area along the African coast and across the equatorial region. This bias map is used to adjust all the eight input SAF fields before starting the DOI. As discussed earlier (Figure 3), the bias is assumed to be constant over the 24 h cycle. One point to emphasize is that even though gaps can be present in the 0400 SAF field, the DOI produces realistic values such that the bias adjustment at the pixel level for other times is not compromised. In the resulting DOISST maps (Figure 8c), it is difficult to distinguish the diurnal cycle, just as with the input maps. It should also be emphasized that SSTs will peak at different GMT times, depending on location. This is because the longitudinal shift in maximum solar heating affects the timing of the maximum SST (∼1400 local time). This diurnal SST cycle is correctly reproduced in the DOISST maps, as illustrated by the example in Figure 8d. At 0°E 10°S, where the UTC time is the same as the local time, the minimum SST occurs at 0400 and increases until 1300. SSTs then decrease in the late afternoon, tapering off at night.
 The DOISST product can be evaluated by performing matchups with all the buoys and then examining the buoy-DOISST difference with respect to the interpolation error maps produced together with the interpolated fields (Figure 9). The interpolation error provides a measure of the goodness of fit of the output and is related to the difference between the observed and expected value for each pixel, considering the distance in space and time of the input data used to reconstruct the field. As such, this error is a function of data availability. For IR sensors, this is highly dependent on cloud cover extent. Thus, the error in the OI nighttime fields can be used to evaluate the bias adjustment. For the 0400 original SAF data (Figure 9a), the bias with respect to the PIRATA buoys can be considered stable (∼0.5 K) when the interpolation error is below 60%. Above 60% error, the bias tends to decrease, reaching zero when the error exceeds 80%. This behavior is not surprising since when the error is very high, the output is dominated by the first guess (Reynolds), which has a smaller bias relative to the buoys (Figure 2). In contrast, the buoy-nighttime AMSR bias is small (<0.1 K) and is independent of the interpolation error (Figure 9b). There are very few matchup opportunities at larger interpolation error since the AMSR fields are relatively complete.
 When the entire OI output data set is analyzed, the buoy-DOISST bias is nearly zero until interpolation error exceeds 50% (Figure 9c). This implies that the bias adjustment is effective and that, on average, the DOISSTs are consistent with the buoys over the diurnal cycle. Above 50% error, the bias starts to increase and reaches 0.3 K at >80% error, which is still an improvement since this is 50% lower than the original bias (Figure 2). The increased bias at error >50% is consistent with the decreasing bias observed in Figure 9a. As a result of the trending of 0400 DOISST toward the first guess (Reynolds) when SAF data are sparse or missing, the interpolated adjustment field will contain a smaller correction factor in these areas. Application of this correction field to the input SAF data over the diurnal cycle results in lower DOISST values in these areas. Moreover, the buoy-DOISST variance is reduced to 0.2 K, compared to 0.5 K in the original SAF data set, indicating that the product is more consistent with the seasonal to diurnal variability present in the buoy observations.
 The DOISST generally compared well with PIRATA data over the 2 year period for all buoys. A clear example (Figure 10a) from the 10°S 6°W buoy shows that the in situ SST fluctuations at seasonal to diurnal frequencies are well reproduced in the interpolated fields. To compare the diurnal signal more easily in the two time series, we subtracted a 24 h moving average. The resulting SST anomalies are shown in Figure 10b.
 The average amplitude of the in situ SST anomalies is about 0.5 K but may reach ∼1.0 K on specific days. For DOISST anomalies, the amplitude is slightly higher but is consistent with the buoys in that both are concurrently high or low. The standard deviation of the buoy anomaly (0.08 K) is smaller than the DOISST anomaly (0.14 K), which is consistent with the expectation that the diurnal cycle is more damped at the 1 m depth of the buoy compared to the satellite penetration depth.
 A more detailed view of Figure 10b can be seen in Figure 10c, which illustrates the overall characteristics of the interpolated product. For the selected month (September 2006), the typical diurnal cycle is reproduced well, with cooler temperatures at night and warmest values around midday. However, there is an apparent phase shift of a few hours between the DOISST and the buoy SSTs, as may be expected for satellite surface estimates and buoy subskin measurements. The largest SST excursion over the diurnal cycle (∼1 K) is observed at the beginning of the month in both time series. In mid-September, both time series have a reduced amplitude, but the DOISST has a larger excursion than the buoy and shows a shorter-term variability (<1 day) that may be related to input data density. The daily total surface flux computed using bulk formulas [Marullo et al., 2003, Appendix A] for the same period shows the integrated effect of wind, insolation, and evaporation on the SST diurnal cycle (Figure 10d). When fluxes are high and positive, the amplitude of the SST diurnal cycle is large. When the fluxes are negative, the SST amplitude tends to decrease.
 It is important to summarize the interpolation performance in terms of reproducing the monthly diurnal cycle at all buoys. Since local surface solar heating is a major factor driving the diurnal SST cycle, the DOISSTs at the buoy location are grouped as a function of local buoy time and averaged for each month. In Figure 11, these results are presented as an anomaly relative to the monthly mean. In general, the DOISST diurnal cycle (red) is of comparable amplitude and shape as the buoy pattern (black), as seen in the single buoy example. As expected, the DOISSTs are low at night and high during the day. The phase shift seen in the single example (Figure 10c) is more evident in this analysis. Except for July, the DOISST leads the buoy SSTs by 3 h. Similar results for GOES have been reported by Gary et al. . This is reasonable, given that the effects of surface heating and wind mixing take longer to propagate to the buoy depth. Moreover, 3 h is the shortest period resolvable due to the sampling interval of the input time series. Another notable pattern is that from June to October, the DOISST diverges from the buoy diurnal trend after 1600 LT. As shown Figure 11, the interpolation error is greatest at this time of day. This strongly suggests that the discrepancy is due to reduced data availability. Increased cloudiness in the afternoon is characteristic of tropical weather.
 This paper is focused on the problem of generating SST fields that resolve the diurnal cycle for modeling applications, using geostationary satellite observations as the sole source of the diurnal signal. Because the goal is primarily to meet modeling needs, emphasis is placed on providing complete SST fields that contain diurnal frequencies in their power spectra even though the corrections might not reproduce local higher-amplitude diurnal warming events. The study focuses on the tropical Atlantic, where the availability of diurnal fields is critical to simulation of atmospheric process associated with the easterly waves that play an important role in the propagation of tropical storms and precipitation distribution [Marullo et al., 2008]. For this area, we develop a methodology to generate a DOISST product from 3-hourly SST fields distributed by SAF [Météo-France, 2006]. The PIRATA buoy array provide a valuable reference in situ data set with which to evaluate the quality of the DOISST methodology, specifically (1) to evaluate the quality of the input SAF data over space and time and (2) to validate the DOISST in terms of the amplitude and phase of the diurnal cycle. Comparisons of the input SAF data to the PIRATA buoys reveal a spatial bias, with the northern stations exhibiting a larger error than the southern stations. This is further confirmed in comparisons with the Coriolis data set, which has a better spatial distribution than the PIRATA buoys. The spatial distribution of the bias is also found to vary seasonally, indicating that the SAF data require a nonstatic adjustment. An analogous satellite-buoy comparison using AMSR, a MW-based polar-orbiting instrument, produces a flat bias pattern. Thus, for our study, AMSR is chosen as a reference field to compute a nighttime SAF adjustment. This adjustment needs to be performed daily due to the bias dependence on atmospheric factors that have short time scales.
6.1. Mechanical Adjustment Versus Physics-Based Adjustment
 If the spatial and temporal dependence of the SAF bias on environmental parameters could be well quantified, a physics-based adjustment of the SAF data could be possible, so this option needs to be explored. This approach would render the DOISST computation independent of AMSR, should undetected biases remain or should the instrument fail. In this region, the ITCZ modulates the seasonal variability of environmental factors known to affect satellite retrievals, that is, aerosols, water vapor content, and wind. Thus, it was not surprising that the SAF bias also showed the same seasonality. The band with high SAF bias occurs within the region of higher water vapor concentration. However, the bias and water vapor maxima do not coincide. Instead, the local bias maxima appear to match dust aerosol events even though the aerosol maxima are more isolated than the bias maxima. This suggests a combined aerosol-water vapor effect.
 An effort was made to quantify these correlations, using data for each pixel for the entire 2 year period. For water vapor, the correlation coefficient, r, is greatest around the equator and just adjacent to the African coast (Figure 12a). Outside of this zone of high correlation, r values are generally low or negative. This indicates that the AMSR-SAF bias near the equator can be attributed primarily to water vapor. Moreover, the high correlation stops at 37.5°W, in correspondence with the transition from SEVIRI to GOES, indicating that GOES-derived SST, based on an algorithm that uses the 3.9 μm channel, has no significant water vapor bias. However, the pattern in Figure 12a does not explain all of the spatial variability of the bias seen in Figure 4, particularly the high bias above 5°N away from the African coast.
 Correlation with AOT (Figure 12b) shows a less distinct spatial pattern, but it is clear that the high correlations (>0.6) cover almost the entire region above 5°N, while low correlations are more typical of the southern area. Although AOT does not distinguish between the aerosol types, previous work has shown that dust aerosols are dominant in the north, while biomass-burning aerosols are more important in the south [Prospero et al., 2002]. Since dust has a greater impact on IR-based SST retrievals, the high correlation with AOT in the northern Atlantic could explain the rest of the bias in Figure 4 not attributable to water vapor. Note that even GOES appears to be affected by aerosols.
 The combined effects of water vapor and aerosols (in terms of AOT and AExp) are summarized in Figure 13. Figures 13a–13c show the average interpolated AMSR-SAF error as a function of AOT and AExp for three water vapor ranges representing dry, medium, and wet conditions. Figures 13c and 13d show the corresponding number of points used to construct Figures 13a–13c and thus provide an indicator of confidence level. Recall that in Figure 6b, low water vapor conditions (within the range in Figure 13a) occur outside the zone of ITCZ influence, roughly below 10°S and above 20°N, while the highest water vapor conditions (of Figure 13c) occur along the ITCZ migration axis at ∼0°N–10°N. The aerosol conditions in these three (water vapor-based) geographic regions can be seen in Figure 7. Under dry conditions (Figure 13a), the error is generally small (±0.4 K), with a slight tendency to be more positive at low AExp. High AOT and low AExp occurred very rarely (refer to Figure 7) compared to the next two cases. Under moderate water vapor conditions (Figure 13b), the error remains small (∼±0.4 K) at low AOT but increases significantly with AOT (to ∼0.8 K) when large (dust) particles dominate (AExp < 0.5). Note that this plot includes biomass-burning-influenced events at ∼10°S characterized by the high AOT and high AExp, as well as sub-Saharan dust storms with high AOT and low AExp (Figure 7). At the highest water vapor range (Figure 13c), the error is amplified along both the AOT and AExp axes. There is a clear increase in error, going from low to high AOT. The largest error occurs at low AExp, but considerable error is also observed at higher AExp, in contrast to Figure 13b, where the large error was only associated with low AExp. These results suggest that the interaction between total water vapor content and aerosols is not linear. Clearly, a more careful study is needed to develop a suitable physics-based correction, but in the meantime, an empirical adjustment based on the comparison with AMSR is a reasonable alternative. The dependence of the error on rapidly changing atmospheric conditions confirms that an empirical correction of SAF data is a prerequisite to a diurnal L4 SST product for the tropical Atlantic and a daily correction is the appropriate time scale.
 Even though a physics-based method was not found, the use of the nighttime AMSR adjustment method is a new innovation. In contrast, the level 4 Atlantic foundation temperature product uses ATSR weekly means on a 2° grid to adjust the level 2 SAF data. The AMSR-based adjustment permits application of the correction on a daily scale and at a higher spatial resolution (0.25°). The increased resolution is more consistent with the natural scales of variability as diagnosed in section 4. AMSR also has almost complete data coverage per scene, unlike other IR-based data sets (Reynolds, ATSR), and biases are small compared to Reynolds [Reynolds et al., 2007]. The key assumption is that the AMSR-SAF bias is constant over one diurnal cycle, which was justified by the analysis of mean daily variability of the buoy-SAF bias (Figure 3). Thus the computation of the daily adjustment field is not critical to this method.
6.2. Evaluation and Potential Improvements
 The nighttime adjustment of SAF to AMSR is a fundamental step of this procedure. As such, understanding of limitations that affect the adjusted field is crucial for implementation of possible improvements. For example, if cloud cover is persistent for several days (greater than the interpolation window) over a large area, the resulting OI 0400 SAF field may be too sensitive to the first guess field (e.g., Reynolds). Our initial analysis has shown that the SAF bias relative to AMSR (and buoys) is generally larger than that of the Reynolds value. Therefore, the bias map could have patches of small values where the first guess is dominant. A possible solution is to enlarge the spatial correlation scale used for OI of the 0400 SAF field. This would produce a smoothed bias adjustment field and decrease the dependence on the first guess. An alternative approach would be to interpolate the original 3-hourly SAF field without making any adjustment and directly adjust the interpolation output. This option could also take into account the day-night bias variability using AMSR. Thus a better adjustment field is generated without smoothing spatial gradients.
 An additional improvement to better reproduce the diurnal cycle is to change the first-guess strategy. The first guess used in this study could be replaced with a new version of Reynolds SST that combines AVHRR and AMSR data [Reynolds et al., 2007]. Alternatively, both daytime and nighttime AMSR passes may be utilized to provide a better first guess. This would minimize the impact of implicitly assuming that the bias field is stationary and invariant over the 24 h period and would also mitigate the problem of insufficient data at 1400 local time that results in an uncharacteristic minimum in the DOISST (Figure 11). A third option is to let the first-guess value change over the 24 h period. A climatological mean diurnal cycle would need to be computed directly from SAF data. The diurnal signal can then be added to the daily Reynolds field to create a first guess. Last, the DOISST from a previous time period could be used. This reduces the impact of SST observations (and associated biases) at any single time, but particular care should be exercised to avoid possible drift of the first guess with time.
 A further improvement is to make the bias correction every 12 h using the AMSR daytime maps in addition to the nighttime adjustment. This approach should ameliorate some minor discrepancies that could appear in areas where the SEVIRI bias exhibits some more evident diurnal variability as in the case of the southeast zones of our investigation area (Figure 14a). However, comparison between Figures 14a and 14b demonstrates that, in the absence of this further correction, our bias adjustment strategy always works in the right direction, substantially reducing the difference between AMSR and DOISST even during day. This is evident north of 10°S–15°S, where the difference between AMSR and the adjusted DOISST is always less than ±0.1 K. South of this latitude the adjustment is less efficient due to the absence of bias in the SEVIRI data during the night versus −0.2 K observed during the day. All these possible improvements need to be tested to determine the best combination. This would require a substantial effort and can be addressed in a future work.
 Overall, the DOISST product was found to closely reproduce in situ data (PIRATA) on daily, monthly, and seasonal scales. In particular, spectral analysis revealed that the frequency of the DOISST product is identical to that of the buoy data, with peaks at 24 and 6 h. However, the phase of the DOISST leads the response of the buoy, while the amplitude is 30% larger. This is reasonable, given that the effects of surface heating and wind mixing is felt closer to the surface and take longer to propagate to buoy depth. Not surprisingly, the discrepancies between the interpolated and buoy SSTs are greater when there is insufficient input SAF data. The interpolation error field generated together with each DOISST map provides a good indication of the product quality at each grid point. For practical purposes, the product can be considered consistent (buoy-DOISST < 0.1) if the interpolation error is lower than 70%. In terms of SST difference relative to the buoys, the variance is also reduced from 0.5 K in the original SAF data set to 0.25 K in the DOISST.
7. Concluding Remarks
 The use of an observationally driven approach to the problem of estimating the diurnal cycle of the SST field has the advantage of being independent of uncertainties in atmospheric forcing. This is a primary limitation of 1-D diurnal warming models and is a major source of uncertainty in model predictions [Pimentel et al., 2008a]. However, this does not mean that models do not have any merit in contributing to the estimate of the diurnal SST cycle. In fact, by providing good initial conditions and forcing, they can supply local diurnal warming estimates when satellite information, with subdaily acquisition frequency, are either scarce or absent. Moreover combined use of new, advanced methods for satellite data analysis and modeling strategies can supply value-added products. In particular Pimentel et al. [2008a] demonstrated that diurnal warming estimates can be reasonably reproduced using an array of 1-D mixed layer models and suggested that data assimilation methods that utilize diurnal signal information in satellite-derived SST observations can further reduce uncertainties in diurnal warming estimates [Pimentel et al., 2008b].
 In this paper we have suggested a possible way to fully exploit information contained in MSG satellite data to further contribute to the diurnal variability research effort using the tropical Atlantic as a test. The approach described in this paper was specifically designed for the tropical Atlantic region between 30°S and 30°N and takes into account the characteristic meteorological and oceanic time scales, as well as length of the day and availability of satellite data for the study area. A possible next step will be to investigate the limitations of the method outside of this area and to propose alternative solutions based on an observationally driven approach that includes physics versus only statistics, using model results. Away from our study area, toward middle and high latitudes, the different environmental conditions and scales involved in the phenomena driving SST variability will certainly require some adjustments. Crucial points to be considered will be space and time scales of variability, latitudinally and seasonally varying day length, the lack of geostationary satellite data at higher latitudes, and limitations in the use of microwave data in relatively small semienclosed or sea-ice-impacted basins. While much work remains to be done, the results presented here clearly demonstrate that an operational diurnal level 4 SST product is achievable.
 This work originated in the context of AMMA - EU WP 1.2 “The Water Cycle” and has been supported by the AMMA - EU project (0040892) and NASA grant NNX08AD55G. SAF SST data were obtained from the EUMETSAT Ocean and Sea Ice Satellite Application Facility at Météo-France. AMSR-E data are produced by Remote Sensing Systems and sponsored by the NASA Earth Science MEaSUREs DISCOVER Project and the AMSR-E Science Team. Data are available at www.remss.com. Reynolds SSTs were obtained from the NOAA Satellite and Information Service, National Environmental Satellite, Data, and Information Service (NESDIS). Coriolis temperatures were obtained from the Coriolis data center (http://www.coriolis.eu.org). PIRATA data were obtained from TAO Project Office of NOAA/PMEL. Thanks are extended to Pierre LeBorgne for his helpful comments.