Assessment of Accuracy of Moderate-Resolution Imaging Spectroradiometer Sea Surface Temperature at High Latitudes Using Saildrone Data

Abstract

The infrared (IR) satellite remote sensing of sea surface skin temperature (SST_skin) is challenging in the northern high-latitude region, especially in the Arctic because of its extreme environmental conditions, and thus the accuracy of SST_skin retrievals is questionable. Several Saildrone uncrewed surface vehicles were deployed at the Pacific side of the Arctic in 2019, and two of them, SD-1036 and SD-1037, were equipped with a pair of IR pyrometers on the deck, whose measurements have been shown to be useful in the derivation of SST_skin with sufficient accuracy for scientific applications, providing an opportunity to validate satellite SST_skin retrievals. This study aims to assess the accuracy of MODIS-retrieved SST_skin from both Aqua and Terra satellites by comparisons with collocated Saildrone-derived SST_skin data. The mean difference in SST_skin from the SD-1036 and SD-1037 measurements is ~0.4 K, largely resulting from differences in the atmospheric conditions experienced by the two Saildrones. The performance of MODIS on Aqua and Terra in retrieving SST_skin is comparable. Negative brightness temperature (BT) differences between 11 μm and 12 μm channels are identified as being physically based, but are removed from the analyses as they present anomalous conditions for which the atmospheric correction algorithm is not suited. Overall, the MODIS SST_skin retrievals show negative mean biases, −0.234 K for Aqua and −0.295 K for Terra. The variations in the retrieval inaccuracies show an association with diurnal warming events in the upper ocean from long periods of sunlight in the Arctic. Also contributing to inaccuracies in the retrieval is the surface emissivity effect in BT differences characterized by the Emissivity-introduced BT difference (EΔBT) index. This study demonstrates the characteristics of MODIS-retrieved SST_skin in the Arctic, at least at the Pacific side, and underscores that more in situ SST_skin data at high latitudes are needed for further error identification and algorithm development of IR SST_skin.

1. Introduction

Satellite remote sensing offers the best way of providing long-period, frequent, global sea surface temperature (SST) maps, which are vital for understanding the climate [1,2], monitoring long-term climate trends [3], and studying some weather systems, such as hurricanes [4,5] and El Niño/La Niña events [6,7], and in supporting weather and ocean forecasting. Currently, measurements from both infrared (IR) and microwave radiometers aboard satellites can be used to derive SSTs, but the IR sensors have a higher spatial resolution with a longer historical record, including the Advanced Very-High-Resolution Radiometer (AVHRR) [8], Moderate-Resolution Imaging Spectroradiometer (MODIS) [9], Visible Infrared Imaging Radiometer Suite (VIIRS) [10], Sea and Land Surface Temperature Radiometer (SLSTR) [11], and Visible and Infrared Scanning Radiometer (VIRR) [12]. They use radiometric measurements at wavelengths of 3.7–4.1 μm and/or 10–12 μm intervals to derive SSTs. However, both bands are sensitive to the presence of clouds, interactions with aerosols, and absorption by atmospheric water vapor. Thus, thermal IR measurements for deriving SST require the atmospheric correction of the measured signals and can only be made in cloud-free conditions. Furthermore, the retrieval of IR satellite SST at high latitudes, particularly in the Arctic region, poses several challenges [13,14], primarily due to the extreme environmental conditions in this area, such as the persistent cloud cover and long twilight [15], sea ice presence introducing complications in distinguishing open water from ice-covered regions [16], and occurrence of extremely cold and dry atmospheres compared with other areas of the global ocean [17].

In addition to being a climatological extreme, the Arctic is a vast and remote region with limited access for in situ measurements, resulting in difficulties in the accuracy assessment of satellite-derived SST and larger uncertainties in the retrievals. As is the case elsewhere, in situ measurements of subsurface SST taken by drifting buoys are the main source of validating data at high latitudes. Their sparsity is much more significant at the northern Pacific side of the Arctic region, incorporating Beaufort Sea, Chukchi Sea, and East Siberian Sea, in contrast to the Greenland, Norwegian, and Barents Seas in the Atlantic Ocean sector, which feature extensive year-round open water at similar latitudes. However, the sea ice melt-back in recent years, especially during warmer months, has led to an improvement in the amount of in situ SST data in the Arctic, which is advantageous to the accuracy assessment and refinement of the atmospheric correction algorithms for SST retrieval [17,18,19].

Nevertheless, different from the sea surface skin temperature (SST_skin) derived from the IR emission from within the conductive laminar sub-layer of ~10–20 μm thickness beneath the air–sea interface detected by IR radiometers, buoys take the ocean temperature referred to as SST_depth at depths of several centimeters to tens of meters [20]. The difference between SST_skin and SST_depth mainly comprise the cool skin effect and diurnal warming. The cool skin effect, which means that SST_skin is cooler than SST_depth, nearly always exists, resulting from the heat loss through the oceanic skin layer to the atmosphere, supplied by the sensible and latent heat fluxes and the net longwave radiation [21]. But such difference can be overwhelmed by the thermal stratifications in the daytime caused by the strong insolation under low wind speeds, i.e., diurnal warming [22,23]. Therefore, using subsurface temperature, SST_depth, to validate IR satellite-derived SST_skin may wrongly attribute some contributions of cool skin and diurnal warming to the inaccuracies of satellite retrievals, underscoring the necessity of collecting SST_skin using measurements from IR radiometer systems on ships or other platforms. Some noteworthy progress has been made with several successful instruments being deployed over the past few decades, such as the Marine Atmospheric Emitted Radiance Interferometer (M-AERI) [24], the Calibrated Infrared In-Situ Measurement System (CIRIMS) [25], the Infrared Sea Surface Temperature Autonomous Radiometer (ISAR) [26], and radiometers mounted on the surface floats of moorings [27]. However, the amount of in situ SST_skin data is still lacking with a limited spatio-temporal extent, especially for high-latitude regions, primarily due to the difficulty and the high cost of deployment on ships, and maintenance of those accurate IR radiometers.

The uncrewed surface vehicles (USVs) are more cost-effective than traditional research vessels. To fill the gap of SST_skin data at high latitudes, especially at the Pacific sector of the Arctic, two Saildrone USVs were deployed in the 2019 Arctic Cruise of the 3rd Multi-Sensor Improved Sea Surface Temperature Project (MISST-3) [28,29] carrying a simple system with two IR radiation pyrometers on the deck to collect the measurements for deriving SST_skin. Although this configuration was experimental, Jia, et al. [30] have demonstrated that the accuracy of Saildrone-derived SST_skin is sufficient for use in scientific research after controlling for quality. Few papers used the Saildrone data to validate either Level-2 satellite SST products or Level-4 SST analyses [31,32], but only SST_depth measurements at −0.6 m from CTD sensors were used for comparisons. CTDs are instruments that measure Conductivity, Temperature, and pressure (closely related to the Depth of the measurement) from which salinity and density can be calculated. Hence, this paper will utilize the unique Saildrone SST_skin dataset at high latitudes to assess the accuracy of MODIS-retrieved SST on the NASA Earth Observing System (EOS) satellites Terra and Aqua, improving the understanding of error characteristics of MODIS SST in the northern Pacific side of the Arctic.

This paper is organized as follows: The MODIS-retrieved SST_skin, Saildrone-derived SST_skin, and other ancillary data are introduced in Section 2. The statistical results of the MODIS–Saildrone comparisons are presented in Section 3. The results of the error analysis are discussed in Section 4, associated with several influential factors. The conclusions are made in Section 5.

2. Data and Methods

2.1. MODIS SST Data

The goal of MODIS SST_skin processing at NASA is to develop and apply consistent atmospheric correction and cloud detection algorithms to long-wave IR (LWIR) measurements to derive SST_skin; the algorithms were developed at the University of Miami’s Rosenstiel School of Marine, Atmospheric, and Earth Science [9,17,33,34]. The NASA Ocean Biology Processing Group (OBPG) applies the algorithms to generate Level-2 SST_skin. The current MODIS LWIR SST_skin retrieval algorithm is a modified version of the nonlinear SST formulation of Walton, et al. [35] as given below:

SST_sat = a₀ + a₁BT₁₁ + a₂(BT₁₁ − BT₁₂)T_sfc +_a₃(sec(θ) − 1)( BT₁₁ − BT₁₂)
+ a₄(mirror) + a₅(θ) + a₆(θ²)

(1)

where SST_sat is the satellite-derived SST_skin; BT₁₁ and BT₁₂ are brightness temperatures (BTs) in the 11 μm and 12 μm wavelength bands; T_sfc is a reference SST; mirror represents the mirror side number with a value of 0 or 1; and θ is the sensor zenith angle. Coefficients a₀–a₆ are derived by regression of matchups between the in situ and satellite measurements for each month of the year with latitude-band dependence. The algorithm is described in detail by Kilpatrick, et al. [9] and Jia and Minnett [17].

The standard Level-2 MODIS SST_skin fields can be accessed through the ocean color web or Physical Oceanography Distributed Active Archive Center (PO.DAAC). Each SST_skin retrieval contains a numeric Quality Level (QL) assigned by running a series of tests, with QL = 0 being the best quality and QL = 4 being the worst. Note that data with QL > 1 are not recommended to be used for scientific studies as they may have significant cloud contamination identified by the cloud classifier algorithm presented by Kilpatrick, et al. [33] or other problems related to sea ice or dust. The pixel size is 1.0 km square at nadir, growing to 2.0 km (along track) to 4.8 km (across track) at the edge of the swath [36].

2.2. Saildrone Cruises and Data

2.2.1. Saildrone Arctic Cruises

Saildrone is an advanced, wind-driven USV manufactured by Saildrone Inc. located in Alameda, CA, USA. It carries a number of solar-powered scientific instruments to collect high-frequency (1 min sampling interval) data including both oceanographic and meteorological parameters. A more detailed introduction to Saildrones is given by Jia, et al. [30]. During a collaborative NOAA-NASA mission in 2019, a fleet of six Saildrones were deployed from Dutch Harbor, Alaska in May. Five of those vehicles navigated through the Bering Strait into the Chukchi Sea, reaching up to ~75°N before making return voyages. This paper reports the assessment of accuracy of MODIS SST_skin using measurements from two Saildrones, SD-1036 and SD-1037, the deployments of which were funded by NASA through the National Oceanographic Partnership Program (NOPP). The navigation tracks and the configuration of two Saildrones are shown in Figure 1.

2.2.2. Saildrone Data

Other than one previous deployment, SD-1036 and SD-1037 are the only two Saildrones equipped with “unicorn”-structure IR broadband pyrometers (8–14 μm) to facilitate the SST_skin derivation. Two pyrometers, manufactured by Heitronics, were installed on the deck at a height of 0.8 m above sea level, viewing the sea surface and the sky at the same nadir angle and zenith angle of 50° when the Saildrone is upright. The measurements from the sky-viewing CT09.10 sensor are used to correct for the component of the upwards radiance due to reflected downwelling atmospheric radiance at the ocean surface in the IR radiation measured by the sea-viewing CT15.10 sensor. Jia, et al. [30] provided the details of the SST_skin retrieval algorithm with the error and uncertainty budget analyses, demonstrating that the uncertainty of Saildrone-derived SST_skin is ~0.12 K without significant systematic bias after quality control. They indicate that the data are suitable for the accuracy assessment of satellite SST_skin retrievals.

SST_depth was taken by several instruments onboard SD-1036 and SD-1037, for each vehicle including two CTDs; one SBE 37 (a CTD manufactured by Sea-Bird Scientific Inc., Bellevue, WA, USA) and one RBR (a CTD manufactured by RBR Ltd., Kanata, ON, Canada), both at a depth of −0.54 m; and seven additional SBE 56 self-recording thermometers at a range of depths from −0.33 to −1.71 m along the keel. Both CTDs and temperature loggers make measurements of SST with an accuracy of ±0.002 K, as stated in the manufacturers’ specifications.

The Saildrones also provide measurements of meteorological variables simultaneously with the SST measurements (1 min interval), such as the three-dimensional wind vector, surface air temperature and relative humidity, barometric pressure, Photosynthetically Active Radiation (PAR) at the surface, etc.

2.3. MERRA-2 Data

Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) [38], a global atmospheric reanalysis produced by the NASA Global Modeling and Assimilation Office (GMAO), provides useful input data for radiative transfer simulations, including atmospheric profiles of temperature and specific humidity and single-level meteorological fields. The MERRA-2 data have a spatial resolution of 0.5° (latitude) × 0.625° (longitude), and 1-hourly temporal resolution for the surface data, 3-hourly for the vertical profile fields.

2.4. Quality Control and Collocation

As mentioned above, the Saildrone SST_skin data must be subjected to rigorous quality control before they can be used in this study. Initially, the measurements collected during the periods when the Saildrone was near sea ice must be pinpointed using images captured by onboard cameras and excluded from subsequent analyses, since the small-scale temperature variations caused by the melting sea ice will not be appropriately sampled in the MODIS field of view. Furthermore, the tilt angles of the vehicle, resulting from both pitching and rolling, should be constrained to ±1.5° and ±5°, respectively, to prevent significant inaccuracies in SST_skin [30,39].

To generate the coefficients in the atmospheric correction algorithm and to assess the accuracy of MODIS SST_skin retrievals, a matchups database (MUDB) has been established including collocated satellite and in situ observations, mostly from buoys [40]. To be incorporated into the MUDB, the MODIS–Saildrone matchups follow the same spatio-temporal criteria, i.e., the time window is within 30 min and the distance is within 10 km. However, due to the high observing frequency (1 min) of Saildrone, there can be multiple Saildrone measurements (up to 60) matched with the same MODIS pixel. For the independence of validation, only one of those is selected as a unique matchup in two reasonable ways based on either the closest timestamp or the smallest separation. As shown in Figure 2, the Aqua MODIS–Saildrone SST_skin differences are sensitive to the spatial discrepancy but with insignificant dependency on the time window for matchups determined by either time-closest or distance-smallest, similar for Terra MODIS. Such patterns were also found by Jia and Minnett [17] using the MODIS and in situ SST matchups at northern high latitudes, and were explained as the matched satellite-derived SST_skin away from the center pixel that may have a higher likelihood of cloud-contaminated retrieval if the center pixel is cloudy. Therefore, the distance-smallest one-to-one MODIS–Saildrone matchups are selected for the following analyses to minimize the separation dependence.

3. Results

Table 1. Statistics of MODIS–Saildrone SST_skin difference (in K), including the mean, median, standard deviation (STD), robust standard deviation (RSD), root mean square (RMS), Pearson correlation coefficient (R), and number of valid matchup data points (Num). The statistics are shown in terms of two Saildrones and two satellites separately, including both quality level (QL) 0 and 1 data.

	Aqua			Terra
	SD-1036	SD-1037	Total	SD-1036	SD-1037	Total
Mean	−0.073	−0.468	−0.263	−0.076	−0.490	−0.291
Median	−0.036	−0.352	−0.214	−0.021	−0.379	−0.207
STD	0.727	0.701	0.741	0.649	0.752	0.734
RSD	0.656	0.588	0.669	0.551	0.565	0.559
RMS	0.730	0.842	0.786	0.653	0.897	0.789
R	0.943	0.947	0.948	0.956	0.945	0.947
Num	411	380	791	409	444	853

presents the statistics of the Aqua and Terra MODIS–Saildrone SST_skin differences during the SD-1036 and SD-1037 cruises. As expected, the performance of MODIS sensors on Aqua and Terra satellites shows comparable results. The mean biases are −0.263 K for Aqua and −0.291 K for Terra, with the overall standard deviations (STDs) of 0.741 K and 0.734 K, respectively. The robust standard deviation (RSD; calculated as the interquartile range divided by 1.35) is less sensitive to the outliers and is also reported here. The RSD is 0.669 K for Aqua, while it is slightly smaller for Terra (0.559 K), indicating a fewer more extreme outliers as shown in Figure 3.

Table 2. As Table 1, but statistics for different QL (also shown for each Saildrone separated by semicolon as SD1036; SD1037) of MODIS SST_skin retrievals.

	Aqua		Terra
	QL = 0	QL = 1	QL = 0	QL = 1
Mean	−0.173 (−0.004; −0.345)	−0.505 (−0.239; −0.844)	−0.198 (0.034; −0.412)	−0.559 (−0.394; −0.706)
Median	−0.138 (0.057; −0.250)	−0.496 (0.315; −0.696)	−0.132 (0.064; −0.279)	−0.492 (−0.272; −0.667)
STD	0.674 (0.672; 0.631)	0.855 (0.826; 0.770)	0.690 (0.636; 0.670)	0.788 (0.581; 0.913)
RSD	0.561 (0.562; 0.529)	0.762 (0.804; 0.682)	0.500 (0.538; 0.476)	0.670 (0.639; 0.610)
RMS	0.695 (0.671; 0.718)	0.991 (0.857; 1.140)	0.717 (0.636; 0.786)	0.965 (0.700; 1.152)
R	0.956 (0.955; 0.960)	0.908 (0.914; 0.923)	0.954 (0.959; 0.956)	0.933 (0.960; 0.919)
Num	577 (291; 286)	214 (120; 94)	631 (304; 327)	222 (105; 117)

shows the statistics of matchups in terms of QL for the MODIS SST_skin products. The negative biases and variation are more pronounced in QL1 retrievals due to their longer atmospheric path lengths. Even though there are few scattered data points in Figure 3, the MODIS- and Saildrone-derived SST_skin demonstrates good quantitative agreement generally. The distributions of SST biases plotted as histograms in Figure 3 show a higher kurtosis than the Gaussian distribution; most values are concentrated into the range of −2 K to 1 K. However, there are still two things that merit attention. One is that the mean and median of the SST difference are significantly different using SD-1036 and SD-1037 as sources of validation data. The other one is that the SST difference has an average negative bias. This section will try to address the first question, and the second one will be discussed in the next section.

As presented by Jia, et al. [30], the Saildrone-derived SST_skin values do not possess significant systematic biases, based on some post-cruise sensor calibrations in the laboratory and congruent wind speed dependence of the cool skin effect with some previous studies [41,42,43,44].

Table 3. Statistics of SST difference between SD-1036 and SD-1037 within 1 km separation measured at one time at various depths. Note that the temperature logger at −1.04 m on SD-1036 did not function.

Depth	Mean	Median	STD	RSD	RMS	R	N
0 m (skin)	0.041	0.040	0.134	0.125	0.140	0.951	237
−0.33 m	0.008	0.008	0.113	0.051	0.113	0.993	903
−0.47 m	0.023	0.010	0.095	0.080	0.097	0.993	299
−0.54 m	0.003	0.011	0.095	0.043	0.095	0.995	889
−0.81 m	−0.001	0.007	0.094	0.041	0.094	0.996	903
−1.20 m	−0.014	0.003	0.093	0.034	0.094	0.995	742
−1.42 m	−0.013	0.003	0.094	0.034	0.095	0.995	742
−1.71 m	−0.011	0.003	0.096	0.031	0.097	0.995	742

shows the statistics of SST comparison at various depths between SD-1036 and SD-1037 when the two Saildrones were within a 1 km separation at the same time. The SST_depth measurements are also filtered by the platform pitch and roll angles as the SST_skin to minimize the tilting effect on the depth of temperature measurement. Note that the discrepancies in the number of paired data at different depths are due to the missing values. The mean difference and variation of SST_skin are small, 0.041 K and 0.134 K, even though a little greater than those of SST_depth, which can be explained by three distinct factors. Firstly, the geophysical variability of ocean temperatures in the thermal skin boundary layer is likely to be larger than the subsurface temperatures resulting from the rapid response to the change in net air–sea heat flux and some surface wave processes [45]. Secondly, the inherent measurement uncertainty of radiometric instruments for SST_skin retrieval is much higher than that of the temperature sensors measuring at depths. Last but not least, the sampling issues may cause some biases and larger variations as the amount of Saildrone SST_skin data is substantially smaller due to missing values. This is indicated in the SST_depth taken at −0.47 m (Table 3). Nevertheless, such a difference for SD-1036 and SD-1037 SST_skin measurements collected within 1 km demonstrates no significant systematic biases between the two vehicles, and obviously cannot account for the big disparity (up to 0.4 K) in the mean biases of MODIS SST_skin when compared to the data from SD-1036 and SD-1037 separately.

Taking the Aqua MODIS-Saildrone matchups for example, Figure 4a,b show the histogram distributions of the MODIS BT difference between 11 μm and 12 μm channels and the air-sea temperature difference (ASTD) derived from the Saildrone measurements, using SST_skin and surface air temperature. For the matchup dataset from the SD-1037 cruise, a larger fraction of BT differences are >0.5 K, but with much fewer ASTDs < 0 K compared to those for the SD-1036 cruise. Figure 4c demonstrates a distinct negative relationship between the BT difference and ASTD, consistent with the distribution patterns in Figure 4a,b. Figure 5 presents the maps of ASTD and bivariate histogram for the longitude and latitude of the Aqua MODIS pixels matched with Saildrone measurements, which can further explain the more positive ASTD cases for SD-1036 matchups. Apparently, there are much more matchups during the SD-1036 cruise concentrated within the range of 70–71.5°N, 160–165°W, where it has been shown that the near-surface air is likely to have been heated by its preceding passage over land [46] based on the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT; [47]) model developed by NOAA’s Air Resources Laboratory, resulting in warmer air over the ocean surface. Thus, the spatial distribution difference leads to the ASTD distribution difference in the two matchup datasets that might also affect the BT difference distribution.

Theoretically, the BT difference is determined by both the sea surface boundary conditions and intervening atmosphere between the surface and the satellite sensor apertures. Relevant atmospheric data from MERRA-2 have been integrated into the MODIS-Saildrone matchups based on the optimal solution for the spatio-temporal difference. Figure 6a,b are the MERRA-2 vertical profiles of specific humidity and air temperature in the lower troposphere beneath the 500 hPa level. Both of them display some differences between the matchups during SD-1036 and SD-1037 cruises. For SD-1037, the near-surface (below 940 hPa pressure level) water vapor content is significantly lower on average, and the mean air temperature is also lower at each level with a larger variability. One possible interpretation is that a few measurements in September and October are in the matchup data for SD-1037 since the IR pyrometers carried on SD-1036 were shut down because of solar power constraints starting early August while those on SD-1037 still operated until the end of the mission. Similarly, there are differences in the total column water vapor distribution (Figure 6c) as well. Using MERRA-2 vertical profiles along with the surface meteorological fields taken by Saildrone as input to the RTTOV (Radiative Transfer for TIROS Operational Vertical Sounder) v13.1 model [48], results in simulated MODIS BT differences between 11 μm and 12 μm (Figure 7). Despite possible inaccuracies in the model simulations, the general pattern shows a similarity to the observations in Figure 4a, with more frequent large BT differences in the SD-1037 matchups, confirming the dissimilar vertical atmospheric conditions contribute to diverse BT difference distributions.

All the results presented above manifest both surface and vertical atmospheric conditions are not homogeneous between the MODIS–Saildrone matched data for the SD-1036 and SD-1037 cruises, resulting in the divergence of BT difference distribution and then the statistics of the MODIS–Saildrone SST_skin comparisons. These differences permit the examination of the performance of the MODIS atmospheric correction algorithm in different environmental conditions. Note that the coefficients of the SST_skin retrieval algorithm for MODIS in Equation (1) are derived from datasets with much bigger populations involving more variability of atmospheric conditions.

To summarize, the stark differences in the mean and median values of the comparisons between the MODIS and Saildrone SST_skin are as follows:

• They are not caused by instrumental artifacts in the Terra and/or Aqua MODIS measurements as the comparisons are very similar for both.
• For the same reasons, they are not caused by different overpass times of the two satellites.
• For the same reasons, they are not caused by inadvertent errors in the coding or applications of cloud screening and atmospheric correction algorithms, nor in the MUDB generation for the two satellite instruments.
• They are not caused by differences in the SST_skin retrievals from the two Saildrones, as when they were operating close together, the differences in the SST_skin values were small and within expectations.

The remaining likely cause of the discrepancies is in the response of the atmospheric correction algorithm to relatively small differences in the atmospheric conditions when the two Saildrones were not operating near each other, namely the different distributions of the ASTD and the lower tropospheric inversions.

4. Discussion

The major contribution to inaccuracies in the MODIS–Saildrone SST_skin comparisons stems from the atmospheric conditions not being fully congruent with those samples used to derive the high-latitude coefficients for the MODIS atmospheric correction algorithm [17]. As shown in Figure 4a, the majority of BT differences are positive, which is the standard situation as water vapor renders the atmosphere more emissive at 12 μm wavelengths than at 11 µm, and the normal negative atmospheric temperature lapse rate causes the signal at 12 µm wavelengths to be lower than at 11 µm. This is the basis of the multi-channel algorithm that corrects atmospheric water vapor effects to derive the surface temperature. But here there are some negative values of BT differences, which can occur when temperature inversions exist in the lower troposphere, i.e., where the air temperature increases with height (Figure 6b), resulting in stronger atmospheric emission at 12 μm at these levels. The effects of negative BT differences are worthy of further study with a larger dataset or by using radiative transfer simulations. The negative BT differences in the MODIS–Saildrone matchups are discarded from a part of our analyses since the current algorithm for computing SST_skin in Equation (1) cannot make appropriate atmospheric corrections for those anomalous conditions. Another issue is that the current MODIS R2019 SST_skin products have a new latitude band above 60°N to derive coefficients to better represent Arctic atmospheres [17], but here there are a few matched data points located below 60°N (Figure 5). To be consistent with the latitudinal boundary of the algorithm coefficient generation, only measurements above 60°N are used for the following analyses. The updated statistics for the MODIS–Saildrone SST_skin difference after applying filters mentioned above are presented in

Table 4. As Table 1, but after removing the MODIS–Saildrone matchups with negative BT differences and those measured below 60°N.

	Aqua			Terra
	SD-1036	SD-1037	Total	SD-1036	SD-1037	Total
Mean	−0.057	−0.417	−0.234	−0.072	−0.501	−0.295
Median	−0.007	−0.335	−0.193	−0.022	−0.392	−0.219
STD	0.670	0.635	0.677	0.647	0.739	0.728
RSD	0.590	0.570	0.638	0.496	0.534	0.532
RMS	0.671	0.759	0.716	0.650	0.892	0.785
R	0.953	0.957	0.953	0.958	0.947	0.949
Num	325	316	641	342	370	712

. The mean and median MODIS SST_skin biases are changed slightly, but the STDs and RSDs are reduced, indicating that the MODIS SST_skin data retrieved from negative BT differences likely have larger biases. A two-sample t-test does not reject the null hypothesis and thus the SST_skin mean biases for MODIS on Aqua and Terra are statistically equivalent. The following part of our analyses will take Aqua MODIS–Saildrone matchups as the example (being very similar to the Terra MODIS–Saildrone matchups) and combine the datasets for two Saildrones to identify some representative error characteristics.

Of course, the statistics of the MODIS–Saildrone SST_skin differences are not simply an assessment of the accuracy of the MODIS retrievals as there are some inaccuracies in the Saildrone SST_skin data despite of rigorous quality control, and it is conceivable that different contributions from the IR radiometers on the two Saildrone radiometer systems could cause the observed discrepancies in the statistics when compared with each Saildrone. However,

Table 5. Statistics of Aqua MODIS SST_skin difference compared with the subsurface SST_depth measured by temperature loggers at −0.33 m depth on the two Saildrones.

	Mean	Median	STD	RSD	RMS	R	Num
SD-1036	0.296	0.390	0.656	0.564	0.718	0.953	325
SD-1037	0.017	0.146	0.679	0.635	0.678	0.949	316
Total	0.158	0.255	0.681	0.605	0.699	0.949	641

shows that there are also distinct discrepancies with comparisons between the MODIS SST_skin retrievals and Saildrone subsurface temperatures, which are independent of the inaccuracies in the Saildrone SST_skin data from each USV. This brings attention back to the inability of the atmospheric correction algorithm to compensate adequately for the surface and atmospheric effects on the measured BTs.

Due to the midnight sun during the Arctic summer, only very few (<5%) night-time data points are in the valid matchups. As introduced in Section 1, the SST_skin can be expressed as the combination of the SST_depth, cool skin effect, and diurnal warming, if present, in the upper ocean:

SST_skin = SST_depth(z) + ∆T_c + ∆T_dw(z)

(2)

where ∆T_c represents the cool skin effect and ∆T_dw is the diurnal warming at the depth z [43]. ∆T_c can be parameterized with a single dependence of the wind speed as presented in some previous studies [41,42,43,44,49,50] with the same form of exponential equation but different coefficients derived using different datasets under various environmental conditions in the global ocean. Jia, et al. [43] used the night-time data from both SD-1036 and SD-1037 to provide new parameterizations for the cool skin effect in the Pacific sector of the Arctic Ocean:

ΔT_c = −0.41 ∗ exp(−U₁₀/2.5) − 0.15

(3)

where U₁₀ is the 10 m wind speed converted from Saildrone anemometer measurements using a logarithmic wind profile. Equation (3) then could be reasonably used to estimate the cool skin effect for the MODIS matched data along the Saildrone deployment tracks in this study. Further, the magnitudes of diurnal warming in the top 1.7 m of the ocean can also be estimated based on Equations (2) and (3). As shown in Figure 8a, large diurnal warming events (>3 K) were identified in the matchups, and have been analyzed in detail by Jia, et al. [46]. The MODIS-Saildrone SST_skin differences tend to be more negative with a greater amplitude of warming, indicating the underestimation of MODIS SST_skin retrievals under strong diurnal warming conditions. This can be interpreted as the non-representative algorithm coefficients in Equation (1) for those cases since the coefficients are derived based on a high-quality subset in the MUDB under wind speeds > 6 m/s with other constraints, whereas the strong diurnal warming occurs at low winds. Similarly, both Merchant, et al. [51] and Zhang, et al. [52] demonstrate that the IR satellite SST_skin retrievals noticeably underestimate the diurnal variability, in the tropical Atlantic and Pacific Oceans. Note that the warming events > 0.5 K in the matchups during the SD-1037 cruise are ~10% more than those for the SD-1036 deployment, and such distribution differences might also contribute to the MODIS SST_skin mean biases’ discrepancy validated by the data from two USVs.

Another insight is that it is inappropriate to use subsurface SST_depth measurements to validate the satellite data mostly collected in the daytime at high latitudes in summer. Using SST_-0.33m taken from Saildrones to compare with the MODIS SST_skin, Table 5 shows that the statistics of the mean and median become positive due to the existence of diurnal warming, and those would apparently mislead the error characteristics analysis for MODIS SST_skin in terms of the performance of the atmospheric correction algorithm.

Since the algorithm coefficients in Equation (1) are derived using buoy-measured SST_depth, the first term, a constant a₀, is reduced by 0.17 K to compensate for the cool skin effect. However, based on Equation (3), the mean cool skin effects for MODIS SST_skin retrievals along the tracks of SD-1036 and SD-1037 are estimated as −0.242 K and −0.238 K, respectively, indicating the use of −0.17 K, which is considered as the global average cool skin effect, is inappropriate, at least for the northern high-latitude regions. Such biases are not explicit in the statistics mainly because of being overwhelmed by diurnal warming. The more negative cool skins imply the generally stronger surface net heat loss from the thermal skin layer into the atmosphere. A physical skin effect scheme would be preferable instead of the −0.17 K correction for the retrieval algorithm, including the models of cool skin, but also the possible warm skin effect [39].

Jia and Minnett [17] revealed the reality of a weak correlation between the MODIS BT difference, BT₁₁–BT₁₂, and the total column water vapor at latitudes above 60°N, and proved that the sea surface emissivity effect could be dominant in the measured BT difference, amplified by the temperature difference between the sea surface and the atmospheric column throughout the surface to the satellite sensor. To correct this emissivity effect, Jia and Minnett [17] introduced an index, the Emissivity-introduced BT difference (EΔBT), with the functional form as

$$E\mathsf{\Delta }BT=({\mathsf{\epsilon }}_{11}-{\mathsf{\epsilon }}_{12}) \ast (T_{\mathrm{s}}{ }_{ }– {\overline{T}}_a)$$

(4)

where ε₁₁ and ε₁₂ are the sea surface emissivities at 11 μm and 12 μm wavelengths. $T_s$ is the surface temperature and $\overline{T}$_a is the effective air temperature at 11 μm and 12 μm associated with the atmospheric downward radiance reaching the surface.

By running the RTTOV model with the same inputs described in Section 3, both surface emissivity and the downwelling emitted radiation (then converted to $\overline{T}$_a by a modified Planck’s function [17]) can be determined. As shown in Figure 8b, the MODIS SST_skin biases appear to be more negative for increasing EΔBT values when EΔBT > 1 K, while the relationship is not evident for EΔBT < 1 K. This threshold is close to the value of 0.95 determined by Jia and Minnett [17] using the MUDB where data are mostly distributed at the Atlantic side of the Arctic. Note that there are some negative outliers at low EΔBT values, which were also found by Jia and Minnett [17], indicating the effects of other error sources, such as undetected cloud contamination or improper atmospheric corrections. Most EΔBT values are <1 K since the water vapor effect in the BT difference can still be pronounced in summer. Due to the limited amount of data, the relationship at large EΔBT, especially >1.5 K, is not very solid. However, the patterns demonstrated here are encouraging since the theory of the emissivity effect on MODIS SST_skin retrievals raised by Jia and Minnett [17] is further proven using SST_skin derivations from in situ measurements as validation data.

5. Conclusions

Accurate satellite-retrieved SST_skin is important for climate change studies and weather prediction, particularly for high-latitude regions, which draw attention due to the Arctic Amplification [53,54]. The deployment in the Pacific sector of the Arctic in the 2019 summer of two Saildrones carrying the “unicorn”-structured IR pyrometers on the deck produced SST_skin with sufficient accuracy [30], which was used to validate the MODIS SST_skin retrievals in this study.

Multiple Saildrone measurements can be matched with the same MODIS pixel using the standard collocation time and space windows due to the high sampling frequency of Saildrone. Therefore, the Saildrone–MODIS matchup with the smallest separation is considered as the unique paired data for a high-quality MODIS pixel since the SST_skin biases are sensitive to the distance rather than the time difference. The mean biases are significantly different (~0.4 K) for the matchups from the SD-1036 and SD-1037 data. Considering the relatively small numbers of comparisons and the divergent environmental conditions along the tracks of two Saildrones, the differences of large mean biases indicate statistics from neither of the two datasets are themselves representative of the characteristics of the conditions in the wider region of the Pacific Sector of the Arctic Ocean, and neither alone would provide meaningful information about the capacities of the atmospheric correction algorithm when applied to MODIS measurements on a larger scale. But the combined data should provide a better representation. The statistics for MODIS on Aqua and Terra are very similar, even for the matchups with individual Saildrones, indicating that the performances of two MODIS sensors are comparable.

For further analysis of error characteristics, measurements with negative BT difference are discarded given the inappropriateness of the atmospheric correction algorithm. In addition, only data points measured above 60°N are analyzed to be consistent with the boundary of the high-latitude band for algorithm coefficients. Overall, the average MODIS SST_skin biases for Aqua and Terra are −0.234 K and −0.295 K, with STDs of 0.677 K and 0.728 K. The negative biases in MODIS SST_skin retrievals are noteworthy. Due to the midnight sun in the Arctic summer, over 95% of total matchups are daytime data with a possible presence of diurnal warming layers in the upper ocean. Figure 8a shows that the MODIS SST_skin products are underestimated especially under large warming events > 2 K because of the lack of such conditions included in the derivation of the algorithm coefficients in Equation (1). Figure 8b demonstrates that the MODIS SST_skin biases tend to be more negative when the surface emissivity effect is dominant in the BT difference between 11 μm and 12 μm bands, scaled by the index EΔBT, defined by Jia and Minnett [17]. The patterns in Figure 8b are similar to those found in Jia and Minnett’s work [17], and it is very encouraging that the retrieval errors resulting from the emissivity effect at high latitudes are further verified by the Saildrone-derived SST_skin data.

Additional research is necessary to improve the accuracy of IR SST_skin retrievals at high northern latitudes. Firstly, the causes of negative BT differences and their impact on the SST_skin retrieval should be investigated. A consequence of the current SST_skin retrievals in conditions where atmospheric temperature inversions occur, leading to negative BT differences, is that spatial features in a satellite-derived SST_skin field are likely to contain contributions, probably significant and possibly dominant, from uncorrected atmospheric variability. It might also be possible that the surface-generated aerosols contribute to the anomalous BT difference measurements, but here we lack aerosol data to examine such an effect, and so the possible influence of Arctic aerosols remains an open question. Moreover, the seemingly inappropriate cool skin correction using a constant value of −0.17 K for the MODIS SST_skin should be re-examined with more matchups with in situ SST_skin measurements, especially at night. The EΔBT index expression requires optimization, probably in terms of parameterizations of the relevant variables, refraining from running radiative transfer simulation for each pixel. Finally, more in situ SST_skin data with high accuracy at high latitudes are needed to further improve the understanding of inaccuracies in IR satellite-derived SST_skin and to refine the algorithms for satellite SST_skin retrievals in this challenging but vitally important area.