In each VIIRS parent field (image hereinafter), we identified every 192 pixel × 192 pixel subarray that has fewer than 2 % of its pixels masked (quality_level <5) because of land, corrupted pixels usually associated with cloud cover, or missing data. This 2 % threshold was established after sampling at a wider range of thresholds (as high as 5 %) and assessing the outputs. For thresholds greater than 2 %, we found that clouds significantly bias estimates of the degree of structure obtained by the machine learning algorithm (discussed in Sect. ) applied to the datasets of cutouts.

We then divided each image into a grid with a cell size of 96 pixels × 96 pixels and selected the closest cutout to the center of each grid cell that satisfies the 2 % threshold (or 0 if none satisfy). This approach randomized the sampling, thus avoiding possible biases that may have emerged from cutouts sampled on a regular grid. In a well-sampled image, this implies each cutout has a ∼ 50 % overlap with its four nearest neighbors and ∼ 25 % with the next four nearest neighbors. Unlike our analysis of Moderate Resolution Imaging Spectroradiometer (MODIS) data, we did not place a restriction on the distance from nadir because the physical size of the VIIRS pixels varies by approximately a factor of 2 from nadir to the swath edge compared with a variation of approximately a factor of 5 for MODIS.

From the full parent dataset, we extracted 2 851 702 cutouts (limiting to <57∘ N; see Sect. ). The geographical distribution of these is shown in Fig. , which highlights the regions of the ocean that are preferentially cloud free (e.g., the equatorial Pacific Ocean and coastal regions). For this and all subsequent geographic plots, we used Hierarchical Equal Area isoLatitude Pixelation (HEALPix, https://healpix.sourceforge.io, last access: 1 November 2023) schema , which tessellates the surface into equal-area curvilinear quadrilaterals and was introduced for all-sky analysis of astronomical data. Throughout the paper, we opted for nside, the HEALPix resolution parameter, to be 64, which yields a HEALPix cell with an area of approximately 100 km × 100 km. Values presented are numbers associated with each HEALPix cell, in this case the number of cutouts in the cell.

For cutouts with one or more masked pixels, we “inpainted” them using the biharmonic algorithm provided in the scikit-image software package ; the algorithm, we found, performs well even for data with steep gradients . We then downscaled the arrays with a local mean to 64 pixels × 64 pixels or approximately 144 km × 144 km at ∼ 2.1 km sampling, which approximately matches the coarsest sampling of the LLC4320 outputs. Note that the actual size of cutouts is a function of distance from nadir; we did not resample the observed data to account for these changes. Last, we demeaned each cutout to produce SST anomaly (SSTa) fields. This defines the final, preprocessed dataset that we use for all VIIRS analyses to follow.

Roughly 9 years (8 years, 11 months) of VIIRS data comprise the ∼ 3 million (2 932 452) VIIRS cutouts, whereas the LLC4320 simulation output used for this study spans only 1 year. To further restrict the VIIRS cutouts to 1 year would leave too few data for a full-globe comparison between satellite observations and the model outputs. For this reason, we compare ∼ 9 years of VIIRS data to the 1-year model simulation.

Our approach to constructing cutouts from the LLC4320 outputs intentionally paralleled the methodology and outputs for VIIRS. We first identified all 64 pixel × 64 pixel regions that have a valid SST value (i.e., avoiding land). The geographic location (lat, long) of each of these was recorded. Second, we considered the full year of LLC4320 outputs taken every 12 h from 17 November 2011 to 15 November 2012 (inclusive). For each cutout in the VIIRS sample, we matched the location to the closest valid 64 pixel × 64 pixel region in the LLC4320 dataset. We then identified the LLC4320 timestamp closest in time from the start of the given year (with the LLC4320 in 12 h intervals). This is akin to matching on the day of the year and then the time of the day to the nearest 12 h. This “climatological” matchup of cutouts was performed to avoid seasonal and regional biases in the sampling.

Much of the analysis presented in subsequent sections of this paper compares the statistics of cutouts in a given HEALPix cell. Ideally, the cutouts associated with a VIIRS–LLC4320 matchup lie in the same HEALPix cell. This, however, is not always the case; the closest LLC4320 cutout to a VIIRS cutout may lie in an adjacent HEALPix cell when the VIIRS cutout lies outside of the LLC4320 grid, generally in coastal waters.

We wished to maintain an approximately constant sampling size of 2.25 km matched to VIIRS or a 144 km × 144 km total for a 64 pixel × 64 pixel cutout. Therefore, we sized the array extracted from the LLC4320 outputs according to the local size of the grid, which varies as approximately cos⁡(lat) for latitudes ≤57∘ N. At latitudes >57∘ N, LLC4320 horizontal grid spacing asymptotes to ∼ 1 km in the polar cap. To avoid the complications brought by different grid characteristics, we constrained our analysis to an area south of 57∘ N.

Each extracted LLC4320 array is downscaled to a 64 pixel × 64 pixel cutout using the local mean. We then injected random noise using a Gaussian deviate with a standard deviation of σ=0.04 K based on an analysis of the noise properties of the VIIRS data . Lastly, we demeaned each cutout to generate SSTa arrays.

The ULMO machine learning algorithm is a probabilistic autoencoder PAE; designed to assign a relative probability of occurrence to each cutout in a large dataset. It is an unsupervised method which learns representations of the diversity of SSTa patterns without human assessment. The PAE combines two deep learning algorithms to perform its analysis. The first is an autoencoder that generates a reduced dimensionality representation (a.k.a., a latent vector) for each cutout in a complex latent space. The second step is a normalizing flow which transforms the autoencoder latent space into a Gaussian manifold with the same dimensionality. One can then calculate the relative probability of any cutout occurring within the Gaussian manifold with standard statistics. We refer to this relative probability as the log-likelihood (LL) metric.

In the following section, we compare distributions of the LL metric for the VIIRS and LLC4320 cutouts in discrete geographical regions across the global ocean. This provides a quantitative technique to compare the SSTa patterns predicted by the OGCM against those observed in the real ocean. We note that because the LL metric is only a scalar description of a given pattern's frequency of occurrence, it is possible – in principle – to have similar LL distributions despite qualitative differences in the SSTa patterns. This would, however, require a remarkable coincidence, and our visual inspection of regions with consistent LL distributions have not revealed any such examples. We also emphasize that the opposite is not true: regions with significantly different LL distributions do have qualitatively differing distributions of SSTa patterns.

Figure  presents galleries of VIIRS and LLC cutouts designed to show how the structure of the cutouts vary as a function of LL. For Fig. a, the entire LL VIIRS population is divided into quintiles. For each quintile, one VIIRS cutout and one LLC cutout is randomly selected from the 50 LL values nearest to the median of the VIIRS LL distribution. The LL of the median values are shown above the VIIRS cutouts. These galleries show a well-defined progression from fields with a large temperature range and accompanying gradients to fields with a smaller temperature range, weaker gradients, and less complex patterns.

The correlation between temperature range and LL seen in Fig. a was noted by in their discussion of the MODIS dataset. In the analysis to follow (Sect. 4.2), we compare LL values of VIIRS cutouts with those for LLC cutouts at the same geographic location, which suggests that the temperature range of the cutouts we compare will be similar. (Admittedly, there are a few regions where this is not the case, and we address this when it occurs.) Important from the perspective of the work presented herein is rather how the characteristics of cutouts vary with LL when the temperature range is bound to a small range. To further provide a sense for how cutout characteristics other than temperature range evolve with LL, we present a second gallery of VIIRS and LLC cutouts in Fig. b. These cutouts are restricted to have 1<ΔT<1.5 K, where ΔT is defined as the difference in 90th and 10th percentiles of the SST distribution: ΔT≡T90-T10, where TN denotes the Nth percentile. These galleries were constructed in the same fashion as those for Fig. a. In this case, the progression is from cutouts for which SST contours are relatively convoluted to cutouts with relatively straighter contours; in other words, the “structure” of the cutouts decreases as LL increases. As with the galleries in Fig. a, the characteristics of the LLC cutouts in this gallery track those of the cutouts in the VIIRS gallery.

As noted above, the galleries of Fig.  show how the structure of the cutouts varies with LL. However, they do not relate the LL to the underlying dynamics, which would be helpful in obtaining a better understanding of regions in which the LLC appears to fail. We are working on trying to establish such a relationship, if one exists, but to date, it eludes us. The lack of such a relationship, however, does not invalidate the results of this work in that whatever the relationship, it applies equally to VIIRS and LLC4320.

In we introduced the ULMO algorithm and trained a model with Level-2 (L2) MODIS data sampled at ∼ 2 km and using 64 pixel × 64 pixel cutouts. While this model could have been applied here to the VIIRS and LLC4320 cutouts, we have generated a new ULMO model from the VIIRS dataset. The same hyperparameters derived for ULMO in were adopted here.

We trained the PAE on 150 000 random VIIRS cutouts from 2013 and used the remainder of the data from that year (181 184 cutouts) for evaluation. We trained the autoencoder for 10 epochs with a batch size of 256 and achieved good learning loss convergence. We then trained the normalizing flow for 10 epochs (batch size of 64) and also achieved good convergence. The VIIRS-trained ULMO model was then applied to all of the VIIRS and LLC4320 cutouts to calculate LL for each.

To highlight the similarities in the LL̃ fields on smaller scales (O(100km)), we remove the large regional differences from LL̃LLC apparent between them (Fig. ). This is done by averaging LL̃VIIRS and LL̃LLC over 100 sequential values based on the HEALPix index. HEALPix cells are arranged longitudinally, so this correction removes zonal structures on the order of 10 000 km or longer, retaining structures on smaller spatial scales. LL̃VIIRS (black) and LL̃LLC (cyan) are shown in Fig. . A “corrected” LL̃LLC, designated as LL̃LLC′, is then determined from 1LL̃LLCi′=LL̃LLCi-1100∑j∈BLL̃LLCj-LL̃VIIRSj, where i∈ all HEALPix cells with at least five cutouts in the VIIRS dataset and five cutouts in the LLC4320 dataset of 2B:⌊i-1100⌋⋅100+1,⌊i-1100⌋⋅100+100 and ⌊x⌋ denotes the largest integer less than or equal to x. LL̃LLC′ values are shown in red in Fig. .

The plots, in Fig. , bin each HEALPix cell by their associated LL̃ values. The left histogram bins the cells according to their LL̃VIIRS and LL̃LLC values, whereas the right histogram bins according to their LL̃VIIRS and LL̃LLC′ values. As noted in Fig. , cutouts in the LLC dataset skew to higher LL values than those found in the VIIRS dataset. The difference in the LL distributions can also be seen in Fig. a, where LL̃LLC values, greater than approximately 200, tend to be higher than LL̃VIIRS values with the separation increasing with LL. It is important to note that here we have binned the HEALPix cells and their LL̃ values, not the cutouts and their LL values. Correcting the LL̃LLC values lowered the LL̃LLC values to be more in line with the LL̃VIIRS values.

The LL̃VIIRS geographic distribution is shown with that of LL̃LLC′ in Fig. . The large-scale similarities in the general shape of the distributions is much more evident in this figure, but of more interest are the many smaller-scale features, which emerge in the corrected distribution. Consider, for example, the LL̃ fields at approximately 45∘ S in the black and red polygons of Fig. . For both LL̃VIIRS and LL̃LLC′ there is a local maximum in LL̃ corresponding to a minimum in the structure of the SSTa cutouts in the black polygon. This feature is associated with a zonal bathymetric ridge at approximately 45∘ S crossed by two meridional ridges, one at 44∘6′ W and the other at 39∘7′ W (Fig. b, although the ridges are difficult to see in this figure). The peaks of these ridges are at depths of approximately 5000 m in a basin extending to depths of 6000 m. Both LL̃ fields show a band of negative LL̃ values to the west and south of the feature. The LL̃VIIRS field also shows a well-defined band to the north and east, while the LL̃LLC fields only shows a suggestion of such a band, but the local minimum is still well defined in both.

The second feature of interest is the thin, hooked band of low LL̃VIIRS values – corresponding to relatively more structure in the cutouts – in the red polygon south of South Africa (Fig. a). This band is reproduced well in the LLC4320 output (Fig. b). Again, referring to the bathymetric image (Fig. b), it is clear that the shape of this feature is a consequence of the underlying bathymetry. Specifically, it appears that a tendril of the retroflected Agulhas Current has flowed to the south before turning toward the east to pass through a gap in the southwest–northeast ridge, partially blocking the main part of the retroflected current. The top of the ridge is found at depths of approximately 2000 m, while the relatively wide gap, through which the tendril passes, is as deep as 3500 m. The manually digitized center of the feature is shown with the dotted black and solid magenta lines in Fig. b; the model appears to reproduce this subtle feature in the circulation quite accurately.

To highlight the regional distributions with significant differences between the structure of satellite-derived and LLC4320-produced SSTa cutouts, we replot the data of Fig.  in Fig.  but mask all values between -197 and 197 in dark gray. These thresholds determine what ΔLL values we consider to be statistically significant; they are the differences in the LL distributions from the first 4 years, 2012–2015, to the last 4 years, 2017–2020, of VIIRS data. Any LL̃VIIRS-LL̃LLC differences within those given thresholds can be attributed to statistical variability between the simulation of a free-running model and observational data. HEALPix cells with ΔLL values beyond these thresholds correspond to regions either for which the retrieved VIIRS cutouts are not good measures of SST or for which the LLC4320 output is associated with deficiencies in the simulation (see Appendix A for more detail).

LL̃VIIRS-LL̃LLC differences evident in Fig.  fall into three general groupings: the wide band of negative values (more structure in the VIIRS cutouts than in the LLC4320 cutouts) centered on the Equator; the less continuous band of positive values in the Southern Ocean; and the very positive (much more LLC4320 structure than VIIRS structure) patches in the vicinity of the separation of western boundary currents from the continental margin, specifically, the Gulf Stream in the western North Atlantic, the Kuroshio in the western North Pacific, the Brazil Current in the South Atlantic, and the Agulhas Current where it retroflects south of South Africa. The equatorial and Southern Ocean bands are also evident in the zonal mean of LL̃VIIRS-LL̃LLC of the unmasked field shown in Fig. b. The zonal mean is roughly flat at -350 from 5∘ S to the Equator; rises rapidly poleward of these two points for about 5∘ of latitude to -150; and then continues to increase approximately linearly but, more slowly, from there (10∘ S and 5∘ N) to a value of 0 at 30∘ N and 30∘ S.

In the text to follow, we address each of the three regions primarily in the context of SST galleries constructed from two small and geographically close regions (three colored rectangles shown in Fig. ), which exemplify characteristics of the differences that we find to be of interest.

In general, there are four possibilities for low values of LL̃VIIRS-LL̃LLC in the equatorial region (15∘ S to 15∘ N).

The year simulated, 2012, is atypical, differing from the 2012–2020 mean. This is very unlikely given the magnitude of the differences, -350 at the Equator, as well as the fact that the zonal mean of LL̃2012–2015-LL̃2017–2020 is essentially flat at 0 equatorward of 50∘ (Fig. ), suggesting little interannual variability.

The rectangular patch [2∘ S–2∘ N, 105–95∘ W] west of the Galapagos Islands in the equatorial Pacific (the yellow rectangle in Figs.  and ) stands out because of the significant step of LL̃VIIRS-LL̃LLC along the Equator. The LL̃ distribution for the region in the rectangle above the Equator is provided in Fig. a, as well as below the Equator in Fig. c. Consistent with the geographic distributions of LL̃ in Fig. , the median LL̃LLC value increases from south to north across the Equator, while the median LL̃VIIRS value decreases, both contributing to a larger structural difference between VIIRS cutouts and LLC4320 cutouts to the north of the Equator than that to the south. Histograms of ΔT are provided because there is a correlation, although weak, between LL and ΔT, while ΔT is a more readily understood measure of similarity and differences between VIIRS and LLC4320 SST fields. The distribution of ΔTLLC is similar across the Equator, while that of VIIRS shows a much longer tail consistent with more variability and lower LL values.

Visual examination of the SST fields supports the above conclusions. Consider SST fields of the VIIRS and LLC4320 cutouts in the yellow rectangle of Fig. , again separating them into those above the Equator and those below. Galleries of nine cutouts each are shown in Fig. . As previously noted each VIIRS cutout was matched in space and according to the day of the year with an LLC4320 cutout. To generate the galleries shown in Fig. , two sets of cutout pairs were formed. One set consisted of 40 % of all pairs in the region for which the VIIRS LL values were closest to the median VIIRS LL value for the region. The second set was similarly constructed, except being based on LLC4320 LL values. The intersection of the two sets defined the pool from which nine cutout pairs were randomly drawn. These pairs for the region above the Equator, 0 to 2∘ N and 105 to 95∘ W, are shown in Fig. a and b. For each VIIRS cutout in Fig. a, its LLC4320 partner is shown in the same location in Fig. b. Similarly, Fig. c and d show pairs for the region below the Equator. (Remember that because the LLC4320 simulation is free running, there is no reason to expect the features in the pairs to be identical or even similar; it is the structure of the fields that is of interest.) Visually, the SST fields of the LLC4320 cutouts are very similar in both regions, showing very little structure with correspondingly large LL values. The VIIRS fields below the Equator show a little more structure than the LLC4320 fields, consistent with the smaller LL values. By contrast, most of the VIIRS fields above the Equator have significantly more structure than any of those in the other three galleries, with correspondingly lower LL values. Also evident in the VIIRS galleries are blemishes in the fields, scattered regions of colder temperatures. We believe these to be unresolved clouds, i.e., clouds not detected by the retrieval algorithm. Because they add structure to the fields, we believe that they decrease the LL value of the cutout. This would reduce the magnitude of LL̃VIIRS-LL̃LLC both above and below the Equator but is not likely to significantly impact the observed LL̃VIIRS(above)-LL̃VIIRS(below). Also, note that the distribution of the number of cutouts per HEALPix cell is symmetric about the Equator in the area of interest (Fig. b), suggesting that the contribution of clouds to corruption of the LL values is also symmetric about the Equator in the rectangle of interest.

Another possible explanation for the lack of SST structure in the equatorial region is the limited spatiotemporal resolution of the prescribed atmospheric forcing (0.14∘ and 6-hourly). A recently completed coupled ocean–atmosphere simulation provides high-frequency/wavenumber interactive forcing (0.0625∘ and 45 s) to the ocean. We intend to repeat the present analysis on this simulation to determine whether the equatorial SST structures of this coupled simulation are more similar to VIIRS.

We examine the same four possibilities for high LL̃VIIRS-LL̃LLC values in the Southern Ocean as we did for low values in the equatorial region.

The year simulated, 2012, is atypical, differing from the 2012–2020 mean. This is possible but unlikely given the extent of the region covered by anomalously high differences and that there were few differences in this region for which LL̃2012–2015-LL̃2017–2020 exceeded the 2σ threshold.

In Fig. c, we replot the masked LL̃VIIRS-LL̃LLC field of Fig.  for the Southern Ocean south of Australia with LL̃VIIRS and LL̃LLC for the same region in the upper two panels. The band of low LL̃VIIRS and LL̃LLC values from 45 to 70∘ E at about 41∘ S corresponds to the significant structure in the field associated with the Antarctic Circumpolar Current (ACC). (Note that this band originates south of South Africa where the Agulhas retroflection joins the ACC, the band of negative values of LL̃VIIRS-LL̃LLC in Fig. .) It appears that the ACC as modeled by LLC4320 for 2012 is slightly to the south of the VIIRS ACC for 2012–2020, with the positive values of LL̃VIIRS-LL̃LLC south of the band and the corresponding negative values to the north of the band. Although a small shift, the fact that the width of the bands for both VIIRS and LLC4320 is virtually identical suggests that the modeled ACC is a bit to the south of the envelope of paths in this period; i.e., the slight shift may be significant in the context of the modeled processes. Apart from the slight shift to the south, the model appears to have reproduced the current quite well in this region. East of about 70∘ E LL̃ for the modeled ACC is substantially more negative than that of the observed values, resulting in the anomalous LL̃VIIRS-LL̃LLC values in this region. Interestingly, east of about 95∘ E, the VIIRS field shows a positive band north and south of the northern branch of the current, as does the LLC4320 field. In fact, the general pattern of LL̃LLC has the same general shape as that of LL̃VIIRS. Therefore it appears that the model has the correct general structure for the flow in this region but, as we now emphasize, is too energetic.

Galleries of SSTa cutouts in the black rectangles of Fig.  (a region for which the model LL̃ values are in general agreement with the VIIRS values) are shown in Fig. a for VIIRS and b for LLC4320. Galleries for the anomalous region, the white rectangles in Fig. , are shown in Fig. c for VIIRS and d for LLC4320. Cutouts for these galleries were randomly selected as described for the generation of galleries for the equatorial region (Fig. ). The anomalous behavior is clear in the lower two panels; the LLC4320 fields are much bolder with substantially lower LL‾ values and larger ΔT values than the VIIRS cutouts. The LLC4320 fields are clearly more energetic. By contrast, LLC4320 cutouts in the region for which there appears to be agreement are more similar to VIIRS cutouts.

One possible explanation for more energetic SST fields in LLC4320 relative to VIIRS is the fact that LLC4320 was inadvertently forced with tidal potential that is 10 % more energetic than the real ocean , resulting in, for example, more energetic internal tides than observed. A second, in our opinion more likely, explanation is that the 148∘ horizontal grid spacing of the simulation, although sufficient to enable the gravest modes of mixed-layer instabilities to be captured, is insufficient to fully represent the smaller-scale instabilities that would damp the magnitude of the resolved instabilities.

The conclusions for the four possibilities of high values in the Gulf Stream are similar to those for the Southern Ocean.

The year simulated, 2012, is atypical, differing from the 2012–2020 mean. This is very unlikely given, as will be shown below, that the modeled Gulf Stream is south of the most extreme southern positions of paths of the Gulf Stream from a number of observational sources.

Figure a shows LL̃VIIRS-LL̃LLC in the Gulf Stream region downstream of the point at which it separates from the continental margin. Figure b shows the same data but masked, showing only the HEALPix cells with values exceeding the thresholds identified in Appendix A, ±197. Also shown in these plots is the mean path of the Gulf Stream (magenta line) and its northern and southern extent (black lines). These were determined from manual digitizations of the path of the stream – defined as the maximum cross-stream SST gradient in the vicinity of the stream – in warmest-pixel composites of all AVHRR 1 km SST fields in contiguous 2 d intervals . The mean path of the stream was determined by averaging, over all 2 d composites between 1982 and 1999, the point at which these paths intersected integral degrees of longitude. The northern and southern extents are the latitudes for which 99 % of the paths lie to the south – the northern extent – and 99 % lie to the north – the southern extent – for 1982–1999. Large positive differences south of the southern extreme suggest that the LLC4320 output contains more structure in its cutouts than VIIRS, whereas VIIRS fields show more structure within the bounds of the northern and southern extremes.

The large patch of positive values west of 60∘ W corresponds to the premature separation of the modeled Gulf Stream from the continental margin reported by based on the mean path and extreme envelope of paths shown in Fig.  and on the Ocean Surface Current Analyses Real-time (OSCAR) surface currents (https://podaac.jpl.nasa.gov/, last access: 1 November 2023, dataset list; search keywords: oceans, ocean circulation; projects: OSCAR) for 2012. Simply put, the modeled Gulf Stream is found some 250 km to the south of the mean observed stream at 70∘ W and approximately 100 km to the south of the southern extreme observed between 1982 and 1986.

The cause of the positive and negative anomalous values of Fig. b become more clear from the individual plots of LL̃VIIRS and LL̃LLC in Fig. c and d, respectively. The most negative values of LL̃ are seen in the satellite-derived fields along the edge of the continental slope and, in particular, south of Georges Bank, south of the eastern side of the Gulf of Maine, and south and east of the Grand Banks. (Note that the relatively sharp gradient in LL̃ values follows the 200 m isobath, shown as dotted red lines in Fig. .) Values remain low to the southern extreme of the Gulf Stream. Recall that these HEALPix values are medians obtained from all cutouts in the >8-year interval. During this period the Gulf Stream meanders in the envelope with regions of significant structure at some times and regions of less structure at others, resulting in less structure on average than is found near the shelf break in very active regions that are topographically constrained – south of Georges Bank and south and east of the Grand Banks. The LLC4320 output also shows the most negative values south of Georges Bank but less so south of the Grand Banks. This is likely associated with the premature separation of the stream from the continental margin, the negative values of LL between 65 and 75∘ W and south of about 36∘30′ N. Two aspects of interest associated with the model field after separating are (1) the relatively smaller width (meridional extent) of the region covered by the Gulf Stream immediately after separation when compared with the broader distribution associated with the VIIRS data and the rapid increase in LL values – decrease in structure – at approximately 62∘ (the stream appears to die at that point) and (2) the positive LL values east of 60∘ W and south of 33∘ N, the cause of the statistically significant negative differences when compared with the VIIRS results. The former may be due to the fact that model simulation is only for 1 year, while the VIIRS data cover >8 years. The reasons for the rapid die-off of the stream and the relative quietness (larger values of LL) east of 62∘ are not obvious.

Next, we examine VIIRS and LLC4320 cutouts inside the Gulf Stream envelope (the white rectangles in Figs. c and d at [40–42∘ N, 60–50∘ W] and outside the observed Gulf Stream in the region of anomalously low LLC4320 values associated with the premature separation of the Gulf Stream (the red rectangles in Fig. c and d at [34–36∘ N, 70–60∘ W]). Galleries of nine cutouts each for both VIIRS and LLC4320 for both regions are shown in Fig. . Cutouts for these galleries were randomly selected as described for the generation of galleries for the equatorial region (Fig. ). The characteristics of the VIIRS cutouts outside of the Gulf Stream (Fig. c) differ substantially from those of the other three galleries, as does the mean LL. VIIRS cutouts within the stream (Fig. a) are similar to those in the LLC4320 gallery of cutouts south of the Gulf Stream (Fig. d), consistent with the suggestion that the modeled stream separates prematurely from the continental margin. The structure of LLC4320 cutouts in the Gulf Stream (Fig. b) lies between that of VIIRS cutouts in the stream (Fig. a) and LLC4320 cutouts south of the stream (Fig. d), as do the LL values. This is consistent with the modeled stream being to the south of the observed stream.