[1, $\star$]KatharinaGallmeier [2,3,4,5, $\star$]J. XavierProchaska [6,
$\star$]PeterCornillon [7]DimitrisMenemenlis [8]MadolynKelm

1]Institute for Defense Analyses, Alexandria, VA, 22305, USA 2]Affiliate of
the Department of Ocean Sciences, University of California, Santa Cruz, CA,
95064, USA 3]Department of Astronomy and Astrophysics, University of
California, Santa Cruz, CA, 95064, USA 4]Kavli Institute for the Physics and
Mathematics of the Universe (Kavli IPMU), 5-1-5 Kashiwanoha, Kashiwa,
277-8583, Japan 5]Simons Pivot Fellow 6]Professor Emeritus, Graduate School of
Oceanography,University of Rhode Island, Narragansett, RI, 02882, USA 7]Jet
Propulsion Laboratory, California Institute of Technology, Pasadena, CA,
91109, USA 8]Earth System Science Department, University of California,
Irvine, Irvine, CA, 92697, USA $\star$]These authors contributed equally to
this work.

J. Xavier Prochaska<EMAIL_ADDRESS>
# An evaluation of the LLC4320 global ocean simulation based on the
submesoscale structure of modeled sea surface temperature fields

###### Abstract

We have assembled 2,851,702 nearly cloud-free cutout images (sized
144$\times$144 km2) of Sea Surface Temperature (SST) data from the entire
2012–2020 Level-2 Visible Infrared Imaging Radiometer Suite (VIIRS) dataset to
perform a quantitative comparison to the ocean model output from the MIT
general circulation model (MITgcm). Specifically, we evaluate outputs from the
LCC4320 $\frac{1}{48}^{\circ}$ global-ocean simulation for a one-year period
starting on November 17, 2011 but otherwise matched in geography and day-of-
year to the VIIRS observations. In lieu of simple (e.g., mean, standard
deviation) or complex (e.g., power spectrum) statistics, we analyze the
cutouts of SST anomalies with an unsupervised Probabilistic AutoEncoder (PAE)
trained to learn the distribution of structures in SST anomaly (SSTa) on
$\sim$10-to-$80$-km scales (i.e., submesoscale-to-mesoscale). A principal
finding is that the LLC4320 simulation reproduces well, over a large fraction
of the ocean, the observed distribution of SST patterns, both globally and
regionally. Globally, the medians of the structure distributions match to
within $2\sigma$ for $65\%$ of the ocean, despite a modest, latitude-dependent
offset. Regionally, the model outputs reproduce mesoscale variations in sea
surface temperature anomaly (SSTa) patterns revealed by the PAE in the VIIRS
data, including subtle features imprinted by variations in bathymetry. We also
identify significant differences in the distribution of SSTa patterns in
several regions: (1) in the vicinity of the point at which western boundary
currents separate from the continental margin, (2) in the Antarctic
Circumpolar Current (ACC), especially in the eastern half of the Indian Ocean,
and (3) in an equatorial band equatorward of $15^{\circ}$. It is clear that
(1) is a result of premature separation in the simulated western boundary
currents. The model output in (2), the Southern Indian Ocean, tends to predict
more structure than observed, perhaps arising from a misrepresentation of the
mixed layer or of energy dissipation and stirring in the simulation. The
differences in (3), the equatorial band, are also likely due to model errors,
perhaps arising from the shortness of the simulation or from the lack of high-
frequency/wavenumber atmospheric forcing. Although we do not yet know the
exact causes for these model-data SSTa differences, we expect that this type
of comparison will help guide future developments of high-resolution global-
ocean simulations.

TEXT

Ocean General Circulation Models are an attempt to reproduce the physics and
thermodynamics associated with large-scale oceanic processes. The first global
implementation of an OGCM with ‘realistic’ coastlines and bathymetry was
undertaken in the early 1970s on a 2${}^{\circ}\times$2∘ grid with 12 vertical
levels (Cox, 1975). A subjective evaluation of this model’s performance
compared the dynamic topography ‘patterns’ of large scale (basin-wide) gyres
determined from ship surveys with those obtained from the model. A more
quantitative evaluation was also performed by comparing the transport through
the Drake Passage determined from hydrographic sections with those obtained
from the model—an excellent overview of the early work on OGCMs is provided in
K. Bryan’s tribute to M. Cox’s work (Bryan, 1991). These spatially coarse
comparisons made clear that the model reproduced some of the general features
of the large-scale circulation but missed others; often those it had missed
were off by significant fractions when quantitative comparisons were made.
Given the coarse resolution—grid spacing often twice that of the width of
major ocean currents such as the Gulf Stream—and the representation for
subgrid-scale processes, which attempt to incorporate the physical
contribution of processes on scales smaller than the grid spacing, it is not
surprising that this model missed some features of large-scale circulation.

In the fifty years since Cox’s work, the processing capacity of computers has
increased dramatically from $\sim$1 megaflop, for the Univac 1108 used by Cox,
to $\mathcal{O}(10^{9})$ megaflops. Likewise, storage capacities have seen
similar increases, more efficient codes have been introduced, and the
observational data needed to constrain and force the models have seen
staggering increases in volume as well as accuracy. Today, the highest-
resolution global OGCMs are run on grids ranging from $\frac{1}{12}^{\circ}$
to $\frac{1}{48}^{\circ}$ with 100 or more vertical levels (see, e.g., Arbic
et al., 2018; Uchida et al., 2022). As a result, these models resolve many
mesoscale processes that earlier models had missed. They reproduce quite well
most of the large-scale patterns in the global ocean as well as the currents
associated with these patterns, offering confidence in studies that use them
to predict the evolution of the ocean and atmosphere on a warming planet.

The evaluation methodology described in this manuscript is meant to be applied
to unconstrained OGCMs of sufficient resolution to develop vigorous mesoscale
and, to some extent, submesoscale variability. At the moment, we lack the
observations and estimation tools that are needed to constrain the amplitude
and phase of individual mesoscale (and submesoscale) eddies globally and in a
dynamically-consistent manner. Therefore, the simulated mesoscale and
submesoscale features of free-running models are not expected to match, one-
to-one, the observations. While comparing the predicted and modeled fields at
an instant in time works for constrained models, the evaluation of free-
running models must be performed statistically, since the mesoscale and
submesoscale details inevitably differ within the observed field and the one
modeled for the same timestamp. Furthermore, to the best of our knowledge,
evaluations of the highest-resolution global, free-running OGCMs have, to
date, focused on scales substantially larger (one and a half to two orders of
magnitude larger) than the horizontal grid spacing of the model (e.g., Fox-
Kemper et al., 2019). As such, these evaluations do not assess the capability
of such models to reproduce statistically valid measures of the submesoscale
structure of their output. The objective of the work presented herein is to
address this deficiency for one of the highest-resolution, global, free-
running OGCMs available, specifically, the $\frac{1}{48}^{\circ}$, 90-level
simulation known as LLC4320. This simulation was developed as part of the
Estimating the Circulation and Climate of the Ocean (ECCO) project in a
collaborative effort between the Massachusetts Institute of Technology (MIT),
the Jet Propulsion Laboratory (JPL), and the NASA Ames Research Center (ARC).

To perform the desired evaluation requires a dataset with global coverage
spanning at least the LLC4320 time period with a daily cadence (or higher). In
addition, it requires observations with spatial sampling comparable to LLC4320
horizontal grid spacing, which ranges from $\sim$2 km at the equator to
$\sim$1 km at $70^{\circ}$ latitude. SST fields obtained from several
different satellite-borne sensors meet these requirements. The selected SST
dataset and the LLC4320 simulation are described in more detail in the next
section. As discussed in §2, we use an unsupervised machine learning algorithm
applied to approximately 150$\times$150 km2 regions, which we refer to as
cutouts, to capture a measure of the structure of the SST fields on such
scales. By adopting this algorithm, we are intentionally agnostic to specific
structures or patterns. The algorithm “learns” the structures that are
dominant in the data and, equally as important, their distribution.
Furthermore, it can be applied in the same fashion to observational data and
model output. This measure of field structure for the satellite-derived SST
fields is then compared statistically with that obtained from similar-sized
squares of the model output. The results of these comparisons are discussed in
§3.

##  1 Data

###  1.1 Satellite-Derived SST Data

The VIIRS instrument carried on the National Polar-orbiting Partnership (NPP)
satellite provided the highest spatial-resolution global SST products, 750 m
at nadir (degrading to 1700 m at the swath edge, with at least daily coverage
for the period covered by the LLC4320 simulation. VIIRS is a multi-detector
instrument for which variations in the gain from detector-to-detector
introduces striping in the resulting fields. In addition, geometric
distortions in pixel location arise as the distance from nadir increases,
referred to as the bow-tie effect, and render regions more than approximately
500 km from nadir useless for our analysis unless they are corrected. These
two issues, striping and inconstant pixel size, significantly impact the
structure of the retrieved SST fields. For this reason, we elected to use the
National Oceanic and Atmospheric Administration’s Level-2P (L2P), $2^{nd}$
full-mission reanalysis (RAN2) of the VIIRS data (Jonasson and Ignatov, 2019),
the only product we are aware of that addresses both of these issues 111The
Advanced Very High Resolution Radiometer (AVHRR) is not a multi-detector
instrument so it does not suffer from the striping and geometric distortion
issues associated with data from VIIRS but the coarser spatial resolution, 1.1
km at nadir, introduces greater degradation in resolution with distance from
nadir and the noisier instrument results in a product with at least twice the
noise than that obtained from VIIRS (Wu et al., 2017). The Sea and Land
Surface Temperature Radiometer (SLSTR) instrument carried on the European
Sentinel satellites provides an interesting alternative dataset but, given our
lack of detailed familiarity with these data, we elected to continue using
VIIRS..

We downloaded all of the $2^{nd}$ full-mission reanalysis (RAN2) L2P files for
the years 2012–2020, inclusive, from the JPL Physical Oceanography Distributed
Active Archive Center (PO.DAAC, https://podaac.jpl.nasa.gov). Each file
contains the retrievals from 10 minutes of satellite data, approximately 5400
scans with 3200 pixels per scan. There are approximately 500,000 files for the
period studied. These $\sim$500,000 files total $\sim$90 Tb and form the basis
of our observational analysis.

###  1.2 SST Output from the LLC4320 Simulation

The LLC4320 simulation was completed in 2015 by coauthor Menemenlis with help
from collaborators at MIT and NASA ARC (see, e.g., Rocha et al., 2016a, b;
Arbic et al., 2018). The LLC4320 simulation is a global-ocean and sea-ice
simulation that represents full-depth ocean processes. The simulation is based
on a Latitude/Longitude/polar-Cap (LLC) configuration of the MIT general
circulation model (MITgcm; Marshall et al., 1997; Hill et al., 2007). The
LLC4320 grid has 13 square tiles with 4320 grid points on each side and 90
vertical levels for a total grid-cell count of 2.2$\times$1010. Nominal
horizontal grid spacing is $\frac{1}{48}^{\circ}$, ranging from 0.75 km near
Antarctica to 2.2 km at the Equator, and vertical levels have $\sim$1-m
thickness near surface to better resolve the diurnal cycle. The simulation is
initialized from an ECCO, data-constrained, global-ocean and sea-ice solution
with nominal $\frac{1}{6}^{\circ}$ horizontal grid spacing (Menemenlis et al.,
2008). From there, model resolution is gradually increased to LLC1080
($\frac{1}{12}^{\circ}$ grid), LLC2160 ($\frac{1}{24}^{\circ}$ grid), and
finally LLC4320 ($\frac{1}{48}^{\circ}$ grid). Configuration details are
similar to those of the $\frac{1}{6}^{\circ}$ ECCO solution except that the
LLC4320 simulation includes atmospheric pressure and tidal forcing. The
inclusion of tides allows successful shelf-slope dynamics, water mass
modification, and their contribution to the global-ocean circulation (Xu et
al., 2013). Surface boundary conditions are from the $0.14^{\circ}$ European
Centre for Medium-range Weather Forecasting (ECMWF) atmospheric operational
model analysis, starting in 2011. Another unique feature of this simulation is
that hourly output of full 3-dimensional model prognostic variables were
saved, making it a remarkable tool for the study of ocean and air-sea exchange
processes and for the simulation of satellite observations. The 0000-GMT and
1200-GMT global SST fields for the uppermost 1-m level of the LLC4320 output
were downloaded using the xmitgcm package for the 365-day period starting on
November 17, 2011 yielding 730 files totaling $\sim$0.5 Tb. Hereinbelow, we
will use LLC and LLC4320 interchangeably to refer to the
$\frac{1}{48}^{\circ}$ MITgcm simulation. Although the entire model domain was
downloaded, only the region from the southern extreme to $57^{\circ}$N was
considered in the geographic analysis to avoid the change in grid geometry
occurring at $57^{\circ}$N.

##  2 Methods

###  2.1 Creation of Comparable SSTa Cutouts

Following our previous study on SST patterns (Prochaska et al., 2021), we
chose to analyze cutouts, approximately $\sim$150$\times$150 km2 regions
extracted from the parent observational and modeled SST fields. The size of
these samples was chosen in part to focus on features at scales of $\sim$30 km
or smaller (i.e., submesoscale). Using these modest-sized cutouts also yields
a massive number of cutouts—O($\sim$106)—with array dimensions that are easily
tractable to machine learning techniques ($\sim$100$\times$100 pixels). In the
following subsections, we detail the procedures to generate such cutouts from
the VIIRS data and LLC4320 outputs that have nearly equal dimension and
geographical coverage.

####  2.1.1 VIIRS Cutouts

In each VIIRS parent field (image hereinafter), we identified every
192$\times$192 pixel2 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 §2.2.1) applied to the datasets of cutouts.

We then divided each image into a grid with cell size of 96$\times$96 pixel2
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 $\sim$50%
overlap with its 4 nearest neighbors and $\sim$25% with the next 4 nearest
neighbors. Unlike our analysis of MODerate-resolution Imaging
Spectroradiometer (MODIS) data, we did not place a restriction on distance
from nadir because the physical size of the VIIRS pixels varies by
approximately a factor of two from nadir to swath edge (Jonasson et al., 2022)
compared with a variation of approximately a factor of five for MODIS.

From the full parent dataset, we extracted 2,851,702 cutouts (limiting to
$<57$ N; see 2.1.2). The geographical distribution of these is shown in Fig.
1, 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 the Hierarchical Equal Area
isoLatitude Pixelation (HEALPix)222 https://healpix.sourceforge.io schema
(Górski et al., 2005), which tesselates the surface into equal-area
curvilinear quadrilaterals and was introduced for all-sky analysis of
astronomical data. Here and throughout the manuscript we adopted nside=64,
which yields a HEALPix cell with approximately 100$\times$100 km2 area. Values
presented are numbers associated with each HEALPix cell; in this case the
number of cutouts in the cell.

Figure 1:  Geographic distribution of cutouts in our 98%-clear VIIRS dataset,
shown using a log10-based scale of color intensity. Each equal-sized (HEALPix)
spatial cell, plotted as dots here, covers approximately 10,000 km2. HEALPix
cells with less than five VIIRS cutouts or less than five LLC4320 cutouts are
shown in white. Land is shown as light gray. Meridional white line at
$\sim$35∘W is due to an LLC4320 sampling artifact.

For cutouts with one or more masked pixels, we “inpainted” them using the
biharmonic algorithm provided in the scikit- image software package (van der
Walt et al., 2014); the algorithm, we found, performs well even for data with
steep gradients (Prochaska et al., 2021). We then downscaled the arrays with a
local mean to 64$\times$64 pixel2 or approximately 144$\times$144 km2 at
$\sim$2.1 km sampling, which approximately matches the coarsest sampling of
the OGCM 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 SSTa fields. This
defines the final, pre-processed dataset that we use for all VIIRS analyses to
follow.

####  2.1.2 LLC4320 Cutouts

Roughly nine years (8 yrs 11 months) of VIIRS data comprise the $\sim$3
million (2,932,452) VIIRS cutouts, whereas the LLC4320 simulation output used
for this study spans only one year. To further restrict the VIIRS cutouts to
one year would leave too little data for a full-globe comparison between
satellite observations and the model outputs. For this reason, we compare
$\sim$9 years of VIIRS data to the one-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$\times$64 pixel2 regions that have a valid SST value (i.e., avoiding land).
The geographic location (lat, lon) of each of these was recorded. Second, we
considered the full year of LLC4320 outputs taken every 12 hours from
2011-11-17 to 2012-11-15 inclusive. For each cutout in the VIIRS sample, we
matched in location to the closest valid 64$\times$64 pixel2 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 hour intervals). This is
akin to matching on day-of-year and then time-of-day to the nearest 12 hours.
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 match-up 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 coast waters.

We wished to maintain an approximately-constant sampling size of 2.25 km
matched to VIIRS or 144$\times$144 km2 total for a 64$\times$64 pixel2 cutout.
Therefore, we sized the array extracted from the LLC4320 outputs according to
the local size of the grid, which varies as approximately $\cos(\rm lat)$ for
latitudes $\leq 57^{\circ}$ N. At latitudes $>57^{\circ}$ N, LLC4320
horizontal grid spacing asymptotes to $\sim$1 km in the polar cap. To avoid
the complications brought by different grid characteristics, we constrained
our analysis to south of $57^{\circ}$ N.

Each extracted LLC4320 array is downscaled to a 64$\times$64 pixel2 cutout
using the local mean. We then injected random noise using a Gaussian deviate
with a standard deviation $\sigma=0.04$ K based on an analysis of the noise
properties of the VIIRS data (Wu et al., 2017). Lastly, we demeaned each
cutout to generate SSTa arrays.

###  2.2 Characterization of the SSTa Cutouts

Each cutout was assigned a Log-Likelihood (LL) metric by the machine learning
algorithm, Ulmo, used for this work. This metric describes the frequency of
occurrence of the cutout within the full set. The LL metric tends to correlate
with the SST structure, at least at the spatial scales of the fields under
consideration here, with structure increasing with decreasing LL (Prochaska et
al., 2021). This simply follows from the fact that the parent sample is
dominated by cutouts with little inherent structure. Comparing the
distribution of LL values across the global ocean thus identifies geographic
regions where the structure of the model output at submesoscale-to-mesoscale
matches (or fails to match) the observations.

####  2.2.1 Brief Overview of Ulmo

The Ulmo machine learning algorithm is a Probabilistic AutoEncoder (PAE; Böhm
and Seljak, 2020) 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
(aka, a latent vector) for each cutout in a complex latent space. The second
step is a normalizing flow (Papamakarios et al., 2019), 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 SST 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 SST 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
SST patterns.

Fig. 2 presents galleries of VIIRS and LLC cutouts designed to show how the
structure of the cutouts vary as a function of LL. For Fig. 2a 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. 2a was noted by
Prochaska et al. (2021) in their discussion of the MODIS dataset. In the
analysis to follow (Section 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. 2b. These cutouts are
restricted to have $1<\Delta T<1.5$ K where $\Delta T$ is defined as the
difference in $90^{th}$ and $10^{th}$ percentiles of the SST distribution:
$\Delta T\equiv T_{90}-T_{10}$ where $T_{N}$ denotes the $N^{th}$-percentile.
These galleries were constructed in the same fashion as those for Fig. 2a. 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 2a, the characteristics of the LLC cutouts in this gallery track
those of the cutouts in the VIIRS gallery.

Figure 2:  Galleries of cutouts showing the progression of structure of the
associated SST fields as a function of LL. (a) Galleries for the entire set of
cutouts. Upper row for VIIRS cutouts, lower row for LLC cutouts. Each cutout
is randomly selected from the 50 cutouts with LL nearest to the median VIIRS
LL value for the associated LL quintile. The LL of the median is shown above
the VIIRS cutout. (b) Similar galleries for all cutouts with $1<\Delta T<1.5$
K where $\Delta T\equiv T_{90}-T_{10}$ with $T_{N}$ denoting the
$N^{th}$-percentile.

####  2.2.2 Training on VIIRS and Evaluation

In Prochaska et al. (2021) we introduced the Ulmo algorithm and trained a
model with Level-2 (L2) MODIS data sampled at $\sim$2 km and using
64$\times$64 pixel2 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 Prochaska et al.
(2021) 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.

##  3 Results/Discussion

We divide the comparison of the VIIRS SST dataset with the LLC4320 model
output, in the context of the patterns learned by Ulmo, into those related to
the shapes of the two LL probability distributions and those related to their
geographic distributions.

###  3.1 Overall Statistical Comparison of VIIRS and LLC4320 LL Values

Figure 3 compares the distribution of the LL metric for the 9 years of VIIRS
observations against the LLC4320 results matched in space and day-of-year. The
two distributions are quite similar, suggesting that, on average, the SST
pattern distribution learned by Ulmo from VIIRS is close to the same
distribution derived from LLC4320. There are, however, differences, subtle for
much of the range of LL values and not so subtle for $LL>800$:

  * $\bullet$

$LL<-375$: This range corresponds to relatively energetic regions, generally
associated with strong currents and large SST gradients (Prochaska et al.,
2021). In these regions, the probability of finding a VIIRS cutout with a
given LL value is lower than that of finding an LLC4320 cutout with the same
LL value. This suggests that in dynamic regions, LLC4320 fields tend to have
slightly more structure than VIIRS fields, i.e., that the fields are possibly
more energetic. An example of cutouts in this LL range is discussed in the
paragraphs following the bolded text Gulf Stream in §3.2.2.

  * $\bullet$

$-375<LL<375$: This corresponds to mid-range fields, generally found at mid-
latitudes (Fig. 4a), away from eastern and western boundary currents. The
probability of finding a VIIRS cutout with a given structure (LL value) in
this LL range is increasingly higher, as LL increases from -375 to 375, than
that of finding an LLC4320 cutout within this LL range. An example of cutouts
in this LL range is discussed in the paragraphs following the bolded text
Southern Ocean in §3.2.2.

  * $\bullet$

$375<LL<800$: In this LL range, the probability for the LLC4320 of finding a
given LL value is higher—less structure—than for VIIRS. SST fields with these
LL values have relatively little structure with retrieval and instrument noise
associated with the satellite-derived fields having a relatively larger impact
on their observed structure. As noted in §2.1.2, white noise was added to the
LLC4320 fields in an attempt to remove the importance of noise in determining
the LL value but, in retrospect, the level of noise may not have been
sufficient to address this, hence the higher probability of finding LLC4320
cutouts in this range. Cutouts with $LL>375$ tend to be found equatorward of
approximately $15^{\circ}$.

  * $\bullet$

$LL>800$: The probability distribution for LLC4320 LL values levels off at 800
falling rapidly to zero for values larger than 1100 or so. By contrast, few
VIIRS cutouts have LL values greater than 800. This is likely due to noise in
the satellite-derived SST cutouts as well as unresolved clouds, discussed in
the paragraphs following the bolded text Equatorial Band in §3.2.2.

Figure 3: Histograms of the LL metric for the full sample of VIIRS and LLC4320
cutouts.

###  3.2 Geographic Comparison of $\widetilde{\rm LL}_{\rm VIIRS}$ and
$\widetilde{\rm LL}_{\rm LLC}$ Values

As mentioned in §2.1.1, we compare the geographic distribution of VIIRS LLs
with that of LLC4320, based on the HEALPix tesselated surface covering the
entire Earth: 41,952 equal-area spatial cells, each of $\sim$100$\times$100
km2 size. Within each cell, we consider the distribution of LL values from the
VIIRS data and LLC4320 output. To minimize the effects of outliers within the
distributions, we utilize the median LL value (designated $\widetilde{\rm LL}$
hereinafter) as a characteristic metric of the structure in SST at a given
location. Furthermore, we only consider HEALPix cells containing a least five
VIIRS cutouts and five LLC4320 cutouts. The distributions for $\widetilde{\rm
LL}_{\rm VIIRS}$ and $\widetilde{\rm LL}_{\rm LLC}$ are shown in Fig. 4 and
their difference, $\Delta_{LL}=$$\widetilde{\rm LL}_{\rm
VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$, in Fig. 5. Recall that LL tends to
increase with decreasing structure in the SST field, hence positive values of
$\Delta_{LL}$ suggest less structure in the satellite-derived cutouts than in
the cutouts of the model output and negative values the contrary.

Figure 4: (a) HEALPix median LL for VIIRS cutouts ($\widetilde{\rm LL}_{\rm
VIIRS}$), (b) $\widetilde{\rm LL}_{\rm LLC}$, (c) Zonal average of
$\widetilde{\rm LL}_{\rm VIIRS}$, and (d) Zonal average of $\widetilde{\rm
LL}_{\rm LLC}$. Each dot in a and b is associated with an equal area HEALPix
cell. White dots correspond to locations with less than five VIIRS cutouts and
less than five LLC4320 cutouts in the HEALPix cell. Land is shown in gray.
Figure 5: (a) $\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm
LLC}$. (b) Zonal mean of $\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm
LL}_{\rm LLC}$. It is apparent that the LLC4320 model has SST patterns with
less structure in Equatorial regions. In contrast, the dynamic regions of the
global ocean (e.g., Western boundary currents) exhibit lower $\widetilde{\rm
LL}_{\rm LLC}$ indicating a higher degree of structure within these areas in
the model output.

Figure 5 suggests that there are significant differences between the
submesoscale-to-mesoscale structure of the simulation and that of the
satellite-derived dataset. However, closer examination of the two plots in
Fig. 4 suggests that there is significant similarity in the larger scale ($>$
several hundred kilometers) of the two fields; our eyes are drawn to the
differences, the large red equatorial regions and blue regions at higher
latitudes, not the similarities. We therefore begin by examining the
similarities of the fields and then consider their differences.

####  3.2.1 Similarities

To highlight the similarities in the $\widetilde{\rm LL}$ fields on smaller
scales ($\mathcal{O}(100\,\rm km)$), we remove from $\widetilde{\rm LL}_{\rm
LLC}$ the large regional differences apparent between them (Fig. 4). This is
done by averaging $\widetilde{\rm LL}_{\rm VIIRS}$ and $\widetilde{\rm
LL}_{\rm LLC}$ over 100 sequential values based on the HEALPix index. Since
the vector of HEALPix cells is arranged geographically, the indicies over
which the average is performed tend to correspond to a relatively tight
geographical region. $\widetilde{\rm LL}_{\rm VIIRS}$ (black) and
$\widetilde{\rm LL}_{\rm LLC}$ (cyan) are shown in Fig. 6. A ‘corrected’
$\widetilde{\rm LL}_{\rm LLC}$, designated as $\widetilde{\rm
LL}^{\prime}_{\rm LLC}$, is then determined from:

$\widetilde{LL}^{\prime}_{LLC_{i}}=\widetilde{LL}_{LLC_{i}}-\frac{1}{100}\displaystyle\sum_{j\in
B}{(\widetilde{LL}}_{LLC_{j}}-\widetilde{LL}_{VIIRS_{j}})$

where $i\in$ all HEALPix cells with at least 5 cutouts in the VIIRS dataset
and 5 cutouts in the LLC4320 dataset,

$B:\left[\lfloor\frac{i-1}{100}\rfloor*100+1,\lfloor\frac{i-1}{100}\rfloor*100+100\right]$

and $\lfloor x\rfloor$ dnotes the largest integer less than or equal to x.
$\widetilde{\rm LL}^{\prime}_{\rm LLC}$ values are shown in red in Fig. 6.

Figure 6:  $\widetilde{\rm LL}$ versus HEALPix cell index: $\widetilde{\rm
LL}_{\rm VIIRS}$ values are black dots, $\widetilde{\rm LL}_{\rm LLC}$ are
cyan, and $\widetilde{\rm LL}^{\prime}_{\rm LLC}$ are red.

The $\widetilde{\rm LL}_{\rm LLC}$ geographic distribution is shown with that
of $\widetilde{\rm LL}^{\prime}_{\rm LLC}$ in Fig. 7. The large scale
similarities in the general shape of the distributions is much more evident in
this figure. Note also that the zonal mean for $\widetilde{\rm LL}_{\rm
VIIRS}$ and that for $\widetilde{\rm LL}^{\prime}_{\rm LLC}$ are now quite
similar for latitudes equatorward of $60^{\circ}$.

It is not just the similarities in the large-scale distribution that we find
intriguing but also a number of small-scale features. Consider, for example,
the $\widetilde{\rm LL}$ fields at approximately $45^{\circ}$S in the black
and red polygons of Fig. 8. For both $\widetilde{\rm LL}_{\rm VIIRS}$ and
$\widetilde{\rm LL}_{\rm LLC}$ there is a local maximum in $\widetilde{\rm
LL}$ corresponding to a minimum in the structure of the SST cutouts in the
black polygon. This feature is associated with a zonal bathymetric ridge at
approximately $45^{\circ}$S crossed by two meridional ridges, one at
$44^{\circ}6^{\prime}$W and the other at $39^{\circ}7^{\prime}$W (Fig. 9b,
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 LL fields show a band of negative $\widetilde{\rm LL}$ values to
the west and south of the feature. The $\widetilde{\rm LL}_{\rm VIIRS}$ field
also shows a well-defined band to the north and east while the $\widetilde{\rm
LL}_{\rm LLC}$ fields only shows a suggestion of such a band but the local
minimum is still well-defined in both.

Figure 7: As in Fig. 4 except $\widetilde{\rm LL}^{\prime}_{\rm LLC}$ is shown
in (b).  Figure 8: As in Fig. 7 but palette constrained to better show
features in the two focus area: black polygon at $\sim$35∘W, 45∘S and red
polygon at $\sim$30∘E, 50∘S.  Figure 9: (a) Uncorrected $\widetilde{\rm
LL}_{\rm LLC}$. (b) Bathymetry. Focus regions: black polygon at $\sim$35∘W,
45∘S and red polygon at $\sim$30∘E, 50∘S. Dotted black and solid magenta lines
in the focus area encircled with the red polygon were manually digitized from
Fig. 4a and Fig. 9a. for VIIRS and LLC4320, respectively.

The second feature of interest is the thin, hooked band of low $\widetilde{\rm
LL}_{\rm VIIRS}$ values—corresponding to relatively more structure in the
cutouts—in the red polygon south of South Africa (Fig. 8a). This band is well
reproduced in the LLC4320 output (Fig. 8b). Again, referring to the
bathymetric image, (Fig. 9b) 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. 9b; the model appears to reproduce quite accurately this
subtle feature in the circulation.

####  3.2.2 Differences

To highlight the regional distributions of significant differences between the
structure of satellite-derived SST cutouts and that of SST cutouts produced by
LLC4320, we replot in Fig. 10 the data of Fig. 5, masking—dark gray—all values
between $-$197 and 197. These thresholds are based on differences between the
$\widetilde{\rm LL}$ distribution obtained from the first four years,
2012–2015, of the VIIRS dataset and the last four years, 2017–2020,
$\widetilde{\rm LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$
(see the Appendix). HEALPix cells with $\widetilde{\rm LL}$ values beyond
these thresholds correspond either to regions for which the retrieved VIIRS
cutouts are not good measures of the SST or that the LLC4320 output is
associated with deficiencies in the simulation.

$\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$ differences
evident in Fig. 10 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 $\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm
LL}_{\rm LLC}$ of the unmasked field shown in Fig. 5b; the zonal mean is
roughly flat at -350 from $5^{\circ}$S to the Equator, rises rapidly poleward
of these two points for about $5^{\circ}$ of latitude to -150 and then
continues to increase approximately linearly, but more slowly, from there
($10^{\circ}$S and $5^{\circ}$N) to a value of zero at $30^{\circ}$N and
$30^{\circ}$S.

In the following 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. 10), which exemplify characteristics
of the differences that we find to be of interest.

Figure 10: As in Fig. 5a with
$|\widetilde{LL}_{VIIRS}-\widetilde{LL}_{LLC}|<{197}$ masked darker gray to
highlight the significant differences between VIIRS observations and the
LLC4320 model outputs. The yellow rectangle ($\sim$110∘W, 0∘N) designates the
focus area for galleries shown in Fig. 13 highlighting Equatorial differences,
the green rectangle ($\sim$120∘E, 55∘S) for galleries shown in Fig. 15
highlighting Southern Ocean differences and the cyan rectangle ($\sim$70∘W,
35∘N) for galleries shown in Fig. 17 highlighting western boundary current
differences.

Equatorial Band:  In general, there are four possibilities for low values of
$\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$ in the
equatorial region ($15^{\circ}$S to $15^{\circ}$N):

  1. 1.

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 $\widetilde{\rm LL}_{\rm
2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$ is essentially flat at 0
equatorward of $50^{\circ}$ (Fig. 20) suggesting little interannual
variability.

  2. 2.

Unresolved clouds in the VIIRS cutouts. Unresolved clouds tend to add
structure to the cutouts; the ‘quieter’ the field, the more significant the
impact noise has on the structure, and the greater the decrease will be in
$\widetilde{\rm LL}$. To address this potential problem, the 194 cutouts of
the HEALPix cell at $36^{\circ}$N, $112^{\circ}30^{\prime}$W were examined for
unresolved clouds. Thirty percent were found to be of high quality, 50% were
found to be significantly contaminated, and there was uncertainty as to how to
classify the remaining 20%. Calculating mean $\widetilde{\rm LL}_{\rm
VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$ for the high quality only cutouts
increased the mean value by 43, small compared to the difference of $-350$ for
this HEALPix cell, so this is not likely the primary explanation for the
differences. We further address this issue below in the context of galleries
of SST fields.

  3. 3.

Noise in the VIIRS SST fields. Cutouts in this part of the ocean tend to have
relatively high $\widetilde{\rm LL}$ values (Fig. 4a), corresponding to
relatively less structure. This means that noise in the field, which is
assumed to change slowly if at all with latitude, will become relatively more
important, decreasing $\widetilde{\rm LL}$. Noise has been added to the
LLC4320 SST fields in an attempt to address this but possibly not enough
resulting in more negative values of $\widetilde{\rm LL}_{\rm
VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$.

  4. 4.

LLC4320 does not reproduce the submesoscale-to-mesoscale structure well in the
Equatorial regions. There is a suggestion based on the examination of a small
patch of this region, discussed below, that the model is missing structure in
at least some parts of this region.

The rectangular patch [($2^{\circ}$S, $2^{\circ}$N), ($105^{\circ}$W,
$95^{\circ}$W)] west of the Galapagos Island in the equatorial Pacific (the
yellow rectangle in Figs. 10 and 11) stands out because of the significant
step of $\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$
along the Equator. The $\widetilde{\rm LL}$ distribution for the region in the
rectangle above the Equator is provided in Fig. 12a and that below the Equator
in Fig. 12c. Consistent with the geographic distributions of $\widetilde{\rm
LL}$ in Fig. 4, the median $\widetilde{\rm LL}_{\rm LLC}$ value increases from
south to north across the Equator while the median $\widetilde{\rm LL}_{\rm
VIIRS}$ 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 $dT$ are provided because there is a
correlation, although weak, between LL and $dT$, while $dT$ is a more readily
understood measure of similarity and differences between VIIRS and LLC4320 SST
fields. The distribution of $dT_{LLC}$ is similar across the Equator, while
that of VIIRS shows a much longer tail consistent with more variability and
lower LL values.

Figure 11: (a) $\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm
LLC}$ for the Equatorial Pacific and Atlantic. (b) $log_{10}$ of the # of
cutouts/HEALPix cell. Thick horizontal black line is the Equator. Yellow
rectangle is the focus area.  Figure 12: (a) Histograms of LL for all VIIRS
(yellow) and LLC4320 (green) cutouts above the Equator in the focus area. (b)
Histograms of $dT$ for the same region as (a). (c) As for (a) except below the
Equator. (d) As for (b) except below the Equator. The median values of the
distributions are indicated for (a) and (c), as are the number of cutouts
contributing to each. The number of cutouts apply to the corresponding $dT$
frames.

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.
11, again separating them into those above the Equator and those below.
Galleries of nine cutouts each are shown in Fig. 13. As previously noted each
VIIRS cutout was matched in space and day-of-year with an LLC4320 cutout. To
generate the galleries shown in Fig. 13, 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 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, $0^{\circ}$
to $2^{\circ}$N and $105^{\circ}$ to $95^{\circ}$W, are shown in Figs. 13a and
b. For each VIIRS cutout in gallery a, its LLC4320 partner is shown in the
same location in gallery b. Similarly, Figs. 13c 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 $\widetilde{\rm LL}_{\rm
VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$ both above and below the Equator but
is not likely to significantly impact the observed $\widetilde{\rm LL}_{\rm
VIIRS(above)}-\widetilde{\rm LL}_{\rm VIIRS(below)}$. Also, note that the
distribution of the number of cutouts per HEALPix cell is symmetric about the
Equator in the area of interest (Fig. 11b) suggesting that the contribution of
clouds to corruption of the LL values is also symmetric about the Equator in
the rectangle of interest.

Figure 13: (a) Gallery for VIIRS cutouts above the Equator in the yellow
rectangle of Fig. 11a. (b) As in (a) but for LLC4320 cutouts. (c) VIIRS
cutouts below the Equator in the yellow rectangle of Fig. 11a. (d) As in (c)
but for LLC4320 cutouts. The mean $\widetilde{\rm LL}$ and $dT$ for all
cutouts in the given region (e.g., $0^{\circ}$ to $2^{\circ}$N, $105^{\circ}$
to $95^{\circ}$W for gallery a) follow the dataset name and the numbers
following in parentheses are the mean $\widetilde{\rm LL}$ and $dT$ of the
cutouts in the gallery. The date and time of each VIIRS cutout is shown above
it and $\widetilde{\rm LL}$ and $dT$ for that cutout follow in parentheses.
The date of the corresponding LLC4320 cutout (same position in the LLC4320
gallery) is the same as that of the VIIRS cutout. The time is the closest of 0
and 1200 to the VIIRS time. It is evident that the gallery from the VIIRS
observations above the Equator shows greater structure than any of the other
subsets.

Southern Ocean:  We examine the same four possibilities for high
$\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$ values in
the Southern Ocean as we did for low values in the Equatorial region:

  1. 1.

The year simulated, 2012, is atypical, differing from the 2012–2020 mean.
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
$\widetilde{\rm LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$
exceeded the $2\sigma$ threshold.

  2. 2.

Unresolved clouds in the VIIRS fields. Very unlikely because clouds in the
VIIRS fields would tend to increase the structure, which would decrease
$\widetilde{\rm LL}$. Hence $\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm
LL}_{\rm LLC}$ would become more positive than if clouds are not present in
the VIIRS fields, rendering the difference more anomalous, not less so.

  3. 3.

Noise in the VIIRS SST fields. Unlikely because the geophysical variability of
SST in these regions tends to overwhelm noise in the VIIRS cutouts.
Furthermore, noise in the VIIRS cutouts would tend to reduce the associated
$\widetilde{\rm LL}$ rendering the differences between uncontaminated
$\widetilde{\rm LL}$ VIIRS values and those obtained from the LLC4320
simulation even larger.

  4. 4.

LLC4320 does not reproduce the submesoscale-to-mesoscale structure well in the
Southern Ocean. There is a suggestion based on the examination of small
patches of this region, which we discuss in more detail below, that the model
has more structure in this region than is recorded in actual observations.
This indicates that the mixed layer or energy dissipation and stirring due to
subgrid-scale physics are not represented with sufficient accuracy in these
regions.

In Fig. 14c, we replot the masked
$\widetilde{LL}_{VIIRS}-\widetilde{LL}_{LLC}$ field of Fig. 9 for the Southern
Ocean south of Australia with $\widetilde{\rm LL}_{\rm VIIRS}$ and
$\widetilde{\rm LL}_{\rm LLC}$ for the same region in the upper two panels.
The band of low $\widetilde{\rm LL}_{\rm VIIRS}$ and $\widetilde{\rm LL}_{\rm
LLC}$ values from $45\ {\rm to}\ 70^{\circ}$E at about $41^{\circ}$S
corresponds to the significant structure in the field associated with the ACC.
(Note that this band originates south of South Africa where the Agulhas
retroflection joins the ACC, the band of negative values of $\widetilde{\rm
LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$ in Fig. 8.) It appears that
the ACC as modeled by LLC4320 for 2012 is slightly to the south of the VIIRS
ACC for 2012–2020; the positive values of $\widetilde{\rm LL}_{\rm
VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$ 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 are
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 $70^{\circ}$E $\widetilde{\rm LL}$ for the modeled ACC
is substantially more negative than that of the observed values, resulting in
the anomalous $\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm
LLC}$ values in this region. Interestingly, the VIIRS field shows a positive
band north and south of the northern branch of the stream as does the LLC4320
field. In fact, the general pattern of the $\widetilde{\rm LL}_{\rm LLC}$ has
the same general shape as that of $\widetilde{\rm LL}_{\rm VIIRS}$. 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.

Figure 14: (a) $\widetilde{\rm LL}_{\rm VIIRS}$ for the focus area of the
Southern Ocean, (b) $\widetilde{\rm LL}_{\rm LLC}$, and (c) masked
$\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$. The black
rectangle ($\sim$116∘W, -50∘S) indicates a region of agreement,
$\overline{LL_{VIIRS}-LL_{LLC}}=-63$. The white rectangle ($\sim$120∘W, -54∘S)
is an anomalous region with $\overline{LL_{VIIRS}-LL_{LLC}}=335$.

Galleries of SSTa cutouts in the black rectangles of Fig. 14 (a region for
which the model $\widetilde{\rm LL}$ values are in general agreement with the
VIIRS values) are shown in Fig. 15a for VIIRS and 15b for LLC4320. Galleries
for the anomalous region, the white rectangles in Fig. 14, are shown in Fig.
15c for VIIRS and 15d for LLC4320. Cutouts for these galleries were randomly
selected as described for the generation of galleries for the equatorial
region (Fig. 13). The anomalous behavior is clear in the lower two panels; the
LLC4320 fields are much bolder with substantially lower $\overline{LL}$ values
and larger $dT$ values. The LLC4320 field is clearly more energetic. By
contrast, LLC4320 cutouts in the region for which there appears to be
agreement are more similar to VIIRS cutouts.

Figure 15: (a) Gallery of 9 randomly selected VIIRS cutouts within the black
rectangle of Fig. 14, the region of ‘agreement’. (b) Similarly for LLC4320
cutouts in the same region of ‘agreement’. (c) VIIRS cutouts in the anomalous
region, the white rectangle in Fig. 14. (d) Same as (c) but for LLC4320
cutouts. Dates, times, LL and $dT$ as in Fig. 13.

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

  1. 1.

The year simulated, 2012, is atypical, differing from the 2012–2020 mean. 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.

  2. 2.

Unresolved clouds in the VIIRS fields. Very unlikely because clouds in the
VIIRS fields would tend to increase the structure, i.e., decrease
$\widetilde{\rm LL}$. Hence cloud-free fields would tend to increase
$\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$, rendering
it more anomalous.

  3. 3.

Noise in the VIIRS SST fields. Unlikely because the geophysical variability of
SST in these regions overwhelms noise in the VIIRS fields but, if it were to
contribute, it would again increase the $\widetilde{\rm LL}_{\rm
VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$, rendering it more anomalous.

  4. 4.

LLC4320 does not reproduce the submesoscale-to-mesoscale structure well in the
Gulf Stream region. As will be shown below, this is likely the cause of the
differences but, unlike the differences in the Southern Ocean, we believe that
these differences are due to premature separation of the Gulf Stream from the
continental margin, i.e., that the Gulf Stream is in the wrong place as
opposed to it being in the correct location but too energetic as appears to
the case in the ACC south of Australia.

Figure 16a shows $\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm
LLC}$ in the Gulf Stream region downstream of the point at which it separates
from the continental margin. Figure 16b shows the same data but masked,
showing only the HEALPix cells with values exceeding the thresholds identified
in the Appendix, $\pm$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-day intervals (Lee, 1996). The mean path of the stream was determined by
averaging, over all 2-day 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—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 $60^{\circ}$W corresponds to the
premature separation of the modeled Gulf Stream from the continental margin
reported by Cornillon and Menemenlis (2018) based on the mean path and extreme
envelope of paths shown in Figs. 16 and on the Ocean Surface Current Analyses
Real-time (OSCAR) surface currents (https://podaac.jpl.nasa.gov/ datasetlist,
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 $70^{\circ}$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. 16b become
more clear from the individual plots of $\widetilde{\rm LL}_{\rm VIIRS}$ and
$\widetilde{\rm LL}_{\rm LLC}$, Fig. 16c and d, respectively. The most
negative values of $\widetilde{\rm LL}$ 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
$\widetilde{\rm LL}$ values follows the 200-m isobath, shown as dotted red
lines in Fig. 16.) 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 the 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 $65^{\circ}$ and $75^{\circ}$W and south of about
$36^{\circ}30^{\prime}{N}$. 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
$62^{\circ}$; the stream appears to die at that point and 2) the positive LL
values east of $60^{\circ}$W and south of $33^{\circ}$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
one year while the VIIRS data cover 8+ years. The reasons for the rapid die-
off of the stream and the relatively quieter (larger values of LL) east of
$62^{\circ}$ are not obvious.

Figure 16: (a) $\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm
LLC}$ for the Gulf Stream region after separation from the continental margin.
(b) Masked $\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$
for same area. (c) $\widetilde{\rm LL}_{\rm VIIRS}$. (d) $\widetilde{\rm
LL}_{\rm LLC}$. Thick magenta line shows the mean Gulf Stream path digitized
from 2-day AVHRR SST composites for 1982–1999. Thick black lines show the
envelope containing 98% of these paths for the same period, 1% beyond the
limits on each side of the envelope. Dotted red line is the 200-m isobath. Red
and white rectangles show the focus areas from which galleries of cutouts are
selected for Fig. 17.

Next, we examine VIIRS and LLC4320 cutouts inside the Gulf Stream envelope
(the white rectangles in Figs. 16c and d at [($40^{\circ}$N, $42^{\circ}$N),
($60^{\circ}$W, $50^{\circ}$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 Figs. 16c and d at
[($34^{\circ}$N, $36^{\circ}$N), ($70^{\circ}$W, $60^{\circ}$W)]). Galleries
of nine cutouts each for both VIIRS and LLC4320 for both regions are shown in
Fig. 17. Cutouts for these galleries were randomly selected as described for
the generation of galleries for the equatorial region (Fig. 13). The
characteristics of the VIIRS cutouts outside of the Gulf Stream (Fig. 17c)
differ substantially from those of the other three galleries as does the mean
LL. VIIRS cutouts within the stream (Fig. 17a) are similar to those in the
LLC4320 gallery of cutouts south of the Gulf Stream (Fig. 17d), consistent the
suggestion that the modeled stream separates prematurely from the continental
margin. The structure of LLC4320 cutouts in the Gulf Stream (Fig. 17b) lies
between that of VIIRS cutouts in the stream (Fig. 17a) and LLC4320 cutouts
south of the stream (Fig. 17d) as do the LL values. This is consistent with
the modeled stream being to the south of the observed stream.

Figure 17: (a) Gallery for VIIRS cutouts in red rectangle of Fig. 16c. (b)
Same for LLC4320 cutouts in red rectangle of Fig. 16d. (c) VIIRS cutouts in
white rectangle of Fig. 16c. (d) LLC4320 cutouts in white rectangle of Fig.
16d. Dates, times, LL and $dT$ as in Fig. 13.

In this manuscript we set out to confront outputs from the well-adopted
LLC4320 simulation with a large dataset of global observations. Specifically,
we have focused on the submesoscale dynamics traced by SST, an observable with
decades of global coverage provided by a series of sensors on remote sensing
satellites. This manuscript used L2 data from VIIRS, restricted to nearly-
clear ($\geq 98\%$ cloud free) cutouts with dimension $\sim$150$\times$150 km2
selected across the ocean.

Our approach for quantitative comparison between data and model is
unconventional. We trained a deep-learning Probabilistic AutoEncoder (PAE) on
the VIIRS data to learn the distribution of SSTa patterns observed in the
ocean and then applied this PAE to geographically and seasonally matched SSTa
cutouts from the LLC4320 model. An advantage of this approach is that it is
intentionally unsupervised; the network learned from the data the features
most characteristic of ocean dynamics traced by SSTa. On the flip side, the
results—especially any differences between data and model—are more difficult
to interpret. The LL metric calculated from the PAE is known to correlate with
$\Delta T$ and other physical measures of SSTa yet with significant scatter
(Prochaska et al., 2021). And uncertainties are not inherently calculated;
instead we have estimated them by applying Ulmo to two independent subsets of
VIIRS data.

Proceeding in this manner, we found that, in general, the distribution of SSTa
patterns present in the VIIRS observations are well-predicted by the LLC4320
model (e.g., Fig. 3). Globally, the medians of the LL distributions from VIIRS
and LLC4320 agree within $2\sigma$ for 65% of the ocean (Fig. 10). However,
there is a modest but significant and latitude-dependent offset between data
and model with the latter exhibiting less structure in the SSTa cutouts near
the Equator and greater structure towards the poles. After correcting for this
latitude-dependent offset, we find that the model frequently recovers
mesoscale features imprinted in the LL distributions and seen in the
$\widetilde{\rm LL}_{\rm VIIRS}$ field. This includes the reproduction of
detailed mesoscale dynamics often forced by deep bathymetric features. We
emphasize here that the VIIRS–LLC4320 comparison is being performed on spatial
scales of $\mathcal{O}(50$ km) and less and that it is changes in the
structure at these scales that is informing the large scale patterns observed,
i.e., the submesoscale structure of cutouts appears to be tied to larger scale
processes. One may conclude that the LLC4320 model has captured salient
mesoscale dynamics across the majority of the ocean.

There are, however, a few notable exceptions. One of these is the location of
the Gulf Stream, a previously known failure of the LLC4320 simulation
(Cornillon and Menemenlis, 2018). Giving confidence to the approach taken in
this manuscript to evaluate the performance of the LLC4320 simulation is the
fact that a known region of concern is clearly identified as problematic.

A more subtle difference occurs at the Equator. We have shown from the VIIRS
data that the structure in the SSTa cutouts just north of the Equator exceeds
that of its southern counterpart (Fig. 13). This difference in SSTa in VIIRS,
however, is not reproduced by the LLC4320 simulation and there is no reason to
believe that cross-Equator differences in the VIIRS data are spurious.

Third, we highlighted inconsistencies between the LLC4320 model and VIIRS
observations in the ACC, where the former frequently exhibits a higher degree
of structure in SSTa and, presumably, more energetic surface currents. We
attribute this increased structure to a misrepresentation of the mixed layer
and of subgrid-scale processes that are responsible for energy dissipation and
stirring.

We hope that our analysis will inspire similar investigations of both global
and regional models. With the construction of large, well-curated datasets, as
we have done with VIIRS, one may construct a series of tests. The construction
of such a dataset requires intentional decisions on how to extract and
preprocess cutouts for direct comparison to model outputs. Furthermore, the
data volume $\mathcal{O}$(100 Tb) is sufficiently large to require best
practices with storage, databasing, and computing. The authors provide their
code (including workflow) with the manuscript and encourage discussion with
parties interested in building their own similar analyses.

We also wish to emphasize several of the weaknesses of our methodology and
identify paths for improvement in future work. First, and perhaps foremost, we
have not accounted for the mismatch in effective spatial resolution between
model and observations. The pixelization of the L2 VIIRS product is $\sim$750
m at nadir hence can resolve features in the few kilometer range. The LLC4320
simulation, meanwhile, has a finest cell size of $\sim$1 km but the
formulation is not expected to properly resolve features on scales less than
$\mathcal{O}(10)$ km (see, e.g., Su et al., 2018). We considered smoothing
(i.e., degrading) the VIIRS data to better match the model outputs but were
not confident that we could do so with high accuracy. Furthermore, the PAE
itself is effectively smoothing the data by passing each cutout through a
512-dimension bottleneck (e.g., see Fig. 3 of Prochaska et al., 2021).

Related to the above discussion, the initial analysis ignored latitude
dependence in SSTa structure, despite the predicted and observed dynamical
differences driven by geophysical fluid dynamics. Further work might, for
example, vary the size of the cutouts proportional to the Rossby Radius of
Deformation. Similarly, if we were to expand the cutout size to larger scales
to better assess mesoscale features, it may become necessary to match the
orientation of the data (here dictated by the satellite path) with the model
(fixed with rows/columns parallel to longitude/latitude).

Another weakness of our implementation is the lack of any error estimation
from the PAE outputs (i.e., for individual LL values). This is a general
weakness of deep learning algorithms (but see Bayesian Neural Nets; e.g.
Shridhar et al., 2019). Therefore, we approached uncertainty estimation using
an empirical estimate generated from subsets of the data (see the Appendix).
While effective, it is approximate and relies on the central limit theorem to
assume a Gaussian deviate. Related, the LL metric of Ulmo has no intrinsically
physical, mathematical or statistical (despite the name) meaning! Future work
focused on comparisons of SSTa or other patterns may consider the scattering
transform (Mallat, 2012; Cheng and Ménard, 2021), which has sound mathematical
underpinning and may allow for proper statistical tests.

Last, but far from least, are the significant “blemishes” in the data that are
absent in the model outputs. Foremost are clouds. The mitigation for clouds
adopted here was to (1) limit to cutouts with fewer than 2% of the pixels
masked by the retrieval algorithm (Jonasson et al., 2022) and (2) inpaint
these masked pixels. The latter step was required for the PAE and is, in
general, required for convolutional neural nets, which expect ‘complete’
fields. In our exploration of the cutouts, however, we identified a high
incidence of clouds that were not masked in the VIIRS data. These ranged from
minor blemishes in otherwise uniform fields where the clouds generate non-
negligible structure (especially evident in Figs. 13a and c) to, in a few
cases, corruption of the entire field in the cutout. Another negative
consequence, perhaps the most serious, is the terrific reduction of potential
data and the resultant geographic biases of the dataset that follow from the
98% clear criterion (Fig. 1). To the greatest extent possible, future work
must continue to identify and mitigate clouds; our own efforts are well
underway.

As we conclude, we emphasize that perhaps the greatest value of this
manuscript was the construction and now dissemination of the large dataset of
cutouts for comparison with ocean models as well as with other satellite-
derived SST datasets. This includes the software to generate and analyze them.
All of these products are publicly available as described below.

All of the data generated and analyzed in this manuscript is publicly
available as parquet tables and hdf5 files at Dryad (LINK TO APPEAR). The code
developed throughout the project is provided at
https://doi.org/10.5281/zenodo.7763845 (doi: 10.5281/zenodo.7763845) or at
https://github.com/AI-for-Ocean-Science/ulmo.

##  Appendix A HEALPix Uncertainty

A question, which arises naturally in the context of Fig. 5, is what
constitutes a statistically significant difference in $\widetilde{\rm LL}$
between the model output and the VIIRS fields. To address this, the VIIRS
dataset is divided into two 4-year segments, 1 February 2012 through 31
January 2016 (referred to as 2012–2015 hereafter) and 1 January 2017 through
31 December 2020 (2017–2020). Subsequently, $\widetilde{\rm LL}$ is calculated
for each HEALPix cell for each of the two periods. Figure 18 shows the
distribution of cutouts for the first of the two periods. Because the periods
for which these data are being calculated are substantially shorter than that
of the dataset from which they are drawn (Fig. 1), the number of HEALPix cells
with less than 5 cutouts (white in Fig. 18) is substantially larger.

Figure 19 shows a histogram of the differences of the two $\widetilde{\rm LL}$
fields $\widetilde{\rm LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm
2017-2020}$. Also shown in Fig. 19 is the histogram of the differences of the
VIIRS and LLC $\widetilde{\rm LL}$ fields, $\widetilde{\rm LL}_{\rm
VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$. The two vertical black lines denote
$\pm 2\sigma$ of the $\widetilde{\rm LL}_{\rm 2012-2015}$$-$$\widetilde{\rm
LL}_{\rm 2017-2020}$ distribution. We use these in the body of the manuscript
to identify significant outliers in the fields. There are three primary
contributors to the variance of the $\widetilde{\rm LL}_{\rm
2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$ distribution. First, there
is the uncertainty associated with the assignment of an LL value by the
machine learning algorithm to each cutout within cell; think of this as
instrument noise. Second, cutouts in each cell are being sampled from a three-
dimensional space-time region, the spatial extent defined by the cell
boundaries (approximately 100 km on a side) and the temporal extent defined by
the four-year period from which each distribution is drawn; think of this as
the uncertainty of estimated values based on the finite sample size. Third,
difference in the $\widetilde{\rm LL}$ value between the period covered by the
two datasets, i.e., the true geophysical difference. For $\widetilde{\rm
LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$, the latter is the
difference between 2012–2015 and 2017–2020. For $\widetilde{\rm LL}_{\rm
VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$ this would be the difference between
the simulated period, 2012, and the period from which the VIIRS data is
sampled, 2012–2020. This means that the variability of $\widetilde{\rm
LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$ places an upper
bound on uncertainty in the LL values, variability due to position within the
cell and the period from which cutouts contributing to the cell are drawn. As
shown in the next paragraph, we believe that the geophysical contribution of
uncertainty to the $\widetilde{\rm LL}_{\rm 2012-2015}$$-$$\widetilde{\rm
LL}_{\rm 2017-2020}$ differences is small hence the variability of
$\widetilde{\rm LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$ is
a good measure of what constitutes a significant deviation between two
datasets. In light of this, we will use two standard deviations of the
$\widetilde{\rm LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$
distribution to identify regions in which the model output agrees/disagrees
with the satellite-derived fields.

Figure 18: Number of VIIRS cutouts per HEALPix cell for the period 2012–2015.
HEALPix cells with less than five cutouts for 2012–2015 or less than five
cutouts for 2017–2020 are shown in white.  Figure 19: Histograms of
$\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$ (blue) and
$\widetilde{\rm LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$
(light brown). Vertical black lines are $\pm 2\sigma$ of $\widetilde{\rm
LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$.

Also of importance in understanding the significance of differences between
$\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm LL}_{\rm LLC}$ is the
degree to which these differences are distributed geographically.
Specifically, shifts in major ocean currents as well as changes in forcing
from one period to another could result in different structures in the
submesoscale-to-mesoscale range, which would display as geographic regions of
positive or negative differences between two periods. Figure 20 suggests that,
with a few exceptions, the distribution of $\widetilde{\rm LL}_{\rm
2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$ is, in fact, quite random,
i.e., at least for this pair of 4-year periods, the differences in
submesoscale-to-mesoscale structure is relatively random. There are, however,
some regions of more than a few HEALPix cells, which stand out as
significantly different between the two periods either in the positive or
negative sense. A narrow negative band is evident along the northern edge of
the ACC south of the Indian Ocean suggesting that the ACC may have shifted
south between 2012–2015 and 2017–2020—more negative values of the difference
correspond to less structure in the second period.

Significant differences are also evident in the vicinity of the Gulf Stream
and Kurshio (Fig. 21b masked to show only HEALPix cells with values more than
two standard deviations from the mean, i.e., significant outliers). Figure 21a
shows the $\widetilde{\rm LL}$ distribution for 2012–2015 (the geographic
distribution of $\widetilde{\rm LL}$ for 2017–2020 is virtually
indistinguishable from that shown for 2012–2015 in this plot). The dark blue
areas on the western side of the North Atlantic and North Pacific north of
approximately $35^{\circ}$N correspond to significant structure in the SST
fields in and north of the associated western boundary currents—the Gulf
Stream and Kuroshio, an observation documented in Prochaska et al. (2021). The
region of enhanced differences between the two periods appears to be on the
northern edge and to the north of these currents. Figure 22 is a blow-up of
the region in the vicinity of the Gulf Stream: Fig. 22a shows the unmasked
$\widetilde{\rm LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$
values and Fig. 22b shows the masked values. The more positive differences
north of the Gulf Stream mean path (magenta line in the figure) suggest an
increase in structure in 2017–2020 compared with that in 2012–2015. That much
of the differences are north of the northernmost extent of the Gulf Stream
(upper black line) argues that not only has the mean path of the stream likely
moved to the north in this period but that this displacement resulted in more
submesoscale-to-mesoscale turbulence in the region north of the stream. Of
particular interest, although not the focus of this manuscript, is the
similarity in the patterns in the vicinity of the Kuroshio suggesting that the
phenomena is hemispheric as opposed to confined to one ocean basin. The point
here is that, although there are some regions of significant differences,
these tend to be relatively small and are, in general, associated with strong
currents—the Gulf Stream, the Kuroshio, and the ACC.

Figure 20: (a) $\widetilde{\rm LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm
2017-2020}$. White areas - less than 5 cutouts in the corresponding HEALPix
cell in 2012–2015 and/or 2017–2020. The same color palette is used in this
figure as in Fig. 5 to facilitate comparison as well as to emphasize the
significant differences in $\widetilde{\rm LL}_{\rm VIIRS}$$-$$\widetilde{\rm
LL}_{\rm LLC}$. (b) Zonal mean of a.  Figure 21:  a) $\widetilde{\rm LL}_{\rm
2012-2015}$ for the northern hemisphere. b) Masked $\widetilde{\rm LL}_{\rm
2012-2015}$$-$$\widetilde{\rm LL}_{\rm 2017-2020}$. Dark gray:
$|$$\widetilde{\rm LL}_{\rm 2012-2015}$$-$$\widetilde{\rm LL}_{\rm
2017-2020}$$|<2\sigma={197}$. Light gray: land. White - less than 5
cutouts/HEALPix cell for both 2012–2015 and 2017–2020.  Figure 22: (a) As in
Figs. 20 and 21 but focused on Gulf Stream region. (b) Masked version of (a).
Magenta line between approximate $75^{\circ}$ W and $45^{\circ}$ W is the mean
path of the Gulf Stream digitized from two-day composites of 1-km AVHRR SST
fields for 1982–1999. Black lines are for the northern most and southernmost
extents of Gulf Stream paths digitized from the same dataset as (a) but for
1982–1986.

KG performed the initial studies on which this manuscript is based. KG, XP and
PC contributed to the subsequent analyses of the data. All contributed to the
writing of the manuscript, which was led by KG. Figures were generated by KG
and PC. XP provided input on the machine learning portion of the project. PC
and DM provided input related to physical oceanography. PC provided the
satellite data expertise. DM provided the modeling expertise. MK and XP
processed the satellite data.

The authors declare that they have no conflict of interest.

###### Acknowledgements.

JXP acknowledges future support from the Simons Foundation and the University
of California, Santa Cruz. DM carried out research at the Jet Propulsion
Laboratory, California Institute of Technology, under a contract with NASA,
with support from the Physical Oceanography (PO) and Modeling, Analysis, and
Prediction (MAP) programs. KG was supported during the summer of 2021 through
the University of Rhode Island/Summer Undergraduate Research Fellowship
Program in Oceanography, NSF award number OCE-1950586. Support for PC was
provided by the Office of Naval Research: ONR N00014-17-1-2963, NASA:
80NSSC18K0837, NASA:80NSSC20K1728 and the State of Rhode Island. The VIIRS L2
SST data were provided by the Group for High Resolution Sea Surface
Temperature and the National Oceanic and Atmospheric Administration and
obtained from the National Aeronautics and Space Administration/Physical
Oceanography Distributed Active Archive Center. The LLC4320 SST fields were
obtained via the xmitgcm package obtained at:
https://xmitgcm.readthedocs.io/en/latest/. Some of the results in this paper
have been derived using the HEALPix (K.M. Górski et al., 2005, ApJ, 622, p759)
package. The authors acknowledge use of the Nautilus cloud computing system
which is supported by the following US National Science Foundation (NSF)
awards: CNS-1456638, CNS-1730158, CNS-2100237, CNS-2120019, ACI-1540112,
ACI-1541349, OAC-1826967, OAC-2112167. High-end computing for the LLC4320
simulation were provided by the NASA Advanced Supercomputing (NAS) Division at
the Ames Research Center.

Acronyms

(A)ATSR

    one or all of ATSR, ATSR-2 and AATSR
AATSR

    Advanced Along Track Scanning Radiometer
ACC

    Antarctic Circumpolar Current
ACCESS

    Advancing Collaborative Connections for Earth System Science
ACL

    Access Control List
ACSPO

    Advanced Clear Sky Processor for Oceans
ADA

    Automatic Detection Algorithm
ADCP

    Acoustic Doppler Current Profiler
ADT

    absolute dynamic topography
AESOP

    Assessing the Effects of Submesoscale Ocean Parameterizations
AGU

    American Geophysical Union
AI

    Artificial Intelligence
AIRS

    Atmospheric Infrared Sounder
AIS

    Ancillary Information Service
AIST

    Advanced Information Systems Techonology
AISR

    Applied Information Systems Research
ADL

    Alexandria Digital Library
API

    Application Program Interface
APL

    Applied Physics Laboratory
API

    Application Program Interface
AMSR

    Advanced Microwave Scanning Radiometer
AMSR2

    Advanced Microwave Scanning Radiometer 2
AMSR-E

    Advanced Microwave Scanning Radiometer - EOS
ANN

     Artificial Neural Network
AOOS

    Alaska Ocean Observing System
APAC

    Australian Partnership for Advanced Computing
APDRC

    Asia-Pacific Data-Research Center
ARC

    ATSR Reprocessing for Climate
ASCII

    American Standard Code for Information Interchange
AS

    Aggregation Server
ASFA

    Aquatic Sciences and Fisheries Abstracts
ASTER

    Advanced Spaceborne Thermal Emission and Reflection Radiometer
ATBD

    Algorithm Theoretical Basis Document
ATSR

    Along Track Scanning Radiometer
ATSR-2

    Second ATSR
AVISO

    Archiving, Validation and Interpretation of Satellite Oceanographic Data
ANU

    Australian National University
AVHRR

    Advanced Very High Resolution Radiometer
AzC

    Azores Current
BAA

    Broad Agency Announcement
BAO

    bi-annual oscillation
BES

    Back-End Server
BMRC

    Bureau of Meteorology Research Centre
BOM

    Bureau of Meteorology
BT

    brightness temperature
BUFR

    Binary Universal Format Representation
CAN

    Cooperative Agreement Notice
CAS

    Community Authorization Service
CC

    cloud cover
CCA

    Cayula-Cornillon Algoritm
CCI

    Climate Change Initiative
CCLRC

    Council for the Central Laboratory of the Research Councils
CCMA

    Center for Coastal Monitoring and Assessment
CCR

    cold core ring
CCS

    California Current System
CCSM

    Community Climate System Model
CCSR

    Center for Climate System Research
CCV

    Center for Computation and Visualization
CDAT

    Climate Data Analysis Tools
CDC

    Climate Diagnostics Center
CDF

    Common Data Format
CDR

    Common Data Representation
CEDAR

    Coupled Energetic and Dynamics and Atmospheric Regions
CEOS

    Committee on Earth Observation Satellites
CERT

    Computer Emergency Response Team
CenCOOS

    Central & Northern California Ocean Observing System
CF

    clear fraction
CGI

    Common Gateway Interface
CHAP

    CISL High Performance Computing Advisory Panel
CIFS

    Common Internet File System
CIMSS

    Cooperative Institute for Meteorological Satellite Studies
CIRES

    Cooperative Institute for Research (in) Environmental Sciences
CISL

    Computational & Information Systems Laboratory
CLASS

    Comprehensive Large Array-data Stewardship System
CLIVAR

    Climate Variability and Predictability
CLS

    Collecte Localisation Satellites
CME

    Community Modeling Effort
CMS

    Centre de Météorologie Spatiale
CNN

    Convolutional Neural Network
COA

    Climate Observations and Analysis
COARDS

    Cooperative Ocean-Atmosphere Research Data Standard
COAPS

    Center for Ocean-Atmospheric Prediction Studies
COBIT

    Control Objectives for Information and related Technology
COCO

    CCSR Ocean Component model
CODAR

    Coastal Ocean Dynamics Applications Radar
CODMAC

    Committee on Data Management, Archiving, and Computing
Co-I

    Co-Investigator
CORBA

    Common Object Request Broker Architecture
COLA

    Center for Ocean-Land-Atmosphere Studies
CPU

    Central Processor Unit
CRS

    Coordinate Reference System
CSA

    Cambridge Scientific Abstracts
CSC

    Coastal Services Center
CSIS

    Center for Strategic and International Studies
CSL

    Constraint Specification Language
CSP

    Chermayeff, Sollogub and Poole, Inc.
CSDGM

    Content Standard for Digital Geospatial Metadata
CSV

    Comma Separated Values
CTD

    Conductivity, Temperature and Salinity
CVSS

    Common Vulnerability Scoring System
CZCS

    Coastal Zone Color Scanner
DAAC

    Distribute Active Archive Center
DAARWG

    Data Archiving and Access Requirements Working Group
DAP

    Data Access Protocol
DAS

    Data set Attribute Structure
DBMS

    Data Base Management System
DBDB2

    Digital Bathymetric Data Base
DChart

    Dapper Data Viewer
DDS

    Data Descriptor Structure
DDX

    XML version of the combined DAS and DDS
DFT

    Discrete Fourier Transform
DIF

    Directory Interchange Format
DISC

    Data and Information Services Center
DIMES

    Diapycnal and Isopycnal Mixing Experiment: Southern Ocean
DMAC

    Data Management and Communications committee
DMR

    Department of Marine Resources
DMSP

    Defense Meteorological Satellite Program
DoD

    Department of Defense
DODS

    Distributed Oceanographic Data System
DOE

    Department of Energy
DSP

    U. Miami satellite data processing software
DSS

    direct statistical simulation
EASy

    Environmental Analysis System
ECCO

    Estimating the Circulation and Climate of the Ocean
ECCO2

    Estimating the Circulation and Climate of the Ocean, Phase II
ECS

    EOSDIS Core System
ECHO

    Earth Observing System Clearinghouse
ECMWF

    European Centre for Medium-range Weather Forecasting
ECV

    Essential Climate Variable
EDC

    Environmental Data Connector
EDJ

    Equatorial Deep Jet
EDFT

    Extended Discrete Fourier Transform
EDMI

    Earth Data Multi-media Instrument
EEJ

    Extra-Equatorial Jet
EIC

    Equatorial Intermediate Current
EICS

    Equatorial Intermediate Current System
EJ

    Equatorial Jets
EKE

    eddy kinetic energy
EMD

    Empirical Mode Decomposition
EOF

    Empirical Orthogonal Function
EOS

    Earth Observing System
EOSDIS

    Earth Observing System Data Information System
EPA

    Environmental Protection Agency
EPSCoR

    Experimental Program to Stimulate Competitive Research
EPR

    East Pacific Rise
ERD

    Environmental Research Division
ERS

    European Remote-sensing Satellite
ESA

    European Space Agency
ESDS

    Earth Science Data Systems
ESDSWG

    Earth Science Data Systems Workign Group
ESE

    Earth Science Enterprise
ESG

    Earth System Grid
ESG II

    Earth System Grid – II
ESIP

    Earth Science Information Partner
ESMF

    Earth System Modeling Framework
ESML

    Earth System Markup Language
ESP

    eastern South Pacfic
ESRI

    Environmental Systems Research Institute
ESR

    Earth and Space Research
ETOPO

    Earth Topography
EUC

    Equatorial Undercurrent
EUMETSAT

    European Organisation for the Exploitation of Meteorological Satellites
Ferret

FASINEX

    Frontal Air-Sea Interaction Experiment
FDS

    Ferret Data Server
FFT

    Fast Fourier Transform
FGDC

    Federal Geographic Data Committee
FITS

    Flexible Image (or Interchange) Transport System
FLOPS

    FLoating point Operations Per Second
FRTG

    Flow Rate Task Group
FreeForm

FNMOC

    Fleet Numerical Meteorology and Oceanography Center
FSU

    Florida State University
FTE

    Full Time Equivalent
ftp

    File Transport Protocol
ftp

    File Transport Protocol
GAC

    Global Area Coverage
GAN

    Generative Adversarial Network
GB

    GigaByte - $10^{9}$ bytes
GCMD

    Global Change Master Directory
GCM

    general circulation model
GCOM-W1

    Global Change Observing Mission - Water
GCOS

    Global Climate Observing System
GDAC

    Global Data Assembly Center
GDS

    GrADS Data Server
GDS2

    GHRSST Data Processing Specification v2.0
GEBCO

    General Bathymetric Charts of the Oceans
GeoTIFF

    Georeferenced Tag Image File Format
GEO-IDE

    Global Earth Observation Integrated Data Environment
GES DIS

    Goddard Earth Sciences Data and Information Services Center
GEMPACK

    General Equilibrium Modelling PACKage
GEOSS

    Global Earth Observing System of Systems
GFDL

    Geophysical Fluid Dynamics Laboratory
GFD

    Geophysical Fluid Dynamics
GHRSST

    Group for High Resolution Sea Surface Temperature
GHRSST-PP

    GODAE High Resolution Sea Surface Temperature Pilot Project
GINI

    GOES Ingest and NOAA/PORT Interface
GIS

    Geographic Information Systems
Globus

GMAO

    Global Modeling and Assimilation Office
GML

    Geography Markup Language
GMT

    Generic Mapping Tool
GODAE

    Global Ocean Data Assimilation Experiment
GOES

    Geostationary Operational Environmental Satellites
GOFS

    Global Ocean Forecasting System
GoMOOS

    Gulf of Maine Ocean Observing System
GOOS

    Global Ocean Observing System
GOSUD

    Global Ocean Surface Underway Data
GPFS

     General Parallel File System
GPU

    Graphics Processing Unit
GRACE

    Gravity Recovery and Climate Experiment
GRIB

    GRid In Binary
GrADS

    Grid Analysis and Display System
GridFTP

    FTP with GRID enhancements
GRIB

    GRid in Binary
GPS

    Global Positioning System
GSFC

    Goddard Space Flight Center
GSI

    Grid Security Infrastructure
GSO

    Graduate School of Oceanography
GTSPP

    Global Temperature and Salinity Profile Program
GUI

    Graphical User Interface
GS

    Gulf Stream
HAO

    High Altitude Observatory
HLCC

    Hawaiian Lee Countercurrent
HCMM

    Heat Capacity Mapping Mission
HDF

    Hierarchical Data Format
HDF-EOS

    Hierarchical Data Format - EOS
HEC

    High-End Computing
HEALPix

    Hierarchical Equal Area isoLatitude Pixelation
HF

    High Frequency
HGE

    High Gradient Event
HPC

    High Performance Computing
HPCMP

    High Performance Computing Modernization Program
HPSS

    High Performance Storage System
HR DDS

    High Resolution Diagnostic Data Set
HRPT

    High Resolution Picture Transmission
HTML

    Hyper Text Markup Language
html

    Hyper Text Markup Language
http

    the hypertext transport protocol
HTTP

    Hyper Text Transfer Protocol
HTTPS

    Secure Hyper Text Transfer Protocol
HYCOM

    HYbrid Coordinate Ocean Model
I-band

    imagery resolution band
IDD

    Internet Data Distribution
IB

    Image Band
IBL

    internal boundary layer
IBM

    Internation Business Machines
ICCs

    Intermediate Countercurrents
IDE

    Integrated Development Environment
IDL

    Interactive Display Language
IDLastro

    IDL Astronomy User’s Library
IDV

    Integrated Data Viewer
IEA

    Integrated Ecosystem Assessment
IEEE

    Institute (of) Electrical (and) Electronic Engineers
IETF

    Internet Engineering Task Force
IFREMER

    Institut Français de Recherche pour l’Exploitation de la MER
IMAPRE

    El Instituto del Mar del Perú
IMF

    Intrinsic Mode Function
IOOS

    Integrated Ocean Observing System
ISAR

    Infrared Sea surface temperature Autonomous Radiometer
ISO

    International Organization for Standardization
ISSTST

    Interim Sea Surface Temperature Science Team
IT

    Information Technology
ITCZ

    Intertropical Convergence Zone
IP

    Internet Provider
IPCC

    Intergovernmental Panel on Climate Change
IPRC

    International Pacific Research Center
IR

    Infrared
IRI

    International Research Institute for Climate and Society
ISO

    International Standards Organization
JASON

    JASON Foundation for Education
JDBC

    Java Database Connectivity
JFR

    Juan Fernández Ridge
JGOFS

    Joint Global Ocean Flux Experiment
JHU

    Johns Hopkins University
JPL

    Jet Propulsion Laboratory
JPSS

    Joint Polar Satellite System
KDE

    Kernel Density Estimation
KVL

    Keyword-Value List
KML

    Keyhole Markup Language
KPP

    K-Profile Parameterization
LAC

    Local Area Coverage
LAN

    Local Area Network
LAS

    Live Access Server
LASCO

    Large Angle and Spectrometric Coronagraph Experiment
LatMIX

    Scalable Lateral Mixing and Coherent Turbulence
LDAP

    Lightweight Directory Access Protocol
LDEO

    Lamont Doherty Earth Observatory
LEAD

    Linked Environments for Atmospheric Discovery
LEIC

    Lower Equatorial Intermediate Current
LES

    Large Eddy Simulation
L1

    Level-1
L2

    Level-2
L2P

    Level-2P
L3

    Level-3
L4

    Level-4
LL

    Log-Likelihood
LLC

    Latitude/Longitude/polar-Cap
LLC4320

     Latitude/Longitude/polar-Cap4320
LLC2160

     LLC2160
LLC1080

     LLC1080
LHF

    Latent Heat Flux
LST

    local sun time
LTER

    Long Term Ecological Research Network
LTSRF

    Long Term Stewardship and Reanalysis Facility
LUT

    Look Up Table
M-band

    moderate resolution band
MABL

    marine atmospheric boundary layer
MADT

    Maps of Absolute Dynamic Topography
MapServer

    MapServer
MAT

    Metadata Acquisition Toolkit
MATLAB

MARCOOS

    Mid-Atlantic Coastal Ocean Observing System
MARCOORA

    Mid-Atlantic Coastal Ocean Observing Regional Association
MB

    MegaByte - $10^{6}$ bytes
MCC

    Maximum Cross-Correlation
MCR

    MATLAB Component Runtime
MCSST

    Multi-Channel Sea Surface Temperature
MDT

    mean dynamic topography
MDB

    Match-up Data Base
MDOT

    mean dynamic ocean topography
MEaSUREs

    Making Earth System data records for Use in Research Environments
MERRA

    Modern Era Retrospective-Analysis for Research and Applications
MERSEA

    Marine Environment and Security for the European Area
MTF

    Modulation Transfer Function
MICOM

    Miami Isopycnal Coordinate Ocean Model
MIRAS

    Microwave Imaging Radiometer with Aperture Synthesis
MITgcm

    MIT general circulation model
MIT

    Massachusetts Institute of Technology
mks

    meters, kilograms, seconds
MLP

    Multilayer Perceptron
ML

    machine learning
MLSO

    Mauna Loa Solar Observatory
MM5

    Mesoscale Model
MMI

    Marine Metadata Initiative
MMS

    Minerals Management Service
MODAS

    Modular Ocean Data Assimilation System
MODIS

    MODerate-resolution Imaging Spectroradiometer
MOU

    Memorandum of Understanding
MPARWG

    Metrics Planning and Reporting Working Group
MSE

    mean square error
MSG

    Meteosat Second Generation
MTPE

    Mission To Planet Earth
MUR

    Multi-sensor Ultra-high Resolution
MV

    Motor Vessel
NAML

    National Association of Marine Laboratories
NAHDO

    National Association of Health Data Organizations
NAS

    Network Attached Storage
NASA

    National Aeronautics and Space Administration
NCAR

    National Center for Atmospheric Research
NCEI

    National Centers for Environmental Information
NCEP

    National Centers for Environmental Prediction
NCDC

    National Climatic Data Center
NCDDC

    National Coastal Data Development Center
NCL

    NCAR Command Language
ncBrowse

NcML

    netCDF Markup Language
NCO

    netCDF Operator
NCODA

    Navy Coupled Ocean Data Assimilation
NCSA

    National Center for Supercomputing Applications
NDBC

    National Data Buoy Center
NDVI

    Normalized Difference Vegetation Index
NEC

    North Equatorial Current
NECC

    North Equatorial Countercurrent
NEFSC

    Northeast Fisheries Science Center
NEIC

    North Equatorial Intermediate Current
netCDF

    NETwork Common Data Format
NEUC

    North Equatorial Undercurrent
NGDC

    National Geophysical Data Center
NICC

    North Intermediate Countercurrent
NIST

    National Institute of Standards and Technology
NLSST

    Non-Linear Sea Surface Temperature
NMFS

    National Marine Fisheries Service
NMS

    New Media Studio
NN

    Neural Network
NOAA

    National Oceanic and Atmospheric Administration
NODC

    National Oceanographic Data Center
NOGAPS

    Navy Operational Global Atmospheric Prediction System
NOMADS

    NOAA Operational Model Archive Distribution System
NOPP

    National Oceanographic Parternership Program
NOS

    National Ocean Service
NPP

    National Polar-orbiting Partnership
NPOESS

    National Polar-orbiting Operational Environmental Satellite System
NSCAT

    NASA SCATterometer
NSEN

    NASA Science and Engineering Network
NSF

    National Science Foundation
NSIPP

    NASA Seasonal-to-Interannual Prediction Project
NRA

    NASA Research Announcement
NRC

    National Research Council
NRL

    Naval Research Laboratory
NSCC

    North Subsurface Countercurrent
NSF

    National Science Foundation
NSIDC

    National Snow and Ice Data Center
NSPIRES

    NASA Solicitation and Proposal Integrated Review and Evaluation System
NSSDC

    National Space Science Data Center
NVODS

    National Virtual Ocean Data System
NWP

    Numerical Weather Prediction
NWS

    National Weather Service
OBPG

    Ocean Biology Processing Group
OB.DAAC

    Ocean Biology DAAC
ODC

    OPeNDAP Data Connector
OC

    ocean color
OCAPI

    OPeNDAP C API
ODSIP

    Open Data Services Invocation Protocol
OFES

    Ocean Model for the Earth Simulator
OCCA

    OCean Comprehensive Atlas
OGC

    Open Geospatial Consortium
OGCM

    Ocean General Circulation Model
OISSTv1

    Optimally Interpolated SST Version 1
ONR

    Office of Naval Research
OLCI

    Ocean Land Colour Instrument
OLFS

    OPeNDAP Lightweight Front-end Server
OOD

    out-of-distribution
OOPC

    Ocean Observation Panel for Climate
OPeNDAP

    Open source Project for a Network Data Access Protocol
OPeNDAPg

    GRID-enabled OPeNDAP tools
OpenGIS

    OpenGIS
OSCAR

    Ocean Surface Current Analyses Real-time
OSI SAF

    Ocean and Sea Ice Satellite Application Facility
OSS

    Office of Space Science
OSTM

    Ocean Surface Topography Mission
OSU

    Oregon State University
OS X

OWL

    Web Ontology Language
OWASP

    Open Web Application Security Project
PAE

    Probabilistic AutoEncoder
PBL

    planetary boundary layer
PCA

    Principal Components Analysis
PDF

    probability distribution function
PDF

    probability density function
PF

    Polar Front
PFEL

    Pacific Fisheries Environmental Laboratory
PI

    Principal Investigator
PIV

    Particle Image Velocimetry
PL

    Project Leader
PM

    Project Member
PMEL

    Pacific Marine Environmental Laboratory
POC

    particulate organic carbon
PO.DAAC

    Physical Oceanography Distributed Active Archive Center
POP

    Parallel Ocean Program
PSD

    Power Spectral Density
PSPT

    Precision Solar Photometric Telescope
PSU

    Pennsylvania State University
PyDAP

    Python Data Access Protocol
PV

    potential vorticity
QC

    quality control
QG

    quasi-geostrophic
QuikSCAT

    Quick Scatterometer
QZJ

    quasi-zonal jet
R2HA2

    Rescue & Reprocessing of Historical AVHRR Archives
RAFOS

    SOFAR, SOund Fixing And Ranging, spelled backward
RAID

    Redundant Array of Independent Disks
RAL

    Rutherford Appleton Laboratory
RAN2

     $2^{nd}$ full-mission reanalysis
RAN3

     $3^{rd}$ full-mission reanalysis
RDF

    Resource Description Language
REASoN

    Research, Education and Applications Solutions Network
REAP

    Realtime Environment for Analytical Processing
ReLU

    Rectified Linear Unit
REU

    Research Experiences for Undergraduates
RFA

    Research Focus Area
RFI

    Radio Frequency Interference
RFC

    Request For Comments
R/GTS

    Regional/Global Task Sharing
RSI

    Research Systems Inc.
RISE

    Radiative Inputs from Sun to Earth
rms

    root mean square
RMI

    Remote Method Invocation
ROMS

    Regional Ocean Modeling System
ROSES

    Research Opportunities in Space and Earth Sciences
RSMAS

    Rosenstiel School of Marine and Atmospheric Science
RSS

    Remote Sensing Sytems
RTM

    radiative transfer model
SACCF

    Southern ACC Front
(SAC)-D

    Satélite de Aplicaciones Científicas-D
SAF

    Subantarctic Front
SAIC

    Science Applications International Corporation
SANS

    SysAdmin, Audit, Networking, and Security
SAR

    synthetic aperature radar
SATMOS

    Service d’Archivage et de Traitement Météorologique des Observations Spatiales
SBE

    Sea-Bird Electronics
SciDAC

    Scientific Discovery through Advanced Computing
SCC

    Subsurface Countercurrent
SCCWRP

    Southern California Coastal Water Research Project
SDAC

    Solar Physics Data Analysis Center
SDS

    Scientific Data Set
SDSC

    San Diego Supercomputer Center
SeaDAS

    SeaWiFS Data Analysis System
SeaWiFS

    Sea-viewing Wide Field-of-view Sensor
SEC

    South Equatorial Current
SECC

    South Equatorial Countercurrent
SECDDS

    Sun Earth Connection Distributed Data Services
SEEDS

    Strategic Evolution of ESE Data Systems
SEIC

    South Equatorial Intermediate Current
SEUC

    Southern Equatorial Undercurrent
SEVIRI

    Spinning Enhanced Visible and Infra-Red Imager
SeRQL

    SeRQL
SGI

    Silican Graphics Incorporated
SHF

    Sensible Heat Flux
SICC

    South Intermediate Countercurrent
SIED

    single image edge detection
SIPS

    Science Investigator–led Processing System
SIR

    Scatterometer Image Reconstruction
SISTeR

    Scanning Infrared Sea Surface Temperature Radiometer
SLA

    sea level anomaly
SLSTR

    Sea and Land Surface Temperature Radiometer
SMAP

    Soil Moisture Active Passive
SMMR

    Scanning Multichannel Microwave Radiometer
SMOS

    Soil Moisture and Ocean Salinity
SMTP

    Simple Mail Transfer Protocol
SOAP

    Simple Object Access Protocol
SOEST

    School of Ocean and Earth Science and Technology
SOFAR

    SOund Fixing And Ranging
SOFINE

    Southern Ocean Finescale Mixing Experiment
SOHO

    Solar and Heliospheric Observatory
SPARC

    Space Physics and Aeronomy Research Collaboratory
SPARQL

    Simple Protocol and RDF Query Language
SPASE

    Space Physics Archive Search Engine
SPCZ

    South Pacific Convergence Zone
SPDF

    Space Physics Data Facility
SPDML

    Space Physics Data Markup Language
SPG

    Standards Process Group
SQL

    Structured Query Language
SSCC

    South Subsurface Countercurrent
SSL

    self-supervised learning
SSO

    Single sign-on
SSES

    Single Sensor Error Statistics
SSH

    sea surface height
SSHA

    sea surface height anomaly
SSMI

    Special Sensor Microwave/Imager
SST

    Sea Surface Temperature
SSTa

    sea surface temperature anomaly
SSS

    sea surface salinity
SSTST

    Sea Surface Temperature Science Team
STEM

    science, technology, engineering and mathematics
STL

    Standard Template Library
STCZ

    Subtropical Convergence Zone
Suomi-NPP

    Suomi-National Polar-orbiting Partnership
SWEET

    Semantic Web for Earth and Environmental Terminology
SWFSC

    Southwest Fisheries Science Center
SWOT

    Surface Water and Ocean Topography
SWRL

    Semantic Web Rule Language
SubEx

    Submesoscale Experiment
SURA

    Southeastern Universities Research Association
SURFO

    Summer Undergraduate Research Fellowship Program in Oceanography
SuperDARN

    Super Dual Auroral Radar Network
TAMU

    Texas A&M University
TB

    TeraByte - $10^{12}$ bytes
TCASCV

    Technology Center for Advanced Scientific Computing and Visualization
TCP

    Transmission Control Protocol
TCP/IP

    Transmission Control Protocol/Internet Protocol
TDS

    THREDDS Data Server
TEX

    external temperature or T-External
THREDDS

    Thematic Realtime Environmental Data Distributed Services
TIDI

    TIMED Doppler Interferometer
TIFF

    Tag Image File Format
TIMED

    Thermosphere, Ionosphere, Mesosphere, Energetics and Dynamics
TLS

    Transport Layer Security
TRL

    Technology Readiness Level
TMI

    TRMM Microwave Imager
TOPEX/Poseidon

    TOPography EXperiment for Ocean Circulation/Poseidon
TRMM

    Tropical Rainfall Measuring Mission
TSG

    thermosalinograph
UCAR

    University Corporation for Atmospheric Research
UCSB

    University of California, Santa Barbara
UCSD

    University of California, San Diego
uCTD

    Underway Conductivity, Temperature and Salinity or Underway CTD
UDDI

    Universal Description, Discovery and Integration
UMAP

    Uniform Manifold Approximation and Projection
UMiami

    University of Miami
Unidata

URI

    University of Rhode Island
UPC

    Unidata Program Committee
URL

    Uniform Resource Locator
USGS

    United States Geological Survey
UTC

    Coordinated Universal Time
UW

    University of Washington
VCDAT

    Visual Climate Data Analysis Tools
VIIRS

    Visible Infrared Imaging Radiometer Suite
VR

    Virtual Reality
VSTO

    Virtual Solar-Terrestrial Observatory
WCR

    Warm Core Ring
WCS

    Web Coverage Service
WCRP

    World Climate Research Program
WFS

    Web Feature Service
WMS

    Web Map Service
W3C

    World Wide Web Consortium
WJ

    Wyrtki Jets
WHOI

    Woods Hole Oceanographic Institution
WKB

    Well Known Binaries
WIMP

    Windows, Icons, Menus, and Pointers
WIS

    World Meteorological Organisation Information System
WOA05

    World Ocean Atlas 2005
WOCE

    World Ocean Circulation Experiment
WP-ESIP

    Working Prototype Earth Science Information Partner
WRF

    Weather & Research Forecasting Model
WSDL

    Web Services Description Language
WSP

    western South Pacfic
WWW

    World Wide Web
XBT

    Expendable BathyThermograph
XML

    Extensible Markup Language
XRAC

    eXtreme Digital Request Allocation Committee
XSEDE

    Extreme Science and Engineering Discovery Environment
YAG

    yttrium aluminium garnet

## References

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  *[SST]: Sea Surface Temperature
  *[VIIRS]: Visible Infrared Imaging Radiometer Suite
  *[MITgcm]: MIT general circulation model
  *[PAE]: Probabilistic AutoEncoder
  *[SSTa]: sea surface temperature anomaly
  *[ACC]: Antarctic Circumpolar Current
  *[OGCMs]: Ocean General Circulation Model
  *[ECCO]: Estimating the Circulation and Climate of the Ocean
  *[MIT]: Massachusetts Institute of Technology
  *[JPL]: Jet Propulsion Laboratory
  *[NPP]: National Polar-orbiting Partnership
  *[L2P]: Level-2P
  *[RAN2]: 2nd full-mission reanalysis
  *[AVHRR]: Advanced Very High Resolution Radiometer
  *[SLSTR]: Sea and Land Surface Temperature Radiometer
  *[PO.DAAC]: Physical Oceanography Distributed Active Archive Center
  *[LLC]: Latitude/Longitude/polar-Cap
  *[LLC1080]: 1080
  *[LLC2160]: 2160
  *[LLC4320]: 4320
  *[ECMWF]: European Centre for Medium-range Weather Forecasting
  *[MODIS]: MODerate-resolution Imaging Spectroradiometer
  *[HEALPix]: Hierarchical Equal Area isoLatitude Pixelation
  *[OGCM]: Ocean General Circulation Model
  *[LL]: Log-Likelihood
  *[L2]: Level-2
  *[OSCAR]: Ocean Surface Current Analyses Real-time
  *[NSF]: National Science Foundation
  *[CTD]: Conductivity, Temperature and Salinity