The dynamic ocean topography (DOT) of the polar seas can be
described by satellite altimetry sea surface height observations combined
with geoid information as well as by ocean models. The altimetry observations are
characterized by an irregular sampling and seasonal sea ice coverage
complicating reliable DOT estimations. Models display various spatiotemporal
resolutions but are limited to their computational and mathematical context
and introduced forcing models. In the present paper, ALES+ retracked
altimetry ranges and derived along-track DOT heights of ESA's Envisat and
water heights of the Finite Element Sea Ice-Ocean Model (FESOM)
are compared to investigate similarities and discrepancies. The goal of the present paper is to
identify to what extent pattern and variability of the northern Nordic seas derived from
measurements and model agree with each other, respectively.
The study period covers the years 2003–2009. An assessment analysis regarding seasonal
DOT variabilities shows good agreement and confirms the dominant impact of the annual
signal in both datasets. A comparison based on estimated regional annual signal components
shows 2–3 times stronger amplitudes of the observations but good agreement of the phase.
Reducing both datasets by constant offsets and the annual signal reveals small regional
residuals and highly correlated DOT time series (Pearson linear correlation coefficient of at
least 0.67). The highest correlations can be found in areas that are ice-free and affected by
ocean currents. However, differences are visible in sea-ice-covered shelf regions. Furthermore,
remaining constant artificial elevations in the observational data can be
attributed to an insufficient
representation of the used geoid. In general, the comparison results in good agreement between
simulated and altimetry-based descriptions of the DOT in the northern Nordic seas.
Introduction
Observing the dynamic ocean topography (DOT) enables the investigation of
important oceanic variables. Variations in the DOT are an indicator of
changes in the ocean circulation, the major current pathways or water mass
redistribution. Knowledge about Arctic water mass distribution and ocean
transport variability is essential to understand and quantify changes in the
global overturning circulation system (e.g., ). These relationships have led to studies and expeditions since
the early 20th century, e.g., by investigating northern polar
circulation.
Nowadays, satellite altimetry, in connection with knowledge about the geoid, is
one possibility to provide instantaneous DOT snapshots on a global scale.
However, in polar regions, altimetry observations obey an irregular sampling
in seasonally sea-ice-covered regions. Nevertheless, the launch of the European Space
Agency's (ESA) Earth observation satellite ERS-1 in 1991 constituted the starting point of
regular observed DOT information in the higher latitudes that now covers more than 25 years.
This was followed by regularly improving radar altimetry as well as significant
progress in gravity field missions (e.g., GOCE and GRACE); remote sensing
missions provided increasingly reliable DOT estimates. In addition to
an expanded remote Earth observation mission constellation, advances in data
processing (e.g., )
also contributed to an increasing accuracy of DOT heights, mainly by improving
radar echoes processing strategies (e.g., use of high-frequency data, enhanced
retracking and radar echo classification algorithms).
Arctic DOT information for different periods and with different spatial
resolutions has been estimated for example by based
on laser altimetry or by based on a combination of laser
and radar altimetry. Moreover, processed monthly
altimetry-derived DOT outputs to combine them with GRACE ocean mass products.
However, all these DOT results are based on grid processing with limited
spatiotemporal resolutions, leading to unavoidable smoothing effects and
leaving space for further DOT product improvements.
In addition to the observational database, model simulations have provided a variety
of different climate variables in polar regions for more than 60 years
(). They are characterized by various spatiotemporal
resolutions and simulation strategies. In spite of difficult observation
conditions at high latitudes, models enable comprehensive analyses of
interactions between the Arctic Ocean and atmospheric circulations. However,
different models show significant discrepancies related to their fundamental
outputs, e.g., sea-surface variability or ocean currents
(). Nevertheless, in contrast to satellite altimetry,
models provide spatially homogeneous and temporally complete sea surface
estimates. In order to get an impression of model accuracies, previous
studies, for example , performed an intercomparison of
different ocean models, tide gauge observations and weekly averaged altimetry
DOT data in the Arctic environment, limited, however, to gridded DOT data
originating from sea-ice-free months. The authors conclude that models can catch
and reproduce the most dominant low-frequency water level variabilities in
the Arctic Ocean. Nevertheless, there is need for improvement in terms of
seasonally independent analyses as well as an increased spatiotemporal
resolution, which would, for example, enable a direct pointwise comparison.
Recent developments in numerical modeling focused on so-called
unstructured mesh representations. According to , unstructured
ocean model grids with local refinements in the region of complex and highly
dynamic circulation patterns (e.g., Fram Strait) allow for
multi-resolution analyses of climate-relevant variables in specific areas of
interest while keeping a coarse spatial representation for other regions
(e.g., ). One of these models is the
Finite Element Sea Ice-Ocean Model (FESOM, ). It includes,
in addition to the ocean variables (sea surface height, temperature, ocean currents
and salinity), a sea ice component mapping the major ice drift pathways.
Furthermore described a FESOM configuration that enables
studies in the Fram Strait region and northern Nordic seas at a daily
temporal resolution and a spatially refined 1 km mesh, resulting in an
eddy-resolving ocean simulation in most of the study domain. Another sea ice
ocean model setup with comparable resolution focusing on the same region is
based on a Regional Ocean Modeling System (ROMS), which applies a grid size of
800 m around Svalbard . The model setup is regional and
nested into a 4 km pan-Arctic setup. In terms of eddy dynamics, the ROMS and
FESOM setups compare very well (personal communication, Tore Hattermann,
January 2018). A slightly
coarser model with up to 2 km resolution in the northern Nordic seas was
described by .
In the present study, along-track high-frequency DOT estimates of ESA's
Envisat as well as water level outputs of FESOM are used for a direct
comparison in order to analyze spatiotemporal correspondence and
discrepancies. The overall motivation for this is the computation of a
spatially homogeneous DOT without the need of gridding methods that smooth
the altimetry spectral data content. Instead of such an interpolation, the
unavoidable data gaps should be filled with model information from a
combination of profiled altimetry data and gridded model data. A careful
comparison of both datasets is a necessary prerequisite for such
combination. The present investigation aims to explore the capacity for a
combination and exploiting the advantages of both quantities. In particular,
it is evaluated if the model outputs can bridge periods when altimetry fails
(e.g., due to sea ice coverage). In the present study, the altimetry database
consists of profiled 20 Hz DOT snapshots that were preprocessed using the
classification presented by . The comparison is conducted in
the northern Nordic seas and the Fram Strait, covering the East Greenland and
the West Spitsbergen currents. The present paper is structured into four main
sections. First, the study area and the applied datasets and their
preprocessing are introduced, followed by Sect. describing
the comparison methods and displaying the obtained results. The last two
sections discuss the results and recapitulate the key aspects.
Study area and datasets
This section provides an overview of the study area, the used
model and the observational database. In addition, more detailed information
on the data preprocessing is given.
The northern Nordic seas and Fram Strait
The study area covers the northern Nordic seas and the Fram
Strait, which connects the North Atlantic with the Arctic Ocean as depicted
in Fig. . The study area is limited to 72 to
82∘ N and 30∘ W to 30∘ E. The bathymetry is complex in this region: the deep
Fram Strait (with depths up to 5 600 m at the Molloy Hole) lies between the
wide northeastern Greenland continental shelf and the Svalbard archipelago, with
the deep Greenland Sea to the south. Seamounts, ridges and steep slopes
affect the ocean circulation.
Overviews of the study area: (a) bathymetry of the northern Nordic
seas and Fram Strait area based on RTopo2 topography model ().
Arrows display major current systems (East Greenland Current, EGC; West Spitsbergen
Current, WSC; East Spitsbergen Current, ESC; Jan Mayen Current, JMC; Yermak Branch,
YB; and Svalbard Branch, SB). Light green arrows indicate inflowing Atlantic water;
orange represents fresh polar and returning Atlantic water.
(b) Averaged sea ice concentration in percentage within 2003–2009 based on
25 km monthly National Snow and Ice Data Center (NSIDC, )
sea ice concentration grids. White lines display depth contours at -450 and -1500 m.
White areas indicate missing or flagged data.
The northern Nordic seas are characterized by contrasting water masses. Warm
and salty waters of Atlantic origin are carried northward by the Norwegian
Atlantic Current e.g.,. After a bifurcation at the Barents
Sea Opening, the remaining current that continues northward is termed the
West Spitsbergen Current WSC, e.g.,. A
fraction of the Atlantic water carried by the WSC recirculates in the Fram
Strait at around 79∘ N and continues to flow southward, forming the Return
Atlantic Water (RAW), whereas the remaining part enters the Arctic Ocean via
the Svalbard and Yermak branches (SB and YB). Along the Greenland continental
shelf break, the East Greenland Current EGC, e.g.,
carries cold and fresh polar water as well as RAW southward.
Sea ice is exported via the Transpolar Drift out of the Arctic through the
Fram Strait. As indicated in Fig. , the sea ice export
occurs at the western side of the strait, which is thus ice-covered
year-round. The eastern part of the Fram Strait is ice-free year-round due
to the presence of warm Atlantic water. Around 10 % of the Arctic sea ice
area is exported through the Fram Strait annually, an order of magnitude
larger than the export through other Arctic gateways .
Model basis: Finite Element Sea Ice-Ocean Model (FESOM)
In this study we use daily mean water level output from the Finite Element
Sea Ice-Ocean Model (FESOM) version 1.4 . FESOM
is an ocean sea ice model which solves the hydrostatic primitive equations in
the Boussinesq approximation. The sea ice component applies the
elastic–viscous–plastic rheology and thermodynamics
following . The finite element method is used to
discretize the governing equations, applying unstructured triangular meshes
in the horizontal and z levels in the vertical. Water level heights (in the
model labeled as sea surface height) η are computed from the following
equation:
∂tη+∇⋅∫z=-Hz=ηudz=0,
where u≡(u,v) is the velocity vector and H is the water
depth. Water elevations are relative to a geopotential surface and therefore
comparable to an altimetry-derived dynamic ocean topography
. The upper limit in the integration is set to zero,
which corresponds to a linear free-surface approximation. This implies that
the ocean volume does not change with time in the model. Thus, the model
conserves volume but not mass. A correction for the global mean steric
height change is not applied. To account for surface freshwater fluxes
(precipitation, evaporation, river runoff, salinity changes due to sea ice
melting and freezing), a virtual salt flux is introduced (see, e.g.,
). The model does not take into account sea level pressure
and ocean tide variations.
The global FESOM configuration used here was optimized for the Fram Strait,
applying a mesh resolution of 1 km in the area 76–82.5∘ N,
20∘ W–20∘ E and a resolution of 4.5 km in the Nordic seas and Arctic Ocean . In the
vertical, 47 z levels are used with a thickness of 10 m in the top 100 m and
coarser vertical resolution with depth. The model bathymetry was taken from
RTopo2 . For comparison, only the surface information
is used (i.e., z=0).
The model is forced by atmospheric reanalysis data COREv.2
characterized by a daily temporal and 2 ∘ spatial resolution, and
interannual monthly river runoff is taken from . Sea surface
salinity restored to the PHC 3.0 climatology is applied
with a restoring velocity of 50 m per 300 days. The simulation covers the
time period 2000 until 2009, and daily model output was saved. A comparison
with observational data (e.g., moorings) revealed that the model performed
well in simulating the circulation structure, hydrography and eddy kinetic
energy in the Fram Strait .
Observational basis: radar altimetry data
In the present study high-frequency radar altimetry data of the ESA satellite
Envisat are used. The altimeter emits radar signals in the Ku band with a
footprint (i.e., circular area on the ground illuminated by the radar) of
approximately 10 km diameter . Envisat belongs to the
pulse-limited altimetry missions and provides observations characterized by a
spatial along-track resolution of circa 372 m (18 Hz). The mission was placed
in orbit in 2002 and provided altimetry data until the end of March 2012. This
study uses high-frequency waveform data that are extracted from the official
Sensor Geophysical Data Records (SGDR) version 2.1 provided by ESA. Data
measured during the nominal mission period (May 2002–October 2010) are organized
into 35-day repeat cycles including a fixed relative orbit number (i.e., pass,
from pole to pole) of 1002 passes per cycle . However,
the first cycles of Envisat are affected by various instrumental issues and
are not considered for the present study. Considering the temporal
availability of FESOM and reliable observations of Envisat, SGDR data of a
period covering 7 complete years (2003–2009) are used. Before using the
Envisat altimetry observations, a classification is performed to eliminate
sea-ice-contaminated measurements. Sea surface heights (SSHs) are calculated
by applying the ALES+ retracking algorithm and geophysical
corrections. Unrealistic or bad height measurements are excluded by
performing an outlier detection based on sea level anomalies. Finally, a
transformation to physical heights (dynamic ocean topography, DOT) is
processed by subtracting geoid heights from SSH. The following subsections
describe the individual preprocessing steps in more detail.
Sea ice and water discrimination
Most of the Arctic regions are affected by seasonal sea ice cover, which
can prevent a reliable estimation of sea surface heights due to a direct
impact on the reflected radar pulses. In order to overcome this difficulty
and to allow for a SSH comparison with FESOM, a classification is performed
to detect small open water gaps (e.g., leads, polynyas) within the sea-ice-covered area. For this purpose an unsupervised classification approach
(i.e., without the use of any training data) based only on radar waveforms and
derived parameters is applied. Several classification methods have been
developed within the last years, which are all based on the analysis of the
returned satellite radar echo (e.g., ).
Most of them impose thresholds on one or more
parameters of the radar waveforms (e.g., maximum power or backscatter
coefficient). In this study, an unsupervised classification approach is
applied, which is independent of any training data. This method performed
best in a recent study assessing the quality of different classification
approaches with respect to very high resolution airborne imagery
. Briefly summarized, the unsupervised classification
approach, described by , groups an unassigned subset of
altimetry radar waveforms into a predefined number of classes by applying a
partitional cluster algorithm (i.e., k-medoids; see
) in order to establish a reference waveform
model to indicate different waveform and surface characteristics. In the
following step, the generated waveform model acts as kind of assignment map
for the remaining waveforms, which are allocated to the particular classes
using a simple k-nearest-neighbor classifier. Further information and
explanations can be found in . The open water (leads, polynyas
and open ocean) observations are used for all following processing steps.
Measurements classified as ice are removed from the dataset. However, it has
to be noted that some misclassifications, e.g., due to the presence of fast
ice, can still remain in the observation dataset . During
sea ice melt season, melt ponds and water bodies on top the sea ice layer can
cause uncertainties in the computation of sea surface heights. The
unsupervised classification is not fully tuned to discriminate carefully
between radar waveforms originating from melt ponds or leads at the sea
surface level. In the case of misclassification the estimated altimeter ranges
can appear too short.
Sea surface height estimation
SSH is obtained by subtracting the measured range between satellite and
water surface (including geophysical corrections) from the orbital altitude
(i.e., ellipsoid height) of the satellite's center of mass. The range can be
calculated by fitting a waveform model (e.g., , or ) to
the individual radar returning signals. More information regarding retracking
strategies can be found for example in . Several retracking
algorithms have been developed and optimized for special applications,
surface conditions or study regions (e.g., open ocean, sea ice or inland water
bodies). According to the northern Nordic seas are
characterized by rapidly changing environmental conditions, making it difficult
to use just one retracking algorithm. However, when combining heights derived
with different retrackers, systematic offsets due to different retracker
biases will be introduced (). The usage of ALES+ overcomes this
problem by adapting a subwaveform application of the classic open ocean
functional form to different shapes of the radar signals, including the typical
peaky signal shape of the returns from small leads and corrupted trailing
edges typical of coastal waveforms. have developed and tested
the algorithm against standard open ocean and lead retrackers and showed
improvements in precision and in terms of comparison with a local tide gauge.
The algorithm was used to develop Arctic and Antarctic products in the
framework of the ESA Sea Level Climate Change Initiative .
After the retracking, the altimeter ranges are corrected for geophysical and
atmospheric effects using external model data. Wind and wave effects are
considered by using the sea state bias estimates of the ALES+ retracking
approach. Furthermore a mean range bias correction, computed by a
multi-mission crossover analysis , is included to eliminate a
known constant offset in the Envisat range measurements. One important
correction is the ocean tide correction since the FESOM model does not
include ocean tides. In this study, we use EOT11a ()
to correct for tidal effects. Even if EOT11a is a
global ocean tide model it performs reasonably well in the Arctic Ocean
. This study performs a validation by comparing different
tide models to tide gauge data. For the Arctic Ocean, EOT11a shows rms values
between 1.4 and 4.6 cm for the four major constituents, and it is the
second best of the seven models in the test. Table lists
all corrections used within the present investigation.
Geophysical and empirical altimetry corrections applied in the
study.
CorrectionsSourcesReferencesIonosphereNOAA Ionosphere Climatology 2009 (NIC09)Wet troposphereECMWF (2.5–2.0∘) for Vienna Mapping Functions (VMF1)Dry troposphereECMWF (2.5–2.0∘) for Vienna Mapping Functions (VMF1)Dynamic atmospheric correctionInverse barometric pressure + (MOG2D)HFOcean tidesGlobal Empirical Ocean Tide model (EOT11a)Pole tidesFrom Envisat SGDR v2.1Solid Earth tidesFrom Envisat SGDR v2.1Radial errorsMulti-mission Cross-Calibration (MMXO) version 15Sea state biasALES+ sea state bias correction
To remove erroneous and unreliable sea surface height observations from the
dataset, an outlier rejection is performed by applying a fixed threshold
criterion. The SSH observations are compared to a long temporal mean sea
surface (MSS), including more than 20 years of altimetry data, and sea level
anomalies (SLAs) are built. The conversion is done by removing the DTU15MSS
developed by from the along-track sea surface heights. Without
being too restrictive within the sea ice zones with a higher noise level than in
open ocean, a threshold of ±2 m is introduced. This rejects 1.54 % of
the high-frequency measurements of Envisat. After removing outliers the
revised dataset is retransformed to sea surface heights by re-adding the MSS.
Dynamic ocean topography estimation
After obtaining sea surface heights the transition to physical heights is
performed with respect to an underlying geoid model (i.e., the computation of
DOT). In the present investigation the high-resolution Optimal Geoid Model
for Modeling Ocean Circulation (OGMOC), developed up to a harmonic degree of
2190 and corresponding to a spatial resolution of nearly 9.13 km, is applied.
This is one of the latest high-resolution global geoid models incorporating
the most recent satellite gravimetry and satellite altimetry datasets.
Moreover it is optimized for estimating ocean currents and it is assumed to
provide the best possible solution for the current application. More details
regarding to the constituents and processing strategy of the geoid can be
found in and . Briefly summarized, OGMOC is a
combination of XGM2016 and the EIGEN6-C4 model
. XGM2016 is used up to degree 619. Between 619 and 719,
XGM2016 and EIGEN6-C4 are combined applying a weighting function. Higher
harmonic degrees (>719) are retained unchanged from the EIGEN6-C4 model.
To minimize noise within the high-frequency altimetry database and to be more
consistent with the spatial resolution of the geoid, the corrected
along-track SSH observations get low-pass filtered by applying a moving
average using a rectangle kernel adapted to the spatial resolution of the
used geoid (9.13 km). Areas with sparse availability of along-track
observations (e.g., leads, polynyas) less than the window size are not
considered in the filtering process and remain unfiltered in the dataset. The
DOT is derived by interpolating the geoid heights to the altimetry locations
and subtracting them from the SSH observations.
Methods and results
The preprocessed ocean heights from altimetry and FESOM are compared with
each other to identify similarities and discrepancies and to explore the
possibility of a combination. Therefore, in the first step, both datasets are
analyzed and examined regarding their temporal and spatial characteristics.
The datasets are investigated in terms of constant offsets, seasonally
occurring patterns (e.g., annual sea level variability) and residual sea
level variations.
The FESOM data are provided on daily unstructured grids with local refinements
in the central Greenland Sea and the Fram Strait. In contrast, the altimetry
observations are sampled along-track and characterized by a high spatial
resolution with irregular data gaps due to sea ice coverage. Figure
displays the inhomogeneously distributed FESOM nodes showing a
maximum resolution of about 1 km. Moreover, three representative days of
altimetry along-track data are shown with different behavior in observation
availability depending on the season and the presence of sea ice. During the
sea ice maximum in March most of the altimetry data
close to the Greenland coast are missing due to a semi-closed sea ice cover.
In contrast, in the summer season the tracks show fewer data gaps.
Locations of selected altimetry observations in wintertime and
summertime. The small black dots indicate the unstructured FESOM grid
nodes migrating at higher latitudes to a apparently closed black background.
In order to allow a direct and pointwise comparison of both datasets, a
resampling of at least one of them is necessary. Since the FESOM data
exhibit a significantly higher spatial and a uniform temporal resolution,
they will be interpolated using a nearest-neighbor algorithm with the times and
locations of the altimetry observations. This prevents an unnecessary
smoothing of the altimetry data.
Assessment of the annual cycle
It can be expected that the annual sea level variability is the
dominant signal contained in both datasets (e.g., ). The
present analysis performs a comparison of the annual and remaining
temporal signal components within the investigation period by fitting
harmonic functions to both datasets.
In the first step, daily height averages for the entire region are computed.
Figure shows the temporal evolution of the daily means
within the investigation period for both datasets. An obvious offset of about
41 cm between the datasets caused by different underlying height references
(geoid vs. bathymetry) is clearly visible. Furthermore, a linear trend or
another long-term systematic behavior is not detectable, probably due to the
short period of only 7 years. However, the altimetry-derived daily
averaged DOT shows larger variations and a standard deviation of 9.0 cm. In
contrast, the modeled data are characterized by a smoother behavior and a
smaller standard deviation of 4.7 cm. These numbers include a clear seasonal
cycle, which is also clearly visible in Fig. 3.
Temporal evolution of daily means of altimetry-derived DOT
observations (blue) and FESOM SSH outputs (interpolated to the locations
of altimetry measurements, red) within the investigation period and study
area (see Sect. ).
In order to examine both datasets concerning their annual period, the daily
means are analyzed by a Fourier analysis (e.g., ). Therefore,
both time series are centered at zero by reducing their constant offsets
before the Fourier coefficients are obtained by applying a least-squares
estimation (e.g., ).
Figure a displays the amplitude spectrum of the
interpolated FESOM and profiled altimetry daily means between 2003 and 2009.
The modeled data are characterized by weaker amplitudes. The annual period
constitutes the most dominant long-period signal. In the case of altimetry, the
annual amplitude represents 6.9 cm and, in the case of FESOM, 3.9 cm of the sea
level variability. Other frequencies can not be physically explained and thus
are not further investigated in the present study. In particular, the
semiannual signal is very small (1.5 cm) and shows no significant impact on
both datasets. The remaining amplitudes are smaller than 1.5 cm in the case of
altimetry (1.0 cm, FESOM).
However, an amplitude of almost 2 cm is detectable for a period of 3 days, which cannot be assigned to ocean or sea-ice-related dynamics. This is
an artifact possibly caused by the irregular data sampling. In order to prove
this hypothesis, the frequency analysis is also performed for the full FESOM
grid. Figure b shows the amplitude spectrum and the
estimated periods for the daily profiled FESOM DOT (red) and the original
FESOM DOT (black). It can be clearly observed that the 3-day period is
not confirmed by the original dataset. Moreover, higher discrepancies can be
found in the short periodic domain, which can be attributed to more
variability due to more input information. However, all other dominant
periods are caught by both datasets. The obtained amplitudes show good
agreement in all periods except for the annual signal. Here, the irregularly
sampled profile data overestimate the amplitude by about 1 cm. This might be
related to alias effects from remaining tidal influence due to the repeat
cycle of Envisat (see Sect. for more details).
Fourier analysis amplitude spectrum of two altimetry locations interpolated
with FESOM data (red) from (a) altimetry-derived DOT along-track observations (blue)
and (b) original FESOM data (black) within the investigation area from 2003 to 2009
(see Sect. ).
As mentioned earlier the annual signal represents the most dominant signal in
both datasets. By introducing the obtained annual Fourier coefficients to a
harmonic fitting, the temporal evolution and the phasing can be shown (see
Fig. ). Aside from differences in the annual amplitudes,
a phase shift of about 29 days is recognizable between the two signals. The
maximum is reached at day of year (DOY) 230 (18 August) for altimetry and
in the case of FESOM at DOY 259 (16 September).
Annual cycles of DOT from along-track altimetry (blue) observations
and FESOM (red) simulations within the investigation time and area (see Sect. ).
However, it is obvious that one single harmonic function cannot represent the
full complexity of the DOT variations in the northern Nordic seas. A detailed
analysis of the annual signal considering different bathymetric features
(e.g., shelf or deep sea areas) brings the opportunity to estimate region-dependent annual amplitudes and phases. This is presented in the following
section.
Spatiotemporal pattern analysis
In order to analyze regionally dependent differences, the profiled altimetry
data are monthly averaged and arranged into along-track bins of 7.5 km length.
The bin structure follows the nominal 1 Hz ground track pattern of Envisat
and reduces the high-frequency measurement noise. Enabling long-term
analyses, only satellite passes are admitted showing an availability of at
least 64 repeat cycles, which corresponds to 96 % of the data in the
evaluation period. Data gaps or missing bins are possible due to sea ice
contamination or failing observations. For FESOM, daily data from the closest
grid node are assigned to each bin. Thus, this dataset exhibits the same
spatial resolution but a better temporal resolution, allowing for a more precise
amplitude estimation.
Figure displays for each bin the estimated annual DOT variations
within 2003–2009. The amplitudes of both datasets show a similar pattern
with smaller values along the major current systems (EGC and WSC) and larger
values along the Greenland and Svalbard coasts and in the area around the
Molloy Hole. In general, the altimetry-derived amplitudes are larger than the
model amplitudes. In the Greenland Basin, a 2–3 times stronger representation
of the annual amplitudes can be observed. Here, the mean altimetry amplitude
reaches 6.3 cm. In the southern and eastern parts of the shelf regions, the
altimetry amplitudes are smaller than the model amplitudes.
The maximum amplitudes in the Greenland Basin appear during August and
September and show a mostly homogeneous distribution in both datasets. In
ice-free regions both datasets show good agreement (also in comparison with
results of , and ). However, in ice-covered shelf regions, the central Fram Strait and close to calving glaciers,
the derived amplitudes differ up to 8 cm. The altimetry estimated annual
maximum on the Greenland Shelf occurs in November, which is confirmed by
FESOM. Nevertheless, obvious phase differences between FESOM and altimetry
can be found east of Spitsbergen, where the observed annual maximum
occurs in the early spring months, in contrast to FESOM displaying a maximum
in autumn. This could perhaps be caused by sea ice interference or strong
ocean variabilities.
In order to account for different hydrological (e.g., glacier melt, water mass
changes), atmospheric (e.g., winds, solar radiation) and oceanographic effects
(e.g., ocean currents) in the study area, the region is subdivided into three
main subareas: the deep basin region (Greenland Basin, <-450 m) and two shelf
regions (Greenland Shelf, Barents Sea). Table provides
outlier-removed (3σ criterion) mean amplitudes and DOYs of the maximum
amplitude for the three subregions, as well as their annual variabilities.
FESOM shows similar amplitudes for all three areas, whereas altimetry
exhibits smaller mean amplitudes for the Barents Sea than for the two other
regions, where the mean amplitudes are about twice the amplitudes of FESOM.
The phase shows good consistency between altimetry and FESOM on the Greenland
Shelf but discrepancies of circa 34.25 days in the Greenland Basin and 19.5 days
in the Barents Sea. A discussion of the differences is provided in Sect. .
Mean annual amplitudes (a, c, e) and the day of year (DOY) of the annual maximum
(b, d, f) per bin for altimetry (a, b) and FESOM (c, d) DOT heights.
The bottom row (e, f) displays
amplitude (in m) and phase differences (in days) of altimetry minus FESOM. RTopo2
bathymetric contours (black) indicate the shelf (-450 m) and the basin (-1500 m) regions.
The dashed lines highlight the Barents Sea boundary (). Note the different
scales of the amplitude color bars.
Offset, averaged annual amplitude (Amp) and DOY/month of
maximum amplitude with variability (Var) in three subregions.
In order to analyze residual differences, both datasets are reduced by their
regional estimated annual signal and constant offsets as given in
Table . Figure shows monthly averaged
along-track residual DOT for altimetry and FESOM for the three study regions.
In all areas, a high correlation between the datasets is visible. For the
Greenland Basin and the Barents Sea, almost no systematic effects are
detectable, whereas the altimetry time series for the Greenland Shelf
exhibits multi-annual anomalies that are less pronounced in the FESOM time
series, which only shows a small, insignificant behavior trends. However, the
investigation period is too short to allow for a reliable interpretation of
the underlying effects.
Monthly time series of averaged residual heights from altimetry (blue)
and FESOM (red). Offsets and annual signals were removed for each region.
Additionally, scatter plots and correlation (ρ) are displayed. Regression
and bisectrix lines are shown by the purple and dashed gray lines, respectively.
Figure shows the geographical distribution of the mean
residual signals and weighted average of standard deviation per bin. Both
datasets display similar spatial patterns. However, obvious differences can
be seen in some areas, e.g., the central Fram Strait and the transition areas
between the deep basin and shelf regions. Comparing the variability of the
residuals, the altimetry-derived DOT shows in general higher values and an
enhanced variations in the ice-covered shelf areas, contrary to FESOM
displaying more variability in regions affected by ocean currents.
Figure shows the differences between the averaged residual DOT
of altimetry and FESOM (left) as well as their correlation per bin (right).
The largest differences occur on the northern Greenland Shelf and in the Fram
Strait, whereas fewer sea-ice-affected areas (e.g., Greenland Basin, Barents
Sea), including the current and eddy regions (e.g., WSC), show good agreement.
The correlations are mainly positive, with values above 0.5 % for 21 % of the
bins. High positive correlations are displayed in the deep basin parts of the
study area. Smaller positive correlations can be found in regions with strong
bathymetric gradients and in northern areas of the major ocean currents
(e.g., WSC, EGC).
Weighted mean residual DOT (a, b) and weighted mean of standard
deviation (c, f) for each bin from altimetry (a, c) and FESOM
(b, d) within 2003–2009.
Note the different scales of standard deviation color bars.
Differences (a) and correlations (b) between altimetry and FESOM binned
along-track residual DOT within the investigation period.
Remarkable elevation differences occur between 80 and 82∘ N. These
patterns are seen in the altimetry-derived DOT but not in the model and
yield up to 0.4 m. They show a constant behavior within the entire
investigation period, which cannot be attributed to seasonal ocean phenomena.
Instead, these artifacts are due to geoid errors caused by residual ocean
signals at polar latitudes (e.g., ).
More discussion related to the geoid can be found in the next section.
Discussion
The comparison of the altimetry-derived and simulated DOT
shows good agreement in terms of highly correlated regional time series and
small residual heights. Predominately positive correlations between both
datasets can be found in ice-free areas (e.g., Greenland Basin) and in regions
affected by ocean currents. FESOM and altimetry display a very similar
frequency behavior for the most dominant periodic DOT variability. In
comparison with previous studies, the along-track altimetry DOT agrees
concerning annual amplitudes and phases as obtained by
and .
However, the analysis also reveals some systematic discrepancies. These can
be explained by three different error sources: they partly originate from
modeling errors of FESOM, partly from measurement uncertainties of altimetry
and partly from errors of the geoid used for computing the altimetry DOT.
These points will be discussed in more detail in the following paragraphs.
FESOM is affected by synthetic smoothing due to the added numerical
diffusion component stabilizing the model runs and preventing the simulated DOT
from uncontrolled variabilities. Moreover, in the present investigation the
FESOM run does not include the latest glacier runoff model, which causes
further irregularities close to northeastern Greenland's coast. Another reason
causing this smoothing effect can be found in the too strongly adjusted sea ice
friction coefficient of the model, damping DOT variabilities in sea-ice-affected regions. The model applies strictly the hydrostatic equations, which
function as an assumption of the real sea state. Furthermore, it does not
include tidal ocean signal and barometric effects and lacks a steric
correction to ensure the global conservation of mass.
While the first two points are taken into account by correcting the altimetry
observations, the latter point is currently not considered in the comparison.
This should be acceptable since the impact on low-frequency regional sea
level patterns is small (). However, it will contribute to
the constant and long-term differences visible in this study. In contrast,
remaining differences in handling the atmospheric sea level pressure
(i.e., caused by uncertainties of the used correction model) will show up in
regional differences. They might be the reason for the observed temporal
shifts of the maximum annual signal in the Greenland Basin. Even more
important is the insufficiently realistic consideration of freshwater
inflow (e.g., by glacier runoff) by FESOM. This can cause phase shifts as well
as reduced annual amplitudes. Furthermore the coarse resolution of
atmospheric forcing is an additional reason for a smoothed sea level
representation and an underestimation of annual amplitudes.
For satellite altimetry, the polar oceans are a challenging region,
especially when sea ice is present. In these areas, the returned radar
echoes are comprised of signals from different surface reflectors such as different
ice types and structures, melt ponds on ice and open water. The challenge is
to extract valuable information about the sea level while disregarding all other
reflectors. Even with the application of a dedicated waveform classification
and special retracking, as performed here, DOT estimates in coastal and
sea ice areas are significantly more noisy than in open ocean. Moreover, the
applied range corrections can be biased by the Arctic Ocean conditions,
leading to more unreliable range estimations in ice-covered shelf regions.
Thus, in these regions, small-scale structures are not thoroughly reliable.
Due to its measurement geometry, satellite altimetry has a high along-track
resolution, but data are scattered in time and space. In addition, in polar
regions, an irregular sampling due to missing data caused by sea ice coverage
must be taken into account. This can significantly influence the estimation
of annual sea level variability, as tests with simulated data with different
sampling revealed (see Sect. ).
However, an interpolation of the dataset as it is done in the majority of
other studies (e.g., )
could be avoided in order to conserve more high-frequency observations and
spectral content.
This study is based on data from Envisat, whose repeat cycle is known to cause
severe alias effects of 365 days for the tidal constituents K1 and P1
(see , and ). Thus, errors in K1 and P1 in the
applied ocean tide model may impact the estimated annual variation of the
altimetry-based DOT. showed that the effect can reach up
to 1–3 cm. For this study, the EOT11a ocean tide model () is
used. Even if that model is proven to be among the best models of the Arctic
Ocean (see ) the differences between FESOM and altimetry in
the bin-wise estimated annual amplitudes could be partially attributed to
this aliasing effect. However, the analysis presented in Sect. ,
which is based on averaged Envisat data, also shows a discrepancy of more
than 1 cm between FESOM and altimetry amplitudes. Thus, the majority of this
difference will be due to the smoothing effect of FESOM.
In addition to simulated and observational data irregularities, stationary artifacts
caused by geoid inaccuracies can be clearly identified in the northern Fram
Strait region. Following these synthetic looking elevations
in the altimetry-derived DOT can be attributed to a combination of geoid
residuals and oceanographic features, which are very challenging to separate
from each other. A significant problem can be seen in the specific components
of the geoid models. The higher spherical harmonics (degrees 720–2190),
describing shorter wavelength patterns (10–30 km), are based on
selective in situ and satellite altimetry gravity observations, which can be
contaminated by sea ice or feature sparse availability. Within this
study, one of the newest geoid models is used, which has been developed for
ocean circulation studies and has been optimized to avoid striations and
orange skin-like features. Nevertheless, it seems to contain the remaining
artificial structures in the study area. According to , the
higher spherical harmonics are covered by EIGEN6-C4 geoid model
, which does not include current satellite altimetry data.
However, mid spherical harmonic degrees, corresponding to a 30–100 km
spatial wavelength, are represented by XGM2016 including
the latest altimetry marine gravity fields. Hence, a better representation of
short wavelength patterns can only be reached by introducing the latest and
updated altimetry data, supported by in situ measurements of the geoid
computations. Similar effects are also visible when using alternative geoid
models .
Conclusions and outlook
In the present paper, high-frequency altimetry-derived DOT is
compared with water elevations of FESOM in order to identify their similarities and
discrepancies as well as their respective benefits. Both datasets are characterized
by different limitations, which prevent a perfect representation of the
dynamic topography in polar regions based on only one approach. The
present investigation demonstrates that model simulations and observations
are both needed to understand the complexity of ocean processes in the polar
latitudes, especially in the Arctic Ocean.
The present paper shows basic agreement between a numerically simulated and
an empirical estimated representation of the DOT in the northern Nordic seas
in terms of annual variability and spatial behavior. However, inconsistencies
due to the higher noise level of the observations, especially in sea ice
areas, and the enhanced smoothing of the model are demonstrated. For example,
an offset of about half a meter exists between the two datasets since the
data of FESOM are not defined with respect to a standard reference frame
. Moreover, the annual sea level variability observed by
the two datasets differs by a few centimeters. The residual heights show a
similar pattern, high temporal correlations and only small differences, which
are mainly related to sea ice coverage and geoid artifacts.
The results presented in this paper indicate that further improvements can be
made to both datasets: the altimetry-derived DOT still needs a better or
more restrictive handling of sea ice observations as well as a more reliable
Arctic geoid. FESOM should be corrected for a global mean steric height
change () in order to ensure the conservation of mass and
to make the observed altimetry heights directly comparable to the model
heights. In addition, an improved handling of freshwater inflow is required
to better account for mass changes due to glacier as well as river runoff.
However, even if these points will be improved, the principal limitations of
observations (measurement noise and data gaps in regions with closed sea ice
coverage) and models (absolute height level) will persist. Thus, it seems
reasonable to exploit the advantages of both datasets through a combination of
model and along-track observations. This will enable the derivation of a
homogeneous DOT, equally sampled in time and space without the need of
smoothing the altimetry measurements by gridding procedures. In such an
approach, the absolute level as well as the annual variability of altimetry
should be preserved, and the continuous spatial representation of the model
should be used to bridge regions influenced by sea ice coverage and to get rid
of unreliable high-latitude geoid artifacts. This will allow for an optimized
determination of the Arctic DOT and the associated surface currents.
Concerning the current availability of altimetry-derived DOT estimations, it
is possible to establish a combination of simulated and observation-based DOT representation covering more than 25 years, enabling climate-relevant
conclusions.
Envisat RA2 altimetry data access is available from ESA
after fast registration submission (10.5270/EN1-85m0a7b,
).
The FESOM data can be requested from Alfred Wegener Institute. A final
combined data product will be provided via PANGAEA (https://www.pangaea.de/,
last access: 13 February 2019)
once the project is completed.
FLM developed the comparison methods, conducted
the data analysis and wrote the majority of the paper. CW provided the
FESOM data and contributed to the manuscript writing. DD supervised
the present study, contributed to the manuscript writing and helped with discussions
of the results. MP developed the retracking algorithm and helped with
the application and discussion concerning the altimetry dataset. WB
initiated the study. FS supervised the research.
The authors declare that they have no conflict of interest.
Acknowledgements
The authors thank the ESA for operating Envisat and for supplying the SGDR v2.1
dataset. The authors thank the Chair of Astronomical and Physical Geodesy,
Technical University of Munich (TUM), for providing the geoid model, OGMOC.
This work was mainly supported by the German Research Foundation (DFG)
through grants BO1228/13-1, DE2174/3-1 and in part through grant OGreen79
as part of the Special Priority Program (SPP)-1889 ”Regional Sea Level Change
and Society” (SeaLevel). We thank Sine M. Hvidegaard
and two further anonymous reviewers for their valuable comments that helped
to improve the manuscript.
This work was supported by the German Research Foundation (DFG) and the
Technical University of Munich (TUM) in the framework of the Open Access
Publishing Program.
Edited by: David M. Holland
Reviewed by: Sine M. Hvidegaard and two anonymous referees
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