Sea surface height and dynamic topography of the ice-covered oceans from CryoSat-2: 2011–2014
Abstract
We examine 4 years (2011–2014) of sea surface heights (SSH) from CryoSat-2 (CS-2) over the ice-covered Arctic and Southern Oceans. Results are from a procedure that identifies and determines the heights of sea surface returns. Along 25 km segments of satellite ground tracks, variability in the retrieved SSHs is between ∼2 and 3 cm (standard deviation) in the Arctic and is slightly higher (∼3 cm) in the summer and the Southern Ocean. Average sea surface tilts (along these 25 km segments) are 0.01 ± 3.8 cm/10 km in the Arctic, and slightly lower (0.01 ± 2.0 cm/10 km) in the Southern Ocean. Intra-seasonal variability of CS-2 dynamic ocean topography (DOT) in the ice-covered Arctic is nearly twice as high as that of the Southern Ocean. In the Arctic, we find a correlation of 0.92 between 3 years of DOT and dynamic heights (DH) from hydrographic stations. Further, correlation of 4 years of area-averaged CS-2 DOT near the North Pole with time-variable ocean-bottom pressure from a pressure gauge and from GRACE, yields coefficients of 0.83 and 0.77, with corresponding differences of <3 cm (RMS). These comparisons contrast the length scale of baroclinic and barotropic features and reveal the smaller amplitude barotropic signals in the Arctic Ocean. Broadly, the mean DOT from CS-2 for both poles compares well with those from the ICESat campaigns and the DOT2008A and DTU13MDT fields. Short length scale topographic variations, due to oceanographic signals and geoid residuals, are especially prominent in the Arctic Basin but less so in the Southern Ocean.
Key Points:
- Time-varying dynamic topography of ice-covered oceans from CryoSat-2
- Assessment with dynamic height from hydrographic stations and ocean bottom pressure
- Relative length scale and amplitude of baroclinic and barotropic signals in Arctic Ocean
1 Introduction
For lower latitude oceans, satellite altimetry has provided synoptic-scale measurements of sea surface topography with the TOPEX/Poseidon and follow-on missions. For the ice-covered oceans of the northern and southern hemispheres, however, sampling of the sea surface is limited to only a few percent of openings within bounds of a satellite's inclination. Moreover, special procedures are required to separate the returns of the ocean surface from those contaminated by sea ice. Since 2003, however, dedicated ice missions (e.g., ICESat, CS-2) with higher orbit inclinations have increased the availability and quality of sea surface height data. An examination of CS-2 sea surface height (SSH) within the ice-covered oceans is the subject of this paper.
Radar altimeters on early ESA's ERS (1990–2011) and Envisat (2002–2012) missions, though not optimized for remote sensing of the sea ice covers, have provided valuable observations of the polar ice covers. Using ERS-2 radar echoes from open leads, Peacock and Laxon [2004] offered a first look at SSH of the Arctic Ocean. Recently, Giles et al. [2012] demonstrated that increases in height of the Beaufort Sea surface, due to increased strength of the Beaufort High and local freshwater content [Proshutinsky et al., 2009], can be seen in a time series (1995–2010) of SSH from these radar altimeters. The CryoSat-2 mission [Wingham et al., 2006], launched in 2010, stems from the experience garnered from these earlier missions.
The higher resolution (footprint: 50–70 m) and precision of the lidar (shot-to-shot repeatability of ∼2–3 cm) on ICESat (2003–2009) [Zwally et al., 2002] allowed unambiguous identification of new openings (of water or thin ice) and supplied another source of SSHs over the polar ocean [Kwok et al., 2004]. Using estimates of SSHs from ICESat, a number of investigators have provided assessments of DOTs of the Arctic Ocean, and produced mean fields from SSH estimates provided by ICESat, ERS and Envisat [e.g., Forsberg and Skourup, 2005; Forsberg et al., 2006; Kwok and Morison, 2011; Farrell et al., 2012]. In particular, Kwok and Morison [2011] found significant correlations (0.92) between ICESat-derived DOTs and dynamic heights from in situ hydrography, highlighting the larger baroclinic signals in the Arctic Ocean. The combined spatial changes in ICESat DOT, GRACE ocean bottom pressure, and hydrography between 2005 and 2008 were used by Morison et al. [2012] to show that recent increases in Arctic freshwater content were due to a cyclonic shift in the ocean pathway of Eurasian runoff is forced by the strengthening of the west-to-east Northern Hemisphere atmospheric circulation associated with the Arctic Oscillation. These results demonstrated an important oceanographic utility of accurate time-varying DOTs.
Both the time-mean and time-varying DOT are of interest to oceanographers. The use of SSH is limited in its broadest applications by the uncertainty in geoid models and their implied geoid slopes [Martel and Wunsch, 1993; Wunsch, 1996]. The time-mean DOT (MDT) used to calculate surface geostrophic currents and ocean transports are particularly sensitive to geoid residuals since accurate models of the gravitational field are required to separate the marine geoid and oceanographic signals. On the other hand, detection of time-varying changes in sea level or ocean surface topography is less sensitive to static geoid residuals. Here, we focus on the time-mean and time-varying signal in the DOTs from CS-2. While ICESat offered only two to three 34 day mapping campaigns annually during its mission life, the monthly maps of SSH from CS-2 provide more frequent temporal mappings of the polar oceans. This allows for a closer look at the time-varying component of the ocean's topography.
In this paper, the SSH of the ice-covered oceans spanning a period of more than 4 years (2011–2014) is examined. The aim is to assess the quality of the 4 year DOT data set of the Arctic and Southern Oceans by examining its variability and, where available, by comparison with time-varying dynamic heights from hydrographic stations and time-varying gravity from satellites. The paper is structured as follows. The next section describes the data sets used in our analyses. In Section 3, the approach used to separate the sea surface returns from radar echoes of sea ice is outlined. Section 4 examines the SSH of the Arctic for the 4 years. The time-varying DOTs are compared with dynamic heights (DH) derived from hydrographic surveys in the Arctic, and with time-varying ocean mass from a bottom pressure sensor near the North Pole and from GRACE. We also compare the Arctic MDTs from ICESat, CS-2, DOT2008A, and DTU13MDT. The DOT results over the Southern Ocean are summarized in section 5. The Antarctic MDTs are also compared with those from ICESat, CS-2, DOT2008A, and DTU13MDT. Summary remarks and conclusions are provided in the last section.
2 Data Description
2.1 CryoSat-2 Altimeter Data Set
We use the altimeter data acquired by the Synthetic Aperture Radar (SAR) Interferometric Radar ALtimeter (SIRAL) instrument on CryoSat-2 (CS-2). This data set is available through ESA's data portal (URL: https://earth.esa.int). The synthesized footprint of the SAR altimeter is nominally 0.31 km by 1.67 km in the along- and across- track directions, and multiple-looks of returns from the surface are used to reduce noise due to radar speckle [Bouzinac, 2013]. The recorded altimetric waveforms (both SAR and SARIn modes) and the required parameters for the analysis in this paper are from the Level 1B and Level 2 products. Waveform amplitudes are sampled according to radar ranges referenced to the WGS84 elliposid. The interferometeric mode of SIRAL (SARIn) has been operated over parts of the Arctic but only the altimetric waveforms are used here. When the radar is operated in the SARIn mode, the processed returns are noisier because of the lower burst mode frequency. No relative adjustments of the SSH's from the SAR and SARIn modes are needed.
2.2 Ocean Bottom Pressure (OBP) Time Series
The 4 year record (2010–2014) of Arctic bottom pressure data from a pressure and tide gauge is from North Pole Environmental Observatory (NPEO). The particular time series of bottom pressure used here is from Arctic Bottom Pressure Recorder (ABPR) 5, which has been in continuous operation from Spring 2010 to Spring 2014 at 89° 58.64'N, 28° 19.55'W. This has been the replacement for the earlier generation ABPR 1-4 in place in the North Pole region between 2004 and 2010 [Morison et al., 2007; Peralta-Ferriz et al., 2011], and is based on those from the tsunami early warning system. Easy-To-Deploy (ETD) bottom pressure gauges have proven to be more reliable and drift free compared to the earlier ABPRs. Any long-term drift errors are removed using monthly OBP observations from GRACE, without compromising the high-frequency variations in OBP.
2.3 Hydrographic Data
Hydrographic data come from the North Pole Environmental Observatory (NPEO) annual April airborne hydrographic surveys from 2011 to 2013. These are similar to those discussed by Morison et al. [2006, 2007] and Alkire et al. [2010]. The 2011–2013 data set includes 36 stations made by landing an aircraft on the sea ice in the North Pole region and measuring ocean temperature and salinity profiles to 800 m depth with a Conductivity-Temperature-Depth (CTD) instrument and recovering water samples for chemical analysis. These data were supplemented with 23 deep-water CTD stations made by the Switchyard program in the Lincoln Sea. Of these, 23 from each of NPEO and Switchyard were south of 88°N and used in our analyses. For comparison with CryoSat-2 altimetry, dynamic heights, the integral of specific volume between pressure surfaces, relative to 500 dbar were computed for each of these 46 stations.
2.4 GRACE Time-Varying Gravity Over Ocean
Estimates of mass changes over the oceans [Chambers and Bonin, 2012; Chambers and Willis, 2010]–in centimeters of equivalent-water-thickness–are based on Release-05 (RL05) of the time-variable gravity coefficients from the GRACE (Gravity Recovery and Climate Experiment) mission provided by the Center for Space Research (CSR) (URL– http://grace.jpl.nasa.gov/data/get-data/monthly-mass-grids-ocean/). The processing includes a correction for the postglacial rebound using the model of Geruo et al. [2013] , and a destriping algorithm [Chambers, 2006] to remove the north–south propagating errors of the gravity coefficients described by Swenson and Wahr [2006]. The data are also filtered with a 500 km-radius Gaussian, and a spherical harmonic filter cutoff at 40. Monthly means of the Ocean Model for Circulation and Tides (OMCT) are added back to the GRACE solutions to obtain OBP variations. A special algorithm has been applied to minimize the leakage from land signals onto ocean signals. The standard error is expected to be about 1 cm (equivalent water thickness) in the low- and midlatitudes, and between 1.5 and 2 cm in the polar and subpolar oceans.
3 Sea Surface Returns
In this section, we first describe our approach to determine the altimetric heights of sea surface returns in CS-2 waveforms (referred to as retracking) from the ice-covered oceans. This is followed by an assessment of the retrieved SSHs.
3.1 Ice/Water Discrimination and Sea Surface Height
CS-2 waveforms contain the range-varying return (power) of the SAR footprints, and the range to the surface is derived from these waveforms. Returns from sea ice are more variable and complex due to large variability in surface relief, but returns from the flat surface of open water leads or thin ice are somewhat simpler. While different CS-2 retracking techniques over sea ice [e.g., Wingham et al., 2006, Laxon et al., 2013, Ricker et al., 2014, Kurtz et al., 2014, Jain et al., 2015] have been suggested and devised, and sensitivities of specific techniques analyzed [Ricker et al., 2014], an optimal retracking approach that addresses the scattering issues in radar echoes especially in footprints that contain mixtures of ice and water has been difficult to establish. Since the focus here is on retrieving SSHs, we describe only those waveform characteristics than allow us to unambiguously identify the nearly pure sea surface returns.
The identification of open water returns in the ice cover relies on the specular character of reflections from leads (containing either open water or thin ice) at near-nadir incidence compared to diffuse reflections from ice floes [Drinkwater, 1991; Laxon, 1994]. Specular returns have typically been identified using relative return strength together with a measure of sharpness of these returns. For discrimination of ice and leads in CS-2 data, Laxon et al. [2013] utilized a pulse “peakiness” (PP) parameter (a relative measure of peak signal strength) together with a stack standard deviation (SSD) parameter, which provides a measure of the variation in along-track surface backscatter [Wingham et al., 2006]. Ricker et al. [2014] used a modified version of the PP that considers the neighborhood of the peak of surface return. Both the PP and SSD are measures derived from the entire waveform, which include off nadir returns, and therefore these measures are sometimes confounded by strong off-nadir returns (sometimes referred to as “snagging”).
In our analysis, we find that the combined peak power (Pc) of the first return with its associated width (Wc) at the half-power point (at the leading-edge) to be effective in isolating specular returns from the nadir sea surface (Figure 1). First, specular returns from flat sea surfaces are expected to have significantly higher return (power) than their diffused counterparts over the sea ice surface. Second, rough surfaces tend to broaden the impulse response (the width between the leading and trailing edges of a surface return). Since mixtures of surface types outside the pulse-limited footprint contaminate the trailing edge of specular peaks in CS-2 waveforms, we find the width of simply the leading edge (Wc) of the first return to be the best indicator of broadening. For the CS-2 radar, the expected full width of the compressed pulse is ∼46.7 cm (see Figure 1), so we expect Wc from relatively flat surfaces to be close to half that value (i.e., ∼23.3 cm), and values >Wc indicate deviations from specularity. A key feature of our retracker is that in contrast to prior approaches, our measures of specularity (peak power and width) are for the first return from the surface, which is of primary interest here, and the returns from the remainder of the waveform (or off nadir parts of the return) do not affect the determination of specularity and surface height.
A near-specular return from open water/thin ice in CryoSat-2 (CS-2) data. Normalized return power is relative to the peak of the return. From near-specular surfaces, the width of the return at its half-power point is approximately the expected width of the compressed pulse of the CS-2 radar (i.e., ∼46.7 cm from radar bandwidth of 320 MHz); the half-width (
)––used in the text––is shown in the figure.
To show that specular returns are distinct in the data set, we examine the distributions of Pc and Wc of the first unambiguous peak in the oversampled (16 times) CS-2 waveforms (Figure 2). An unambiguous peak is one in which the leading edge is clearly defined, i.e., without any local minima in the range interval between its half- and peak- power points. In the seasonal distributions of Pc and Wc from the Arctic and Southern Oceans (Figure 2), it can be seen that the population densities are higher – more localized—where specular returns are expected (i.e., high Pc's with Wc's that are close to the half-width of the range impulse response of ∼23.3 cm). The population of specular returns is marked by a distinct mode in the top left corner (with high Pc and narrow Wc) of the joint distributions. In the fall and winter Arctic, the scatter of
(∼23.1 to 24.6 cm), near the half-width of the modeled range impulse response of the SIRAL radar and
(43.7–45.8 dB-fW) are both small. In the summer arctic, the variability of
is lower (∼22.8 to 23.9 cm) but
is somewhat higher (44.7–51.8 dB-fW). In the Antarctic, the seasonal range of
is generally higher by 1 – 2 cm, but
is lower (41.4 – 46.4 dB-fW),
Joint distribution of peak received power (
) and leading edge width (
) of the first surface returns in CS-2 waveforms. (a) Arctic (2011–2013): January through April, June, July, and September through December. (b) Antarctic (2010–2013): July through October, December, January, and March through June. Quantities in each panel are mean/standard deviation of
and
at the mode of the distributions (top-right corner), and fractional coverage (center) of those samples designated as sea surface returns. Sea surface returns are those samples with
> 40 dB-fW (above dashed while line) and widths (
) to the left of the black and slanted red lines.
In our procedure, we designate those returns with Pc > 40 dB-fW and with Wc to the left of the slanted red line (in Figure 2) to be specular returns from leads; the height (
) is defined by the half-power point. Seasonally, the fraction of CS-2 returns designated as sea surface returns varies as expected (i.e., higher in the fall than in the spring). Due to the increased coverage of open water and melt ponds in the Arctic summer, that fraction is dominated by sea surface returns (e.g., 0.95 in July 2011). Within the nominal footprint of CS-2 (0.31 km by 1.67 km), the likelihood of finding open water or melt ponds in the summer is high. This, however, was not observed in the antarctic summer and may be attributable to the near absence of melt ponds in the Southern Ocean ice cover [Andreas and Ackley, 1982]. In the following section, we assess the quality of the height retrievals and the potential impact of melt ponds on surface height.
3.2 Assessment of Sea Surface Heights
Before the retrieved heights are assessed, sources of surface height variability due to tides, and atmospheric loading (provided in Bouzinac [2013]), and the geoid (EGM2008) are removed. Statistics are then calculated for each 25 km along-track segment that contains at least three
estimates. When the separation between available
samples spans more than half the length of a segment, the tilts of the surface along-track (
) are also calculated. The detilted standard deviation (
) and
from each segment are used to serve as measures of variability and noise in our retracking process; detilting removes residual surface slopes present in the data. The monthly mean
of all 25 km segments for the Arctic (Figure 3a) shows that variability in the retrieved SSHs is consistently ∼2.5 cm in the Arctic for the winter months, and higher (∼3 cm) in the summer months in all years (2011–2013). In the Southern Ocean, the mean
of the 25 km segments is also ∼3 cm in all months (Figure 3d) but also somewhat higher during the summer. Examples of two monthly fields of
(Figures 3b and 3e) and mean fields of
from the three CS-2 years (Figures 3c and 3f) provide an indication of the spatial behavior of these parameters. The
are also generally higher near the ice edge perhaps due to variability associated with wave penetration into the ice cover.
Variability of retrieved sea surface heights in 25 km along-track segments. (a) Monthly variability (±RMS) in the Arctic after removing segment tilt (2011–2013). (b) Example shows spatial distribution of detilted standard deviation from May 2012. (c) Average tilt (along-track slope) of the sea surface for all months (in absolute value of tilt) between 2011 and 2013. (d) Same as Figure 3a except for statistics in the Antarctic. (e) Example shows distribution of detilted standard deviation from August 2012. (f) Same as Figure 3c except for the Antarctic. Quantities in bottom right corner of Figures 3c and 3f are the means and standard deviations of the surface tilt (absolute value) within the field. Black box delineates the area shown in Figure 4.
In the 3 years of CS-2 data, the calculated
in the 25 km segments show low surface tilts (<2 cm/10 km) over most of the arctic as well as the antarctic. Average sea surface tilts (
) are 0.01 ± 3.8 cm/10 km in the Arctic, and slightly lower (0.01 ± 2.0 cm/10 km) in the Southern Ocean. Surface tilts are due to ocean topography, geoid residual, and noise in the retrievals. In particular, coherent patterns of higher
in the Arctic are concentrated in those areas with surface tilts that are likely due to geoid residuals associated with deep ocean ridges. In more detail, Figure 4 examines the consistency in surface tilts within a box in the Eurasian Basin. The 3 years of
fields (Figures 4b–4d) show along-track
and tilts that could be as high as 15 cm/10 km over the Nansen and Lomonosov ridges. This demonstrates the consistency in the retrieved surface heights.
EGM2008 geoid and along-track sea surface tilts associated with deep ocean ridges (Nansen, Lomonosov, and part of the Mendeleyev). (a) Shaded relief of the EGM2008 geoid. Segment tilts in (b) 2011. (c) 2012. (d) 2013. Location of geographic area (1200 km on a side) on Arctic map is shown in Figure 4a. Consistent signs in surface tilts (along 25 km segments) in the Cartesian frame of reference are produced by accounting for the directions of ascending versus descending satellite tracks.
In the arctic summer, contributions of specular returns from melt ponds with hydraulic heads (i.e., pond surfaces that are above sea level) are expected to bias estimates of surface heights. The development of hydraulic heads depends on both snowmelt and the permeability of the underlying ice, and varies with the progression of the ablation season. With measurements from the SHEBA camp in 1998, Eicken et al. [2002] reported that while most of the ponds in level, undeformed sea ice exhibit maximum elevations of around 20 cm above sea level, they could exceed 0.5 m in heavily ridged areas. Eicken et al. [2002] also added that in a majority of level-ice ponds, the hydraulic head decreases to zero (i.e., ponds drain) as the season progresses, with ponds remaining only in ridged or deformed ice. The slight increase in
between June and July in the Arctic for all the years seems consistent with the added variability due the hydraulic heads over melt ponds. However, there does not seem to be evidence of significant observable biases due to ponds in our examination of the seasonal variability and our comparisons of dynamic ocean topography with time-varying bottom pressure and time-varying gravity from GRACE (see discussion in section 4).
4 Arctic Ocean
In this section, we examine 4 years (2011–2014) of SSH and DOT from CS-2 data, and compare DOT estimates with DHs derived from hydrography, with OBP from a pressure recorder at the North Pole, and time-varying gravity from GRACE.
4.1 SSH and DOT (2011–2014)
Here, time-varying DOT is the pointwise difference between the height of the sea surface from CS-2 and the sum of the heights due to the geoid (EGM2008) [Pavlis et al., 2012], tides (ocean, load, and solid earth), and atmospheric loading (the inverted barometer effect).
Figure 5 shows the seasonal mean fields of DOT from the 4 years of CS-2 record. The fields are sampled on a uniform 25 km grid and each grid-value represents the average SSH of all 25 km along-track CS-2 segments that fall within that grid cell. The motivation in constructing these gridded 25 km fields is to show the mix of oceanographic signals and geoid residuals in regions of steep bathymetric and geoid changes (such as ocean ridges) seen in the gridded 25 km fields. The DOTs produced by this method require additional filtering to produce a time-mean DOT (or MDT) that is suitable for computation of time-mean surface geostrophic currents and ocean transports. However, it is also important to note that static residuals do not impact the pointwise detection of time-varying changes in sea-level or ocean surface topography over shorter time scales.
Seasonal mean fields of dynamic topography of the Arctic Ocean from CS-2 in (a) 2011: January–April, May–August, and September–December, (b) 2012, (c) 2013, and (d) 2014 (25 km grid).
Broadly, the DOT varies by ∼1.5 m across the Arctic Ocean (color palette spans the range between 0.2 and −1.3 m) with the Amerasian Basin higher than the Eurasian Basin. The most prominent large-scale features are the distinct dome of ∼40 cm of the Beaufort Gyre, the persistent drop of ∼80 cm in SSH through Bering Strait that drives the Pacific inflow into the Arctic Ocean, and the drop of about 40 cm between the northern part of the Canada Basin and the Amundsen Basin that drives the Transpolar Drift of sea ice and upper ocean currents. These static features have been discussed elsewhere [e.g., Kwok and Morison, 2011].
At shorter length scales, the smaller features in the Eurasian Basin appearing as ∼40-cm bumps and holes at about 100 km scale are possibly associated with residuals in the marine geoid (as discussed in section 3). At the same time they could be the ocean response to perhaps unrecognized bathymetric variability. A highly simplified example illustrates this. With simplifying assumptions, the conservation of angular momentum requires potential vorticity,
, be conserved as a background irrotational flow moves over varying ocean bathymetry. Here ζ is the relative vorticity, f the Coriolis parameter, and h is ocean depth. The relative vorticity is proportional to the Laplacian of DOT, η, i.e.,
, and for potential vorticity to be conserved over a seamount of depth h2 in an ocean of depth h1 requires η2 over the seamount to obey
. For h2 equal to 75% of h1, the DOT forms a parabolic bulge ∼33 cm high over a 50 km radius seamount. We expect unresolved bathymetry may have a mix of geoid errors and hydrodynamically induced mean DOT deflections at small scales.
The gridded CS-2 fields provide a synoptic view of the variability of the Arctic Ocean SSH. While the visual changes in the Eurasian Basin seem to be small over the four seasons, the time-varying height of the dome of Beaufort Gyre (e.g., from high in September–December 2012 to its low May–August 2013) dominates the ocean signal. The O(40 cm) year-to-year and seasonal variability in DOT over the Siberian shelves is consistent with the second EOF of monthly Arctic Ocean bottom pressure measured by the GRACE [Peralta-Ferriz et al., 2014b]. In shallow water OBP variations equal DOT variations over a broad range of time-scales, and according to the findings of Peralta-Ferriz et al. [2014b], these over the Siberian shelves are strongly correlated with the Arctic Oscillation Index. In a high AO state water is forced onto the shelves, and in a low AO state water is drawn off the shelves. Streaks near the coasts are artifacts due to lower density of samples as coverage reduces when the ground tracking separation increases at lower polar latitudes.
The intraseasonal variability in the 4 years for gridded fields, and spatial density of along-track segments used in the calculations are shown in Figure 6. Intraseasonal variability refers to the standard deviation of all along-track samples within each grid cell in the fall (September–December), winter (January–April), and summer (May–August). As a reminder, at least three CS-2 sea surface observations contribute to the calculation of the mean height of each along-track segment. The spatial density is determined by the availability of open leads as well as the convergence of the satellite tracks near the poleward bounds of the altimeter orbit. Clearly, the density and number of observations increases significantly with latitude. Variability is expected to be higher over parts of the Arctic Ocean (in dashed boxes) where the SARIn mode is operated.
Variability of gridded monthly fields of Arctic ocean topography in 4 years CS-2 data. (left) January–April (middle) May–August (right) September–December. Bottom plots show number of samples in each 25 km grid cell. CS-2 data acquired in SARIn mode (inside dashed polygons) are noisier and shows higher variability.
The intraseasonal variability ranges to ∼20 cm, and the lower values within the range (∼3–5 cm) are expected to be associated with the noise floor in SSH. The noise sources include those from uncertainties in absolute altimetric range (e.g., orbits, timing, propagation delay, etc.), un-modeled geophysical variability (e.g., tides, atmospheric loading, etc.) and surface retrieval errors. In these fields, static features such as residuals (such as those over the ocean ridges discussed earlier) have disappeared leaving only those signals that are dynamic over the timeframe of interest. Most of the small DOT features in the Eurasian Basin (in Figure 5), except for the linear feature over the Gakkel Ridge, are no longer visible. In fact, variability in the Eurasian Basin is small compared to other parts of the Arctic. Variability over the Siberian shelves stands out in all seasons where gradients in variability are large at the shelf break. Poleward of the shelf breaks, the fields show the highest variability in the Canada Basin (8–10 cm) during the fall (September–December), followed by the winter (January–April), and then summer (May–August).
The magnitude of variability during the Arctic summer suggests that the large-scale effects of melt ponds may be small during the summer. Since melt ponds begin to form in June and then peak around mid-to-late July [Eicken et al., 2002], we would expect those ponds with surfaces with hydraulic heads to be some centimeters above sea level to introduce additional variability into the surface topography in the May–August fields. To the contrary, we find the observed variability in the summer months to be comparable to those from the winter and fall. However, the evidence only suggests that the effects seem small at least at this scale of investigation, thus it would be wrong to conclude that there are no effects due to ponds over a surface with a mix of open leads and melt ponds.
4.2 Comparison of DOT With Dynamic Height (DH) (2011–2013)
To assess the quality of the CS-2 DOTs, we compare monthly mean DOTs (smoothed with a 250 km kernel) with 3 years of dynamic height relative to a 500 dbar level of no motion from 82 hydrographic stations in the central Arctic Ocean from the North Pole Environmental Observatory (NPEO at http://psc.apl.washington.edu/northpole) and Switchyard (http://www.ldeo.columbia.edu/Switchyard) projects. The correlation between variations in DOT and surface DH relative to 500 dbar at the hydrographic stations (Figure 7) is 0.92 (0.88–0.95 for 99% confidence limits). The standard deviation of the difference between DOT and the DH is 3.6 cm over a range of ∼30 cm. The stations span an extent of over 1000 km, and include two major basins in the western (Makarov Basin) and eastern (Amundsen Basin) Arctic Ocean with markedly different water mass structures. The only adjustment in this comparison has been to recognize that the DH's from hydrography are not absolute and so to shift all values of DH by the same constant such that the average of DH at the hydrographic stations matches the average of DOT at the hydrographic stations.
Arctic Ocean dynamic height (DH) versus monthly mean dynamic topography. (a) Locations of hydrography-derived DH estimates (relative to 500 dbar) in 2011, 2012, and 2013. (b) DH from hydrography versus monthly DOT from CS-2 at the 2008 hydrographic stations. Monthly DOTs have been smoothed with a 100 km Gaussian kernel.
As all the hydrographic stations in this comparison are above 80oN, the number of SSH retrievals that contributes to the mean SSH at each 25 km grid is quite high (>75 in a month at more than 3 retrievals per 25 km segment), and the number becomes higher after smoothing over the kernel extent. Given the number of independent satellite observations, the small mean difference between DH and the monthly DOTs is perhaps not surprising. On the other hand, we expect some differences between DH and DOT because of the effect on DH of departures from zero velocity at 500 dbar due to barotropic currents; the good comparison of DH and DOT suggests the circulation is mainly baroclinic.
4.3 Comparison of DOT With Ocean Bottom Pressure (OBP) at North Pole
The ocean bottom pressure (OBP) is the sum of DOT and the steric pressure anomaly (SPA, due to changes in water density). At interannual and longer time-scales baroclinic circulation tends to dominate and, consequently, OBP variations are expected to be smaller than DOT variations due to adjustment in the density distribution, i.e., the SPA [Bingham and Hughes, 2008; Vinogradova et al., 2007]. Comparisons among ICESat-derived DOT, GRACE OBP, and in situ hydrography [Morison et al., 2012] generally confirm the dominance of baroclinic over barotropic circulation change at multiyear timescales and basin circulation length-scales. However, observations suggest that even at these time and length scales bottom pressure variations can amount to 25% of the DOT variations [Morison et al., 2012], more than is suggested by numerical models [Peralta-Ferriz et al., 2014b].
Here, we compare the DOT from CS-2 with two sources of bottom pressure: monthly mean OBP measured at the North Pole by an Arctic Bottom Pressure Recorder (ABPR) [Morison et al., 2007; Peralta-Ferriz et al., 2014a] and from time-varying gravity from the GRACE mission. As the ocean is predominately hydrostatic, the time-varying gravity fields produced by the GRACE mission can be used to estimate the fluctuating part of OBP [Dickey et al., 1997; Wahr et al., 1998, 2002]. For considering OBP in the central Arctic Ocean, Peralta-Ferriz et al. [2014a] compare a time-series of OBP measured with the ABPR at the North Pole since 2010 (ABPR5) and OBP measured by GRACE. After using GRACE to correct the ABPR pressures for an initial instrumental drift of 15–20 cm-water equivalent pressure, they found an RMS difference between GRACE and ABPR5 OBP of 1.87 cm and a correlation over 5 years, 2010–2014, of R=0.84.
Figure 8 compares the time-series from 2011 to 2014 of monthly-averaged CS-2 derived DOT with monthly-averaged OBP from GRACE and ABPR5 at the North Pole. The correlations among the records are good (R of ABPR versus CS-2 = 0.83, R of GRACE versus CS-2 = 0.72, and R of GRACE versus ABPR = 0.84). Month-to-month variations are nearly identical. Given the usual dominance of baroclinic adjustment over most regions of the Arctic Ocean as discussed above and with respect to Figure 7, it is remarkable how well the interannual variations in CS-2 DOT agree with the GRACE and ABPR OBP. To within the RMS difference (∼2.5 cm) the downward trend from 2011 to 2012 and upward trend from 2012 to 2014 of the DOT and OBP agree, suggesting ICESat-2 DOT interpolated to the Pole is dominated by barotropic changes. In part this is because: 1) interpolated DOT values presented in Figure 8 (using a large area mean: 800 km box in this case) essentially averages over much of the spatial variability in DH/DOT (of ∼30 cm) seen in Figure 8 or the CS-2 DOT variability seen in Figure 8 (in gray), and 2) bottom pressure is spatially coherent over large spatial scales related to the fact that the barotropic surface wave speed is high.
Comparison of monthly mean CS-2 DOT with ocean bottom pressure time series from a pressure gauge at the North Pole Enviromental Observatory (NPEO) and GRACE measurements near the North Pole. Monthly CS-2 estimates are an average of all retrievals within an 800 km box in (a) centered at the Pole (standard deviations of DOTs within the box are shown in gray).
In the extreme, OBP as measured by GRACE and the ABPRs at the North Pole is well correlated with basin-wide changes in ocean mass from submonthly variations forced by winds in Fram Strait and the subarctic seas [Peralta-Ferriz et al., 2011], through seasonal variation forced by runoff [Peralta-Ferriz and Morison, 2010], and at longer time-scales appearing as the first empirical orthogonal mode of OBP variation [Peralta-Ferriz et al., 2014b]. These basin-wide variations in mass, being similar everywhere, are dominantly barotropic. They are typically on the order of 2–10 cm peak-to-peak, similar to the variations shown in Figure 8. The measurements of DH characterizing baroclinic change and DOT across a wide region straddling the North Pole (Figure 7) show at least twice the range of temporal variability of DOT and OBP at the Pole (Figure 8). It appears that CS-2, spatially averaged around the Pole, is capturing the barotropic large-scale mass fluctuations, and the higher resolution CS-2 observations are capturing the more energetic, smaller-scale baroclinic variations.
Mean dynamic topography of the ice-covered Arctic Ocean. (a) ICESat (Mean of Feb-Mar, 2003–2008) [Kwok and Morison, 2011], (b) CryoSat-2 (2011–2014). (c) DOT2008A. (d) DTU13MDT All fields have been smoothed with a 250-km Gaussian kernel.
4.4 Mean Dynamic Topography (MDT)
Here, we compare the time-mean dynamic topography (MDT) from CS-2, ICESat [Kwok and Morison, 2011], DOT2008A [Pavlis et al, 2012], and DTU13MDT [Andersen et al., 2015]. The time-mean DOTs (2011–2014) in Figure 7 are constructed by averaging all monthly fields (in Figure 5). The MDTs are then smoothed with a 250 km Gaussian averaging-kernel to reduce the noise in the sea surface measurements and the contribution of residual geoid errors (at wavelengths shorter than the width of the kernel). To suppress geoid errors, McAdoo et al. [2013] suggest that a Gaussian kernel with a width of at least 250 km is necessary. But, increasing the length-scale also suppresses oceanographic signals. Perhaps the choice of length-scale should adapt to the expected local geoid uncertainties and strength of the mean oceanographic signal over the region and time span of interest; this depends on specific uses of the derived DOT as discussed earlier.
The four MDT fields are compared in Figure 9. The global DOT2008A MDT model, estimated using the DNSC08B [Andersen and Knudsen, 2009] mean sea surface, is one of the oceanographic products provided with the release of the EGM2008 gravitational model. To cover the Arctic Ocean, the DNSC08B MSS blends ERS-2, Envisat, and ICESat SSH data below 86oN with interpolated SSH above that latitude. Examination of the ICESat and CS-2 MDTs shows that even though they are from different epochs with potential biases between the two instruments, their spatial patterns are substantially the same: there is a well defined dome in the Canada Basin and east-west gradients across the Amerasian and Eurasian Basins. The DOT2008A MDT, however, has a very different character: the Beaufort dome is more similar to a ridge that extends to the Canadian Arctic Archipelago (CAA), and to the Arctic coasts of Ellesmere Island and Greenland. This perhaps suggests residual biases in combining ERS-2, Envisat, SSH due to the difficulty in separation of ice from open water in the larger footprints. The DTU13MDT, an updated version of DNSC08B that incorporates both ICESat and CS-2 SSHs, shows a better defined Beaufort dome although the higher relief next to the CAA seems to be biases from the earlier SSH estimates from ERS-2 and Envisat (seen in the DNSC08B field—Figure 9c.).
5 Ice-Covered Southern Ocean
Here, the 4 years (2011–2014) of CS-2 SSH and DOT of the ice-covered Southern Ocean are discussed and the DOTs are compared with those from ICESat, DOT2008A, and DTU13MDT. At this writing, we are not aware of assessments of time-varying these DOTs (especially those from CS-2) in the published literature. Since a coincident time series of DH and OBP (from moorings within the ice-covered ocean) that spans the CS-2 record is not available, we do not provide comparisons of time-varying DOTs with these parameters (as was done for the Arctic in section 4). Thus, the discussion here is somewhat limited to observed variability and comparison with the above DOT fields.
5.1 DOT (2011–2014)
Similar to the Arctic fields, short time-scale variability in heights have been removed from the SSH from CS-2. Figure 10 shows the mix of oceanographic signals and geoid residuals in the 4 years of gridded seasonal-mean DOT fields of the ice-covered Southern Ocean. Again, the DOTs produced by this method require additional filtering to produce a time-mean DOT (or MDT) that is suitable for computation of time-mean surface geostrophic currents and ocean transports.
Seasonal mean fields of dynamic topography of the ice-covered Southern Ocean from CS-2 in (a) 2011: January–April, May–August, and September–December, (b) 2012, (c) 2013, and (d) 2014 (25 km grid).
Over the ice-covered Southern Ocean, the DOT varies by ∼0.7 m (color palette spans the range between −1.4 and −2.1 m). The trough associated with cyclonic circulation in the Weddell Sea stands out. The negative extreme in global DOT (<−2.1 m), which has a range between 0.8 m and −2.13 m, is apparently located in the northern Weddell Sea at ∼(66oS 4oW) [Lemoine et al., 1998]. Large topographic gradients can be seen in the northern extremes of the winter ice edge (∼60oS) where it extends into the Antarctic Circumpolar Current. At larger spatial scales, time-varying changes seem to be smaller over the seasons. At shorter length scales, distinct smaller features north of the Antarctic coast (between 10oW and 40oE) seem to be associated with residuals in the marine geoid (as discussed in section 3). North-south oriented streaks are aliasing effects due to reduced density of samples as the orbits diverge away from the pole.
The intraseasonal variability (defined earlier) in the 4 years for gridded fields, and spatial density of along-track segments used in the calculations are shown in Figure 11. As a reminder, at least three CS-2 sea surface observations contribute to the calculation of the mean height of each along-track segment. Compared to the Arctic, the spatial density of observations or coverage by the satellite tracks is lower since all of the Southern Ocean ice cover are equator-ward of ∼70oS. Clearly, in the Southern Ocean, the density and number of observations have not benefitted from orbit convergence near the pole.
Variability of gridded monthly fields of Southern Ocean topography in 4 years CS-2 data. (left) January–April, (middle) May–August, (right) September–December. Bottom plots show number samples in each 25 km grid cell. Note height scale is half of that used in Figure 6.
Intraseasonal variability (Figure 11) ranges to ∼10 cm, about half of that seen in the Arctic. Similarly, the lower values within the range of ∼3–5 cm are expected to be associated with the noise floor in SSH. Static topographic features (oceanographic or geoid residuals) are no longer visible leaving only those signals that are dynamic over the timeframe of interest. Visually, variability is highest near the ice edge and east of the Antarctic Peninsula. However, given the level of variability it may be more difficult to detect the smaller changes within the ice cover.
5.2 Comparison With ICESat, DOT2008A, DTU13MDT
The MDTfrom CS-2, ICESat, DOT2008A [Pavlis et al., 2012], and DTU13MDT [Andersen et al., 2015] are shown Figure 12. The CS-2 MDT is the time-mean DOT (2011–2014) smoothed with a 250 km Gaussian-kernel. As in the Arctic, examination of the ICESat and CS-2 MDTs shows that even though they are from different epochs with potential biases between the two instruments, their spatial patterns are substantially the same. The Weddell Gyre is present in both MDT, although there is more extensive coverage by the CS-2 retrievals that extend farther north. The exception is the higher DOTs in coastal Bellingshausen and Amundsen seas in the ICESat field. The DOT2008A MDT is also somewhat different, again suggesting residual biases in combining ERS-2, Envisat, and ICESat SSHs. The DTU13MDT, an updated version of DNSC08B that incorporates both ICESat and CS-2 SSHs, shows reduced topographic variability near the Amundsen and Bellingshausen coasts that seems more consistent with that observed in ICESat and CS-2.
Mean dynamic topography of the ice-covered Southern Ocean. (a) ICESat (Mean of November–October 2003–2008). (b) CryoSat-2 (2011–2014). (c) DOT2008A. (d) DTU13MDT All fields have been smoothed with a 250 km Gaussian s kernel.
6 Conclusions
In this paper, we examine 4 years (2011–2014) of sea surface heights (SSH) of the ice-covered Arctic and Southern Oceans from the CryoSat-2 (CS-2) altimeter. The physical basis and the procedure for identifying sea surface returns in the mix of ice and water returns are described. The resulting SSH fields were assessed at different time and length scales. Variability of SSH over 25 km segments suggests that the precision in retrieved SSHs is between ∼2–3 cm (standard deviation) in the Arctic, and slightly higher (∼3 cm) in the Arctic summer and Southern Ocean.
We find the variability of DOTs over quasi-static surface features (e.g., those associated with deep ocean ridges) to be useful for assessment of consistency of retrievals. Surface slopes calculated over these features, if reproducible in the time-varying monthly fields, are indicative of the precision of the DOTs. Results from 3 years suggest that surface slopes higher than a few centimeters in 10 kilometers can be consistently measured. In the Arctic, we find surface slopes that are up to 15–20 cm in 10 km at length scales of tens of kilometers. Average sea surface tilts (along these 25 km segments) are 0.01 ± 3.8 cm/10 km in the Arctic, and slightly lower (0.01 ± 2.0 cm/10 km) in the Southern Ocean. Examination shows that the intraseasonal variability of DOT in the ice-covered Arctic is nearly twice as high as that of the Southern Ocean.
There are two main sources of small-scale topography (tens of km) in the CS-2 DOT fields: oceanographic and geoid residuals. A simple calculation assuming conservation of potential vorticity shows that these short length scale surface features (the bumps and holes at ∼10 km, see Figure 5), frequently attributed to geoid residuals, may also be hydrodynamically induced in a background of irrotational flow. Hence, it is important to note that these small-scale surface features may be a sum of oceanographic signals and geoid residuals. Separation of these signals may be difficult, however, without higher resolution geoid models.
The CS-2 DOT fields are compared with other observations. In the Arctic, monthly mean CS-2 DOT are correlated with dynamic heights (DH) at 82 hydrographic stations (R=0.92), with 4 years of ocean-bottom pressure from a pressure gauge (R=0.83) and with mass variations from GRACE (R=0.77) at the North Pole. Over a wide range of water mass structures, the CS-2 DOT at ∼25 km resolution agree with DH from hydrographic measurements and thus well represent the baroclinic component of geostrophic surface circulation (Figure 7). Further, CS-2 DOT averaged over the scale of baroclinic circulation features reveals smaller amplitude signals (Figure 8) that are expressions of larger spatial scale barotropic variations that register as bottom pressure (measured by a pressure gauge) – useful for comparison with bottom pressure measurements from GRACE or pressure gauges. This also contrasts the length-scale of time-varying DOT and observed bottom pressure (from OBP or GRACE), or baroclinic and barotropic features in the Arctic Ocean.
Broadly, the time-mean DOT (MDTs) from CS-2 from both poles compares with those from the ICESat campaigns, and the DOT2008A and DTU13MDT models. Qualitatively, these fields are similar and include all the expected large-scale oceanographic features. We attribute some of the differences to the different epochs of the composites and the quality of the satellite data that comprised the estimate of the mean.
To date, CS-2 has provide the densest spatial and temporal sampling of the SSH of the ice-covered polar oceans that extends to 89oN. The present assessment serves as one measure of the quality of the CS-2 retrievals and its potential utility in understanding the changes in the circulation of the Arctic and Southern Oceans.
Acknowledgments
GRACE ocean data were processed by Don P. Chambers, supported by the NASA MEaSUREs Program, and are available at http://grace.jpl.nasa.gov. Suzanne Dickinson has calculated the correlations of the CS-2 DOT with Arctic dynamic heights and Cecilia Peralta-Ferriz has provided the North Pole ABPR data. The work at the Polar Science Center was supported by NASA grants NNX13AP72G and NNX12AK74G and NSF grant ARC-0856330. RK carried out this work at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
