Two Decades of Arctic Sea-Ice Thickness from Satellite Altimeters: Retrieval Approaches and Record of Changes (2003–2023)

Abstract

There now exists two decades of basin-wide coverage of Arctic sea ice from three dedicated polar-orbiting altimetry missions (ICESat, CryoSat-2, and ICESat-2) launched by NASA and ESA. Here, we review our retrieval approaches and discuss the composite record of Arctic ice thickness (2003–2023) after appending two more years (2022–2023) to our earlier records. The present availability of five years of snow depth estimates—from differencing lidar (ICESat-2) and radar (CryoSat-2) freeboards—have benefited from the concurrent operation of two altimetry missions. Broadly, the dramatic volume loss (5500 km³) and Arctic-wide thinning (0.6 m) captured by ICESat (2003–2009), primarily due to the decline in old ice coverage between 2003 and 2007, has slowed. In the central Arctic, away from the coasts, the CryoSat-2 and shorter ICESat-2 records show near-negligible thickness trends since 2007, where the winter and fall ice thicknesses now hover around 2 m and 1.3 m, from a peak of 3.6 m and 2.7 m in 1980. Ice volume production has doubled between the fall and winter with the faster-growing seasonal ice cover occupying more than half of the Arctic Ocean at the end of summer. Seasonal ice behavior dominates the Arctic Sea ice’s interannual thickness and volume signatures.

1. Introduction

Since the first estimates of Arctic Sea ice thickness from satellite-derived freeboards [1], (i.e., the vertical height of the floating ice above the local sea surface), there have been progress and improvements in our ability to retrieve this vital climate indicator. Presently, two dedicated polar observatories (CryoSat-2 [2] and ICESat-2 [3]) provide sea ice freeboards to monitor sea ice thickness of both the Arctic and Southern Oceans. Our understanding of the efficacy of the procedures employed in thickness retrievals was informed by measurements from the field, and airborne programs like NASA’s Operation IceBridge [4], which has provided a multiyear record of lidar- and radar-altimetry of the ice cover for over a decade. For quality assessments, Arctic sea-ice thickness estimates have been compared with correlative ice thickness data sets from upward-looking sonars acquired by submarines [5,6] and moorings [7,8], and by airborne electromagnetic sounding [9]. These correlative measurements, albeit of limited quantity, are valuable because they are less likely to be subjected to the same error sources and potential biases that affect altimetry-based estimates. Even though it is still a challenge to provide a comprehensive assessment of the expected errors [10,11], comparisons with correlative data sets, the evaluation of consistency in seasonal/regional behavior, and inter-satellite estimates have provided reliable bounds on the expected errors at length scales that are useful for monitoring broad decadal changes and for model assessments. The significant decadal thinning and volume losses of the ice cover from these satellite retrievals were reported in climate assessments [12,13].

In this paper, we update the record of Arctic sea-ice thickness reported in IPCC AR5 [12], and AR6 [13] with two additional years of altimetry data (2021–2023) acquired by two current altimetry missions (CryoSat-2 and ICESat-2) operated by ESA and NASA. Including the thickness estimates from the completed ICESat mission (2003–2009), the record of satellite retrievals now spans two decades. Here, we provide a summary of our approaches used to construct the present two-decade record, recognizing that there are different approaches utilized by other investigators available in the published literature (e.g., [10,14,15,16]); it is not intended as a review of the variety of approaches. More importantly, as with most retrievals from orbiting observatories, some shortcomings and improvements await a better understanding of the impacts of the geophysical behavior of the ice cover on algorithmic assumptions. These are addressed as we discuss the retrieval approaches.

This paper focuses on the remote sensing aspects of the retrievals and not on the interpretation of the decadal changes associated with polar and global climate. It is organized as follows. The following section describes the derived freeboards from the three altimeters (IS, CS-2, and IS-2) used to construct the records of ice thickness and snow depth data sets. Section 3 summarizes the approaches used in retrieving ice thicknesses from the lidar and radar freeboards and discusses the assumptions, the selection of parameters, our current understanding of the sources of uncertainties (quantified and unquantified), and the limitations of these data sets. Section 4 reviews the availability of snow depth and our approach for estimating this parameter by differencing lidar and radar freeboards. Section 5 discusses the assessments of these retrievals, examines the retrieved ice thickness and calculated volume over this satellite record (2003–2023), and their behavior within the context of thickness estimates from other platforms (e.g., submarine, airborne, seafloor moorings, etc.). The last section concludes the paper.

2. Data Description

The input to the ice thickness/snow retrieval process is the surface height profiles of ice and water derived from altimetric waveforms. While crucial, the steps to derive freeboard from altimeter range are varied and generally dependent on instrument design and operation, and beyond the scope of this paper. Instead, we describe the derived radar and lidar freeboards (ICESat (IS), CryoSat-2 (CS-2), and ICESat-2 (IS-2))—the starting point in our thickness calculations—their profiling characteristics (spatial and temporal sampling), and the time span of their records utilized in this paper. We note here that, except for the CS-2 and IS-2 freeboards between 2021 and 2023 (new here), the freeboard derivation procedures and data sets used herein can be found in the publications cited herein. For interested readers, the details of the freeboard retrieval procedures used here are provided in the citations in the text.

2.1. ICESat (2003–2009)

The ICESat (IS) platform [17] carries the Geoscience Laser Altimeter System (GLAS) that consists of two lidar channels—1064 nm and 532 nm; the longer wavelength infra-red data intended for surface profiling are used here. The single-beam 1064 channel samples the Earth’s surface from an orbit with an inclination of 94° and footprints of ~70 m in diameter spaced at ~170-m intervals. The orbit inclination allows the polar oceans to be covered to 86° latitude. The expected accuracy in elevation determination over relatively low-slope surfaces (e.g., ice sheets) is ~14 cm. Laser lifetime considerations limited the temporal coverage and data acquisitions to a set of discrete campaigns in which the 33-day near-repeat sub-cycle of a 91-day repeat orbit is surveyed at three- to six-month intervals. We use the operational periods that covered the falls (Oct–Nov) of 2003 through 2008 and the winters (Feb–Mar) of 2004 through 2009. The National Snow and Ice Data Center (NSIDC) distributes the IS surface profiles. IS freeboards are derived using procedures in [18].

2.2. CryoSat-2

The primary payload on CryoSat-2 (CS-2) is the SAR/Interferometric Radar Altimeter (SIRAL) [2] with an orbit inclination that allows coverage to 88° in latitude. The Synthetic Aperture Radar (SAR) mode, which samples the surface with a processed footprint of ~0.31 km by 1.67 km along- and across-track, is used here. The SAR mode sharpens the along-track beam (~0.31 km) for improved detection and resolution of narrow open water leads needed in freeboard calculations. Profiles of freeboard along the satellite track are from the Level 2 CS-2 waveforms (Baseline E) available at the ESA data portal (https://science-pds.cryosat.esa.int); URL accessed on 24 February 2024. The procedures for estimating freeboards used here are detailed in [11].

2.3. ICESat-2

The ICESat-2 (IS-2) observatory [3] is in a 91-day exact repeat orbit with an inclination of 92°, allowing mapping to 88° latitude in both the northern and southern hemispheres. The six-beam Advanced Topographic Laser Altimeter System (ATLAS) operates at 524 nm and profiles the surface at a pulse repetition rate of 10 kHz. At orbital velocities, individual laser footprints of ~11 m (in diameter) are separated by ~0.7 m. Freeboards are from one sea ice data set—designated as ATL10 (Release 006 [19])—produced by the IS-2 project and archived at NSIDC. The ATL10 products provide variable along-track resolution (~27 to 200 m) sea ice freeboard estimates within 10-km segments that contain at least one sea surface reference. The freeboards used in the following analyses are from the three strong beams and averaged onto a 25-km grid. At the time of writing, IS-2 coverage for Release 006 is available between 14 October 2018 and 27 December 2023. The freeboard retrieval procedures are documented in [20]. An assessment using airborne data [21] indicates that the uncertainty in IS-2 freeboard retrievals is ~2–4 cm.

2.4. Multiyear Sea Ice Coverage and Sea Ice Extent

Gridded fields of MYI coverage (2003–2018) are from QuikSCAT and ASCAT acquisitions processed using the approach in [22]. Both instruments are moderate-resolution wide-swath scatterometers that provide daily coverage of the Arctic Ocean. Uncertainty in the classification is ±10% in area coverage with near even mixtures of MYI and seasonal ice, and better quality in areas with nearly pure ice types (i.e., first-year or multiyear ice). After 2018, the delineation of ice types is based on their separation in the observed ice thickness distributions. The September sea ice extent record used here is from NSIDC [23].

3. Estimation of Ice Thickness

In this section, we first describe the assumed layered geometry of the floating ice and provide overviews of our approach to calculate ice thickness from lidar and radar freeboards. Second, we discuss potential non-systematic uncertainties (i.e., due to scattering from ice and snow) in the two freeboards derived from satellite altimetry. Last, we summarize the choice of parameters used in our calculations and the limitations in providing reliable expectations of thickness uncertainties, given our current knowledge of the behavior of these parameters. Snow depth for calculating snow loading, an essential input in using satellite freeboards in thickness calculations, is discussed in Section 4.

3.1. Freeboards from Altimeters

The two-layer model (in Figure 1) shows the simple geometry of the snow- and ice-layers of the floating sea ice assumed in our thickness calculations. Total- and ice-freeboards are, respectively, defined as the vertical distance of the air–snow ${(h}_f)$ and snow–ice ${(h}_{fi})$ interfaces above the local sea surface ${(h}_{ssh})$. The total freeboard ${(h}_f)$, is the sum of the thicknesses of the snow- ${(h}_{fs})$ and ice- ($h_{fi}$) layers:

$$h_f=h_{fs}+h_{fi}.$$

(1)

For the thickness calculations below (Section 3.2), scattering from lidar wavelengths (IS, IS-2) are assumed to be from the air–snow interface and at radar wavelengths (CS-2), during winter conditions, to be from the snow–ice interface. That is, the lidar-derived freeboards are equivalent to the total freeboards ($h_f=h_f^{IS}\mathrm{and}{h}_f=h_f^{IS2}$), and in the absence of a snow layer, the radar-derived freeboards to the ice freeboards ($h_{fi}=h_{fi}^{CS2}$). In the presence of a snow layer ${(h}_{fs})$, the propagation delay in the snow at the altimeter wavelength is accounted for as follows:

$$h_{fi}=h_{fi}^{CS2}+h_{fs}\left({\eta }_s-1\right).$$

(2)

where ${\eta }_s$ is the refractive index of snow; this parameter is dependent on snow density. The considerations and validity of these assumptions are discussed in the following sections.

Since freeboards (radar or lidar) are referenced to the height of local sea surfaces ${(h}_{ssh})$ adjacent to open water leads, the availability of open leads along the profiled surface controls the density of retrievals. As the sea surface varies along the length of an altimeter segment, the spatial length scale over which one could assume the sea surface height to be constant depends on the acceptable freeboard uncertainty and the expected spatial variability of the sea surface height. A more detailed discussion can be found in [24]. For IS and CS-2, sea ice freeboard estimates are computed in 25 km segments that contain at least one sea surface reference. For IS-2, the segment lengths are 10 km.

3.2. Freeboard-to-Thickness Calculations

Assuming isostatic equilibrium, the equations used to calculate sea ice thickness ($h_i$) from total (snow+ice, $h_f$) or ice freeboards ($h_{fi}$) are below:

$$h_i\left(h_f,h_{fs}\right)=\left({\displaystyle \frac{{\rho }_w}{{\rho }_w-{\rho }_i}}\right)h_f+\left({\displaystyle \frac{{\rho }_s-{\rho }_w}{{\rho }_w-{\rho }_i}}\right)h_{fs}\hspace{1em}\hspace{1em}(\mathrm{from} \mathrm{total}/\mathrm{lidar} \mathrm{freeboard})$$

(3)

$$h_i\left(h_{fi},h_{fs}\right)=\left({\displaystyle \frac{{\rho }_w}{{\rho }_w-{\rho }_i}}\right)h_{fi}+\left({\displaystyle \frac{{\rho }_s}{{\rho }_w-{\rho }_i}}\right)h_{fs}\hspace{1em}\hspace{1em}(\mathrm{from} \mathrm{ice} \mathrm{freeboard})$$

(4)

${\rho }_w,{\rho }_i$, and ${\rho }_s$ are the bulk densities of water, ice, and snow, respectively. These two equations are written to show their explicit dependence on the total and ice freeboards to highlight how the observables from radar ($h_{fi})$ and lidar ($h_f$) relate to the density ratios that appear. Both equations require contemporaneous knowledge of the snow properties (i.e., snow depth—$h_{fs}$ and bulk snow density—${\rho }_s$) of the snow layer (discussed in Section 4). Even though the equations seem straightforward, our current understanding of the behavior of these parameters at the length- and time-scale required to quantify their impact on our retrievals is still incomplete.

3.3. Uncertainties in the Freeboards

For our thickness calculations, scattering from lidar wavelengths (IS, IS-2) is assumed to be from the air–snow (a–s) interface and at radar wavelengths (CS-2), during winter conditions (below −5 °C), to be from the snow–ice (s–i) interface. However, there are considerations regarding potential biases in the resultant thickness estimates if these surface scattering assumptions do not hold.

3.3.1. Location of Snow–Ice (s–i) Interface (Radar Freeboard)

All estimates of Arctic ice thickness from radar freeboards (e.g., CS-2) to date assume that the altimetric returns originate from the snow–ice (s–i) interface to satisfy the need for a well-defined interface in the layered model (Figure 1). It was pointed out in numerous works [10,25,26] that radar penetration into the overlying snow layer is still a subject of investigation and may introduce biases into thickness calculations. Field radar experiments [26,27] were inconclusive but suggest that the dominant returns appeared to be closer to the s–i interface, although a clear dependence on temperature was indicated.

At K_u-band frequencies (i.e., CS-2), the retracking points (RP—where the exact range to the surface is designated) are displaced from the actual ice surface when elevated snow salinities (due to brine wicking and flooding) are found near the s–i interface, or volume scattering in the presence of moisture in the snow layer when the air temperature is just below freezing [25,28]. For Antarctic sea ice, in particular, the salinity of snow layers that has a high-salinity (>10) basal component (0–3 cm thick) and sometimes dampness due to brine wicking when the snow is thin [29] introduces a significant dielectric discontinuity at the s–i interface and will have an impact on CS-2 freeboards.

A scattering model using salinity profiles from snow pits (collected in the Canadian Arctic Archipelago) [30,31] prescribed a potential adjustment of ~7 cm of the RP from first-year ice throughout most of the year. A 7 cm adjustment everywhere results in a reduction in an estimated FYI ice thickness of approximately 0.37 m. While the physical basis of a displacement of the RP due to brine wicking is sound, a better understanding of the seasonal evolution of these geophysical processes and the magnitude of this adjustment (from more comprehensive field programs) is needed if these realistic adjustments were to be applied to individual freeboard estimates. Also, we do find biases of this magnitude in our comparisons with correlative thickness measurements (from submarine and moored upward-looking sonars, Section 5) presented below. In all our thickness calculations, no adjustments for scattering due to potential biases due to a brine layer are made to the sea ice freeboard from CS-2.

3.3.2. Location of Air–Snow (a–s) Interface (Lidar Freeboard)

Snow grains at the IS-2 wavelength (green) absorb light very weakly; thus, in the absence of light-absorbing impurities, the photons in a lidar pulse can scatter off multiple snow grains before returning to the lidar. Multiple scattering adds to the path lengths of photons in the return pulse. This leads to a lowering of the detected surface (or freeboard) in determining the a–s interface. The overall effect of volume scattering on the return depends on the optical properties of the snow and ice; the magnitude of the subsurface-scattering bias delay depends in part on the scattering density of the snow and its bulk absorbance, both of which are determined by the density and grain or bubble size close to the surface. Compared to older snow, fresh snow on sea ice has a smaller effective grain radius (1–2 mm). This means that a photon in fresh snow will experience more scattering events per distance traveled compared to a photon traveling through aged snow and thus will have a much higher probability of exiting the snowpack sooner; this overall effect is a reduction in the pathlengths due to multiple scattering in the aggregate return [32]. A modeling study [33] over the ice sheet suggests decimeter-level biases for snow grains up to 5 mm if the entire photon distribution (including the long tails) is used in determining the a–s interface.

Even though the near-surface snow properties are not known at the time of data acquisition, the effects can be reduced in the surface-finding process. In the IS-2 sea ice surface-finding algorithm [21], the potential effects of subsurface scattering are mitigated by windowing of the photon height distributions to avoid tails (the delayed photons) in the distributions. Only a narrow portion ($\pm 2\sigma )$ around the peak of the return pulse is used. If the signal is sufficiently strong, these steps will lead to an altimetry window that captures the large amplitude parts of a return near the surface. This is a similar approach employed by the IS-2 surface finding algorithm implemented for ice sheet returns [34]. The modeling study suggests that this approach reduces the biases by a factor of 2–3 [33]. Nevertheless, care should be exercised in interpreting surface heights in situations where larger grain size is expected, especially during or near the melt seasons [35], when temperature cycling changes the surface grain size.

3.4. Bulk Densities of Sea Water and Sea Ice

In our calculations, we take the average bulk density of surface seawater (${\rho }_w$) to be 1024 kg/m³. The variability is expected to be in the range of a few parts per thousand, and the introduced error is negligible compared to the other terms in Equations (3) and (4).

The bulk density of sea ice, however, varies with ice age and thickness [28] and with the broad density distinction based on ice type, i.e., first-year or seasonal ice (FYI) and multiyear ice (MYI). Density variations in FYI are associated with brine rejection during growth, reducing the entrained brine volume and lowering the ice density. Lower densities in MYI ice are due to the inclusion of proportionally less brine and more gas from summer drainage, where the salinity of the freeboard portion approaches fresh ice. In isostatic balance, errors in thickness calculations due to uncertainties in bulk density are introduced through the multiplier ${\displaystyle \frac{{\rho }_w}{{\rho }_w-{\rho }_i}}$ in Equations (3) and (4). Lower ice densities reduce the contribution of the freeboard to the thickness estimates.

Several investigators [36,37,38,39] have reviewed sea ice densities from field expeditions, and the effect of their variabilities on thickness calculations is summarized [11]. Density measurements from the Arctic Ice Dynamics Joint Experiment (AIDJEX) [40] and Sever Expeditions from the 1980s point to a dependence of bulk density on ice type and thickness. In particular, [39] suggest that, for thickness retrievals, the densities of FYI and MYI should be more appropriately ${\rho }_i^{FY}=917\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$ and ${\rho }_i^{MY}=882\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$ rather than represented by a single density of ${\rho }_i=917\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$. Lowering the density by 35 kg/m³ of MYI decreases the calculated ice thickness by ~25–30%.

While the retrieved thickness should depend on ice densities, it is difficult to reconcile the differences in the three parameterizations suggested [36,37,38,39] for thickness calculations from a remote sensing perspective. With the younger (<3 years) MY ice cover found in the Arctic in recent years [32], the mean ${\rho }_i^{MY}$ may perhaps be different from that obtained from the much older MY ice from the 1970s and 1980s. In one study [11], CS-2 ice thickness estimates were calculated using a uniform density for FYI and MYI (i.e., ${\rho }_i^{FY}={\rho }_i^{MY}=917\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$) and then using distinct densities for the two ice types (${\rho }_i^{FY}=917\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$ and ${\rho }_i^{MY}=882\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$). Specifically, the following parameterization is used to calculate the area-averaged bulk density,

$${\rho }_i\left(f_{FY}\right)={\rho }_i^{MY}\left(1-f_{FY}\right)+{\rho }_i^{FY}{f}_{FY}$$

(5)

where the fractional coverage of FYI ($f_{FY}$) from analyzed fields of scatterometer data [11]. When the results were compared with correlative ice thickness data sets (from submarines, mooring, IceBridge, airborne EM sensing), they did not find a 25–30% decrease in MYI thickness (which could be up to 1 m in thickness difference for 3 m ice). In fact, the single-density retrievals show population differences that are less than 0.2 m (see

Table 1. Comparisons with correlative data sets.

Mission	Data Source	Differences (m); Correlation
ICESat	BGEP/AIM ULS	−0.14 ± 0.51 (0.58)
	Submarine ULS	−0.10 ± 0.42 (0.63)
CryoSat-2	BGEP ULS	0.06 ± 0.29 (0.79)
	Submarine ULS	0.07 ± 0.44 (0.62)
	Airborne EM (ice+snow)	0.12 ± 0.82 (0.67)
	Operation IceBridge (lidar+radar)	−0.16 ± 0.87 (0.53)

Notes: Airborne EM data provide the thickness of snow plus ice, and not solely ice. The increased scatter in the OIB comparisons is likely due to incomplete sampling due to cloud cover.

)—significantly less than that suggested [38]—and with correlations that are higher than using two different densities (see comparisons in [11] for details). That was the rationale for assuming a single density and suggests a more moderated dependence on ice density.

We realize, however, that there could be compensating errors in our calculations that could hide the efficacy of our selected parameters. Also, biases are not easily separable in these calculations and bulk assessments of thickness estimates.

4. Snow Depth and Density

As mentioned earlier, snow loading in the thickness calculations above requires co-incident measurements of snow depth ($h_{fs})$ and its bulk density ${(\rho }_s)$. Currently, there are no direct measurements of snow depth estimates at the time- and space-scales desired for freeboard-to-thickness retrievals. Below, we provide overviews of the three approaches we used to estimate snow depth in constructing our thickness record. The first and most straightforward approach adapts the somewhat dated monthly climatology [41] to prescribe the snow depth and density over MYI and FYI. The second accumulates snowfall (obtained from atmospheric reanalysis products) on a drifting sea ice cover to produce large-scale time-variable snow depth estimates. The last, more recently developed, approach is based on observed differences in near-contemporaneous lidar (IS-2) and radar (CS-2) freeboard coverage of the Arctic Ocean made possible by the concurrent operation of two altimeter missions. Below, we summarize each of these approaches.

4.1. Snow Depth from Climatology

The Warren snow depth climatology [41] characterizes the average monthly snow depth ($h_{fs})$ and density ${(\rho }_s)$, from field measurements collected between 1954 and 1991. For the entire CS-2 record, we use a slightly modified version of this monthly snow depth ($h_{fs}^W)$ and density (${\rho }_s^W)$ climatology to adapt the somewhat dated compilation to better reflect more recent Arctic conditions, i.e., later onset of freeze-up and beginning of snow accumulation [38,42]. Henceforth, we refer to this climatology as mW99. To address the differences in snow accumulation over FYI and MYI (the field measurements are primarily from older ice) we follow an approach [10] where only a fraction ($\alpha$) of the climatological snow depth is used to represent the reduced snow accumulation over FYI, viz.

$$\begin{gathered} h_{fs}\left(X,t,f_{FY}\right)=h_{fs}^W\left(X,t\right)\left(1-f_{FY}\right)+\alpha h_{fs}^W(X,t)f_{FY} \\ \mathrm{and}, {\rho }_s={\rho }_s^W\left(t\right). \end{gathered}$$

(6)

The fraction ($\alpha$) was suggested by airborne snow depth retrievals from Operation IceBridge [43] over different ice types. First-year ice fractions ($f_{FY}$) are from analyzed fields of spaceborne scatterometer data (QuikSCAT and ASCAT) [22]. The use of $\alpha$ = 0.7 provided the best agreement when our thickness retrievals were compared to correlative data sets [42]; these comparisons are summarized in more detail in Section 5. This approach is used to calculate sea ice thickness for the entire CS-2 record shown in the results, which spans the period between 2010 and 2023.

4.2. Snow Depth Reconstruction from Snowfall in Atmospheric Reanalysis

In our approach [38], snowfall (from atmospheric reanalysis products) accumulated on a drifting sea ice cover is used to produce estimates of snow depth. Others have also used variations of this approach, with procedures for wind-driven redistribution and models for snow layering, to construct seasonal snow depth for the purpose of estimating snow loading in thickness calculations [44,45,46]. Briefly, our process involves cycles of accumulation and advection. The accumulation process begins in September, prior to the summer minimum in the Arctic Ocean sea–ice coverage. Snow accumulation (in snow water equivalent) is recorded at ice parcels on an array of sea ice drift trajectories constructed from ice motion fields. At the beginning of the growth season, ice parcels are located on a uniform 10 km grid before the grid becomes deformed due to the non-uniform drift of individual parcels. Procedurally, the daily cycle of accumulation and ice advection is carried out at each point, this mimics the snow accumulation process in a moving field. To account for surface conditions, snow accumulation occurs only when the 2 m air temperature (from the ERA-Interim fields in our case) is below freezing and the ice concentration is greater than 50%. If the ice concentration drops below 50%, the snow is removed from that location. Since ice concentrations rarely drop below 50% inside the perennial pack, these relatively simple conditions are more relevant to the accumulation process over seasonal ice during the advance of the ice cover in the fall. With these conditions, less snow accumulates where the ice cover is formed later in the season. The IS-derived ice thickness record (2003–2009) reported in [42] is constructed using these fields.

4.3. Snow Depth by Differencing Lidar and Radar Freeboards

Snow depth ($h_{fs}$) can be calculated when near-contemporaneous total freeboard ($h_f$) as measured by IS-2, and sea ice freeboard ($h_{fi}$) are available (see Figure 1) [47]:

$$h_{fs}=h_f^{IS2}-h_{fi}$$

(7)

At temperatures below freezing and assuming that the scattering from the snow–ice interface dominates the returns at K_u-band wavelengths (CS-2 altimeter), the ice freeboard ($h_{fi}$) can be related to the radar-measured CS-2 freeboard $h_{fi}^{CS2}$ by the following:

$$h_{fi}=h_{fi}^{CS2}+h_{fs}\left({\eta }_s-1\right).$$

(8)

As discussed earlier, the observed radar freeboard, $h_{fi}^{CS2}$, must be adjusted to reflect the shorter propagation path length (compared to free space) in the presence of a snow layer ($h_{fs}$) atop the ice surface. Here, ${\eta }_s$ is the refractive index and at microwave frequencies (i.e., K_u-band) [48],

$${\eta }_s=c/c_s({\rho }_s)={(1+0.51{\rho }_s)}^{1.5}$$

(9)

and c is the speed of light in vacuo. The second term in Equation (8) accounts for the reduced speed of the radar wave (c_s) in a snow layer with bulk density ${\rho }_s$. Combining Equations (7) and (8), and solving for $h_{fs}$ gives:

$$h_{fs}={\displaystyle \frac{(h_f^{IS2}-h_{fi}^{CS2})}{{\eta }_s}}$$

(10)

This equation relates snow depth to the IS-2 and CS-2 freeboard differences (i.e., the observables) with one free parameter, ${\eta }_s$, which is dependent on the bulk snow density. We refer to this altimeter-derived estimate as $∆f_s$, to distinguish this estimate from the more generic snow depth, $h_{fs}$, used in the text. In our calculations below, we use the modified climatological snow density with lower bulk density in the fall, shown in Figure 2 [38], derived from [41]. Since this is strictly based on the difference between two observations, there is no dependence on ice type (as discussed earlier).

Snow depths from near-contemporaneous fields of freeboards were calculated using daily gridded fields of IS-2 and CS-2 freeboards (on 25 km grids). Differences are calculated between samples with time separations |∆T| < 10 days, where there are available CS-2 freeboards within a 75 km box. More detailed discussions of procedures and the sensitivities of differing time-separated samples can be found here [49,50]. Retrievals are within a few centimeters (<5 cm) of the available snow depth data acquired by Operation [50] in April 2019 [51]. All IS-2 thickness estimates between 2019 and 2023, when CS-2 and IS-2 freeboards are available, were calculated using snow depth estimates utilizing this approach. The time-variable thickness estimates using snow depth from observed freeboards are compared to those using climatology (described above) in the following section.

5. Results

This section discusses the Arctic sea–ice thickness record from IS, CS-2, and IS-2. We note here that the satellite record between 2003 and 2020 was reported elsewhere [11,42,49,52,53], and the discussion of those changes is abbreviated. The focus on the updated record that includes 2021–2023, processed with the same approaches described in Section 3; these additional two years of IS-2 and CS-2 retrievals are viewed within the context of the entire record. Thickness retrievals using snow depth from climatology and those calculated from differencing freeboards from the five overlapping years of concurrent CS-2 and IS-2 operation (2018–2023) are compared. Here, we first review the assessments of the thickness estimates that were conducted with correlative data sets. Second, we describe the thickness changes over the 20-year satellite record. Third, Arctic-wide volume changes are discussed. Fourth, snow depths from freeboard differences are compared to those from climatology. Last, the thickness changes within the submarine data release area (DRA) in the central Arctic, which date back to 1975, are summarized.

5.1. Assessments with Correlative Measurements

For assessment of the satellite retrievals, thickness estimates were compared with correlative data sets of ice thickness from upward-looking sonars (ULS) acquired by submarines and fixed moorings, and by airborne electromagnetic sounding [11,42]. As mentioned earlier, these correlative measurements, albeit of limited quantity, are valuable because they are less likely to be subjected to the same error sources and potential biases that affect altimetry-based retrievals. The assessments [11,42] are summarized in Table 1. Comparisons of IS retrievals (2003–2008) with thickness estimates from available moored and submarine ULS’s give differences of −0.14 ± 0.51 (0.58) and −0.10 ± 0.42 (0.63), respectively. The quantity within brackets shows the correlation between the two data sets. Similarly, CS-2 thickness estimates were also assessed with various thickness measurements for five winters (between 2010 and 2014) [11]. Differences are 0.06 ± 0.29 m (0.79) (ice draft from moorings), 0.07 ± 0.44 m (0.62) (submarine ice draft), 0.12 ± 0.82 m (0.67) (airborne electromagnetic profiles), and −0.16 ± 0.87 m (0.53) (Operation IceBridge).

Inter-satellite biases between the two satellite-derived thickness records, in the case of IS (2003–2009) and CS-2 (2010-present), where there were no overlaps between altimeter acquisitions, can be assessed using consistent in situ measurements that span both records. In this case, we have ice drafts for the overlapping IS and CS-2 periods from moorings deployed by the Beaufort Gyre Exploration Project (BGEP) [54]. Assessment of ICESat and CS-2 estimates of ice draft from these moorings yield mean differences of 0.14 m and 0.06 m (as listed above), respectively; a quantity that includes errors from the ULS thickness estimates. It should be noted that our present understanding of both the satellite and in situ data sets is insufficient to resolve any inter-satellite bias to a higher degree of certainty [10,11]. However, these analyses provide a measure of confidence in our retrievals.

It is important to emphasize that the space–time variability and potential biases of the competing ice parameters used in the retrievals (e.g., snow depth, snow, and ice density, etc.) have not been sufficiently quantified for reliable analysis of the uncertainties in thickness calculations using traditional error propagation methodologies. Ideally, the expected errors should be time- and space-dependent. Thus, filling the gaps in our knowledge of the error characteristics of the parameters used in the thickness calculations here remains a challenge [10,11,42].

We also note that differences and correlations in Table 1 are between two estimated quantities that are almost never (except on rare occasions) co-registered in time and space, and errors in both these quantities would likely increase the differences and lower the true correlations. Here, we take the uncertainties in our thickness retrievals to be ~0.5 m based on comparisons with the more extensive correlative data sets of ULS data sets from submarines and moorings (Table 1); the variability ranges from 0.29 to 0.51 m. We do not select the airborne EM comparisons because the AEM measurements include the thickness of the snow, and thus not an ice thickness estimate. As for the Operation IceBridge data sets, there are missing data due to cloud cover when compared to our gridded fields of area averages, and thus the larger variance in the difference. This was also reported in [1].

5.2. Sea Ice Thickness

Figure 2 shows the winter thickness fields for the satellite record, and Figure 3 summarizes the changes in the thickness record together with changes in Arctic MYI and FYI coverage. The composite fields are sampled averages on a uniform 25 km grid. Area-averaged ice thickness is calculated within the Arctic basin (of ~7 × 10⁶ km²) bounded by the gateways into the Pacific Ocean (Bering Strait), the Canadian Arctic Archipelago (CAA), and the Greenland (Fram Strait) and Barents Seas. Broadly, the large Arctic thinning (green diamonds, Figure 3a), which occurred prior to 2007, is clearly seen in the IS record [42]. Subsequently, the 13 years of the CS-2 record (from 2010) show more moderate changes and variability in the average basin-wide thickness of 1.8 ± 0.12 m and seems associated with the variability in winter MYI thickness, which is more sensitive to ice deformation and export. There is an overall thinning of ~1.2 m from the 3 m peak thickness in the IS record, which can be compared to the 0.8 m reported in [55] The winter FYI thickness in the CS-2 record (red circles) hovers around 1.4 ± 0.1 m and can be compared to an average FYI thickness of 2.0 ± 0.16 m for the IS record—a smaller change than the basin-wide average primarily driven by the continued loss of thick MYI.

MYI coverage (Figure 3b) has continued to decline since the beginning of the scatterometer record of MYI coverage in 1999 [52]. The last year of the record (2023) saw the winter MYI coverage at less than 1.5 × 10⁶ km². The remaining area of MYI is, not unexpectedly, located north of the Greenland coast and the CAA has an average thickness that is generally >2.5 m. This region was referred to as the ‘last’ ice area of the Arctic Ocean [56]. The CS-2 MYI record (blue circles) shows a slight positive trend and an increase in thickness variability. This trend in thickness is concurrent with decreasing MYI coverage in the Arctic Basin, which is compensated by increases in FYI coverage (seen in Figure 3b).

The increase in sea ice thickness in 2013/14 is accompanied by a notable increase in sea ice volume (higher by ~2500 km³)—this anomaly is discussed in more detail in the next section. Over the record, winter MYI ice thicknesses are correlated to fall ice volume (correlation > 0.60), suggesting sensitivity to and preconditioning by end-of-summer conditions. Throughout the growth season, however, the combination of three processes introduces additional variability in thickness: growth, ice export, and ice convergence. These processes decorrelate the time series. A more in-depth examination of this observed ‘coupling’ is interesting but beyond the scope of the paper, where our focus is on the description of the trends.

Between 2018 and 2023, the CS-2 record (circles) can be compared with the IS-2/CS-2 record (triangles). As mentioned earlier, the thickness estimates for the entire CS-2 record is computed with snow depths from a modified climatology (mW99), and the IS-2/CS-2 record uses snow depths from freeboard (lidar–radar) differences. There is general agreement (with less than 0.1 m) between the ice thickness estimates for all ice types, with the CS-2 estimates consistently higher than the IS-2 estimates. We attribute this to differences in snow depth, which will be addressed in Section 5.4.

5.3. Sea Ice Volume

Ice volume within a grid cell is the product of the mean cell thickness and cell area, and the total is the volume sum of all grid cells within the Arctic Basin (as defined above). Figure 4 shows the estimates for the satellite record to 2023, an updated version of Figure 2 in [49]. Except for the notable increase in total volume in 2013 (discussed above), the trend in the 13-year CS-2 record is insignificant compared with the volume losses during the IS period. The 5-year IS record (2004–2008) depicts losses in Arctic Ocean ice volume at 8020 km³/decade and 12,370 km³/decade in winter (Feb–Mar) and fall (Oct–Nov). The decline in fall volume (~5500 km³) is much higher than the decline in winter volume; this represents a loss of 38% from the peak fall volume in the IS record. These are remarkably steeper trends than the volume loss in the CS-2 record of 740 km³/decade in winter and a slightly positive trend of 540 km³/decade in the fall. The additional two years of CS-2 do not contribute significantly to the trend of the 13-year CS-2 record. The large trend in the shorter IS volume record is heavily weighted by the record-setting minimum ice extent in 2007, which also saw a large loss of ice area (and MYI area) at the end of the melt season [42].

As noted above, the increase in sea ice thickness and ice volume (higher by ~2500 km³) in 2013/2014 (see Figure 2 and Figure 3) was attributed to a near-record extreme ice convergence event north of the CAA and Greenland coasts together with cooler summer air temperatures during the summer of 2013 (compared to 2011–2014 averages) [11,57,58], The convergence and lower temperatures preconditioned the thicker ice condition and higher volume at the beginning of the growth season in 2013 ((Figure 4). The anomalous volume increase, not seen again in the 13-year CS-2 record, is primarily due to ice dynamics; the decline in ice volumes (from this anomaly) in the following years suggests a return to the slow decline after this event. That is, this thicker ice does not typically melt in the region where it is formed but must be advected to a region (e.g., southern Beaufort) with warmer temperatures that are more conducive to melt. Typically, it takes a year or two for this ice to be transported to the southern Beaufort. The signature of thicker ice from the 2013 summer conditions seems to have persisted in the Arctic for more than a year.

Figure 4b shows estimates of ice production calculated as the difference between ice volume seen in the winter and fall. The increase in seasonal ice production has doubled by the faster-growing seasonal ice cover that now occupies more than half of the Arctic Ocean at the end of summer, with the largest increase after the record-setting sea minimum ice extent in 2007 (captured in the IS record). The positive trend in fall volume increase (Figure 4a) is partly offset by the decrease in winter volume. It is likely that higher ice volume in the fall (faster growth prior to the Oct/Nov reference used here), slows the observed increases in growth during winter.

There is better agreement between the winter ice volume estimates (Figure 4a) from snow depth climatology (Section 4.2) and from freeboard differences (described in Section 4.3). The higher CS-2 ice volume estimates in the fall (calculated from climatological snow depths) are due to the higher prescribed snow depth at the beginning of the season. This is examined next.

5.4. Snow Depth

Figure 5a contrasts the development of monthly $∆f_s$ and mW99 snow depths for the five seasons where near-coincident CS-2 and IS-2 freeboard estimates are available; Figure 5b shows the differences between the two estimates. Here, we first discuss mW99 before examining the differences between the $∆f_s$ and mW99 snow depths. A more detailed discussion of the first three years of $∆f_s$ and mW99 can be found in [49], but the 5-year record here provides a broader view of interannual variability.

Broadly, the seasonal behavior of monthly snow depths (dashed lines) from mW99 are similar. The only source of variability between one year and the next is the area-weighting of the interpolated monthly climatology based on ice types (see Section 4.1, Equation (6)). The beginning- and end-of-season (Oct/Apr) averages of 18/33 (MYI), 8/19 (FYI), and 13/22 (basin-wide) cm, show thinner snow depths on FYI compared to MYI. The quantities before and after the slashes are the October and April area averages, respectively. Interannual variability in the monthly snow depth averages for all are close to 1 cm. One shortcoming of climatology is that it does not capture the true interannual variability in the development of snow cover. This highlights a source of error in the use of climatology for estimates of snow loading in thickness calculations.

As expected, the altimeter-derived snow depths, $∆f_s$, exhibit more interannual variability. The area-averaged MYI snow depths exhibited the lowest Oct/Apr values of 17/26 cm in 2020/21 and the highest values of 19/32 cm in 2022–2023. While the mW99 estimates increase monotonically through the season, the $∆f_s$ estimates sometimes exhibit higher snow depths in October compared to November (e.g., 2019/20 and 2020/21). This can be attributed to the thinner snow cover in the advancing ice cover between October and November, where the larger expanse of thinner snow reduces the area-averaged snow depths below that of the October average. The interannual variability of the area-averaged monthly snow depths is highest over MYI (at ~2 cm) in April.

The seasonal evolution of the satellite-derived and climatological snow depths (Figure 5a) shows that mW99 snow depths are generally higher than ∆f_s. Over MYI, these differences increase between October and April. On FYI, ∆f_s is lower than mW99 snow depth, especially in the fall (October to December). The October mW99 snow depths over FYI (red-dashed) are generally higher than the $∆f_s$ because of the challenge of adjusting the early season snow depth ‘climatology’ based on the advance of the ice cover at the end of the summer, especially with the continued decline of the summer ice extent and potential impact of different snow characteristics (e.g., snow density, grain size, ice density) on FYI and MYI. Overall, the differences for all ice types are less than 5 cm (Figure 5b). This suggests that if the ∆f_s are reliable estimates of the actual snow depth, then the use of mW99 snow depths would lead to an area-averaged bias of ~0.1–0.2 m in the retrieved Arctic ice thickness, even though locally the differences would be higher. As an example, the impact of snow depth on thickness retrievals is highlighted in the last two rows of Figure 2. Compared to the use of climatological snow cover (third row), the use of satellite-derived snow cover gave a thinner and more variable ice cover in the Kara Sea and near the Barents Sea Opening (last row) into the Arctic Ocean, which will of geophysical interest in regional investigations.

5.5. Thickness Changes in the Submarine Data Release Area (DRA), 1975–2023

The ICESat, CS-2, and IS-2 records are placed in the context of thicknesses from declassified submarine ice-draft data sets in the DRA following [55]. The ice draft record in the DRA (which covers ~38% of the Arctic Ocean)—analyzed by a regression model—includes measurements from 34 submarine cruises equally distributed in spring and fall between 1975 and 2000. Briefly, the regression model [5] is selected to separate the interannual change, the annual cycle, and the spatial field; the resultant standard deviation in the regression residuals of 0.46 m. The regression analysis gives an annual mean ice draft declined from a peak of 3.13 m in 1980 to a minimum of 2.0 m in 2000, a decrease of 1.13 m (1.21 m in thickness). The steepest rate of decrease is –0.08 m/yr in 1990; the rate slows to a negligible rate of –0.007 m/yr at the end of the record.

Figure 6 shows the combined time series from the regression analysis (RA), and the IS, CS-2 and IS-2 thickness retrievals from 1975 to 2023 for a total record length of 45 years. The data sets are compared at the center of the fall and winter IS campaigns (November 1 and March 1). The values of the winter/summer IS and CS-2 data points (in blue/red) represent the mean thickness within the DRA. The time series of concatenated IS and regression model thickness estimation show a thinning in winter thickness of 1.75 m from 3.64 m in 1980 to 1.89 m in the last year of the IS record. They found a thinning rate of –0.08 m/yr in 1990 compared to a slightly higher winter/summer rate of –0.10/–0.20 m/yr in the 5-year ICESat record (2003–2008). The two records show a long-term trend of sea ice thinning.

The thickness trends in the 13-year CS-2 record (2011–2023) are negligible: 0.01 m/yr and 0.01 m/yr in the winter and fall, respectively. The mean winter CS-2 thickness in the DRA was 1.98 m at the end of the 13-year record—the mean over the record is ~2.0 m. In the overall satellite record, the five IS years seem to have captured the steepest declines in thickness (especially the sharp decrease in thickness after the record-setting years of 2005 and 2007); the thinning in the DRA seems to be almost negligible in the CS-2 years.

The overall thinning in DRA ice thickness since the maximum thickness of 3.64 m (1980) in the results of the submarine regression model has not changed significantly during the winter (Feb–Mar); the mean ice thickness is now close to 2 m—a decrease in thickness of 1.64 m. In the fall (Oct–Nov), the mean thickness increased from less than 1 m after the end of the summer of 2007 to an average thickness of 1.3 m in the CS-2 record. Still, the most significant contrast in the record is between the thickness in the 1980s and that observed during the latter half of the last decade. In the earlier years, the thinning is remarkable in that it occurred in a period associated with significant losses of MYI coverage in the DRA. The changes in the CS-2 and IS-2 records can be expected to be smaller with coverage of thinner seasonal in most of the DRA that is less conditioned by the behavior of older ice.

In addition to the RA and satellite thicknesses, two other thickness data sets are plotted (Figure 6) for comparison: Electromagnetic surveys in the vicinity of the North Pole (1991–2004) and FYI thickness estimates from the acquisitions of Operation IceBridge (2011–2016). There is general agreement in the thinning and, in the case of OIB, the interannual variability. Even though these data do not provide the spatial coverages as those from satellite altimeters, they provide correlative information of the general trends and variability of the satellite data sets used to provide an indication of the broad decline in the thickness of Arctic sea ice.

6. Conclusions

This paper summarized the approaches used in our thickness retrievals and reviewed the 20-year record of Arctic ice thickness/volume estimates from ICESat, CryoSat-2, and ICESat-2 derived using these approaches. In particular, the basin-scale satellite thickness retrievals cover record-setting extremes in end-of-summer ice extent in 2005, 2007, and 2012. The new satellite record, presented here, includes the five years of CS-2 and IS-2 (launched in Oct 2018) thickness estimates and basin-wide snow depth estimates from differencing freeboards from the lidar and radar altimeter. The new snow depth estimates provide a perspective on the use of climatology for the computation of snow loading. The satellite record of thinning and volume loss of Arctic sea ice is placed within the context of analyzed submarine data sets that date back to 1975. The combined record (of submarine and satellite altimeter thickness), spanning 48 years, provides a broad overview of the multi-decadal changes in the data release area of the central Arctic. Many of the features in the satellite and combined records (prior to 2018) were reported elsewhere but, for completeness, are also noted below. The highlights are as follows:

• Over the satellite record, there is an overall thinning of ~1.2 m from the 3 m peak winter thickness in the IS record to the mean winter thickness of 1.8 ± 0.12 m in the 13-year CS-2 record. The low variability of winter FYI thickness in the CS-2 record, hovering around 1.4 ± 0.1 m, can be compared to the thicker FYI of 2.0 ± 0.2 m in the IS record prior to 2007. While the MYI thickness has declined from ~3.5 m in the IS record, there is more variability in the CS-2 record (2.6 ± 0.2 m) even as the MYI coverage continues to decrease. We attribute the variability to the smaller MYI areas, now located north of Greenland and CAA coasts, that consist of areas more prone to ice convergence and associated thickness changes.
• The 5-year IS record (2004–2008) depicts losses in Arctic Ocean ice volume at 8020 km³/decade in winter (Feb–Mar) and 12,370 km³/decade in fall (Oct–Nov), In the IS record, the total decline in fall volume (~5500 km³) is much higher than the decline in winter volume and represents a loss of 38% from the peak fall volume. In contrast, the volume loss in the CS-2 record is negligible by comparison (740 km³/decade in winter with a slightly positive increase of 540 km³/decade).
• Seasonal ice production (difference between winter and fall volume) has doubled by the faster-growing seasonal ice that now occupies more than half of the Arctic Ocean at the end of summer, with the largest increase after the record-setting minimum ice extent seen in 2007 (captured in the IS record).
• The larger thickness and volume trends in the shorter IS record are heavily weighted by the record-setting minimum ice extent in 2007, which also saw a large loss of ice area (and MYI area) at the end of that record [42]. No significant trends in thickness or volume are seen in the 13-year CS-2 record.
• The overall thinning in DRA ice thickness since the maximum thickness of 3.64 m (1980) in the results of the submarine regression model has not changed significantly during the winter (Feb–Mar); the mean ice thickness is now close to 2 m—a decrease of 1.64 m. In the fall (Oct–Nov), the mean thickness increased by less than 1 m after the end of the summer of 2007 to an average thickness of 1.3 m in the CS-2 record. Still, the most significant contrast in the record is between the thickness in the 1980s and that observed during the latter half of the last decade. Again, in the earlier years, the thinning is remarkable in that it occurred in a period associated with large losses of MYI coverage in the DRA. The changes in the CS-2 and IS-2 records can be expected to be smaller with thinner seasonal ice coverage in most of the DRA.
• Overall, the area-averaged snow depths prescribed by climatology (used to compute snow loading) are generally higher (by <5 cm) than those from freeboard differences. While the climatological snow depths do not provide spatial and interannual variability, the comparisons provide a measure of confidence of thickness estimates using solely climatological predictions. The resulting area-averaged thicknesses using snow depths from climatology are generally 0.1–0.2 m thicker than from observed freeboard differences.

For the past two decades, the significant losses of thick MYI dominated the thickness and volume signatures in satellite records (since 1999). The regime shift of the Arctic ice cover towards a largely seasonal ice cover (of >70% in January), reported by many investigators (e.g., [52,59,60,61]), is significant since it changes the expected annual balance growth, melt, and export. As seen in these satellite records, seasonal ice has a thinner snow cover, grows faster, and increases seasonal ice production, even though a significant fraction of this seasonal ice does not become thick enough to survive the summer. Based on this record, the signature of Arctic sea ice thickness and volume now reflects the behavior of seasonal ice, with more moderate volume and thickness trends when compared to years with higher coverage of thicker MYI ice.

Comprehensive assessments of the expected uncertainties in altimeter-derived sea thickness remain a challenge. Residual sources of errors include uncertainties associated with freeboard determination (i.e., location of the scattering horizon for different wavelengths) and the selection of parameters for sea ice thickness calculations (i.e., snow and ice densities, snow depth). Comparisons of retrievals with correlative data sets provide a measure of confidence in our estimates. Future dedicated missions and field programs will be useful for furthering our understanding of some of the retrieval limitations and uncertainties reported in this study. NASA is exploring the next generation of lidar instruments for polar observations. In particular, ESA’s CRISTAL mission [62], the successor of CryoSat-2, is the next polar altimetry mission planned for launch in ~2027. CRISTAL will provide new estimates of snow depth from differencing coincident freeboard measurements at K_a and K_u-band. The payload will also include a passive microwave radiometer with frequency channels ranging from 18.7 to 166 GHz, which will provide independent information on snow properties, including surface type and snow depth. This unique combination of measurements will allow for deeper insights for improvements in retrievals of sea ice freeboard and thickness from altimeter observations.