Satellite Radar Altimeter Data Research Articles

Extraction and analysis of elevation changes in Antarctic ice sheet from CryoSat-2 and Sentinel-3 radar altimeters

New radar altimeters have supported elevation modeling with greater accuracy and extended periods in recent years. Sentinel-3 has been rarely used in previous studies for monitoring the Antarctic ice sheet. The CryoSat-2 and Sentinel-3 satellite radar altimeter data were combined to extract the elevation changes in the Antarctic ice sheet. First, a subregional data filtering method based on a clustering algorithm was proposed to improve the accuracy of the elevation change results for the outliers in the original measurements. Next, an improved model-fitting model that incorporated multiple parameters was used to extract elevation changes, and the results were validated using airborne laser altimetry data and ICESat-2 data. The average changes in the Antarctic ice sheet elevation from 2016 to 2019 were −4.3 ± 0.9 cm / y. The elevation changes of the ice shelf edges with large slopes and complex topography were much larger than the interior. Some specific areas showed substantial elevation changes. The most significant surface decreases occurred at the Pine Island Glacier and the Totten Glacier, while a pronounced surface heightening existed at the Kamb Ice Stream. We reveal an effective method for combining Antarctic ice sheet data from new radar altimeters. This method supports the long-term monitoring of the Antarctic ice sheet and global climate change in the future.

Direct conversion of latitude and height from one ellipsoid to another

I suggest a method for converting geodetic height and latitude from one oblate ellipsoid of revolution to another having the same center and symmetry axis. Unlike other approaches, the method here does not obtain height and latitude from Earth-centered, Earth-fixed (ECEF) Cartesian coordinates; this feature allows height conversion with high accuracy even in cases where the data format limits the precision of the latitude data. Height and latitude conversions can be expressed as a Fourier series in even multiples of latitude, with height changes having only cosines and latitude changes having only sines. The absolute difference of the flattenings of the two ellipsoids furnishes a simple upper bound on the maximum absolute latitude change. Conversions between the TOPEX and WGS84 ellipsoids, a practical necessity for the inter-mission comparison of satellite laser and radar altimeter data, illustrate the findings. Because the differences in the flattenings and semi-major axes of these ellipsoids are small, truncating the Fourier series after the term in twice the latitude gives an approximate conversion with an error less than 9 times 10–12 radians of latitude and about 6 times 10–6 m of height.

Enhancement of a global lake and reservoir database to aid climate studies and resource monitoring utilizing satellite radar altimetry

Here, we describe the expansion and enhancement of a large (surface area ≥100 km2) lake and reservoir database (1.GREALD). These efforts have also resulted in the spin-off of two additional databases, one containing lakes and reservoirs (2.GREALD, area 10–99 km2), and the other containing ephemeral lakes (3.GELD, area ≥100 km2). These databases are unique sources for projects that utilize satellite radar altimeter data to monitor surface water levels. While 1.GREALD aims to be a complete catalog, 2.GREALD focuses on reservoirs in response to applied sciences programs that monitor water and energy resources. The creation of 3.GELD has climate change objectives as well as water resources and ecosystem conservation applications. The recording of information pertaining to the potential overpasses (waterbody crossings) of the current and archive satellite altimeters is a primary objective as is the need to highlight any form of controlled water level variation. The permanent water databases now contain 6282 entries, half experience some form of anthropogenic influence and ∼430 have been identified as potential climatically sensitive terminal lakes. The revised integral surface area distribution is a power law with exponent −1.016. Statistics reveal that with altimetric repeat visit times of 10-day to monthly, at least 80% of the permanent water bodies (≥10 km2) have been overflown at some period since the 1990s. Current information on water use and reservoir formation date show that the primary use of the reservoir class is hydroelectric power, and that China, Brazil, India, Turkey, and Vietnam dominate the dam building in recent decades.

Waveform Decontamination for Improving Satellite Radar Altimeter Data Over Nearshore Area: Upgraded Algorithm and Validation

One of the thorniest problems in altimetry community is retrieving accurate coastal sea surface height, especially in the last several kilometers offshore. It is confirmed in previous studies that decontaminating waveforms is beneficial to improve the quality of coastal SSHs. In this article, we proposed an upgraded strategy for waveform decontamination, including a novel realignment algorithm and gate-wise outlier detector. We validated the new strategy in four test regions using Jason-2 altimeter data. In the validation process, we compared retracked SSHs by 16 retrackers, which include retrackers provided in SGDR (Sensor Geophysical Data Record), ALES (Adaptive Leading Edge Subwaveform), and PISTACH (Prototype Innovant de Système de Traitement pour les Applications Côtières et l’Hydrologie) products. Comparison results verified that retracking the waveforms decontaminated using our new method can greatly improve the SSHs in the coastal region. The 20% threshold retracker (DW-TR20) and the ICE1 retracker (DW-ICE1) based on the decontaminated waveforms outperform other retrackers, especially in 0–4 km zone offshore. DW-TR20 and DW-ICE1 can provide robust SSHs with a consistent accuracy in 0–20 km coastal band and a high correlation (>0.9) with nearby gauge data. To conclude, the upgraded waveform decontamination strategy provides a promising solution for coastal altimetry, which makes it possible to extend reliable observations to the last several kilometers offshore.

Evaluation of Shipboard and Satellite‐Derived Bathymetry and Gravity Data Over Seamounts in the Northwest Pacific Ocean

AbstractEarth's surface topography/bathymetry and gravity fields provide important constraints on crustal structure and the tectonic processes that act on it due, for example, to plate flexure and mantle convection. Such studies require, however, high accuracy measurements at a wide range of spatial scales. During the past few decades much progress has been made in the acquisition of bathymetry and gravity data using both shipboard and satellite altimeter methods. Surprisingly, there have been few comparisons of these data. During April–June, 2019 we had the opportunity onboard a R/V Marcus G. Langseth cruise in the northwest Pacific Ocean to compare data acquired with an EM122 Kongsberg swath bathymetry system and a refurbished Bell Aerospace BGM‐3 gravimeter with the most recent global bathymetry and gravity fields. We find that while the recovery of bathymetry and gravity from satellite radar altimeter data in areas of sparse shipboard data has been impressive, root mean square discrepancies in the range 175.5–303.4 m and 2.6–6.3 mGal exist between shipboard and satellite‐derived data. While these discrepancies are small, they are highly correlated and therefore have implications for the density structure, rock type and geological processes occurring on the deep seafloor. Shipboard data should continue to be acquired, especially over features such as seamounts, banks, and ridges that are associated with short wavelength (<25 km wavelength) bathymetric and gravimetric features beyond that is recoverable in satellite‐derived data.

The Cyclonic Eddy Train in the Indian Ocean Sector of the Southern Ocean as Revealed by Satellite Radar Altimeters and In Situ Measurements

AbstractWe investigated dynamic ocean topography (DOT) to reveal the oceanic subpolar circulation and possible pathway of modified Circumpolar Deep Water (CDW) in the Indian Ocean sector of the Southern Ocean. Satellite radar altimeter data sets were employed to develop monthly DOT in both open water and ice‐covered areas throughout the course of a year. A 0.2° × 0.2° gridded DOT was reconstructed for investigation of the oceanic structure at fine scale. The reconstructed DOT exhibited a “cyclonic eddy train” consisting of the Vincennes eddy, Poinsett eddy, and Sabrina eddies. The relationship between the depth of each eddy and the wind curl showed negative correlations for the Vincennes eddy and Sabrina eddies during wintertime only. Therefore, winds are not the main drivers of the eddies. A hydrographic section in 2017 clearly revealed the vertical structure of the Vincennes eddy. The absolute velocity estimated by the DOT and in situ geostrophic velocity showed equatorward Antarctic Bottom Water (AABW) transport at 6–8 cm s−1 on the western side and poleward transport of CDW at 3–4 cm s−1 on the eastern side of the Vincennes eddy. The net transports of the AABW and CDW layers in the Vincennes eddy were 0.6 ± 0.4 Sv (equatorward) and 0.5 ± 0.36 Sv (poleward), respectively. The order of magnitude of the AABW current speed was confirmed by in situ mooring data. The vertical profiles of absolute velocity suggest the possibility of estimating CDW transport using a satellite altimeter.

Calibration and verification of century based wave climate data record along the Turkish coasts using satellite altimeter data

In order to produce consistent reanalysis of the climate system, ECMWF (The European Centre for Medium-Range Weather Forecasts) has produced firstly an uncoupled atmospheric reanalysis ERA-20C, and then a coupled climate reanalysis, called CERA-20C, which covers the period January 1900 to December 2010. Both data sets are available at 3-hour time increments. Such a century long data can be an alternative to calculate the extreme waves corresponding to low probability of occurrences without extrapolation of extreme value statistics’ results which may contribute to the error in the estimation of design waves in case of small number of wave data. In this study, main purpose is to calibrate and verify the century-based wave data in order to derive the longest and the consistent wave data along the Turkish coasts as a first time to be used in the extreme wave analysis. For this purpose, first of all, significant wave height data of ERA-20C and CERA-20C are compared by using ENVISAT data over the whole Black Sea for 2007–2008 as a pilot study. Comparison results show that both datasets give similar results but CERA-20C seems to be better in terms of statistical error measures. Then CERA-20C significant wave height data are calibrated using satellite Radar Altimeter data set. Jason family of satellites (TOPEX, Jason-1 and 2) and Envisat family of satellites (ERS-2 and Envisat) are inter-calibrated to get the consistent satellite data sets with a total duration of 18 years (1995–2012) for Envisat family and 26 years (1992–2017) for Jason family in order to be used in calibration of CERA-20C wave height. The mean wave period is also estimated from RA backscatter coefficients (Ku and C bands) and the significant wave height by using Artificial Neural Network Method. Then the estimated mean wave periods are used for the calibration of CERA-20C wave period. Calibrated CERA-20C data are compared with in-situ measurements for the verification purposes. Results of verification study show that the calibrated CERA-20C wave data agree well with the in-situ measurements in terms of Quantile-Quantile analysis with lower deviations from y = x line and capture the largest sea states. In fact, CERA-20C, century-based wave data become appropriate to determine the extreme waves to be used in the design of coastal structures along the Turkish coasts.

Estimating Arctic sea ice thickness and volume using CryoSat-2 radar altimeter data

Arctic sea ice is a major element of the Earth’s climate system. It acts to regulate regional heat and freshwater budgets and subsequent atmospheric and oceanic circulation across the Arctic and at lower latitudes. Satellites have observed a decline in Arctic sea ice extent for all months since 1979. However, to fully understand how changes in the Arctic sea ice cover impact on our global weather and climate, long-term and accurate observations of its thickness distribution are also required. Such observations were made possible with the launch of the European Space Agency’s (ESA’s) CryoSat-2 satellite in April 2010, which provides unparalleled coverage of the Arctic Ocean up to 88°N. Here we provide an end-to-end, comprehensive description of the data processing steps employed to estimate Northern Hemisphere sea ice thickness and subsequent volume using CryoSat-2 radar altimeter data and complementary observations. This is a sea ice processor that has been under constant development at the Centre for Polar Observation and Modelling (CPOM) since the early 1990s. We show that there is no significant bias in our satellite sea ice thickness retrievals when compared with independent measurements. We also provide a detailed analysis of the uncertainties associated with our sea ice thickness and volume estimates by considering the independent sources of error in the retrieval. Each month, the main contributors to the uncertainty are snow depth and snow density, which suggests that a crucial next step in Arctic sea ice research is to develop improved estimates of snow loading. In this paper we apply our theory and methods solely to CryoSat-2 data in the Northern Hemisphere. However, they may act as a guide to developing a sea ice processing system for satellite radar altimeter data over the Southern Hemisphere, and from other Polar orbiting missions.

Forecasting Arabian Sea level rise using exponential smoothing state space models and ARIMA from TOPEX and Jason satellite radar altimeter data

Sea level rise is a threat to coastal habitation and is corroborating evidence for global warming. The present study investigated the combined use of quantitative forecasting methods for sea level rise using exponential smoothing state space models (ESMs) and an autoregressive integrated moving average (ARIMA) model fed with sea level data over 17 years (1994–2010). Two levels of ESMs were employed: double (model levels with trend) and triple (model levels, trend and seasonal decomposition). The overall data analysis revealed the better performance of ARIMA in terms of index of agreement (d = 0.79), root-mean-square error (RMSE = 32.8 mm) and mean absolute error (MAE = 25.55 mm) than the triple ESM (d = 0.76; RMSE = 39.86 mm; MAE = 35.02 mm) and double ESM (d = 0.14; RMSE = 52.71 mm; MAE = 45.99 mm) models. The present study results suggest that the rate of Arabian Sea level rise is high, and if this is not taken into consideration many coastal areas may become subject to climate-change-induced habitat loss in future.

Elevation change around Dome A region of Antarctica from EnviSat satellite radar altimetry during 2002–2012

The expected responses of ice sheets to climate warming are growth in the thickness of the inland ice areas and thinning near the margins. In recent decades, researchers have identified glacier acceleration along Antarctic ice sheet coastal margins. However, the study of ice sheet interiors where seasonal accumulation eventually balances ice wastage at the lower elevation is poorly understood. In this paper, the ice sheet elevation change around Dome A region is analyzed from 2002 to 2012 using two million elevation change measurements from EnviSat satellite radar altimeter data covering an area of about 7000 km2. A declining trend of 0.572 ± 1.31 mm/year which means that the Dome A region was in balance during the last decade can be captured. In addition, two obvious changes in accumulation which divide elevation change time series into three independent equilibration stages are also extracted. In order to explain this phenomenon, two speculations related to snowfall and firn compaction are proposed in this paper.

A Matching Method for Establishing Correspondence Between Satellite Radar Altimeter Data and Transponder Data Generated During Calibration

This letter presents a method for matching satellite radar altimeter data and transponder data generated during in situ calibration. The transponder generates a measurement error when it measures the arrival time of the altimeter's transmitted signal and embeds the error in both the transponder's recorded data and the altimeter's recorded data. The second-order finite difference sequence of this error sequence can be extracted from the raw data; thus, the correspondence between two identical but mismatched second-order difference sequences can be uniquely established. The measurement error is utilized, and a data matching method that can uniquely establish the correspondence between the altimeter's recorded data sequence and the transponder's recorded data sequence is presented. This postprocessing method does not increase the real-time signal processing workload of the transponder. Furthermore, the principles underlying this method can be used for any transponder that can adjust the response signal delay during calibration.

Merging and Analysis of Elevation Time Series Over Greenland Ice Sheet From Satellite Radar Altimetry

Spatial–temporal variability and changes of Greenland ice sheet elevation from 1992 to 2008 are analyzed from merged ERS-1, ERS-2, and Envisat satellite radar altimeter data. A methodology for determining intersatellite biases was developed and applied in order to merge measurements from these different satellites and to create continuous and consistent time series. Intersatellite biases of elevation and backscatter coefficient have shown to be significantly affected by the bias between measurements in ascending and descending orbits. Adjustment of elevation time series for its dependence on backscatter coefficient and other waveform parameters performed in this paper substantially reduced the amplitude of elevation seasonal variations and locally corrected elevation change-rate estimates by up to several centimeters per year. It was found that the correction depends not only on the variations in the waveform parameters but also on the temporal variations of the correlation gradients, which represent the sensitivity of the elevation change to the change in the waveform parameters. An elevation change rate of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$+2.8 \pm 0.2\ \hbox{cm/year}$</tex></formula> from 1992 to 2008 over 76% of the Greenland ice sheet area was found. Increases in surface elevation from 1995 observed over the high-elevation regions of Greenland were followed by an elevation decrease from 2006. For the whole period of 1992–2008, the elevation increase is 4.0 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\pm$</tex></formula> 0.2 cm/year over 87% of the area above 1500 m. In contrast, over 38% of the low-elevation areas below 1500 m, the rate of elevation change is <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$-7.0 \pm 1.0\ \hbox{cm/year}$</tex></formula> , and the surface elevation decrease that started from 2000 has continued.

Mediterranean Sea level variations: Analysis of the satellite altimetric data, 1992–2008

Sixteen years of satellite radar altimeter data are analyzed to investigate the sea-level variation (SLV) of the Mediterranean Sea. The time evolution of the overall mean sea level of the Mediterranean Sea follows its own regional dynamics. The geographical distribution of the seasonal signal (annual and semi-annual) indicates that the major features of the Mediterranean Sea circulation are driving the highest seasonal variability, and that an eastward propagation exists between the western and eastern basins. While in previous studies the trend of SLV has been modeled as linear, in this study with a longer record of observations we found that a quadratic acceleration term is statistically significant for practically the whole basin, especially in those regions where the trend provides a significant contribution to the SLV. The inclusion of the quadratic acceleration term accounts better for the Mediterranean SLV trend, as the residual low frequency SLV in wintertime is highly correlated with NAO at zero time lag in almost the whole basin. The residual high-frequency signal variability, on the other hand, can be explained by mesoscale phenomena, such as eddies and gyres. Our comprehensive analysis of the Mediterranean SLV provides source observations for monitoring and understanding of both regular and transient phenomena.

Antarctic ice-shelf thickness from satellite radar altimetry

AbstractIce-shelf thickness is an important boundary condition for ice-sheet and sub-ice-shelf cavity modelling. It is required near the grounding line to calculate the ice flux used to determine ice-sheet mass balance by comparison with the upstream accumulation. In this mass budget approach, the accuracy of the ice thickness is one of the limiting factors in the calculation. We present a satellite retrieval of the ice thickness for all Antarctic ice shelves using satellite radar altimeter data from the geodetic phases of the European Remote-sensing Satellite (ERS-1) during 1994–95 supplemented by ICESat data for regions south of the ERS-1 latitudinal limit. Surface elevations derived from these instruments are interpolated on to regular grids using kriging, and converted to ice thicknesses using a modelled firn-density correction. The availability of a new spatial variable firn-density correction significantly reduces the error in ice thickness as this was previously the dominant error source. Comparison to airborne data shows good agreement, particularly when compared to SOAR CASERTZ data on the largest ice shelves. Biases range from −13.0 m for areas where the assumption of hydrostatic equilibrium breaks down, to 53.4 m in regions where marine ice may be present.

A new 1 km digital elevation model of Antarctica derived from combined radar and laser data – Part 2: Validation and error estimates

Abstract. We have developed a new digital elevation model (DEM) of Antarctica from a combination of satellite radar and laser altimeter data. Here, we assess the accuracy of the DEM by comparison with airborne altimeter data from four campaigns covering a wide range of surface slopes and ice sheet regions. Root mean squared (RMS) differences varied from 4.75 m, when compared to a densely gridded airborne dataset over the Siple Coast region of West Antarctica to 33.78 m when compared to a more limited dataset over the Antarctic Peninsula where surface slopes are high and the across track spacing of the satellite data is relatively large. The airborne data sets were employed to produce an error map for the DEM by developing a multiple linear regression model based on the variables known to influence errors in the DEM. Errors were found to correlate highly with surface slope, roughness and density of satellite data points. Errors ranged from typically ~1 m over the ice shelves to between about 2 and 6 m for the majority of the grounded ice sheet. In the steeply sloping margins, along the Peninsula and mountain ranges the estimated error is several tens of metres. Less than 2% of the area covered by the satellite data had an estimated random error greater than 20 m.

Precision and Accuracy of Satellite Radar and Laser Altimeter Data Over the Continental Ice Sheets

The unprecedented accuracy of elevations retrieved from the Ice Cloud and Land Elevation Satellite (ICESat) laser altimeter is investigated and used to characterize the range errors in the Environmental Satellite (Envisat) and European Remote Sensing 2 Satellite (ERS-2) radar altimeters over the continental ice sheets. Cross-mission crossover analysis between time-coincident ERS-2-, Envisat-, and ICESat-retrieved elevations and comparisons to an ICESat-derived digital elevation map are used to quantify the radar elevation error budget as a function of surface slope and to investigate the effectiveness of a method to account for the radar altimeter slope-induced error. The precision and accuracy of the elevations retrieved from the ICESat Geoscience Laser Altimeter System and the European Space Agency radar altimeters on ERS-2 and Envisat are calculated over the Greenland and Antarctic ice sheets using a crossover analysis. As a result of this work, the laser precision is found to vary as a function of surface slope from 14 to 59 cm, and the radar precision varies from 59 cm to 3.7 m for ERS-2 and from 28 cm to 2.06 m for Envisat. Envisat elevation retrievals when compared with ICESat results over regions with less than 0.1deg surface slopes show a mean difference of 9plusmn5 cm for Greenland and -40plusmn98 cm over Antarctica. ERS-2 elevation retrievals over these same low surface slope regions differ from ICESat results by -56plusmn72 cm over Greenland and 1.12plusmn1.16 m over Antarctica. At higher surface slopes of 0.7deg to 0.8deg, the Envisat/ICESat differences increase to -2.27plusmn23 m over Greenland and to 0.05plusmn26 m over Antarctica

Improved Methods for Analysis of Decadal Elevation-Change Time Series Over Antarctica

In this paper, several techniques to improve the processing and analysis of decadal elevation-change time series (ECTS) constructed using satellite radar altimeter data over the Antarctic ice sheet are described. First, a method that improves both the quality and quantity of ice-sheet ECTS is introduced. By dynamically selecting the reference month used in constructing ECTS for a given local region, the maximum number of elevation-change estimates are used in a matrix processing technique. This can improve ECTS quality while also generating ECTS in new areas, leading to a significant increase in spatial coverage. Next, an improved autoregressive (IAR) approach is presented for modeling nonlinear medium-period variations in decadal Antarctic ECTS. This builds upon previous work where an AR model was used to characterize seasonal and interannual variations in ice-sheet ECTS. The improved approach avoids overdecomposition by adopting an iterative local average filter to estimate nonlinear medium-period trends. Monte Carlo simulations show that the IAR method significantly outperforms the AR method when realistic nonlinear trends are present. Because of these characteristics, the IAR model is able to adequately characterize seasonal, interannual, and medium-period nonlinear signals present in decadal ECTS and extract their long-term trends with very small error. This is important for accurate measurement of decadal elevation change over the Antarctic ice sheet and for assessing the impact of these changes on the global sea level

The accuracy of digital elevation models of the Antarctic continent

The accuracy of two widely used digital elevation models of Antarctica was assessed using data from the Geoscience Laser Altimeter System onboard ICESat. The digital elevation models were derived from satellite radar altimeter and terrestrial data sets. The first, termed JLB97, was produced predominantly from ERS-1 data while the second, termed, RAMPv2 included other sources of data in areas of high relief and poor coverage by ERS-1. The accuracy of the models was examined as a function of surface slope and original data source. Large errors, in excess of 100 m, were ubiquitous in both models in areas where terrestrially-derived elevation data had been used but were more extensive in RAMPv2. Elsewhere, the systematic error (bias) was found to be a monotonic function of slope for JLB97, with a more complex, less predictable bias for RAMPv2. The magnitude of the global, slope-dependent, bias ranged from less than a metre to slightly over 10 m but with much larger regional deviations. The random error ranged from about 1 m to over 100 m depending on the DEM and slope. The random error was consistently over a factor two larger for RAMPv2 compared to JLB97.

HERZFELD, U. C. 2004. Atlas of Antarctica. Topographic Maps from Geostatistical Analysis of Satellite Radar Altimeter Data. xvi+364 pp. Berlin, Heidelberg, New York: Springer-Verlag. Price Euros 149.95 (+VAT at local rate), SFr 254.00, £115.50, US $159.00 (hard covers). ISBN 3 540 43457 7

Think for a while about the vast area of Antarctica that is covered by gently sloping ice. Much of that area, especially in the interior of the continent, has neither been visited on the ground, nor covered in detail by air-borne surveys. How are topographic contours to be drawn on maps of such areas? The answer is either by joining up the few available dots and tracks aided by guesswork, or by using satellite radar altimetry. Herzfeld’s book presents a new series of maps of Antarctica derived from satellite radar altimeter data showing topography of the ice/snow surface. This is therefore a valuable contribution to Antarctic studies. Despite …

An autoregressive model for analysis of ice sheet elevation change time series

We present an autoregressive (AR) model that can effectively characterize both seasonal and interannual variations in ice sheet elevation change time series constructed from satellite radar or laser altimeter data. The AR model can be used in conjunction with weighted least squares regression to accurately estimate any longer term linear trend present in the cyclically varying elevation change time series. This approach is robust in that it can account for seasonal and interannual elevation change variations, missing points in the time series, signal aperiodicity, time series heteroscedasticity, and time series with a noninteger number of yearly cycles. In addition, we derive a theoretically valid estimate of the uncertainty (standard error) in the long-term linear trend. Monte Carlo simulations were conducted that closely emulated actual characteristics of five-year elevation change time series from Antarctica. The Monte Carlo results indicate that the autoregressive approach yields long-term linear trends that are less biased than two other approaches that have been recently used for analysis of ice sheet elevation change time series. In addition, the simulation results demonstrate that the variability (uncertainty) of the long-term linear trend estimates from the AR approach is in very good agreement with the derived theoretical standard error estimates.