Altimetry Errors Research Articles

How well can satellite altimetry and firn models resolve Antarctic firn thickness variations?

Abstract. Elevation changes of the Antarctic Ice Sheet (AIS) related to surface mass balance and firn processes vary strongly in space and time. Their subdecadal natural variability is large and hampers the detection of long-term climate trends. Firn models or satellite altimetry observations are typically used to investigate such firn thickness changes. However, there is a large spread among firn models. Further, they do not fully explain observed firn thickness changes, especially on smaller spatial scales. Reconciled firn thickness variations will facilitate the detection of long-term trends from satellite altimetry; the resolution of the spatial patterns of such trends; and, hence, their attribution to the underlying mechanisms. This study has two objectives. First, we quantify interannual Antarctic firn thickness variations on a 10 km grid scale. Second, we characterise errors in both the altimetry products and firn models. To achieve this, we jointly analyse satellite altimetry and firn modelling results in time and space. We use the timing of firn thickness variations from firn models and the satellite-observed amplitude of these variations to generate a combined product (“adjusted firn thickness variations”) over the AIS for 1992–2017. The combined product characterises spatially resolved variations better than either firn models alone or altimetry alone. It provides a higher resolution and a more precise spatial distribution of the variations compared to model-only solutions and eliminates most of the altimetry errors compared to altimetry-only solutions. Relative uncertainties in basin-mean time series of the adjusted firn thickness variations range from 20 % to 108 %. At the grid cell level, relative uncertainties are higher, with median values per basin in the range of 54 % to 186 %. This is due to the uncertainties in the large and very dry areas of central East Antarctica, especially over large megadune fields, where the low signal-to-noise ratio poses a challenge for both models and altimetry to resolve firn thickness variations. A large part of the variance in the altimetric time series is not explained by the adjusted firn thickness variations. Analysis of the altimetric residuals indicate that they contain firn model errors, such as firn signals not captured by the models, and altimetry errors, such as time-variable radar penetration effects and errors in intermission calibration. This highlights the need for improvements in firn modelling and altimetry analysis.

What Matters in the Effectiveness of Airborne Collision Avoidance Systems? Monte Carlo Simulation of Uncertainties for TCAS II and ACAS Xa

TCAS II is a rule-based airborne collision avoidance system (ACAS) that is used in current commercial air transport operations, and ACAS Xa is a new optimization-based system. Operational validation studies have mainly used deterministic simulations of ACAS performance using various sets of encounters. Recently a new approach was developed, which employs Monte Carlo (MC) simulation of agent-based models to evaluate the impact of sensor errors and pilot response variability. This paper contrasts the results of both approaches in a comparison of TCAS II and ACAS Xa for various types of synthetic encounters. It was found that conventional estimates of near mid-air collision (NMAC) probabilities are often lower than the estimates achieved using MC simulation, and that the biases in the P(NMAC) estimates are consistently larger for ACAS Xa than for TCAS II. Contributions to unresolved risk are largest for pilot performance, then for encounter types, and finally for sensor errors. The contribution of non-responding pilots is much larger than the differences between TCAS II and ACAS Xa. It is concluded that the agent-based MC simulation overcomes the limitations in traditional evaluation of altimetry errors and pilot response, providing an independent means to effectively analyze the robustness of ACASs.

Improving Sea Surface Height Reconstruction by Simultaneous Ku- and Ka-Band Near-Nadir Single-Pass Interferometric SAR Altimeter

Wide swath near-nadir interferometric altimetry is a newly developed technology for sea surface height (SSH) measurement. However, the absence of actual measurement data makes this novel SSH mapping technique difficult to verify and apply for wide swath interferometric altimeters. To verify the designed performance of the scheduled wide swath single-pass interferometric altimeter in the "Guanlan Mission", an airborne campaign was carried out off the coast of Rizhao, China on November 16, 2020. An airborne dual-frequency interferometric radar altimeter system (ADIRAS) with a single-pass mode was utilized for SSH measurement as the first flight. Two pioneering and fundamental works have been conducted: an intensive altimetry error analysis according to the ADIRAS parameter settings along the incident direction, an effective SSH reconstruction approach based on a multichannel likelihood (ML) function, and detailed validation procedures through airborne campaigns illustrated in this study. The results indicated that the difference between the wave-induced sea surface elevation (WSSE) variances derived by the ML approach and GNSS buoy was 2 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , which was smaller than the results of the single band on Ku (11 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) and Ka (6 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). Moreover, the estimated Significant Waves Height (SWH) bias of joint bands was 10 cm, which was also superior to that of Ku (39 cm) and Ka (24 cm). Both simulated data and real airborne dual-frequency InSAR data were employed in this study for cross-validation of the proposed method. This approach represents an effective technique for SSH reconstruction of future spaceborne/airborne interferometric altimeters.

LINE OF SIGHT AUTO-CALIBRATION FOR CO3D ROLLING SHUTTER MATRIX DETECTOR

Abstract. The accurate calibration of the line of sight (LOS) is very important for a high-resolution imaging satellite, especially in a system as Co3D, whose mission is to produce 3D elevation models. A calibration error immediately translates into an altimetry error. Co3D has a matrix and the reading of the lines is done in rolling shutter, each line is read at a different date. So, the geometry of the image is affected by the dynamic perturbations of the attitude during the acquisition time.The objective of the study is to propose a calibration method accurate to 0.1 pixel at 90 percentile. The images needed for calibration must only require one or two satellite passes over the same site, and be compatible with the pointing agility. The method must be robust to residual errors in attitude knowledge.The assumptions of the simulations have been modified in this article to keep the performance of Co3D confidential.

Preliminary study on echo saturation identification and altimetry error correction of laser altimetry satellite waveform

Preliminary study on echo saturation identification and altimetry error correction of laser altimetry satellite waveform

Construction of the Mean Sea Surface Model Combined HY-2A With DTU18 MSS in the Antarctic Ocean

A new Mean Sea Surface (MSS) model called Shandong University of Science and Technology Antarctic Mean Sea Surface model (SDUST_ANT MSS) in the Antarctic Ocean is presented and validated in this paper. The SDUST_ANT MSS updates the DTU18 MSS with 6 years of Exact Repeat Mission (ERM) and Geodetic Mission (GM) data from HY-2A. Collinear adjustment was applied to all the ERM data to obtain the along-track mean sea surface height. Oceanic variability has been removed from the GM data. Crossover adjustment was applied to both the ERM and GM data. We constructed the HY-2A_MSS using HY-2A altimetry data based on optimal interpolation method. Several types of errors (such as white noise, residual effect of oceanic variability, and long wavelength bias) have been taken into account for the determination of MSS using optimal interpolation method. The SDUST_ANT MSS was constructed by mapping HY-2A_MSS onto the DTU18 MSS. The SDUST_ANT MSS was compared with DTU18 MSS and CNES_CLS15 MSS. At wavelengths below 150 km, differences between models are consistent with seafloor topographic gradient. At wavelengths above 150 km, differences are affected by the mesoscale activities and the altimetry errors in coastal areas. The errors of the three models, as indicated by their power spectral densities (PSDs), are of similar orders of magnitude. The absolute error is slightly smaller in SDUST_ANT than in CNES_CLS15 or DTU18.

Estimating Vertical Land Motion and Residual Altimeter Systematic Errors Using a Kalman‐Based Approach

AbstractVertical land motion (VLM) is the connection between absolute sea‐level (ASL) from a satellite altimeter (ALT) and relative sea‐level from a tide gauge (TG). VLM is often sparsely observed yet is required for understanding sea‐level rise. Many studies have sought to exploit ALT and TG data to infer VLM, yet regionally correlated systematic errors in altimetry have not been considered. We have developed a Kalman filtering and smoothing framework to simultaneously estimate location‐specific VLM and residual mission‐specific systematic errors in a geocentric reference frame. We used ALT minus TG, ALT crossovers and global positioning system (GPS) bedrock height observations in a multi‐stage solution approach that gradually separated time‐variable parameter estimates in an ill‐posed problem. We evaluated the performance of the method using the Jason‐series along‐track data in the Baltic Sea, where glacial isostatic adjustment is the dominant driver of VLM. We estimated local VLM variability at TGs of up to ∼4.5 mm/yr which is not evident in spatially interpolated GPS velocities. The estimated regional altimeter errors are significant and within the range of ∼±0.5–2.5 mm/yr. Our approach improves agreement between ASL estimates from ALT and TG records, provides a ∼20% decrease in root mean squared error of latitudinal ASL variability at TGs, and a reduction of the ASL rate from altimetry by ∼0.3 mm/yr across the region. This method advances the ALT‐TG approach to determining VLM at TG locations and systematic errors of altimetry, which is broadly applicable to other regional‐ and global‐scale studies.

Local sea level trends, accelerations and uncertainties over 1993\u20132019

Satellite altimetry missions provide a quasi-global synoptic view of sea level variations over more than 25 years and provide regional sea level (SL) indicators such as trends and accelerations. Estimating realistic uncertainties on these quantities is crucial to address current climate science questions. While uncertainty estimates are available for the global mean sea level (GMSL), information is not available at local scales so far. We estimate a local satellite altimetry error budget and use it to derive local error variance-covariance matrices, and estimate confidence intervals on trends and accelerations at the 90% confidence level. Over 1993–2019, we find that the average local sea level trend uncertainty is 0.83 mm.yr−1 with values ranging from 0.78 to 1.22 mm.yr−1. For accelerations, uncertainties range from 0.057 to 0.12 mm.yr−1, with a mean value of 0.062. We also perform a sensitivity study to investigate a range of plausible error budgets. Local error levels, error variance-covariance matrices, SL trends and accelerations, along with corresponding uncertainties are provided.

Assessment of DUACS Sentinel-3A Altimetry Data in the Coastal Band of the European Seas: Comparison with Tide Gauge Measurements

The quality of the Data Unification and Altimeter Combination System (DUACS) Sentinel-3A altimeter data in the coastal area of the European seas is investigated through a comparison with in situ tide gauge measurements. The comparison was also conducted using altimetry data from Jason-3 for inter-comparison purposes. We found that Sentinel-3A improved the root mean square differences (RMSD) by 13% with respect to the Jason-3 mission. In addition, the variance in the differences between the two datasets was reduced by 25%. To explain the improved capture of Sea Level Anomaly by Sentinel-3A in the coastal band, the impact of the measurement noise on the synthetic aperture radar altimeter, the distance to the coast, and Long Wave Error correction applied on altimetry data were checked. The results confirmed that the synthetic aperture radar altimeter instrument onboard the Sentinel-3A mission better solves the signal in the coastal band. Moreover, the Long Wave Error processing contributes to reduce the errors in altimetry, enhancing the consistency between the altimeter and in situ datasets.

Introducing Along-Track Error Correlations for Altimetry Data in a Regional Ocean Prediction System

AbstractBecause of the systematic error in the processing of altimetry data, sea level anomaly (SLA) observation errors are likely affected by nonnegligible spatial correlations. To account for these, we exploit the synergy of altimetry data with in situ profiles from gliders, piloted to follow the altimetry tracks during the Long-Term Glider Mission for Environmental Characterization 2017 (LOGMEC17) observational campaign in the Ligurian Sea. The assimilation of along-track unfiltered sea level anomalies in a regional ocean analysis and forecast system is consequently optimized by means of introducing spatial correlations for the SLA observation errors. In particular, collocated data of glider and altimetry are used to derive an along-track error covariance model for the sea level anomaly assimilation, assuming that most of the covariance behavior versus separation distance stems from altimetry. Spatial scales of the altimetry error are found to have a correlation radius of about 12 km for the dataset utilized in the Ligurian Sea, using a simple Gaussian shape for the error correlation, shorter than the correlation radius found through assimilation output diagnostics. A variational data assimilation system is modified to relax the usual assumption of uncorrelated altimetry observation errors, thus allowing for along-track error correlations. Its implementation provides promising results in the regional ocean prediction system, outperforming in most verification skill scores the use of uncorrelated observational errors without compromising the analysis scheme efficiency.

Assessment of UAV-photogrammetric mapping accuracy based on variation of ground control points

Civil engineering uses digital elevation models (DEMs) and orthophotos as basic material to be able to design and execute any project. UAV photogrammetry has made it possible to obtain this type of information in an economic and practical way. However, it is necessary to know the accuracy of the data and that it is within the admissible limits. There are many factors that affect the accuracy of products resulting from UAV photogrammetry. Of all of these, the effect of the number of ground control points (GCPs) and their distribution in the study area are especially significant. Different distributions of GCPs have been studied to try to optimize the products obtained by UAV photogrammetry. Of all the distributions tested, the best results were obtained with edge distribution and stratified distribution. Therefore, it is necessary to place GCPs around the edge of the study area to minimize planimetry errors. In addition, it is advisable to create a stratified distribution inside the study area with a density of around 0.5–1 GCP × ha−1 to minimize altimetry errors. The combination of these two distributions minimizes the total error obtained.

ALTIMETRY ASSESSMENT OF ASTER GDEM v2 AND SRTM v3 DIGITAL ELEVATION MODELS: A CASE STUDY IN URBAN AREA OF BELO HORIZONTE, MG, BRAZIL

Abstract: This work is an altimetry evaluation study involving Digital Elevation Models ASTER GDEM version 2 and SRTM version 3. Both models are readily available free of charge, however as they are built from different remote sensing methods it is also expected that they present different data qualities. LIDAR data with 25 cm vertical accuracy were used as reference for assessment validation. The evaluation study, carried out in urbanized area, investigated the distribution of the residuals and the relationship between the observed errors with land slope classes. Remote sensing principles, quantitative statistical methods and the Cartographic Accuracy Standard of Digital Mapping Products (PEC-PCD) were considered. The results indicated strong positive linear correlation and the existence of a functional relationship between the evaluated models and the reference model. Residuals between -4.36 m and 3.11 m grouped 47.7% of samples corresponding to ASTER GDEM and 63.7% of samples corresponding to SRTM. In both evaluated models, Root Mean Square Error values increased with increasing of land slope. Considering 1: 50,000 mapping scale the PEC-PCD classification indicated class B standard for SRTM and class C for ASTER GDEM. In all analyzes, SRTM presented smaller altimetry errors compared to ASTER GDEM, except in areas with steep relief.

Numerical Computation of the Electromagnetic Bias in GNSS-R Altimetry

In radar altimetry, the electromagnetic (EM) bias is originated by the smaller reflectivity of wave crests than troughs; thus, the average sea surface height is underestimated. Bias uncertainty is currently the largest factor in altimetry error budgets. The EM bias in a bistatic forward-scattering configuration at L-band, such as in Global Navigation Satellite Systems Reflectometry (GNSS-R) altimetry, remains one of the major sources of uncertainty in the altimetry error budget. In this paper, the EM bias is computed using numerical simulations. To do so, a time-dependent synthetic non-Gaussian sea surface is created using the Pierson–Moskowitz and Elfouhaily sea surface height spectra and spreading function. The sea surface is then discretized in facets and “illuminated” using a right-hand circular polarization GNSS signal, previously recorded by an up-looking antenna connected to a data logger. The waves scattered from each facet are then computed using the physical optics method under the Kirchhoff approximation, and the radar cross section of each facet is computed. The scattered electric fields are “collected” by a down-looking left-hand circular polarization antenna, and the EM bias is computed based on its fundamental definition. The numerical model is validated against Millet's model (a combined model of the weakly non-linear and modulation transfer models) with real data at C- and Ku-bands. Then, the numerical model is applied at L-band, for bistatic configurations, including different azimuth angles and different wind speeds. It is found that the EM bias is almost insensitive to the sea surface spectra selected and increases with increasing wind speed and incidence/scattering angle (up to ∼-20 cm at $\theta_{i,s}=45^{\circ}$ and $U_{10}=12 \mbox{m/s}$ ), and it also exhibits a non-negligible azimuthal dependence, which must be accounted for in the error budgets of upcoming GNSS-R altimetry missions.

Investigating the uncertainty of satellite altimetry products for hydrodynamic modelling

AbstractSatellite altimetry products are increasingly used in many hydraulic applications, and recent studies demonstrate their suitability for the calibration of hydraulic models. The study investigates the effect of satellite‐data uncertainty on the calibration of a quasi‐two‐dimensional (quasi‐2D) model of the middle‐lower portion of the Po river (~140 km). We refer to extended (~16 years of observations) ERS and ENVISAT altimetry products (i.e. River and Lake Hydrology data, RLH) to investigate the effect of (i) record length (i.e. number of satellite measurements at a given satellite track) and (ii) data uncertainty (i.e. altimetry measurements errors) on the calibration of the quasi‐2D model. We first present an assessment of ERS and ENVISAT altimetry errors and then perform the investigations in a Monte Carlo framework by generating datasets of synthetic altimetry products. The results of our analysis further emphasize the suitability of satellite data for the calibration of hydraulic models, providing also a quantitative assessment of the effect of the uncertainty of altimetry products. The analysis highlights the higher accuracy of ENVISAT data, which ensures a stable calibration with ~1.5 years of data (Mean Absolute Error, MAE, lower than 0.4 m, ~0.2 m of which results directly from the uncertainty of ENVISAT data). ERS‐based calibrations become stable with longer series (~3.5–5 years of data), and the negative effect of uncertainty in ERS data is higher (i.e. MAE of 0.6–0.9 m, of which 0.4–0.6 m results from the uncertainty of ERS measurements). Copyright © 2015 John Wiley &amp; Sons, Ltd.

Altimetry Combined with Hydrography for Ocean Transport Estimation

Abstract A method to estimate mass and heat transports across hydrographic sections using hydrography together with altimetry data in a geostrophic inverse box model is presented. Absolute surface velocities computed from Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO) altimetry products made up of a combination of sea surface height measurements and geoid estimate are first compared to ship acoustic Doppler current profiler (S-ADCP) measurements of the Observatoire de la Variabilité Interannuelle et Décennale (OVIDE) project along hydrographic sections repeated every 2 yr in summer from Portugal to Greenland. The RMS difference between S-ADCP and altimetry velocities averaged on distances of about 100 km accounts for 3.3 cm s−1. Considering that the uncertainty of S-ADCP velocities is found at 1.5 cm s−1, altimetry errors are estimated at 3 cm s−1. Transports across OVIDE sections previously obtained using S-ADCP data to constrain the geostrophic inverse box model are used as a reference. The new method is found useful to estimate absolute transports across the sections, as well as part of their variability. Despite associated uncertainties that are about 50% larger than when S-ADCP is used, the results for the North Atlantic Current and heat transports, with uncertainties of 10%–15%, reproduce the already observed variability. The largest uncertainties are found in the estimates of the East Greenland Irminger Current (EGIC) transport (30%), induced by larger uncertainties associated with altimetry data at the western boundary.

Combinations of Satellite Crossovers to Study Orbit and Residual Errors in Altimetry

We define combinations of dual‐ and single‐satellite crossover differences to isolate both stationary orbit‐geopotential and non‐geopotential errors in altimetry data. Specifically two types of combinations are found useful. While no combination of differences can resolve the full radial error of single or paired satellites, an approximation of the mean or geographically correlated error of the generally dominant lower orbit of a pair can be found from one kind (substitutions). (The variable part of the error is always available from the single‐satellite crossover differences.) A second useful combination type is found to yield no geopotential orbit error (zeros): uniquely, these can reveal errors in altimetry from imperfect media corrections as well as oceanographic changes in sealevel. The later circumstance is particularly important when the missions for a pair of satellites are disparate in time.

Topography of the Martian tropical regions with ISM

The measurement of the CO 2 column density on Mars, from the 2 μm band, in the Phobos/ISM spectra allows the determination of the altitude of the surface of Mars, with a horizontal spatial resolution of 20 km. The uncertainties involved in this method are described and compared with previous measurements of the Martian topography. Several topographic maps have been calculated, in the region of the high Martian volcanoes and Valles Marineris. Comparison with topographic maps derived from Mariner 9 and Viking measurements shows a good agreement. An average accuracy of about 400 m is obtained, which constitutes a significant improvement, compared with previous altimetry errors, of the order of 1 km. The method has a uniform accuracy over a full observation sequence (about 3000 km wide), and is complementary to the Viking photogrammetric measurements, more accurate on a 100 km scale.

AN INVESTIGATION INTO THE NATURE OF THE ISOBARIC SURFACE IN KENYA

AbstractIn an investigation into altimetry errors, consideration was given to the nature and behaviour of the isobaric surface. From the evidence obtained there are indications that there is a relationship between the problems of heighting by vertical angles and altimetry, and that there is corroboration for this evidence by other experiments conducted to investigate the coefficient of refraction of air.

Recent developments in pressure altimetry

Some of the more significant accomplishments of recent years relating to the improvement of instruments, the measurement and compensation of the errors of static-pressure systems, and the collection of information on the flight technical error are reviewed. Previous studies of the relation between altimetry errors and vertical separation standards are discussed, and the problem of assessing vertical separation standards is examined from an approach different from that used in those studies. On the basis of the present review, the need for further work is indicated for standardizing the calibrations of static-pressure systems, for collecting additional information on the flight technical error, for developing an altitude-deviation monitoring and warning device, and for improving the maintenance practices relating to the testing and installation of the instruments.