NASA's Ice, Cloud and Land Elevation Satellite (ICESat) mission is designed to measure changes in elevation of the Greenland and Antarctic ice sheets beginning in January 2003. Time-series of elevation changes will enable determination of the present- day mass balance of the ice sheets, study of associations between observed ice changes and polar climate, and estimation of the present and future contributions of the ice sheets to global sea level rise. Other scientific objectives of ICESat include: global measurements of cloud heights and the vertical structure of clouds and aerosols; precise measurements of land topography and vegetation canopy heights; and measurements of sea ice roughness, sea ice thickness, ocean surface elevations, and surface reflectivity. The Geoscience Laser Altimeter System (GLAS) on ICESat has a 1064 nm laser channel for surface altimetry and dense cloud heights and a 532 nm lidar channel for the vertical distribution of clouds and aerosols. Differences between the characteristics of laser and radar altimetry, such as effective depth of the backscattered signal, elevation accuracy, and footprint location, and their relevance to inter-relating measurements from ERS, Envisat, ICESat, and Cryosat are discussed. Preliminary ICESat results obtained during the calibration and validation period of ICESat are described. ICESat is designed to operate for 3 to 5 years and should be followed by successive missions to measure ice changes for at least 15 years.

ICESat's Laser Measurements of Polar Ice and Atmospheres

KLEMAS, V., 2011. Remote sensing techniques for studying coastal ecosystems: an overview. Journal of Coastal Research, 27(1), 2–17. West Palm Beach (Florida), ISSN 0749-0208. Advances in sensor design and data analysis techniques are making remote sensing systems practical and attractive for use in research and management of coastal ecosystems, such as wetlands, estuaries, and coral reefs. Multispectral and hyperspectral imagers are available for mapping coastal land cover, concentrations of organic/inorganic suspended particles, and dissolved substances in coastal waters. Thermal infrared scanners can map sea surface temperatures accurately and chart coastal currents, while microwave radiometers can measure ocean salinity, soil moisture, and other hydrologic parameters. Radar imagers, scatterometers, and altimeters provide information on ocean waves, ocean winds, sea surface height, and coastal currents, which strongly influence coastal ecosystems. Using airborne light detecting and ranging systems, one can produce bathymetric maps, even in moderately turbid coastal waters. Since coastal ecosystems have high spatial complexity and temporal variability, they frequently have to be observed from both satellite and aircraft in order to obtain the required spatial, spectral, and temporal resolutions. A reliable field data collection approach using ships, buoys, and field instruments with a valid sampling scheme is required to calibrate and validate the remotely sensed information. The objective of this paper is to present an overview of practical remote sensing techniques that can be used in studies of coastal ecosystems.

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Remote Sensing Techniques for Studying Coastal Ecosystems: An Overview

In this contribution it is shown that the so-called “total least-squares estimate” (TLS) within an errors-in-variables (EIV) model can be identified as a special case of the method of least-squares within the nonlinear Gauss–Helmert model. In contrast to the EIV-model, the nonlinear GH-model does not impose any restrictions on the form of functional relationship between the quantities involved in the model. Even more complex EIV-models, which require specific approaches like “generalized total least-squares” (GTLS) or “structured total least-squares” (STLS), can be treated as nonlinear GH-models without any serious problems. The example of a similarity transformation of planar coordinates shows that the “total least-squares solution” can be obtained easily from a rigorous evaluation of the Gauss–Helmert model. In contrast to weighted TLS, weights can then be introduced without further limitations. Using two numerical examples taken from the literature, these solutions are compared with those obtained from certain specialized TLS approaches.

Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation

The Earth Orientation Center of the International Earth Rotation and Reference Systems Service (IERS) has the task to provide the scientific community with the international reference time series of Earth orientation parameters (EOP), referred to as IERS EOP C04 or C04. These series result from a combination of operational EOP series derived from VLBI, GNSS, SLR, and DORIS. The C04 series were updated to provide EOP series consistent with the set of station coordinates of the ITRF 2014. The new C04, referred to as IERS EOP 14C04, is aligned onto the most recent versions of the conventional reference frames (ITRF 2014 and ICRF2). Additionally, the combination algorithm was revised to include an improved weighting of the intra-technique solutions. Over the period 2010–2015, differences to the IVS combination exhibit standard deviations of 40 
 $$\upmu $$
 as for nutation and 10 
 $$\upmu $$
 s for UT1. Differences to the IGS combination reveal a standard deviation of 30 
 $$\upmu $$
 as for polar motion. The IERS EOP 14C04 was adopted by the IERS directing board as the IERS reference series by February 1, 2017.

The IERS EOP 14C04 solution for Earth orientation parameters consistent with ITRF 2014

The weighted total least squares (TLS) method has been developed to deal with observation equations, which are functions of both unknown parameters of interest and other measured data contaminated with random errors. Such an observation model is well known as an errors-in-variables (EIV) model and almost always solved as a nonlinear equality-constrained adjustment problem. We reformulate it as a nonlinear adjustment model without constraints and further extend it to a partial EIV model, in which not all the elements of the design matrix are random. As a result, the total number of unknowns in the normal equations has been significantly reduced. We derive a set of formulae for algorithmic implementation to numerically estimate the unknown model parameters. Since little statistical results about the TLS estimator in the case of finite samples are available, we investigate the statistical consequences of nonlinearity on the nonlinear TLS estimate, including the first order approximation of accuracy, nonlinear confidence region and bias of the nonlinear TLS estimate, and use the bias-corrected residuals to estimate the variance of unit weight.

Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis

Precise transformations between the international celestial and terrestrial reference frames are needed for many advanced geodetic and astronomical tasks including positioning and navigation on Earth and in space. To perform this transformation at the time of observation, that is for real-time applications, accurate predictions of the Earth orientation parameters (EOP) are needed. The Earth orientation parameters prediction comparison campaign (EOP PCC) that started in October 2005 was organized for the purpose of assessing the accuracy of EOP predictions. This paper summarizes the results of the EOP PCC after nearly two and a half years of operational activity. The ultra short-term (predictions to 10 days into the future), short-term (30 days), and medium-term (500 days) EOP predictions submitted by the participants were evaluated by the same statistical technique based on the mean absolute prediction error using the IERS EOP 05 C04 series as a reference. A combined series of EOP predictions computed as a weighted mean of all submissions available at a given prediction epoch was also evaluated. The combined series is shown to perform very well, as do some of the individual series, especially those using atmospheric angular momentum forecasts. A main conclusion of the EOP PCC is that no single prediction technique performs the best for all EOP components and all prediction intervals.

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Achievements of the Earth orientation parameters prediction comparison campaign

Coordinate transformation is one of the most commonly used processes in geodesy and surveying. Coordinates of points in one coordinate system are to be obtained in another coordinate system. To this end, the transformation parameters between two individual coordinate systems are calculated from the identical points, coordinates of which are known in both systems. This is achieved by the least-squares (LS) estimation. LS estimation is the classical approach in adjustment computations. It consists of a functional model that depicts the functional relation between the unknowns and the observations, and a stochastic model that represents the relative accuracies between the observations. In some cases, such as coordinate transformation, errors occur both in the observation vector and the design matrix. In classical approach, this is usually ignored and this ignorance remains as an uncertainty in the solution results. One way to take these errors in design matrix into account is to use Total Least Squar...

Total Least Squares Solution of Coordinate Transformation

The short-term prediction of Earth rotation parameters (ERP) (length-of-day and polar motion) is studied up to 10 days by means of ANFIS (adaptive network based fuzzy inference system). The prediction is then extended to 40 days into the future by using the formerly predicted values as input data. The ERP C04 time series with daily values from the International Earth Rotation Service (IERS) serve as the data base. Well-known effects in the ERP series, such as the impact of the tides of the solid Earth and the oceans or seasonal variations of the atmosphere, were removed a priori from the C04 series. The residual series were used for both training and validation of the network. Different network architectures are discussed and compared in order to optimize the network solution. The results of the prediction are analyzed and compared with those of other methods. Short-term ERP values predicted by ANFIS show root-mean-square errors which are equal to or even lower than those from the other considered methods. The presented method is easy to use.

Prediction of Earth rotation parameters by fuzzy inference systems

Deformation analysis is one of the main research fields in geodesy. Deformation analysis process comprises measurement and analysis phases. Measurements can be collected using several techniques. The output of the eval- uation of the measurements is mainly point positions. In the deformation analysis phase, the coordinate changes in the point positions are investigated. Several models or ap- proaches can be employed for the analysis. One approach is based on a Helmert or similarity coordinate transforma- tion where the displacements and the respective covariance matrix are transformed into a unique datum. Traditionally a Least Squares (LS) technique is used for the transforma- tion procedure. Another approach that could be introduced as an alternative methodology is the Total Least Squares (TLS) that is considerably a new approach in geodetic applications. In this study, in order to determine point displacements, 3-D coordinate transformations based on the Helmert transforma- tion model were carried out individually by the Least Squares (LS) and the Total Least Squares (TLS), respectively. The data used in this study was collected by GPS technique in a landslide area located nearby Istanbul. The results obtained from these two approaches have been compared.

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Deformation analysis with Total Least Squares

Prediction of Earth rotation parameters (ERPs) is of importance especially for near real-time applications including navigation, remote sensing, and hazard monitoring. Therefore, prediction of ERPs at least over a few days in the future is necessary. Fuzzy-inference systems (FIS) are increasingly popular and have advantage over classical FFT that lacks stochastic stability due to non-stationarity, multiscaling, and persistent autocorrelations. Wavelet filtering can be used to handle such phenomenon. A FIS rule-base created from ERP time series, where the volatilities (returns) of the preprocessed series are used, and high frequency signals removed, is summarized. The performance of this system, trained using the fuzzy-wavelet method, is compared with that of a conventional FIS, trained on raw time series. The results show that the predictions by the fuzzy-wavelet method are superior to the FIS-only model for short-term predictions (up to 10 days in future). The improvement of prediction accuracy is found to be about 30% in terms of RMS error.

Orhan Akyilmaz

Papers

Achievements of the Earth orientation parameters prediction comparison campaign

Total Least Squares Solution of Coordinate Transformation

Prediction of Earth rotation parameters by fuzzy inference systems

Deformation analysis with Total Least Squares

Fuzzy-wavelet based prediction of Earth rotation parameters