The new level of precision and global coverage provided by satellite altimetry is rapidly advancing studies of ocean circulation. It allows for new insights into marine geodesy, ice sheet movements, plate tectonics, and for the first time provides high-resolution bathymetry for previously unmapped regions of our watery planet and crucial information on the large-scale ocean features on intra-season to interannual time scales. Satellite Altimetry and Earth Sciences has integrated the expertise of the leading international researchers to demonstrate the techniques, missions, and accuracy of satellite altimetry, including altimeter measurements, orbit determination, and ocean circulation models. Satellite altimetry is helping to advance studies of ocean circulation, tides, sea level, surface waves and allowing new insights into marine geodesy. Satellite Altimetry and Earth Sciences provides high resolution bathymetry for previously unmapped regions of our watery planet. Satellite Altimetry and Earth Sciences is for a very broad spectrum of academics, graduate students, and researchers in geophysics, oceanography, and the space and earth sciences. International agencies that fund satellite-based research will also appreciate the handy reference on the applications of satellite altimetry.

Satellite altimetry and Earth sciences :a handbook of techniques and applications

You must turn in your code as well as output files. Please generate a report that contains the code and ouput in a single readable format. Getting Started  You may want to download Irfanview image viewing software. It handles pretty much any image type, lets you convert, and provides batch processing.  Download the sample images from the class website. The following question operates on the city.jpg image. (a) Perform image smoothing using a 7×7 averaging filter and a Gaussian filter with σ = 0.5 and 3. Compare the outputs. (b) Perform edge enhancement using the Sobel operator (Matlab's default parameters). Repeat using the Laplacian and Laplacian of Guassian operators. Compare the outputs 2. Frequency Domain Filtering The following question operates on the city.jpg image. (a) Find the Fourier transform of the image. Be sure to center the frequencies. (b) Perform image smoothing in the frequency domain using the filters defined in the previous problem. Compare the output images from the two methods (spatial and frequency) and the time for operation. (c) Perform edge enhancement using the filters defined in the previous problem. (d) Define a lowpass filter in the frequency domain with radius of 1/4 the height. Show the result. Repeat with a similar sized Guassian and compare the results. Give the σ parameter you used and show the output transform image. (e) Repeat with a rectangular filter with the same dimension as the ideal lowpass. Compare the results between the ideal filter and the rectangular approximation. 3. Canny Edge Detection (a) Give the convolution kernels for determining the gradient. You may examine the function gradient.m to help with the explanation. (It may be easiest to apply the gradient to an impulse and inspect the results. (b) Implement the simplified version of the Canny edge detector (single scale). The syntax of the function should be where E contains the detected edges, M the smoothed gradient magnitude, A contains the gradient angle, I is the input image, sig is the σ parameter for the smoothing filter, and tau= [τ h , τ l ] is the two element vector containing the hysteresis thresholds. See Algorithm 6.4 for non-maximal suppression and Algorithm 6.5 for hysteresis thresh-olding. (It may be more efficient to implement the hysteresis as edge tracking)

http://ieeexplore.ieee.org/iel5/5/31355/01457626.pdf

Multidimensional digital signal processing

Our understanding of how global climatic changes are translated into ice-sheet fluctuations and sea-level change is currently limited by a lack of knowledge of the configuration of ice sheets prior to the Last Glacial Maximum (LGM). Here, we compile a synthesis of empirical data and numerical modelling results related to pre-LGM ice sheets to produce new hypotheses regarding their extent in the Northern Hemisphere (NH) at 17 time-slices that span the Quaternary. Our reconstructions illustrate pronounced ice-sheet asymmetry within the last glacial cycle and significant variations in ice-marginal positions between older glacial cycles. We find support for a significant reduction in the extent of the Laurentide Ice Sheet (LIS) during MIS 3, implying that global sea levels may have been 30–40 m higher than most previous estimates. Our ice-sheet reconstructions illustrate the current state-of-the-art knowledge of pre-LGM ice sheets and provide a conceptual framework to interpret NH landscape evolution. How global climatic changes are translated into ice-sheet fluctuations and sea-level change is not well understood. Here the authors present a compilation of empirical data and numerical modelling results of pre-LGM Northern Hemisphere ice sheet changes and show pronounced ice-sheet asymmetry within the last glacial cycle and significant variations in ice-marginal positions between older glacial cycles.

The configuration of Northern Hemisphere ice sheets through the Quaternary.

Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible because it works with a user-defined weight matrix; and it is attractive because it allows one to directly apply the existing body of knowledge of LS theory. In this contribution, we present the LS-VCE method for different scenarios and explore its various properties. The method is described for three classes of weight matrices: a general weight matrix, a weight matrix from the unit weight matrix class; and a weight matrix derived from the class of elliptically contoured distributions. We also compare the LS-VCE method with some of the existing VCE methods. Some of them are shown to be special cases of LS-VCE. We also show how the existing body of knowledge of LS theory can be used to one’s advantage for studying various aspects of VCE, such as the precision and estimability of VCE, the use of a-priori variance component information, and the problem of nonlinear VCE. Finally, we show how the mean and the variance of the fixed effect estimator of the linear model are affected by the results of LS-VCE. Various examples are given to illustrate the theory.

/pdf/least-squares-variance-component-estimation-45k4p2blaz.pdf

Least-squares variance component estimation

The primary goal of the German TanDEM-X mission is the generation of a highly accurate and global Digital Elevation Model (DEM) with global accuracies of at least 10 m absolute height error (linear 90% error). The global TanDEM-X DEM acquired with single-pass SAR interferometry was finished in September 2016. This paper provides a unique accuracy assessment of the final TanDEM-X global DEM using two different GPS point reference data sets, which are distributed across all continents, to fully characterize the absolute height error. Firstly, the absolute vertical accuracy is examined by about three million globally distributed kinematic GPS (KGPS) points derived from 19 KGPS tracks covering a total length of about 66,000 km. Secondly, a comparison is performed with more than 23,000 “GPS on Bench Marks” (GPS-on-BM) points provided by the US National Geodetic Survey (NGS) scattered across 14 different land cover types of the US National Land Cover Data base (NLCD). Both GPS comparisons prove an absolute vertical mean error of TanDEM-X DEM smaller than ±0.20 m, a Root Means Square Error (RMSE) smaller than 1.4 m and an excellent absolute 90% linear height error below 2 m. The RMSE values are sensitive to land cover types. For low vegetation the RMSE is ±1.1 m, whereas it is slightly higher for developed areas (±1.4 m) and for forests (±1.8 m). This validation confirms an outstanding absolute height error at 90% confidence level of the global TanDEM-X DEM outperforming the requirement by a factor of five. Due to its extensive and globally distributed reference data sets, this study is of considerable interests for scientific and commercial applications.

Accuracy assessment of the global TanDEM-X Digital Elevation Model with GPS data

Over the past few years, a significant amount of research has been conducted on the formulation of carrier phase corrections in order to enhance ambiguity resolution and to increase the distances over which precise positioning can be achieved. Recently the use of a network of multiple GPS reference stations for generating carrier phase-based corrections has emerged with great promise for use in real-time environments. However, little research has been conducted on the distribution of these corrections to potential GPS users located within, and surrounding, the network coverage area. This is an integral part of real-time kinematic DGPS, and it must be adequately addressed before a practical realization of the multireference station concept is implemented. The focus of this paper is to present a comprehensive summary of some of the multiple reference station methods, with specific attention directed toward the correction generation and dissemination processes. More specifically, the various multi-reference station methodologies have been categorized according to their underlying correction generation framework, but will be discussed in terms of the correction dissemination options presented by the various authors. The for main categories of methods investigated in this paper are: (a) partial derivative algorithms, (b) linear interpolation algorithms, (c) condition adjustment algorithms, and (d) virtual reference station methodologies. © 2001 John Wiley & Sons, Inc.

An Overview of Multi-Reference Station Methods for Cm-Level Positioning

An analysis on the optimal combination of geoid, orthometric and ellipsoidal height data

The well-known statistical tool of variance component estimation (VCE) is implemented in the combined least-squares (LS) adjustment of heterogeneous height data (ellipsoidal, orthometric and geoid), for the purpose of calibrating geoid error models. This general treatment of the stochastic model offers the flexibility of estimating more than one variance and/or covariance component to improve the covariance information. Specifically, the iterative minimum norm quadratic unbiased estimation (I-MINQUE) and the iterative almost unbiased estimation (I-AUE) schemes are implemented in case studies with observed height data from Switzerland and parts of Canada. The effect of correlation among measurements of the same height type and the role of the systematic effects and datum inconsistencies in the combined adjustment of ellipsoidal, geoid and orthometric heights on the estimated variance components are investigated in detail. Results give valuable insight into the usefulness of the VCE approach for calibrating geoid error models and the challenges encountered when implementing such a scheme in practice. In all cases, the estimated variance component corresponding to the geoid height data was less than or equal to 1, indicating an overall downscaling of the initial covariance (CV) matrix was necessary. It was also shown that overly optimistic CV matrices are obtained when diagonal-only cofactor matrices are implemented in the stochastic model for the observations. Finally, the divergence of the VCE solution and/or the computation of negative variance components provide insight into the selected parametric model effectiveness.

Calibration of geoid error models via a combined adjustment of ellipsoidal, orthometric and gravimetric geoid height data

The detection and monitoring of surface water and its extent are critical for understanding floodwater hazards. Flooding and undermining caused by surface water flow can result in damage to critical infrastructure and changes in ecosystems. Along major transportation corridors, such as railways, even small bodies of water can pose significant hazards resulting in eroded or washed out tracks. In this study, heterogeneous data from synthetic aperture radar (SAR) satellite missions, optical satellite-based imagery and airborne light detection and ranging (LiDAR) were fused for surface water detection. Each dataset was independently classified for surface water and then fused classification models of the three datasets were created. A multi-level decision tree was developed to create an optimal water mask by minimizing the differences between models originating from single datasets. Results show a water classification uncertainty of 4–9% using the final fused models compared to 17–23% uncertainty using single polarization SAR. Of note is the use of a high resolution LiDAR digital elevation model (DEM) to remove shadow and layover effects in the SAR observations, which reduces overestimation of surface water with growing vegetation. Overall, the results highlight the advantages of fusing multiple heterogeneous remote sensing techniques to detect surface water in a predominantly natural landscape.

Fusion of SAR, Optical Imagery and Airborne LiDAR for Surface Water Detection

The optimal combination of global positioning system ~GPS! geometric heights with gravimetrically derived geoid undula- tions for the determination of orthometric heights above mean sea level ~GPS/geoid leveling!, or more precisely with respect to a vertical geodetic datum, requires the incorporation of a parametric corrector surface model. Such a parametric model is needed to absorb the datum inconsistencies and systematic distortions inherent among the different types of height data. An analysis for the achievable accuracy of relative GPS/geoid leveling is performed in this paper, using the covariance ~CV! matrix of the estimated parameters in the corrector surface model, the standard measuring accuracy of GPS height differences, and the relative internal accuracy of a gravimetric geoid model. A test network of spirit leveled GPS control points located in the southwestern part of Canada has been used to perform a simulative integrated least-squares adjustment of all three types of height data, and to obtain the CV matrix of the parameters in the corrector surface model. The input CV matrices for the GPS and the orthometric height values at the control network points have been computed through separate simulative adjustments that take into account the measuring accuracy of GPS and spirit leveling. The input accuracy for the geoid undulation differences is based on the performance evaluation of the GSD95 Canadian geoid model in western Canada. The focus is placed on studying the effects of the combined relative accuracy of GPS and geoid data, in conjunction with a number of different parametric corrector surface models, for GPS/geoid leveling on new baselines within the test network area.

Georgia Fotopoulos

Papers

An Overview of Multi-Reference Station Methods for Cm-Level Positioning

An analysis on the optimal combination of geoid, orthometric and ellipsoidal height data

Calibration of geoid error models via a combined adjustment of ellipsoidal, orthometric and gravimetric geoid height data

Fusion of SAR, Optical Imagery and Airborne LiDAR for Surface Water Detection

How Accurately Can We Determine Orthometric Height Differences from GPS and Geoid Data