Ute Christina Herzfeld

Insights into spatial sensitivities of ice mass response to environmental change from the SeaRISE ice sheet modeling project I: Antarctica

Sophie Nowicki, Robert A. Bindschadler, Ayako Abe-Ouchi, Andy Aschwanden, Ed Bueler, Hyeungu Choi, Jim Fastook, Glen Granzow, Ralf Greve, Gail Gutowski, Ute Herzfeld, Charles Jackson, Jesse Johnson, Constantine Khroulev, Eric Larour, Anders Levermann, William H. Lipscomb, Maria A. Martin, Mathieu Morlighem, Byron R. Parizek, David Pollard, Stephen F. Price, Diandong Ren, Eric Rignot, Fuyuki Saito, Tatsuru Sato, Hakime Seddik, Helene Seroussi, Kunio Takahashi, Ryan Walker, and Wei Li Wang

Automated geostatistical seafloor classification—principles, parameters, feature vectors, and discrimination criteria

Abstract A geostatistical method for automated seafloor classification is developed and applied to bathymetrie data for a 150 × 100 km area at 26 °N on the western flank of the Mid-Atlantic Ridge. The objective of seafloor classification is to characterize seafloor properties quantitatively, and to use such spatial characteristics to distinguish roughness provinces, and geologic and morphologic units automatically. The method presented here is based on the calculation of directional variograms as spatial structure functions. Parameters determined from filtered variogram functions are used to compose feature vectors, which are shown to be characteristic of morphologic prototypes and surface roughness types, and therefore facilitate a classification. Discrimination criteria include spacing and strike of abyssal hill terrain, smoothness resulting from sediment cover, and parameters related to complexity and morphological significance of abyssal hills and their slopes. Complications of automating the process concern robustness of parameter estimation, optimal window size, and subselection of data. By moving the classification operation through the study area and color-coding property classes, seafloor classification maps are obtained. The concepts of characteristic parameters, feature vectors and discrimination criteria are illustrated in applications to bathymetric data from the western flank of the Mid-Atlantic Ridge. Resultant classification maps are presented, with classes including roughness provinces and morphologic units.

Surge of Bering Glacier and Bagley Ice Field, Alaska : an update to August 1995 and an interpretation of brittle-deformation patterns

In the summers of 1993, 1994 and 1995, video and Global Positioning System location data and 35 mm photographs were collected in a series of systematic survey flights undertaken over the Bering Glacier and Bagley Ice Field system (Alaska) in an effort to characterize surge-crevasse patterns and surge propagation. During survey flights in late August 1995, we observed that the 1993-94 Bering Glacier surge was continuing and still expanding, affecting new areas farther up in Bagley Ice Field. New crevasse fields, similar in pattern to the first surge crevasses we had observed in June 1993 below Khitrov Hills and in other isolated areas of central Bering Glacier and in July 1994 near the head of Bering Glacier (near the junction of Bering Glacier and Bagley Ice Field, in both upper Bering Glacier and Bagley Ice Field), were opening in eastern Bagley Ice Field and in the Steller side of Bagley Ice Field. The type of crevasses seen in the new fields suggested that the surge was propagating into these areas. By analysis and interpretation of the brittle-deformation patterns apparent in the crevasse patterns, some aspects of the past kinematic framework of the surge can be deduced. This approach may lead to a more general classification of ice-surface structures and to their linkage to ongoing processes.

Algorithm for Detection of Ground and Canopy Cover in Micropulse Photon-Counting Lidar Altimeter Data in Preparation for the ICESat-2 Mission

NASAs Ice, Cloud and Land Elevation Satellite-II (ICESat-2) mission is a decadal survey mission (2016 launch). The mission objectives are to measure land ice elevation, sea ice freeboard, and changes in these variables, as well as to collect measurements over vegetation to facilitate canopy height determination. Two innovative components will characterize the ICESat-2 lidar: 1) collection of elevation data by a multibeam system and 2) application of micropulse lidar (photon-counting) technology. A photon-counting altimeter yields clouds of discrete points, resulting from returns of individual photons, and hence new data analysis techniques are required for elevation determination and association of the returned points to reflectors of interest. The objective of this paper is to derive an algorithm that allows detection of ground under dense canopy and identification of ground and canopy levels in simulated ICESat-2 data, based on airborne observations with a Sigma Space micropulse lidar. The mathematical algorithm uses spatial statistical and discrete mathematical concepts, including radial basis functions, density measures, geometrical anisotropy, eigenvectors, and geostatistical classification parameters and hyperparameters. Validation shows that ground and canopy elevation, and hence canopy height, can be expected to be observable with high accuracy by ICESat-2 for all expected beam energies considered for instrument design (93.01%-99.57% correctly selected points for a beam with expected return of 0.93 mean signals per shot (msp), and 72.85%-98.68% for 0.48 msp). The algorithm derived here is generally applicable for elevation determination from photon-counting lidar altimeter data collected over forested areas, land ice, sea ice, and land surfaces, as well as for cloud detection.

Quantitative spatial models of Atlantic primary productivity: An application of geomathematics

The role of physical oceanographical, geochemical, and sedimentological data in the problem of estimating ocean primary productivity is analyzed using geostatistical and algebraic multivariate spatial methods. The available maps mirror difficulties in measuring productivity directly and quantifying biological observations, which result in a very spotty survey coverage of the worlds oceans. This paper takes an approach of estimating the target productivity from related sedimentological, physical oceanographical, and marine geochemical variables. The variables are considered as a multivariate spatial system. Geostatistical estimation is applied to fill in the survey gaps, and the individual data sets are then integrated into a multivariate spatial model using algebraic map comparison. Results are used in the quality assessment and calibration of transform models between the proxy variables and primary productivity. For the Atlantic Ocean, case studies are carried out for phosphate distribution at the 100 m level, foraminifera abundance in sediments, and sea surface temperature. The utility of each proxy variable in the prediction of productivity is discussed. A new map of phosphate concentration at the 100 m level with full coverage of the Atlantic Ocean is compiled by application of geostatistics to an enlarged data base containing new observations. Primary productivity can be predicted from this phosphate map, using transforms that involve also distance from the coastline, and latitude (photosynthesis restriction). Foraminifera abundance is in principle closely related to productivity and is of importance in view of a paleoceanographic reconstruction, but difficulties in measuring and quantifying reflected in the quality of the data set prohibit a direct estimation. The relationship between higher fertility and lower temperature known from upwelling areas does not provide a simple global predictor; instead, sea surface temperature seasonality is an indicator of primary productivity under the constraint of regional availability of nutrients.

Geostatistical analysis of glacier-roughness data

Abstract In most glaciological and hydrological models, surface roughness of snow and ice is an important parameter. However, roughness is generally used only as an estimated parameter for lack of available observations. In this paper, we present a method to collect and analyze ice-surface-roughness data using a specially designed instrument for survey and geostatistical methods for analysis. The glacier-roughness sensor (GRS), built at the University of Trier, records variations in microtopography at 0.2 m × 0.1 m resolution when pulled across an ice surface. Global positioning system data are used for location. After several processing steps, the data are analyzed using geostatistical methods. The mathematical tool used to achieve a morphological characterization of ice-surface types is the variogram. GRS data, variograms and surface roughness analysis are ideal matches for morphological characterization, because none of them requires or provides absolute elevation values. Morphology is described not by absolute elevation values, but by the change of elevation in space which is the derivative of elevation (surface-roughness values). The variogram is calculated from incremental values. Parameters extracted from variograms of GRS data serve to distinguish lake surfaces, wind structures, ridge-and- vaUey systems, melting structures and blue-ice areas. Examples are from Jakobshavn Isbræ drainage basin, West Greenland.

Analysis and simulation of scale-dependent fractal surfaces with application to seafloor morphology

Abstract Common theories on fractal surfaces as observed in geology assume a universality law, in most instances the simplest type of universality, which is self-similarity or self-affinity; in the case of multifractals, another well-known special type of fractals, a more complex form of scale invariance is described using one generating process. The assumption of a scale-invariant universality law, however, implies that a geological object was created by a single underlying process, which is clearly in contradiction to geological knowledge and measurable observations. The processes of crust generation, seafloor spreading, sediment deposition, and erosion work at different specific homogeneity ranges of scale, and such scale dependency is observed in many data sets collected for topographic surfaces. This necessitates the design of methods and algorithms for analysis and simulation of fractal surfaces with scale-dependent spatial characteristica. A suite of algorithms and programs for this purpose is compiled and presented in this paper. Numerical algorithms build on geostatistics, Fourier theory, and some “fractal” methods. The approach presented here uses a dimension parameter for characterization of roughness and an anisotropy factor, given with respect to a principal direction, to capture anisotropic properties. Analytical methods are an isarithm method, a variogram method, a Fourier method, and an isarithm-type Fourier method for estimation of a dimension parameter. In applications to bathymetric data from the western flank of the mid-Atlantic ridge, the variogram method is found most accurate and produces results consistent with geological observations. Interpolation, unconditional simulation and conditional simulation algorithms based on Fourier methods and Fractional Brownian Surfaces localized in scale are combined to construct and merge grids of different scales with specific roughness and anisotropy characteristics, resultant in surfaces with scale-dependent properties which almost exactly reproduce those observed from geophysical data in the seafloor case studies. The scale-dependent simulation methods serve to (1) extrapolate in scale beyond the observed resolution, if roughness and anisotropic properties are known from another area with similar characteristics, and thus provide information on subscale properties for surveys with instrumentation of lower resolution, and (2) extrapolate and simulate in space, if an area has only partly been covered by a survey.

On the influence of kriging parameters on the cartographic output—A study in mapping subglacial topography

Geostatistics provides a suite of methods, summarized as kriging, to analyze a finite data set to describe a continuous property of the Earth. Kriging methods consist of moving window optimum estimation techniques, which are based on a least-squares principle and use a spatial structure function, usually the variogram. Applications of kriging techniques have become increasingly wide-spread, with ordinary kriging and universal kriging being the most popular ones. The dependence of the final map or model on the input, however, is not generally understood. Herein we demonstrate how changes in the kriging parameters and the neighborhood search affect the cartographic result. Principles are illustrated through a glaciological study. The objective is to map ice thickness and subglacial topography of Storglaciären, Kebnekaise Massif, northern Sweden, from several sets of radio-echo soundings and hot water drillings. New maps are presented.

Is the ocean floor a fractal

The topographic structure of the ocean bottom is investigated at different scales of resolution to answer the question: Can the seafloor be described as a fractal process? Methods from geostatistics, the theory of regionalized variables, are used to analyze the spatial structure of the ocean floor at different scales of resolution. The key to the analysis is the variogram criterion: Self-similarity of a stochastic process implies self-similarity of its variogram. The criterion is derived and proved here: it also is valid for special cases of self-affinity (in a sense adequate for topography). It has been proposed that seafloor topography can be simulated as a fractal (an object of Hausdorff dimension strictly larger than its topological dimension), having scaling properties (self-similarity or self-affinity). The objective of this study is to compare the implications of these concepts with observations of the seafloor. The analyses are based on SEABEAM bathymetric data from the East Pacific Rise at 13°N/104°W and at 9°N/104°W and use tracks that run both across the ridge crest and along the ridge flank. In the geostatistical evaluation, the data are considered as a stochastic process. The spatial continuity of this process is described by variograms that are calculated for different scales and directions. Applications of the variogram criterion to scale-dependent variogram models yields the following results: Although the seafloor may be a fractal in the sense of the definition involving the Hausdorff dimension, it is not self-similar, nor self-affine (in the given sense). Mathematical models of scale-dependent spatial structures are presented, and their relationship to geologic processes such as ridge evolution, crust formation, and sedimentation is discussed.

Derivation of deformation characteristics in fast-moving glaciers

Abstract Crevasse patterns are the writings in a glaciers history book—the movement, strain and deformation frozen in ice. Therefore by analysis of crevasse patterns we can learn about the ice-dynamic processes which the glacier has experienced. Direct measurement of ice movement and deformation is time-consuming and costly, in particular for large glaciers; typically, observations are lacking when sudden changes occur. Analysis of crevasse patterns provides a means to reconstruct past and ongoing deformation processes mathematically. This is especially important for fast-moving ice. Ice movement and deformation are commonly described and analyzed using continuum mechanics and measurements of ice velocities or strain rates. Here, we present a different approach to the study of ice deformation based on principles of structural geology. Fast ice movement manifests itself in the occurrence of crevasses. Because crevasses remain after the deformation event and may be transported, overprinted or closed, their analysis based on aerial videography and photography or satellite data gives information on past deformation events and resulting strain states. In our treatment, we distinguish (A) continuously fast-moving glaciers and ice streams, and (B) surge-type glaciers, based on observations of two prototypes, Jakobshavns Isbrae, Greenland, for (A), and Bering Glacier, Alaska, during the 1993–1995 surge, for (B). Classes of ice-deformation types are derived from aerial images of ice surfaces using structural geology, i.e. structural glaciology. For each type, the deformation gradient matrix is formed. Relationships between invariants used in structural geology and continuum mechanics and the singular value decomposition are established and applied to ice-surface classification. Deformation during a surge is mostly one of the extensional deformation types. Continuously, or infinitesimally repeated, deformation acting in continuously fast-moving ice causes different typical crevasse patterns. The structural-geology approach also includes a way to treat the problem of shear, as observed in the margins of fast-moving ice streams within slow-moving surrounding ice. In this paper we provide the first link between a physical analysis of ice-surface deformation and a connectionist-geostatistical analysis of the same problem.