Radial basis function methods exhibit several very attractive properties such as a high order convergence of the approximated solution and flexibility to the domain geometry. However the method in its classical formulation becomes impractical for problems with relatively large numbers of degrees of freedom due to the ill-conditioning and dense structure of coefficient matrix. To overcome the latter issue we employ a localisation technique, namely a partition of unity method, while the former issue was previously addressed by several authors and was of less concern in this thesis. In this thesis we develop radial basis function partition of unity methods for partial differential equations arising in financial mathematics and glaciology. In the applications of financial mathematics we focus on pricing multi-asset equity and credit derivatives whose models involve several stochastic factors. We demonstrate that localised radial basis function methods are very effective and well-suited for financial applications thanks to the high order approximation properties that allow for the reduction of storage and computational requirements, which is crucial in multi-dimensional problems to cope with the curse of dimensionality. In the glaciology application we in the first place make use of the meshfree nature of the methods and their flexibility with respect to the irregular geometries of ice sheets and glaciers. Also, we exploit the fact that radial basis function methods are stated in strong form, which is advantageous for approximating velocity fields of non-Newtonian viscous liquids such as ice, since it allows to avoid a full coefficient matrix reassembly within the nonlinear iteration. In addition to the applied problems we develop a least squares radial basis function partition of unity method that is robust with respect to the node layout. The method allows for scaling to problem sizes of a few hundred thousand nodes without encountering the issue of large condition numbers of the coefficient matrix. This property is enabled by the possibility to control the coefficient matrix condition number by the rate of oversampling and the mode of refinement.

Am 24. September 2014 hat Professor Reinhard Dietrich sein 65. Lebensjahr vollendet. Zurückblicken kann er auf eine überaus reiche Lehr- und Forschungstätigkeit. Fast genau 20 Jahre war er Professor für Theoretische und Physikalische Geodäsie an der TU Dresden, bevor er zum 1. Oktober 2012 in den Ruhestand eintrat. Sein Geburtstag ist uns, die während dieser Zeit mit ihm zusammen forschen und lehren durften, Anlass, eine Festschrift zu verfassen und dem Jubilar sowie allen Kollegen und Freunden an die Hand zu geben. Eine Würdigung seiner Lehr- und Forschungstätigkeit können Sie auf den folgenden Seiten nachlesen.:Vorwort 7 „Grenzen setzt uns nur die eigene Phantasie“ Reinhard Dietrich – Versuch einer Würdigung 9 GNSS – ein Werkzeug für globale und regionale geophysikalische Forschung 17 Zum Stand des Höhenbezugsrahmens in Deutschland 37 Geodätische Erdsystemforschung mittels Satellitenfernerkundung 53 Wasser und Eis – Satellitendaten zur Bilanzierung von Massentransporten 69 Geodätische Bestimmung glaziologischer Parameter in Grönland 83 Geodätische Arbeiten im Gebiet des subglazialen Lake Vostok 93 Feuerland: Symptome einer aktiven Plattengrenze 107 Anhang A – Verzeichnis der Promotionen 117 Anhang B – Publikationsliste R. Dietrich 119

Beitrag zu GNSS anläßlich einer Festschrift zum 65. Geburtstag von Prof. Reinhard Dietrich.

Beitrag zum Thema "Geodätische Bestimmung glaziologischer Parameter in Grönland" anläßlich einer Festschrift zum 65. Geburtstag von Prof. Reinhard Dietrich.

Sea level rise concerns millions of people in coastal areas across the globe. One of the largest uncertainties to project future sea level rise is the frontal ablation (accounting for calving and submarine melt) at marine ice margins, around the Greenland and Antarctic Ice Sheet. High rates of frontal ablation have been observed to imply, through loss of the buttressing effect but not limited to it, increased mass loss from marine terminating glaciers and hence, associated sea level rise. This study focuses on calving processes at a freshwater lake in northern Sweden, which represents a simpler environment to study calving processes than the marine one, because impacts of tides, salinity, and circulation (all known to be relevant at marine ice-ocean boundaries) can be neglected. A multi-method approach to quantify and characterize calving events is presented here, exploring and analysing the underwater acoustic soundscape at a calving glacier front, in connection with optical, image-based methods such as time- lapse photography, and photogrammetry based on footage acquired by an uncrewed aerial vehicle (UAV). An acoustic detector is developed, tested and applied to data set acquired during 2020, and results indicate that the acoustic detector can be an important complement in the range of tools used to observe, and quantify, calving. Applied in remote locations, where continuous monitoring is difficult and where optical methods are of limited use, collecting acoustic data and monitoring calving by means of its acoustic signature could render insights previously not available (because of lacking data and methodology).

This research documents the Holocene glacial history of Mount Hood, Cascade Mountains, Oregon by analyzing a set of three lateral moraines abutting Eliot Glacier, the largest glacier on the mountain. This study seeks to: 1) establish the relative ages of these lateral moraines and 2) determine if these features represent distinct glacial advances. The hypothesis is that the lateral moraines for Eliot Glacier represent three distinct periods of glacial advance based on their position relative to the current glacier and other diagnostic indicators. Soil profiles of three positions (shoulder, backslope, and footslope) on the distal side of each lateral moraine were described in the field and samples were taken from each horizon for laboratory analyses of pH and particle size. The results of the soil analysis show that the soils developing on the moraine closest to the current glacier are poorly developed and significantly younger than the other two features. The closest moraine likely dates to the Little Ice Age (600-150 YBP) and has soils with an A/C profile and a classification of Andic Cryopsamment. The soils on the middle and furthest moraines from the glacier are similar in the profile sequence (Andic Haplocryepts). Silt bulges were noted in the mid-slope pits. The furthest moraine has deeper horizons and more color development than the middle moraine. Ash layers were found in the backslope soil profile (36-51cm deep) on the middle moraine. Additional lab testing confirms the ash layers originated from Mount Hood, but no date can be assigned. The eruptive history of Mount Hood points to the Timberline eruptive period (1,500 YBP) as a likely candidate for one of the ash deposits. This evidence suggests the middle moraine was actively forming during this period and is intermediate in age between the furthest moraine and the Little Ice Age Moraine; hence, this sequence of moraines indicates three distinct periods of glacial advance in the Neoglacial.

Eight glaciers, covering an area of 1.63 km2, reside on the northern and northeastern slopes of the Goat Rocks tallest peaks in the Cascades of central Washington. At least three glacial stands occurred downstream from these glaciers. Closest to modern glacier termini are Little Ice Age (LIA) moraines that were deposited between 1870 and 1899 AD, according to the lichenometric analysis. They are characterized by sharp, minimally eroded crests, little to no soil cover, and minimal vegetation cover. Glacier reconstructions indicate that LIA glaciers covered 8.29 km2, 76% more area than modern ice coverage. The average LIA equilibrium line altitude (ELA) of 1995 ± 70 m is ~150 m below the average modern ELA of 2149 ± 76 m. To satisfy climate conditions at the LIA ELA, the winter snow accumulation must have been 8 to 43 cm greater and mean summer temperatures 0.2 to 1.3 ºC cooler than they are now. Late Pleistocene to early Holocene (LPEH) aged moraines are located between 100 and 400 m below the LIA deposits. They have degraded moraine crests, few surface boulders, and considerable vegetation and soil cover. Volcanic ashes indicate LPEH moraines were deposited before 1480 AD while morphometric data suggest deposition during the late Pleistocene or early Holocene. The average LPEH ELA of 1904 ± 110 m is ~ 240 m and ~90 m below the modern and LIA ELAs, respectively. The climate change necessary to maintain a glacier with an ELA at that elevation for LPEH conditions requires the winter accumulation to increase by 47 to 48 cm weq and the mean summer temperature to cool by 1.4 to 1.5 ºC. Last glacial maximum (LGM) moraines are located more than 30 km downstream from modern glacial termini. They are characterized by hummocky topography, rounded moraine crests, complete vegetation cover, and well developed soil cover. Moraine morphometry, soil characteristics, and distance from modern glacial termini indicate that deposition occurred at least 15 ka BP during an expansive cooling event, the last being the LGM. The LGM ELA of 1230 m is ~920 m below the modern ELA. The climate change necessary to maintain a glacier with an ELA at that elevation for LGM conditions requires the mean summer temperature to cool by 5.6 ºC with no change in precipitation.

A glacier responds to changes in climate by subsequent retreat and advance as a result of changes in snow inputs and outputs. Understanding these changes is important because shrinking glaciers limit and diminish local water resources. They contribute to alpine runoff in the late-summer months by delaying the maximum runoff until late in the melt season. A comprehensive glacier and perennial snowfield inventory has not been completed for the Three Sisters in Central Oregon. Using aerial photography, Digital Elevation Models (DEMs), previous studies, and historical ground based photographs these glacier and perennial snowfields were defined and their surface area change was quantified along with surface area and volume change for the 15 named glaciers for multiple years. The glaciers and perennial snowfields totaled 9.03 ± 1.65 km2 in 1949 and decreased to 7.1 ± 1.16 km2 in 2003 giving a total loss of -1.914 ± 0.974 km2 ( 21%). The 15 named glaciers totaled 12.43 ± 0.417 km2 in ~1900 and decreased to 5.65 ± 0.135 km2 in 2003 giving a total loss of -6.70 ± 0.439 km2 (54%) with more loss occurring in the early part of the century. It's estimated that the 15 named glaciers lost roughly 61% of volume from 1900 to 2010. From 1957 to 2010 their surface's dropped in elevation on average by -8.9m, losing an estimated 71.96 x 106 ± 2.87 x 106 m3 (53%) in total volume, seen across accumulation and ablation zones, with more loss happening from 1957 to 1990. There was no relationship found between topography and area. A small correlation was found between slope and increased volume change. Debris cover on glacier surfaces has increased and showed a correlation between decreasing area loss (no correlation with volume changes).

Numerous small alpine glaciers occupy the high elevation regions of the central and southern Siena Nevada, California. These glaciers change size in response to variations in climate and are therefore important indicators of climate change. An inventory based on USGS topographic maps (l :24,000) revealed 1719 glaciers and perennial snow and ice features for a total area of 39.l5 ±7.52 km2. The number of 'true' glaciers, versus non-moving ice, is estimated to be 118, covering 15.87 ± 1.69 Km2. All glaciers were located on north to northeast aspects, at elevations >3000 m. Historical photographs, geologic evidence, and field mapping were used to determine the magnitude of area loss over the past century at 14 glaciers. These glaciers decreased in area by 31% to 78%, averaging 55%. The rate of area change was determined for multiple time periods for a subset of seven glaciers. Rapid retreat occurred over the first half of the twentieth century beginning in the 1920s in response to warm/dry conditions and continued through the mid-1970s. Recession ceased during the early 1980s, when some glaciers advanced. Since the 1980s each of the seven study glaciers resumed retreat. The uniform timing of changes in area amongst study glaciers suggests a response to regional climate, while the magnitude of change is influenced by local topographic effects. Glacier area changes correlate with changes in spring and summer air temperatures. Winter precipitation is statistically unrelated to changes in glacier area. Headwall cliffs above the glaciers alter the glacier responses by reducing incoming shortwave radiation and enhancing snow accumulation via avalanching.

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