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Determining the optimal grid resolution for topographic analysis on an airborne lidar dataset
(2019)
Digital elevation models (DEMs) are a gridded representation of the surface of the Earth and typically contain uncertainties due to data collection and processing. Slope and aspect estimates on a DEM contain errors and uncertainties inherited from the representation of a continuous surface as a grid (referred to as truncation error; TE) and from any DEM uncertainty. We analyze in detail the impacts of TE and propagated elevation uncertainty (PEU) on slope and aspect.
Using synthetic data as a control, we define functions to quantify both TE and PEU for arbitrary grids. We then develop a quality metric which captures the combined impact of both TE and PEU on the calculation of topographic metrics. Our quality metric allows us to examine the spatial patterns of error and uncertainty in topographic metrics and to compare calculations on DEMs of different sizes and accuracies.
Using lidar data with point density of ∼10 pts m−2 covering Santa Cruz Island in southern California, we are able to generate DEMs and uncertainty estimates at several grid resolutions. Slope (aspect) errors on the 1 m dataset are on average 0.3∘ (0.9∘) from TE and 5.5∘ (14.5∘) from PEU. We calculate an optimal DEM resolution for our SCI lidar dataset of 4 m that minimizes the error bounds on topographic metric calculations due to the combined influence of TE and PEU for both slope and aspect calculations over the entire SCI. Average slope (aspect) errors from the 4 m DEM are 0.25∘ (0.75∘) from TE and 5∘ (12.5∘) from PEU. While the smallest grid resolution possible from the high-density SCI lidar is not necessarily optimal for calculating topographic metrics, high point-density data are essential for measuring DEM uncertainty across a range of resolutions.
Determining the optimal grid resolution for topographic analysis on an airborne lidar dataset
(2019)
Digital elevation models (DEMs) are a gridded representation of the surface of the Earth and typically contain uncertainties due to data collection and processing. Slope and aspect estimates on a DEM contain errors and uncertainties inherited from the representation of a continuous surface as a grid (referred to as truncation error; TE) and from any DEM uncertainty. We analyze in detail the impacts of TE and propagated elevation uncertainty (PEU) on slope and aspect.
Using synthetic data as a control, we define functions to quantify both TE and PEU for arbitrary grids. We then develop a quality metric which captures the combined impact of both TE and PEU on the calculation of topographic metrics. Our quality metric allows us to examine the spatial patterns of error and uncertainty in topographic metrics and to compare calculations on DEMs of different sizes and accuracies.
Using lidar data with point density of ∼10 pts m−2 covering Santa Cruz Island in southern California, we are able to generate DEMs and uncertainty estimates at several grid resolutions. Slope (aspect) errors on the 1 m dataset are on average 0.3∘ (0.9∘) from TE and 5.5∘ (14.5∘) from PEU. We calculate an optimal DEM resolution for our SCI lidar dataset of 4 m that minimizes the error bounds on topographic metric calculations due to the combined influence of TE and PEU for both slope and aspect calculations over the entire SCI. Average slope (aspect) errors from the 4 m DEM are 0.25∘ (0.75∘) from TE and 5∘ (12.5∘) from PEU. While the smallest grid resolution possible from the high-density SCI lidar is not necessarily optimal for calculating topographic metrics, high point-density data are essential for measuring DEM uncertainty across a range of resolutions.
The advances in modern geodetic techniques such as the global navigation satellite system (GNSS) and synthetic aperture radar (SAR) provide surface deformation measurements with an unprecedented accuracy and temporal and spatial resolutions even at most remote volcanoes on Earth. Modelling of the high-quality geodetic data is crucial for understanding the underlying physics of volcano deformation processes. Among various approaches, mathematical models are the most effective for establishing a quantitative link between the surface displacements and the shape and strength of deformation sources. Advancing the geodetic data analyses and hence, the knowledge on the Earth’s interior processes, demands sophisticated and efficient deformation modelling approaches. Yet the majority of these models rely on simplistic assumptions for deformation source geometries and ignore complexities such as the Earth’s surface topography and interactions between multiple sources.
This thesis addresses this problem in the context of analytical and numerical volcano deformation modelling. In the first part, new analytical solutions for triangular dislocations (TDs) in uniform infinite and semi-infinite elastic media have been developed. Through a comprehensive investigation, the locations and causes of artefact singularities and numerical instabilities associated with TDs have been determined and these long-standing drawbacks have been addressed thoroughly. This approach has then been extended to rectangular dislocations (RDs) with full rotational degrees of freedom. Using this solution in a configuration of three orthogonal RDs a compound dislocation model (CDM) has been developed. The CDM can represent generalized volumetric and planar deformation sources efficiently. Thus, the CDM is relevant for rapid inversions in early warning systems and can also be used for detailed deformation analyses. In order to account for complex source geometries and realistic topography in the deformation models, in this thesis the boundary element method (BEM) has been applied to the new solutions for TDs. In this scheme, complex surfaces are simulated as a continuous mesh of TDs that may possess any displacement or stress boundary conditions in the BEM calculations. In the second part of this thesis, the developed modelling techniques have been applied to five different real-world deformation scenarios. As the first and second case studies the deformation sources associated with the 2015 Calbuco eruption and 2013–2016 Copahue inflation period have been constrained by using the CDM. The highly anisotropic source geometries in these two cases highlight the importance of using generalized deformation models such as the CDM, for geodetic data inversions. The other three case studies in this thesis involve high-resolution dislocation models and BEM calculations. As the third case, the 2013 pre-explosive inflation of Volcán de Colima has been simulated by using two ellipsoidal cavities, which locate zones of pressurization in the volcano’s lava dome. The fourth case study, which serves as an example for volcanotectonics interactions, the 3-D kinematics of an active ring-fault at Tendürek volcano has been investigated through modelling displacement time series over the 2003–2010 time period. As the fifth example, the deformation sources associated with North Korea’s underground nuclear test in September 2017 have been constrained. These examples demonstrate the advancement and increasing level of complexity and the general applicability of the developed dislocation modelling techniques.
This thesis establishes a unified framework for rapid and high-resolution dislocation modelling, which in addition to volcano deformations can also be applied to tectonic and humanmade deformations.
This dissertation combines field and geochemical observations and analyses with numerical modeling to understand the formation of vein-hosted Sn-W ore in the Panasqueira deposit of Portugal, which is among the ten largest worldwide. The deposit is located above a granite body that is altered by magmatic-hydrothermal fluids in its upper part (greisen). These fluids are thought to be the source of metals, but that was still under debate. The goal of this study is to determine the composition and temperature of hydrothermal fluids at Panasqueira, and with that information to construct a numerical model of the hydrothermal system. The focus is on analysis of the minerals tourmaline and white mica, which formed during mineralization and are widespread throughout the deposit. Tourmaline occurs mainly in alteration zones around mineralized veins and is less abundant in the vein margins. White mica is more widespread. It is abundant in vein margins as well as alteration zones, and also occurs in the granite greisen. The laboratory work involved in-situ microanalysis of major- and trace elements in tourmaline and white mica, and boron-isotope analysis in both minerals by secondary ion mass spectrometry (SIMS).
The boron-isotope composition of tourmaline and white mica suggests a magmatic source. Comparison of hydrothermally-altered and unaltered rocks from drill cores shows that the ore metals (W, Sn, Cu, and Zn) and As, F, Li, Rb, and Cs were introduced during the alteration. Most of these elements are also enriched in tourmaline and mica, which confirms their potential value as exploration guides to Sn-W ores elsewhere.
The thermal evolution of the hydrothermal system was estimated by B-isotope exchange thermometry and the Ti-in-quartz method. Both methods yielded similar temperatures for the early hydrothermal phase: 430° to 460°C for B-isotopes and 503° ± 24°C for Ti-in-quartz. Mineral pairs from a late fault zone yield significantly lower median temperatures of 250°C. The combined results of thermometry with variations in chemical and B-isotope composition of tourmaline and mica suggest that a similar magmatic-hydrothermal fluid was active at all stages of mineralization. Mineralization in the late stage shows the same B-isotope composition as in the main stage despite a ca. 250°C cooling, which supports a multiple injection model of magmatic-hydrothermal fluids.
Two-dimensional numerical simulations of convection in a multiphase NaCl hydrothermal system were conducted: (a) in order to test a new approach (lower dimensional elements) for flow through fractures and faults and (b) in order to identify conditions for horizontal fluid flow as observed in the flat-lying veins at Panasqueira. The results show that fluid flow over an intrusion (heat and fluid source) develops a horizontal component if there is sufficient fracture connectivity. Late, steep fault zones have been identified in the deposit area, which locally contain low-temperature Zn-Pb mineralization. The model results confirm that the presence of subvertical faults with enhanced permeability play a crucial role in the ascent of magmatic fluids to the surface and the recharge of meteoric waters. Finally, our model results suggest that recharge of meteoric fluids and mixing processes may be important at later stages, while flow of magmatic fluids dominate the early stages of the hydrothermal fluid circulation.
The habilitation thesis presented here includes results from several studies dealing with fluid-rock interactions and rock deformation processes in active fault zones. The focus in all of these studies is on the influence of clay minerals on the geochemical and the hydro-mechanical behavior of the fault rocks. The research was conducted on rock cores and cuttings from four scientific drilling projects at the San Andreas Fault (USA), the Nankai Trough subduction zone and the Japan Trench subduction zone (Japan), as well as the Alpine Fault in New Zealand. These ICDP (International Continental Scientific Drilling Program) and IODP (International Ocean Discovery Program) funded projects were all conducted with the aim to monitor and better understand earthquakes.
Chapter 1 contains a short introduction to the topic with basic principles and objectives regarding the research approach. Chapter 2 describes the state of the art in clay mineral and fault zone science, gives a short description of the individual drilling projects and their locations on which the research was based, and summarizes the most important analytical methods used. Chapter 3 comprises ten peer-reviewed publications that are connected thematically and methodologically. The papers were published in the years 2006-2015, and additional related publications including myself as co-author are given in the literature list. The ten publications address different questions concerning the formation of clay minerals and processes of fluid-rock interaction in active fault zones. Six papers contain results from the SAFOD drilling project, USA (San Andreas Fault Observatory at Depth), with the main focus on fluid-rock interaction processes in fault rocks and the formation and location of clay minerals. Three publications report on research from the NanTroSEIZE drilling project (Nankai Trough Seismogenic Zone Experiment) and the JFAST drilling project (Japan Trench Fast Drilling Project). Both projects are situated in Japan. Here, the swelling behavior of smectite clay minerals in relation to changing environmental conditions (e.g. temperature and/or humidity) was investigated. The last publication included here concerns a study from the DFDP project (Deep Fault Drilling Project) in New Zealand, where I investigated the deformation of clay minerals on the context of the hydro-mechanical behavior of the fault zone rocks. I was first author in nine of the publications and in charge of the project preparation, measurements and data analyses, and the completion of the manuscript. As co-author on the other publication I was responsible for electronmicroscopy analyses (SEM and TEM) and their interpretation.
The key results from the publications in Chapter 3 are discussed in Chapter 4 with additional considerations from more recent papers. Following the major theses in Chapter 5, Chapter 6 highlights a future research project in clay mineralogy research at the GFZ. An appendix includes more detailed descriptions of the laboratory equipment and lists of all publications, conference contributions and teaching courses and modules.
The semiarid northeast of Brazil is one of the most densely populated dryland regions in the world and recurrently affected by severe droughts. Thus, reliable seasonal forecasts of streamflow and reservoir storage are of high value for water managers. Such forecasts can be generated by applying either hydrological models representing underlying processes or statistical relationships exploiting correlations among meteorological and hydrological variables. This work evaluates and compares the performances of seasonal reservoir storage forecasts derived by a process-based hydrological model and a statistical approach.
Driven by observations, both models achieve similar simulation accuracies. In a hindcast experiment, however, the accuracy of estimating regional reservoir storages was considerably lower using the process-based hydrological model, whereas the resolution and reliability of drought event predictions were similar by both approaches. Further investigations regarding the deficiencies of the process-based model revealed a significant influence of antecedent wetness conditions and a higher sensitivity of model prediction performance to rainfall forecast quality.
Within the scope of this study, the statistical model proved to be the more straightforward approach for predictions of reservoir level and drought events at regionally and monthly aggregated scales. However, for forecasts at finer scales of space and time or for the investigation of underlying processes, the costly initialisation and application of a process-based model can be worthwhile. Furthermore, the application of innovative data products, such as remote sensing data, and operational model correction methods, like data assimilation, may allow for an enhanced exploitation of the advanced capabilities of process-based hydrological models.
The semiarid northeast of Brazil is one of the most densely populated dryland regions in the world and recurrently affected by severe droughts. Thus, reliable seasonal forecasts of streamflow and reservoir storage are of high value for water managers. Such forecasts can be generated by applying either hydrological models representing underlying processes or statistical relationships exploiting correlations among meteorological and hydrological variables. This work evaluates and compares the performances of seasonal reservoir storage forecasts derived by a process-based hydrological model and a statistical approach.
Driven by observations, both models achieve similar simulation accuracies. In a hindcast experiment, however, the accuracy of estimating regional reservoir storages was considerably lower using the process-based hydrological model, whereas the resolution and reliability of drought event predictions were similar by both approaches. Further investigations regarding the deficiencies of the process-based model revealed a significant influence of antecedent wetness conditions and a higher sensitivity of model prediction performance to rainfall forecast quality.
Within the scope of this study, the statistical model proved to be the more straightforward approach for predictions of reservoir level and drought events at regionally and monthly aggregated scales. However, for forecasts at finer scales of space and time or for the investigation of underlying processes, the costly initialisation and application of a process-based model can be worthwhile. Furthermore, the application of innovative data products, such as remote sensing data, and operational model correction methods, like data assimilation, may allow for an enhanced exploitation of the advanced capabilities of process-based hydrological models.
We measure valence-to-core x-ray emission spectra of compressed crystalline GeO₂ up to 56 GPa and of amorphous GeO₂ up to 100 GPa. In a novel approach, we extract the Ge coordination number and mean Ge-O distances from the emission energy and the intensity of the Kβ'' emission line. The spectra of high-pressure polymorphs are calculated using the Bethe-Salpeter equation. Trends observed in the experimental and calculated spectra are found to match only when utilizing an octahedral model. The results reveal persistent octahedral Ge coordination with increasing distortion, similar to the compaction mechanism in the sequence of octahedrally coordinated crystalline GeO₂ high-pressure polymorphs.
We measure valence-to-core x-ray emission spectra of compressed crystalline GeO₂ up to 56 GPa and of amorphous GeO₂ up to 100 GPa. In a novel approach, we extract the Ge coordination number and mean Ge-O distances from the emission energy and the intensity of the Kβ'' emission line. The spectra of high-pressure polymorphs are calculated using the Bethe-Salpeter equation. Trends observed in the experimental and calculated spectra are found to match only when utilizing an octahedral model. The results reveal persistent octahedral Ge coordination with increasing distortion, similar to the compaction mechanism in the sequence of octahedrally coordinated crystalline GeO₂ high-pressure polymorphs.
Skarn deposits are found on every continents and were formed at different times from Precambrian to Tertiary. Typically, the formation of a skarn is induced by a granitic intrusion in carbonates-rich sedimentary rocks. During contact metamorphism, fluids derived from the granite interact with the sedimentary host rocks, which results in the formation of calc-silicate minerals at the expense of carbonates. Those newly formed minerals generally develop in a metamorphic zoned aureole with garnet in the proximal and pyroxene in the distal zone. Ore elements contained in magmatic fluids are precipitated due to the change in fluid composition. The temperature decrease of the entire system, due to the cooling of magmatic fluids and the entering of meteoric water, allows retrogression of some prograde minerals.
The Hämmerlein skarn deposit has a multi-stage history with a skarn formation during regional metamorphism and a retrogression of primary skarn minerals during the granitic intrusion. Tin was mobilized during both events. The 340 Ma old tin-bearing skarn minerals show that tin was present in sediments before the granite intrusion, and that the first Sn enrichment occurred during the skarn formation by regional metamorphism fluids. In a second step at ca. 320 Ma, tin-bearing fluids were produced with the intrusion of the Eibenstock granite. Tin, which has been added by the granite and remobilized from skarn calc-silicates, precipitated as cassiterite.
Compared to clay or marl, the skarn is enriched in Sn, W, In, Zn, and Cu. These metals have been supplied during both regional metamorphism and granite emplacement. In addition, the several isotopic and chemical data of skarn samples show that the granite selectively added elements such as Sn, and that there was no visible granitic contribution to the sedimentary signature of the skarn
The example of Hämmerlein shows that it is possible to form a tin-rich skarn without associated granite when tin has already been transported from tin-bearing sediments during regional metamorphism by aqueous metamorphic fluids. These skarns are economically not interesting if tin is only contained in the skarn minerals. Later alteration of the skarn (the heat and fluid source is not necessarily a granite), however, can lead to the formation of secondary cassiterite (SnO2), with which the skarn can become economically highly interesting.