Mathematical models for erosion and the optimal transportation of sediment

We investigate a mathematical theory for the erosion of sediment which begins with the study of a non-linear, parabolic, weighted 4-Laplace equation on a rectangular domain corresponding to a base segment of an extended landscape. Imposing natural boundary conditions, we show that the equation admits entropy solutions and prove regularity and uniqueness of weak solutions when they exist. We then investigate a particular class of weak solutions studied in previous work of the first author and produce numerical simulations of these solutions. After introducing an optimal transportation problem for the sediment flow, we show that this class of weak solutions implements the optimal transportation of the sediment

Exhumation, rift-flank uplift, and the thermal evolution of the Rwenzori Mountains determined by combined (U-Th)/He and U-Pb thermochronometry

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 2006.Includes bibliographical references (p. 19-22).Rising over 5 km along the border of Uganda and the Democratic Republic of the Congo, the Rwenzori Mountains represent an extreme example of basement rift-flank uplift in the western branch of the East African Rift, a phenomenon common throughout the East African Rift System and characteristic of continental rift systems in general. A thermochronologic study combining (U-Th)/He and U-Pb analysis of apatite, titanite, and zircon separated from crystalline basement rocks was conducted across the Rwenzori block to characterize the timing and rate of rift-flank exhumation related to continental extension in east-central Africa. The thermochronologic data coupled with field and remote sensing observations make the case for recent and non-steady state uplift of the massif. Uranium-lead thermochronology indicate that, prior to Upper Neogene rifting, the rocks of the Rwenzori experienced a protracted history of slow cooling without major tectonothermal perturbation since at least the Paleoproterozoic (ca. 1900 Ma).(cont.) Stream channel steepness profiles and thermochronometry along the western slope of the range show it to be the main active scarp that accommodates uplift. Relatively old (U-Th)/He zircon and apatite dates (>400 Ma, >70 Ma respectively) along the high peaks and eastern slope of the range reflect a transient lag period resulting from yet-insufficient exhumation to remove the inherited pre-rift cratonic thermal structure. This non-steady state condition of rapid uplift outpacing erosion has resulted in preservation of relict landsurfaces, truncated spurs, hanging valleys, uplifted river terraces, and vast stranded bogs at high elevation. Given the low cooling rate and geothermal gradient prior to rifting implied by U-Pb thermochronometry we determine that no more than 1.7 km of erosion could have accompanied uplift on the order of at least 5 km in the Rwenzori region. Biostratigraphic evidence suggests the range rose from beneath local baselevel within the last 2.5 Ma. This requires a minimum average uplift rate of 1.6 km/Myr. Regardless of the active rock uplift rate of the Rwenzori, net exhumation cannot yet have exceeded the depth of the (U-Th)/He closure isotherm in apatite (<1.7 km). These results highlight the danger of modeling young orogenic systems using the simplifying assumption of topographic steady state.by Daniel MacPhee.S.M

Subgrid-Scale Dynamics of Water Vapour, Heat, and Momentum over a Lake

We examine the dynamics of turbulence subgrid (or sub-filter) scales over a lake surface and the implications for large-eddy simulations (LES) of the atmospheric boundary layer. The analysis is based on measurements obtained during the Lake-Atmosphere Turbulent EXchange (LATEX) field campaign (August-October, 2006) over Lake Geneva, Switzerland. Wind velocity, temperature and humidity profiles were measured at 20Hz using a vertical array of four sonic anemometers and open-path gas analyzers. The results indicate that the observed subgrid-scale statistics are very similar to those observed over land surfaces, suggesting that the effect of the lake waves on surface-layer turbulence during LATEX is small. The measurements allowed, for the first time, the study of subgrid-scale turbulent transport of water vapour, which is found to be well correlated with the transport of heat, suggesting that the subgrid-scale modelling of the two scalars may be coupled to save computational resources during LE

On the Numerics, Generation, and Scaling of Fluvial Landscapes

The Smith and Bretherton model for fluvial erosion consists of a pair of partial differential equations: one governing water flow and one governing sediment flow. Numerical solutions of these equations have been shown to provide realistic models of the evolution of fluvial landscapes. Further analysis of these equations and their numerical solutions show that they possess scaling laws that are known to exist in nature. The preservation of these scaling laws in simulations is highly dependent on the numerical method used. Two numerical methods, both optimized for overland flow, have been used to simulate these surfaces. The implicit method exhibits the correct scaling laws, but the explicit method fails to do so. These equations, and the resulting models, help bridge the gap between the deterministic and stochastic theories of landscape evolution. Despite current advances in processing power and parallelism, numerical simulations of these surfaces take months of computation time. Some alterations can be made to code parameters to decrease computation time, but sacrifice accuracy of the resulting surfaces. Using the known deterministic and stochastic theories of these equations, the large scales of the model are generated from a series of elementary functions. The small scales are generated using Hurst fractal interpolation; a modified version of fractal interpolation functions, a relatively recent technique of interpolation explained herein. The generated surfaces provide great insight into the scaling laws satisfied by these surfaces

The American Geophysical Union Chapman Conference on Tectonics and Topography

The Chapman Conference on Tectonics and Topography was held 31 Aug. - 4 Sep. 1992. The conference was designed to bring together disparate groups of earth scientists who increasingly found themselves working on similar problems but in relative isolation. Thus, process geomorphologists found themselves face-to-face with numerical modelers and field geomorphologists, hydrologists encountered geologists, and tectonophysicists found people with related data. The keynote speakers represented a wide variety of disciplines, all of which were relevant to the interdisciplinary theme of the conference. One of the most surprising issues that surfaced was the relative dearth of data that exists about erosion--process and rates. This was exacerbated by a reminder that erosion is critical to the evaluation of surface uplift

Ending the Cinderella Status of Terraces and Lynchets in Europe : The Geomorphology of Agricultural Terraces and Implications for Ecosystem Services and Climate Adaptation

Terraces and lynchets are ubiquitous worldwide and can provide increasingly important Ecosystem Services (ESs), which may be able to mitigate aspects of climate change. They are also a major cause of non-linearity between climate and erosion rates in agricultural systems as noted from alluvial and colluvial studies. New research in the ‘critical zone’ has shown that we must now treat soil production as an ecologically sensitive variable with implications for soil carbon sequestration. In this review and synthesis paper we present a modified classification of agricultural terraces, review the theoretical background of both terraces and lynchets, and show how new techniques are transforming the study of these widespread and often ancient anthropogenic landforms. The problems of dating terraces and the time-consuming nature of costly surveys has held back the geomorphological and geoarchaeological study of terraces until now. The suite of techniques now available, and reviewed here,includes Digital Elevation Models (DEMs) - Structure from Motion (SfM) photogrammetry, Airborne and Terrestrial Laser Scanning (ALS-TLS); optically stimulated luminescence (OSL and pOSL), portable x-ray fluorescence (pXRF), Fourier-transform infra-red analysis (FTIR), phytoliths from plants, and potentially environmental DNA. Three process-related geomorphological questions arise from using this suite of methods; a) can they provide both a chronology of formation and use history, b) can we identify the sources of all the soil components? c) can terrace soil formation and ecosystem services be modelled at the slope to catchment scale? The answers to these questions can also inform the management of the large areas of abandoned and under-used terraces that are resulting from both the economics of farming and rural population changes. Where possible, examples are drawn from a recently started ERC project (TerrACE; ERC-2018-2023; https://www.terrace.no/) that is working at over 15 sites in Europe ranging from Norway to Greece

Thermochronology, landscape evolution and hydrogeology of the Katonga Valley in south west Uganda

The reversed river systems of south west Uganda attracted geoscientists to study the geomorphology of the region in the mid 20th century. During the succeeding fifty years the population and GDP per capita have both risen between five and six fold with a consequent increase in water demand. This thesis aims to apply modern quantitative techniques and theoretical developments to improve our understanding of the landscape evolution of the Katonga Valley and contribute to the groundwater resource assessment of associated alluvial deposits. Karoo-age glaciogenic strata were discovered filling the western valley. Subsequent apatite fission track analyses reveal that the currently exposed rocks were reheated to a temperature consistent with over 2 km of burial during the Mesozoic. Therefore, it is inferred that the western River Katonga has preferentially eroded a Gondwanan paleovalley exhumed from beneath the former sedimentary cover. Electrical resistivity tomography of the valley fill has identified three broad cycles of erosion and deposition, including: 1) The Gondwanan palaeovalley with indurated glaciogenic strata; 2) The Neogene relict valley with fluviolacustrine sediments; and, 3) The late Quaternary channel and with recent wetland deposits. Downwarping of the Victoria Basin in the east produced the first drainage divide on the originally westward flowing River Katonga during the middle Pleistocene. Downthrow of the George Basin in the west led to rejuvenation of the western landscape prior to the formation of a second drainage divide due to rift flank uplift. Sand and gravel associated with an old denuded landscape survives in terraces above the water table in the central valley. Variable climate and fluctuating lake levels led to the deposition of fluviolacustrine deposits in the eastern valley. Pumping tests in this silty sand indicate that the transmissivity is almost always adequate for village water use and is sometimes commensurate with town water supplies

Volume 1

"Europe’s Lost Frontiers was the largest directed archaeological research project undertaken in Europe to investigate the inundated landscapes of the Early Holocene North Sea – the area frequently referred to as ‘Doggerland’. Funded through a European Research Council Advanced Grant (project number 670518), the project ran from 2015 to 2021, and involved more than 30 academics, representing institutions spread geographically from Ireland to China. A vast area of the seabed was mapped, and multiple ship expeditions were launched to retrieve sediment cores from the valleys of the lost prehistoric landscapes of the North Sea. This data has now been analysed to provide evidence of how the land was transformed in the face of climate change and rising sea levels. This volume is the first in a series of monographs dedicated to the analysis and interpretation of data generated by the project. As a precursor to the publication of the detailed results, it provides the context of the study and method statements. Later volumes will present the mapping, palaeoenvironment, geomorphology and modelling programmes of Europe’s Lost Frontiers. The results of the project confirm that these landscapes, long held to be inaccessible to archaeology, can be studied directly and provide an archaeological narrative. This data will become increasingly important at a time when contemporary climate change and geo-political crises are pushing development within the North Sea at an unprecedented rate, and when the opportunities to explore this unique, heritage landscape may be significantly limited in the future.