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Due to the challenges in upscaling daily climatic forcing to geological time, physically realistic models describing how rainfall drives fluvial erosion are lacking. To bridge this gap between short-term hydrology and long-term geomorphology, we derive a theoretical framework for long-term fluvial erosion rates driven by realistic climate by integrating an established stochastic-mechanistic model of hydrology into a threshold-stochastic formulation of stream power. The hydrological theory provides equations for the daily streamflow probability distribution as a function of climatic boundary conditions. The new parameters introduced are rooted firmly in established climatic and hydrological theory. This allows us to account for how fluvial erosion rates respond to changes in rainfall intensity, frequency, evapotranspiration rates, and soil moisture dynamics in a way that is consistent with existing theories. We use this framework to demonstrate how hydroclimatic conditions and erosion threshold magnitude control the degree of nonlinearity between steepness index and erosion rate. We find that hydrological processes can have a significant influence on how erosive a particular climatic forcing will be. By accounting for the influence of hydrology on fluvial erosion, we conclude that climate is an important control on erosion rates and long-term landscape evolution.
Many regions central to our understanding of tectonics and landscape evolution are active or ancient magmatic terranes, and robust interpretation of low-temperature thermochronologic ages in these settings requires careful attention to the drivers of rock heating and cooling, including magmatism. However, we currently lack a quantitative framework for evaluating the potential role of magmatic coolingthat is, post-magmatic thermal relaxationin shaping cooling age patterns in regions with a history of intrusive magmatism. Here we use analytical approximations and numerical models to characterize how low-temperature thermochronometers document cooling inside and around plutons in steadily exhuming environments. Our models predict that the thermal field a pluton intrudes into, specifically the ambient temperatures relative to the closure temperature of a given thermochronometer, is as important as the pluton size and temperature in controlling the pattern and extent of thermochronometer resetting in the country rocks around a pluton. We identify one advective and several conductive timescales that govern the relationship between the crystallization and cooling ages inside a pluton. In synthetic vertical age-elevation relationships (AERs), resetting next to plutons results in changes in AER slope that could be misinterpreted as past changes in exhumation rate if the history of magmatism is not accounted for. Finally, we find that large midcrustal plutons, such as those emplaced at similar to 10-15-km depth, can reset the low-temperature thermochronometers far above them in the upper crusta result with considerable consequences for thermochronology in arcs and regions with a history of magmatic activity that may not have a surface expression.
It is widely recognized that collisional mountain belt topography is generated by crustal thickening and lowered by river bedrock erosion, linking climate and tectonics(1-4). However, whether surface processes or lithospheric strength control mountain belt height, shape and longevity remains uncertain. Additionally, how to reconcile high erosion rates in some active orogens with long-term survival of mountain belts for hundreds of millions of years remains enigmatic. Here we investigate mountain belt growth and decay using a new coupled surface process(5,6) and mantle-scale tectonic model(7). End-member models and the new non-dimensional Beaumont number, Bm, quantify how surface processes and tectonics control the topographic evolution of mountain belts, and enable the definition of three end-member types of growing orogens: type 1, non-steady state, strength controlled (Bm > 0.5); type 2, flux steady state(8), strength controlled (Bm approximate to 0.4-0.5); and type 3, flux steady state, erosion controlled (Bm < 0.4). Our results indicate that tectonics dominate in Himalaya-Tibet and the Central Andes (both type 1), efficient surface processes balance high convergence rates in Taiwan (probably type 2) and surface processes dominate in the Southern Alps of New Zealand (type 3). Orogenic decay is determined by erosional efficiency and can be subdivided into two phases with variable isostatic rebound characteristics and associated timescales. The results presented here provide a unified framework explaining how surface processes and lithospheric strength control the height, shape, and longevity of mountain belts.
Natural thermoluminescence (TL) in rocks reflects a dynamic equilibrium between radiation-induced TL growth and decay via thermal and athermal pathways. When rocks exhume through Earth's crust and cool from high to low temperature, this equilibrium level increases as the temperature dependent thermal decay decreases. This phenomenon can be exploited to extract thermal histories of rocks. The main advantage of TL is that a single TL glow curve has a wide range of thermal stabilities (lifetime <ka to Ba), and hence can provide multiple constraints on thermal histories. Here we constrain the distribution of kinetic parameters of TL in feldspar using a glow curve deconvolution method and fitting infinitesimal sub-peaks using a general order kinetic model. Each peak corresponds to a different but closely located energy level E. Forward modeling is applied for different time-temperature histories to estimate the sensitivity and limitation of each signal for different cooling rates. The results show that it is possible to constrain thermal histories between ∼30 °C and ∼80 °C. The results also illustrate that shallower traps, i.e. with lower activation energies, can be exploited to constrain lower cooling histories >100 °C/Ma, whereas deeper traps, i.e. with higher activation energies, provide constraints on thermal histories for higher cooling rates (>300 °C/Ma). Finally, we show how the path of rock exhumation (i.e., depth vs. time) can be constrained using an inverse approach. The newly developed methodology is applied to rapidly cooled samples from the Namche Barwa massif, eastern Himalaya to suggest a trend in exhumation rate with time that follows an inverse correlation with global temperature and glaciers equilibrium altitude line (ELA).
There has been recent progress in the understanding of the evolution of Quaternary climate. Simultaneously, there have been improvements in the understanding of glacial erosion processes, with better parameter constraints. Despite this, there remains much debate about whether or not the observed cooling over the Quaternary has driven an increase in glacial erosion rates. Most studies agree that the erosional response to climate change must be transient; therefore, the time scale of the climatic change and the response time of glacial erosion must be accounted for. Here we analyze the equations governing glacial erosion in a steadily uplifting landscape with variable climatic forcing and derive expressions for two fundamental response time scales. The first time scale describes the response of the glacier and the second one the glacial erosion response. We find that glaciers have characteristic time scales of the order of 10 to 10,000 years, while the characteristic time scale for glacial erosion is of the order of a few tens of thousands to a few million years. We then use a numerical model to validate the approximations made to derive the analytical solutions. The solutions show that short period forcing is dampened by the glacier response time, and long period forcing (>1 Myr) may be dampened by erosional response of glaciers when the rock uplift rates are high. In most tectonic and climatic conditions, we expect to see the strongest response of glacial erosion to periodic climatic forcing corresponding to Plio-Pleistocene climatic cycles. Finally, we use the numerical model to predict the response of glacial systems to the observed climatic forcing of the Quaternary, including, but not limited to, the Milankovich periods and the long-term secular cooling trend. We conclude that an increase of glacial erosion in response to Quaternary cooling is physically plausible, and we show that the magnitude of the increase depends on rock uplift and ice accumulation rates.
The marine sedimentary record contains unique information about the history of erosion, uplift and climate of the adjacent continent. Inverting this record has been the purpose of many numerical studies. However, limited attention has been given to linking continental erosion to marine sediment transport and deposition in large-scale surface process evolution models. Here we present a new numerical method for marine sediment transport and deposition that is directly coupled to a landscape evolution algorithm solving for the continental fluvial and hillslope erosion equations using implicit and O(N) algorithms. The new method takes into account the sorting of grain sizes (e.g., silt and sand) in the marine domain using a non-linear multiple grain-size diffusion equation and assumes that the sediment flux exported from the continental domain is proportional to the bathymetric slope. Specific transport coefficients and compaction factors are assumed for the two different grain sizes to simulate the stratigraphic architecture. The resulting set of equations is solved using an efficient (O(N) and implicit) algorithm. It can thus be used to invert stratigraphic geometries using a Bayesian approach that requires a large number of simulations. This new method is used to invert the sedimentary geometry of a natural example, the Ogooue Delta (Gabon), over the last similar to 5 Myr. The objective is to unravel the set of erosional histories of the adjacent continental domain compatible with the observed geometry of the offshore delta. For this, we use a Bayesian inversion scheme in which the misfit function is constructed by comparing four geometrical parameters between the natural and the simulated delta: the volume of sediments stored in the delta, the surface slope, the initial and the final shelf lengths. We find that the best-fit values of the transport coefficients for silt in the marine domain are in the range of 300 - 500 m(2)/yr, in agreement with previous studies on offshore diffusion. We also show that, in order to fit the sedimentary geometry, erosion rate on the continental domain must have increased by a factor of 6 to 8 since 5.3 Ma. (C) 2019 Elsevier B.V. All rights reserved.
Long-term river evolution depends partly on crustal deformation, which shapes the topography crossed by rivers. On glacial timescales, ice-sheet growth and decay can produce crustal vertical motion of ∼10 mm/yr resulting from the solid Earth's adjustment to variations in ice and water loads, comparable to tectonically-driven rates in the most rapidly uplifting mountains on Earth. This process of glacial isostatic adjustment (GIA) can influence river courses and drainage basins substantially, particularly near former ice margins. We explore the extent to which GIA influenced the evolution of rivers along the United States east coast during the last glacial cycle. We compute gravitationally self-consistent GIA responses that incorporate recent constraints on the Laurentide Ice Sheet history through the last glacial build-up phase, and we connect the predicted variations in topography to abrupt changes in river dynamics recorded in the Hudson, Delaware, Susquehanna, and Potomac Rivers from 40 ka to present. To the extent that increases in sediment transport capacity imply increases in river incision rate, the GIA-driven changes in slope and drainage area are consistent with episodes of erosion and sedimentation observed in the Hudson, Delaware, and Potomac Rivers, but inconsistent with the observed accelerated river incision in the Susquehanna River at 30-14 ka. These analyses add to a growing body of evidence showing that GIA strongly influences river evolution over millennial timescales.
Glaciers and rivers are the main agents of mountain erosion. While in the fluvial realm empirical relationships and their mathematical description, such as the stream power law, improved the understanding of fundamental controls on landscape evolution, simple constraints on glacial topography and governing scaling relations are widely lacking. We present a steady state solution for longitudinal profiles along eroding glaciers in a coupled system that includes tectonics and climate. We combined the shallow ice approximation and a glacial erosion rule to calculate ice surface and bed topography from prescribed glacier mass balance gradient and rock uplift rate. Our approach is inspired by the classic application of the stream power law for describing a fluvial steady state but with the striking difference that, in the glacial realm, glacier mass balance is added as an altitude-dependent variable. From our analyses we find that ice surface slope and glacial relief scale with uplift rate with scaling exponents indicating that glacial relief is less sensitive to uplift rate than relief in most fluvial landscapes. Basic scaling relations controlled by either basal sliding or internal deformation follow a power law with the exponent depending on the exponents for the glacial erosion rule and Glen's flow law. In a mixed scenario of sliding and deformation, complicated scaling relations with variable exponents emerge. Furthermore, a cutoff in glacier mass balance or cold ice in high elevations can lead to substantially larger scaling exponents which may provide an explanation for high relief in high latitudes.
Quantifying the pace of ice-sheet growth is critical to understanding ice-age climate and dynamics. Here, we show that the diversion of the Hudson River (northeastern North America) late in the last glaciation phase (ca. 30 ka), which some previous studies have speculated was due to glacial isostatic adjustment (GIA), can be used to infer the timing of the Laurentide Ice Sheet’s growth to its maximum extent. Landscapes in the vicinity of glaciated regions have likely responded to crustal deformation produced by ice-sheet growth and decay through river drainage reorganization, given that rates of uplift and subsidence are on the order of tens of meters per thousand years. We perform global, gravitationally self-consistent simulations of GIA and input the predicted crustal deformation field into a landscape evolution model. Our calculations indicate that the eastward diversion of the Hudson River at 30 ka is consistent with exceptionally rapid growth of the Laurentide Ice Sheet late in the glaciation phase, beginning at 50–35 ka.