scholarly journals Effect of rock uplift and Milankovitch timescale variations in precipitation and vegetation cover on catchment erosion rates

2021 ◽  
Author(s):  
Hemanti Sharma ◽  
Todd A. Ehlers ◽  
Christoph Glotzbach ◽  
Manuel Schmid ◽  
Katja Tielbörger
Keyword(s):  
Vegetation Cover ◽  
Vegetation Change ◽  
Transient State ◽  
Climatic Conditions ◽  
Sediment Flux ◽  
Uplift Rate ◽  
Erosion Rates ◽  
Uplift Rates ◽  
Phase Lags ◽  
Climate Forcings

Abstract. Catchment erosion and sedimentation are influenced by variations in the rates of rock uplift (tectonics), and periodic fluctuations in climate and vegetation cover. In this study we applied the Landlab-SPACE landscape evolution modelling approach. This study focuses on quantifying the effects changing climate and vegetation on erosion and sedimentation over distinct climate-vegetation settings. As catchment evolution is subjected to tectonic and climate forcings at millennial to million-year time-scales, the simulations are performed over different tectonic scenarios and periodicities of climate-vegetation change. We present a series of generalized experiments that explore the sensitivity of catchment hillslope and fluvial erosion and sedimentation for different rock uplift rates (0.05 mm a−1, 0.1 mm a−1, 0.2 mm a−1) and Milankovitch climate periodicities (23 kyr, 41 kyr and 100 kyr). Model inputs were parameterized for two different climate and vegetation conditions at two sites in the Chilean Coastal Cordillera at ~26° S (arid and sparsely vegetated) and ~33° S (mediterranean). For each setting, steady state topographies were produced for each uplift rate before introducing periodic variations in precipitation and vegetation cover. Following this, the sensitivity of these landscapes was analysed for 3 Myr in a transient state. Results suggest that regardless of the uplift rate, transients in precipitation and vegetation cover resulted in transients in erosion rates in the direction of change in precipitation and vegetation. While the transients in sedimentation were observed to be in the opposite direction of change in the precipitation and vegetation cover, with phase lags of ~1.5–2.5 kyr. These phase lags can be attributed to the changes in plant functional type (PFT) distribution induced by the changes in climatic conditions, which is beyond the scope of this study. These effects being most pronounced over longer period changes (100 kyr) and higher rock uplift rates (0.2 mm yr−1). This holds true for both vegetation and climate settings. Furthermore, transient changes in catchment erosion due to varying vegetation and precipitation were between ~35 %–110 % of the background (rock uplift) rate and are measureable with some techniques (e.g. sediment flux histories, cosmogenic nuclides). Taken together, we find that vegetation-dependent erosion and sedimentation are influenced by Milankovitch timescale changes in climate, but that these transient changes are superimposed upon tectonically driven rates of rock uplift.

Effect of rock uplift and Milankovitch timescale variations in precipitation and vegetation cover on catchment erosion rates

2021 ◽  
Vol 9 (4) ◽  
pp. 1045-1072 ◽  
Author(s):  
Hemanti Sharma ◽  
Todd A. Ehlers ◽  
Christoph Glotzbach ◽  
Manuel Schmid ◽  
Katja Tielbörger
Keyword(s):  
Vegetation Cover ◽  
Vegetation Change ◽  
Transient State ◽  
Sediment Flux ◽  
Uplift Rate ◽  
Fluvial Erosion ◽  
Erosion Rates ◽  
Uplift Rates ◽  
Phase Lags ◽  
Climate Forcings

Abstract. Catchment erosion and sedimentation are influenced by variations in the rates of rock uplift (tectonics) and periodic fluctuations in climate and vegetation cover. This study focuses on quantifying the effects of changing climate and vegetation on erosion and sedimentation over distinct climate–vegetation settings by applying the Landlab–SPACE landscape evolution model. As catchment evolution is subjected to tectonic and climate forcings at millennial to million-year timescales, the simulations are performed for different tectonic scenarios and periodicities in climate–vegetation change. We present a series of generalized experiments that explore the sensitivity of catchment hillslope and fluvial erosion as well as sedimentation for different rock uplift rates (0.05, 0.1, 0.2 mm a−1) and Milankovitch climate periodicities (23, 41, and 100 kyr). Model inputs were parameterized for two different climate and vegetation conditions at two sites in the Chilean Coastal Cordillera at ∼26∘ S (arid and sparsely vegetated) and ∼33∘ S (Mediterranean). For each setting, steady-state topographies were produced for each uplift rate before introducing periodic variations in precipitation and vegetation cover. Following this, the sensitivity of these landscapes was analyzed for 3 Myr in a transient state. Results suggest that regardless of the uplift rate, transients in precipitation and vegetation cover resulted in transients in erosion rates in the direction of change in precipitation and vegetation. The transients in sedimentation were observed to be in the opposite direction of change in the precipitation and vegetation cover, with phase lags of ∼1.5–2.5 kyr. These phase lags can be attributed to the changes in plant functional type (PFT) distribution induced by the changes in climate and the regolith production rate. These effects are most pronounced over longer-period changes (100 kyr) and higher rock uplift rates (0.2 mm yr−1). This holds true for both the vegetation and climate settings considered. Furthermore, transient changes in catchment erosion due to varying vegetation and precipitation were between ∼35 % and 110 % of the background (rock uplift) rate and would be measurable with commonly used techniques (e.g., sediment flux histories, cosmogenic nuclides). Taken together, we find that vegetation-dependent erosion and sedimentation are influenced by Milankovitch timescale changes in climate but that these transient changes are superimposed upon tectonically driven rates of rock uplift.

Influence of oscillating vegetation cover, precipitation, and sediment transport on topography: Insights from a landscape evolution model

2020 ◽  
Author(s):  
Hemanti Sharma ◽  
Todd A. Ehlers ◽  
Manuel Schmid
Keyword(s):  
Sediment Transport ◽  
Vegetation Cover ◽  
Landscape Evolution ◽  
Sediment Flux ◽  
Temperate Climate ◽  
Vegetation Density ◽  
Coupled Oscillations ◽  
Erosion Rates ◽  
Uplift Rates ◽  
Surface Vegetation

<p>Erosion and sediment transport in river catchments depend significantly on tectonics, climate and associated vegetation-cover. In this study, we used a numerical modelling approach to quantify the effects of temporal variations in precipitation rates and vegetation-cover over different uplift rates (0.05 mm a<sup>-1</sup>, 0.1 mm a<sup>-1</sup>, 0.2 mm a<sup>-1</sup>) and periodicities (23 kyr, 41 kyr and 100 kyr) of climate and associated vegetation-cover oscillations on erosion, sediment transport and deposition at catchment scale. Landlab, a landscape evolution modelling toolkit was modified to incorporate surface vegetation-cover dependent hillslope and coupled detachment-transport limited fluvial processes, weathering and soil production. The model was applied to (two) sites in the Coastal Chilean Cordillera namely Pan de Acuzar (~26), and La Campana (~33). These sites show a steep gradient in climate and vegetation density from arid climate and sparse vegetation density in northern latitudes to wetter temperate climate and abundant vegetation in the south, with granitic bedrock. The model simulations were run for 15 Myr to create steady-state topographies for both model domains. The sensitivity of these landscapes to changing climate and surface vegetation-cover was analyzed for 3 Myr for five transient model scenarios: (1) oscillating precipitation and constant vegetation cover, (2) constant precipitation and oscillating vegetation cover, (3) coupled oscillations in precipitation and vegetation cover, (4) coupled oscillations in precipitation and vegetation cover with variable periodicities, (5) coupled oscillations in precipitation and vegetation cover with variable rock uplift rates. The results suggest that erosion and sediment transport in densely vegetated landscapes are dominated by changes in precipitation, rather than vegetation-cover change in the southern study area (La Campana), as a result of higher amplitude of precipitation change i.e., 460 mm. Arid (northern) and sparsely vegetated landscapes are dominated by changes in vegetation density rather than precipitation, explained by higher erosion rates in periods with no surface vegetation-cover. Coupled oscillations in climate and vegetation cover suggested dampened influence of transient forcing on climate or vegetation-cover. The influence of periodicity of climate oscillations is significantly pronounced for shorter period (23 kyr oscillations) in terms of erosion rates. Results from different uplift rates suggested a positive linear relationship of topographic elevation and slope, erosion and sediment transport. However, sediment thickness decreases with increasing uplift rates, attributed to higher sediment flux on hillslopes due to linear dependence of slope on rock uplift rates.  These results broadly demonstrate the implications of long term climate change with associated vegetation density on geomorphic processes shaping the topography.</p>

scholarly journals Analytical long-profile models of coupled glacier-fluvial systems

2020 ◽  
Author(s):  
Eric Deal ◽  
Günther Prasicek
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
Climatic Conditions ◽  
Tectonic Geomorphology ◽  
Uplift Rate ◽  
Equilibrium Line Altitude ◽  
Glacial Erosion ◽  
Deep Time ◽  
Fluvial Systems ◽  
Uplift Rates

<p>Glaciers are an effective agent of erosion and landscape evolution, capable of driving high rates of erosion and sediment production. Glacial erosion is therefore an important process mediating the effect of climate on erosion rates and tectonics. Further, as a source of sediment, glacial erosion also has implications for the carbon and silicate cycles, with the potential for longterm feedbacks.  Understanding the interaction of climate, tectonics, glacial erosion and topography will lead to more insight into how glaciers can impact these processes. Simple, analytical long-profile models of fluvial incision are fundamental in tectonic geomorphology and critical for addressing fluvial analogues of problems such as those posed above. The advantage of these simple long-profile models is that they can be applied when information about forcing and boundary conditions is minimal (e.g. in deep time), and they can aid in the development of intuition about how such systems respond in general to different forcing. While models of glacial erosion have existed for quite some time, they tend to be complicated and computationally expensive. Currently, analytical long-profile models do not exist for glacial systems. At the same time, the patterns of glacial erosion and sediment transport, and how these processes respond to climate is fundamentally different than fluvial systems, and cannot be addressed properly with purely fluvial models.</p><p>Building on previous work, we introduce several simplifications to make the equations for coupled glacier-fluvial long-profile models easier to use and show that these simplifications have minimal effect on the steady state solution. We then use these new equations to develop an analytical solution for glacier-fluvial long-profiles at erosional steady state. The solution provides glacier geometry, including length and slope, ice thickness, and overall orogen relief for a given uplift rate, rock erodibility, profile length and climatic conditions. To explore the effect of glaciation on the balance between climate, erosion and orogen geometry, we integrate this solution into a critical wedge orogen theory. We find that the total orogen relief should be closely tied to the equilibrium line altitude (ELA), in line with the glacial buzzsaw theory. In addition, our theory predicts that the geometry and average uplift rate of glaciated critical wedge orogens respond more sensitively to changes in climate than those dominated by fluvial erosion. We suggest that the lowered ELA during glacial maxima over the last few million years could have triggered narrowing of critical orogens, with an associated increase in uplift rates within the active orogen core. </p>

Eighty years of change: vegetation in the montane ecoregion of Jasper National Park, Alberta, Canada

2002 ◽  
Vol 32 (11) ◽  
pp. 2010-2021 ◽  
Author(s):  
Jeanine M Rhemtulla ◽  
Ronald J Hall ◽  
Eric S Higgs ◽  
S Ellen Macdonald
Keyword(s):  
National Park ◽  
Vegetation Change ◽  
Fire Regime ◽  
Reference Conditions ◽  
Habitat Diversity ◽  
Climatic Conditions ◽  
Aerial Photographs ◽  
Contributing Factors ◽  
Jasper National Park ◽  
Closed Canopy

Repeat ground photographs (taken in 1915 and 1997) from a series of topographical survey stations and repeat aerial photographs (flown in 1949 and 1991) were analysed to assess changes in vegetation composition and distribution in the montane ecoregion of Jasper National Park, in the Rocky Mountains of Alberta, Canada. A quantitative approach for assessing relative vegetation change in repeat ground photographs was developed and tested. The results indicated a shift towards late-successional vegetation types and an increase in crown closure in coniferous stands. Grasslands, shrub, juvenile forest, and open forests decreased in extent, and closed-canopy forests became more prevalent. The majority of forest stands succeeded to dominance by coniferous species. Changes in vegetation patterns were likely largely attributable to shifts in the fire regime over the last century, although climatic conditions and human activity may also have been contributing factors. Implications of observed changes include decreased habitat diversity, increased possibility of insect outbreaks, and potential for future high-intensity fire events. Results of the study increase knowledge of historical reference conditions and may help to establish restoration goals for the montane ecoregion of the park.

Formation and preservation of marine terraces during multiple sea level stands

2021 ◽  
Author(s):  
Luca C Malatesta ◽  
Noah J. Finnegan ◽  
Kimberly Huppert ◽  
Emily Carreño
Keyword(s):  
Sea Level ◽  
Basic Assumption ◽  
Cumulative Exposure ◽  
Marine Terrace ◽  
Uplift Rate ◽  
Marine Terraces ◽  
Uplift Rates ◽  
Ca 50 ◽  
Wave Erosion ◽  
Mis 5E

<p>Marine terraces are a cornerstone for the study of paleo sea level and crustal deformation. Commonly, individual erosive marine terraces are attributed to unique sea level high-stands. This stems from early reasoning that marine platforms could only be significantly widened under moderate rates of sea level rise as at the beginning of an interglacial and preserved onshore by subsequent sea level fall. However, if marine terraces are only created during brief windows at the start of interglacials, this implies that terraces are unchanged over the vast majority of their evolution, despite an often complex submergence history during which waves are constantly acting on the coastline, regardless of the sea level stand.<span> </span></p><p>Here, we question the basic assumption that individual marine terraces are uniquely linked to distinct sea level high stands and highlight how a single marine terrace can be created By reoccupation of the same uplifting platform by successive sea level stands. We then identify the biases that such polygenetic terraces can introduce into relative sea level reconstructions and inferences of rock uplift rates from marine terrace chronostratigraphy.</p><p>Over time, a terrace’s cumulative exposure to wave erosion depends on the local rock uplift rate. Faster rock uplift rates lead to less frequent (fewer reoccupations) or even single episodes of wave erosion of an uplifting terrace and the generation and preservation of numerous terraces. Whereas slower rock uplift rates lead to repeated erosion of a smaller number of polygenetic terraces. The frequency and duration of terrace exposure to wave erosion at sea level depend strongly on rock uplift rate.</p><p>Certain rock uplift rates may therefore promote the generation and preservation of particular terraces (e.g. those eroded during recent interglacials). For example, under a rock uplift rate of ca. 1.2 mm/yr, Marine Isotope Stage (MIS) 5e (ca. 120 ka) would resubmerge a terrace eroded ca. 50 kyr earlier for tens of kyr during MIS 6d–e stages (ca. 190–170 ka) and expose it to further wave erosion at sea level. This reoccupation could accordingly promote the formation of a particularly wide or well planed terrace associated with MIS 5e with a greater chance of being preserved and identified. This effect is potentially illustrated by a global compilation of rock uplift rates derived from MIS 5e terraces. It shows an unusual abundance of marine terraces documenting uplift rates between 0.8 and 1.2 mm/yr, supporting the hypothesis that these uplift rates promote exposure of the same terrace to wave erosion during multiple sea level stands.</p><p>Hence, the elevations and widths of terraces eroded during specific sea level stands vary widely from site-to-site and depend on local rock uplift rate. Terraces do not necessarily correspond to an elevation close to that of the latest sea level high-stand but may reflect the elevation of an older, longer-lived, occupation. This leads to potential misidentification of terraces if each terrace in a sequence is assumed to form uniquely at successive interglacial high stands and to reflect their elevations.</p>

scholarly journals Vegetation change (1988–2010) in Camdeboo National Park (South Africa), using fixed-point photo monitoring: The role of herbivory and climate

Koedoe ◽  
2013 ◽  
Vol 55 (1) ◽  
Author(s):  
Mmoto L. Masubelele ◽  
Michael T. Hoffman ◽  
William Bond ◽  
Peter Burdett
Keyword(s):  
South Africa ◽  
Fixed Point ◽  
National Parks ◽  
Vegetation Cover ◽  
National Park ◽  
Vegetation Change ◽  
Growth Form ◽  
Annual Rainfall ◽  
Management Interventions

Fixed-point photo monitoring supplemented by animal census data and climate monitoring potential has never been explored as a long-term monitoring tool for studying vegetation change in the arid and semi-arid national parks of South Africa. The long-term (1988–2010), fixed-point monitoring dataset developed for the Camdeboo National Park, therefore, provides an important opportunity to do this. Using a quantitative estimate of the change in vegetation and growth form cover in 1152 fixed-point photographs, as well as series of step-point vegetation surveys at each photo monitoring site, this study documented the extent of vegetation change in the park in response to key climate drivers, such as rainfall, as well as land use drivers such as herbivory by indigenous ungulates. We demonstrated the varied response of vegetation cover within three main growth forms (grasses, dwarf shrubs [< 1 m] and tall shrubs [> 1 m]) in three different vegetation units and landforms (slopes, plains, rivers) within the Camdeboo National Park since 1988. Sites within Albany Thicket and Dwarf Shrublands showed the least change in vegetation cover, whilst Azonal vegetation and Grassy Dwarf Shrublands were more dynamic. Abiotic factors such as drought and flooding, total annual rainfall and rainfall seasonality appeared to have the greatest influence on growth form cover as assessed from the fixed-point photographs. Herbivory appeared not to have had a noticeable impact on the vegetation of the Camdeboo National Park as far as could be determined from the rather coarse approach used in this analysis and herbivore densities remained relatively low over the study duration.Conservation implications: We provided an historical assessment of the pattern of vegetation and climatic trends that can help evaluate many of South African National Parks’ biodiversity monitoring programmes, especially relating to habitat change. It will help arid parks in assessing the trajectories of vegetation in response to herbivory, climate and management interventions.

scholarly journals A simple approach for monitoring vegetation change using time series remote sensing analysis: A case study from the Thathe Vondo Area in Limpopo Province, South Africa

2021 ◽  
Vol 117 (7/8) ◽  
Author(s):  
Nndanduleni Muavhi
Keyword(s):  
Time Series ◽  
Vegetation Cover ◽  
Vegetation Change ◽  
Vegetation Index ◽  
Simple Approach ◽  
Limpopo Province ◽  
Difference Image ◽  
Normalised Difference Vegetation Index ◽  
Gain And Loss ◽  
The Difference

This study presents a simple approach of spatiotemporal change detection of vegetation cover based on analysis of time series remotely sensed images. The study was carried out at Thathe Vondo Area, which is characterised by episodic variation of vegetation gain and loss. This variation is attributable to timber and tea plantations and their production cycles, which periodically result in either vegetation gain or loss. The approach presented here was implemented on two ASTER images acquired in 2007 and 2017. It involved the combined use of band combination, unsupervised image classification and Normalised Difference Vegetation Index (NDVI) techniques. True colour composite (TCC) images for 2007 and 2017 were created from combination of bands 1, 2 and 3 in red, blue and green, respectively. The difference image of the TCC images was then generated to show the inconsistencies of vegetation cover between 2007 and 2017. For analytical simplicity and interpretability, the difference image was subjected to ISODATA unsupervised classification, which clustered pixels in the difference image into eight classes. Two ISODATA derived classes were interpreted as vegetation gain and one as vegetation loss. These classes were confirmed as regions of vegetation gain and loss by NDVI values of 2007 and 2017. In addition, the polygons of vegetation gain and loss regions were created and superimposed over the TCC images to further demonstrate the spatiotemporal vegetation change in the area. The vegetation change statistics show vegetation gain and loss of 10.62% and 2.03%, respectively, implying a vegetation gain of 8.59% over the selected decade.

scholarly journals Impact of change in erosion rate and landscape steepness on hillslope and fluvial sediments grain size in the Feather River Basin (Sierra Nevada, California)

2014 ◽  
Vol 2 (2) ◽  
pp. 1047-1092 ◽  
Author(s):  
M. Attal ◽  
S. M. Mudd ◽  
M. D. Hurst ◽  
B. Weinman ◽  
K. Yoo ◽  
...  
Keyword(s):  
Grain Size ◽  
River Basin ◽  
Sierra Nevada ◽  
Sediment Flux ◽  
Fluvial Sediments ◽  
Sediment Grain Size ◽  
Erosion Rates ◽  
Wide Range ◽  
Feather River ◽  
Order Of Magnitude

Abstract. The characteristics of the sediment transported by rivers (e.g., sediment flux, grain size distribution – GSD –) dictate whether rivers aggrade or erode their substrate. They also condition the architecture and properties of sedimentary successions in basins. In this study, we investigate the relationship between landscape steepness and the grain size of hillslope and fluvial sediments. The study area is located within the Feather River Basin in Northern California, and studied basins are underlain exclusively by tonalite lithology. Erosion rates in the study area vary over an order of magnitude, from > 250 mm ka−1 in the Feather River canyon to < 15 mm ka−1 on an adjacent low relief plateau. We find that the coarseness of hillslope sediment increases with increasing hillslope steepness and erosion rates. We hypothesize that, in our soil samples, the measured ten-fold increase in D50 and doubling of the amount of fragments larger than 1 mm when slope increases from 0.38 to 0.83 m m−1 is due to a decrease in the residence time of rock fragments, causing particles to be exposed for shorter periods of time to processes that can reduce grain size. For slopes in excess of 0.7 m m−1, landslides and scree cones supply much coarser sediment to rivers, with D50 and D84 more than one order of magnitude larger than in soils. In the tributary basins of the Feather River, a prominent break in slope developed in response to the rapid incision of the Feather River. Downstream of the break in slope, fluvial sediment grain size increases, due to an increase in flow competence (mostly driven by channel steepening) but also by a change in sediment source and in sediment dynamics: on the plateau upstream of the break in slope, rivers transport easily mobilised fine-grained sediment derived exclusively from soils. Downstream of the break in slope, mass wasting processes supply a wide range of grain sizes that rivers entrain selectively, depending on the competence of their flow. Our results also suggest that in this study site, hillslopes respond rapidly to an increase in the rate of base-level lowering compared to rivers.

scholarly journals Physical and Numerical Analysis of Bioclimatic Strategies Implemented on Social Housing

2018 ◽  
Author(s):  
Cesar Augusto Real-Ramirez ◽  
Jose Maria Velazquez-Soto ◽  
Rosalba Orduña-Martinez ◽  
Jesus Isidro Gonzalez-Trejo
Keyword(s):  
Social Housing ◽  
Transient State ◽  
Climatic Conditions ◽  
Design Strategies ◽  
Bioclimatic Design ◽  
Physical Measurements ◽  
Similar Criterion ◽  
Economic Technology ◽  
Low Speed Wind Tunnel ◽  
Performance Research

This paper presents the results of aerodynamical performance research focused on maintaining the thermal comfort and increasing the energy efficiency of a typical social housing unit located in a high-density urban area. Bioclimatic design strategies are used to develop a sustainable and economic technology in existing housing clusters in Mexico City. A full-scale prototype, built on campus facilities, was used to study the flow conditions around the design. All scaled prototypes implement similar criterion. Furthermore, a scaled prototype is evaluated within a low speed wind tunnel installation. Additionally, numerical simulations were performed at transient state based on previous physical measurements and historical local climatic conditions to determine preferable modifications.

scholarly journals Long-term geomorphological evolution of the axial zone of the Campania-Lucania Apennine, southern Italy: a review

2017 ◽  
Vol 68 (1) ◽  
pp. 57-67 ◽  
Author(s):  
Marcello Schiattarella ◽  
Salvatore Ivo Giano ◽  
Dario Gioia
Keyword(s):  
Southern Italy ◽  
Morphological Evolution ◽  
Structural Data ◽  
Middle Pleistocene ◽  
Southern Apennines ◽  
Axial Zone ◽  
Entire Study ◽  
Erosion Rates ◽  
Uplift Rates ◽  
Land Surfaces

Abstract Uplift and erosion rates have been calculated for a large sector of the Campania-Lucania Apennine and Calabrian arc, Italy, using both geomorphological observations (elevations, ages and arrangement of depositional and erosional land surfaces and other morphotectonic markers) and stratigraphical and structural data (sea-level related facies, base levels, fault kinematics, and fault offset estimations). The values of the Quaternary uplift rates of the southern Apennines vary from 0.2 mm/yr to about 1.2–1.3 mm/yr. The erosion rates from key-areas of the southern Apennines, obtained from both quantitative geomorphic analysis and missing volumes calculations, has been estimated at 0.2 mm/yr since the Middle Pleistocene. Since the Late Pleistocene erosion and uplift rates match well, the axial-zone landscape could have reached a flux steady state during that time, although it is more probable that the entire study area may be a transient landscape. Tectonic denudation phenomena — leading to the exhumation of the Mesozoic core of the chain — followed by an impressive regional planation started in the Late Pliocene have to be taken into account for a coherent explanation of the morphological evolution of southern Italy.

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