In-situ cosmogenic 10Be (and 26Al) concentrations in alluvial sediments provide a spatially averaged signal of the erosion rate of the catchment area. Catchmentwide erosion rates reflect the production rate of the entire basin, and their calculation requires knowledge of the complete production rate model. Available calculators determine production rates on a pixel-based approach and achieve computational efficiency by relying on a scaling method that ignores geomagnetic field strength variations. Here we introduce a new python-based tool that determines erosion rates based on the hypsometry of the catchment. The method relies on the fact that production rates are much more sensitive to changes in elevation than latitude. Our tool has two main advantages: (1) computation time is short (<30 seconds) and independent of the scaling method; there is no need to neglect magnetic field variations, and (2) because production rate scaling is performed by a widely used online calculator, the results are fully comparable to exposure ages or point-based erosion rates determined with the same calculator; future updates to production rate scaling are immediately effective for catchmentwide erosion rate calculation. We demonstrate in two case studies that (1) for similar scaling methods, our calculator reproduces pixel-based results within a few percent, and (2) erosion rates determined with different scaling methods may differ by >20%, differences can vary systematically with erosion rate, and using a time-constant scaling method may result in a bias in the interpretation of catchmentwide erosion rates.

At time-scales of 102 to 105 years, erosion by rivers, landslides and glaciers can exceed 5 mm/y. Sustained denudation at these rates is sufficient to account for many of the rapid rates of unloading or cooling that are revealed by geobarometric or thermochronologic studies. Because feedbacks exist among many surface processes, determinations of erosion rates on a few geomorphic processes can be adequate to estimate mean rates across an entire landscape. Rates of fluvial and glacial incision exert a dominant control on landscape lowering, because these rates set the local base level and modulate the flux from adjacent hillslopes. When rates of deformation are sufficiently rapid and sustained, a collisional orogen approaches a dynamic equilibrium or topographic steady state. Due to variations in erosion rates as a function of Late Cenozoic climate changes, such a steady state should be defined at time-scales longer than one climate cycle. During dynamic equilibrium, the geomorphic system displays a predictable configuration of interacting rivers, hillslopes and glaciated process zones. A dynamic equilibrium appears to prevail near Nanga Parbat, Pakistan, and the Southern Alps of New Zealand, where spatial variations in geomorphic erosion rates mimic variations in bedrock cooling rates at time-scales of 106 y.

Formerly closed drainage basins provide exceptional settings for quantifying fluvial incision and landscape dissection at different time scales. Endorheic basins trap all the sediment eroded within the watershed, which allows estimates of post–basin opening erosion patterns. The Duero Basin was a former closed basin and is presently drained by the Duero River into the Atlantic Ocean. During the Cenozoic, the basin experienced a long endorheic period, marked by the formation of continental carbonates and evaporites. The retrogressive erosion of the Atlantic drainage coming from the Portuguese coast subsequently captured the internal drainage, and significant fluvial dissection occurred. Presently, the basin contains a relatively well-preserved sedimentary fill. Gridding and surface fitting in this paper provide the first attempt to reconstruct the surface of the top of the former endorheic sedimentary sequence to quantify the erosional impact of the basin opening. At least 2251±524 km3 of sediment was removed from the formerly closed basin following the start of exorheism. This volume represents a mean basin-surface lowering of 65±13 m. Erosion estimates and landscape dissection patterns are consistent with geologic evidence of progressive establishment of an outward drainage system.

Analysis of five basement samples from the Vestfold Hills (East Antarctica) reveals pooled apatite fission track (FT) ages ranging from 188 to 264 Ma and mean lengths of 13.7 to 14.9 μm. Quantitative thermal histories derived from these data give consistent results indicating onset of cooling/denudation began sometime prior to 240 Ma, with final cooling below 105°–125°C occurring between 240 and 220 Ma (Triassic). A Cretaceous denudation phase can be inferred from the sedimentary record of the Prydz Bay offshore the Vestfold Hills. The two denudational episodes are likely associated with Palaeozoic large-scale rifting processes that led to the formation of the adjacent Lambert Graben, and to the Cretaceous Gondwana break-up between Antarctica and India. Subsequent evolution of the East Antarctic passive continental margin likely occurred throughout the Cenozoic based on the depositional record in Prydz Bay and constraints (though tentative) from FT data.

A simple flexural model is used to explore the relationship between magmatic underplating and denudation. First, we show how denudation can be calculated as a function of underplating. The distribution and density of underplate are obviously important parameters in determining the wavelength and amplitude of denudation. However, the denudational pattern can be considerably modulated by the flexural rigidity of the lithosphere. Several other parameters also play a significant role. For example, we show how variations in pre-existing bathymetry and in present-day topography affect denudational calculations. We have applied our simple algorithm to the problem of Paleogene underplating beneath the British Isles. Forward and inverse modelling of travel-time data from a wide-angle seismic experiment which traversed the British Isles suggests that a large pod of high velocity material occurs at Moho depths beneath the Irish Sea. The shape and inferred density of this pod are used to calculate the amplitude and wavelength of denudation for different flexural rigidities. We compare our predictions with the observed pattern of Paleogene denudation and conclude that the bulk of the observed denudation can be accounted for by magmatic underplating associated in a general way with the Iceland Plume. Notwithstanding this agreement, there is compelling evidence for additional mild uplift events especially during the Neogene. These mild events may reflect fluctuating dynamic topography associated with the Iceland Plume.

New apatite fission-track (AFT) ages from Heimefrontfjella and Mannefallknausane indicate that the Mesoproterozoic basement and Permian sedimentary cover rocks were heated to c. 100°C during the Mesozoic. Heating was due to the burial by up to 2000 m of Jurassic lavas at c. 180 Ma, when the area was affected by the Bouvet/Karoo hot spot. Near the developing coastline, the lava pile was quickly eroded and in part deposited on the continental shelf as pebbly and coarse-grained volcaniclastic sandstones. The AFT data indicate that farther inland the lava pile was not eroded until c. 100 Ma, and the Palaeozoic unconformity between the Mesoproterozoic basement and Permo–Carboniferous sedimentary rocks as a reference plane remained at temperatures of c. 80°C. Formation of an up to 800 m b.s.l. deep graben in from Heimefrontfjella as well as flexural uplift and rapid denudational cooling of the not extended crust from Heimefrontfjella southwards occurred at c. 100 Ma. It is speculated that a period of major plate reorganisation and new rifting at c. 100 Ma is responsible for affecting a much wider continental margin as far inland as Heimefrontfjella and producing a total relief in excess of 3500 m.

The role played by Cenozoic deformation in denudation and landscape development in Ireland has historically been difficult to assess because of the lack of widespread pre-glacial Cenozoic deposits onshore. Here we combine analysis of apatite fission-track data and geomorphic observations to place constraints on the timing, kinematics and magnitude of onshore deformation in southeastern Ireland. Relationships between apatite fission-track central age and elevation for samples from the Wicklow and Blackstairs Mountains and Tullow Lowland suggest that these rocks record an exhumed apatite partial annealing zone, which after cooling was dismembered by differential vertical displacements of up to several hundred metres. We use inverted models of sample thermal history to show that samples across the region experienced very similar thermal histories up to and including a cooling event in late Paleocene or early Eocene time. This effectively rules out strongly spatially heterogeneous denudation, and implies that differential rock uplift occurred in post-early Eocene time. The central age–elevation relationships define at least three spatial domains with internally consistent apatite fission-track data, separated by known faults or topographic escarpments. Geomorphic analysis of these structures shows that patterns of catchment incision and sinuosity, as well as the presence of antecedent drainage, are best explained by differential vertical displacements at or near the domain boundaries. The kinematics and magnitudes of these displacements are consistent with those implied by the apatite fission-track results, and are compatible with other examples of known Cenozoic deformation from Ireland and the adjacent continental margin.