Abstract. Laboratory-scale experiments of erosion have demonstrated that landscapes have a natural (or intrinsic) response time to a change in precipitation rate. In the last few decades there has been growth in the development of numerical models that attempt to capture landscape evolution over long timescales. However, there is still an uncertainty regarding the validity of the basic assumptions of mass transport that are made in deriving these models. In this contribution we therefore return to a principal assumption of sediment transport within the mass balance for surface processes; we explore the sensitivity of the classic end-member landscape evolution models and the sediment fluxes they produce to a change in precipitation rates. One end-member model takes the mathematical form of a kinetic wave equation and is known as the stream power model, in which sediment is assumed to be transported immediately out of the model domain. The second end-member model is the transport model and it takes the form of a diffusion equation, assuming that the sediment flux is a function of the water flux and slope. We find that both of these end-member models have a response time that has a proportionality to the precipitation rate that follows a negative power law. However, for the stream power model the exponent on the water flux term must be less than one, and for the transport model the exponent must be greater than one, in order to match the observed concavity of natural systems. This difference in exponent means that the transport model generally responds more rapidly to an increase in precipitation rates, on the order of 10 5 years for post-perturbation sediment fluxes to return to within 50 % of their initial values, for theoretical landscapes with a scale of 100 × 100 km. Additionally from the same starting conditions, the amplitude of the sediment flux perturbation in the transport model is greater, with much larger sensitivity to catchment size. An important finding is that both models respond more quickly to a wetting event than a drying event, and we argue that this asymmetry in response time has significant implications for depositional stratigraphies. Finally, we evaluate the extent to which these constraints on response times and sediment fluxes from simple models help us understand the geological record of landscape response to rapid environmental changes in the past, such as the Paleocene-Eocene thermal maximum (PETM). In the Spanish Pyrenees, for instance, a relatively rapid (10 to 50 kyr) duration of the deposition of gravel is observed for a climatic shift that is thought to be towards increased precipitation rates. We suggest that the rapid response observed is more easily explained through a diffusive transport model because (1) the model has a faster response time, which is consistent with the documented stratigraphic data, (2) there is a high-amplitude spike in sediment flux, and (3) the assumption of instantaneous transport is difficult to justify for the transport of large grain sizes as an alluvi...
We present in this work the development of a solar data assimilation method based on an axisymmetric mean field dynamo model and magnetic surface data, our mid-term goal is to predict the solar quasi cyclic activity. Here we focus on the ability of our algorithm to constrain the deep meridional circulation of the Sun based on solar magnetic observations. To that end, we develop a variational data assimilation technique. Within a given assimilation window, the assimilation procedure minimizes the differences between data and the forecast from the model, by finding an optimal meridional circulation in the convection zone, and an optimal initial magnetic field, via a quasi-Newton algorithm. We demonstrate the capability of the technique to estimate the meridional flow by a closed-loop experiment involving 40 years of synthetic, solar-like data. By assimilating the synthetic magnetic proxies annually, we are able to reconstruct a (stochastic) time-varying meridional circulation which is also slightly equatorially asymmetric. We show that the method is robust in estimating a flow whose level of fluctuation can reach 30% about the average, and that the horizon of predictive capability of the method is of the order of 1 cycle length.
Abstract. Laboratory-scale experiments of erosion have demonstrated that landscapes have a natural (or intrinsic) response time to a change in precipitation rate. In the last few decades there has been a growth in the development of numerical models that attempt to capture landscape evolution over long time-scales. Recently, a sub-set of these numerical models have been used to invert river profiles for past tectonic conditions even during variable climatic conditions. However, there is still an 5 uncertainty over validity of the basic assumption of mass transport that are made in deriving these models. In this contribution we therefore return to a principle assumption of sediment transport within the mass balance for surface processes, and explore the sensitivity of the classic end-member landscape evolution models to change in precipitation rates. One end-member model takes the mathematical form of a kinetic wave equation and is known as the stream power model, where sediment is assumed to be transported immediately out of the model domain. The second end-member model takes the form of a diffusion equation, 10 and assumes that the sediment flux is a function of the water flux and slope. We find that both of these end-member models have a response time that has a proportionality to the precipitation rate that follows a negative power law. For the stream power model the exponent on the water flux term must be less than one, and for the sediment transport model the exponent must be greater than one in order to match the observed concavity of natural systems. This difference in exponent means that sediment transport model responds more rapidly to an increase in precipitation rates, on the order of 10 5 years for a landscape with 15 a scale of 10 5 m. In nature, landscape response times to a rapid environmental change have been estimated for events such as the Paleocene-Eocene thermal maximum (PETM). In the Spanish Pyrenees, a relatively rapid, 20 to 100 kyr, duration of deposition of gravel during the PETM is observed for a climatic shift that is thought to be towards increased precipitation rates. We suggest the rapid response observed is more easily explained through a diffusive sediment transport model, as (1) this model has a faster response time, consistent with the documented stratigraphic data, and (2) the assumption of instantaneous 20 transport is difficult to justify for the transport of large grain sizes as an alluvial bed-load.
The purpose of this article is to discuss several modern aspects of remeshing, which is the task of modifying an ill-shaped tetrahedral mesh with bad size elements so that it features an appropriate density of high-quality elements. After a brief sketch of classical stakes about meshes and local mesh operations, we notably expose (i) how the local size of the elements of a mesh can be adapted to a user-defined prescription (guided, e.g., by an error estimate attached to a numerical simulation), (ii) how a mesh can be deformed to efficiently track the motion of the underlying domain, (iii) how to construct a mesh of an implicitly-defined domain, and (iv) how remeshing procedures can be conducted in a parallel fashion when large-scale applications are targeted. These ideas are illustrated with several applications involving high-performance computing. In particular, we show how mesh adaptation and parallel remeshing strategies make it possible to achieve a high accuracy in large-scale simulations of complex flows, and how the aforementioned methods for meshing implicitly defined surfaces allow to represent faithfully intricate geophysical interfaces, and to account for the dramatic evolutions of shapes featured by shape optimization processes.
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