to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

https://hal.inria.fr/inria-00070738/document

A well-balanced positivity preserving second-order scheme for shallow water flows on unstructured meshes

Resume Considering the three-dimensional Navier–Stokes equations with a free moving surface boundary condition and hydrostatic approximation, we study the derivation, with asymptotic analysis, of a new two-dimensional viscous shallow water model in rotating framework, with irregular topography, linear and quadratic bottom friction terms and capillary effects. A new formulation of the viscous effects, consistent with a previous one-dimensional analysis, is obtained. Finally, we propose some simple numerical experiments in order to validate the proposed model.

Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects

The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighborhing layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic pressure and prove energy and hyperbolicity properties of the model. We also give a kinetic interpretation leading to effective numerical schemes with positivity and energy properties. Numerical tests show the versatility of the approach and its ability to compute recirculation cases with wind forcing.

/pdf/a-multilayer-saint-venant-system-with-mass-exchanges-for-40fvn6kfdt.pdf

A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation*

A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation

The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional model at the second order with respect to the ratio between the vertical scale and the longitudinal scale. The derived model is shown to be symmetrizable through a suitable change of variables. Finally, we propose some numerical tests with the aim to validate the proposed model.

/pdf/a-new-two-dimensional-shallow-water-model-including-pressure-4ebyjbgddt.pdf

A new two-dimensional shallow water model including pressure effects and slow varying bottom topography

Ecosystems in the Alps are considered hotspots of climate and land use change. In addition, alpine regions are usually characterized by complex morphologies, which make measurement (especially in the long term) of states and fluxes of water, energy and matter particularly challenging. Therefore, there is a limited availability of information and modelling tools to characterize actual ecosystem conditions, and to simulate future scenarios. Despite the fact that in high altitude areas meteorological forcing is extremely variable in space and time, much of the variability of actual evapotranspiration (AET) in the above-mentioned regions is largely related to land surface properties such as aspect, shadowing and slope. Therefore, a simple, radiation driven, calibration free, bucket hydrological model for predicting AET and estimating the soil–water balance is proposed here (i.e. CLIME-MG). Conventional meteorological data from a network of automatic weather stations together with a 10 m digital terrain model (aggregated at 30 m), and a land cover map are used to inform the model. All the parameters and values required are obtained or calculated from data provided in literature. CLIME-MG has proved to perform well for AET modelling of mountain grassland. The model is validated both temporally and spatially. Temporal validation of AET is performed using eddy-covariance datasets from two different high mountain sites: a sunny and steep abandoned pasture facing S-E at an altitude of 1730 m, and a meadow with a S-SE aspect located at an altitude of 2555 m. Spatial validation is performed by comparing CLIME-MG simulations with the Landsat-based METRIC model evapotranspiration output. Results show good daily temporal performance, especially in wetter periods with recurring rainfall events. Sensitivity of the correlation coefficient between measured and modeled AET values to some key parameters such as effective porosity, and the vegetation and stress coefficients was found to be quite low. Spatial validation of hourly results shows SPAEF values in the range 0.21–0.34 between the outputs of the two models (with a similar spatial structure ruled by the DTM). Boxplots of deviations between CLIME and METRIC with respect to morphological characteristics has highlighted some dependency on elevation and slope (but not on aspect and soil depth); this suggests an opportunity to refine the modelisation of the grassland AET processes. Finally, spatial results demonstrated the non-sensitivity of the proposed model to local elevation and to the distance from the meteorological stations. 

Stefania Ferrari

Papers

A new two-dimensional shallow water model including pressure effects and slow varying bottom topography

A Calibration Free Radiation Driven Model for Estimating Actual Evapotranspiration of Mountain Grasslands (CLIME-MG)