Constraining DALECv2 using multiple data streams and ecological constraints: analysis and application

We use a variational method to assimilate multiple data streams into the terrestrial ecosystem carbon cycle model DALECv2. Ecological and dynamical constraints have recently been introduced to constrain unresolved components of this otherwise ill-posed problem. Here we recast these constraints as a multivariate Gaussian distribution to incorporate them into the variational framework and we demonstrate their benefit through a linear analysis. Using an adjoint method we study a linear approximation of the inverse problem: firstly we perform a sensitivity analysis of the different outputs under consideration, and secondly we use the concept of resolution matrices to diagnose the nature of the ill-posedness and evaluate regularisation strategies. We then study the non linear problem with an application to real data. Finally, we propose a modification to the model: introducing a spin-up period provides us with a built-in formulation of some ecological constraints which facilitates the variational approach

Constraining DALEC v2 using multiple data streams and ecological constraints: analysis and application.

We use a variational method to assimilate multiple data streams into the terrestrial ecosystem carbon cycle model DALECv2. Ecological and dynamical constraints have recently been introduced to constrain unresolved components of this otherwise ill-posed problem. Here we recast these constraints as a multivariate Gaussian distribution to incorporate them into the variational framework and we demonstrate their benefit through a linear analysis. Using an adjoint method we study a linear approximation of the inverse problem: firstly we perform a sensitivity analysis of the different outputs under consideration, and secondly we use the concept of resolution matrices to diagnose the nature of the ill-posedness and evaluate regularisation strategies.We then study the non linear problem with an application to real data. Finally, we propose a modification to the model: introducing a spin-up period provides us with a built-in formulation of some ecological constraints which facilitates the variational approach

Solutions and Singularities of the Semigeostrophic Equations via the Geometry of Lagrangian Submanifolds

Using Monge-Amp\`ere geometry, we study the singular structure of a class of nonlinear Monge-Amp\`ere equations in three dimensions, arising in geophysical fluid dynamics. We extend seminal earlier work on Monge-Amp\`ere geometry by examining the role of an induced metric on Lagrangian submanifolds of the cotangent bundle. In particular, we show that the signature of the metric serves as a classification of the Monge-Amp\`ere equation, while singularities and elliptic-hyperbolic transitions are revealed by the degeneracies of the metric. The theory is illustrated by application to an example solution of the semigeostrophic equations.Comment: 22 pages, 5 figure

Improvements in forecasting intense rainfall: results from the FRANC (forecasting rainfall exploiting new data assimilation techniques and novel observations of convection) project

The FRANC project (Forecasting Rainfall exploiting new data Assimilation techniques and Novel observations of Convection) has researched improvements in numerical weather prediction of convective rainfall via the reduction of initial condition uncertainty. This article provides an overview of the project’s achievements. We highlight new radar techniques: correcting for attenuation of the radar return; correction for beams that are over 90% blocked by trees or towers close to the radar; and direct assimilation of radar reflectivity and refractivity. We discuss the treatment of uncertainty in data assimilation: new methods for estimation of observation uncertainties with novel applications to Doppler radar winds, Atmospheric Motion Vectors, and satellite radiances; a new algorithm for implementation of spatially-correlated observation error statistics in operational data assimilation; and innovative treatment of moist processes in the background error covariance model. We present results indicating a link between the spatial predictability of convection and convective regimes, with potential to allow improved forecast interpretation. The research was carried out as a partnership between University researchers and the Met Office (UK). We discuss the benefits of this approach and the impact of our research, which has helped to improve operational forecasts for convective rainfall event

Semigeostrophic time evolution of velocity gradient tensor invariants

The behaviour of quadratic invariants of the velocity gradient tensor is explored when the time evolution is governed by semigeostrophic forms of the shallow water equations. The evolution equation of a certain Jacobian involving the geostrophic flow is formally similar to its counterpart under the primitive shallow water equations. The resultant deformation and the Frobenius norm do not behave in this symmetrical way. A product of the study is a straightforward derivation of the semigeostrophic potential vorticity conservation property. Results are extended to 3D baroclinic flow by using isentropic coordinates

Semigeostrophic time evolution of velocity gradient tensor invariants

The behaviour of quadratic invariants of the velocity gradient tensor is explored when the time evolution is governed by semigeostrophic forms of the shallow water equations. The evolution equation of a certain Jacobian involving the geostrophic flow is formally similar to its counterpart under the primitive shallow water equations. The resultant deformation and the Frobenius norm do not behave in this symmetrical way. A product of the study is a straightforward derivation of the semigeostrophic potential vorticity conservation property. Results are extended to 3D baroclinic flow by using isentropic coordinates

Monge-Ampère Structures and the Geometry of Incompressible Flows

Autre type de document (Document non publié)We show how a symmetry reduction of the equations for incompressible hydrodynamics in three dimensions leads naturally to a Monge-Amp\`ere structure, and Burgers'-type vortices are a canonical class of solutions associated with this structure. The mapping of such solutions, which are characterised by a linear dependence of the third component of the velocity on the coordinate defining the axis of rotation, to solutions of the incompressible equations in two dimensions is also shown to be an example of a symmetry reduction The Monge-Amp\`ere structure for incompressible flow in two dimensions is shown to be hypersymplectic.</p