Events

We propose a method for accounting for model error due to unresolved scales within the context of ensemble Kalman filtering. This method estimates a model error correction to the forecast step by using historical reanalysis increments to build a model error covariance matrix. We compare two different versions of the method; a time-constant model error treatment where the same model error bias correction is added after each forecast, and a time- varying treatment where the bias correction randomly varies with each forecast. We compare both methods with the standard method of dealing with model error through inflation and localization, and illustrate our results with numerical simulations on a low order nonlinear system showing chaotic dynamics. The results show that the filter skill is significantly improved through the proposed model error treatments, and that both methods require far less parameter tuning than the standard approach. This is joint work with Alberto Carrassi.

Kriging is a non-parametric regression method used in geostatistics for estimating curves and surfaces and forms the core of most statistical methods for spatial data. In climate science these methods are very useful for estimating how climate varies over a geographic region when the observational data is sparse or the computer model runs are limited. A statistical challenge is to implement spatial methods for large sample sizes, a common feature of many geophysical problems. Here a new family of covariance models is proposed that expands the field in a set of basis functions and places a Gaussian Markov random field (GMRF) latent model on the basis coefficients. The idea, in contrast to fixed rank Kriging, is to use many basis functions organized on lattices. In addition, the basis functions add more smoothness and larger scale spatial dependence that a GMRF alone. The computational efficiency arises because one can choose basis functions with compact support and also a precision matrix for the GMRF that is very sparse. The impact is that evaluating the model likelihood and computing spatial predictions is feasible even for tens of thousands of spatial observations. Moreover, by the varying the support of the basis functions and the correlations among basis coefficients it is possible to entertain multi-resolution and nonstationary spatial models. A practical example is also presented for a subset of the North American Regional Climate Change and Assessment Program model data. Here fields on the order 10^4 observations are compared within the R data analysis environment.

A

At mid-to-high latitudes, the stratosphere contains >25 percent of the column of atmospheric mass. Large-scale vertically-propagating waves alter the strength of the stratospheric polar vortex and drive a synchronised meridional circulation. These stratospheric changes are associated with substantial effects on surface weather and climate, especially on the Northern and Southern Annular Modes (NAM, SAM) and associated long-lasting shifts in the jet streams, storm tracks, pre- cipitation, and likelihood of blocking events. Despite unambiguous observations of this phenomenon, as well as numerical simulations, the primary dynamics of this downward coupling are not understood. I will show that the meridional circulation extends below the tropopause, modulating the day-to-day thickness of the troposphere, especially at high northern latitudes. The vertical displacement of the polar air column acts like a plunger controlling the movement of water in a pipe. The return flow in the troposphere is also synchronised to the strength of the polar vortex. I will make the case that the altered meridional circulation acts as a trigger for tropospheric eddy feedbacks. This conceptual framework predicts surface pressure variations similar to the NAM, and linear variation of tropospheric phenomena with the strength of the polar vortex. The results point to the importance of the Arctic tropopause layer for assessing the fidelity of stratosphere– troposphere coupling in climate and weather forecast models.

Abstract: I will give a gentle introduction to some deep and important quantum phenomena associated with topology. The first is the Aharonov-Bohm effect, and the second is quantum statistics for identical particles. No prior knowledge of quantum mechanics will be assumed. I will go on to discuss some new work on quantum statistics in discrete spaces associated with recent developments in characterizing their topology.

To combine high resolution atmospheric flow models with state-of-the-art data assimilation and statistical analyses is one of the biggest current challenges for numerical weather and climate prediction. In this talk we will show how hierarchical multiscale or multilevel methods can be designed to tackle this challenge. They are essential as scalable PDE solvers for individual simulations, but their biggest potential lies in accelerating standard Monte Carlo (or ensemble-type) methods for statistical analyses and for data assimilation, including Markov chain Monte Carlo methods which are of great interest also in the atmospheric sciences. Monte Carlo methods are notorious for their slow convergence and high computational cost. In this talk we will present revolutionary recent developments to mitigate and overcome this serious problem using novel multilevel strategies that can lead to a more than 100-fold acceleration of existing ensemble-type methods. The talk will focus on methodology. Most of the applications are so far mainly coming from subsurface flow.

Variational data assimilation techniques in numerical weather prediction make use of the tangent linear and adjoint versions of the weather forecast model. Inclusion of the moist atmospheric processes, such as convection and precipitation, in the linear model is highly beneficial. Doing so allows the sensitivity to moisture to be effectively measured and enables the assimilation of observations of clouds and precipitation. However, the schemes developed to model the so called `moist physics' do not generally behave in a linear way. Many of the processes being represented are inherently nonlinear and artificial switches in the numerics are commonplace. Here we show a how the Jacobian, with various perturbation structures, can be used for analysing the linearity and stability for a given scheme. Using this method, linearised versions of the in situ moist physics schemes are developed and implemented in NASA's GEOS-5 data assimilation tools. The benefits of including moist physics are shown through observation impact experiments and in sensitivity studies.

Computational technique based on the symbolic description utilizing kneading invariants is proposed for exploration of parametric chaos in three exemplary systems with the Lorenz attractor: the canonical model itself, a normal model from mathematics, and a laser model from nonlinear optics. The technique allows for uncovering the stunning complexity and universality of the patterns discovered in the bi-parametric scans of the given models and detects their organizing centers: codimension-two T-points and separating saddles. This work is joint with Tingli Xing and Roberto Barrio.

In the first part of this talk (Aston), we describe the qualitative behaviour of one of the simplest car- bon cycle models, the Data Assimilation Linked Ecosystem Carbon (DALEC) model, which is a simple vegetation model of processes involved in the carbon cycle of forests. We review the dynamical structure of the model. Our analysis shows that the dynamics of both evergreen and deciduous forests in DALEC are dependent on a few key parameters and it is possible to find a limit point where there is stable sustainable behaviour on one side but unsustainable conditions on the other side. The fact that typical parameter values reside close to this limit point highlights the difficulty of predicting even the correct trend without sufficient data and has implications for the use of data assimilation methods. In the second part of the talk (Delahaies), will review techniques from four-dimensional variational data assimilation applied to DALEC. Using synthetic flux tower measurements together with a linearization of DALEC model, we show that the assimilation problem is highly ill-posed, and that parameters related to slow processes are not observable. We study the impact of regularization methods (TSVD, Tikhonov, and random Gaussian matrices) on the quality of the analysis and on the reduction of the uncertainty.

A consistent theoretical description of friction is certainly one of the most challenging topics nature has still in stock. While talk won't contribute to this fundamental issue, we rather analyse a simple phenomenological model. In particular, we will focus on the impact of stochastic forcing on dry friction and the associated stick-slip transition. Analytical solutions of the Fokker-Planck equation and of the corresponding eigenvalue problem will be presented, uncovering the dynamical phenomena in this piecewise smooth stochastic model.

Grand environmental challenges are spread across a host of different environmental media and issues including climate change, carbon in soils, water and air, water quality and quantity, air pollution, transport and the urban environment, radioactivity, biodiversity and landscape fragmentation. Grand technology issues include: development of sensors able to measure pollutants such as pm2.5, nitrates, novel organic compounds (e.g. pharmaceuticals) at environmental levels (such as ppb), integration and synthesis of observations from a variety of sensor networks, development of statistical models to handle large data sets and visualisation and communication challenges. Improvements in monitoring impact will significantly enhance our ability to detect and attribute change (in the presence of considerable natural variability). In this presentation, I will consider a variety of environmental change situations and think about the distinguishing statistical techniques that are needed.

MAGIC course lecture to replace cancelled lecture.

MAGIC course lecture to replace cancelled lecture.

MAGIC course lecture to replace cancelled lecture.