Controlling instabilities along a 3DVar analysis cycle by assimilating in the unstable subspace: a comparison with the EnKF

A hybrid scheme obtained by combining 3DVar with the Assimilation in the Unstable Subspace (3DVar-AUS) is tested in a QG model, under perfect model conditions, with a fixed observational network, with and without observational noise. The AUS scheme, originally formulated to assimilate adaptive observations, is used here to assimilate the fixed observations that are found in the region of local maxima of BDAS vectors (Bred vectors subject to assimilation), while the remaining observations are assimilated by 3DVar. The performance of the hybrid scheme is compared with that of 3DVar and of an EnKF. The improvement gained by 3DVar-AUS and the EnKF with respect to 3DVar alone is similar in the present model and observational configuration, while 3DVar-AUS outperforms the EnKF during the forecast stage. The 3DVar-AUS algorithm is easy to implement and the results obtained in the idealized conditions of this study encourage further investigation toward an implementation in more realistic contexts

Recent advances in the development of a European Mars climate model in Oxford

Since the early 1990s, efforts have been under way in Oxford to develop a range of numerical weather and climate prediction models for various studies of the Martian atmosphere and near-surface environment. Early versions of the Oxford model were more in the way of 'process models', aimed at relatively idealised studies e.g. of baroclinic instability[1] and low-level western boundary currents in the cross-equatorial solsticial Hadley circulation[2]. Since the mid-1990s, however, the group in Oxford have worked closely with the modelling group at LMD in Paris to develop a joint suite of more sophisticated and comprehensive numerical models of Mars' atmosphere. This collaboration, partly sponsored in recent years by the European Space Agency in connection with the associated development of a climate database for Mars[3], culminated in a suite of global circulation models[4], in which both groups share a library of parametrisation schemes, but in which the Oxford team use a spectral representation of horizontal fields (in the form of spherical harmonics) and the LMD group use a grid-point finite difference representation. These models were described in some detail by Forget et al.[4], and their preliminary validation and use in the construction of first versions of the European Mars Climate Database by Lewis et al.[3]. In the present report, we will review further developments which have taken place since the latter papers were published. Aspects of these developments which are common to both the LMD and Oxford groups will also be covered in the companion contribution by Forget et al. in this meeting, and so will only be touched on briefly here. Instead, we will concentrate on those advances which are more specific to the Oxford version of the model. In the following sections, we outline the main new developments to the model formulation since 1999. Subsequent sections then describe some recent examples where the new model is being utilised to advance a diverse range of studies of Mars atmospheric science

Mars Pathfinder meteorological observations on the basis of results of an atmospheric global circulation model

The Mars Pathfinder Meteorological Package (ASI/MET) will measure the local pressure, temperature, and winds at its future landing site, somewhere between the latitudes 0 deg N and 30 deg N. Comparable measurements have already been obtained at the surface of Mars by the Viking Landers at 22 deg N (VL1) and 48 deg N (VL2), providing much useful information on the martian atmosphere. In particular the pressure measurements contain very instructive information on the global atmospheric circulation. At the Laboratoire de Meteorologie Dynamique (LMD), we have analyzed and simulated these measurements with a martian atmospheric global circulation model (GCM), which was the first to simulate the martian atmospheric circulation over more than 1 year. The model is able to reproduce rather accurately many observed features of the martian atmosphere, including the long- and short-period oscillations of the surface pressure observed by the Viking landers. From a meteorological point of view, we think that a landing site located near or at the equator would be an interesting choice

The Ising-Sherrington-Kirpatrick model in a magnetic field at high temperature

We study a spin system on a large box with both Ising interaction and Sherrington-Kirpatrick couplings, in the presence of an external field. Our results are: (i) existence of the pressure in the limit of an infinite box. When both Ising and Sherrington-Kirpatrick temperatures are high enough, we prove that: (ii) the value of the pressure is given by a suitable replica symmetric solution, and (iii) the fluctuations of the pressure are of order of the inverse of the square of the volume with a normal distribution in the limit. In this regime, the pressure can be expressed in terms of random field Ising models

Ensemble variational assimilation as a probabilistic estimator – Part 2: The fully non-linear case

The method of ensemble variational assimilation (EnsVAR), also known as ensemble of data assimilations (EDA), is implemented in fully non-linear conditions on the Lorenz-96 chaotic 40-parameter model. In the case of strong-constraint assimilation, it requires association with the method of quasi-static variational assimilation (QSVA). It then produces ensembles which possess as much reliability and resolution as in the linear case, and its performance is at least as good as that of ensemble Kalman filter (EnKF) and particle filter (PF). On the other hand, ensembles consisting of solutions that correspond to the absolute minimum of the objective function (as identified from the minimizations without QSVA) are significantly biased. In the case of weak-constraint assimilation, EnsVAR is fully successful without need for QSVA.</p

The Mars Climate Database

The Mars Climate Database (MCD) [1] is a database of statistics describing the climate and environment of the Martian atmosphere. It was constructed directly on the basis of output from mulitannual integrations of two general circulation models (GCMs)developed by Laboratoire de Météorologie Dynamique du CNRS, France, the University of Oxford, UK, and Instituto de Astrofisica de Andalucia, Spain, with support from the European Space Agency (ESA) and Centre National d–Etudes Spatiales (CNES). A description of the MCD is given along with a comparison between spacecraft observations of Mars and results predicted at similar locations and times in the MCD. The MCD can be used as a tool for mission planning and has been applied to prepare for several missions in Europe and the USA. It also provides information for mission design specialists on the mean state and variability of the Martian environment from the surface to above 120km. The GCMs on which the database is founded, include a set of physical parameterizations (radiative transfer in the visible and thermal infrared ranges, turbulent mixing, condensation-sublimation of CO2, thermal conduction in the soil and representation of gravity waves) and two different codes for the representation of large scale dynamics: a spectral code for the AOPP version and a grid-point code for the LMD version. The GCMs correctly reproduce the main meteorological features of Mars, as observed by the Mariner 9 and Viking orbiters, the Viking landers, and Mars Global Surveyor (MGS). As well as the standard statistical measures for mission design studies, the MCD includes a novel representation of large-scale variability, using empirical eigenfunctions derived from an analysis of the full simulations, and small-scale variability based on parameterizations of processes such as gravity wave propagation. The database allows the user to choose from 5 dust storm scenarios including a best guess, default scenario, deduced from recent MGS observations, an upper boundary for an atmosphere without dust storms, as observed by Viking the landers, and a clear, cold, lower boundary scenario, as observed by Phobos 2 and from Earth. The full version of the MCD is available on CDROM (for UNIX systems and PCs) and is also accessible through an interactive WWW interface at http://www-mars.lmd.jussieu.fr/

The universal Glivenko-Cantelli property

Let F be a separable uniformly bounded family of measurable functions on a standard measurable space, and let N_{[]}(F,\epsilon,\mu) be the smallest number of \epsilon-brackets in L^1(\mu) needed to cover F. The following are equivalent: 1. F is a universal Glivenko-Cantelli class. 2. N_{[]}(F,\epsilon,\mu)0 and every probability measure \mu. 3. F is totally bounded in L^1(\mu) for every probability measure \mu. 4. F does not contain a Boolean \sigma-independent sequence. It follows that universal Glivenko-Cantelli classes are uniformity classes for general sequences of almost surely convergent random measures.Comment: 26 page

Dynamical robustness of biological networks with hierarchical distribution of time scales

We propose the concepts of distributed robustness and r-robustness, well adapted to functional genetics. Then we discuss the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks. First, we obtain the following result for linear networks: for large multiscale systems with hierarchical distribution of time scales the variance of the inverse relaxation time (as well as the variance of the stationary rate) is much lower than the variance of the separate constants. Moreover, it can tend to 0 faster than 1/n, where n is the number of reactions. We argue that similar phenomena are valid in the nonlinear case as well. As a numerical illustration we use a model of signalling network that can be applied to important transcription factors such as NFkB

Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution

We prove that for-linear, discrete, time-varying, deterministic system (perfect-model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance matrices to be less than or equal to the number of nonnegative Lyapunov exponents of the system. Further, the support of these error covariance matrices is shown to be confined to the space spanned by the unstable-neutral backward Lyapunov vectors, providing the theoretical justification for the methodology of the algorithms that perform assimilation only in the unstable-neutral subspace. The equivalent property of the autonomous system is investigated as a special case

Recalibrating wind‐speed forecasts using regime‐dependent ensemble model output statistics

This is the final version. Available on open access from Wiley via the DOI in this recordRaw output from deterministic numerical weather prediction models is typically subject to systematic biases. Although ensemble forecasts provide invaluable information regarding the uncertainty in a prediction, they themselves often misrepresent the weather that occurs. Given their widespread use, the need for high-quality wind speed forecasts is well-documented. Several statistical approaches have therefore been proposed to recalibrate ensembles of wind speed forecasts, including a heteroscedastic truncated regression approach. An extension to this method that utilises the prevailing atmospheric flow is implemented here in a quasigeostrophic simulation study and on GEFS reforecast data, in the hope of alleviating errors owing to changes in the synoptic-scale atmospheric state. When the wind speed strongly depends on the underlying weather regime, the resulting forecasts have the potential to provide substantial improvements in skill upon conventional post-processing techniques. This is particularly pertinent at longer lead times, where there is more improvement to be gained upon current methods, and in weather regimes associated with wind speeds that differ greatly from climatology. In order to realise this potential, an accurate prediction of the future atmospheric regime is required.Natural Environment Research Council (NERC