Controlling overestimation of error covariance in ensemble Kalman filters with sparse observations: A variance limiting Kalman filter

We consider the problem of an ensemble Kalman filter when only partial observations are available. In particular we consider the situation where the observational space consists of variables which are directly observable with known observational error, and of variables of which only their climatic variance and mean are given. To limit the variance of the latter poorly resolved variables we derive a variance limiting Kalman filter (VLKF) in a variational setting. We analyze the variance limiting Kalman filter for a simple linear toy model and determine its range of optimal performance. We explore the variance limiting Kalman filter in an ensemble transform setting for the Lorenz-96 system, and show that incorporating the information of the variance of some un-observable variables can improve the skill and also increase the stability of the data assimilation procedure.Comment: 32 pages, 11 figure

Circular 61

Rapeseed is the oil-bearing seed from plants of the Brassica genus. It grows well in the cooler agricultural regions o f the world and for this reason has long been thought to be a promising crop for interior Alaska. Rapeseed has been grow n in India and China for thousands and in Europe for hundreds o f years (Bolton 1980). Its history in North America began in 1943 when a small quantity of seed was imported into Canada. In recent years, its production has been largely that from cultivars bred for production of seed low in erucic acid and glucosinolate content. Seed from these cultivars is referred to by the Canadian Rapeseed Industry as canola. Its qualities are desirable in the edible-oil market, the largest market for products from canola seed. Canada is now one of the world’s largest producers and is the world’s largest exporter o f rapeseed. The meal that remains after oil extraction is high in protein and is used as a supplement in livestock feeds. The whole seed can also be used as a feed supplement. Some cultivars o f rapeseed that are high in erucic acid are also grow n for use in plastics and industrial oils (Genser and Eskin 1979). In addition, forage rapeseed cultivars can be used as livestock pasture. Research concerning the production of rapeseed has been addressed by the Agricultural and Forestry Experiment Station (AFES) for several years. O f specific concern has been the selection of appropriate cultivars (Wooding et al. 1978), response to various nitrogen (N) rates, row spacings and seeding rates (Lewis and Knight 1987), performance in reduced-tillage systems in rotation with barley (Knight and Lewis 1986), the potential for frost seeding in late fall and early spring (Knight and Sparrow 1984) and response to boron (B) to enhance early seed ripening (Wooding 1985). In addition, in 1978 the Cooperative Extension Service (CES) began conducting seminars on production o f rapeseed for Alaskan farmers. In 1979 and 1980, CES employed Dr. J.L . Bolton, a rapeseed specialist from the University o f Alberta, in an extension capacity to give technical assistance to farmers on producing rapeseed (Bolton 1980)

On finite-size Lyapunov exponents in multiscale systems

We study the effect of regime switches on finite size Lyapunov exponents (FSLEs) in determining the error growth rates and predictability of multiscale systems. We consider a dynamical system involving slow and fast regimes and switches between them. The surprising result is that due to the presence of regimes the error growth rate can be a non-monotonic function of initial error amplitude. In particular, troughs in the large scales of FSLE spectra is shown to be a signature of slow regimes, whereas fast regimes are shown to cause large peaks in the spectra where error growth rates far exceed those estimated from the maximal Lyapunov exponent. We present analytical results explaining these signatures and corroborate them with numerical simulations. We show further that these peaks disappear in stochastic parametrizations of the fast chaotic processes, and the associated FSLE spectra reveal that large scale predictability properties of the full deterministic model are well approximated whereas small scale features are not properly resolved.Comment: Accepted for publication in Chao

The aerodynamic response of airborne discs

A study has been conducted to characterize the flow over a free-flying disc. In this study, three types of discs are analyzed in a series of stationary experiments, and a single disc is analyzed in a spinning experiment. Two dimensionless parameters dominate the experiments, the Reynolds number and the tip speed ratio. The first experiment measured the lift and drag at varying angles of attack on a stationary disc. The second stationary experiment was a unique measurement of the center of lift of a disc as a function of velocity. The third stationary experiment was a tuft test to describe the boundary layer, done at different velocities and angles of attack. The spinning disc experiment utilized smoke to visualize the flow around the disc and ascertain the effects of spin on vorticity and boundary layer separation. Results showed that the center of lift was behind the geometric center at low velocity and moved rapidly forward with increasing velocity. Tuft and smoke tests showed that the boundary layer was attached across the entire surface with strong vortices shed from the sides and from the rear of the disc. The flow was primarily affected by the disc\u27s leading edge with secondary effects from the domed contour

Acceptable Vibrations on Green Concrete

This thesis contains the results of various green concrete samples subjected to different vibration intensities to determine how green concrete withstands against these vibration intensities. The green concrete was exposed to these vibrations at times before, during, and after the concrete had set. The concrete was also exposed to different timed durations while being subjected to the different vibration levels. Every batch of concrete mixed included a controlled (un-vibrated) set of cylinders and a vibrated set of cylinders. The compressive strength and the resistivity of these concrete cylinders were measured and compared to determine if there was any significant difference between the two sets. It was found that the vibrations subjected to the cylinders did not create a significant effect; given the vibrations levels and timed durations stay within the limits of this study

Towards AMR Simulations of Galaxy Formation

Numerical simulations present a fundamental building block of our modern theoretical understanding of the Universe. As such the work in this thesis is primarily concerned with understanding fundamental differences that lie between the different hydrodynamic schemes. In chapter 3 I outline the optimisations I make to the FLASH code to enable larger simulations to be run. These include developing and testing a new FFT gravity solver. With these complete, in chapter 4 I present results from a collaborative code comparison project in which we test a series of different hydrodynamics codes against a suite of demanding test problems with astrophysical relevance. As the problems have known solutions, we can quantify their performance and are able to develop a resolution criteria which allows for the two different types to be reliably compared. In chapter 5 we develop an analytic model for ram pressure stripping of the hot gaseous haloes of galaxies in groups and clusters. We test the model against a suite of hydrodynamic simulations in the SPH GADGET-2 code. To ensure that the spurious suppression of hydrodynamic instabilities by SPH codes does not bias our results, I compare our findings to those obtained with the FLASH AMR code and find excellent agreement. Chapter 6 presents work in which we unambiguously determine the origin of the difference between the entropy cores formed in AMR and SPH codes. By running mergers of model clusters we are able to systematically explore the various proposed mechanisms and determine that turbulent mixing generates the higher entropy cores within AMR codes but is suppressed in SPH codes. The startling differences between the two hydrodynamic schemes presented in chapter 6 leads me to investigate their affect upon different sub-grid physical recipes. In chapter 7 I present the implementation of a sub-grid star formation recipe in FLASH and find strong differences in the way the two codes model pressure laws. I extend the work in chapter 8 by implementing a kinetic supernova feedback mechanism in FLASH and contrasting it with the results from the GADGET-2 code. I find that AMR codes dissipate energy much more efficiently than in SPH codes