George Galanis

A one-dimensional Kalman filter for the correction of near surface temperature forecasts

It is a common fact that Numerical Weather Prediction (NWP) models exhibit systematic errors in the forecasts of near surface weather parameters. This is a result not only of shortcomings in the physical parameterisation but also of the inability of these models to handle successfully sub-grid phenomena. Furthermore, predictions covering areas that are not close to grid points are usually based on interpolations of the results of the models, a fact which also increases the ‘noise’ in the final outputs. The 2m-temperature, for example, is one of the most commonly biased variables, where the magnitude of this bias depends, among other factors, on the geographical location and the season.

Second order tangent bundles of infinite dimensional manifolds

Abstract The second order tangent bundle T2M of a smooth manifold M consists of the equivalent classes of curves on M that agree up to their acceleration. It is known [Analele Stiintifice ale Universitatii Al. I. Cuza 28 (1982) 63] that in the case of a finite n-dimensional manifold M, T2M becomes a vector bundle over M if and only if M is endowed with a linear connection. Here we extend this result to M modeled on an arbitrarily chosen Banach space and more generally to those Frechet manifolds which can be obtained as projective limits of Banach manifolds. The result may have application in the study of infinite dimensional dynamical systems.

Set Differential Equations in Fréchet Spaces

Abstract It is known that a Fréchet space 𝔽 can be realized as a projective limit of a sequence of Banach spaces . The space Kc (𝔽) of all compact, convex subsets of a Fréchet space, 𝔽, is realized as a projective limit of the semilinear metric spaces . Using the notion of Hukuhara derivative for maps with values in Kc (𝔽), we prove the local and global existence theorems for an initial value problem associated with a set differential equation.

Wave height characteristics in the north Atlantic ocean: a new approach based on statistical and geometrical techniques

The main characteristics of the significant wave height in an area of increased interest, the north Atlantic ocean, are studied based on satellite records and corresponding simulations obtained from the numerical wave prediction model WAM. The two data sets are analyzed by means of a variety of statistical measures mainly focusing on the distributions that they form. Moreover, new techniques for the estimation and minimization of the discrepancies between the observed and modeled values are proposed based on ideas and methodologies from a relatively new branch of mathematics, information geometry. The results obtained prove that the modeled values overestimate the corresponding observations through the whole study period. On the other hand, 2-parameter Weibull distributions fit well the data in the study. However, one cannot use the same probability density function for describing the whole study area since the corresponding scale and shape parameters deviate significantly for points belonging to different regions. This variation should be taken into account in optimization or assimilation procedures, which is possible by means of information geometry techniques.

Isomorphism classes for Banach vector bundle structures of second tangents

On a smooth Banach manifold M, the equivalence classes of curves that agree up to acceleration form the second order tangent bundle T^2M of M. This is a vector bundle in the presence of a linear connection on M and the corresponding local structure is heavily dependent on the choice of connection. In this paper we study the extent of this dependence and we prove that it is closely related to the notions of conjugate connections and second order differentials. In particular, the vector bundle structure on T^2M remains invariant under conjugate connections with respect to diffeomorphisms of M.

On a Type of Fréchet Principal Bundles over Banach Bases

In this paper we study a certain class of Fréchet principal bundles. Those which have structural groups obtained as projective limits of Banach Lie groups. In particular, we prove that each bundle of the previous type can be thought of as a projective limit of Banach principal bundles and any connection of them is a generalized limit of Banach connections. Using the previous, we achieve to translate in the Fréchet case basic geometric properties known so far only for Banach bundles.

Conjugate connections and differential equations on infinite dimensional manifolds

On a smooth manifold M, the vector bundle structures of the second order tangent bundle, T^2M bijectively correspond to linear connections. In this paper we classify such structures for those Frechet manifolds which can be considered as projective limits of Banach manifolds. We investigate also the relation between ordinary differential equations on Frechet spaces and the linear connections on their trivial bundle; the methodology extends to solve differential equations on those Frechet manifolds which are obtained as projective limits of Banach manifolds. Such equations arise in theoretical physics. We indicate an extension of the Earle and Eells foliation theorem to the Frechet case.

Universal connections in Fréchet principal bundles

A new methodology leading to the construction of a universal connection for Fréchet principal bundles is proposed in this paper. The classical theory, applied successfully so far for finite dimensional and Banach modelled bundles, collapses within the framework of Fréchet manifolds. However, based on the replacement of the space of continuous linear mappings by an appropriate topological vector space, we endow the bundle J1P of 1-jets of the sections of a Fréchet principal bundle P with a connection form by means of which we may “reproduce” every connection of P.

Towards a Study of Different Types of Extreme Wind Speed Conditions

Within a complex and competitive framework set by today’s research activities in environmental sciences, atmospheric datasets of high accuracy are required along with statistical analysis beyond the conventional standards. In particular, the credible evaluation of potential extreme conditions related to wind speed, is of critical importance for a number of applications such as wind farm siting, marine applications, pollutant dispersion associated to accidents etc. In the present work, a multi-parametric approach based on the principles of Extreme Value Theory is discussed. This approach is focused both on the upper and lower tail of wind speed probability distribution. More specifically Intensity-Duration-Frequency (IDF) curves are adopted to depict the relation between wind speed and the duration of the event in terms of return periods. The outcomes of the IDF curves are compared to other methodologies while various tools are employed for the fine tuning of the proposed techniques and the quantification of the associated uncertainties. For the needs of the study, a 10-year, hindcast simulation of the numerical atmospheric model Skiron coupled with the wave model WAM is utilized. The study area is the Mediterranean, focusing especially on areas with increased interest for renewable energy activities.

Marine Boundary Layer Offshore and Coastal Coupled Simulations

Air-sea interaction is a very complicated problem with many parameters that need to be studied. Wind profile near the sea surface is significantly affected by the wave characteristics (e.g. white cap formation, wave height), sea spraying and droplet evaporation. Moreover, sea spraying could be responsible for alterations in the stability conditions and the flow might become over-stable and semi-laminar. Working towards the analysis and study of the above issues, the development of a direct coupled system between the atmospheric system RAMS/ICLAMS and the wave model WAM is proposed with the additional online implementation of wave parameters into the atmospheric model. Test cases of different coupling approaches over the Atlantic and Mediterranean shoreline are performed towards the quantification of improvement of relevant high resolution wave and wind forecasts.