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Ensemble Kalman filter on high and infinite dimensional spaces
Kasanický, Ivan ; Hlubinka, Daniel (advisor) ; Pannekoucke, Olivier (referee) ; Antoch, Jaromír (referee)
Title: Ensemble Kalman filter on high and infinite dimensional spaces Author: Mgr. Ivan Kasanický Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Daniel Hlubinka, Ph.D., Department of Probability and Mathematical Statistics Consultant: prof. RNDr. Jan Mandel, CSc., Department of Mathematical and Statistical Sciences, University of Colorado Denver Abstract: The ensemble Kalman filter (EnKF) is a recursive filter, which is used in a data assimilation to produce sequential estimates of states of a hidden dynamical system. The evolution of the system is usually governed by a set of di↵erential equations, so one concrete state of the system is, in fact, an element of an infinite dimensional space. In the presented thesis we show that the EnKF is well defined on a infinite dimensional separable Hilbert space if a data noise is a weak random variable with a covariance bounded from below. We also show that this condition is su cient for the 3DVAR and the Bayesian filtering to be well posed. Additionally, we extend the already known fact that the EnKF converges to the Kalman filter in a finite dimension, and prove that a similar statement holds even in a infinite dimension. The EnKF su↵ers from a low rank approximation of a state covariance, so a covariance localization is required in...
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Time-domain modelling of global barotropic ocean tides
Einšpigel, David ; Martinec, Zdeněk (advisor) ; Haagmans, Roger (referee) ; Matyska, Ctirad (referee)
Traditionally, ocean tides have been modelled in frequency domain with forcing of selected tidal constituents. It is a natural approach, however, non-linearities of ocean dynamics are implicitly neglected. An alternative approach is time-domain modelling with forcing given by the full lunisolar potential, i.e., all tidal constituents are included. This approach has been applied in several ocean tide models, however, a few challenging tasks still remain to solve, for example, the assimilation of satellite altimetry data. In this thesis, we present DEBOT, a global and time-domain barotropic ocean tide model with the full lunisolar forcing. DEBOT has been developed "from scratch". The model is based on the shallow water equations which are newly derived in geographical (spherical) coordinates. The derivation includes the boundary conditions and the Reynolds tensor in a physically consistent form. The numerical model employs finite differences in space and a generalized forward-backward scheme in time. The validity of the code is demonstrated by the tests based on integral invariants. DEBOT has two modes for ocean tide modelling: DEBOT-h, a purely hydrodynamical mode, and DEBOT-a, an assimilative mode. We introduce the assimilative scheme applicable in a time-domain model, which is an alternative to existing...
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Software environment for data assimilation in radiation protection
Majer, Peter ; Šmídl, Václav (advisor) ; Hofman, Radek (referee)
In this work we apply data assimilation onto meteorological model WRF for local domain. We use bayesian statistics, namely Sequential Monte Carlo method combined with particle filtering. Only surface wind data are considered. An application written in Python programming language is also part of this work. This application forms interface with WRF, performs data assimilation and provides set of charts as output of data assimilation. In case of stable wind conditions, wind predictions of assimilated WRF are significantly closer to measured data than predictions of non-assimilated WRF. In this kind of conditions, this assimilated model can be used for more accurate short-term local weather predictions. Powered by TCPDF (www.tcpdf.org)
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Utilization of analysis of the spatial relationships between meteorological variables in data assimilation into a numerical weather prediction model
Sedláková, Klára ; Sokol, Zbyněk (advisor) ; Řezáčová, Daniela (referee)
UTILIZATION OF ANALYSIS OF THE SPATIAL RELATIONSHIPS BETWEEN METEOROLO- GICAL VARIABLES IN DATA ASSIMILATION INTO A NUMERICAL WEATHER PREDICTION MODEL Quality of initial conditions has a big impact on the accuracy of numerical forecast. The aim of the preparation of the initial conditions is to modify the first guess of the atmospheric state based on the observed data of the meteorological variables so it fit the actual atmospheric state. At present these conditions are usually prepared by objective analysis or by assimilating measured data into model fields. One of the method of the data assimilation is a 3D variational method (3D VAR). It prepares the initial model conditions so that the model fields correspond to actual measured values, while maintaining the spatial relationships between the values of model variables. By utulising the spatial relationships we can improve the initial conditions and so the forecast. In this work we concentrate on study of the spatial relationship in the convective storms based on correlation analysis of the model variables. We used the model data from COSMO model with horizontal resolution 2.8 km, which were describing 152 convective storms in all the vertical levels. The analysis proved storng relationship between vertical speed, vertical speed and air...
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Online System for Fire Danger Rating in Colorado
Vejmelka, Martin ; Kochanski, A. ; Mandel, J.
A method for the data assimilation of fuel moisture surface observations has been developed for the purpose of incorporation in wildfire forecasting and fire danger rating. In this work, we describe the method itself and also an online computer system that implements the method and combines it with the Real-Time Mesoscale Analysis to track local weather conditions and estimate the fuel moisture content in the state of Colorado. We discuss the construction of the system and future development.
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Bayesian Methods for Optimization of Radiation Monitoring Networks
Šmídl, Václav ; Hofman, Radek
Release of radioactive material into the atmosphere is the last possible resort of any accident in a nuclear power plant. It is an extremely rare event, however with severe consequences for potentially many people living in proximity of the power plant. Awareness of radiation security has been increased after the Chernobyl accident, and almost every country is now equipped with monitoring network of on-line connected receptors continually measuring radiation levels. Initial configurations of the network were designed by experts using their experience.In this report, we are concerned with local scale modeling of less severe accident in the range of tens of kilometers from the nuclear power plant. Both the stationary and mobile groups will be discussed. The preferred model of uncertainty is the empirical density which will be assimilated with measurements using the sequential Monte Carlo methodology. We will discuss influence of various loss functions.
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Data assimilation methods for early and late phase of radiation accident - A comprehensive review with examples of methods examined within solution of the grant projet VG20102013018
Hofman, Radek ; Pecha, Petr ; Šmídl, Václav
The task of the decision support in the case of a radiation accident is to provide up-to-date information on the radiation situation, prognosis of its future evolution and possible conse- quences. The reliability of predictions can be significantly improved using data assimilation, which refers to a group of mathematical methods allowing an efficient combination of ob- served data with a numerical model. The concerns application of the advanced data assimilation methods in the field of radiation protection. We focus on assessment of off-site consequences in the case of a radiation accident when radionuclides are released into the environment. In this report we present a comprehensive review of data assimilation evaluated for pur- poses of inclusion into the data assimilation and decision support system ASIM developed within the grant project VG20102013018 provided by the Ministry of the Interior of the Czech Republic.
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