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Diagnostics of background error covariances in a connected global and regional data assimilation system
Bučánek, Antonín ; Brožková, Radmila (advisor) ; Sokol, Zbyněk (referee) ; Derková, Mária (referee)
The thesis deals with the preparation of initial conditions for nume- rical weather prediction in high resolution limited area models. It focuses on the problem of preserving the large-scale part of the global driving model analysis, which can not be determined in sufficient quality in limited-area models. For this purpose, the so-called BlendVar scheme is used. The scheme consists of the appli- cation of the Digital Filter (DF) Blending method, which assures the transmission of a large-scale part of the analysis of the driving model to the limited area model, and of the three-dimensional variational method (3D-Var) at high resolution. The thesis focuses on the appropriate background error specification, which is one of the key components of 3D-Var. Different approaches to modeling of background errors are examined, including the possibility of taking into account the flow- dependent character of background errors. Approaches are also evaluated from the point of view of practical implementation. Study of evolution of background errors during DF Blending and BlendVar assimilation cycles leads to a new pro- posal for the preparation of a background error covariance matrix suitable for the BlendVar assimilation scheme. The use of the new background error covariance matrix gives the required property...
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Non-conventional data assimilation in high resolution numerical weather prediction model with study of the slow manifold of the model
Benáček, Patrik ; Brožková, Radmila (advisor) ; Derková, Mária (referee) ; Randriamampianina, Roger (referee)
Satellite instruments currently provide the largest source of infor- mation to today's data assimilation (DA) systems for numerical weather predic- tion (NWP). With the development of high-resolution models, the efficient use of observations at high density is essential to improve small-scale information in the weather forecast. However, a large amount of satellite radiances has to be removed from DA by horizontal data thinning due to uncorrelated observation error assumptions. Moreover, satellite radiances include systematic errors (biases) that may be even larger than the observation signal itself, and must be properly removed prior to DA. Although the Variational Bias Correction (VarBC) scheme is widely used by global NWP centers, there are still open questions regarding its use in Limited-Area Models (LAMs). This thesis aims to tackle the obser- vation error difficulties in assimilating polar satellite radiances in the meso-scale ALADIN system. Firstly, we evaluate spatial- and inter-channel error correla- tions to enhance the positive effect of data thinning. Secondly, we study satellite radiance bias characteristics with the key aspects of the VarBC in LAMs, and we compare the different VarBC configurations with regards to forecast performance. This work is a step towards improving the...
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Model of error covariances for the assimilation of radar reflectivity into a NWP model
Sedláková, Klára ; Sokol, Zbyněk (advisor) ; Zacharov, Petr (referee)
MODEL OF ERROR COVARIANCES FOR THE ASSIMILATION OF RADAR REFLECTIVITY INTO NWP MODEL Predicting events with a severe convection is not easy due to the small spatial scale and rapid development of this phenomenon. But being able to predict such events is important in view of the dangerous phenomena that accompany these events, such as flash floods, strong winds, hailstorms or atmospheric electricity. Improved forecast can be achieved by more precisely defined initial conditions that enter the model. These data must match the scale of the studied phenomenon. Therefore, radar data is used in this case. Although the NWP model should describe real processes due to the simplifications and approximations the model's behavior does not entirely correspond the reality. Therefore, if we want the model to generate precipitation, we must ensure that the values of the model variables and their relationship are such that the process is started. To find out these relationships, we want to use a covariant model. In this paper, we focused on the correlation analysis of the model variables in the regions of convection between radar reflection, its conversion to the intensity of precipitation and other model variables. The COSMO data with a horizontal resolution of 2.8 km were used, which were describing approximately...
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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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Diagnostics of background error covariances in a connected global and regional data assimilation system
Bučánek, Antonín ; Brožková, Radmila (advisor)
The thesis deals with the preparation of initial conditions for nume- rical weather prediction in high resolution limited area models. It focuses on the problem of preserving the large-scale part of the global driving model analysis, which can not be determined in sufficient quality in limited-area models. For this purpose, the so-called BlendVar scheme is used. The scheme consists of the appli- cation of the Digital Filter (DF) Blending method, which assures the transmission of a large-scale part of the analysis of the driving model to the limited area model, and of the three-dimensional variational method (3D-Var) at high resolution. The thesis focuses on the appropriate background error specification, which is one of the key components of 3D-Var. Different approaches to modeling of background errors are examined, including the possibility of taking into account the flow- dependent character of background errors. Approaches are also evaluated from the point of view of practical implementation. Study of evolution of background errors during DF Blending and BlendVar assimilation cycles leads to a new pro- posal for the preparation of a background error covariance matrix suitable for the BlendVar assimilation scheme. The use of the new background error covariance matrix gives the required property...
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Non-conventional data assimilation in high resolution numerical weather prediction model with study of the slow manifold of the model
Benáček, Patrik ; Brožková, Radmila (advisor) ; Derková, Mária (referee) ; Randriamampianina, Roger (referee)
Satellite instruments currently provide the largest source of infor- mation to today's data assimilation (DA) systems for numerical weather predic- tion (NWP). With the development of high-resolution models, the efficient use of observations at high density is essential to improve small-scale information in the weather forecast. However, a large amount of satellite radiances has to be removed from DA by horizontal data thinning due to uncorrelated observation error assumptions. Moreover, satellite radiances include systematic errors (biases) that may be even larger than the observation signal itself, and must be properly removed prior to DA. Although the Variational Bias Correction (VarBC) scheme is widely used by global NWP centers, there are still open questions regarding its use in Limited-Area Models (LAMs). This thesis aims to tackle the obser- vation error difficulties in assimilating polar satellite radiances in the meso-scale ALADIN system. Firstly, we evaluate spatial- and inter-channel error correla- tions to enhance the positive effect of data thinning. Secondly, we study satellite radiance bias characteristics with the key aspects of the VarBC in LAMs, and we compare the different VarBC configurations with regards to forecast performance. This work is a step towards improving the...
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Diagnostics of background error covariances in a connected global and regional data assimilation system
Bučánek, Antonín ; Brožková, Radmila (advisor)
The thesis deals with the preparation of initial conditions for nume- rical weather prediction in high resolution limited area models. It focuses on the problem of preserving the large-scale part of the global driving model analysis, which can not be determined in sufficient quality in limited-area models. For this purpose, the so-called BlendVar scheme is used. The scheme consists of the appli- cation of the Digital Filter (DF) Blending method, which assures the transmission of a large-scale part of the analysis of the driving model to the limited area model, and of the three-dimensional variational method (3D-Var) at high resolution. The thesis focuses on the appropriate background error specification, which is one of the key components of 3D-Var. Different approaches to modeling of background errors are examined, including the possibility of taking into account the flow- dependent character of background errors. Approaches are also evaluated from the point of view of practical implementation. Study of evolution of background errors during DF Blending and BlendVar assimilation cycles leads to a new pro- posal for the preparation of a background error covariance matrix suitable for the BlendVar assimilation scheme. The use of the new background error covariance matrix gives the required property...
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Diagnostics of background error covariances in a connected global and regional data assimilation system
Bučánek, Antonín ; Brožková, Radmila (advisor) ; Sokol, Zbyněk (referee) ; Derková, Mária (referee)
The thesis deals with the preparation of initial conditions for nume- rical weather prediction in high resolution limited area models. It focuses on the problem of preserving the large-scale part of the global driving model analysis, which can not be determined in sufficient quality in limited-area models. For this purpose, the so-called BlendVar scheme is used. The scheme consists of the appli- cation of the Digital Filter (DF) Blending method, which assures the transmission of a large-scale part of the analysis of the driving model to the limited area model, and of the three-dimensional variational method (3D-Var) at high resolution. The thesis focuses on the appropriate background error specification, which is one of the key components of 3D-Var. Different approaches to modeling of background errors are examined, including the possibility of taking into account the flow- dependent character of background errors. Approaches are also evaluated from the point of view of practical implementation. Study of evolution of background errors during DF Blending and BlendVar assimilation cycles leads to a new pro- posal for the preparation of a background error covariance matrix suitable for the BlendVar assimilation scheme. The use of the new background error covariance matrix gives the required property...
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Model of error covariances for the assimilation of radar reflectivity into a NWP model
Sedláková, Klára ; Sokol, Zbyněk (advisor) ; Zacharov, Petr (referee)
MODEL OF ERROR COVARIANCES FOR THE ASSIMILATION OF RADAR REFLECTIVITY INTO NWP MODEL Predicting events with a severe convection is not easy due to the small spatial scale and rapid development of this phenomenon. But being able to predict such events is important in view of the dangerous phenomena that accompany these events, such as flash floods, strong winds, hailstorms or atmospheric electricity. Improved forecast can be achieved by more precisely defined initial conditions that enter the model. These data must match the scale of the studied phenomenon. Therefore, radar data is used in this case. Although the NWP model should describe real processes due to the simplifications and approximations the model's behavior does not entirely correspond the reality. Therefore, if we want the model to generate precipitation, we must ensure that the values of the model variables and their relationship are such that the process is started. To find out these relationships, we want to use a covariant model. In this paper, we focused on the correlation analysis of the model variables in the regions of convection between radar reflection, its conversion to the intensity of precipitation and other model variables. The COSMO data with a horizontal resolution of 2.8 km were used, which were describing approximately...
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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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