Refine
Year of publication
Document Type
- Article (53)
- Postprint (14)
- Monograph/Edited Volume (1)
- Review (1)
Keywords
- data assimilation (7)
- ensemble Kalman filter (7)
- Bayesian inference (4)
- Data assimilation (3)
- GNSS Reflectometry (3)
- gradient flow (3)
- localization (3)
- wind speed (3)
- DDM simulation (2)
- Ensemble Kalman filter (2)
- Fokker-Planck equation (2)
- continuous-time data assimilation (2)
- correlated noise (2)
- eye movements (2)
- multi-scale diffusion processes (2)
- multiplicative noise (2)
- nonlinear filtering (2)
- optimal transport (2)
- parameter estimation (2)
- rain attenuation (2)
- rain effect (2)
- sequential data assimilation (2)
- Advanced scatterometer (ASCAT) (1)
- Atmosphere (1)
- Bayesian inverse problems (1)
- COVID-19 (1)
- CRPS (1)
- Data-driven modelling (1)
- Dynamical systems (1)
- Ensemble Kalman (1)
- Ensemble Kalman Filter (1)
- Error analysis (1)
- European Centre for Medium-Range Weather Forecasts (ECMWF) (1)
- Force splitting (1)
- Fuzzy logic (1)
- GNSS forward scatterometry (1)
- GNSS reflectometry (1)
- Gaussian kernel estimators (1)
- Gaussian mixtures (1)
- Generalized hybrid Monte Carlo (1)
- Hamiltonian dynamics (1)
- Kalman Bucy filter (1)
- Kalman filter (1)
- Kalman-Bucy Filter (1)
- Lagrangian modeling (1)
- Lagrangian modelling (1)
- Lagrangian-averaged equations (1)
- Langevin dynamics (1)
- MCMC (1)
- MCMC modelling (1)
- McKean-Vlasov (1)
- Modified Hamiltonians (1)
- Molecular dynamics (1)
- Mollification (1)
- Monte Carlo method (1)
- Multigrid (1)
- Multiple time stepping (1)
- NWP (1)
- Nonlinear filters (1)
- Numerical weather prediction (1)
- Optimal transportation (1)
- Paleoclimate reconstruction (1)
- Poincare inequality (1)
- Proxy forward modeling (1)
- RMSE (1)
- Random feature maps (1)
- Sequential data assimilation (1)
- Sinkhorn approximation (1)
- Spectral analysis (1)
- Stochastic epidemic model (1)
- Stormer-Verlet method (1)
- Strike-slip fault model (1)
- TDS-1 (1)
- TechDemoSat-1 (TDS-1) (1)
- Turbulence (1)
- accuracy (1)
- adaptive (1)
- affine (1)
- affine invariance (1)
- asymptotic behavior (1)
- balanced dynamics (1)
- canonical discretization schemes (1)
- chemistry (1)
- climate reconstructions (1)
- co-limitation (1)
- conservative discretization (1)
- constrained Hamiltonian systems (1)
- convergence assessment (1)
- differential-algebraic equations (1)
- distribution (1)
- dynamical model (1)
- dynamical models (1)
- electromagnetic scattering (1)
- ensemble (1)
- ensembles (1)
- feedback particle filter (1)
- filter (1)
- fluid mechanics (1)
- forecasting (1)
- framework (1)
- fuzzy logic (1)
- geophysics (1)
- gradient-free (1)
- gradient-free sampling methods (1)
- high resolution paleoclimatology (1)
- highly (1)
- holonomic constraints (1)
- hybrids (1)
- hydrostatic atmosphere (1)
- idealised turbulence (1)
- interacting particle systems (1)
- interacting particles (1)
- interindividual differences (1)
- invariance (1)
- likelihood (1)
- likelihood function (1)
- limiting factors (1)
- linear programming (1)
- linearly implicit time stepping methods (1)
- mean-field equations (1)
- mesoscale forecasting (1)
- model comparison (1)
- model fitting (1)
- models (1)
- multilevel Monte Carlo (1)
- non-dissipative regularisations (1)
- nonlinear data assimilation (1)
- numerical analysis/modeling (1)
- numerical weather prediction (1)
- numerical weather prediction/forecasting (1)
- ocean surface (1)
- oscillatory systems (1)
- paleoclimate reconstruction (1)
- particle filter (1)
- particle filters (1)
- proposal densities (1)
- proxy forward modeling (1)
- rain detection (1)
- rain splash (1)
- reading (1)
- reanalysis (1)
- regularization (1)
- resampling (1)
- saccades (1)
- semi-Lagrangian method (1)
- shallow-water equations (1)
- short-range prediction (1)
- smoother (1)
- sparse proxy data (1)
- spread correction (1)
- stability (1)
- stiff ODE (1)
- stochastic differential equations (1)
- stochastic systems (1)
- symplectic methods (1)
- temporal discretization (1)
- transdimensional inversion (1)
- transformations (1)
- variability (1)
- verification (1)
- weight-based formulations (1)
- well-posedness (1)
Institute
We evaluate the Hamiltonian particle methods (HPM) and the Nambu discretization applied to shallow-water equations on the sphere using the test suggested by Galewsky et al. (2004). Both simulations show excellent conservation of energy and are stable in long-term simulation. We repeat the test also using the ICOSWP scheme to compare with the two conservative spatial discretization schemes. The HPM simulation captures the main features of the reference solution, but wave 5 pattern is dominant in the simulations applied on the ICON grid with relatively low spatial resolutions. Nevertheless, agreement in statistics between the three schemes indicates their qualitatively similar behaviors in the long-term integration.
Many methods have been proposed for the stabilization of higher index differential-algebraic equations (DAEs). Such methods often involve constraint differentiation and problem stabilization, thus obtaining a stabilized index reduction. A popular method is Baumgarte stabilization, but the choice of parameters to make it robust is unclear in practice. Here we explain why the Baumgarte method may run into trouble. We then show how to improve it. We further develop a unifying theory for stabilization methods which includes many of the various techniques proposed in the literature. Our approach is to (i) consider stabilization of ODEs with invariants, (ii) discretize the stabilizing term in a simple way, generally different from the ODE discretization, and (iii) use orthogonal projections whenever possible. The best methods thus obtained are related to methods of coordinate projection. We discuss them and make concrete algorithmic suggestions.
We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been successfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method.
A Hamiltonian system in potential form (formula in the original abstract) subject to smooth constraints on q can be viewed as a Hamiltonian system on a manifold, but numerical computations must be performed in Rn. In this paper methods which reduce "Hamiltonian differential algebraic equations" to ODEs in Euclidean space are examined. The authors study the construction of canonical parameterizations or local charts as well as methods based on the construction of ODE systems in the space in which the constraint manifold is embedded which preserve the constraint manifold as an invariant manifold. In each case, a Hamiltonian system of ordinary differential equations is produced. The stability of the constraint invariants and the behavior of the original Hamiltonian along solutions are investigated both numerically and analytically.
Many methods have been proposed for the simulation of constrained mechanical systems. The most obvious of these have mild instabilities and drift problems. Consequently, stabilization techniques have been proposed A popular stabilization method is Baumgarte's technique, but the choice of parameters to make it robust has been unclear in practice. Some of the simulation methods that have been proposed and used in computations are reviewed here, from a stability point of view. This involves concepts of differential-algebraic equation (DAE) and ordinary differential equation (ODE) invariants. An explanation of the difficulties that may be encountered using Baumgarte's method is given, and a discussion of why a further quest for better parameter values for this method will always remain frustrating is presented. It is then shown how Baumgarte's method can be improved. An efficient stabilization technique is proposed, which may employ explicit ODE solvers in case of nonstiff or highly oscillatory problems and which relates to coordinate projection methods. Examples of a two-link planar robotic arm and a squeezing mechanism illustrate the effectiveness of this new stabilization method.
In diesem Beitrag wird der Zusammenhang zwischen Algebrodifferentialgleichungen (ADGL) und Vektorfeldern auf Mannigfaltigkeiten untersucht. Dazu wird zunächst der Begriff der regulären ADGL eingeführt, wobei unter eirter regulären ADGL eine ADGL verstanden wird, deren Lösungsmenge identisch mit der Lösungsmenge eines Vektorfeldes ist. Ausgehend von bekannten Aussagen über die Lösungsmenge eines Vektorfeldes werden analoge Aussagen für die Lösungsmenge einer regulären ADGL abgeleitet. Es wird eine Reduktionsmethode angegeben, die auf ein Kriterium für die Begularität einer ADGL und auf die Definition des Index einer nichtlinearen ADGL führt. Außerdem wird gezeigt, daß beliebige Vektorfelder durch reguläre ADGL so realisiert werden können, daß die Lösungsmenge des Vektorfeldes mit der der realisierenden ADGL identisch ist. Abschließend werden die für autonome ADGL gewonnenen Aussagen auf den Fall der nichtautonomen ADGL übertragen.
Technical and physical systems, especially electronic circuits, are frequently modeled as a system of differential and nonlinear implicit equations. In the literature such systems of equations are called differentialalgebraic equations (DAEs). It turns out that the numerical and analytical properties of a DAE depend on an integer called the index of the problem. For example, the well-known BDF method of Gear can be applied, in general, to a DAE only if the index does not exceed one. In this paper we give a geometric interpretation of higherindex DAEs and indicate problems arising in connection with such DAEs by means of several examples.
The novel space-borne Global Navigation Satellite System Reflectometry (GNSS-R) technique has recently shown promise in monitoring the ocean state and surface wind speed with high spatial coverage and unprecedented sampling rate. The L-band signals of GNSS are structurally able to provide a higher quality of observations from areas covered by dense clouds and under intense precipitation, compared to those signals at higher frequencies from conventional ocean scatterometers. As a result, studying the inner core of cyclones and improvement of severe weather forecasting and cyclone tracking have turned into the main objectives of GNSS-R satellite missions such as Cyclone Global Navigation Satellite System (CYGNSS). Nevertheless, the rain attenuation impact on GNSS-R wind speed products is not yet well documented. Evaluating the rain attenuation effects on this technique is significant since a small change in the GNSS-R can potentially cause a considerable bias in the resultant wind products at intense wind speeds. Based on both empirical evidence and theory, wind speed is inversely proportional to derived bistatic radar cross section with a natural logarithmic relation, which introduces high condition numbers (similar to ill-posed conditions) at the inversions to high wind speeds. This paper presents an evaluation of the rain signal attenuation impact on the bistatic radar cross section and the derived wind speed. This study is conducted simulating GNSS-R delay-Doppler maps at different rain rates and reflection geometries, considering that an empirical data analysis at extreme wind intensities and rain rates is impossible due to the insufficient number of observations from these severe conditions. Finally, the study demonstrates that at a wind speed of 30 m/s and incidence angle of 30 degrees, rain at rates of 10, 15, and 20 mm/h might cause overestimation as large as approximate to 0.65 m/s (2%), 1.00 m/s (3%), and 1.3 m/s (4%), respectively, which are still smaller than the CYGNSS required uncertainty threshold. The simulations are conducted in a pessimistic condition (severe continuous rainfall below the freezing height and over the entire glistening zone) and the bias is expected to be smaller in size in real environments.
The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean–Vlasov equations as the starting point to derive ensemble Kalman–Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems.
Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, including the geosciences, but their application to high-dimensional geoscience systems has been limited due to their inefficiency in high-dimensional systems in standard settings. However, huge progress has been made, and this limitation is disappearing fast due to recent developments in proposal densities, the use of ideas from (optimal) transportation, the use of localization and intelligent adaptive resampling strategies. Furthermore, powerful hybrids between particle filters and ensemble Kalman filters and variational methods have been developed. We present a state-of-the-art discussion of present efforts of developing particle filters for high-dimensional nonlinear geoscience state-estimation problems, with an emphasis on atmospheric and oceanic applications, including many new ideas, derivations and unifications, highlighting hidden connections, including pseudo-code, and generating a valuable tool and guide for the community. Initial experiments show that particle filters can be competitive with present-day methods for numerical weather prediction, suggesting that they will become mainstream soon.