Refine
Year of publication
Document Type
- Article (55)
- Postprint (13)
- Monograph/Edited Volume (1)
- Review (1)
Language
- English (70) (remove)
Keywords
- data assimilation (7)
- ensemble Kalman filter (7)
- Bayesian inference (5)
- 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 augmentation (1)
- Data-driven modelling (1)
- Dynamical systems (1)
- Earthquake modeling (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)
- Gaussian process (1)
- Generalized hybrid Monte Carlo (1)
- Hamiltonian dynamics (1)
- Hawkes process (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)
- Sampling (1)
- Self-exciting point process (1)
- Sequential data assimilation (1)
- Sinkhorn approximation (1)
- Sinkhorn problem (1)
- Spatio-temporal ETAS model (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)
- diffusion maps (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)
- graph Laplacian (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)
- kernel methods (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
It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high-frequency adjustment processes in the model dynamics. Various methods have been devised to spread out the analysis increments continuously over a fixed time interval centred about the analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow-fast extension of the popular Lorenz-96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter.
The problem of an ensemble Kalman filter when only partial observations are available is considered. In particular, the situation is investigated where the observational space consists of variables that 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 a variance-limiting Kalman filter (VLKF) is derived in a variational setting. The VLKF for a simple linear toy model is analyzed and its range of optimal performance is determined. The VLKF is explored in an ensemble transform setting for the Lorenz-96 system, and it is shown that incorporating the information of the variance of some unobservable variables can improve the skill and also increase the stability of the data assimilation procedure.
We develop a multigrid, multiple time stepping scheme to reduce computational efforts for calculating complex stress interactions in a strike-slip 2D planar fault for the simulation of seismicity. The key elements of the multilevel solver are separation of length scale, grid-coarsening, and hierarchy. In this study the complex stress interactions are split into two parts: the first with a small contribution is computed on a coarse level, and the rest for strong interactions is on a fine level. This partition leads to a significant reduction of the number of computations. The reduction of complexity is even enhanced by combining the multigrid with multiple time stepping. Computational efficiency is enhanced by a factor of 10 while retaining a reasonable accuracy, compared to the original full matrix-vortex multiplication. The accuracy of solution and computational efficiency depend on a given cut-off radius that splits multiplications into the two parts. The multigrid scheme is constructed in such a way that it conserves stress in the entire half-space.
We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.
Atomic oscillations present in classical molecular dynamics restrict the step size that can be used. Multiple time stepping schemes offer only modest improvements, and implicit integrators are costly and inaccurate. The best approach may be to actually remove the highest frequency oscillations by constraining bond lengths and bond angles, thus permitting perhaps a 4-fold increase in the step size. However, omitting degrees of freedom produces errors in statistical averages, and rigid angles do not bend for strong excluded volume forces. These difficulties can be addressed by an enhanced treatment of holonomic constrained dynamics using ideas from papers of Fixman (1974) and Reich (1995, 1999). In particular, the 1995 paper proposes the use of "flexible" constraints, and the 1999 paper uses a modified potential energy function with rigid constraints to emulate flexible constraints. Presented here is a more direct and rigorous derivation of the latter approach, together with justification for the use of constraints in molecular modeling. With rigor comes limitations, so practical compromises are proposed: simplifications of the equations and their judicious application when assumptions are violated. Included are suggestions for new approaches.
The adsorption of molecules to the surface of carbon nanostructures opens a new field of hybrid systems with distinct and controllable properties. We present a microscopic study of the optical absorption in carbon nanotubes functionalized with molecular spiropyran photoswitches. The switching process induces a change in the dipole moment leading to a significant coupling to the charge carriers in the nanotube. As a result, the absorption spectra of functionalized tubes reveal a considerable redshift of transition energies depending on the switching state of the spiropyran molecule. Our results suggest that carbon nanotubes are excellent substrates for the optical readout of spiropyran-based molecular switches. The gained insights can be applied to other noncovalently functionalized one-dimensional nanostructures in an externally induced dipole field.
We develop a hydrostatic Hamiltonian particle-mesh (HPM) method for efficient long-term numerical integration of the atmosphere. In the HPM method, the hydrostatic approximation is interpreted as a holonomic constraint for the vertical position of particles. This can be viewed as defining a set of vertically buoyant horizontal meshes, with the altitude of each mesh point determined so as to satisfy the hydrostatic balance condition and with particles modelling horizontal advection between the moving meshes. We implement the method in a vertical-slice model and evaluate its performance for the simulation of idealized linear and nonlinear orographic flow in both dry and moist environments. The HPM method is able to capture the basic features of the gravity wave to a degree of accuracy comparable with that reported in the literature. The numerical solution in the moist experiment indicates that the influence of moisture on wave characteristics is represented reasonably well and the reduction of momentum flux is in good agreement with theoretical analysis.
The ensemble Kalman filter has emerged as a promising filter algorithm for nonlinear differential equations subject to intermittent observations. In this paper, we extend the well-known Kalman-Bucy filter for linear differential equations subject to continous observations to the ensemble setting and nonlinear differential equations. The proposed filter is called the ensemble Kalman-Bucy filter and its performance is demonstrated for a simple mechanical model (Langevin dynamics) subject to incremental observations of its velocity.
We generalize the popular ensemble Kalman filter to an ensemble transform filter, in which the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation of the Bayesian filter analysis step. We call the new filter algorithm the ensemble Gaussian-mixture filter (EGMF). The EGMF is implemented for three simple test problems (Brownian dynamics in one dimension, Langevin dynamics in two dimensions and the three-dimensional Lorenz-63 model). It is demonstrated that the EGMF is capable of tracking systems with non-Gaussian uni- and multimodal ensemble distributions.
Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables.