16 problems

In a model of atmospheric dynamics, suppose that the atmospheric temperature field is observed continuously in time. Charney et al.'s observability conjecture. Knowledge of the con…

The convergence conjecture. As $\delta\to0$, the sequence ${\bf x}_n$ will converge to the approximating solutions obtained by the continuous-in-time nudging method given as Algori…

In a filtering experiment, KME-Dynamics is compared with the Ensemble Kalman Filter and a Kalman-adjusted KME-Dynamics method. The KME-Dynamics inference step involves a linear inv…

Exponential-instability conjecture. Similar exponential instability phenomena should persist: the initial state may be substantially separated from a reference solution while the c…

Charney's conjecture. Temperature measurements alone should be sufficient to reconstruct the whole state of the atmosphere.

The singular evolutive interpolated Kalman filter is a data assimilation method intended to reduce computational cost relative to the ensemble Kalman filter. Computational-efficien…

Let $mu$ denote the observer relaxation or nudging parameter in a dynamic data-assimilation observer for the two-dimensional Navier–Stokes equations. Consider observer regimes in w…

Let $q^e=\tilde q-q$ and $\eta^e=\tilde\eta-\eta$ denote the errors in the velocity potential and surface deviation, respectively, and let $\lambda$ be the observer-design paramete…

Let $N$ be the number of grid points, let $m_h$ be the number of nodes in the probe, let $lambda$ be the minimum length scale, and let $Delta x$ be the spatial grid spacing. An int…

In fluid measurements, let the averaging window be the time interval over which observations are averaged, and let the turnover time be the characteristic circulation time of an ed…

Let $h$ be the observation function and let $f$ and $g$ be the drift and control coefficient functions in the data assimilation problem. Assume that $h$ is linear in $x$ and that…

Let $X_T$ be the set of states reachable by solutions of … from admissible initial data and forcings in $\mathcal{E}$ during some time $0\leq t^*\leq T$. Assume that $V$ solves the…

Let $M=40$ denote the case in which the observation operator observes 40 directions, and let $M=60$ denote the case in which all directions are observed. The root mean square error…

Let $f_a$ denote the observation frequency, let the observation errors have specified variances, and consider the subsequent background ensembles and the observations used at the a…

Standard ensemble methods for Bayesian inverse problems are considered together with systematic approaches that account for the mathematical structure of the underlying inverse pro…

The thermosyphon dynamics are represented by an electromagnetic model (EM), and data assimilation (DA) couples the model to observations. A persistent spike in background error occ…