Estimation of systematic error in an equatorial ocean model using data assimilation

Assimilation of temperature observations into an ocean model near the equator often results in a dynamically unbalanced state with unrealistic overturning circulations. The way in which these circulations arise from systematic errors in the model or its forcing is discussed. A scheme is proposed, based on the theory of state augmentation, which uses the departures of the model state from the observations to update slowly evolving bias fields. Results are summarized from an experiment applying this bias correction scheme to an ocean general circulation model. They show that the method produces more balanced analyses and a better fit to the temperature observations.

Adjoint methods in data assimilation for estimating model error

Data assimilation aims to incorporate measured observations into a dynamical system model in order to produce accurate estimates of all the current (and future) state variables of the system. The optimal estimates minimize a variational principle and can be found using adjoint methods. The model equations are treated as strong constraints on the problem. In reality, the model does not represent the system behaviour exactly and errors arise due to lack of resolution and inaccuracies in physical parameters, boundary conditions and forcing terms. A technique for estimating systematic and time-correlated errors as part of the variational assimilation procedure is described here. The modified method determines a correction term that compensates for model error and leads to improved predictions of the system states. The technique is illustrated in two test cases. Applications to the 1-D nonlinear shallow water equations demonstrate the effectiveness of the new procedure.

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.

Bayesian estimation of the spatial Durbin error model with an application to voter turnout in the 2004 presidential election

The potential for spatial dependence in models of voter turnout, although plausible from a theoretical perspective, has not been adequately addressed in the literature. Using recent advances in Bayesian computation, we formulate and estimate the previously unutilized spatial Durbin error model and apply this model to the question of whether spillovers and unobserved spatial dependence in voter turnout matters from an empirical perspective. Formal Bayesian model comparison techniques are employed to compare the normal linear model, the spatially lagged X model (SLX), the spatial Durbin model, and the spatial Durbin error model. The results overwhelmingly support the spatial Durbin error model as the appropriate empirical model.

Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

Spatial coding of touch at the fingers: Insights from double simultaneous stimulation within and between hands

We studied the effect of tactile double simultaneous stimulation (DSS) within and between hands to examine spatial coding of touch at the fingers. Participants performed a go/no-go task to detect a tactile stimulus delivered to one target finger (e.g., right index), stimulated alone or with a concurrent non-target finger, either on the same hand (e.g., right middle finger) or on the other hand (e.g., left index finger=homologous; left middle finger=non-homologous). Across blocks we also changed the unseen hands posture (both hands palm down, or one hand rotated palm-up). When both hands were palm-down DSS interference effects emerged both within and between hands, but only when the non-homologous finger served as non-target. This suggests a clear segregation between the fingers of each hand, regardless of finger side. By contrast, when one hand was palm-up interference effects emerged only within hand, whereas between hands DSS interference was considerably reduced or absent. Thus, between hands interference was clearly affected by changes in hands posture. Taken together, these findings provide behavioral evidence in humans for multiple spatial coding of touch during tactile DSS at the fingers. In particular, they confirm the existence of representational stages of touch that distinguish between body-regions more than body-sides. Moreover, they show that the availability of tactile stimulation side becomes prominent when postural update is required.

Resolution of sharp fronts in the presence of model error in variational data assimilation

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong constraint 4DVar (L2-norm)method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.

Isolation of Actinomyces hyovaginalis from sheep and comparison with isolates obtained from pigs

Actinomyces hyovaginalis, an organism initially described from pigs, was recovered from nine sheep and a moufflon. Further strains of A. hyovaginalis were recovered from five samples from pigs over the same period. 16S rRNA sequencing and extensive phenotyping demonstrated high similarity between the ovine and porcine isolates; however differences with respect to erythritol, adonitol and l-arabitol fermentation were detected. Ovine isolates were made from various sample sites including abscesses and highlight the importance of the accurate identification of the various coryneform isolates which affect sheep. A. hyovaginalis can be added to the growing list of coryneforms which can cause disease in sheep including Corynebacterium pseudotuberculosis, Trueperella pyogenes and Arcanobacterium pluranimalium.