A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, Pf. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.

The inflation hedging characteristics of US and UK investments: a multi-factor error correction approach

Historic analysis of the inflation hedging properties of stocks produced anomalous results, with equities often appearing to offer a perverse hedge against inflation. This has been attributed to the impact of real and monetary shocks to the economy, which influence both inflation and asset returns. It has been argued that real estate should provide a better hedge: however, empirical results have been mixed. This paper explores the relationship between commercial real estate returns (from both private and public markets) and economic, fiscal and monetary factors and inflation for US and UK markets. Comparative analysis of general equity and small capitalisation stock returns in both markets is carried out. Inflation is subdivided into expected and unexpected components using different estimation techniques. The analyses are undertaken using long-run error correction techniques. In the long-run, once real and monetary variables are included, asset returns are positively linked to anticipated inflation but not to inflation shocks. Adjustment processes are, however, gradual and not within period. Real estate returns, particularly direct market returns, exhibit characteristics that differ from equities.

I and I: immunity to error through misidentification of the subject

Abstract I argue for the following claims: [1] all uses of I (the word ‘I’ or thought-element I) are absolutely immune to error through misidentification relative to I. [2] no genuine use of I can fail to refer. Nevertheless [3] I isn’t univocal: it doesn’t always refer to the same thing, or kind of thing, even in the thought or speech of a single person. This is so even though [4] I always refers to its user, the subject of experience who speaks or thinks, and although [5] if I’m thinking about something specifically as myself, I can’t fail to be thinking of myself, and although [6] a genuine understanding use of I always involves the subject thinking of itself as itself, whatever else it does or doesn’t involve, and although [7] if I take myself to be thinking about myself, then I am thinking about myself.

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.