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Data assimilation is an iterative approach to the problem of estimating the state of a dynam-ical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to " forecast " the current state,(More)
In this paper, we introduce a new, local formulation of the ensemble Kalman Filter approach for atmospheric data assimilation. Our scheme is based on the hypothesis that, when the Earth's surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than(More)
We present a measure-theoretic condition for a property to hold " almost everywhere " on an infinite-dimensional vector space, with particular emphasis on function spaces such as C k and L p. Like the concept of " Lebesgue almost every " on finite-dimensional spaces, our notion of " prevalence " is translation invariant. Instead of using a specific measure(More)
A B S T R A C T The accuracy and computational efficiency of a parallel computer implementation of the Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme on the model component of the 2004 version of the Global Forecast System (GFS) of the National Centers for Environmental Prediction (NCEP) is investigated. Numerical experiments are(More)
A B S T R A C T We modify the local ensemble Kalman filter (LEKF) to incorporate the effect of forecast model bias. The method is based on augmentation of the atmospheric state by estimates of the model bias, and we consider different ways of modeling (i.e. parameterizing) the model bias. We evaluate the effectiveness of the proposed augmented state(More)
We consider the image of a fractal set X in a Banach space under typical linear and nonlinear projections π into R N. We prove that when N exceeds twice the box-counting dimension of X, then almost every (in the sense of prevalence) such π is one-to-one on X, and we give an explicit bound on the Hölder exponent of the inverse of the restriction of π to X.(More)
We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition and generalize recent results for the critical coupling strength. We find that, under appropriate conditions, the coupling strength(More)
We consider a piecewise smooth expanding map of the interval possessing two invariant subsets of positive Lebesgue measure and exactly two ergodic absolutely continuous invariant probability measures (ACIMs). When this system is perturbed slightly to make the invariant sets merge, we describe how the unique ACIM of the perturbed map can be approximated by a(More)