Nonlinear stability and ergodicity of ensemble based Kalman filters

The ensemble Kalman filter (EnKF) and ensemble square root filter (ESRF) are data assimilation methods used to combine high dimensional, nonlinear dynamical models with observed data. Despite their widespread usage in climate science and oil reservoir simulation, very little is known about the long-time behavior of these methods and why they are effective when applied with modest ensemble sizes in large dimensional turbulent dynamical systems. By following the basic principles of energy dissipation and controllability of filters, this paper establishes a simple, systematic and rigorous framework for the nonlinear analysis of EnKF and ESRF with arbitrary ensemble size, focusing on the dynamical properties of boundedness and geometric ergodicity. The time uniform boundedness guarantees that the filter estimate will not diverge to machine infinity in finite time, which is a potential threat for EnKF and ESQF known as the catastrophic filter divergence. Geometric ergodicity ensures in addition that the filter has a unique invariant measure and that initialization errors will dissipate exponentially in time. We establish these results by introducing a natural notion of observable energy dissipation. The time uniform bound is achieved through a simple Lyapunov function argument, this result applies to systems with complete observations and strong kinetic energy dissipation, but also to concrete examples with incomplete observations. With the Lyapunov function argument established, the geometric ergodicity is obtained by verifying the controllability of the filter processes; in particular, such analysis for ESQF relies on a careful multivariate perturbation analysis of the covariance eigen-structure.Comment: 38 page

Beyond recurrent costs: an institutional analysis of the unsustainability of donor-supported reforms in agricultural extension

International donors have spent billions of dollars over the past four decades in developing and/or reforming the agricultural extension service delivery arrangements in developing countries. However, many of these reforms, supported through short-term projects, became unsustainable once aid funding had ceased. The unavailability of recurrent funding has predominantly been highlighted in the literature as the key reason for this undesirable outcome, while little has been written about institutional factors. The purpose of this article is to examine the usefulness of taking an institutional perspective in explaining the unsustainability of donor-supported extension reforms and derive lessons for improvement. Using a framework drawn from the school of institutionalism in a Bangladeshi case study, we have found that a reform becomes unsustainable because of poor demands for extension information and advice; missing, weak, incongruent, and perverse institutional frameworks governing the exchange of extension goods (services); and a lack of institutional learning and change during the reform process. Accordingly, we have argued that strategies for sustainable extension reforms should move beyond financial considerations and include such measures as making extension goods (services) more tangible and monetary in nature, commissioning in-depth studies to learn about local institutions, crafting new institutions and/or reforming the weak and perverse institutions prevailing in developing countries. We emphasize the need to address three categories of institutions – regulative, normative, and cultural-cognitive – and call for an alignment among them. We further argue that, in order to be sustainable, a reform should take a systemic approach in institutional capacity building and, for this to be possible, adopt a long-term program approach, as opposed to a short-term project approach

Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time

The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations associated with the filter, which are required to make a useable algorithm in practice, are derived in an ad hoc fashion. The aim of this paper is to initiate the development of a systematic analysis of the EnKF, in particular to do so in the small ensemble size limit. The perspective is to view the method as a state estimator, and not as an algorithm which approximates the true filtering distribution. The perturbed observation version of the algorithm is studied, without and with variance inflation. Without variance inflation well-posedness of the filter is established; with variance inflation accuracy of the filter, with resepct to the true signal underlying the data, is established. The algorithm is considered in discrete time, and also for a continuous time limit arising when observations are frequent and subject to large noise. The underlying dynamical model, and assumptions about it, is sufficiently general to include the Lorenz '63 and '96 models, together with the incompressible Navier-Stokes equation on a two-dimensional torus. The analysis is limited to the case of complete observation of the signal with additive white noise. Numerical results are presented for the Navier-Stokes equation on a two-dimensional torus for both complete and partial observations of the signal with additive white noise

Physiotherapy students\u27 perceptions and experiences of clinical prediction rules

Objectives: Clinical reasoning can be difficult to teach to pre-professional physiotherapy students due to their lack of clinical experience. It may be that tools such as clinical prediction rules (CPRs) could aid the process, but there has been little investigation into their use in physiotherapy clinical education. This study aimed to determine the perceptions and experiences of physiotherapy students regarding CPRs, and whether they are learning about CPRs on clinical placement. Design: Cross-sectional survey using a paper-based questionnaire. Participants: Final year pre-professional physiotherapy students (n=371, response rate 77%) from five universities across five states of Australia. Results: Sixty percent of respondents had not heard of CPRs, and a further 19% had not clinically used CPRs. Only 21% reported using CPRs, and of these nearly three-quarters were rarely, if ever, learning about CPRs in the clinical setting. However most of those who used CPRs (78%) believed CPRs assisted in the development of clinical reasoning skills and none (0%) was opposed to the teaching of CPRs to students. The CPRs most commonly recognised and used by students were those for determining the need for an X-ray following injuries to the ankle and foot (67%), and for identifying deep venous thrombosis (63%). Conclusions: The large majority of students in this sample knew little, if anything, about CPRs and few had learned about, experienced or practiced them on clinical placement. However, students who were aware of CPRs found them helpful for their clinical reasoning and were in favour of learning more about them

Exhaust jet wake and thrust characteristics of several nozzles designed for VTOL DOWNWASH suppression. Tests in and out of ground effect with 70 deg F and 1200 deg F nozzle discharge temperatures

Jet wake degradation and thrust characteristics of exhaust nozzles designed for VTOL downwash suppression and fuselage and ground effect

Acoustic oscillations in solar and stellar flaring loops

Evolution of a coronal loop in response to an impulsive energy release is numerically modelled. It is shown that the loop density evolution curves exhibit quasi-periodic perturbations with the periods given approximately by the ratio of the loop length to the average sound speed, associated with the second standing harmonics of an acoustic wave. The density perturbations have a maximum near the loop apex. The corresponding field-aligned flows have a node near the apex. We suggest that the quasi-periodic pulsations with periods in the range 10-300 s, frequently observed in flaring coronal loops in the radio, visible light and X-ray bands, may be produced by the second standing harmonic of the acoustic mode