Variational data assimilation for the initial-value dynamo problem

The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries

The CEDAR Project

The LHC project at CERN requires both the handling of a huge amount of engineering information and the control of the coherence of this information as the design work evolves on the machine and the experiments. A commercial Engineering Data Management System, (EDMS), is being implemented to manage data for the design, construction, installation and maintenance of both the accelerator and the experiments. This CERN-wide project is called CEDAR The World Wide Web is used to make the information accessible at CERN and in the external collaborating laboratories around the world. In this paper we describe the objectives of the CEDAR project, the different subprojects in the machine and the experiments as well as the first results of the implementation work

Variation in beliefs about 'fracking' between the UK and US

In decision-making on the politically-contentious issue of unconventional gas development, the UK Government and European Commission are attempting to learn from the US experience. Although economic, environmental, and health impacts and regulatory contexts have been compared cross-nationally, public perceptions and their antecedents have not. We conducted similar online panel surveys of national samples of UK and US residents simultaneously in September 2014 to compare public perceptions and beliefs affecting such perceptions. The US sample was more likely to associate positive impacts with development (i.e., production of clean energy, cheap energy, and advancing national energy security). The UK sample was more likely to associate negative impacts (i.e., water contamination, higher carbon emissions, and earthquakes). Multivariate analyses reveal divergence cross-nationally in the relationship between beliefs about impacts and support/opposition – especially for beliefs about energy security. People who associated shale gas development with increased energy security in the UK were over three times more likely to support development than people in the US with this same belief. We conclude with implications for policy and communication, discussing communication approaches that could be successful cross-nationally and policy foci to which the UK might need to afford more attention in its continually evolving regulatory environment

The evolution of the ISOLDE control system

The ISOLDE on-line mass separator facility is operating on a Personal Computer based control system since spring 1992. Front End Computers accessing the hardware are controlled from consoles running Microsoft WindowsTM through a Novell NetWare4TM local area network. The control system is transparently integrated in the CERN wide office network and makes heavy use of the CERN standard office application programs to control and to document the running of the ISOLDE isotope separators. This paper recalls the architecture of the control system, shows its recent developments and gives some examples of its graphical user interface

Oracle-based optimization applied to climate model calibration

In this paper, we show how oracle-based optimization can be effectively used for the calibration of an intermediate complexity climate model. In a fully developed example, we estimate the 12 principal parameters of the C-GOLDSTEIN climate model by using an oracle- based optimization tool, Proximal-ACCPM. The oracle is a procedure that finds, for each query point, a value for the goodness-of-fit function and an evaluation of its gradient. The difficulty in the model calibration problem stems from the need to undertake costly calculations for each simulation and also from the fact that the error function used to assess the goodness-of-fit is not convex. The method converges to a Fbest fit_ estimate over 10 times faster than a comparable test using the ensemble Kalman filter. The approach is simple to implement and potentially useful in calibrating computationally demanding models based on temporal integration (simulation), for which functional derivative information is not readily available

A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother. © 2008 Springer Science + Business Media LLC

Pattern Recognition in a Bimodal Aquifer Using the Normal-Score Ensemble Kalman Filter

The ensemble Kalman filter (EnKF) is now widely used in diverse disciplines to estimate model parameters and update model states by integrating observed data. The EnKF is known to perform optimally only for multi-Gaussian distributed states and parameters. A new approach, the normal-score EnKF (NS-EnKF), has been recently proposed to handle complex aquifers with non-Gaussian distributed parameters. In this work, we aim at investigating the capacity of the NS-EnKF to identify patterns in the spatial distribution of the model parameters (hydraulic conductivities) by assimilating dynamic observations in the absence of direct measurements of the parameters themselves. In some situations, hydraulic conductivity measurements (hard data) may not be available, which requires the estimation of conductivities from indirect observations, such as piezometric heads. We show how the NS-EnKF is capable of retrieving the bimodal nature of a synthetic aquifer solely from piezometric head data. By comparison with a more standard implementation of the EnKF, the NS-EnKF gives better results with regard to histogram preservation, uncertainty assessment, and transport predictions. © 2011 International Association for Mathematical Geosciences.The authors gratefully acknowledge the financial support by the Spanish Ministry of Science and Innovation through project CGL2011-23295. The first author appreciates the financial aid from China Scholarship Council (CSC No. [2007]3020).Zhou, H.; Li, L.; Hendricks Franssen, H.; Gómez-Hernández, JJ. (2012). Pattern Recognition in a Bimodal Aquifer Using the Normal-Score Ensemble Kalman Filter. Mathematical Geosciences. 44(2):169-185. https://doi.org/10.1007/s11004-011-9372-3S169185442Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans Signal Process 50(2):174–188Bertino L, Evensen G, Wackernagel H (2003) Sequential data assimilation techniques in oceanography. Int Stat Rev 71(2):223–241Burgers G, Jan van Leeuwen P, Evensen G (1998) Analysis scheme in the ensemble Kalman filter. Mon Weather Rev 126(6):1719–1724Carrera J, Neuman SP (1986b) Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability, and solution algorithms. Water Resour Res 22(2):211–227Chen Y, Zhang D (2006) Data assimilation for transient flow in geologic formations via ensemble Kalman filter. Adv Water Resour 29:1107–1122Delhomme JP (1979) Spatial variability and uncertainty in groundwater flow parameters: a geostatistical approach. Water Resour Res 15(2):269–280Evensen G (1994) Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J Geophys Res 99(C5):10143–10162Evensen G (2007) Data assimilation: the ensemble Kalman filter. Springer, Berlin, 279 ppFernàndez-Garcia D, Illangasekare T, Rajaram H (2005) Differences in the scale dependence of dispersivity and retardation factors estimated from forced-gradient and uniform flow tracer tests in three-dimensional physically and chemically heterogeneous porous media. Water Resour Res 41(3):W03012Gómez-Hernández JJ, Journel AG (1993) Joint sequential simulation of multi-Gaussian fields. In: Soares A (ed) Geostatistics Tróia ’92, vol 1. Kluwer Academic, Dordrecht, pp 85–94Gómez-Hernández JJ, Wen XH (1998) To be or not to be multi-Gaussian? A reflection on stochastic hydrogeology. Adv Water Resour 21(1):47–61Gu Y, Oliver DS (2006) The ensemble Kalman filter for continuous updating of reservoir simulation models. J Energy Resour Technol 128:79–87Harbaugh AW, Banta ER, Hill MC, McDonald MG (2000) MODFLOW-2000, the U.S. geological survey modular ground-water model—user guide to modularization concepts and the ground-water flow process. Tech rep. Open-File Report 00-92, U.S. Department of the Interior, U.S. Geological Survey. Reston, Virginia, 121 ppHendricks Franssen HJ, Kinzelbach W (2008) Real-time groundwater flow modeling with the Ensemble Kalman Filter: joint estimation for states and parameters and the filter inbreeding problem. Water Resour Res 44:W09408Hendricks Franssen HJ, Kinzelbach W (2009) Ensemble Kalman filtering versus sequential self-calibration for inverse modelling of dynamic groundwater flow systems. J Hydrol 365(3–4):261–274Houtekamer PL, Mitchell HL (2001) A sequential ensemble Kalman filter for atmospheric data assimilation. Mon Weather Rev 129:123–137Journel AG, Deutsch CV (1993) Entropy and spatial disorder. Math Geol 25(3):329–355Li L, Zhou H, Gómez-Hernández JJ (2011a) A comparative study of three-dimensional hydraulic conductivity upscaling at the macrodispersion experiment (MADE) site, Columbus air force base, Mississippi (USA). J Hydrol 404(3–4):278–293Li L, Zhou H, Gómez-Hernández JJ (2011b) Transport upscaling using multi-rate mass transfer in three-dimensional highly heterogeneous porous media. Adv Water Resour 34(4):478–489Moradkhani H, Sorooshian S, Gupta HV, Houser PR (2005) Dual state-parameter estimation of hydrological models using ensemble Kalman filter. Adv Water Resour 28:135–147Naevdal G, Johnsen L, Aanonsen S, Vefring E (Mar. 2005) Reservoir monitoring and continuous model updating using ensemble Kalman filter. SPE J 10(1):66–74Pardo-Igúzquiza E, Dowd PA (2003) CONNEC3D: a computer program for connectivity analysis of 3D random set models. Comput Geosci 29:775–785Schöniger A, Nowak W, Hendricks Franssen HJ (2011) Parameter estimation by ensemble Kalman filters with transformed data: approach and application to hydraulic tomography. Water Resour Res (submitted)Simon E, Bertino L (2009) Application of the Gaussian anamorphosis to assimilation in a 3-D coupled physical-ecosystem model of the North Atlantic with the EnKF: a twin experiment. Ocean Sci 5:495–510Stauffer D, Aharony A (1994) Introduction to percolation theory. Taylor and Francis, London. 181 ppStrébelle S 2000. Sequential simulation drawing structures from training images. PhD thesis, Stanford University. 187 ppStrebelle S (2002) Conditional simulation of complex geological structures using multiple-point statistics. Math Geol 34(1):1–21Wen X, Chen W (2006) Real-time reservoir model updating using ensemble Kalman filter: the confirming approach. SPE J 11(4):431–442Wen X, Chen W (2007) Some practical issues on real time reservoir updating using ensemble Kalman filter. SPE J 12(2):156–166Zhou H, Gómez-Hernández JJ, Hendricks Franssen H-J, Li L (2011) An approach to handling non-gaussianity of parameters and state variables in ensemble Kalman filtering. Adv Water Resour 34(7):844–864Zinn B, Harvey C (2003) When good statistical models of aquifer heterogeneity go bad: a comparison of flow, dispersion, and mass transfer in connected and multivariate Gaussian hydraulic conductivity fields. Water Resour Res 39(3):105

The management and survival outcomes of nasopharyngeal cancer in the Nordic countries

Peer reviewe

Multiscale Weighted Ensemble Kalman Filter for Fluid Flow Estimation

International audienceThis paper proposes a novel multi-scale uid ow data as- similation approach, which integrates and complements the advantages of a Bayesian sequential assimilation technique, the Weighted Ensem- ble Kalman lter (WEnKF) [12], and an improved multiscale stochastic formulation of the Lucas-Kanade (LK) estimator. The proposed scheme enables to enforce a physically plausible dynamical consistency of the estimated motion elds along the image sequence.