State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing

Determining the magnitude and location of neural sources within the brain that are responsible for generating magnetoencephalography (MEG) signals measured on the surface of the head is a challenging problem in functional neuroimaging. The number of potential sources within the brain exceeds by an order of magnitude the number of recording sites. As a consequence, the estimates for the magnitude and location of the neural sources will be ill-conditioned because of the underdetermined nature of the problem. One well-known technique designed to address this imbalance is the minimum norm estimator (MNE). This approach imposes an $L^2$ regularization constraint that serves to stabilize and condition the source parameter estimates. However, these classes of regularizer are static in time and do not consider the temporal constraints inherent to the biophysics of the MEG experiment. In this paper we propose a dynamic state-space model that accounts for both spatial and temporal correlations within and across candidate intracortical sources. In our model, the observation model is derived from the steady-state solution to Maxwell's equations while the latent model representing neural dynamics is given by a random walk process.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS483 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Toward reliable ensemble Kalman filter estimates of CO 2 fluxes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95036/1/jgrd18220.pd

Online Localization and Tracking of Multiple Moving Speakers in Reverberant Environments

We address the problem of online localization and tracking of multiple moving speakers in reverberant environments. The paper has the following contributions. We use the direct-path relative transfer function (DP-RTF), an inter-channel feature that encodes acoustic information robust against reverberation, and we propose an online algorithm well suited for estimating DP-RTFs associated with moving audio sources. Another crucial ingredient of the proposed method is its ability to properly assign DP-RTFs to audio-source directions. Towards this goal, we adopt a maximum-likelihood formulation and we propose to use an exponentiated gradient (EG) to efficiently update source-direction estimates starting from their currently available values. The problem of multiple speaker tracking is computationally intractable because the number of possible associations between observed source directions and physical speakers grows exponentially with time. We adopt a Bayesian framework and we propose a variational approximation of the posterior filtering distribution associated with multiple speaker tracking, as well as an efficient variational expectation-maximization (VEM) solver. The proposed online localization and tracking method is thoroughly evaluated using two datasets that contain recordings performed in real environments.Comment: IEEE Journal of Selected Topics in Signal Processing, 201

Methods for assimilating remotelysensed water storage changes into hydrological models

Understanding physical processes within the water cycle is a challenging issue that requires merging information from various disciplines. The Gravity Recovery And Climate Experiment (GRACE) mission provides a unique opportunity to measure time-variable gravity fields, which can be converted to global total water storage anomalies (TWSA). These observations represent a vertical integral of all individual water compartments, which is difficult to observe by in-situ or other remote-sensing techniques. Knowledge about interactions between hydrological fluxes and terrestrial water storage compartments is reflected in large-scale hydrological models that nowadays increase in complexity to simulate all relevant physical processes within the global water cycle. Hydrological models are driven by climate forcing fields and their parameters are usually calibrated against river discharge to ensure a realistic water balance on river basin scale. However, errors in climate forcing fields, model parameters, and model structure limit the reliability of hydrological models. Therefore, it is necessary to improve model simulations by introducing measurements, which is known as data assimilation or data-model fusion. In this thesis, a novel calibration and data assimilation (C/DA) framework is developed to merge remotely-sensed large scale TWSA with hydrological models. To implement this framework, the WaterGAP Global Hydrology Model (WGHM) is chosen, which is a sophisticated 0.5°x0.5° conceptual model that simulates daily water changes in surface and sub-surface water compartments (including groundwater), and considers water consumption. In particular, a flexible approach is introduced to assimilate GRACE TWSA as (sub-)basin or gridded averages into WGHM, while for the first time, implementing the observation error correlations in the C/DA system. A sensitivity analysis is performed to identify significant parameters in the largest river basins world-wide. It is also investigated whether GRACE TWSA can be used to calibrate model parameters. To reduce sampling errors and to improve the computational efficiency, the classical ensemble Kalman filter (EnKF) technique is extended to a square root analysis (SQRA) scheme, and the singular evolutive interpolated Kalman (SEIK) filter. The relationships between these algorithms are addressed. A simple model and WGHM are used to describe the mathematical details of the data assimilation techniques. The observation error model, spatial resolution of observations, choice of filtering algorithm, and model ensemble size are assessed within a realistic synthetic experiment designed for the Mississippi River Basin, USA. Real GRACE products are also integrated into WGHM over this region. Investigations indicate that introducing GRACE TWSA constrains the water balance equation and corrects for insufficiently known climate forcing, in particular precipitation. Individual water states and fluxes are also adjusted but more improvements are expected by assimilating further in-situ and remotely-sensed observations. The processing choices represent important impacts on the final results. The C/DA framework is transferred to the Murray-Darling River Basin, Australia, to improve the simulation of hydrological changes under a long-term drought condition. GRACE C/DA introduces a negative trend to WGHM simulated TWSA. A validation with in-situ groundwater measurements indicates that the trend is correctly associated with the groundwater compartment. Thus, the C/DA helps to identify deficits in model simulations and improves the understanding of hydrological processes. The promising results provide a first step towards more complex C/DA applications on global scale and in conjunction with further terrestrial water storage observations.Methoden zur Assimilierung von satelliten-basierten Wasserspeicheränderungen in hydrologische Modelle Zum Verständnis der physikalischen Prozesse des Wasserkreislaufes ist das Zusammenführen von Kenntnissen verschiedener Disziplinen erforderlich. Die Messungen zeitabhängiger Gravitationsfelder der Gravity Recovery And Climate Experiment (GRACE) Satellitenmission liefern einzigartige Erkenntnisse über globale Gesamtwasserspeicher-änderungen (GWSA). Diese Größe repräsentiert die Summe aller einzelnen Wasserspeicherkomponenten, welche nur unzulänglich durch lokale oder andere satellitengestützte Verfahren beobachtet werden kann. Großskalige hydrologische Modelle simulieren Interaktionen zwischen terrestrischen Wasserspeicherkomponenten. Ihre Komplexität steigt heutzutage immer weiter, um alle relevanten physikalischen Prozesse im globalen Wasserkreislauf abzubilden. Sie werden durch Klimadaten angetrieben und durch Modellparameter gesteuert. Zur Gewährleistung einer realistischen Wasserbilanz in Flusseinzugsgebieten werden letztere üblicherweise gegen Durchflussmessungen kalibriert. Dennoch limitieren Unsicherheiten in den Klimadaten, in den Modellparametern und in der Modellstruktur die Zuverlässigkeit hydrologischer Prädiktionen. Um Simulationen zu verbessern ist daher die Integration von Beobachtungsdaten notwendig, welches unter dem Begriff der Datenassimilierung bekannt ist. In dieser Arbeit wird ein neuer Kalibrierungs- und Datenassimilierungsansatz (K/DA) zur Kombination von großskalig beobachteten GWSA und hydrologischen Modellen am Beispiel des WaterGAP Global Hydrology Model (WGHM) entwickelt. WGHM ist ein konzeptionelles Wasserbilanzmodell, das tägliche Wasseränderungen auf und im Boden (inklusive Grundwasser) auf einer räumlichen Skala von 0,5°x0,5° berechnet und anthropogene Wasserentnahmen berücksichtigt. Insbesondere wird ein flexibler Ansatz zur Integration gegitterter und räumlich gemittelter GWSA eingeführt, während die Korrelationen der Beobachtungsfehler zum ersten Mal in der Assimilierung berücksichtigt werden. Eine Sensitivitätsanalyse identifiziert maßgebliche Parameter für die weltweit größten Flusseinzugsgebiete. Es wird außerdem untersucht, ob GRACE-GWSA zur Parameter-kalibrierung herangezogen werden können. Um Stichprobenfehler zu reduzieren und um die rechnerische Effizienz zu steigern, wird die klassische Ensemble Kalman Filter (EnKF) Methode um das Square Root Analysis (SQRA) Schema und den Singular Evolutive Interpolated Kalman (SEIK) Filter erweitert. Die Zusammenhänge dieser Algorithmen werden dargestellt. Die mathematischen Details der Methoden werden anhand eines einfachen Modells und des WGHM beschrieben. Das Modell der Beobachtungsfehler, die Auflösung der Beobachtungen, die Auswahl der Filteralgorithmen und die Größe des Modellensembles werden in einem realistischen synthetischen Experiment für das Flusseinzugsgebiet des Mississippis (USA) analysiert. GRACE-GWSA werden ebenfalls für dieser Region in das WGHM integriert. Untersuchungen zeigen, dass die Wasserbilanz an die Daten angepasst wird und ungenaue Klimadaten, insbesondere Niederschlag, ausgeglichen werden. Wasserspeicher-komponenten werden ebenfalls angepasst, würden aber durch die Assimilierung weiterer lokaler und satellitengestützter Daten profitieren. Der K/DA Ansatz hat einen entscheidenden Einfluss auf die Ergebnisse. Der entwickelte Ansatz wird auf das Einzugsgebiet des Murray und Darling Flusses (Australien) übertragen, um die Simulation hydrologischer Änderungen während einer Trockenperiode zu verbessern. GRACE-K/DA führt einen negativen Trend in das Modell ein. Die Validierung mit lokalen Grundwasserdaten bestätigt, dass der Trend korrekt mit dem Grundwasserspeicher assoziiert wird. Die K/DA ermöglicht somit Defizite in Modellsimulationen zu identifizieren und verbessert das Verständnis hydrologischer Prozesse. Die vielversprechenden Ergebnisse bereiten einen ersten Schritt in Richtung globaler K/DA in Verbindung mit weiteren hydrologischen Beobachtungen

Diagnosing atmospheric motion vector observation errors for an operational high resolution data assimilation system

Atmospheric motion vectors (AMVs) are wind observations derived by tracking cloud or water vapour features in consecutive satellite images. These observations are incorporated into Numerical Weather Prediction (NWP) through data assimilation. In the assimilation algorithm, the weighting given to an observation is determined by the uncertainty associated with its measurement and representation. Previous studies assessing AMV uncertainty have used direct comparisons between AMVs with co-located radiosonde data and AMVs derived from Observing System Simulation Experiments (OSSEs). These have shown that AMV error is horizontally correlated with characteristic length scale up to 200 km. In this work, we take an alternative approach and estimate AMV error variance and horizontal error correlation using background and analysis residuals obtained from the Met Office limited area, 3 km horizontal grid length data assimilation system. The results show that the observation error variance profile ranges from 5.2 to 14.1 s m2s− 2, with the highest values occurring at high and medium heights. This is indicative that the maximum error variance occurs where wind speed and shear, in combination, are largest. With the exception of AMVs derived from the High Resolution Visible channel, the results show horizontal observation error correlations at all heights in the atmosphere, with correlation lengthscales ranging between 140 and 200 km. These horizontal lengthscales are significantly larger than current AMV observation thinning distances used in the Met Office high resolution assimilation

A state-space mixed membership blockmodel for dynamic network tomography

In a dynamic social or biological environment, the interactions between the actors can undergo large and systematic changes. In this paper we propose a model-based approach to analyze what we will refer to as the dynamic tomography of such time-evolving networks. Our approach offers an intuitive but powerful tool to infer the semantic underpinnings of each actor, such as its social roles or biological functions, underlying the observed network topologies. Our model builds on earlier work on a mixed membership stochastic blockmodel for static networks, and the state-space model for tracking object trajectory. It overcomes a major limitation of many current network inference techniques, which assume that each actor plays a unique and invariant role that accounts for all its interactions with other actors; instead, our method models the role of each actor as a time-evolving mixed membership vector that allows actors to behave differently over time and carry out different roles/functions when interacting with different peers, which is closer to reality. We present an efficient algorithm for approximate inference and learning using our model; and we applied our model to analyze a social network between monks (i.e., the Sampson's network), a dynamic email communication network between the Enron employees, and a rewiring gene interaction network of fruit fly collected during its full life cycle. In all cases, our model reveals interesting patterns of the dynamic roles of the actors.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS311 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A water storage reanalysis over the European continent: assimilation of GRACE data into a high-resolution hydrological model and validation

Continental water storage and redistribution within the Earth’s system are key variables of the terrestrial water cycle. Changes in water storage and fluxes may affect resources for drinking water and irrigation, lead to drought or flood conditions, or cause severe changes of ecosystems e.g., through salinification. Hydrological models, which map water storages and fluxes, are being continuously improved and deepen our understanding of geophysical processes related to the water cycle. However, models are built on a simplified representation of reality, which leads to limited predicting skills of the simulation results. Assimilating remotely sensed total water storage variability from the Gravity Recovery and Climate Experiment (GRACE) mission has become a valuable tool for reducing uncertainties of hydrological model simulations. Simultaneously, coarse GRACE observations are disaggregated spatially and temporally through data assimilation. In this thesis, GRACE data are assimilated into the Community Land Model version 3.5 (CLM3.5) yielding a unique daily 12.5 km reanalysis of total water storage evolution over Europe (2003 to 2010). Independent observations are evaluated to identify model deficits and to validate the performance of data assimilation. For the first time, the effect of data assimilation on modeled total water storage is also shown on the level of GRACE K-band observations. Optimal strategies for assimilating GRACE data into a high-resolution hydrological model are investigated through synthetic experiments. These experiments address the choice of the assimilation algorithm, localization, inflation of the ensemble of model states, ensemble size, error model of the observations, and spatial resolution of the observation grid. As the assimilation of GRACE data into CLM3.5 is realized within the Terrestrial Systems Modeling Platform (TerrSysMP), future assimilation experiments can be extended for the groundwater and atmosphere components included in TerrSysMP.Eine Reanalyse des europäischen Wasserspeichers: Assimilierung von GRACE Daten in ein hochaufgelöstes hydrologisches Modell und Validierung Änderungen im kontinentalen Wasserspeicher und im Transport von Wasser durch das Erdsystem sind wichtige Einflussgrößen für die Verfügbarkeit von Frischwasserresourcen, die Entstehung von Dürren und Überschwemmungen, sowie für die Erhaltung von Ökosystemen, welche z.B. durch Versalzung gefährdet werden. Hydrologische Modelle, die die Speicherung und den Transport von Wassermassen abbilden, werden stetig verbessert und helfen unser Verständnis von hydrologischen Prozessen zu vertiefen. Allerdings ermöglichen hydrologische Modelle nur eine vereinfachte Abbildung der Realität, sodass die Aussagekraft der Simulationsergebnisse beschränkt ist. Die Assimilierung von Wasserspeicheränderungen, gemessen von den GRACE (Gravity Recovery and Climate Experiment) Satelliten, kann hydrologische Simulationen verbessern und erlaubt gleichzeitig eine räumliche und zeitliche Differenzierung der grobaufgelösten GRACE Beobachtungen. In dieser Doktorarbeit werden GRACE Daten in das Land-Oberflächen-Modell CLM3.5 (Community Land Model Version 3.5) assimiliert, um eine neuartige Reanalyse täglicher Wasserspeicheränderungen (2003 bis 2010) für Europa mit 12.5 km Auflösung zu generieren. Durch unabhängige Beobachtungen werden Defizite des Modells identifiziert und das Ergebnis der Datenassimilierung beurteilt. Zum ersten Mal wird auch die Auswirkung der Assimilierung direkt auf Basis der GRACE K-Band Beobachtungen untersucht. Mit Hilfe synthetischer Experimente wird die beste Strategie zur Assimilierung von GRACE Daten in ein hochaufgelöstes hydrologisches Modell ermittelt. Dabei wird der Einfluss unterschiedlicher Assimilierungsstrategien untersucht, unter anderem die Wahl des Assimilierungsalgorithmus, die Lokalisierung des Einflussbereichs von Beobachtungen, die Erhöhung der Spannweite der Ensemblemitglieder des Modells, die Ensemblegröße, das Fehlermodell der Beobachtung und die räumliche Auflösung des Beobachtungsgitters. Da die Assimilierung von GRACE in das CLM3.5 Modell unter Verwendung von TerrSysMP (Terrestrial Systems Modeling Platform) geschieht, können die Assimilierungsexperimente in Zukunft auf die zusätzliche Verwendung des in TerrSysMP enthaltenen Grundwasser- und des Atmosphärenmodells erweitert werden.</p