On the growth of errors in data assimilation systems

Considerable progress has taken place in numerical weather prediction over the last decade. It has been possible to extend predictive skills in the extra-tropics of the Northern Hemisphere during the winter from less than five days to seven days. Similar improvements, albeit on a lower level, have taken place in the Southern Hemisphere. Another example of improvement in the forecasts is the prediction of intense synoptic phenomena such as cyclogenesis which on the whole is quite successful with the most advanced operational models (Bengtsson (1989), Gadd and Kruze (1988)). A careful examination shows that there are no single causes for the improvements in predictive skill, but instead they are due to several different factors encompassing the forecasting system as a whole (Bengtsson, 1985). In this paper we will focus our attention on the role of data-assimilation and the effect it may have on reducing the initial error and hence improving the forecast. The first part of the paper contains a theoretical discussion on error growth in simple data assimilation systems, following Leith (1983). In the second part we will apply the result on actual forecast data from ECMWF. The potential for further forecast improvements within the framework of the present observing system in the two hemispheres will be discussed.

Data management for the ocean sciences - perspectives for the next decade

There is remarkable agreement in expectations today for vastly improved ocean data management a decade from now -- capabilities that will help to bring significant benefits to ocean research and to society. Advancing data management to such a degree, however, will require cultural and policy changes that are slow to effect. The technological foundations upon which data management systems are built are certain to continue advancing rapidly in parallel. These considerations argue for adopting attitudes of pragmatism and realism when planning data management strategies. In this paper we adopt those attitudes as we outline opportunities for progress in ocean data management. We begin with a synopsis of expectations for integrated ocean data management a decade from now. We discuss factors that should be considered by those evaluating candidate “standards”. We highlight challenges and opportunities in a number of technical areas, including “Web 2.0” applications, data modeling, data discovery and metadata, real-time operational data, archival of data, biological data management and satellite data management. We discuss the importance of investments in the development of software toolkits to accelerate progress. We conclude the paper by recommending a few specific, short term targets for implementation, that we believe to be both significant and achievable, and calling for action by community leadership to effect these advancements.

Correlations of control variables in variational data assimilation

Variational data assimilation systems for numerical weather prediction rely on a transformation of model variables to a set of control variables that are assumed to be uncorrelated. Most implementations of this transformation are based on the assumption that the balanced part of the flow can be represented by the vorticity. However, this assumption is likely to break down in dynamical regimes characterized by low Burger number. It has recently been proposed that a variable transformation based on potential vorticity should lead to control variables that are uncorrelated over a wider range of regimes. In this paper we test the assumption that a transform based on vorticity and one based on potential vorticity produce an uncorrelated set of control variables. Using a shallow-water model we calculate the correlations between the transformed variables in the different methods. We show that the control variables resulting from a vorticity-based transformation may retain large correlations in some dynamical regimes, whereas a potential vorticity based transformation successfully produces a set of uncorrelated control variables. Calculations of spatial correlations show that the benefit of the potential vorticity transformation is linked to its ability to capture more accurately the balanced component of the flow.

Data Communications for Engineers

Written for communications and electronic engineers, technicians and students, this book begins with an introduction to data communications, and goes on to explain the concept of layered communications. Other chapters deal with physical communications channels, baseband digital transmission, analog data transmission, error control and data compression codes, physical layer standards, the data link layer, the higher layers of the protocol hierarchy, and local are networks (LANS). Finally, the book explores some likely future developments.

Multi-target out-of-sequence data association

In data fusion systems, one often encounters measurements of past target locations and then wishes to deduce where the targets are currently located. Recent research on the processing of such out-of-sequence data has culminated in the development of a number of algorithms for solving the associated tracking problem. This paper reviews these different approaches in a common Bayesian framework and proposes an architecture that orthogonalises the data association and out-of-sequence problems such that any combination of solutions to these two problems can be used together. The emphasis is not on advocating one approach over another on the basis of computational expense, but rather on understanding the relationships between the algorithms so that any approximations made are explicit.

On instabilities in data assimilation algorithms

Data assimilation algorithms are a crucial part of operational systems in numerical weather prediction, hydrology and climate science, but are also important for dynamical reconstruction in medical applications and quality control for manufacturing processes. Usually, a variety of diverse measurement data are employed to determine the state of the atmosphere or to a wider system including land and oceans. Modern data assimilation systems use more and more remote sensing data, in particular radiances measured by satellites, radar data and integrated water vapor measurements via GPS/GNSS signals. The inversion of some of these measurements are ill-posed in the classical sense, i.e. the inverse of the operator H which maps the state onto the data is unbounded. In this case, the use of such data can lead to significant instabilities of data assimilation algorithms. The goal of this work is to provide a rigorous mathematical analysis of the instability of well-known data assimilation methods. Here, we will restrict our attention to particular linear systems, in which the instability can be explicitly analyzed. We investigate the three-dimensional variational assimilation and four-dimensional variational assimilation. A theory for the instability is developed using the classical theory of ill-posed problems in a Banach space framework. Further, we demonstrate by numerical examples that instabilities can and will occur, including an example from dynamic magnetic tomography.

Nonlinear error dynamics for cycled data assimilation methods

We investigate the error dynamics for cycled data assimilation systems, such that the inverse problem of state determination is solved at tk, k = 1, 2, 3, ..., with a first guess given by the state propagated via a dynamical system model from time tk − 1 to time tk. In particular, for nonlinear dynamical systems that are Lipschitz continuous with respect to their initial states, we provide deterministic estimates for the development of the error ||ek|| := ||x(a)k − x(t)k|| between the estimated state x(a) and the true state x(t) over time. Clearly, observation error of size δ > 0 leads to an estimation error in every assimilation step. These errors can accumulate, if they are not (a) controlled in the reconstruction and (b) damped by the dynamical system under consideration. A data assimilation method is called stable, if the error in the estimate is bounded in time by some constant C. The key task of this work is to provide estimates for the error ||ek||, depending on the size δ of the observation error, the reconstruction operator Rα, the observation operator H and the Lipschitz constants K(1) and K(2) on the lower and higher modes of controlling the damping behaviour of the dynamics. We show that systems can be stabilized by choosing α sufficiently small, but the bound C will then depend on the data error δ in the form c||Rα||δ with some constant c. Since ||Rα|| → ∞ for α → 0, the constant might be large. Numerical examples for this behaviour in the nonlinear case are provided using a (low-dimensional) Lorenz '63 system.

Four-dimensional data assimilation

Numerical weather prediction can be regarded as an initial value problem whereby the governing atmospheric equations are integrated forward from fully determined initial values of the meteorological parameters. However, in spite of the considerable improvements of the observing systems in recent years, the initial values are known only incompletely and inaccurately and one of the major tasks of any forecasting centre is to determine the best possible initial state from available observations.

Exploring strategies for coupled 4D-Var data assimilation using an idealised atmosphere-ocean model

Operational forecasting centres are currently developing data assimilation systems for coupled atmosphere-ocean models. Strongly coupled assimilation, in which a single assimilation system is applied to a coupled model, presents significant technical and scientific challenges. Hence weakly coupled assimilation systems are being developed as a first step, in which the coupled model is used to compare the current state estimate with observations, but corrections to the atmosphere and ocean initial conditions are then calculated independently. In this paper we provide a comprehensive description of the different coupled assimilation methodologies in the context of four dimensional variational assimilation (4D-Var) and use an idealised framework to assess the expected benefits of moving towards coupled data assimilation. We implement an incremental 4D-Var system within an idealised single column atmosphere-ocean model. The system has the capability to run both strongly and weakly coupled assimilations as well as uncoupled atmosphere or ocean only assimilations, thus allowing a systematic comparison of the different strategies for treating the coupled data assimilation problem. We present results from a series of identical twin experiments devised to investigate the behaviour and sensitivities of the different approaches. Overall, our study demonstrates the potential benefits that may be expected from coupled data assimilation. When compared to uncoupled initialisation, coupled assimilation is able to produce more balanced initial analysis fields, thus reducing initialisation shock and its impact on the subsequent forecast. Single observation experiments demonstrate how coupled assimilation systems are able to pass information between the atmosphere and ocean and therefore use near-surface data to greater effect. We show that much of this benefit may also be gained from a weakly coupled assimilation system, but that this can be sensitive to the parameters used in the assimilation.

Comparison of low-power wireless communication technologies for wearable health-monitoring applications

Health monitoring technologies such as Body Area Network (BAN) systems has gathered a lot of attention during the past few years. Largely encouraged by the rapid increase in the cost of healthcare services and driven by the latest technological advances in Micro-Electro-Mechanical Systems (MEMS) and wireless communications. BAN technology comprises of a network of body worn or implanted sensors that continuously capture and measure the vital parameters such as heart rate, blood pressure, glucose levels and movement. The collected data must be transferred to a local base station in order to be further processed. Thus, wireless connectivity plays a vital role in such systems. However, wireless connectivity comes at a cost of increased power usage, mainly due to the high energy consumption during data transmission. Unfortunately, battery-operated devices are unable to operate for ultra-long duration of time and are expected to be recharged or replaced once they run out of energy. This is not a simple task especially in the case of implanted devices such as pacemakers. Therefore, prolonging the network lifetime in BAN systems is one of the greatest challenges. In order to achieve this goal, BAN systems take advantage of low-power in-body and on-body/off-body wireless communication technologies. This paper compares some of the existing and emerging low-power communication protocols that can potentially be employed to support the rapid development and deployment of BAN systems.

Capturing and sharing our collective expertise on climate data: the CHARMe project

For users of climate services, the ability to quickly determine the datasets that best fit one's needs would be invaluable. The volume, variety and complexity of climate data makes this judgment difficult. The ambition of CHARMe ("Characterization of metadata to enable high-quality climate services") is to give a wider interdisciplinary community access to a range of supporting information, such as journal articles, technical reports or feedback on previous applications of the data. The capture and discovery of this "commentary" information, often created by data users rather than data providers, and currently not linked to the data themselves, has not been significantly addressed previously. CHARMe applies the principles of Linked Data and open web standards to associate, record, search and publish user-derived annotations in a way that can be read both by users and automated systems. Tools have been developed within the CHARMe project that enable annotation capability for data delivery systems already in wide use for discovering climate data. In addition, the project has developed advanced tools for exploring data and commentary in innovative ways, including an interactive data explorer and comparator ("CHARMe Maps") and a tool for correlating climate time series with external "significant events" (e.g. instrument failures or large volcanic eruptions) that affect the data quality. Although the project focuses on climate science, the concepts are general and could be applied to other fields. All CHARMe system software is open-source, released under a liberal licence, permitting future projects to re-use the source code as they wish.

Cross layer based protocols for energy aware and critical data delivery related applications using wireless sensor networks

Wireless Sensor Networks (WSNs) have been an exciting topic in recent years. The services offered by a WSN can be classified into three major categories: monitoring, alerting, and information on demand. WSNs have been used for a variety of applications related to the environment (agriculture, water and forest fire detection), the military, buildings, health (elderly people and home monitoring), disaster relief, and area or industrial monitoring. In most WSNs tasks like processing the sensed data, making decisions and generating emergency messages are carried out by a remote server, hence the need for efficient means of transferring data across the network. Because of the range of applications and types of WSN there is a need for different kinds of MAC and routing protocols in order to guarantee delivery of data from the source nodes to the server (or sink). In order to minimize energy consumption and increase performance in areas such as reliability of data delivery, extensive research has been conducted and documented in the literature on designing energy efficient protocols for each individual layer. The most common way to conserve energy in WSNs involves using the MAC layer to put the transceiver and the processor of the sensor node into a low power, sleep state when they are not being used. Hence the energy wasted due to collisions, overhearing and idle listening is reduced. As a result of this strategy for saving energy, the routing protocols need new solutions that take into account the sleep state of some nodes, and which also enable the lifetime of the entire network to be increased by distributing energy usage between nodes over time. This could mean that a combined MAC and routing protocol could significantly improve WSNs because the interaction between the MAC and network layers lets nodes be active at the same time in order to deal with data transmission. In the research presented in this thesis, a cross-layer protocol based on MAC and routing protocols was designed in order to improve the capability of WSNs for a range of different applications. Simulation results, based on a range of realistic scenarios, show that these new protocols improve WSNs by reducing their energy consumption as well as enabling them to support mobile nodes, where necessary. A number of conference and journal papers have been published to disseminate these results for a range of applications.

Full interference cancellation for two-path relay cooperative networks

This paper proposes the full interference cancellation (FIC) algorithm to cancel the inter-relay interference (IRI) in the two-path cooperative system. Arising from simultaneous data transmission from the source and relay nodes, IRI may significantly decrease the performance if it is not carefully handled. Compared to the existing partial interference cancellation (PIC) scheme, the FIC approach is more robust yet with less complexity. Numerical results are also given to verify the proposed scheme.

Interference cancellation in two-path successive relay system with network coding

This paper proposes a novel interference cancellation algorithm for the two-path successive relay system using network coding. The two-path successive relay scheme was proposed recently to achieve full date rate transmission with half-duplex relays. Due to the simultaneous data transmission at the relay and source nodes, the two-path relay suffers from the so-called inter-relay interference (IRI) which may significantly degrade the system performance. In this paper, we propose to use the network coding to remove the IRI such that the interference is first encoded with the network coding at the relay nodes and later removed at the destination. The network coding has low complexity and can well suppress the IRI. Numerical simulations show that the proposed algorithm has better performance than existing approaches.

An ocean modelling and assimilation guide to using GOCE geoid products

We review the procedures and challenges that must be considered when using geoid data derived from the Gravity and steady-state Ocean Circulation Explorer (GOCE) mission in order to constrain the circulation and water mass representation in an ocean 5 general circulation model. It covers the combination of the geoid information with timemean sea level information derived from satellite altimeter data, to construct a mean dynamic topography (MDT), and considers how this complements the time-varying sea level anomaly, also available from the satellite altimeter. We particularly consider the compatibility of these different fields in their spatial scale content, their temporal rep10 resentation, and in their error covariances. These considerations are very important when the resulting data are to be used to estimate ocean circulation and its corresponding errors. We describe the further steps needed for assimilating the resulting dynamic topography information into an ocean circulation model using three different operational fore15 casting and data assimilation systems. We look at methods used for assimilating altimeter anomaly data in the absence of a suitable geoid, and then discuss different approaches which have been tried for assimilating the additional geoid information. We review the problems that have been encountered and the lessons learned in order the help future users. Finally we present some results from the use of GRACE geoid in20 formation in the operational oceanography community and discuss the future potential gains that may be obtained from a new GOCE geoid.