Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Impact of hydrographic data assimilation on the modelled Atlantic meridional overturning circulation

Here we make an initial step toward the development of an ocean assimilation system that can constrain the modelled Atlantic Meridional Overturning Circulation (AMOC) to support climate predictions. A detailed comparison is presented of 1° and 1/4° resolution global model simulations with and without sequential data assimilation, to the observations and transport estimates from the RAPID mooring array across 26.5° N in the Atlantic. Comparisons of modelled water properties with the observations from the merged RAPID boundary arrays demonstrate the ability of in situ data assimilation to accurately constrain the east-west density gradient between these mooring arrays. However, the presence of an unconstrained "western boundary wedge" between Abaco Island and the RAPID mooring site WB2 (16 km offshore) leads to the intensification of an erroneous southwards flow in this region when in situ data are assimilated. The result is an overly intense southward upper mid-ocean transport (0–1100 m) as compared to the estimates derived from the RAPID array. Correction of upper layer zonal density gradients is found to compensate mostly for a weak subtropical gyre circulation in the free model run (i.e. with no assimilation). Despite the important changes to the density structure and transports in the upper layer imposed by the assimilation, very little change is found in the amplitude and sub-seasonal variability of the AMOC. This shows that assimilation of upper layer density information projects mainly on the gyre circulation with little effect on the AMOC at 26° N due to the absence of corrections to density gradients below 2000 m (the maximum depth of Argo). The sensitivity to initial conditions was explored through two additional experiments using a climatological initial condition. These experiments showed that the weak bias in gyre intensity in the control simulation (without data assimilation) develops over a period of about 6 months, but does so independently from the overturning, with no change to the AMOC. However, differences in the properties and volume transport of North Atlantic Deep Water (NADW) persisted throughout the 3 year simulations resulting in a difference of 3 Sv in AMOC intensity. The persistence of these dense water anomalies and their influence on the AMOC is promising for the development of decadal forecasting capabilities. The results suggest that the deeper waters must be accurately reproduced in order to constrain the AMOC.

PDM 2006: Proceedings of the International Workshop on Data Mining

Recently major processor manufacturers have announced a dramatic shift in their paradigm to increase computing power over the coming years. Instead of focusing on faster clock speeds and more powerful single core CPUs, the trend clearly goes towards multi core systems. This will also result in a paradigm shift for the development of algorithms for computationally expensive tasks, such as data mining applications. Obviously, work on parallel algorithms is not new per se but concentrated efforts in the many application domains are still missing. Multi-core systems, but also clusters of workstations and even large-scale distributed computing infrastructures provide new opportunities and pose new challenges for the design of parallel and distributed algorithms. Since data mining and machine learning systems rely on high performance computing systems, research on the corresponding algorithms must be on the forefront of parallel algorithm research in order to keep pushing data mining and machine learning applications to be more powerful and, especially for the former, interactive. To bring together researchers and practitioners working in this exciting field, a workshop on parallel data mining was organized as part of PKDD/ECML 2006 (Berlin, Germany). The six contributions selected for the program describe various aspects of data mining and machine learning approaches featuring low to high degrees of parallelism: The first contribution focuses the classic problem of distributed association rule mining and focuses on communication efficiency to improve the state of the art. After this a parallelization technique for speeding up decision tree construction by means of thread-level parallelism for shared memory systems is presented. The next paper discusses the design of a parallel approach for dis- tributed memory systems of the frequent subgraphs mining problem. This approach is based on a hierarchical communication topology to solve issues related to multi-domain computational envi- ronments. The forth paper describes the combined use and the customization of software packages to facilitate a top down parallelism in the tuning of Support Vector Machines (SVM) and the next contribution presents an interesting idea concerning parallel training of Conditional Random Fields (CRFs) and motivates their use in labeling sequential data. The last contribution finally focuses on very efficient feature selection. It describes a parallel algorithm for feature selection from random subsets. Selecting the papers included in this volume would not have been possible without the help of an international Program Committee that has provided detailed reviews for each paper. We would like to also thank Matthew Otey who helped with publicity for the workshop.

Sequential variations of phytoplankton growth and mortality in an NPZ model: a remote-sensing-based assessment

Radiometric data in the visible domain acquired by satellite remote sensing have proven to be powerful for monitoring the states of the ocean, both physical and biological. With the help of these data it is possible to understand certain variations in biological responses of marine phytoplankton on ecological time scales. Here, we implement a sequential data-assimilation technique to estimate from a conventional nutrient–phytoplankton–zooplankton (NPZ) model the time variations of observed and unobserved variables. In addition, we estimate the time evolution of two biological parameters, namely, the specific growth rate and specific mortality of phytoplankton. Our study demonstrates that: (i) the series of time-varying estimates of specific growth rate obtained by sequential data assimilation improves the fitting of the NPZ model to the satellite-derived time series: the model trajectories are closer to the observations than those obtained by implementing static values of the parameter; (ii) the estimates of unobserved variables, i.e., nutrient and zooplankton, obtained from an NPZ model by implementation of a pre-defined parameter evolution can be different from those obtained on applying the sequences of parameters estimated by assimilation; and (iii) the maximum estimated specific growth rate of phytoplankton in the study area is more sensitive to the sea-surface temperature than would be predicted by temperature-dependent functions reported previously. The overall results of the study are potentially useful for enhancing our understanding of the biological response of phytoplankton in a changing environment.

Modelling the time-evolution of phytoplankton size spectra from satellite remote sensing

A dynamic size-structured model is developed for phytoplankton and nutrients in the oceanic mixed layer and applied to extract phytoplankton biomass at discrete size fractions from remotely sensed, ocean-colour data. General relationships between cell size and biophysical processes (such as sinking, grazing, and primary production) of phytoplankton were included in the model through a bottom–up approach. Time-dependent, mixed-layer depth was used as a forcing variable, and a sequential data-assimilation scheme was implemented to derive model trajectories. From a given time-series, the method produces estimates of size-structured biomass at every observation, so estimates seasonal succession of individual phytoplankton size, derived here from remote sensing for the first time. From these estimates, normalized phytoplankton biomass size spectra over a period of 9 years were calculated for one location in the North Atlantic. Further analysis demonstrated that strong relationships exist between the seasonal trends of the estimated size spectra and the mixed-layer depth, nutrient biomass, and total chlorophyll. The results contain useful information on the time-dependent biomass flux in the pelagic ecosystem.

Simultaneous mobile sink allocation in home environments with applications in mobile consumer robotics

This paper presents a novel mobile sink area allocation scheme for consumer based mobile robotic devices with a proven application to robotic vacuum cleaners. In the home or office environment, rooms are physically separated by walls and an automated robotic cleaner cannot make a decision about which room to move to and perform the cleaning task. Likewise, state of the art cleaning robots do not move to other rooms without direct human interference. In a smart home monitoring system, sensor nodes may be deployed to monitor each separate room. In this work, a quad tree based data gathering scheme is proposed whereby the mobile sink physically moves through every room and logically links all separated sub-networks together. The proposed scheme sequentially collects data from the monitoring environment and transmits the information back to a base station. According to the sensor nodes information, the base station can command a cleaning robot to move to a specific location in the home environment. The quad tree based data gathering scheme minimizes the data gathering tour length and time through the efficient allocation of data gathering areas. A calculated shortest path data gathering tour can efficiently be allocated to the robotic cleaner to complete the cleaning task within a minimum time period. Simulation results show that the proposed scheme can effectively allocate and control the cleaning area to the robot vacuum cleaner without any direct interference from the consumer. The performance of the proposed scheme is then validated with a set of practical sequential data gathering tours in a typical office/home environment.

Incorporating data received after a sequential trial has stopped into the final analysis: implementation and comparison of methods

In a sequential clinical trial, accrual of data on patients often continues after the stopping criterion for the study has been met. This is termed “overrunning.” Overrunning occurs mainly when the primary response from each patient is measured after some extended observation period. The objective of this article is to compare two methods of allowing for overrunning. In particular, simulation studies are reported that assess the two procedures in terms of how well they maintain the intended type I error rate. The effect on power resulting from the incorporation of “overrunning data” using the two procedures is evaluated.

Design considerations in the sequential analysis of matched case–control data

A role for sequential test procedures is emerging in genetic and epidemiological studies using banked biological resources. This stems from the methodology's potential for improved use of information relative to comparable fixed sample designs. Studies in which cost, time and ethics feature prominently are particularly suited to a sequential approach. In this paper sequential procedures for matched case–control studies with binary data will be investigated and assessed. Design issues such as sample size evaluation and error rates are identified and addressed. The methodology is illustrated and evaluated using both real and simulated data sets.

Dynamic data reconciliation for sequential modular simulators: application to a mixing process

This paper describes a method for dynamic data reconciliation of nonlinear systems that are simulated using the sequential modular approach, and where individual modules are represented by a class of differential algebraic equations. The estimation technique consists of a bank of extended Kalman filters that are integrated with the modules. The paper reports a study based on experimental data obtained from a pilot scale mixing process.

Dynamic data reconciliation for sequential modular simulators

In this paper the implementation of dynamic data reconciliation techniques for sequential modular models is described. The paper is organised as follows. First, an introduction to dynamic data reconciliation is given. Then, the online use of rigorous process models is introduced. The sequential modular approach to dynamic simulation is briefly discussed followed by a short review of the extended Kalman filter. The second section describes how the modules are implemented. A simulation case study and its results are also presented.

Fine-root turnover rates of European forests revisited: an analysis of data from sequential coring and ingrowth cores

Background and Aims Forest trees directly contribute to carbon cycling in forest soils through the turnover of their fine roots. In this study we aimed to calculate root turnover rates of common European forest tree species and to compare them with most frequently published values. Methods We compiled available European data and applied various turnover rate calculation methods to the resulting database. We used Decision Matrix and Maximum-Minimum formula as suggested in the literature. Results Mean turnover rates obtained by the combination of sequential coring and Decision Matrix were 0.86 yr−1 for Fagus sylvatica and 0.88 yr−1 for Picea abies when maximum biomass data were used for the calculation, and 1.11 yr−1 for both species when mean biomass data were used. Using mean biomass rather than maximum resulted in about 30 % higher values of root turnover. Using the Decision Matrix to calculate turnover rate doubled the rates when compared to the Maximum-Minimum formula. The Decision Matrix, however, makes use of more input information than the Maximum-Minimum formula. Conclusions We propose that calculations using the Decision Matrix with mean biomass give the most reliable estimates of root turnover rates in European forests and should preferentially be used in models and C reporting.

Stochastic modelling of rainfall from satellite data

Satellite-based rainfall monitoring is widely used for climatological studies because of its full global coverage but it is also of great importance for operational purposes especially in areas such as Africa where there is a lack of ground-based rainfall data. Satellite rainfall estimates have enormous potential benefits as input to hydrological and agricultural models because of their real time availability, low cost and full spatial coverage. One issue that needs to be addressed is the uncertainty on these estimates. This is particularly important in assessing the likely errors on the output from non-linear models (rainfall-runoff or crop yield) which make use of the rainfall estimates, aggregated over an area, as input. Correct assessment of the uncertainty on the rainfall is non-trivial as it must take account of • the difference in spatial support of the satellite information and independent data used for calibration • uncertainties on the independent calibration data • the non-Gaussian distribution of rainfall amount • the spatial intermittency of rainfall • the spatial correlation of the rainfall field This paper describes a method for estimating the uncertainty on satellite-based rainfall values taking account of these factors. The method involves firstly a stochastic calibration which completely describes the probability of rainfall occurrence and the pdf of rainfall amount for a given satellite value, and secondly the generation of ensemble of rainfall fields based on the stochastic calibration but with the correct spatial correlation structure within each ensemble member. This is achieved by the use of geostatistical sequential simulation. The ensemble generated in this way may be used to estimate uncertainty at larger spatial scales. A case study of daily rainfall monitoring in the Gambia, west Africa for the purpose of crop yield forecasting is presented to illustrate the method.

Data assimilation for marine monitoring and prediction: The MERCATOR operational assimilation systems and the MERSEA developments

During the past 15 years, a number of initiatives have been undertaken at national level to develop ocean forecasting systems operating at regional and/or global scales. The co-ordination between these efforts has been organized internationally through the Global Ocean Data Assimilation Experiment (GODAE). The French MERCATOR project is one of the leading participants in GODAE. The MERCATOR systems routinely assimilate a variety of observations such as multi-satellite altimeter data, sea-surface temperature and in situ temperature and salinity profiles, focusing on high-resolution scales of the ocean dynamics. The assimilation strategy in MERCATOR is based on a hierarchy of methods of increasing sophistication including optimal interpolation, Kalman filtering and variational methods, which are progressively deployed through the Syst`eme d’Assimilation MERCATOR (SAM) series. SAM-1 is based on a reduced-order optimal interpolation which can be operated using ‘altimetry-only’ or ‘multi-data’ set-ups; it relies on the concept of separability, assuming that the correlations can be separated into a product of horizontal and vertical contributions. The second release, SAM-2, is being developed to include new features from the singular evolutive extended Kalman (SEEK) filter, such as three-dimensional, multivariate error modes and adaptivity schemes. The third one, SAM-3, considers variational methods such as the incremental four-dimensional variational algorithm. Most operational forecasting systems evaluated during GODAE are based on least-squares statistical estimation assuming Gaussian errors. In the framework of the EU MERSEA (Marine EnviRonment and Security for the European Area) project, research is being conducted to prepare the next-generation operational ocean monitoring and forecasting systems. The research effort will explore nonlinear assimilation formulations to overcome limitations of the current systems. This paper provides an overview of the developments conducted in MERSEA with the SEEK filter, the Ensemble Kalman filter and the sequential importance re-sampling filter.