On state and parameter estimation in chaotic systems

State-of-the-art predictions of atmospheric states rely on large-scale numerical models of chaotic systems. This dissertation studies numerical methods for state and parameter estimation in such systems. The motivation comes from weather and climate models and a methodological perspective is adopted. The dissertation comprises three sections: state estimation, parameter estimation and chemical data assimilation with real atmospheric satellite data. In the state estimation part of this dissertation, a new filtering technique based on a combination of ensemble and variational Kalman filtering approaches, is presented, experimented and discussed. This new filter is developed for large-scale Kalman filtering applications. In the parameter estimation part, three different techniques for parameter estimation in chaotic systems are considered. The methods are studied using the parameterized Lorenz 95 system, which is a benchmark model for data assimilation. In addition, a dilemma related to the uniqueness of weather and climate model closure parameters is discussed. In the data-oriented part of this dissertation, data from the Global Ozone Monitoring by Occultation of Stars (GOMOS) satellite instrument are considered and an alternative algorithm to retrieve atmospheric parameters from the measurements is presented. The validation study presents first global comparisons between two unique satellite-borne datasets of vertical profiles of nitrogen trioxide (NO3), retrieved using GOMOS and Stratospheric Aerosol and Gas Experiment III (SAGE III) satellite instruments. The GOMOS NO3 observations are also considered in a chemical state estimation study in order to retrieve stratospheric temperature profiles. The main result of this dissertation is the consideration of likelihood calculations via Kalman filtering outputs. The concept has previously been used together with stochastic differential equations and in time series analysis. In this work, the concept is applied to chaotic dynamical systems and used together with Markov chain Monte Carlo (MCMC) methods for statistical analysis. In particular, this methodology is advocated for use in numerical weather prediction (NWP) and climate model applications. In addition, the concept is shown to be useful in estimating the filter-specific parameters related, e.g., to model error covariance matrix parameters.

University students’ regulation of learning and text processing – examples from medical and teacher education

The general aim of the thesis was to study university students’ learning from the perspective of regulation of learning and text processing. The data were collected from the two academic disciplines of medical and teacher education, which share the features of highly scheduled study, a multidisciplinary character, a complex relationship between theory and practice and a professional nature. Contemporary information society poses new challenges for learning, as it is not possible to learn all the information needed in a profession during a study programme. Therefore, it is increasingly important to learn how to think and learn independently, how to recognise gaps in and update one’s knowledge and how to deal with the huge amount of constantly changing information. In other words, it is critical to regulate one’s learning and to process text effectively. The thesis comprises five sub-studies that employed cross-sectional, longitudinal and experimental designs and multiple methods, from surveys to eye tracking. Study I examined the connections between students’ study orientations and the ways they regulate their learning. In total, 410 second-, fourth- and sixth-year medical students from two Finnish medical schools participated in the study by completing a questionnaire measuring both general study orientations and regulation strategies. The students were generally deeply oriented towards their studies. However, they regulated their studying externally. Several interesting and theoretically reasonable connections between the variables were found. For instance, self-regulation was positively correlated with deep orientation and achievement orientation and was negatively correlated with non-commitment. However, external regulation was likewise positively correlated with deep orientation and achievement orientation but also with surface orientation and systematic orientation. It is argued that external regulation might function as an effective coping strategy in the cognitively loaded medical curriculum. Study II focused on medical students’ regulation of learning and their conceptions of the learning environment in an innovative medical course where traditional lectures were combined wth problem-based learning (PBL) group work. First-year medical and dental students (N = 153) completed a questionnaire assessing their regulation strategies of learning and views about the PBL group work. The results indicated that external regulation and self-regulation of the learning content were the most typical regulation strategies among the participants. In line with previous studies, self-regulation wasconnected with study success. Strictly organised PBL sessions were not considered as useful as lectures, although the students’ views of the teacher/tutor and the group were mainly positive. Therefore, developers of teaching methods are challenged to think of new solutions that facilitate reflection of one’s learning and that improve the development of self-regulation. In Study III, a person-centred approach to studying regulation strategies was employed, in contrast to the traditional variable-centred approach used in Study I and Study II. The aim of Study III was to identify different regulation strategy profiles among medical students (N = 162) across time and to examine to what extent these profiles predict study success in preclinical studies. Four regulation strategy profiles were identified, and connections with study success were found. Students with the lowest self-regulation and with an increasing lack of regulation performed worse than the other groups. As the person-centred approach enables us to individualise students with diverse regulation patterns, it could be used in supporting student learning and in facilitating the early diagnosis of learning difficulties. In Study IV, 91 student teachers participated in a pre-test/post-test design where they answered open-ended questions about a complex science concept both before and after reading either a traditional, expository science text or a refutational text that prompted the reader to change his/her beliefs according to scientific beliefs about the phenomenon. The student teachers completed a questionnaire concerning their regulation and processing strategies. The results showed that the students’ understanding improved after text reading intervention and that refutational text promoted understanding better than the traditional text. Additionally, regulation and processing strategies were found to be connected with understanding the science phenomenon. A weak trend showed that weaker learners would benefit more from the refutational text. It seems that learners with effective learning strategies are able to pick out the relevant content regardless of the text type, whereas weaker learners might benefit from refutational parts that contrast the most typical misconceptions with scientific views. The purpose of Study V was to use eye tracking to determine how third-year medical studets (n = 39) and internal medicine residents (n = 13) read and solve patient case texts. The results revealed differences between medical students and residents in processing patient case texts; compared to the students, the residents were more accurate in their diagnoses and processed the texts significantly faster and with a lower number of fixations. Different reading patterns were also found. The observed differences between medical students and residents in processing patient case texts could be used in medical education to model expert reasoning and to teach how a good medical text should be constructed. The main findings of the thesis indicate that even among very selected student populations, such as high-achieving medical students or student teachers, there seems to be a lot of variation in regulation strategies of learning and text processing. As these learning strategies are related to successful studying, students enter educational programmes with rather different chances of managing and achieving success. Further, the ways of engaging in learning seldom centre on a single strategy or approach; rather, students seem to combine several strategies to a certain degree. Sometimes, it can be a matter of perspective of which way of learning can be considered best; therefore, the reality of studying in higher education is often more complicated than the simplistic view of self-regulation as a good quality and external regulation as a harmful quality. The beginning of university studies may be stressful for many, as the gap between high school and university studies is huge and those strategies that were adequate during high school might not work as well in higher education. Therefore, it is important to map students’ learning strategies and to encourage them to engage in using high-quality learning strategies from the beginning. Instead of separate courses on learning skills, the integration of these skills into course contents should be considered. Furthermore, learning complex scientific phenomena could be facilitated by paying attention to high-quality learning materials and texts and other support from the learning environment also in the university. Eye tracking seems to have great potential in evaluating performance and growing diagnostic expertise in text processing, although more research using texts as stimulus is needed. Both medical and teacher education programmes and the professions themselves are challenging in terms of their multidisciplinary nature and increasing amounts of information and therefore require good lifelong learning skills during the study period and later in work life.

How Prescribed Policy Can Mislead when Data Are Defective: a Follow-Up to Srinivasan (1994) Using General Equilibrium.

We highlight an example of considerable bias in officially published input-output data (factor-income shares) by an LDC (Turkey), which many researchers use without question. We make use of an intertemporal general equilibrium model of trade and production to evaluate the dynamic gains for Turkey from currently debated trade policy options and compare the predictions using conservatively adjusted, rather than official, data on factor shares.

Sensitivity of large-scale atmospheric analyses to humidity observations and its impact on the global water cycle and tropical and extratropical weather systems in ERA40

Reanalysis data obtained from data assimilation are increasingly used for diagnostic studies of the general circulation of the atmosphere, for the validation of modelling experiments and for estimating energy and water fluxes between the Earth surface and the atmosphere. Because fluxes are not specifically observed, but determined by the data assimilation system, they are not only influenced by the utilized observations but also by model physics and dynamics and by the assimilation method. In order to better understand the relative importance of humidity observations for the determination of the hydrological cycle, in this paper we describe an assimilation experiment using the ERA40 reanalysis system where all humidity data have been excluded from the observational data base. The surprising result is that the model, driven by the time evolution of wind, temperature and surface pressure, is able to almost completely reconstitute the large-scale hydrological cycle of the control assimilation without the use of any humidity data. In addition, analysis of the individual weather systems in the extratropics and tropics using an objective feature tracking analysis indicates that the humidity data have very little impact on these systems. We include a discussion of these results and possible consequences for the way moisture information is assimilated, as well as the potential consequences for the design of observing systems for climate monitoring. It is further suggested, with support from a simple assimilation study with another model, that model physics and dynamics play a decisive role for the hydrological cycle, stressing the need to better understand these aspects of model parametrization. .

A comparison of recent reanalysis datasets using objective feature tracking: Storm tracks and tropical easterly waves

Data from four recent reanalysis projects [ECMWF, NCEP-NCAR, NCEP - Department of Energy ( DOE), NASA] have been diagnosed at the scale of synoptic weather systems using an objective feature tracking method. The tracking statistics indicate that, overall, the reanalyses correspond very well in the Northern Hemisphere (NH) lower troposphere, although differences for the spatial distribution of mean intensities show that the ECMWF reanalysis is systematically stronger in the main storm track regions but weaker around major orographic features. A direct comparison of the track ensembles indicates a number of systems with a broad range of intensities that compare well among the reanalyses. In addition, a number of small-scale weak systems are found that have no correspondence among the reanalyses or that only correspond upon relaxing the matching criteria, indicating possible differences in location and/or temporal coherence. These are distributed throughout the storm tracks, particularly in the regions known for small-scale activity, such as secondary development regions and the Mediterranean. For the Southern Hemisphere (SH), agreement is found to be generally less consistent in the lower troposphere with significant differences in both track density and mean intensity. The systems that correspond between the various reanalyses are considerably reduced and those that do not match span a broad range of storm intensities. Relaxing the matching criteria indicates that there is a larger degree of uncertainty in both the location of systems and their intensities compared with the NH. At upper-tropospheric levels, significant differences in the level of activity occur between the ECMWF reanalysis and the other reanalyses in both the NH and SH winters. This occurs due to a lack of coherence in the apparent propagation of the systems in ERA15 and appears most acute above 500 hPa. This is probably due to the use of optimal interpolation data assimilation in ERA15. Also shown are results based on using the same techniques to diagnose the tropical easterly wave activity. Results indicate that the wave activity is sensitive not only to the resolution and assimilation methods used but also to the model formulation.

An Integrated Traffic and Pedestrian Model_based Vision System

The paper describes a novel integrated vision system in which two autonomous visual modules are combined to interpret a dynamic scene. The first module employs a 3D model-based scheme to track rigid objects such as vehicles. The second module uses a 2D deformable model to track non-rigid objects such as people. The principal contribution is a novel method for handling occlusion between objects within the context of this hybrid tracking system. The practical aim of the work is to derive a scene description that is sufficiently rich to be used in a range of surveillance tasks. The paper describes each of the modules in outline before detailing the method of integration and the handling of occlusion in particular. Experimental results are presented to illustrate the performance of the system in a dynamic outdoor scene involving cars and people.

Four-dimensional variational assimilation of ozone profiles from the Microwave Limb Sounder on the Aura satellite

Ozone profiles from the Microwave Limb Sounder (MLS) onboard the Aura satellite of the NASA's Earth Observing System (EOS) were experimentally added to the European Centre for Medium-range Weather Forecasts (ECMWF) four-dimensional variational (4D-var) data assimilation system of version CY30R1, in which total ozone columns from Scanning Imaging Absorption Spectrometer for Atmospheric CHartographY (SCIAMACHY) onboard the Envisat satellite and partial profiles from the Solar Backscatter Ultraviolet (SBUV/2) instrument onboard the NOAA-16 satellite have been operationally assimilated. As shown by results for the autumn of 2005, additional constraints from MLS data significantly improved the agreement of the analyzed ozone fields with independent observations throughout most of the stratosphere, owing to the daily near-global coverage and good vertical resolution of MLS observations. The largest impacts were seen in the middle and lower stratosphere, where model deficiencies could not be effectively corrected by the operational observations without the additional information on the ozone vertical distribution provided by MLS. Even in the upper stratosphere, where ozone concentrations are mainly determined by rapid chemical processes, dense and vertically resolved MLS data helped reduce the biases related to model deficiencies. These improvements resulted in a more realistic and consistent description of spatial and temporal variations in stratospheric ozone, as demonstrated by cases in the dynamically and chemically active regions. However, combined assimilation of the often discrepant ozone observations might lead to underestimation of tropospheric ozone. In addition, model deficiencies induced large biases in the upper stratosphere in the medium-range (5-day) ozone forecasts.

The GlobMODEL demonstrator: assimilation of new satellite products in an operational meteorological center

As part of its Data User Element programme, the European Space Agency funded the GlobMODEL project which aimed at investigating the scientific, technical, and organizational issues associated with the use and exploitation of remotely-sensed observations, particularly from new sounders. A pilot study was performed as a "demonstrator" of the GlobMODEL idea, based on the use of new data, with a strong European heritage, not yet assimilated operationally. Two parallel assimilation experiments were performed, using either total column ozone or ozone profiles retrieved at the Royal Netherlands Meteorological Institute (KNMI) from the Ozone Monitoring Instrument (OMI). In both cases, the impact of assimilating OMI data in addition to the total ozone columns from the SCanning Imaging Absorption spectroMeter for Atmospheric CartograpHY (SCIAMACHY) on the European Centre for Medium Range Weather Forecasts (ECMWF) ozone analyses was assessed by means of independent measurements. We found that the impact of OMI total columns is mainly limited to the region between 20 and 80 hPa, and is particularly important at high latitudes in the Southern hemisphere where the stratospheric ozone transport and chemical depletion are generally difficult to model with accuracy. Furthermore, the assimilation experiments carried out in this work suggest that OMI DOAS (Differential Optical Absorption Spectroscopy) total ozone columns are on average larger than SCIAMACHY total columns by up to 3 DU, while OMI total columns derived from OMI ozone profiles are on average about 8 DU larger than SCIAMACHY total columns. At the same time, the demonstrator brought to light a number of issues related to the assimilation of atmospheric composition profiles, such as the shortcomings arising when the vertical resolution of the instrument is not properly accounted for in the assimilation. The GlobMODEL demonstrator accelerated scientific and operational utilization of new observations and its results - prompted ECMWF to start the operational assimilation of OMI total column ozone data.

The Wheal Jane wetlands model for bioremediation of acid mine drainage

Acid mine drainage (AMD) is a widespread environmental problem associated with both working and abandoned mining operations. As part of an overall strategy to determine a long-term treatment option for AMD, a pilot passive treatment plant was constructed in 1994 at Wheal Jane Mine in Cornwall, UK. The plant consists of three separate systems, each containing aerobic reed beds, anaerobic cell and rock filters, and represents the largest European experimental facility of its kind. The systems only differ by the type of pretreatment utilised to increase the pH of the influent minewater (pH <4): lime dosed (LD), anoxic limestone drain (ALD) and lime free (LF), which receives no form of pretreatment. Historical data (1994-1997) indicate median Fe reduction between 55% and 92%, sulphate removal in the range of 3-38% and removal of target metals (cadmium, copper and zinc) below detection limits, depending on pretreatment and flow rates through the system. A new model to simulate the processes and dynamics of the wetlands systems is described, as well as the application of the model to experimental data collected at the pilot plant. The model is process based, and utilises reaction kinetic approaches based on experimental microbial techniques rather than an equilibrium approach to metal precipitation. The model is dynamic and utilises numerical integration routines to solve a set of differential equations that describe the behaviour of 20 variables over the 17 pilot plant cells on a daily basis. The model outputs at each cell boundary are evaluated and compared with the measured data, and the model is demonstrated to provide a good representation of the complex behaviour of the wetland system for a wide range of variables. (C) 2004 Elsevier B.V/ All rights reserved.

Impacts of forestry on nitrogen in upland and lowland catchments: a comparison of the River Severn at Plynlimon in mid-Wales and the Bedford Ouse in south-east England using the INCA Model

The impacts of afforestation at Plynlimon in the Severn catchment, mid-Wales. and in the Bedford Ouse catchment in south-east England are evaluated using the INCA model to simulate Nitrogen (N) fluxes and concentrations. The INCA model represents the key hydrological and N processes operating in catchments and simulates the daily dynamic behaviour as well as the annual fluxes. INCA has been applied to five years of data front the Hafren and Hore headwater sub-catchments (6.8 km(2) area in total) of the River Severn at Plytilimon and the model was calibrated and validated against field data. Simulation of afforestation is achieved by altering the uptake rate parameters in the model. INCA simulates the daily N behaviour in the catchments with good accuracy as well as reconstructing the annual budgets for N release following clearfelling a four-fold increase in N fluxes was followed by a slow recovery after re-afforestation. For comparison, INCA has been applied to the large (8380 km(2)) Bedford Ouse catchment to investigate the impact of replacing 20% arable land with forestry. The reduction in fertiliser inputs from arable farming and the N uptake by the forest are predicted to reduce the N flux reaching the main river system, leading to a 33% reduction in N-Nitrate concentrations in the river water.

Modelling monsoons: understanding and predicting current and future behaviour

The global monsoon system is so varied and complex that understanding and predicting its diverse behaviour remains a challenge that will occupy modellers for many years to come. Despite the difficult task ahead, an improved monsoon modelling capability has been realized through the inclusion of more detailed physics of the climate system and higher resolution in our numerical models. Perhaps the most crucial improvement to date has been the development of coupled ocean-atmosphere models. From subseasonal to interdecadal time scales, only through the inclusion of air-sea interaction can the proper phasing and teleconnections of convection be attained with respect to sea surface temperature variations. Even then, the response to slow variations in remote forcings (e.g., El Niño—Southern Oscillation) does not result in a robust solution, as there are a host of competing modes of variability that must be represented, including those that appear to be chaotic. Understanding the links between monsoons and land surface processes is not as mature as that explored regarding air-sea interactions. A land surface forcing signal appears to dominate the onset of wet season rainfall over the North American monsoon region, though the relative role of ocean versus land forcing remains a topic of investigation in all the monsoon systems. Also, improved forecasts have been made during periods in which additional sounding observations are available for data assimilation. Thus, there is untapped predictability that can only be attained through the development of a more comprehensive observing system for all monsoon regions. Additionally, improved parameterizations - for example, of convection, cloud, radiation, and boundary layer schemes as well as land surface processes - are essential to realize the full potential of monsoon predictability. A more comprehensive assessment is needed of the impact of black carbon aerosols, which may modulate that of other anthropogenic greenhouse gases. Dynamical considerations require ever increased horizontal resolution (probably to 0.5 degree or higher) in order to resolve many monsoon features including, but not limited to, the Mei-Yu/Baiu sudden onset and withdrawal, low-level jet orientation and variability, and orographic forced rainfall. Under anthropogenic climate change many competing factors complicate making robust projections of monsoon changes. Absent aerosol effects, increased land-sea temperature contrast suggests strengthened monsoon circulation due to climate change. However, increased aerosol emissions will reflect more solar radiation back to space, which may temper or even reduce the strength of monsoon circulations compared to the present day. Precipitation may behave independently from the circulation under warming conditions in which an increased atmospheric moisture loading, based purely on thermodynamic considerations, could result in increased monsoon rainfall under climate change. The challenge to improve model parameterizations and include more complex processes and feedbacks pushes computing resources to their limit, thus requiring continuous upgrades of computational infrastructure to ensure progress in understanding and predicting current and future behaviour of monsoons.

A singular vector perspective of 4DVAR: The spatial structure and evolution of baroclinic weather systems

The extent to which the four-dimensional variational data assimilation (4DVAR) is able to use information about the time evolution of the atmosphere to infer the vertical spatial structure of baroclinic weather systems is investigated. The singular value decomposition (SVD) of the 4DVAR observability matrix is introduced as a novel technique to examine the spatial structure of analysis increments. Specific results are illustrated using 4DVAR analyses and SVD within an idealized 2D Eady model setting. Three different aspects are investigated. The first aspect considers correcting errors that result in normal-mode growth or decay. The results show that 4DVAR performs well at correcting growing errors but not decaying errors. Although it is possible for 4DVAR to correct decaying errors, the assimilation of observations can be detrimental to a forecast because 4DVAR is likely to add growing errors instead of correcting decaying errors. The second aspect shows that the singular values of the observability matrix are a useful tool to identify the optimal spatial and temporal locations for the observations. The results show that the ability to extract the time-evolution information can be maximized by placing the observations far apart in time. The third aspect considers correcting errors that result in nonmodal rapid growth. 4DVAR is able to use the model dynamics to infer some of the vertical structure. However, the specification of the case-dependent background error variances plays a crucial role.

Very large inverse problems in atmosphere and ocean modelling

For the very large nonlinear dynamical systems that arise in a wide range of physical, biological and environmental problems, the data needed to initialize a numerical forecasting model are seldom available. To generate accurate estimates of the expected states of the system, both current and future, the technique of ‘data assimilation’ is used to combine the numerical model predictions with observations of the system measured over time. Assimilation of data is an inverse problem that for very large-scale systems is generally ill-posed. In four-dimensional variational assimilation schemes, the dynamical model equations provide constraints that act to spread information into data sparse regions, enabling the state of the system to be reconstructed accurately. The mechanism for this is not well understood. Singular value decomposition techniques are applied here to the observability matrix of the system in order to analyse the critical features in this process. Simplified models are used to demonstrate how information is propagated from observed regions into unobserved areas. The impact of the size of the observational noise and the temporal position of the observations is examined. The best signal-to-noise ratio needed to extract the most information from the observations is estimated using Tikhonov regularization theory. Copyright © 2005 John Wiley & Sons, Ltd.

A singular vector perspective of 4D-Var: Filtering and interpolation

Four-dimensional variational data assimilation (4D-Var) combines the information from a time sequence of observations with the model dynamics and a background state to produce an analysis. In this paper, a new mathematical insight into the behaviour of 4D-Var is gained from an extension of concepts that are used to assess the qualitative information content of observations in satellite retrievals. It is shown that the 4D-Var analysis increments can be written as a linear combination of the singular vectors of a matrix which is a function of both the observational and the forecast model systems. This formulation is used to consider the filtering and interpolating aspects of 4D-Var using idealized case-studies based on a simple model of baroclinic instability. The results of the 4D-Var case-studies exhibit the reconstruction of the state in unobserved regions as a consequence of the interpolation of observations through time. The results also exhibit the filtering of components with small spatial scales that correspond to noise, and the filtering of structures in unobserved regions. The singular vector perspective gives a very clear view of this filtering and interpolating by the 4D-Var algorithm and shows that the appropriate specification of the a priori statistics is vital to extract the largest possible amount of useful information from the observations. Copyright © 2005 Royal Meteorological Society