Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

A global empirical system for probabilistic seasonal climate prediction

Preparing for episodes with risks of anomalous weather a month to a year ahead is an important challenge for governments, non-governmental organisations, and private companies and is dependent on the availability of reliable forecasts. The majority of operational seasonal forecasts are made using process-based dynamical models, which are complex, computationally challenging and prone to biases. Empirical forecast approaches built on statistical models to represent physical processes offer an alternative to dynamical systems and can provide either a benchmark for comparison or independent supplementary forecasts. Here, we present a simple empirical system based on multiple linear regression for producing probabilistic forecasts of seasonal surface air temperature and precipitation across the globe. The global CO2-equivalent concentration is taken as the primary predictor; subsequent predictors, including large-scale modes of variability in the climate system and local-scale information, are selected on the basis of their physical relationship with the predictand. The focus given to the climate change signal as a source of skill and the probabilistic nature of the forecasts produced constitute a novel approach to global empirical prediction. Hindcasts for the period 1961–2013 are validated against observations using deterministic (correlation of seasonal means) and probabilistic (continuous rank probability skill scores) metrics. Good skill is found in many regions, particularly for surface air temperature and most notably in much of Europe during the spring and summer seasons. For precipitation, skill is generally limited to regions with known El Niño–Southern Oscillation (ENSO) teleconnections. The system is used in a quasi-operational framework to generate empirical seasonal forecasts on a monthly basis.

The prediction of Northern Hemisphere tropical cyclone extended life cycles by the ECMWF Ensemble and Deterministic Prediction Systems. Part I: tropical cyclone stage

This study has explored the prediction errors of tropical cyclones (TCs) in the European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS) for the Northern Hemisphere summer period for five recent years. Results for the EPS are contrasted with those for the higher-resolution deterministic forecasts. Various metrics of location and intensity errors are considered and contrasted for verification based on IBTrACS and the numerical weather prediction (NWP) analysis (NWPa). Motivated by the aim of exploring extended TC life cycles, location and intensity measures are introduced based on lower-tropospheric vorticity, which is contrasted with traditional verification metrics. Results show that location errors are almost identical when verified against IBTrACS or the NWPa. However, intensity in the form of the mean sea level pressure (MSLP) minima and 10-m wind speed maxima is significantly underpredicted relative to IBTrACS. Using the NWPa for verification results in much better consistency between the different intensity error metrics and indicates that the lower-tropospheric vorticity provides a good indication of vortex strength, with error results showing similar relationships to those based on MSLP and 10-m wind speeds for the different forecast types. The interannual variation in forecast errors are discussed in relation to changes in the forecast and NWPa system and variations in forecast errors between different ocean basins are discussed in terms of the propagation characteristics of the TCs.

Proteins and their interacting partners: an introduction to protein–ligand binding site prediction methods

Elucidating the biological and biochemical roles of proteins, and subsequently determining their interacting partners, can be difficult and time consuming using in vitro and/or in vivo methods, and consequently the majority of newly sequenced proteins will have unknown structures and functions. However, in silico methods for predicting protein–ligand binding sites and protein biochemical functions offer an alternative practical solution. The characterisation of protein–ligand binding sites is essential for investigating new functional roles, which can impact the major biological research spheres of health, food, and energy security. In this review we discuss the role in silico methods play in 3D modelling of protein–ligand binding sites, along with their role in predicting biochemical functionality. In addition, we describe in detail some of the key alternative in silico prediction approaches that are available, as well as discussing the Critical Assessment of Techniques for Protein Structure Prediction (CASP) and the Continuous Automated Model EvaluatiOn (CAMEO) projects, and their impact on developments in the field. Furthermore, we discuss the importance of protein function prediction methods for tackling 21st century problems.

The utility of convection-permitting ensembles for the prediction of stationary convective bands

This study examines convection-permitting numerical simulations of four cases of terrain-locked quasi-stationary convective bands over the UK. For each case, a 2.2-km grid-length 12-member ensemble and 1.5-km grid-length deterministic forecast are analyzed, each with two different initialization times. Object-based verification is applied to determine whether the simulations capture the structure, location, timing, intensity and duration of the observed precipitation. These verification diagnostics reveal that the forecast skill varies greatly between the four cases. Although the deterministic and ensemble simulations captured some aspects of the precipitation correctly in each case, they never simultaneously captured all of them satisfactorily. In general, the models predicted banded precipitation accumulations at approximately the correct time and location, but the precipitating structures were more cellular and less persistent than the coherent quasi-stationary bands that were observed. Ensemble simulations from the two different initialization times were not significantly different, which suggests a potential benefit of time-lagging subsequent ensembles to increase ensemble size. The predictive skill of the upstream larger-scale flow conditions and the simulated precipitation on the convection-permitting grids were strongly correlated, which suggests that more accurate forecasts from the parent ensemble should improve the performance of the convection-permitting ensemble nested within it.

Application of data assimilation to ocean and climate prediction

Ocean prediction systems are now able to analyse and predict temperature, salinity and velocity structures within the ocean by assimilating measurements of the ocean’s temperature and salinity into physically based ocean models. Data assimilation combines current estimates of state variables, such as temperature and salinity, from a computational model with measurements of the ocean and atmosphere in order to improve forecasts and reduce uncertainty in the forecast accuracy. Data assimilation generally works well with ocean models away from the equator but has been found to induce vigorous and unrealistic overturning circulations near the equator. A pressure correction method was developed at the University of Reading and the Met Office to control these circulations using ideas from control theory and an understanding of equatorial dynamics. The method has been used for the last 10 years in seasonal forecasting and ocean prediction systems at the Met Office and European Center for Medium-range Weather Forecasting (ECMWF). It has been an important element in recent re-analyses of the ocean heat uptake that mitigates climate change.

Interdecadal changes on the seasonal prediction of the western North Pacific summer climate around the late 1970s and early 1990s

Identifying predictability and the corresponding sources for the western North Pacific (WNP) summer climate in the case of non-stationary teleconnections during recent decades benefits for further improvements of long-range prediction on the WNP and East Asian summers. In the past few decades, pronounced increases on the summer sea surface temperature (SST) and associated interannual variability are observed over the tropical Indian Ocean and eastern Pacific around the late 1970s and over the Maritime Continent and western–central Pacific around the early 1990s. These increases are associated with significant enhancements of the interannual variability for the lower-tropospheric wind over the WNP. In this study, we further assess interdecadal changes on the seasonal prediction of the WNP summer anomalies, using May-start retrospective forecasts from the ENSEMBLES multi-model project in the period 1960–2005. It is found that prediction of the WNP summer anomalies exhibits an interdecadal shift with higher prediction skills since the late 1970s, particularly after the early 1990s. Improvements of the prediction skills for SSTs after the late 1970s are mainly found around tropical Indian Ocean and the WNP. The better prediction of the WNP after the late 1970s may arise mainly from the improvement of the SST prediction around the tropical eastern Indian Ocean. The close teleconnections between the tropical eastern Indian Ocean and WNP summer variability work both in the model predictions and observations. After the early 1990s, on the other hand, the improvements are detected mainly around the South China Sea and Philippines for the lower-tropospheric zonal wind and precipitation anomalies, associating with a better description of the SST anomalies around the Maritime Continent. A dipole SST pattern over the Maritime Continent and the central equatorial Pacific Ocean is closely related to the WNP summer anomalies after the early 1990s. This teleconnection mode is quite predictable, which is realistically reproduced by the models, presenting more predictable signals to the WNP summer climate after the early 1990s.

The impact of a thermodynamic sea-ice module in the COSMO numerical weather prediction model on simulations for the Laptev Sea, Siberian Arctic

Previous versions of the Consortium for Small-scale Modelling (COSMO) numerical weather prediction model have used a constant sea-ice surface temperature, but observations show a high degree of variability on sub-daily timescales. To account for this, we have implemented a thermodynamic sea-ice module in COSMO and performed simulations at a resolution of 15 km and 5 km for the Laptev Sea area in April 2008. Temporal and spatial variability of surface and 2-m air temperature are verified by four automatic weather stations deployed along the edge of the western New Siberian polynya during the Transdrift XIII-2 expedition and by surface temperature charts derived from Moderate Resolution Imaging Spectroradiometer (MODIS) satellite data. A remarkable agreement between the new model results and these observations demonstrates that the implemented sea-ice module can be applied for short-range simulations. Prescribing the polynya areas daily, our COSMO simulations provide a high-resolution and high-quality atmospheric data set for the Laptev Sea for the period 14-30 April 2008. Based on this data set, we derive a mean total sea-ice production rate of 0.53 km3/day for all Laptev Sea polynyas under the assumption that the polynyas are ice-free and a rate of 0.30 km3/day if a 10-cm-thin ice layer is assumed. Our results indicate that ice production in Laptev Sea polynyas has been overestimated in previous studies.

Seasonal forecasts of tropical cyclone activity in a high-atmospheric-resolution coupled prediction system

Seasonal forecast skill of the basinwide and regional tropical cyclone (TC) activity in an experimental coupled prediction system based on the ECMWF System 4 is assessed. As part of a collaboration between the Center for Ocean–Land–Atmosphere Studies (COLA) and the ECMWF called Project Minerva, the system is integrated at the atmospheric horizontal spectral resolutions of T319, T639, and T1279. Seven-month hindcasts starting from 1 May for the years 1980–2011 are produced at all three resolutions with at least 15 ensemble members. The Minerva system demonstrates statistically significant skill for retrospective forecasts of TC frequency and accumulated cyclone energy (ACE) in the North Atlantic (NA), eastern North Pacific (EP), and western North Pacific. While the highest scores overall are achieved in the North Pacific, the skill in the NA appears to be limited by an overly strong influence of the tropical Pacific variability. Higher model resolution improves skill scores for the ACE and, to a lesser extent, the TC frequency, even though the influence of large-scale climate variations on these TC activity measures is largely independent of resolution changes. The biggest gain occurs in transition from T319 to T639. Significant skill in regional TC forecasts is achieved over broad areas of the Northern Hemisphere. The highest-resolution hindcasts exhibit additional locations with skill in the NA and EP, including land-adjacent areas. The feasibility of regional intensity forecasts is assessed. In the presence of the coupled model biases, the benefits of high resolution for seasonal TC forecasting may be underestimated.

Understanding advances in the simulation of the Madden-Julian Oscillation in a numerical weather prediction model.

The Madden-Julian Oscillation (MJO) is the dominant mode of intraseasonal variability in the Trop- ics. It can be characterised as a planetary-scale coupling between the atmospheric circulation and organised deep convection that propagates east through the equatorial Indo-Pacific region. The MJO interacts with weather and climate systems on a near-global scale and is a crucial source of predictability for weather forecasts on medium to seasonal timescales. Despite its global signifi- cance, accurately representing the MJO in numerical weather prediction (NWP) and climate models remains a challenge. This thesis focuses on the representation of the MJO in the Integrated Forecasting System (IFS) at the European Centre for Medium-Range Weather Forecasting (ECMWF), a state-of-the-art NWP model. Recent modifications to the model physics in Cycle 32r3 (Cy32r3) of the IFS led to ad- vances in the simulation of the MJO; for the first time the observed amplitude of the MJO was maintained throughout the integration period. A set of hindcast experiments, which differ only in their formulation of convection, have been performed between May 2008 and April 2009 to asses the sensitivity of MJO simulation in the IFS to the Cy32r3 convective parameterization. Unique to this thesis is the attribution of the advances in MJO simulation in Cy32r3 to the mod- ified convective parameterization, specifically, the relative-humidity-dependent formulation for or- ganised deep entrainment. Increasing the sensitivity of the deep convection scheme to environmen- tal moisture is shown to modify the relationship between precipitation and moisture in the model. Through dry-air entrainment, convective plumes ascending in low-humidity environments terminate lower in the atmosphere. As a result, there is an increase in the occurrence of cumulus congestus, which acts to moisten the mid-troposphere. Due to the modified precipitation-moisture relationship more moisture is able to build up which effectively preconditions the tropical atmosphere for the transition to deep convection. Results from this thesis suggest that a tropospheric moisture control on convection is key to simulating the interaction between the physics and large-scale circulation associated with the MJO.

Multiprobabilistic prediction in early medical diagnoses

This paper describes the methodology of providing multiprobability predictions for proteomic mass spectrometry data. The methodology is based on a newly developed machine learning framework called Venn machines. Is allows to output a valid probability interval. The methodology is designed for mass spectrometry data. For demonstrative purposes, we applied this methodology to MALDI-TOF data sets in order to predict the diagnosis of heart disease and early diagnoses of ovarian cancer and breast cancer. The experiments showed that probability intervals are narrow, that is, the output of the multiprobability predictor is similar to a single probability distribution. In addition, probability intervals produced for heart disease and ovarian cancer data were more accurate than the output of corresponding probability predictor. When Venn machines were forced to make point predictions, the accuracy of such predictions is for the most data better than the accuracy of the underlying algorithm that outputs single probability distribution of a label. Application of this methodology to MALDI-TOF data sets empirically demonstrates the validity. The accuracy of the proposed method on ovarian cancer data rises from 66.7 % 11 months in advance of the moment of diagnosis to up to 90.2 % at the moment of diagnosis. The same approach has been applied to heart disease data without time dependency, although the achieved accuracy was not as high (up to 69.9 %). The methodology allowed us to confirm mass spectrometry peaks previously identified as carrying statistically significant information for discrimination between controls and cases.

Advancing polar prediction capabilities on daily to seasonal time scales

It is argued that existing polar prediction systems do not yet meet users’ needs; and possible ways forward in advancing prediction capacity in polar regions and beyond are outlined. The polar regions have been attracting more and more attention in recent years, fuelled by the perceptible impacts of anthropogenic climate change. Polar climate change provides new opportunities, such as shorter shipping routes between Europe and East Asia, but also new risks such as the potential for industrial accidents or emergencies in ice-covered seas. Here, it is argued that environmental prediction systems for the polar regions are less developed than elsewhere. There are many reasons for this situation, including the polar regions being (historically) lower priority, with less in situ observations, and with numerous local physical processes that are less well-represented by models. By contrasting the relative importance of different physical processes in polar and lower latitudes, the need for a dedicated polar prediction effort is illustrated. Research priorities are identified that will help to advance environmental polar prediction capabilities. Examples include an improvement of the polar observing system; the use of coupled atmosphere-sea ice-ocean models, even for short-term prediction; and insight into polar-lower latitude linkages and their role for forecasting. Given the enormity of some of the challenges ahead, in a harsh and remote environment such as the polar regions, it is argued that rapid progress will only be possible with a coordinated international effort. More specifically, it is proposed to hold a Year of Polar Prediction (YOPP) from mid-2017 to mid-2019 in which the international research and operational forecasting community will work together with stakeholders in a period of intensive observing, modelling, prediction, verification, user-engagement and educational activities.