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.

The compositional and configurational heterogeneity of matrix habitats shape woodland carabid communities in wooded-agricultural landscapes

Landscape heterogeneity (the composition and configuration of matrix habitats) plays a major role in shaping species communities in wooded-agricultural landscapes. However, few studies consider the influence of different types of semi-natural and linear habitats in the matrix, despite their known ecological value for biodiversity. Objective To investigate the importance of the composition and configuration of matrix habitats for woodland carabid communities and identify whether specific landscape features can help to maintain long-term populations in wooded-agricultural environments. Methods Carabids were sampled from woodlands in 36 tetrads of 4 km2 across southern Britain. Landscape heterogeneity including an innovative representation of linear habitats was quantified for each tetrad. Carabid community response was analysed using ordination methods combined with variation partitioning and additional response trait analyses. Results Woodland carabid community response was trait-specific and better explained by simultaneously considering the composition and configuration of matrix habitats. Semi-natural and linear features provided significant refuge habitat and functional connectivity. Mature hedgerows were essential for slow-dispersing carabids in fragmented landscapes. Species commonly associated with heathland were correlated with inland water and woodland patches despite widespread heathland conversion to agricultural land, suggesting that species may persist for some decades when elements representative of the original habitat are retained following landscape modification. Conclusions Semi-natural and linear habitats have high biodiversity value. Landowners should identify features that can provide additional resources or functional connectivity for species relative to other habitat types in the landscape matrix. Agri-environment options should consider landscape heterogeneity to identify the most efficacious changes for biodiversity.

What is the shape of an air bubble on a liquid surface?

We have calculated the equilibrium shape of the axially symmetric meniscus along which a spherical bubble contacts a flat liquid surface, by analytically integrating the Young-Laplace equation in the presence of gravity, in the limit of large Bond numbers. This method has the advantage that it provides semi-analytical expressions for key geometrical properties of the bubble in terms of the Bond number. Results are in good overall agreement with experimental data and are consistent with fully numerical (Surface Evolver) calculations. In particular, we are able to describe how the bubble shape changes from hemispherical, with a shallow flat bottom, to lenticular, with a deeper, curved bottom, as the Bond number is decreased.

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.

Reverse correlation reveals how observers sample visual information when estimating three-dimensional shape

Human observers exhibit large systematic distance-dependent biases when estimating the three-dimensional (3D) shape of objects defined by binocular image disparities. This has led some to question the utility of disparity as a cue to 3D shape and whether accurate estimation of 3D shape is at all possible. Others have argued that accurate perception is possible, but only with large continuous perspective transformations of an object. Using a stimulus that is known to elicit large distance-dependent perceptual bias (random dot stereograms of elliptical cylinders) we show that contrary to these findings the simple adoption of a more naturalistic viewing angle completely eliminates this bias. Using behavioural psychophysics, coupled with a novel surface-based reverse correlation methodology, we show that it is binocular edge and contour information that allows for accurate and precise perception and that observers actively exploit and sample this information when it is available.

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.