Several sets of equations which can be used to find the vertical velocity are examined. A distinction is made between assumptions that are based on physical considerations and those based on computational necessity. Since the equations are solved as boundary value problems it is necessary to impose boundary conditions. These are discussed. Investigations are made into the use of the overrelaxation method for solving partial differential equations with either Dirichlet or Neumann boundary conditions. Emphasis is placed upon the determination of the optimum overrelaxation factor. A simple method of calculating this factor for the ω-equation is tested. The derivation, meaning and solution of the balance equation is discussed. New methods of solving this equation are introduced and are compared with existing methods. The boundary conditions for the linear balance equation are investigated and this leads to the derivation of a new boundary condition for the balance equation. The geostrophic ω-equation is examined and the elliptic condition is derived. Appropriate boundary conditions for ω are discussed and the effects of the form of the static stability on ω and ϴt are investigated. Simple models of the atmosphere are used from which several inferences are drawn. These are tested with case studies. The inconsistency of the usual boundary conditions for ω and ϴt, is also examined.

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The sheer volume of citizen weather data collected and uploaded to online data hubs is immense. However as with any citizen data it is difficult to assess the accuracy of the measurements. Within this project we quantify just how much data is available, where it comes from, the frequency at which it is collected, and the types of automatic weather stations being used. We also list the numerous possible sources of error and uncertainty within citizen weather observations before showing evidence of such effects in real data. A thorough intercomparison field study was conducted, testing popular models of citizen weather stations. From this study we were able to parameterise key sources of bias. Most significantly the project develops a complete quality control system through which citizen air temperature observations can be passed. The structure of this system was heavily informed by the results of the field study. Using a Bayesian framework the system learns and updates its estimates of the calibration and radiation-induced biases inherent to each station. We then show the benefit of correcting for these learnt biases over using the original uncorrected data. The system also attaches an uncertainty estimate to each observation, which would provide real world applications that choose to incorporate such observations with a measure on which they may base their confidence in the data. The system relies on interpolated temperature and radiation observations from neighbouring professional weather stations for which a Bayesian regression model is used. We recognise some of the assumptions and flaws of the developed system and suggest further work that needs to be done to bring it to an operational setting. Such a system will hopefully allow applications to leverage the additional value citizen weather data brings to longstanding professional observing networks.

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Climate change projections include increasing intensity and frequency in periods of extreme weather. Investigating individual experiences of past episodes through archivebased research and oral histories can provide valuable insights to the nature of humanenvironment interactions during periods of extreme weather. Analysis of three case studies of varying meteorological, temporal and geographical characteristics, namely the 1846 flooding, the 1887–88 drought and 1946/47 winter on a local scale of southwest Wales from a qualitative perspective enables the detection of details which would not otherwise have been recognised in global and/or statistical equivalents, especially as acute meteorological extremes that straddle temporal boundaries are unlikely to be detected within compilations of instrumental data. This research highlights how individuals and communities document, are impacted, respond and mitigate against periods of extreme weather. Individual and community vulnerability to extreme weather is found to be affected by factors of amplification and resilience, namely: i) dependency on agriculture, because of its temporalities of recovery and is highly meteorologically-influenced by rain, drought and snow; ii) geographical extent of the extreme weather, as it can affect the level of aid received from remote beneficiaries; iii) technological advancements, which can help before, during and after the extreme weather by forecasting and facilitating effective responses; iv) class and economic standing, as the poor are disproportionately impacted by extreme weather; and, v) memory, through the meteorological and wider temporal context. In the light of current climate predictions, individual and/or community scale studies should form a key focus of research in addition to those which focus on policy or national responses.

Progress in numerical weather prediction (NWP) is made through better understand¬ing of the physical processes represented in numerical models and their impacts on the dynamics of large-scal~ weather systems. Here, potential vorticity (PV) tracer diagnostics are used to investigate the representation of processes in the Met Office Unified Model (MetG:l1). An exact budget of the PV tracers is derived and a "dynamics-tracer inconsistency" diagnostic implemented to quantify non-conservation of PV by the dynamical core which was not previously accounted for. It is shown that non-conservation of PV by the dy¬namical core can have comparable tendencies to the dominant physical processes implying that non-conservation of PV by a dynamical core can, and should, be quantified alongside PV modification by physical processes. Recent work has shown that the sharpness of the extratropical tropopause declines with lead time in KWP models. In the MetUM, the advection scheme is shown to result in an exponential decay of tropopause sharpness and non-conservative processes are shown to sharpen the tropopause. The systematic errors in tropopause-level PV are comparable to the tendencies associated with physical processes, suggesting that the systematic error in tropopause sharpness could be significantly rednced through realistic adjustments to the model physics. I' Turbulent mixing within the boundary layer has been previously shown to produce positive PV anomalies that can be advected into cyclones and reduce growth rates through an increase in static stability; however, it is unclear whether N\VP models correctly represent this mechanism. In the MetUM, the generation of these positive PV anomalies is found to be less clear due to large cancellations with other physical processes in the cold sector. Front-relative compositing .is used to separate the cold and warm sectors, providing the basis for investigating PV generation in the boundary layer systematically by compositing over many fronts.

This thesis will provide an overview of the knowledge of interplanetary coronal mass ejections (ICMEs), and of the methods used to predict the arrival of Earth-directed ICMEs in near-Earth space. The ability to accurately predict both their transit time and arrival speed is important, as ICMEs are a space weather hazard, and may have detrimental effects on human technology. I present three pieces of research: an analysis of real-time predictions of ICME arrival speed and transit time made from Solar TErrestrial RElations Observatory (STEREO) real-time data by SolarStormwatch’s citizen scientists; an analysis of hindcasts of ICME arrival speed and transit time made using STEREO’s higher resolution science data, covering the same time period as the first research piece; and a study of the drag force model, and its use as a quick method for predicting ICME arrival speed and transit time. This work could provide useful information on the best image resolution for accurate ICME predictions for future missions to study ICME propagation.