The influence of viscous and latent heating on crystal-rich magma flow in a conduit

The flow dynamics of crystal-rich high-viscosity magma is likely to be strongly influenced by viscous and latent heat release. Viscous heating is observed to play an important role in the dynamics of fluids with temperature-dependent viscosities. The growth of microlite crystals and the accompanying release of latent heat should play a similar role in raising fluid temperatures. Earlier models of viscous heating in magmas have shown the potential for unstable (thermal runaway) flow as described by a Gruntfest number, using an Arrhenius temperature dependence for the viscosity, but have not considered crystal growth or latent heating. We present a theoretical model for magma flow in an axisymmetric conduit and consider both heating effects using Finite Element Method techniques. We consider a constant mass flux in a 1-D infinitesimal conduit segment with isothermal and adiabatic boundary conditions and Newtonian and non-Newtonian magma flow properties. We find that the growth of crystals acts to stabilize the flow field and make the magma less likely to experience a thermal runaway. The additional heating influences crystal growth and can counteract supercooling from degassing-induced crystallization and drive the residual melt composition back towards the liquidus temperature. We illustrate the models with results generated using parameters appropriate for the andesite lava dome-forming eruption at Soufriere Hills Volcano, Montserrat. These results emphasize the radial variability of the magma. Both viscous and latent heating effects are shown to be capable of playing a significant role in the eruption dynamics of Soufriere Hills Volcano. Latent heating is a factor in the top two kilometres of the conduit and may be responsible for relatively short-term (days) transients. Viscous heating is less restricted spatially, but because thermal runaway requires periods of hundreds of days to be achieved, the process is likely to be interrupted. Our models show that thermal evolution of the conduit walls could lead to an increase in the effective diameter of flow and an increase in flux at constant magma pressure.

Can wavelets improve the representation of forecast error covariances in variational data assimilation?

Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude-height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet- based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.

A regime-dependent balanced control variable based on potential vorticity

In this paper it is argued that rotational wind is not the best choice of leading control variable for variational data assimilation, and an alternative is suggested and tested. A rotational wind parameter is used in most global variational assimilation systems as a pragmatic way of approximately representing the balanced component of the assimilation increments. In effect, rotational wind is treated as a proxy for potential vorticity, but one that it is potentially not a good choice in flow regimes characterised by small Burger number. This paper reports on an alternative set of control variables which are based around potential vorticity. This gives rise to a new formulation of the background error covariances for the Met Office's variational assimilation system, which leads to flow dependency. It uses similar balance relationships to traditional schemes, but recognises the existence of unbalanced rotational wind which is used with a new anti-balance relationship. The new scheme is described and its performance is evaluated and compared to a traditional scheme using a sample of diagnostics.

Theory and observations of ice particle evolution in cirrus using Doppler radar: evidence for aggregation

Vertically pointing Doppler radar has been used to study the evolution of ice particles as they sediment through a cirrus cloud. The measured Doppler fall speeds, together with radar-derived estimates for the altitude of cloud top, are used to estimate a characteristic fall time tc for the `average' ice particle. The change in radar reflectivity Z is studied as a function of tc, and is found to increase exponentially with fall time. We use the idea of dynamically scaling particle size distributions to show that this behaviour implies exponential growth of the average particle size, and argue that this exponential growth is a signature of ice crystal aggregation.

The response of a uniform horizontal temperature gradient to heating

The response of a uniform horizontal temperature gradient to prescribed fixed heating is calculated in the context of an extended version of surface quasigeostrophic dynamics. It is found that for zero mean surface flow and weak cross-gradient structure the prescribed heating induces a mean temperature anomaly proportional to the spatial Hilbert transform of the heating. The interior potential vorticity generated by the heating enhances this surface response. The time-varying part is independent of the heating and satisfies the usual linearized surface quasigeostrophic dynamics. It is shown that the surface temperature tendency is a spatial Hilbert transform of the temperature anomaly itself. It then follows that the temperature anomaly is periodically modulated with a frequency proportional to the vertical wind shear. A strong local bound on wave energy is also found. Reanalysis diagnostics are presented that indicate consistency with key findings from this theory.

Unimodality of wave amplitude in the northern Hemisphere

A novel statistic for local wave amplitude of the 500-hPa geopotential height field is introduced. The statistic uses a Hilbert transform to define a longitudinal wave envelope and dynamical latitude weighting to define the latitudes of interest. Here it is used to detect the existence, or otherwise, of multimodality in its distribution function. The empirical distribution function for the 1960-2000 period is close to a Weibull distribution with shape parameters between 2 and 3. There is substantial interdecadal variability but no apparent local multimodality or bimodality. The zonally averaged wave amplitude, akin to the more usual wave amplitude index, is close to being normally distributed. This is consistent with the central limit theorem, which applies to the construction of the wave amplitude index. For the period 1960-70 it is found that there is apparent bimodality in this index. However, the different amplitudes are realized at different longitudes, so there is no bimodality at any single longitude. As a corollary, it is found that many commonly used statistics to detect multimodality in atmospheric fields potentially satisfy the assumptions underlying the central limit theorem and therefore can only show approximately normal distributions. The author concludes that these techniques may therefore be suboptimal to detect any multimodality.

Is Antarctic climate most sensitive to ozone depletion in the middle or lower stratosphere?

Antarctic stratospheric ozone depletion has been associated with an observed downward trend in tropospheric geopotential height and temperature. Stratospheric ozone depletion peaks in October–November, whereas tropospheric trends are largest in December–January, concurrent with maximum ozone changes close to the tropopause. Surface temperatures are most sensitive to ozone loss near the tropopause, therefore it has been suggested that the observed tropospheric response is forced mainly by ozone depletion in the lower stratosphere. In this study the climate response to ozone depletion exclusively below 164 hPa is simulated using HadSM3-L64, and compared with simulations in which ozone depletion is prescribed exclusively above 164 hPa. Results indicate that the tropospheric response is dominated by ozone changes above 164 hPa, with ozone changes in the lowermost stratosphere playing an insignificant role. A tropospheric response is also seen in fall/winter which agrees well with observations and has not been found in modeling studies previously.

First CRDS-measurements of water vapour continuum in the 940nm absorption band

Measurements of near-infrared water vapour continuum using continuous wave cavity ring down spectroscopy (cw- CRDS) have been performed at around 10611.6 and 10685:2 cm1. The continuum absorption coefficients for N2- broadening have been determined for two temperatures and wavenumbers. These results represent the first near-IR continuum laboratory data determined within the complex spectral environment in the 940nm water vapour band and are in reasonable agreement with simulations using the semiempirical CKD formulation.

Data assimilation for a coastal area morphodynamic model: Morecambe Bay

This paper investigates the use of data assimilation in coastal area morphodynamic modelling using Morecambe Bay as a study site. A simple model of the bay has been enhanced with a data assimilation scheme to better predict large-scale changes in bathymetry observed in the bay over a 3-year period. The 2DH decoupled morphodynamic model developed for the work is described, as is the optimal interpolation scheme used to assimilate waterline observations into the model run. Each waterline was acquired from a SAR satellite image and is essentially a contour of the bathymetry at some level within the inter-tidal zone of the bay. For model parameters calibrated against validation observations, model performance is good, even without data assimilation. However the use of data assimilation successfully compensates for a particular failing of the model, and helps to keep the model bathymetry on track. It also improves the ability of the model to predict future bathymetry. Although the benefits of data assimilation are demonstrated using waterline observations, any observations of morphology could potentially be used. These results suggest that data assimilation should be considered for use in future coastal area morphodynamic models.

The biometeorology of high-altitude insect layers.

Flight at high altitude is part of a migration strategy that maximises insect population displacement. This thesis represents the first substantial analysis of insect migration and layering in Europe. Vertical-looking entomological radar has revealed specific characteristics of high-altitude flight: in particular layering (where a large proportion of the migrating insects are concentrated in a narrow altitude band). The meteorological mechanisms underpinning the formation of these layers are the focus of this thesis. Aerial netting samples and radar data revealed four distinct periods of high-altitude insect migration: dawn, daytime, dusk, and night-time. The most frequently observed nocturnal profiles during the summertime were layers. It is hypothesised that nocturnal layers initiate at a critical altitude (200–500 m above ground level) and time (20:00–22:00 hours UTC). Case study analysis, statistical analysis, and a Lagrangian trajectory model showed that nocturnal insect layers probably result from the insects’ response to meteorological conditions. Temperature was the variable most correlated with nocturnal insect layer presence and intensity because insects are poikilothermic, and temperatures experienced during high-altitude migration in temperate climates are expected to be marginal for many insects’ flight. Hierarchical effects were detected such that other variables—specifically wind speed—were only correlated with insect layer presence and intensity once temperatures were warm. The trajectory model developed comprised: (i) insect flight characteristics; (ii) turbulent winds (which cause vertical spread of the layer); and (iii) mean wind speed, which normally leads to horizontal displacements of hundreds of kilometres in a single migratory flight. This thesis has revealed that there is considerable migratory activity over the UK in the summer months, and a range of fascinating phenomena can be observed (including layers). The UK has moved from one of the least studied to perhaps the best studied environments of aerial insect migration and layering in the world.