C. D. Westbrook
University of Reading
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Featured researches published by C. D. Westbrook.
Journal of the Atmospheric Sciences | 2010
Andrew J. Heymsfield; C. D. Westbrook
Accurate estimates for the fall speed of natural hydrometeors are vital if their evolution in clouds is to be understood quantitatively. In this study, laboratory measurements of the terminal velocity yt for a variety of ice particle models settling in viscous fluids, along with wind-tunnel and field measurements of ice particles settling in air, have been analyzed and compared to common methods of computing yt fromthe literature.It is observed that while these methods work well for a number of particle types, they fail for particles with open geometries, specifically those particles for which the area ratio Ar is small (Ar is defined as the area of the particleprojectednormaltotheflow dividedbytheareaofacircumscribing disc).Inparticular, thefallspeeds of stellar and dendritic crystals, needles, open bullet rosettes, and low-density aggregates are all overestimated. These particle types are important in many cloud types: aggregates in particular often dominate snow precipitation at the ground and vertically pointing Doppler radar measurements. Based on the laboratory data, a simple modification to previous computational methods is proposed, based on the area ratio. This new method collapses the available drag data onto an approximately universal curve, and the resulting errors in the computed fall speeds relative to the tank data are less than 25% in all cases. Comparison with the (much more scattered) measurements of ice particles falling in air show strong support for this new method, with the area ratio bias apparently eliminated.
Journal of Applied Meteorology and Climatology | 2012
Robin J. Hogan; Lin Tian; Philip Brown; C. D. Westbrook; Andrew J. Heymsfield; J.D. Eastment
AbstractThe assumed relationship between ice particle mass and size is profoundly important in radar retrievals of ice clouds, but, for millimeter-wave radars, shape and preferred orientation are important as well. In this paper the authors first examine the consequences of the fact that the widely used “Brown and Francis” mass–size relationship has often been applied to maximum particle dimension observed by aircraft Dmax rather than to the mean of the particle dimensions in two orthogonal directions Dmean, which was originally used by Brown and Francis. Analysis of particle images reveals that Dmax ≃ 1.25Dmean, and therefore, for clouds for which this mass–size relationship holds, the consequences are overestimates of ice water content by around 53% and of Rayleigh-scattering radar reflectivity factor by 3.7 dB. Simultaneous radar and aircraft measurements demonstrate that much better agreement in reflectivity factor is provided by using this mass–size relationship with Dmean. The authors then examine t...
Journal of Atmospheric and Oceanic Technology | 2010
Ewan J. O'Connor; Anthony J. Illingworth; Ian M. Brooks; C. D. Westbrook; Robin J. Hogan; Fay Davies; Barbara J. Brooks
Abstract A method of estimating dissipation rates from a vertically pointing Doppler lidar with high temporal and spatial resolution has been evaluated by comparison with independent measurements derived from a balloon-borne sonic anemometer. This method utilizes the variance of the mean Doppler velocity from a number of sequential samples and requires an estimate of the horizontal wind speed. The noise contribution to the variance can be estimated from the observed signal-to-noise ratio and removed where appropriate. The relative size of the noise variance to the observed variance provides a measure of the confidence in the retrieval. Comparison with in situ dissipation rates derived from the balloon-borne sonic anemometer reveal that this particular Doppler lidar is capable of retrieving dissipation rates over a range of at least three orders of magnitude. This method is most suitable for retrieval of dissipation rates within the convective well-mixed boundary layer where the scales of motion that the D...
Physical Review E | 2004
C. D. Westbrook; Robin C. Ball; P. R. Field; Andrew J. Heymsfield
A simple model of irreversible aggregation under differential sedimentation of particles in a fluid is presented. The structure of the aggregates produced by this process is found to feed back on the dynamics in such a way as to stabilise both the exponents controlling the growth rate, and the fractal dimension of the clusters produced at readily predictable values. The aggregation of ice crystals to form snowflakes is considered as a potential application of the model.
Geophysical Research Letters | 2011
C. D. Westbrook; Anthony J. Illingworth
Using 4 years of radar and lidar observations of layer clouds from the Chilbolton Observatory in the UK, we show that almost all (95%) ice particles formed at temperatures >-20°C appear to originate from supercooled liquid clouds. At colder temperatures, there is a monotonic decline in the fraction of liquid-topped ice clouds: 50% at -27°C, falling to zero at -37°C (where homogeneous freezing of water droplets occurs). This strongly suggests that deposition nucleation plays a relatively minor role in the initiation of ice in mid-level clouds. It also means that the initial growth of the ice particles occurs predominantly within a liquid cloud, a situation which promotes rapid production of precipitation via the Bergeron-Findeison mechanism.
Journal of the Atmospheric Sciences | 2008
C. D. Westbrook; Robin J. Hogan; Anthony J. Illingworth
A new method of accurately calculating the capacitance of realistic ice particles is described: such values are key to accurate estimates of deposition and evaporation (sublimation) rates in numerical weather models. The trajectories of diffusing water molecules are directly sampled, using random ‘walkers’. By counting how many of these trajectories intersect the surface of the ice particle (which may be any shape) and how many escape outside a spherical boundary far from the particle, the capacitance of a number of model ice particle habits have been estimated, including hexagonal columns and plates, ‘scalene’ columns and plates, bullets, bullet-rosettes, dendrites, and realistic aggregate snowflakes. For ice particles with sharp edges and corners this method is an efficient and straightforward way ofsolving Laplace’s equation for the capacitance. Provided that a large enough number of random walkers are used to sample the particle geometry (∼ 10 4 ) the authors expect the calculated capacitances to be accurate to within ∼ 1%. The capacitance for our modelled aggregate snowflakes (C/Dmax = 0.25, normalised by the maximum dimension Dmax) is shown to be in close agreement with recent aircraft measurements of snowflake sublimation rates. This result shows that the capacitance of a sphere (C/Dmax = 0.5) which is commonly used in numerical models, overestimates the evaporation rate of snowflakes by a factor of two. The effect of vapor ‘screening’ by crystals growing in the vicinity of one another has also been investigated. The results clearly show that neighbouring crystals growing on a filament in cloud chamber experiments can strongly constrict the vapor supply to each other, and the resulting growth rate measurements may severely underestimate the rate for a single crystal in isolation (by a factor of 3 in our model setup).
Quarterly Journal of the Royal Meteorological Society | 2010
C. D. Westbrook; Anthony J. Illingworth; Ewan J. O'Connor; Robin J. Hogan
The properties of planar ice crystals settling horizontally have been investigated using a vertically pointing Doppler lidar. Strong specular reflections were observed from their oriented basal facets, identified by comparison with a second lidar pointing 4° from zenith. Analysis of 17 months of continuous high-resolution observations reveals that these pristine crystals are frequently observed in ice falling from mid-level mixed-phase layer clouds (85% of the time for layers at −15 °C). Detailed analysis of a case study indicates that the crystals are nucleated and grow rapidly within the supercooled layer, then fall out, forming well-defined layers of specular reflection. From the lidar alone the fraction of oriented crystals cannot be quantified, but polarimetric radar measurements confirmed that a substantial fraction of the crystal population was well oriented. As the crystals fall into subsaturated air, specular reflection is observed to switch off as the crystal faces become rounded and lose their faceted structure. Specular reflection in ice falling from supercooled layers colder than −22 °C was also observed, but this was much less pronounced than at warmer temperatures: we suggest that in cold clouds it is the small droplets in the distribution that freeze into plates and produce specular reflection, whilst larger droplets freeze into complex polycrystals. The lidar Doppler measurements show that typical fall speeds for the oriented crystals are ≈ 0.3 m s−1, with a weak temperature correlation; the corresponding Reynolds number is Re ∼ 10, in agreement with light-pillar measurements. Coincident Doppler radar observations show no correlation between the specular enhancement and the eddy dissipation rate, indicating that turbulence does not control crystal orientation in these clouds. Copyright
Geophysical Research Letters | 2004
C. D. Westbrook; Robin C. Ball; P. R. Field; Andrew J. Heymsfield
Aggregation of ice crystals is a key process governing precipitation. Individual ice crystals exhibit considerable diversity of shape, and a wide range of physical processes could influence their aggregation; despite this we show that a simple computer model captures key features of aggregate shape and size distribution reported recently from cirrus clouds. The results prompt a new way to plot the experimental size distributions leading to remarkably good dynamical scaling. That scaling independently confirms that there is a single dominant aggregation mechanism at play, albeit our model (based on undeflected trajectories to contact) does not capture its form exactly.
Quarterly Journal of the Royal Meteorological Society | 2008
C. D. Westbrook
Estimates for the sedimentation rate of realistic ice crystals at sizes smaller than 100 µm are presented. These calculations, which exploit new results for the capacitance of ice crystals, are compared with laboratory studies and found to be in good agreement. The results highlight a weakness in contemporary ice particle fall speed parametrizations for very small crystals, which can lead to sedimentation rates being overestimated by a factor of two. The theoretical approach applied here may also be useful for calculating the sedimentation rate and mobility of non-spherical aerosol particles. Copyright
Journal of the Atmospheric Sciences | 2014
Robin J. Hogan; C. D. Westbrook
AbstractIn this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times...