Rainfall estimation by rain gauge-radar combination: a concurrent multiplicative-additive approach

A procedure (concurrent multiplicative-additive objective analysis scheme [CMA-OAS]) is proposed for operational rainfall estimation using rain gauges and radar data. On the basis of a concurrent multiplicative-additive (CMA) decomposition of the spatially nonuniform radar bias, within-storm variability of rainfall and fractional coverage of rainfall are taken into account. Thus both spatially nonuniform radar bias, given that rainfall is detected, and bias in radar detection of rainfall are handled. The interpolation procedure of CMA-OAS is built on Barnes' objective analysis scheme (OAS), whose purpose is to estimate a filtered spatial field of the variable of interest through a successive correction of residuals resulting from a Gaussian kernel smoother applied on spatial samples. The CMA-OAS, first, poses an optimization problem at each gauge-radar support point to obtain both a local multiplicative-additive radar bias decomposition and a regionalization parameter. Second, local biases and regionalization parameters are integrated into an OAS to estimate the multisensor rainfall at the ground level. The procedure is suited to relatively sparse rain gauge networks. To show the procedure, six storms are analyzed at hourly steps over 10,663 km2. Results generally indicated an improved quality with respect to other methods evaluated: a standard mean-field bias adjustment, a spatially variable adjustment with multiplicative factors, and ordinary cokriging.

The chaotic frequency hopping signals for MIMO radar

In multiple-input multiple-output (MIMO) radar systems, the transmitters emit orthogonal waveforms to increase the spatial resolution. New frequency hopping (FH) codes based on chaotic sequences are proposed. The chaotic sequences have the characteristics of good encryption, anti-jamming properties and anti-intercept capabilities. The main idea of chaotic FH is based on queuing theory. According to the sensitivity to initial condition, these sequences can achieve good Hamming auto-correlation while also preserving good average correlation. Simulation results show that the proposed FH signals can achieve lower autocorrelation side lobe level and peak cross-correlation level with the increasing of iterations. Compared to the LFM signals, this sequence has higher range-doppler resolution.

Image retrieval techniques for THz applications in cultural heritage

Techniques to retrieve reliable images from complicated objects are described, overcoming problems introduced by uneven surfaces, giving enhanced depth resolution and improving image contrast. The techniques are illustrated with application to THz imaging of concealed wall paintings.

A radar-based rainfall climatology of Great Britain and Ireland

The Met Office 1km radar-derived precipitation-rate composite over 8 years (2006–2013) is examined to evaluate whether it provides an accurate representation of annual-average precipitation over Great Britain and Ireland over long periods of time. The annual-average precipitation from the radar composite is comparable with gauge measurements, with an average error of +23mmyr−1 over Great Britain and Ireland, +29mmyr−1 (3%) over the United Kingdom and –781mmyr−1 (46%) over the Republic of Ireland. The radar-derived precipitation composite is useful over the United Kingdom including Northern Ireland, but not accurate over the Republic of Ireland, particularly in the south.

Convective updraught evaluation in high-resolution NWP simulations using single-Doppler radar measurements

This study presents an evaluation of the size and strength of convective updraughts in high-resolution simulations by the UK Met Office Unified Model (UM). Updraught velocities have been estimated from range–height indicator (RHI) Doppler velocity measurements using the Chilbolton advanced meteorological radar, as part of the Dynamical and Microphysical Evolution of Convective Storms (DYMECS) project. Based on mass continuity and the vertical integration of the observed radial convergence, vertical velocities tend to be underestimated for convective clouds due to the undetected cross-radial convergence. Velocity fields from the UM at a resolution corresponding to the radar observations are used to scale such estimates to mitigate the inherent biases. The analysis of more than 100 observed and simulated storms indicates that the horizontal scale of updraughts in simulations tend to decrease with grid length; the 200 m grid length agreed most closely with the observations. Typical updraught mass fluxes in the 500 m grid length simulations were up to an order of magnitude greater than observed, and greater still in the 1.5 km grid length simulations. The effect of increasing the mixing length in the sub-grid turbulence scheme depends on the grid length. For the 1.5 km simulations, updraughts were weakened though their horizontal scale remained largely unchanged. Progressively more so for the sub-kilometre grid lengths, updraughts were broadened and intensified; horizontal scale was now determined by the mixing length rather than the grid length. In general, simulated updraughts were found to weaken too quickly with height. The findings were supported by the analysis of the widths of reflectivity patterns in both the simulations and observations.

Joint retrievals of cloud and drizzle in marine boundary layer clouds using ground-based radar, lidar and zenith radiances

Active remote sensing of marine boundary-layer clouds is challenging as drizzle drops often dominate the observed radar reflectivity. We present a new method to simultaneously retrieve cloud and drizzle vertical profiles in drizzling boundary-layer clouds using surface-based observations of radar reflectivity, lidar attenuated backscatter, and zenith radiances under conditions when precipitation does not reach the surface. Specifically, the vertical structure of droplet size and water content of both cloud and drizzle is characterised throughout the cloud. An ensemble optimal estimation approach provides full error statistics given the uncertainty in the observations. To evaluate the new method, we first perform retrievals using synthetic measurements from large-eddy simulation snapshots of cumulus under stratocumulus, where cloud water path is retrieved with an error of 31 g m−2 . The method also performs well in non-drizzling clouds where no assumption of the cloud profile is required. We then apply the method to observations of marine stratocumulus obtained during the Atmospheric Radiation Measurement MAGIC deployment in the Northeast Pacific. Here, retrieved cloud water path agrees well with independent three-channel microwave radiometer retrievals, with a root mean square difference of 10–20 g m−2.

Rayleigh scattering by hexagonal ice crystals and the interpretation of dual-polarisation radar measurements

Dual-polarisation radar measurements provide valuable information about the shapes and orientations of atmospheric ice particles. For quantitative interpretation of these data in the Rayleigh regime, common practice is to approximate the true ice crystal shape with that of a spheroid. Calculations using the discrete dipole approximation for a wide range of crystal aspect ratios demonstrate that approximating hexagonal plates as spheroids leads to significant errors in the predicted differential reflectivity, by as much as 1.5 dB. An empirical modification of the shape factors in Gans's spheroid theory was made using the numerical data. The resulting simple expressions, like Gans's theory, can be applied to crystals in any desired orientation, illuminated by an arbitrarily polarised wave, but are much more accurate for hexagonal particles. Calculations of the scattering from more complex branched and dendritic crystals indicate that these may be accurately modelled using the new expression, but with a reduced permittivity dependent on the volume of ice relative to an enclosing hexagonal prism.

The potential of flood forecasting using a variable-resolution global Digital Terrain Model and flood extents from Synthetic Aperture Radar images

A basic data requirement of a river flood inundation model is a Digital Terrain Model (DTM) of the reach being studied. The scale at which modeling is required determines the accuracy required of the DTM. For modeling floods in urban areas, a high resolution DTM such as that produced by airborne LiDAR (Light Detection And Ranging) is most useful, and large parts of many developed countries have now been mapped using LiDAR. In remoter areas, it is possible to model flooding on a larger scale using a lower resolution DTM, and in the near future the DTM of choice is likely to be that derived from the TanDEM-X Digital Elevation Model (DEM). A variable-resolution global DTM obtained by combining existing high and low resolution data sets would be useful for modeling flood water dynamics globally, at high resolution wherever possible and at lower resolution over larger rivers in remote areas. A further important data resource used in flood modeling is the flood extent, commonly derived from Synthetic Aperture Radar (SAR) images. Flood extents become more useful if they are intersected with the DTM, when water level observations (WLOs) at the flood boundary can be estimated at various points along the river reach. To illustrate the utility of such a global DTM, two examples of recent research involving WLOs at opposite ends of the spatial scale are discussed. The first requires high resolution spatial data, and involves the assimilation of WLOs from a real sequence of high resolution SAR images into a flood model to update the model state with observations over time, and to estimate river discharge and model parameters, including river bathymetry and friction. The results indicate the feasibility of such an Earth Observation-based flood forecasting system. The second example is at a larger scale, and uses SAR-derived WLOs to improve the lower-resolution TanDEM-X DEM in the area covered by the flood extents. The resulting reduction in random height error is significant.

Diagnosing observation error correlations for Doppler radar radial winds in the Met Office UKV model using observation-minus-background and observation-minus-analysis statistics

With the development of convection-permitting numerical weather prediction the efficient use of high resolution observations in data assimilation is becoming increasingly important. The operational assimilation of these observations, such as Dopplerradar radial winds, is now common, though to avoid violating the assumption of un- correlated observation errors the observation density is severely reduced. To improve the quantity of observations used and the impact that they have on the forecast will require the introduction of the full, potentially correlated, error statistics. In this work, observation error statistics are calculated for the Doppler radar radial winds that are assimilated into the Met Office high resolution UK model using a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. This is the first in-depth study using the diagnostic to estimate both horizontal and along-beam correlated observation errors. By considering the new results obtained it is found that the Doppler radar radial wind error standard deviations are similar to those used operationally and increase as the observation height increases. Surprisingly the estimated observation error correlation length scales are longer than the operational thinning distance. They are dependent on both the height of the observation and on the distance of the observation away from the radar. Further tests show that the long correlations cannot be attributed to the use of superobservations or the background error covariance matrix used in the assimilation. The large horizontal correlation length scales are, however, in part, a result of using a simplified observation operator.

On mathematical and physical principles of transformations of the coherent radar backscatter matrix

The congruential rule advanced by Graves for polarization basis transformation of the radar backscatter matrix is now often misinterpreted as an example of consimilarity transformation. However, consimilarity transformations imply a physically unrealistic antilinear time-reversal operation. This is just one of the approaches found in literature to the description of transformations where the role of conjugation has been misunderstood. In this paper, the different approaches are examined in particular in respect to the role of conjugation. In order to justify and correctly derive the congruential rule for polarization basis transformation and properly place the role of conjugation, the origin of the problem is traced back to the derivation of the antenna height from the transmitted field. In fact, careful consideration of the role played by the Green’s dyadic operator relating the antenna height to the transmitted field shows that, under general unitary basis transformation, it is not justified to assume a scalar relationship between them. Invariance of the voltage equation shows that antenna states and wave states must in fact lie in dual spaces, a distinction not captured in conventional Jones vector formalism. Introducing spinor formalism, and with the use of an alternate spin frame for the transmitted field a mathematically consistent implementation of the directional wave formalism is obtained. Examples are given comparing the wider generality of the congruential rule in both active and passive transformations with the consimilarity rule.

Les dangers de la guerre. L'image du guerrier dans le Brut de La3amon

A study of the lexis and imagery of warfare in the early C13 English adaptation of Wace's Roman de Brut by the English poet La3amon. The narrator's stance is analysed the light of the poet's priestly identity, revealing an undercurrent of disapproval of the glorification of the warrior found in La3amon's sources, and moral concern for combatants engaged in 'unjust' wars of conquest.

Digital image correlation analysis of the load transfer by implant-supported restorations

This study compared splinted and non-splinted implant-supported prosthesis with and without a distal proximal contact using a digital image correlation method. An epoxy resin model was made with acrylic resin replicas of a mandibular first premolar and second molar and with threaded implants replacing the second premolar and first molar. Splinted and non-splinted metal-ceramic screw-retained crowns were fabricated and loaded with and without the presence of the second molar. A single-camera measuring system was used to record the in-plane deformation on the model surface at a frequency of 1.0 Hz under a load from 0 to 250 N. The images were then analyzed with specialist software to determine the direct (horizontal) and shear strains along the model. Not splinting the crowns resulted in higher stress transfer to the supporting implants when the second molar replica was absent. The presence of a second molar and an effective interproximal contact contributed to lower stress transfer to the supporting structures even for non-splinted restorations. Shear strains were higher in the region between the molars when the second molar was absent, regardless of splinting. The opposite was found for the region between the implants, which had higher shear strain values when the second molar was present. When an effective distal contact is absent, non-splinted implant-supported restorations introduce higher direct strains to the supporting structures under loading. Shear strains appear to be dependent also on the region within the model, with different regions showing different trends in strain changes in the absence of an effective distal contact. (C) 2011 Elsevier Ltd. All rights reserved.