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.

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.

Collocating satellite-based radar and radiometer measurements — methodology and usage examples

Collocations between two satellite sensors are occasions where both sensors observe the same place at roughly the same time. We study collocations between the Microwave Humidity Sounder (MHS) on-board NOAA-18 and the Cloud Profiling Radar (CPR) on-board CloudSat. First, a simple method is presented to obtain those collocations and this method is compared with a more complicated approach found in literature. We present the statistical properties of the collocations, with particular attention to the effects of the differences in footprint size. For 2007, we find approximately two and a half million MHS measurements with CPR pixels close to their centrepoints. Most of those collocations contain at least ten CloudSat pixels and image relatively homogeneous scenes. In the second part, we present three possible applications for the collocations. Firstly, we use the collocations to validate an operational Ice Water Path (IWP) product from MHS measurements, produced by the National Environment Satellite, Data and Information System (NESDIS) in the Microwave Surface and Precipitation Products System (MSPPS). IWP values from the CloudSat CPR are found to be significantly larger than those from the MSPPS. Secondly, we compare the relation between IWP and MHS channel 5 (190.311 GHz) brightness temperature for two datasets: the collocated dataset, and an artificial dataset. We find a larger variability in the collocated dataset. Finally, we use the collocations to train an Artificial Neural Network and describe how we can use it to develop a new MHS-based IWP product. We also study the effect of adding measurements from the High Resolution Infrared Radiation Sounder (HIRS), channels 8 (11.11 μm) and 11 (8.33 μm). This shows a small improvement in the retrieval quality. The collocations described in the article are available for public use.

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.

The Cold War and its aftermath in the Americas: the search for a synthetic interpretation of U.S. policy

More than two decades have passed since the fall of the Berlin Wall and the transfer of the Cold War file from a daily preoccupation of policy makers to a more detached assessment by historians. Scholars of U.S.-Latin American relations are beginning to take advantage both of the distance in time and of newly opened archives to reflect on the four decades that, from the 1940s to the 1980s, divided the Americas, as they did much of the world. Others are seeking to understand U.S. policy and inter-American relations in the post-Cold War era, a period that not only lacks a clear definition but also still has no name. Still others have turned their gaze forward to offer policies in regard to the region for the new Obama administration. Numerous books and review essays have addressed these three subjects—the Cold War, the post-Cold War era, and current and future issues on the inter-American agenda. Few of these studies attempt, however, to connect the three subjects or to offer new and comprehensive theories to explain the course of U.S. policies from the beginning of the twentieth century until the present. Indeed, some works and policy makers continue to use the mind-sets of the Cold War as though that conflict were still being fought. With the benefit of newly opened archives, some scholars have nevertheless drawn insights from the depths of the Cold War that improve our understanding of U.S. policies and inter-American relations, but they do not address the question as to whether the United States has escaped the longer cycle of intervention followed by neglect that has characterized its relations with Latin America. Another question is whether U.S. policies differ markedly before, during, and after the Cold War. In what follows, we ask whether the books reviewed here provide any insights in this regard and whether they offer a compass for the future of inter-American relations. We also offer our own thoughts as to how their various perspectives could be synthesized to address these questions more comprehensively.

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.