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.

The impact of European legislative and technology measures to reduce air pollutants on air quality, human health and climate

European air quality legislation has reduced emissions of air pollutants across Europe since the 1970s, affecting air quality, human health and regional climate. We used a coupled composition-climate model to simulate the impacts of European air quality legislation and technology measures implemented between 1970 and 2010. We contrast simulations using two emission scenarios; one with actual emissions in 2010 and the other with emissions that would have occurred in 2010 in the absence of technological improvements and end-of-pipe treatment measures in the energy, industrial and road transport sectors. European emissions of sulphur dioxide, black carbon (BC) and organic carbon in 2010 are 53%, 59% and 32% lower respectively compared to emissions that would have occurred in 2010 in the absence of legislative and technology measures. These emission reductions decreased simulated European annual mean concentrations of fine particulate matter(PM2.5) by 35%, sulphate by 44%, BC by 56% and particulate organic matter by 23%. The reduction in PM2.5 concentrations is calculated to have prevented 80 000 (37 000–116 000, at 95% confidence intervals) premature deaths annually across the European Union, resulting in a perceived financial benefit to society of US$232 billion annually (1.4% of 2010 EU GDP). The reduction in aerosol concentrations due to legislative and technology measures caused a positive change in the aerosol radiative effect at the top of atmosphere, reduced atmospheric absorption and also increased the amount of solar radiation incident at the surface over Europe. We used an energy budget approximation to estimate that these changes in the radiative balance have increased European annual mean surface temperatures and precipitation by 0.45 ± 0.11 °C and by 13 ± 0.8 mm yr−1 respectively. Our results show that the implementation of European legislation and technological improvements to reduce the emission of air pollutants has improved air quality and human health over Europe, as well as having an unintended impact on the regional radiative balance and climate.