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.

Daily thin-ice thickness maps from modis thermal infrared imagery

Accurate knowledge of ice-production rates within the marginal ice zones of the Arctic Ocean requires monitoring of the thin-ice distribution within polynyas. The thickness of the ice layer controls the heat loss and hence the new-ice formation. An established thinice algorithm using high-resolution MODIS data allows deriving the ice-thickness distribution within polynyas. The average uncertainty is ±4.7 cm for ice thicknesses below 0.2 m. In this study, the ice-thickness distributions within the Laptev Sea polynya for the two winter seasons 2007/08 and 2008/09 are calculated. Then, a new method is applied to determine a daily MODIS thin-ice product.

Improvement and sensitivity analysis of thermal thin-ice thickness retrievals

Considering the sea ice decline in the Arctic during the last decades, polynyas are of high research interest since these features are core areas of new ice formation. The determination of ice formation requires accurate retrieval of polynya area and thin-ice thickness (TIT) distribution within the polynya.We use an established energy balance model to derive TITs with MODIS ice surface temperatures (Ts) and NCEP/DOE Reanalysis II in the Laptev Sea for two winter seasons. Improvements of the algorithm mainly concern the implementation of an iterative approach to calculate the atmospheric flux components taking the atmospheric stratification into account. Furthermore, a sensitivity study is performed to analyze the errors of the ice thickness. The results are the following: 1) 2-m air temperatures (Ta) and Ts have the highest impact on the retrieved ice thickness; 2) an overestimation of Ta yields smaller ice thickness errors as an underestimation of Ta; 3) NCEP Ta shows often a warm bias; and 4) the mean absolute error for ice thicknesses up to 20 cm is ±4.7 cm. Based on these results, we conclude that, despite the shortcomings of the NCEP data (coarse spatial resolution and no polynyas), this data set is appropriate in combination with MODIS Ts for the retrieval of TITs up to 20 cm in the Laptev Sea region. The TIT algorithm can be applied to other polynya regions and to past and future time periods. Our TIT product is a valuable data set for verification of other model and remote sensing ice thickness data.

Selective environmental stress caused by magmatic sulfur emissions from continental flood basalt eruptions

Several biotic crises during the past 300 million years have been linked to episodes of continental flood basalt volcanism, and in particular to the release of massive quantities of magmatic sulphur gas species. Flood basalt provinces were typically formed by numerous individual eruptions, each lasting years to decades. However, the environmental impact of these eruptions may have been limited by the occurrence of quiescent periods that lasted hundreds to thousands of years. Here we use a global aerosol model to quantify the sulphur-induced environmental effects of individual, decade-long flood basalt eruptions representative of the Columbia River Basalt Group, 16.5–14.5 million years ago, and the Deccan Traps, 65 million years ago. For a decade-long eruption of Deccan scale, we calculate a decadal-mean reduction in global surface temperature of 4.5 K, which would recover within 50 years after an eruption ceased unless climate feedbacks were very different in deep-time climates. Acid mists and fogs could have caused immediate damage to vegetation in some regions, but acid-sensitive land and marine ecosystems were well-buffered against volcanic sulphur deposition effects even during century-long eruptions. We conclude that magmatic sulphur from flood basalt eruptions would have caused a biotic crisis only if eruption frequencies and lava discharge rates had been high and sustained for several centuries at a time.

A reversal of climatic trends in the North Atlantic since 2005

In the mid-1990s the North Atlantic subpolar gyre warmed rapidly, which had important climate impacts, such as increased hurricane numbers, and changes to rainfall over Africa, Europe and North America. Evidence suggests that the warming was largely due to a strengthening of the ocean circulation, particularly the Atlantic Meridional Overturning Circulation (AMOC). Since the mid-1990s direct and indirect measurements have suggested a decline in the strength of the ocean circulation, which is expected to lead to a reduction in northward heat transport. Here we show that since 2005 a large volume of the upper North Atlantic Ocean has cooled significantly by approximately -0.45C or 1.5x10^22 J, reversing the previous warming trend. By analysing observations and a state-of-the-art climate model, we show that this cooling is consistent with a reduction in the strength of the ocean circulation and heat transport, linked to record low densities in the deep Labrador Sea. The low density in the deep Labrador Sea is primarily due to deep ocean warming since 1995, but a long-term freshening also played a role. The observed upper ocean cooling since 2005 is not consistent with the hypothesis that anthropogenic aerosols directly drive Atlantic temperatures.

CHP toolkit: case study of LAIe sensitivity to discontinuity of canopy cover in fruit plantations

This paper presents an open-source canopy height profile (CHP) toolkit designed for processing small-footprint full-waveform LiDAR data to obtain the estimates of effective leaf area index (LAIe) and CHPs. The use of the toolkit is presented with a case study of LAIe estimation in discontinuous-canopy fruit plantations. The experiments are carried out in two study areas, namely, orange and almond plantations, with different percentages of canopy cover (48% and 40%, respectively). For comparison, two commonly used discrete-point LAIe estimation methods are also tested. The LiDAR LAIe values are first computed for each of the sites and each method as a whole, providing “apparent” site-level LAIe, which disregards the discontinuity of the plantations’ canopies. Since the toolkit allows for the calculation of the study area LAIe at different spatial scales, between-tree-level clumpingcan be easily accounted for and is then used to illustrate the impact of the discontinuity of canopy cover on LAIe retrieval. The LiDAR LAIe estimates are therefore computed at smaller scales as a mean of LAIe in various grid-cell sizes, providing estimates of “actual” site-level LAIe. Subsequently, the LiDAR LAIe results are compared with theoretical models of “apparent” LAIe versus “actual” LAIe, based on known percent canopy cover in each site. The comparison of those models to LiDAR LAIe derived from the smallest grid-cell sizes against the estimates of LAIe for the whole site has shown that the LAIe estimates obtained from the CHP toolkit provided values that are closest to those of theoretical models.