Ku-band radar penetration into snow cover Arctic sea ice using airborne data

Satellite radar altimetry provides data to monitor winter Arctic sea-ice thickness variability on interannual, basin-wide scales. When using this technique an assumption is made that the peak of the radar return originates from the snow/ice interface. This has been shown to be true in the laboratory for cold, dry snow as is the case on Arctic sea ice during winter. However, this assumption has not been tested in the field. We use data from an airborne normal-incidence Ku-band radar altimeter and in situ field measurements, collected during the CryoSat Validation Experiment (CryoVEx) Bay of Bothnia, 2006 and 2008 field campaigns, to determine the dominant scattering surface for Arctic snow-covered sea ice. In 2006, when the snow temperatures were close to freezing, the dominant scattering surface in 25% of the radar returns appeared closer to the snow/ice interface than the air/snow interface. However, in 2008, when temperatures were lower, the dominant scattering surface appeared closer to the snow/ice interface than the air/snow interface in 80% of the returns

Boltzmann-conserving classical dynamics in quantum time-correlation functions: "Matsubara dynamics".

We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or "classical Wigner approximation") results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their "Matsubara" values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ(2) at ħ(0) (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting "Matsubara" dynamics is inherently classical (since all terms O(ħ(2)) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.T.J.H.H., M.J.W., and S.C.A. acknowledge funding from the U.K. Engineering and Physical Sciences Research Council. A.M. acknowledges the European Lifelong Learning Programme (LLP) for an Erasmus student placement scholarship. T.J.H.H. also acknowledges a Research Fellowship from Jesus College, Cambridge and helpful discussions with Dr. Adam Harper.This is the author accepted manuscript. The final version is available from AIP via http://dx.doi.org/10.1063/1.491631

Snow property controls on modelled Ku-band altimeter estimates of first-year sea ice thickness: Case studies from the Canadian and Norwegian Arctic

Uncertainty in snow properties impacts the accuracy of Arctic sea ice thickness estimates from radar altimetry. On firstyear sea ice (FYI), spatiotemporal variations in snow properties can cause the Ku-band main radar scattering horizon to appear above the snow/sea ice interface. This can increase the estimated sea ice freeboard by several centimeters, leading to FYI thickness overestimations. This study examines the expected changes in Kuband main scattering horizon and its impact on FYI thickness estimates, with variations in snow temperature, salinity and density derived from 10 naturally occurring Arctic FYI Cases encompassing saline/non-saline, warm/cold, simple/complexly layered snow (4 cm to 45 cm) overlying FYI (48 cm to 170 cm). Using a semi-empirical modeling approach, snow properties from these Cases are used to derive layer-wise brine volume and dielectric constant estimates, to simulate the Ku-band main scattering horizon and delays in radar propagation speed. Differences between modeled and observed FYI thickness are calculated to assess sources of error. Under both cold and warm conditions, saline snow covers are shown to shift the main scattering horizon above from the snow/sea ice interface, causing thickness retrieval errors. Overestimates in FYI thicknesses of up to 65% are found for warm, saline snow overlaying thin sea ice. Our simulations exhibited a distinct shift in the main scattering horizon when the snow layer densities became greater than 440 kg/m3 , especially under warmer snow conditions. Our simulations suggest a mean Ku-band propagation delay for snow of 39%, which is higher than 25%, suggested in previous studies

Atomic-scale representation and statistical learning of tensorial properties

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general formulation of such a symmetry-adapted Gaussian process regression model, and how it can be implemented based on a scheme that generalizes the popular smooth overlap of atomic positions representation. We give examples of the performance of this framework when learning the polarizability and the ground-state electron density of a molecule

Machine-learning of atomic-scale properties based on physical principles

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear functionals of the potential energy, such as the total energy and atomic forces. We then give a detailed account of the Smooth Overlap of Atomic Positions (SOAP) representation and kernel, showing how it arises from an abstract representation of smooth atomic densities, and how it is related to several popular density-based representations of atomic structure. We also discuss recent generalisations that allow fine control of correlations between different atomic species, prediction and fitting of tensorial properties, and also how to construct structural kernels---applicable to comparing entire molecules or periodic systems---that go beyond an additive combination of local environments

Retrieval of Snow Depth on Arctic Sea Ice From Surface-Based, Polarimetric, Dual-Frequency Radar Altimetry

Snow depth on sea ice is an Essential Climate Variable and a major source of uncertainty in satellite altimetry-derived sea ice thickness. During winter of the MOSAiC Expedition, the “KuKa” dual-frequency, fully polarized Ku- and Ka-band radar was deployed in “stare” nadir-looking mode to investigate the possibility of combining these two frequencies to retrieve snow depth. Three approaches were investigated: dual-frequency, dual-polarization and waveform shape, and compared to independent snow depth measurements. Novel dual-polarization approaches yielded r2 values up to 0.77. Mean snow depths agreed within 1 cm, even for data sub-banded to CryoSat-2 SIRAL and SARAL AltiKa bandwidths. Snow depths from co-polarized dual-frequency approaches were at least a factor of four too small and had a r2 0.15 or lower. r2 for waveform shape techniques reached 0.72 but depths were underestimated. Snow depth retrievals using polarimetric information or waveform shape may therefore be possible from airborne/satellite radar altimeters

Demonstration of Metabolic and Cellular Effects of Portal Vein Ligation Using Multi-Modal PET/MRI Measurements in Healthy Rat Liver.

OBJECTIVES: In the early recognition of portal vein ligation (PVL) induced tumor progression, positron emission tomography and magnetic resonance imaging (PET/MRI) could improve diagnostic accuracy of conventionally used methods. It is unknown how PVL affects metabolic patterns of tumor free hepatic tissues. The aim of this preliminary study is to evaluate the effect of PVL on glucose metabolism, using PET/MRI imaging in healthy rat liver. MATERIALS AND METHODS: Male Wistar rats (n = 30) underwent PVL. 2-deoxy-2-(18F)fluoro-D-glucose (FDG) PET/MRI imaging (nanoScan PET/MRI) and morphological/histological examination were performed before (Day 0) and 1, 2, 3, and 7 days after PVL. Dynamic PET data were collected and the standardized uptake values (SUV) for ligated and non-ligated liver lobes were calculated in relation to cardiac left ventricle (SUVVOI/SUVCLV) and mean liver SUV (SUVVOI/SUVLiver). RESULTS: PVL induced atrophy of ligated lobes, while non-ligated liver tissue showed compensatory hypertrophy. Dynamic PET scan revealed altered FDG kinetics in both ligated and non-ligated liver lobes. SUVVOI/SUVCLV significantly increased in both groups of lobes, with a maximal value at the 2nd postoperative day and returned near to the baseline 7 days after the ligation. After PVL, ligated liver lobes showed significantly higher tracer uptake compared to the non-ligated lobes (significantly higher SUVVOI/SUVLiver values were observed at postoperative day 1, 2 and 3). The homogenous tracer biodistribution observed before PVL reappeared by 7th postoperative day. CONCLUSION: The observed alterations in FDG uptake dynamics should be taken into account during the assessment of PET data until the PVL induced atrophic and regenerative processes are completed