Uncertainty of ICESat-2 ATL06- and ATL08-Derived Snow Depths for Glacierized and Vegetated Mountain Regions

Seasonal snow melt dominates the hydrologic budget across a large portion of the globe. Snow accumulation and melt vary over a broad range of spatial scales, preventing accurate extrapolation of sparse in situ observations to watershed scales. The lidar onboard the Ice, Cloud, and land Elevation, Satellite (ICESat-2) was designed for precise mapping of ice sheets and sea ice, and here we assess the feasibility of snow depth-mapping using ICESat-2 data in more complex and rugged mountain landscapes. We explore the utility of ATL08 Land and Vegetation Height and ATL06 Land Ice Height differencing from reference elevation datasets in two end member study sites. We analyze ∼3 years of data for Reynolds Creek Experimental Watershed in Idaho\u27s Owyhee Mountains and Wolverine Glacier in southcentral Alaska\u27s Kenai Mountains. Our analysis reveals decimeter-scale uncertainties in derived snow depth and glacier mass balance at the watershed scale. Both accuracy and precision decrease as slope increases: the magnitudes of the median and median of the absolute deviation of elevation errors (MAD) vary from ∼0.2 m for slopes \u3c 5° to \u3e 1 m for slopes \u3e 20°. For glacierized regions, failure to account for intra- and inter-annual evolution of glacier surface elevations can strongly bias ATL06 elevations, resulting in under-estimation of the mass balance gradient with elevation. Based on these results, we conclude that ATL08 and ATL06 observations are best suited for characterization of watershed-scale snow depth and mass balance gradients over relatively shallow slopes with thick snowpacks. In these regions, ICESat-2 elevation residual-derived snow depth and mass balance transects can provide valuable watershed scale constraints on terrain parameter- and model-derived estimates of snow accumulation and melt

Intermediate Tail Dependence: A Review and Some New Results

The concept of intermediate tail dependence is useful if one wants to quantify the degree of positive dependence in the tails when there is no strong evidence of presence of the usual tail dependence. We first review existing studies on intermediate tail dependence, and then we report new results to supplement the review. Intermediate tail dependence for elliptical, extreme value and Archimedean copulas are reviewed and further studied, respectively. For Archimedean copulas, we not only consider the frailty model but also the recently studied scale mixture model; for the latter, conditions leading to upper intermediate tail dependence are presented, and it provides a useful way to simulate copulas with desirable intermediate tail dependence structures.Comment: 25 pages, 1 figur

Importance Sampling and Stratification for Copula Models

An importance sampling approach for sampling from copula models is introduced. The proposed algorithm improves Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at least one of its components is large. Such problems often arise from dependence models in finance and insurance. The importance sampling framework we propose is particularly easy to implement for Archimedean copulas. We also show how the proposal distribution of our algorithm can be optimized by making a connection with stratified sampling. In a case study inspired by a typical insurance application, we obtain variance reduction factors sometimes larger than 1000 in comparison to standard Monte Carlo estimators when both importance sampling and quasi-Monte Carlo methods are used.NSERC, Grant 238959 NSERC, Grant 501

Distorted Copulas: Constructions and Tail Dependence

Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails

Carbon isotope discrimination in leaves of the common paperbark tree, Melaleuca quinquenervia, as a tool for quantifying past tropical and subtropical rainfall

Quantitative reconstructions of terrestrial climate are highly sought after but rare, particularly in Australia. Carbon isotope discrimination in plant leaves (Δleaf) is an established indicator of past hydroclimate because the fractionation of carbon isotopes during photosynthesis is strongly influenced by water stress. Leaves of the evergreen tree Melaleuca quinquenervia have been recovered from the sediments of some perched lakes on North Stradbroke and Fraser Islands, south-east Queensland, eastern Australia. Here, we examine the potential for using M. quinquenervia ∆leaf as a tracer of past rainfall by analysing carbon isotope ratios (δ13C) of modern leaves. We firstly assess Δleaf variation at the leaf and stand scale and find no systematic pattern within leaves or between leaves due to their position on the tree. We then examine the relationships between climate and Δleaf for an 11 year timeseries of leaves collected in a litter tray. M. quinquenervia retains its leaves for 1-4 years; thus cumulative average climate data are used. There is a significant relationship between annual mean ∆leaf and mean annual rainfall of the hydrological year for 1-4 years (i.e. 365-1460 days) prior to leaf fall (r2=0.64, p=0.003, n=11). This relationship is marginally improved by accounting for the effect of pCO2 on discrimination (r2=0.67, p=0.002, n=11). The correlation between rainfall and Δleaf, and the natural distribution of Melaleuca quinquenervia around wetlands of eastern Australia, Papua New Guinea and New Caledonia offers significant potential to infer past rainfall on a wide range of spatial and temporal scales

Implementing Loss Distribution Approach for Operational Risk

To quantify the operational risk capital charge under the current regulatory framework for banking supervision, referred to as Basel II, many banks adopt the Loss Distribution Approach. There are many modeling issues that should be resolved to use the approach in practice. In this paper we review the quantitative methods suggested in literature for implementation of the approach. In particular, the use of the Bayesian inference method that allows to take expert judgement and parameter uncertainty into account, modeling dependence and inclusion of insurance are discussed

Interest in coloured objects and behavioural budgets of individual captive freshwater turtles

Recent studies showed that freshwater turtles display inter-individual differences in variousbehavioural traits, which may influence their health and welfare in captivity due to differences inresponse to husbandry and enrichment strategies and in ability to cope with the limitations of thecaptive environment. This study investigated a possible correlation between individual level ofescape behaviour under standard enrichment conditions and level of interest in coloured objects ina group of cooters Pseudemys sp. and sliders Trachemys scripta ssp. on display at a public aquarium.Interest in different colours, colour preference and individual differences in behavioural changes inthe presence of the new enrichment were also studied. Turtles categorised as ‘high’ and ‘moderateescape behaviour’ (17–34 of behavioural budget) showed more interest in coloured objects andtended to display less escape behaviour in their presence, while turtles categorised as ‘low escapebehaviour’ (<10 of behavioural budget) were less interested in coloured objects and tended todisplay more escape behaviour in their presence. Overall, there was more interest in yellow than inred, white or green objects, with more contacts with coloured objects before feeding and at the startof each observation period and a preference for yellow against red objects. The individual differencesin behavioural changes in the presence of the new enrichment suggested that more studies into colourpreference and response to novelty in turtles would be beneficial to ensure that no individuals areunduly stressed by new enrichments

Interannual snow accumulation variability on glaciers derived from repeat, spatially extensive ground-penetrating radar surveys

There is significant uncertainty regarding the spatiotemporal distribution of seasonal snow on glaciers, despite being a fundamental component of glacier mass balance. To address this knowledge gap, we collected repeat, spatially extensive high-frequency ground-penetrating radar (GPR) observations on two glaciers in Alaska during the spring of 5 consecutive years. GPR measurements showed steep snow water equivalent (SWE) elevation gradients at both sites; continental Gulkana Glacier's SWE gradient averaged 115&thinsp;mm 100&thinsp;m−1 and maritime Wolverine Glacier's gradient averaged 440&thinsp;mm 100&thinsp;m−1 (over &gt;&thinsp;1000&thinsp;m). We extrapolated GPR point observations across the glacier surface using terrain parameters derived from digital elevation models as predictor variables in two statistical models (stepwise multivariable linear regression and regression trees). Elevation and proxies for wind redistribution had the greatest explanatory power, and exhibited relatively time-constant coefficients over the study period. Both statistical models yielded comparable estimates of glacier-wide average SWE (1&thinsp;% average difference at Gulkana, 4&thinsp;% average difference at Wolverine), although the spatial distributions produced by the models diverged in unsampled regions of the glacier, particularly at Wolverine. In total, six different methods for estimating the glacier-wide winter balance average agreed within ±11&thinsp;%. We assessed interannual variability in the spatial pattern of snow accumulation predicted by the statistical models using two quantitative metrics. Both glaciers exhibited a high degree of temporal stability, with ∼85&thinsp;% of the glacier area experiencing less than 25&thinsp;% normalized absolute variability over this 5-year interval. We found SWE at a sparse network (3 stakes per glacier) of long-term glaciological stake sites to be highly correlated with the GPR-derived glacier-wide average. We estimate that interannual variability in the spatial pattern of winter SWE accumulation is only a small component (4&thinsp;%–10&thinsp;% of glacier-wide average) of the total mass balance uncertainty and thus, our findings support the concept that sparse stake networks effectively measure interannual variability in winter balance on glaciers, rather than some temporally varying spatial pattern of snow accumulation.</p

Lepton Flavor Non-Conservation

In the present work we review the most prominent lepton flavor violating processes (\mu \ra e\gamma, \mu \ra 3e, $(\mu , e)$ conversion, $M-\bar M$ oscillations etc), in the context of unified gauge theories. Many currently fashionable extensions of the standard model are considered, such as: {\it i)} extensions of the fermion sector (right-handed neutrino); {\it ii)} minimal extensions involving additional Higgs scalars (more than one isodoublets, singly and doubly charged isosinglets, isotriplets with doubly charged members etc.); {\it iii)} supersymmetric or superstring inspired unified models emphasizing the implications of the renormalization group equations in the leptonic sector. Special attention is given to the experimentaly most interesting $(\mu - e)$ conversion in the presence of nuclei. The relevant nuclear aspects of the amplitudes are discussed in a number of fashionable nuclear models. The main features of the relevant experiments are also discussed, and detailed predictions of the above models are compared to the present experimental limits.Comment: (IOA-300/93, review article, 83p, 6 epsf figures , available upon request from [email protected])