Multivariable variogram and its application to the linear model of coregionalization

In this article, we present the multivariable variogram, which is defined in a way similar to that of the traditional variogram, by the expected value of a distance, squared, in a space withp dimensions. Combined with the linear model of coregionalization, this tool provides a way for finding the elementary variograms that characterize the different spatial scales contained in a set of data withp variables. In the case in which the number of elementary components is less than or equal to the number of variables, it is possible, by means of nonlinear regression of variograms and cross-variograms, to estimate the coregionalization parameters directly in order to obtain the elementary variables themselves, either by cokriging or by direct matrix inversion. This new tool greatly simplifies the procedure proposed by Matheron (1982) and Wackernagel (1985). The search for the elementary variograms is carried out using only one variogram (multivariable), as opposed to thep(p + 1)/2 required by the Matheron approach. Direct estimation of the linear coregionalization model parameters involves the creation of semipositive definite coregionalization matrices of rank 1.     

Generalized cross-validation for covariance model selection

A weighted cross-validation technique known in the spline literature as generalized cross-validation (GCV), is proposed for covariance model selection and parameter estimation. Weights for prediction errors are selected to give more importance to a cluster of points than isolated points. Clustered points are estimated better by their neighbors and are more sensitive to model parameters. This rational weighting scheme also provides a simplifying significantly the computation of the cross-validation mean square error of prediction. With small- to medium-size datasets, GCV is performed in a global neighborhood. Optimization of usual isotropic models requires only a small number of matrix inversions. A small dataset and a simulation are used to compare performances of GCV to ordinary cross-validation (OCV) and least-squares filling (LS).     

The fifth order geomagnetic multipole: The duotrigintupole

Summary The notion of a dipole is generalized to the case of the fifth order spherical harmonic coefficients of the geomagnetic potential. The corresponding five axes and fifth order multipole strength are computed for ten epochs in the interval 1845 to 1965.     

Lunar behaviour of boron contrasted with the terrestrial boron cycle

Abstract— Fifty-eight lunar rocks have been analysed by prompt gamma neutron activation for B, Gd and Sm. The data were interpreted together with published analyses for Li and other elements. The behaviour of B in lunar rocks is virtually identical to that of Sm, Gd, Li and the other incompatible LIL (Large Ion Lithophile) and HFS (High Field Strength) elements, collectively known as the KREEP component. To a first approximation, the distribution of B concentrations in all lunar rocks can be described as a two-component mixture of KREEP, with ～32 ppm, and B-free mare basalts and anorthositic rocks. The lunar B abundance, estimated from correlations with other KREEP elements, is ～0.14 ppm. Alpha-track images of the analysed lunar rocks were made from thin sections specially prepared to avoid contamination from terrestrial B. They provided surprising evidence that the distributions of B and Li within individual rocks fall into four categories: (1) substitution in mineral structures; (2) in irregular minute particles, disseminated through the rock with no apparent connection with mineralogy; (3) as aggregate properties of rock fragments, acquired prior to assembly in a breccia; and, (4) as aggregate properties of a breccia matrix, distinct from unaffected clasts. Only category (1) is encountered in terrestrial rocks. Categories (2), (3) and (4) become progressively more important as the abundance of KREEP components increases, and it is concluded that the alpha-track images probably show the localisation of not only B and Li but all the KREEP elements. In terrestrial rocks, such textures could be understood in terms of successive episodes of permeation by solutions followed by brecciation, then cementation. It is difficult to adapt such a mechanism to a dry Moon, with brecciation imposed by impact melting. The linear correlation of lunar B and Gd contrasts strongly with the relationship seen in terrestrial rocks, where the presence of water creates a terrestrial B cycle quite different from that of Gd and other lunar incompatible elements.     

Changes in stream water quality due to logging of the boreal forest in the Montmorency Forest,Québec

Summer stream water quality was monitored before and following the logging of 50% of the boreal forest within three small watersheds (<50 ha) nested in the ‘Ruisseau des Eaux‐Volées’ Experimental Watershed, Montmorency Forest (Québec, Canada). Logging was conducted in winter, on snow cover according to recommended best management practices (BMPs) to minimize soil disturbance and protect advance growth. A 20‐m forest buffer was maintained along perennial streams. In watershed 7·2, cut‐blocks were located near the stream network and logging was partially allowed within the riparian buffer zone. In watersheds 7·5 and 7·7, logging occurred farther away from the stream network. Observations were also made for watershed 7·3 that collected the runoff from watersheds 7·2 and 7·5, and watershed 7·6, the uproad portion of watershed 7·7. The control watershed 0·2 was contiguous to the impacted watersheds and remained undisturbed. Following clearcutting, changes in summer daily maximum and minimum stream temperatures remained within ± 1 °C while changes in diurnal variation did not decrease by more than 0·5 °C. Concentrations of NO₃^? greatly increased by up to 6000% and concentrations of K⁺ increased by up to 300% during the second summer after logging. Smaller increases were observed for Fe_total (up to 71%), specific conductance (up to 26%), and Mg²⁺ (up to 19%). Post‐logging pH decreased slightly by no more than 7% while PO₄^3? concentration remained relatively constant. Suspended sediment concentrations appeared to increase during post‐logging, but there was not enough pre‐logging data to statistically confirm this result. Logging of moderate intensity and respecting established BMPs may account for the limited changes of water quality parameters and the low exceedances of the criteria for the protection of aquatic life. The proximity of the cutover to the stream network and logging within the riparian zone did not appear to affect water quality. Copyright © 2008 John Wiley & Sons, Ltd.     

The water impacts of climate change mitigation measures

A variety of proposed activities to mitigate greenhouse gas emissions will impact on scarce water resources, which are coming under increasing pressure in many countries due to population growth and shifting weather patterns. However, the integrated analysis of water and carbon impacts has been given limited attention in greenhouse mitigation planning. In this Australian case study, we analyse a suite of 74 mitigation measures ranked as highest priority by one influential analysis, and we find that they have highly variable consequences for water quantity. We find: (1) The largest impacts result from land-based sequestration, which has the potential to intercept large quantities of water and reduce catchment yields, estimated to exceed 100 Mm³/MtCO₂-e of carbon mitigated (100,000 l per tonne CO₂-e). (2) Moderate impacts result from some renewable power options, including solar thermal power with a water cost estimated at nearly 4 Mm³/MtCO₂-e. However, the water impacts of solar thermal power facilities could be reduced by designing them to use existing power-related water supplies or to use air or salt-water cooling. (3) Wind power, biogas, solar photovoltaics, energy efficiency and operational improvements to existing power sources can reduce water demand through offsetting the water used to cool thermal power generation, with minor savings estimated at 2 Mm³/MtCO₂-e and amounting to nearly 100 Mm³ of water saved in Australia per annum in 2020. This integrated analysis significantly changes the attractiveness of some mitigation options, compared to the case where water impacts are not considered.     

The lower limit of the Doppler factor for a Fermi blazar sample

We selected 457 blazars(193 flat spectrum radio quasars, 61 lowsynchrotron peaked blazars, 69 intermediate-synchrotron peaked blazars and 134high-synchrotron peaked blazars) from the second Fermi-LAT catalog(2FGL) of γ-ray sources, which have X-ray observations. We calculated the lower limits for their Doppler factors, δγ, and compared the lower limits with the available Doppler factors and the apparent superluminal velocities in the literature.     

Envisat and SARAL/AltiKa Observations of the Antarctic Ice Sheet: A Comparison Between the Ku-band and Ka-band

The AltiKa altimeter onboard SARAL is a joint CNES/ISRO mission launched in February 2013 that has the same 35 days repeat orbit of the previous European altimeters, Envisat, and ERS-1/2. SARAL/AltiKa is thus a unique opportunity to extend the repeat observations of this orbit that have been surveyed since 1991. However, the altimeter operates in Ka-band, which is higher than the previous frequencies, and offers new paths of investigation. The penetration depth is theoretically reduced from around 10 m in Ku-band to less than 1 m in Ka-band, such that the volume echo originates from the near subsurface. Second, the sharper antenna aperture leads to a narrower leading edge that reduces the impact of the ratio between surface and volume echoes of the height retrieval. Indeed, the spatial and temporal observations of AltiKa at cross-over points and along-track indicate that the impact of backscatter changes on the height decreasesfrom 0.3 m/dB for the Ku-band to only 0.05 m/dB for the Ka-band. Therefore, the height measurement is stable over time. Moreover, the volume echo in the Ka-band results from the near subsurface layer and is mostly controlled by ice grain size, unlike the Ku-band.     

SN 2009ip and SN 2010mc as dual-shock Quark-Novae

In recent years a number of double-humped supernovae （SNe） have been discovered. This is a feature predicted by the dual-shock Quark-Nova （QN） model where an SN explosion is followed （a few days to a few weeks later） by a QN explo- sion. SN 2009ip and SN 2010mc are the best observed examples of double-humped SNe. Here, we show that the dual-shock QN model naturally explains their light curves including the late time emission, which we attribute to the interaction between the mixed SN and QN ejecta and the surrounding circumstellar matter. Our model applies to any star （O-stars, luminous blue variables, Wolf-Rayet stars, etc.） provided that the mass involved in the SN explosion is ~ 20 Mo which provides good conditions for forming a QN.