Variogram Model Selection via Nonparametric Derivative Estimation

Before optimal linear prediction can be performed on spatial data sets, the variogram is usually estimated at various lags and a parametric model is fitted to those estimates. Apart from possible a priori knowledge about the process and the user's subjectivity, there is no standard methodology for choosing among valid variogram models like the spherical or the exponential ones. This paper discusses the nonparametric estimation of the variogram and its derivative, based on the spectral representation of positive definite functions. The use of the estimated derivative to help choose among valid parametric variogram models is presented. Once a model is selected, its parameters can be estimated—for example, by generalized least squares. A small simulation study is performed that demonstrates the usefulness of estimating the derivative to help model selection and illustrates the issue of aliasing. MATLAB software for nonparametric variogram derivative estimation is available at http://www-math.mit.edu/~gorsich/derivative.html. An application to the Walker Lake data set is also presented.     

New Approach to Study Extended Evolution of Supergranular Flows and Their Advection of Magnetic Elements

Using velocity and magnetogram data extracted from the full-disk field of view of MDI during the 1999 Dynamics Program, we have studied the dynamics of small-scale magnetic elements (3–7 Mm in size) over time periods as long as six days while they are readily visible on the solar disk. By exploiting concurrent time series of magnetograms and Doppler images, we have compared the motion of magnetic flux elements with the supergranular velocity field inferred from the correlation tracking of mesogranular motions. Using this new method (which combines the results from correlation tracking of mesogranules with detailed analysis of simultaneous magnetograms), it is now possible to correlate the motions of the velocity field and magnetic flux for long periods of time and at high temporal resolution. This technique can be utilized to examine the long-term evolution of supergranulation and associated magnetic fields, for it can be applied to data that span far longer time durations than has been possible previously. As tests of its efficacy, we are able to use this method to verify many results of earlier investigations. We confirm that magnetic elements travel at approximately 350 m s ^–1 throughout the duration of their lifetime as they are transported by supergranular outflows. We also find that the positions of the magnetic flux elements coincide with the supergranular network boundaries and adjust as the supergranular network itself evolves over the six days of this data set. Thus we conclude that this new method permits us to study the extended evolution of the supergranular flow field and its advection of magnetic elements. Since small-scale magnetic elements are strongly advected by turbulent convection, their dynamics can give important insight into the properties of the subsurface convection.     

Large-scale structure, the cosmic microwave background and primordial non-Gaussianity

Cosmic microwave background and large-scale structure data will shortly improve dramatically with the Microwave Anisotropy Probe and Planck Surveyor , and the Anglo-Australian 2-Degree Field and Sloan Digital Sky Survey. It is therefore timely to ask which of the microwave background and large-scale structure will provide a better probe of primordial non-Gaussianity. In this paper we consider this question, using the bispectrum as a discriminating statistic. We consider several non-Gaussian models and find that in each case the microwave background will provide a better probe of primordial non-Gaussianity. Our results suggest that if microwave background maps appear Gaussian, then apparent deviations from Gaussian initial conditions in galaxy surveys can be attributed with confidence to the effects of biasing. We demonstrate this precisely for the spatial bispectrum induced by local non-linear biasing.     

Equilibrium interface segregation in the diopside-forsterite system II: Applications of interface enrichment to mantle geochemistry

Segregation of incompatible elements at grain interfaces may have considerable influence on the physical and chemical properties of mantle rocks. Using a recently developed predictive model to estimate the interface enrichment of elements based on their mineral/melt partitioning (Hiraga and Kohlstedt, companion paper), we consider interface enrichment for a simplified model peridotite consisting of olivine, orthopyroxene, and clinopyroxene. Our calculated results reveal the following: (1) Significant amounts of heavy alkali elements and rare gases likely reside at grain-grain interfaces, whereas interface concentrations of less incompatible are less pronounced. (2) The contribution of the chemical components stored at interfaces to whole-rock chemistry strongly depends on mineral mode and, most importantly, on grain size. (3) Grain size reduction resulting from dynamic recrystallization can increase the total storage of highly incompatible elements on grain interfaces and thereby will diminish their concentration in mineral grains. (4) Analysis of Cs concentrations in mantle clinopyroxenes potentially provides estimates of the grain size of mantle rocks. (5) Transport through peridotite will be dominated by diffusion along interfaces rather than through grain interiors for elements less compatible than Lu.     

Abundance and distribution of PGE and Au in the island-arc mantle: implications for sub-arc metasomatism

Ultramafic xenoliths from a veined mantle wedge beneath the Kamchatka arc have non-chondritic, fractionated chondrite-normalized platinum-group element (PGE) patterns. Depleted (e.g., low bulk-rock Al₂O₃ and CaO contents) mantle harzburgites show clear enrichment in the Pd group relative to the Ir group PGEs and, in most samples, Pt relative to Rh and Pd. These PGE signatures most likely reflect multi-stage melting which selectively concentrates Pt in Pt–Fe alloys while strongly depleting the sub-arc mantle wedge in incompatible elements. Elevated gold concentrations and enrichment of strongly incompatible enrichment (e.g., Ba and Th) in some harzburgites suggest a late-stage metasomatism by slab-derived, saline hydrous fluids. Positive Pt, Pd, and Au anomalies coupled with Ir depletions in heavily metasomatized pyroxenite xenoliths probably reflect the relative mobility of the Pd and Ir groups (especially Os) during sub-arc metasomatism which is consistent with Os systematics in arc mantle nodules. Positive correlations between Pt, Pd, and Au and various incompatible elements (Hf, U, Ta, and Sr) also suggest that both slab-derived hydrous fluids and siliceous melts were involved in the sub-arc mantle metasomatism beneath the Kamchatka arc.     

Chromite crystallization in a multicellular magma flow: Evidence from a chromitite dike in the Oman ophiolite

The investigated chromitite dike is located at the top of an upwelling mantle structure of the Oman ophiolite (Maqsad diapir), in undeformed dunites displaying evidence for magma impregnation and circulation, just below the paleo-ridge axis. The chromitite dike is undeformed, its shape is that of an upward widening tube. It exhibits an internal layering which is roughly perpendicular to the cavity axis and comprises a vertical succession of four main layers showing a graded-bedding. Chromitite magmatic structures are beautifully preserved and result from a progressive crystallization from small euhedral crystals to wide octahedron-shaped nodules; dissolution textures provide evidence for late magmatic desequilibrium; sedimentation structures include flattening of the largest nodules. The silicate matrix comprises poikilitic forsterite and a locally abundant association of primary pargasite and plagioclase and alteration minerals (vesuvianite-chlorite-dolomite); pargasite inclusions are very abundant in the chromite. Chromite composition changes from one layer to the other and from core to rim in the chromite nodules (chromium decreases and titanium increases); Ti contents are generally high (0.4 to 0.8 wt.% TiO₂) with respect to podiform chromites. Platinum-group elements are not abundant but they show a strong fractionation at the scale of the orebody and of the main graded-bedded layers (Pd/Ir ratio varies from 0.5 to 11.5). REE patterns of chromitite parallel to those of gabbros and furthermore display a sea water related hydrothermal alteration (Ce negative anomaly).

The chromitite dike of Maqsad provides evidence for the crystallization of chromitite bodies in subvertical magma conduits below oceanic ridges; it corroborates the model of Cassard et al. (1981) and Lago et al. (1982) concerning the formation of chromitite pods in ophiolites which were later deformed and transposed into the horizontal plane due to the plastic flow prevailing away from the paleo-axial zone. Layering and chromite compositional variations are ascribed to a multicellular convective system segregating various stocks of chromite particles either in the upwelling flow of fresh magma or in the convective cells of fractionated residual magma in the confined part of the cavity. The estimated life-time for the magma influx is very short (<2 months). The parent-magma was probably of MORB-type and already fractionated (Ti-rich and PGE-poor), which is consistent with the strong evidence of magma-peridotite interactions in the core of the Maqsad diapir. Hydrous fluids were present during chromite crystallization (pargasite inclusions) suggesting that fluid-rich melts occur in the upper mantle.     

Planetary-Scale Wave Structures of the Earth’s Atmosphere Revealed from the COSMIC Observations

GPS radio occultation（GPS RO） method,an active satellite-to-satellite remote sensing technique,is capable of producing accurate,all-weather,round the clock,global refractive index,density,pressure,and temperature profiles of the troposphere and stratosphere.This study presents planetary-scale equatorially trapped Kelvin waves in temperature profiles retrieved using COSMIC（Constellation Observing System for Meteorology,Ionosphere,and Climate） satellites during 2006-2009 and their interactions with background atmospheric conditions.It is found that the Kelvin waves are not only associated with wave periods of higher than 10 days（slow Kelvin waves） with higher zonal wave numbers（either 1 or 2）,but also possessing downward phase progression,giving evidence that the source regions of them are located at lower altitudes.A thorough verification of outgoing longwave radiation（OLR） reveals that deep convection activity has developed regularly over the Indonesian region,suggesting that the Kelvin waves are driven by the convective activity.The derived Kelvin waves show enhanced（diminished） tendencies during westward（eastward） phase of the quasi-biennial oscillation（QBO） in zonal winds,implying a mutual relation between both of them.The El Nino and Southern Oscillation（ENSO） below 18 km and the QBO features between 18 and 27km in temperature profiles are observed during May 2006-May 2010 with the help of an adaptive data analysis technique known as Hilbert Huang Transform（HHT）.Further,temperature anomalies computed using COSMIC retrieved temperatures are critically evaluated during different phases of ENSO,which has revealed interesting results and are discussed in light of available literature.     

Atmospheric boundary-layer structure observed during a haze event due to forest-fire smoke

During a haze event in Baltimore, U.S.A. from July 6 to 8, 2002, smoke from forest fires in the Québec region (Canada), degraded air quality and impacted upon local climate, decreasing solar radiation and air temperature. The smoke particles in and above the atmospheric boundary layer (ABL) served as a tracer and provided a unique opportunity to investigate the ABL structure, especially entrainment. Elastic backscatter lidar measurements taken during the haze event distinctly reveal the downward sweeps (or wisps) of smoke-laden air from the free atmosphere into the ABL. Visualisations of mechanisms such as dry convection, the entrainment process, detrainment, coherent entrainment structures, and mixing inside the ABL, are presented. Thermals overshooting at the ABL top are shown to create disturbances in the form of gravity waves in the free atmosphere aloft, as evidenced by a corresponding ripple structure at the bottom of the smoke layer. Lidar data, aerosol ground-based measurements and supporting meteorological data are used to link free atmosphere, mixed-layer and ground-level aerosols. During the peak period of the haze event (July 7, 2002), the correlation between time series of elastic backscatter lidar data within the mixed layer and the scattering coefficient from a nephelometer at ground level was found to be high (R=0.96 for z =324 m, and R=0.89 for z=504 m). Ground-level aerosol concentration was at a maximum about 2 h after the smoke layer intersected with the growing ABL, confirming that the wisps do not initially reach the ground.     

Concentration profiles of particles settling in the neutral and stratified atmospheric boundary layer

An expression for the vertical equilibrium concentration profile of heavy particles, including the effects of canopy on the eddy diffusivity as well as corrections for atmospheric stability, is proposed. This expression is validated against measurements of vertical concentration profiles of corn pollen above a corn field. The fitted theoretical profiles show that particle settling is correctly accounted for. The sensitivity to variations in the turbulent Schmidt number, settling velocity and stability corrections are explicitly characterized. The importance of independent measurements of the surface flux of pollen in future experiments is noted.