Some thoughts on inference in the analysis of spatial data

Statistical inference is important for all those who engage in the analysis of spatial data. The issue is becoming increasingly important given the explosion in the availability of spatial data and the proliferation of Geographic Information Systems (GIS) across different academic disciplines and application areas. The aim of this paper is to provide a brief overview of some of the concepts and controversies inherent in statistical inference in the hope of raising the level of awareness within the geographic information science community that different points of view exist when it comes to inference. We argue that the concept of statistical inference in spatial data analysis and spatial modelling is perhaps broader than many GIS users imagine. In particular, we argue that different types of inference exist and that process inference is just as valid as sample inference, even though the latter appears to dominate the GIS literature.     

A local stability analysis of astronomical disks

Abstract

A fifth-order dispersion relation describing the local stability of a differentially rotating flow against small perturbations is derived. Finite viscosity and conductivity and both vertical (parallel to the rotation axis) and radial gradients in density, temperature and pressure are included. A general form is assumed for the equation of state, although this is not exploited in the paper. A number of special cases are studied: with negligible viscosity and conductivity, it is shown that modes can often be separated into two high frequency (modified acoustic), two intermediate frequency (combined inertial and internal waves) and a low frequency mode. In convectively unstable situations the intermediate frequency modes may be replaced by a damped/growing pair of instablities. Various criteria for mode excitation are given. It is shown that viscosity always inhibits instability at very short wavelengths, while non-zero conductivity may destabilize the flow. At intermediate wavelengths viscosity could also play a destabilizing role. A parameter study of the effects of fluctuations in the conductivity shows that it could cause mode excitation under certain circumstances.     

Climate change and the oceans – What does the future hold?

The ocean has been shielding the earth from the worst effects of rapid climate change by absorbing excess carbon dioxide from the atmosphere. This absorption of CO₂ is driving the ocean along the pH gradient towards more acidic conditions. At the same time ocean warming is having pronounced impacts on the composition, structure and functions of marine ecosystems. Warming, freshening (in some areas) and associated stratification are driving a trend in ocean deoxygenation, which is being enhanced in parts of the coastal zone by upwelling of hypoxic deep water. The combined impact of warming, acidification and deoxygenation are already having a dramatic effect on the flora and fauna of the oceans with significant changes in distribution of populations, and decline of sensitive species. In many cases, the impacts of warming, acidification and deoxygenation are increased by the effects of other human impacts, such as pollution, eutrophication and overfishing.     

Trace-element composition and zoning in clinopyroxene- and amphibole-group minerals: Implications for element partitioning and evolution of carbonatites

The present work is a first comprehensive study of the trace-element composition and zoning in clinopyroxene- and amphibole-group minerals from carbonatites, incorporating samples from 14 localities worldwide (Afrikanda, Aley, Alnö, Blue River, Eden Lake, Huayangchuan, Murun, Oka, Ozernaya Varaka, Ozernyi, Paint Lake, Pinghe, Prairie Lake, Turiy Mys). The new electron-microprobe data presented here significantly extend the known compositional range of clinopyroxenes and amphiboles from carbonatites. These data confirm that calcic and sodic clinopyroxenes from carbonatites are not separated by a compositional gap, instead forming an arcuate trend from nearly pure diopside through intermediate aegirine–augite compositions confined to a limited range of CaFeSi₂O₆ contents (15–45 mol%) to aegirine with < 25 mol% of CaMgSi₂O₆ and a negligible proportion of CaFeSi₂O₆. A large set of LA-ICPMS data shows that the clinopyroxenes of different composition are characterized by relatively low levels of Cr, Co and Ni (≤ 40 ppm) and manifold variations in the concentration of trivalent lithophile and some incompatible elements (1–150 ppm Sc, 26–6870 ppm V, 5–550 ppm Sr, 90–2360 ppm Zr, and nil to 150 ppm REE), recorded in some cases within a single crystal. The relative contribution of clinopyroxenes to the whole-rock Rb, Nb, Ta, Th and U budget is negligible. The major-element compositional range of amphiboles spans from alkali- and Al-poor members (tremolite) to Na–Al-rich Mg- or, less commonly, Fe-dominant members (magnesiohastingsite, hastingsite and pargasite), to calcic–sodic, sodic and potassic–sodic compositions intermediate between magnesio-ferrikatophorite, richterite, magnesioriebeckite, ferri-nyböite and (potassic-)magnesio-arfvedsonite. In comparison with the clinopyroxenes, the amphiboles contain similar levels of tetravalent high-field-strength elements (Ti, Zr and Hf) and compatible transition elements (Cr, Co and Ni), but are capable of incorporating much higher concentrations of Sc and incompatible elements (up to 500 ppm Sc, 43 ppm Rb, 1470 ppm Sr, 1230 ppm Ba, 80 ppm Pb, 1070 ppm REE, 140 ppm Y, and 180 ppm Nb). In some carbonatites, amphiboles contribute as much as 25% of the Zr + Hf, 15% of the Sr and 35% of the Rb + Ba whole-rock budget. Both clinopyroxenes and amphiboles may also host a significant share (~ 10%) of the bulk heavy-REE content. Our trace-element data show that the partitioning of REE between clinopyroxene (and, in some samples, amphibole) and the melt is clearly bimodal and requires a revision of the existing models assuming single-site REE partitioning. Clinopyroxenes and amphiboles from carbonatites exhibit a diversity of zoning patterns that cannot be explained exclusively on the basis of crystal chemistry and relative compatibility of different trace-element in these minerals. Paragenetic analysis indicates that in most cases, the observed zoning patterns develop in response to removal of selected trace elements by phases co-precipitating with clinopyroxene and amphibole (especially magnetite, fluorapatite, phlogopite and pyrochlore). With the exception of magnesiohastingsite–richterite sample from Afrikanda, the invariability of trace-element ratios in the majority of zoned clinopyroxene and amphibole crystals implies that fluids are not involved in the development of zoning in these minerals. The implications of the new trace-element data for mineral exploration targeting REE, Nb and other types of carbonatite-hosted rare-metal mineralization are discussed.     

面理弯切轴测量技术在造山带研究中的应用——以美国阿肯色河地区为例

基于变形分解理论提出的面理弯切轴测量技术,通过对变斑晶中多期面理的测定分析,为厘定造山运动中的变形过程提供了新的精确定量研究手段。面理弯切轴数据已经被用于解决地质领域多种问题,例如:研究造山运动过程中变形变质历史以及在区域和造山带尺度对比多期变质作用;论证变斑晶生长过程是否发生旋转;变斑晶成核生长与区域变形过程之间的关系;重建板块运动历史过程;约束不同地质事件的发生时限;划分复杂变形分解类型以及岩浆侵位机制及时限研究。本文主要介绍面理弯切轴测量方法的原理、具体测定方法、研究意义及应用范围,并以美国阿肯色地区为例,详细介绍了面理弯切轴测量技术在造山运动过程区域变形历史重建中的应用。     

A simple model illustrating the virtue of replication for long-term information preservation

Each year destructive events might cause loss of data in members of an archival federation. This paper provides a ‘back-of-the-envelope’ model for the fraction of the federated data collection that survives after a certain number of years. It also discusses some simple parameterizations of factors that contribute to the trade offs between cost and survival of information.     

A Truncated Pareto Model to Estimate the Under Recovery of Large Diamonds

The metallurgical recovery processes in diamond mining may, under certain circumstances, cause an under-recovery of large diamonds. In order to predict high quantiles or tail probabilities we use a Bayesian approach to fit a truncated Generalized Pareto Type distribution to the tail of the data consisting of the weights of individual diamonds. Based on the estimated tail probability, the expected number of diamonds larger than a specified weight can be estimated. The difference between the expected and observed frequencies of diamond weights above an upper threshold provides an estimate of the number of diamonds lost during the recovery process.     

How well do integrated assessment models simulate climate change?

Integrated assessment models (IAMs) are regularly used to evaluate different policies of future emissions reductions. Since the global costs associated with these policies are immense, it is vital that the uncertainties in IAMs are quantified and understood. We first demonstrate the significant spread in the climate system and carbon cycle components of several contemporary IAMs. We then examine these components in more detail to understand the causes of differences, comparing the results with more complex climate models and earth system models (ESMs), where available. Our results show that in most cases the outcomes of IAMs are within the range of the outcomes of complex models, but differences are large enough to matter for policy advice. There are areas where IAMs would benefit from improvements (e.g. climate sensitivity, inertia in climate response, carbon cycle feedbacks). In some cases, additional climate model experiments are needed to be able to tune some of these improvements. This will require better communication between the IAM and ESM development communities.     

Hurricane effects on subtropical pine rocklands of the Florida Keys

We investigate the effects of Hurricane Wilma??s storm surge (23?C24 October 2005) on the dominant tree Pinus elliottii var densa (South Florida slash pine) and rare plant species in subtropical pine rocklands of the Lower Florida Keys. We examine the role of elevation on species abundance in 1995 (Hurricane Betsy in 1965), 2005 (Hurricane Georges in 1998), and 2008 (Hurricane Wilma in 2005) to investigate if hurricanes influence abundance by eliminating plants at lower elevation on Big Pine Key, the largest island in the Lower Florida Keys. We compare densities before and after Hurricane Wilma over the 2005?C2008 sampling period and examine the role of elevation on changes in pine and rare species densities three years after Hurricane Wilma. We use elevation to assess the impact of hurricanes because elevation determined whether a location was influenced by storm surge (maximum surge of 2 m) in the Lower Florida Keys, where pine rocklands occur at a maximum elevation of 3 m. In 1995 (30 years after a major storm), elevation did not explain the abundance of South Florida slash pine or Chamaecrista lineata, but explained significant variation in abundance of Chamaesyce deltoidea. The latter two species are rare herbaceous plants restricted to pine rocklands. In 2008, 3 years after Hurricane Wilma, the positive relationship between elevation and abundance was strongest for South Florida slash pine, C. deltoidea, and C. lineata. Effects of Hurricane Wilma were not significant for rare species with wider distribution, occurring in plant communities adjacent to pine rocklands and in disturbed rocklands. Our results suggest that hurricanes drive population dynamics of South Florida slash pine and rare species that occur exclusively in pine rocklands at higher elevations. Rare species restricted to pine rocklands showed dramatic declines after Hurricane Wilma and were eliminated at elevations <0.5 m. Widely distributed rare species did not show significant changes in density after Hurricane Wilma. Abundance increased with elevation for South Florida slash pine and C. lineata after the hurricane. In an environment influenced by sea level rise, concrete plans to conserve pine ecosystems are warranted. Results from this study will help define conservation strategies by strengthening predictive understanding of plant responses to disturbance in the backdrop of sea level rise.     

Assessment of sea level rise impacts on human population and real property in the Florida Keys

Comparative analysis of the energy and carbon balances of wood vs. non-wood products is a complex issue. In this paper we discuss the definition of an appropriate functional unit and the establishment of effective system boundaries in terms of activity, time and space, with an emphasis on the comparison of buildings. The functional unit can be defined at the level of building component, complete building, or services provided by the built environment. Energy use or carbon emissions per unit of mass or volume of material is inadequate as a functional unit because equal masses or volumes of different materials do not fulfil the same function. Activity-based system boundaries include life cycle processes such as material production, product operation, and post-use material management. If the products compared are functionally equivalent, such that the impacts occurring during the operation phase are equal, we suggest that this phase may be dropped from the analysis allowing a focus on material flows. The use of wood co-products as biofuel can be analytically treated through system expansion, and compared to an alternative of providing the same energy service with fossil fuels. The assumed production of electricity used for material processing is another important energy-related issue, and we suggest that using marginal production data is more appropriate than average production. Temporal system boundaries include such aspects of the wood life cycle as the dynamics of forest growth including regeneration and saturation, the availability of residue biofuels at different times, and the duration of carbon storage in products. The establishment of spatial boundaries can be problematic, because using wood-based materials instead of non-wood materials requires more land area to capture solar energy and accumulate biomass. We discuss several possible approaches to meet this challenge, including the intensification of land use to increase the time rate of biomass production. Finally, we discuss issues related to scaling up an analysis of wood substitution from the micro-level to the macro-level of national, regional or global.