A Geostatistical Framework for Area‐to‐Point Spatial Interpolation

The spatial prediction of point values from areal data of the same attribute is addressed within the general geostatistical framework of change of support; the term support refers to the domain informed by each datum or unknown value. It is demonstrated that the proposed geostatistical framework can explicitly and consistently account for the support differences between the available areal data and the sought‐after point predictions. In particular, it is proved that appropriate modeling of all area‐to‐area and area‐to‐point covariances required by the geostatistical frame‐work yields coherent (mass‐preserving or pycnophylactic) predictions. In other words, the areal average (or areal total) of point predictions within any arbitrary area informed by an areal‐average (or areal‐total) datum is equal to that particular datum. In addition, the proposed geostatistical framework offers the unique advantage of providing a measure of the reliability (standard error) of each point prediction. It is also demonstrated that several existing approaches for area‐to‐point interpolation can be viewed within this geostatistical framework. More precisely, it is shown that (i) the choropleth map case corresponds to the geostatistical solution under the assumption of spatial independence at the point support level; (ii) several forms of kernel smoothing can be regarded as alternative (albeit sometimes incoherent) implementations of the geostatistical approach; and (iii) Tobler's smooth pycnophylactic interpolation, on a quasi‐infinite domain without non‐negativity constraints, corresponds to the geostatistical solution when the semivariogram model adopted at the point support level is identified to the free‐space Green's functions (linear in 1‐D or logarithmic in 2‐D) of Poisson's partial differential equation. In lieu of a formal case study, several 1‐D examples are given to illustrate pertinent concepts.     

Reconstructing Population Density Surfaces from Areal Data: A Comparison of Tobler's Pycnophylactic Interpolation Method and Area-to-Point Kriging

We compare Tobler's pycnophylactic interpolation method with the geostatistical approach of area-to-point kriging for distributing population data collected by areal unit in 18 census tracts in Ann Arbor for 1970 to reconstruct a population density surface. In both methods, (1) the areal data are reproduced when the predicted population density is upscaled; (2) physical boundary conditions are accounted for, if they exist; and (3) inequality constraints, such as the requirement of non-negative point predictions, are satisfied. The results show that when a certain variogram model, that is, the de Wijsian model corresponding to the free-space Green's function of Laplace's equation, is used in the geostatistical approach under the same boundary condition and constraints with Tobler's approach, the predicted population density surfaces are almost identical (up to numerical errors and discretization discrepancies). The implications of these findings are twofold: (1) multiple attribute surfaces can be constructed from areal data using the geostatistical approach, depending on the particular point variogram model adopted—that variogram model need not be the one associated with Tobler's solution and (2) it is the analyst's responsibility to justify whether the smoothness criterion employed in Tobler's approach is relevant to the particular application at hand. A notable advantage of the geostatistical approach over Tobler's is that it allows reporting the uncertainty or reliability of the interpolated values, with critical implications for uncertainty propagation in spatial analysis operations.     

Loose‐footed Sails of the Egyptian New Kingdom Ships

The relief from the temple of Ramesses III (1184–1153 BC) in Medinet Habu is often considered to be the most ancient representation of a brailed sail. According to many researchers, the loose‐footed sail and the system of brails were invented in the ancient countries of the Syro‐Canaanite coast and were later adopted by the Ancient Egyptians. However, iconographic material from Ancient Egypt testifies to the indigenous origin of a loose‐footed sail. The article presents an unknown relief from the Amarna period (1352–1336 BC) that further supports this hypothesis.     

The Wadi al‐Hijr (Sultanate of Oman) in the third millennium BC

In 2010–11 a pedestrian survey of the western end of Wadi al‐Hijr in northern Oman identified 1507 archaeological features in a 124 km² area. Data were collected on each feature's architectural characteristics, associated artefact assemblages, topographic and environmental locations, condition of remains, and relations to other archaeological features. The majority of datable features belong to the third millennium BC and divide unequally between the Hafit and Umm an‐Nar periods. While the majority of these third‐millennium BC features were tombs, other feature types were identified, including towers, settlements, quarries, dams, enclosures, and possible platforms. Third‐millennium BC features were organised into clusters and ranged considerably in size, from a few features to several hundred. All of the clusters established during the Hafit period were maintained in the Umm an‐Nar period, suggesting a continuity throughout the third millennium. Some preliminary hypotheses regarding settlement patterns are suggested.     

A Geostatistical Linear Regression Model for Small Area Data. 一种适用于小区域数据的地统计线性回归模型

We present a new linear regression model for use with aggregated, small area data that are spatially autocorrelated. Because these data are aggregates of individual‐level data, we choose to model the spatial autocorrelation using a geostatistical model specified at the scale of the individual. The autocovariance of observed small area data is determined via the natural aggregation over the population. Unlike lattice‐based autoregressive approaches, the geostatistical approach is invariant to the scale of data aggregation. We establish that this geostatistical approach also is a valid autoregressive model; thus, we call this approach the geostatistical autoregressive (GAR) model. An asymptotically consistent and efficient maximum likelihood estimator is derived for the GAR model. Finite sample evidence from simulation experiments demonstrates the relative efficiency properties of the GAR model. Furthermore, while aggregation results in less efficient estimates than disaggregated data, the GAR model provides the most efficient estimates from the data that are available. These results suggest that the GAR model should be considered as part of a spatial analyst's toolbox when aggregated, small area data are analyzed. More important, we believe that the GAR model's attention to the individual‐level scale allows for a more flexible and theory‐informed specification than the existing autoregressive approaches based on an area‐level spatial weights matrix. Because many spatial process models, both in geography and in other disciplines, are specified at the individual level, we hope that the GAR covariance specification will provide a vehicle for a better informed and more interdisciplinary use of spatial regression models with area‐aggregated data.     

Geostatistical Prediction and Simulation of Point Values from Areal Data

The spatial prediction and simulation of point values from areal data are addressed within the general geostatistical framework of change of support (the term support referring to the domain informed by each measurement or unknown value). It is shown that the geostatistical framework (i) can explicitly and consistently account for the support differences between the available areal data and the sought-after point predictions, (ii) yields coherent (mass-preserving or pycnophylactic) predictions, and (iii) provides a measure of reliability (standard error) associated with each prediction. In the case of stochastic simulation, alternative point-support simulated realizations of a spatial attribute reproduce (i) a point-support histogram (Gaussian in this work), (ii) a point-support semivariogram model (possibly including anisotropic nested structures), and (iii) when upscaled, the available areal data. Such point-support-simulated realizations can be used in a Monte Carlo framework to assess the uncertainty in spatially distributed model outputs operating at a fine spatial resolution because of uncertain input parameters inferred from coarser spatial resolution data. Alternatively, such simulated realizations can be used in a model-based hypothesis-testing context to approximate the sampling distribution of, say, the correlation coefficient between two spatial data sets, when one is available at a point support and the other at an areal support. A case study using synthetic data illustrates the application of the proposed methodology in a remote sensing context, whereby areal data are available on a regular pixel support. It is demonstrated that point-support (sub-pixel scale) predictions and simulated realizations can be readily obtained, and that such predictions and realizations are consistent with the available information at the coarser (pixel-level) spatial resolution.     

Nonlinear Multivariate Spatial Modeling Using NLPCA and Pair‐Copulas

A novel geostatistical modeling approach is developed to model nonlinear multivariate spatial dependence using nonlinear principal component analysis (NLPCA) and pair‐copulas. In spatial studies, multivariate measurements are frequently collected at each location. The dependence between such measurements can be complex. In this article, a multivariate geostatistical model is developed that can capture both nonlinear spatial dependence across locations and nonlinear dependence between measurements at a particular location. Nonlinear multivariate dependence between spatial variables is removed using NLPCA. Subsequently, a pair‐copula based model is fitted to each transformed variable to model the univariate nonlinear spatial dependencies. NLPCA and pair‐copulas, within the proposed model, are compared with stepwise conditional transformation (SCT) and conventional kriging. The results show that, for the two case studies presented, the proposed model that utilizes NLPCA and pair‐copulas reproduces nonlinear multivariate structures and univariate distributions better than existing methods based on SCT and kriging.     

Pore‐scale investigation on stress‐dependent characteristics of granular packs and the impact of pore deformation on fluid distribution

Understanding the effect of changing stress conditions on multiphase flow in porous media is of fundamental importance for many subsurface activities including enhanced oil recovery, water drawdown from aquifers, soil confinement, and geologic carbon storage. Geomechanical properties of complex porous systems are dynamically linked to flow conditions, but their feedback relationship is often oversimplified due to the difficulty of representing pore‐scale stress deformation and multiphase flow characteristics in high fidelity. In this work, we performed pore‐scale experiments of single‐ and multiphase flow through bead packs at different confining pressure conditions to elucidate compaction‐dependent characteristics of granular packs and their impact on fluid flow. A series of drainage and imbibition cycles were conducted on a water‐wet, soda‐lime glass bead pack under varying confining stress conditions. Simultaneously, X‐ray micro‐CT was used to visualize and quantify the degree of deformation and fluid distribution corresponding with each stress condition and injection cycle. Micro‐CT images were segmented using a gradient‐based method to identify fluids (e.g., oil and water), and solid phase redistribution throughout the different experimental stages. Changes in porosity, tortuosity, and specific surface area were quantified as a function of applied confining pressure. Results demonstrate varying degrees of sensitivity of these properties to confining pressure, which suggests that caution must be taken when considering scalability of these properties for practical modeling purposes. Changes in capillary number with confining pressure are attributed to the increase in pore velocity as a result of pore contraction. However, this increase in pore velocity was found to have a marginal impact on average phase trapping at different confining pressures.     

Accuracy of Count Data Estimated by the Point‐in‐Polygon Method

This paper analyzes the accuracy of count data estimated by the point‐in‐polygon method. A point‐in‐polygon interpolation model is proposed, based on a stochastic distribution of points and the target zone, in order to represent a variety of situations. The accuracy of estimates is numerically investigated in relation to the size of the target zone and the distribution of points, and the optimal location of representative points is discussed. The major findings of this paper are as follows: (1) though the relative accuracy of estimates generally increases monotonously with the size of the target zone, the monotoneity is often disturbed by the periodicity in the spatial configuration of source zones and the point distribution; (2) the point‐in‐polygon and the areal weighting interpolation methods have the same accuracy of estimates when points are concentrated in less than 12–15 percent area around the representative point in source zones; (3) the point‐in‐polygon method is not so robust against the locational gap between points and the representative point; (4) the optimal location of representative points is given by the spatial median of points.     

Placing Sanctuaries in Their Socio‐Political Landscapes: A Diachronic Approach to the Late Iron Age Communities in South‐East Iberia (Fourth–Second Centuries BC)

This paper explores the relationship between the historical dynamics and the transformations observed in pre‐Roman cult places in eastern Iberia between the fourth and second centuries BC. These are analysed through a case study: the sanctuary of La Luz (Murcia), located in the Segura Valley, in south‐east Iberia. Three main religious changes are discussed from this perspective: the development of the sanctuary in the fourth century BC, the changes observed in its archaeological record in the third century BC, and finally its destruction in the second century BC. These offer a diachronic view of the transformations, and illustrate the different levels at which they were expressed, from the archaeological record to the landscape. The work aims to provide a different perspective from previous studies in this area and a new view of the cult places in south‐east Iberia within their socio‐political landscape and the Mediterranean historical context.     

Gazetteer of small‐scale monuments in prehistoric Hadramawt,Yemen: a radiocarbon chronology from the RASA‐AHSD Project research 1996–2008

This paper provides a new, interpretive gazetteer and chronology of Hadramawt’s highland monuments based on results from archaeological survey and test excavations by the RASA‐AHSD (Roots of Agriculture in southern Arabia‐Arabian Human Social Dynamics) Project. With the exception of a few incidental sightings and an unpublished pipeline survey, the prehistoric record of southern Yemen’s highland plateau has been largely unknown. There are few settlements, so that understanding human landscape history must begin with the numerous small‐scale stone monuments left by mobile people. With examples representing monuments from the fifth, fourth, third and first millennia BC, the corpus of small excavations and radiocarbon dates reported here provides the first guide to the monument types of South Arabian highlands. Monument building began under more moist conditions and appears to have commemorated animal sacrifices long before commemorating mortuary rites and interment. There appears to be a temporal break of 1000 years before the widespread and varied practices of Bronze Age tomb construction, which lasted through the third millennium BC. After another break in monument construction, tombs were reused in the first millennium BC, sometimes with successive ritual visits. The data presented offer new material for the interpretation of the lives and activities of prehistoric pastoralists throughout the Holocene.     

Grave‐goods from the long chamber tomb “Dibba 76/1” (Fujairah,UAE): a first inventory

The aim of this paper is to present the rich set of finds collected inside the grave Dibba 76/1, in the Emirate of Fujairah, during a season of rescue excavation conducted under the direction of S. Ali Hassan in 1994. The recovered grave‐goods include pottery, soft‐stone vessels, metal finds, personal ornaments, coins, and other items. Although comparable with other corpuses of material excavated in south‐eastern Arabia, the material of Dibba 76/1 stands out for the inner variety of the different artefacts’ classes and their remarkable chronological heterogeneity. The study of the grave‐goods suggests that Dibba 76/1 was reused over several centuries, showing a strong continuity in the funerary destination of this specific place from the end of the Wadi Suq period (2000–1600 BC) to the first phases of the late pre‐Islamic period (250 BC–AD 400), and the full integration of the area of Dibba in the succession of the various cultural facies known during this long time span.     

Zooarchaeological Evidence for Domestic Rituals in the Iron Age Communities of North‐Eastern Iberia (Present‐Day Catalonia) (Sixth–Second Century BC)

Many socio‐economic changes occurred in southern Europe during the first millennium BC. In north‐eastern Iberia societies evolved from the small‐scale local groups of the Late Bronze Age to the more complex societies of the Iron Age. Together with a diversity of material changes (detected in pottery, agricultural techniques, architecture, etc.), a new ritual manifestation is attested in the Ancient Iberian Period (about 550 BC), lasting until some time after the Roman conquest. This consisted of sheep and goats (among other species) being carefully deposited below the floors of some domestic buildings. In this article the characteristics of these associated bone groups are described and their significance is discussed.     

Fracture spacing during hydro‐fracturing of cap‐rocks

Layered low permeability rock units, like shales, represent seals or ‘cap‐rocks’ in a variety of geological settings. A continuous increase in the fluid pressure gradients across a virtually impermeable rock layer will ultimately lead to hydro‐fracturing. Depending on the boundary conditions, such fracturing may lead to the formation of a set of sub‐parallel cracks oriented more or less perpendicular to the cap‐rock layer. In this article, we propose a new numerical model that describes interactions between multiple cross‐cutting fractures in an elastic low permeability rock layer. The width of each fracture and the spacing between them are modeled as a force balance between the fluid pressure and the elastic forces in the cap‐rock and between each fracture. The model indicates that the system of fractures evolves toward a spatially periodic steady‐state distribution with a fixed fracture spacing and aperture. The results are similar for incompressible and compressible fluids. The steady‐state conditions depend on only two dimensionless parameters, and the fracture spacing is only weakly dependent on the cap‐rock thickness. This is in contrast to fracturing produced by simple extension of an elastic rock layer beyond the fracture strength, in which case fracture spacing is proportional to layer thickness.     

A late fourth‐ to early third‐millennium grave from Bahrain,c.3100–2600 BC

This article presents an exceptional burial that was excavated in 1986 by the National Museum of Bahrain. The presence of two ‘Jemdat Nasr’ style ceramic vessels in the grave makes it a unique testimony of occupation on Bahrain Island in the late fourth to mid‐third millennium BC. A local cooking vessel also uncovered from the grave represents the earliest local pottery production so far uncovered in Bahrain.     

Equality‐led Development and the Demand‐ and Supply‐side Effects

This contribution to the Forum Debate on global development focuses on the dimension of functional income distribution between labour and capital and its demand‐side and supply‐side effects. The article summarizes recent literature that has sought to explain the reasons behind the global fall in the labour share. It then discusses the demand‐side effects of the declining wage share on growth, based on the post‐Keynesian/post‐Kaleckian literature. The author presents an alternative policy scenario for the G20 based on a mix of increasing wage share and public investment, before discussing the supply‐side effects of rising inequality. The article concludes with some policy implications for equality‐led development.     

Recent Excavation and Recording at the New Neolithic Rock Art Site of Vallée Aux Noirs,Buthiers (Seine‐et‐Marne,France)

Following the exceptional discovery of Neolithic engravings on a boulder at Vallée aux Noirs in the Fontainebleau forest, south of Paris, an excavation trench was opened in order to access the buried part of the decorated rock panel and explore the stratigraphic context of the artwork. A palaeosol was found two metres below the modern ground level, underneath multiple layers of sterile sandy soil forming a very compact sequence from which only one archaeological artefact was recovered – an Iron Age fibula (c.200–300 BC). Dating of the palaeosol was attempted through two different methods: AMS dates from charcoal suggest a significant span from the Early Bronze Age to the Iron Age, while two more consistent OSL dates point to formation of the palaeosol during the Late Neolithic (3500–3000 cal BC). The entire engraved rock surface (16 m²), including its buried part, was fully recorded. Four main semiotic groups were identified: a typical fifth‐millennium crook‐hafted axe with a ring, two boats with steering oars, and a central, very tall human figure dominating the composition from its 3.5‐metre height.     

Rescue excavation of a third‐millennium BC tomb at Al‐Khubayb,Sultanate of Oman

A third‐millennium BC tomb was subject to a rescue excavation in connection with the construction of a new road near the village of Al‐Khubayb in the Sultanate of Oman. It yielded a small number of finds, especially small metal objects that belonged to a later reuse of the tomb in the Samad period. As all diagnostic finds from the tomb date to the reuse, its architectural elements were the only indicator for the construction date of the tomb. Besides its small size and large wall thickness, which might suggest that the tomb is a transitional type between the Hafit and the Umm an‐Nar periods, its separation into two chambers and its facade made of white, dressed stones, can be seen as a clue for a construction date of the tomb in the Umm an‐Nar period.     

La frontière asymétrique : Franco‐Ontariens et Anglo‐Québécois dans la région de la capitale nationale

The francophone and anglophone minorities of Gatineau‐Ottawa appear to benefit from a privileged location. Living very close to their respective majorities, they simply have to cross the border in order to access resources to live in their own language and share their culture. However, a qualitative analysis of the discourse by Anglo‐Quebeckers and Franco‐Ontarians about their everyday life in the Nation's Capital Region shows that the border has more complex and often contradictory effects. In this article, we focus our attention on four particular manifestations of the border: (1) the border is transparent so that one can cross the Ottawa River without hindrance in certain contexts yet rather opaque in others; (2) one may transcend minority status through the strategic use of the border; (3) it creates a multi‐topic imaginary geography in which the border itself often becomes mobile; and (4) finally, the border can act as a mirror when the cross‐cultural intermixing it allows causes the Anglo‐Quebeckers and Franco‐Ontarians to question their identities, a questioning which would not be as intense in the absence of the border. The comparison of these two minorities makes it possible to highlight the asymmetrical nature of the effects of the border on their everyday life, identities, and sense of belonging.