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.     

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.     

An Enhanced Finite Element Macro-Model for the Realistic Simulation of Localized Cracks in Masonry Structures: A Large-Scale Application

ABSTRACT

Finite element macro-modeling approaches are widely used for the analysis of large-scale masonry structures. Despite their efficiency, they still face two important challenges: the realistic representation of damage and a reasonable independency of the numerical results to the used discretization. In this work, the classical smeared crack approach is enhanced with a crack-tracking algorithm, originating from the analysis of localized cracking in quasi-brittle materials. The proposed algorithm is for the first time applied to a large-scale wall exhibiting multiple shear and flexural cracking. Discussion covers structural aspects, as the response of the structure under different assumptions regarding the floor rigidity, but also numerical issues, commonly overlooked in the simulation of large structures, such the mesh-dependency of the numerical results.     

Archaeological Ethnography,Heritage Management,and Community Archaeology: A Pragmatic Approach from Crete

This article examines the introduction of archaeological ethnography as an approach to establish positioned research and bring context-specific and reflexive considerations into community archaeology projects. It considers recent critiques of heritage management in archaeology and the role of archaeologists as experts in it, contending that smaller and less prominent sites exist in different contexts and pose different problems than large-scale projects usually addressed in the literature. We describe how the ‘Three Peak Sanctuaries of Central Crete’ project, investigating prehistoric Minoan ritual sites, involves communities and stakeholders and what demands the latter pose on experts in the field. Archaeological work is always already implicated in local development projects which create and reproduce power hierarchies. It is therefore important that archaeologists maintain their critical distance from official heritage discourses, as they are materialized in development programmes, while at the same time engaging with local expectations and power struggles; they also have to critically address and position their own assumptions. We use examples from our community archaeology project to propose that these goals can be reached through archaeological ethnographic fieldwork that should precede any archaeological project to inform its methodological decisions, engage stakeholders, and collaboratively shape heritage management strategies.     

Byzantine-Muslim conspiracies against the crusades: history and myth

This article examines Latin allegations of Byzantine-Muslim conspiracies against the crusades in the course of the twelfth century, the charges surviving in various chronicles, reports and letters. While their sensational elements have been noted, the Latin accounts portraying Byzantine rulers as allies of the ‘infidels’ against the crusades and the crusader states have generally been taken more or less at face value by modern scholars. A closer examination discloses how these allegations of Byzantine-Muslim collusion were based on rumour, which mainly evolved and flourished among the rank and file of the crusader armies. They eventually found their way into the chronicles, having become more outlandish in transmission. The functions they fulfilled ranged from creating a scapegoat for the failures of the Crusade of 1101 and Second Crusade, to interpretation and explanation, or rather misinterpretation, in the case of the Third Crusade. Despite the fact that, in general, these theories do not seem to have appealed to Latin emperors, kings, and nobles, paradoxically it was a noble of the Fourth Crusade, Baldwin IX of Flanders, together with his clerical advisers, who finally exploited them in May and June 1204 in order to justify the Latin conquest of Christian Constantinople.     

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.     

Area‐to‐Point Prediction Under Boundary Conditions

This article proposes a geostatistical solution for area‐to‐point spatial prediction (downscaling) taking into account boundary effects. Such effects are often poorly considered in downscaling, even though they often have significant impact on the results. The geostatistical approach proposed in this article considers two types of boundary conditions (BC), that is, a Dirichlet‐type condition and a Neumann‐type condition, while satisfying several critical issues in downscaling: the coherence of predictions, the explicit consideration of support differences, and the assessment of uncertainty regarding the point predictions. An updating algorithm is used to reduce the computational cost of area‐to‐point prediction under a given BC. In a case study, area‐to‐point prediction under a Dirichlet‐type BC and a Neumann‐type BC is illustrated using simulated data, and the resulting predictions and error variances are compared with those obtained without considering such conditions.     

Crusaders and mercenaries: the west-European soldiers of the Laskarids of Nicaea (1204–1258)

The so-called empire of Nicaea was one of the new political entities that emerged in the aftermath of the Fourth Crusade in 1204. The raison d'être of Nicaea was the recovery of Constantinople and the restoration of the Byzantine Empire. Consequently, the Nicaean rulers were almost constantly involved in wars against the Latin empire of Constantinople. Nevertheless, west-European soldiers made up a large part of the Nicaean armies. This article examines the impact of these troops on the military ideology and military organization of Nicaea during the reign of the rulers of the Laskarid dynasty.     

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.