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What’s new in ArcGIS Desktop 10.6.1:
ArcGIS (Desktop, Engine, Server) 10.6.1 Geoprocessing Service Patch
This patch has client and server performance improvements for when geoprocessing services return results containing a large number of records. It also addresses an issue where geoprocessing services fail to publish or restart if tied to a map service referencing an enterprise geodatabase.
Issues Addressed with this patch
BUG-000114882 – There is a noticeable performance bottleneck associated with returning very large output result sets from geoprocessing services.
BUG-000104843 – Geoprocessing services fail to publish or restart if the ‘View results with a map service’ option is checked and the data source is a registered enterprise geodatabase.
ArcGIS 10.6.1 (Desktop, Engine, Server) Buffering Degenerated Polygon Patch
This patch addresses an issue where calling the Buffer method on a polygon, which is created from a degenerate envelope, causes a failure. This patch is required for all 10.6.1 users and Esri recommends that you install this patch at your earliest opportunity.
Issues Addressed with this patch
BUG-000115147 – When calling ITopologicalOperator::Buffer on a polygon, if the polygon is degenerated to a point, the buffer call crashes.
ArcGIS 10.6.1 Issues Addressed List
GIS by ESRI™
Welcome to ArcGIS Geostatistical Analyst
Welcome to the ESRI® ArcGISŽ Geostatistical Analyst extension for advanced surface modeling using deterministic and geostatistical methods? Geostatistical Analyst extends ArcMapŽ by adding an advanced toolbar containing tools for exploratory spatial data analysis and a geostatistical wizard to lead you through the process of creating a statistically valid surface? New surfaces generated with Geostatistical Analyst can subsequently be used in geographic information system (GIS) models and in visualization using ArcGIS extensions such as ArcGIS Spatial Analyst and ArcGIS 3D AnalystŽ?
Geostatistical Analyst is revolutionary because it bridges the gap between geostatistics and GIS? For some time, geostatistical tools have been available, but never integrated tightly within GIS modeling environments? Integration is important because, for the first time, GIS professionals can begin to quantify the quality of their surface models by measuring the statistical error of predicted surfaces?
Surface fitting using Geostatistical Analyst involves three key steps (demonstrated on the following pages):
LExploratory spatial data analysis
LStructural analysis (calculation and modeling of the surface properties of nearby locations)
LSurface prediction and assessment of results
The software contains a series of easy-to-use tools and wizards that guide you through each of these steps? It also includes a number of unique tools for statistical spatial data analysis?
Exploratory spatial data analysis
Using measured sample points from a study area, Geostatistical Analyst can create accurate predictions for other unmeasured locations within the same area. Exploratory spatial data analysis tools included with Geostatistical Analyst are used to assess the statistical properties of data such as spatial data variability, spatial data dependence, and global trends.
Peter J. Diggle
Paulo J. Ribeiro Jr.
1.1 Motivating examples
The term spatial statistics is used to describe a wide range of statistical models and methods intended for the analysis of spatially referenced data. Cressie (1993) provides a general overview. Within spatial statistics, the term geostatistics refers to models and methods for data with the following characteristics.
Firstly, values Yi : i = 1, . . . , n are observed at a discrete set of sampling locations xi within some spatial region A. Secondly, each observed value Yi is either a direct measurement of, or is statistically related to, the value of an underlying continuous spatial phenomenon, S(x), at the corresponding sampling location xi. This rather abstract formulation can be translated to a variety of more tangible scientific settings, as the following examples demonstrate.
Example 1.1. Surface elevations
The data for this example are taken from Davis (1972). They give the measured surface elevations yi at each of 52 locations xi within a square, A, with sidelength 6.7 units. The unit of distance is 50 feet (≈15.24 meters), whereas one unit in y represents 10 feet (≈3.05 meters) of elevation.
Figure 1.1 is a circle plot of the data. Each datum (xi, yi) is represented by a circle with centre at xi and radius proportional to yi. The observed elevations range between 690 and 960 units. For the plot, we have subtracted 600 from each observed elevation, to heighten the visual contrast between low and high values. Note in particular the cluster of low values near the top-centre of the plot.
The objective in analysing these data is to construct a continuous elevation map for the whole of the square region A. Let S(x) denote the true elevation at an arbitrary location x. Since surface elevation can be measured with negligible error, in this example each yi is approximately equal to S(xi). Hence, a reasonable requirement would be that the map resulting from the analysis should interpolate the data. Our notation, distinguishing between a measurement process Y and an underlying true surface S, is intended to emphasise that this is not always the case.
Example 1.2. Residual contamination from nuclear weapons testing
The data for this example were collected from Rongelap Island, the principal island of Rongelap Atoll in the South Pacific, which forms part of the Marshall Islands. The data were previously analysed in Diggle et al. (1998) and have the format (xi, yi, ti) : i = 1, . . . , 157, where xi identifies a spatial location, yi is a photon emission count attributable to radioactive caesium, and ti is the time (in seconds) over which yi was accumulated.
These data were collected as part of a more wide-ranging, multidisciplinary investigation into the extent of residual contamination from the U.S. nuclear weapons testing programme, which generated heavy fallout over the island in the 1950s. Rongelap island has been uninhabited since 1985, when the inhabitants left on their own initiative after years of mounting concern about the possible adverse health effects of the residual contamination. Each ratio yi/ti gives a crude estimate of the residual contamination at the corresponding location xi but, in contrast to Example 1.1, these estimates are subject to nonnegligible statistical error. For further discussion of the practical background to these data, see Diggle, Harper and Simon (1997).
By: Tomislav Hengl
1.1 Basic concepts
Geostatistics is a subset of statistics specialized in analysis and interpretation of geographically referenced data (Goovaerts, 1997; Webster and Oliver, 2001; Nielsen and
Wendroth, 2003). In other words, geostatistics comprises statistical techniques that are
adjusted to spatial data. Typical questions of interest to a geostatistician are:
how does a variable vary in space?
what controls its variation in space?
where to locate samples to describe its spatial variability?
how many samples are needed to represent its spatial variability?
what is a value of a variable at some new location?
what is the uncertainty of the estimate?
In the most pragmatic context, geostatistics is an analytical tool for statistical analysis of sampled field data. Today, geostatistics is not only used to analyse point data but
also increasingly in combination with various GIS layers: e.g. to explore spatial variation
in remote sensing data, to quantify noise in the images and for their filtering (e.g. filling
of the voids/missing pixels), to improve generation of DEMs and for their simulations,
to optimize spatial sampling, selection of spatial resolution for image data and selection
of support size for ground data (Kyriakidis et al., 1999; Atkinson and Quattrochi, 2000).
According to the bibliographic research of Zhou et al. (2007), the top 10 application
fields of geostatistics (the largest number of research articles) are: (1) geosciences, (2)
water resources, (3) environmental sciences, (4) agriculture and/or soil sciences, (5/6)
mathematics and statistics, (7) ecology, (8) civil engineering, (9) petroleum engineering
and (10) limnology. The list could be extended and differs from country to country of
course. Evolution of applications of geostatistics can also be followed through the activities of the following research groups: geoENVia, IAMG, pedometrics, geocomputation
and spatial accuracy.
One of the main uses of geostatistics is to predict values of a sampled variable
over the whole area of interest, which is referred to as spatial prediction or spatial
interpolation. Note that there is a small difference between the two because prediction can imply both interpolation and extrapolation, so we will more commonly use the term
spatial prediction in this handbook, even though the term spatial interpolation has been
more widely accepted (Lam, 1983; Mitas and Mitasova, 1999; Dubois and Galmarini,
An important distinction between geostatistical and conventional mapping of environmental variables is that the geostatistical prediction is based on application of quantitative, statistical techniques. Unlike the traditional approaches to mapping, which
rely on the use of empirical knowledge, in the case of geostatistical mapping we completely rely on the actual measurements and (semi-)automated algorithms. Although
this sounds as if the spatial prediction is done purely by a computer program, the analysts have many options to choose whether to use linear or non-linear models, whether to
consider spatial position or not, whether to transform or use the original data, whether
to consider multicolinearity effects or not. So it is also an expert-based system in a way.
In summary, geostatistical mapping can be defined as analytical production of
maps by using field observations, auxiliary information and a computer program that calculates values at locations of interest (a study area). It typically
comprises the following five steps:
(1.) design the sampling and data processing,
(2.) collect field data and do laboratory analysis,
(3.) analyse the points data and estimate the model,
(4.) implement the model and evaluate its performance,
(5.) produce and distribute the output geoinformation1.
Today, increasingly, the natural resource inventories need to be regularly updated or
improved in detail, which means that after step (5), we often need to consider collection
of new samples or additional samples that are then used to update an existing GIS layer.
In that sense, it is probably more valid to speak about geostatistical monitoring