Spatial Statistics

Looking for beautiful books? Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. Other books in this series. Regional Economic Development Robert J. Metropolitan Innovation Systems Manfred M.

Progress in Spatial Analysis : Methods and Applications

National Transport Models Lars Lundqvist. European Regional Growth Bernard Fingleton. Agglomeration and Firm Performance Fiorenza Belussi. Service Industries and Regions Juan R. Names, Ethnicity and Populations Pablo Mateos. Advances in Spatial Econometrics Luc Anselin. Back cover copy Space is increasingly recognized as a legitimate factor that influences many processes and conceptual frameworks, including notions of spatial coherence and spatial heterogeneity that have been demonstrated to provide substance to both theory and explanation.

Table of contents Theory and Methods. Roads, Zoning and Spatial Externalities. The Case of Knox County, Tennessee. An Instrumental Variable Approach. Evidence from Local Regressions. All Earth-based spatial—temporal location and extent references should be relatable to one another and ultimately to a "real" physical location or extent.

Progress in Spatial Analysis

This key characteristic of GIS has begun to open new avenues of scientific inquiry. The first known use of the term "geographic information system" was by Roger Tomlinson in the year in his paper "A Geographic Information System for Regional Planning". In John Snow determined the source of a cholera outbreak in London by marking points on a map depicting where the cholera victims lived, and connecting the cluster that he found with a nearby water source. This was one of the earliest successful uses of a geographic methodology in epidemiology. While the basic elements of topography and theme existed previously in cartography , the John Snow map was unique, using cartographic methods not only to depict but also to analyze clusters of geographically dependent phenomena.

This work was originally drawn on glass plates but later plastic film was introduced, with the advantages of being lighter, using less storage space and being less brittle, among others. When all the layers were finished, they were combined into one image using a large process camera. Once color printing came in, the layers idea was also used for creating separate printing plates for each color.

Computer hardware development spurred by nuclear weapon research led to general-purpose computer "mapping" applications by the early s. A rating classification factor was also added to permit analysis. It supported a national coordinate system that spanned the continent, coded lines as arcs having a true embedded topology and it stored the attribute and locational information in separate files.

As a result of this, Tomlinson has become known as the "father of GIS", particularly for his use of overlays in promoting the spatial analysis of convergent geographic data. CGIS lasted into the s and built a large digital land resource database in Canada. It was developed as a mainframe -based system in support of federal and provincial resource planning and management.

Its strength was continent-wide analysis of complex datasets. The CGIS was never available commercially. This was renamed in to MapInfo for Windows when it was ported to the Microsoft Windows platform. This began the process of moving GIS from the research department into the business environment. More recently, a growing number of free, open-source GIS packages run on a range of operating systems and can be customized to perform specific tasks.

Several articles on the history of GIS have been published.

Spatial Analysis 2 Overlay Operations & Analysis in GIS

Modern GIS technologies use digital information, for which various digitized data creation methods are used. The most common method of data creation is digitization , where a hard copy map or survey plan is transferred into a digital medium through the use of a CAD program, and geo-referencing capabilities.

With the wide availability of ortho-rectified imagery from satellites, aircraft, Helikites and UAVs , heads-up digitizing is becoming the main avenue through which geographic data is extracted. Heads-up digitizing involves the tracing of geographic data directly on top of the aerial imagery instead of by the traditional method of tracing the geographic form on a separate digitizing tablet heads-down digitizing.

GIS uses spatio-temporal space-time location as the key index variable for all other information. Just as a relational database containing text or numbers can relate many different tables using common key index variables, GIS can relate otherwise unrelated information by using location as the key index variable. Any variable that can be located spatially, and increasingly also temporally, can be referenced using a GIS. Units applied to recorded temporal-spatial data can vary widely even when using exactly the same data, see map projections , but all Earth-based spatial—temporal location and extent references should, ideally, be relatable to one another and ultimately to a "real" physical location or extent in space—time.

Related by accurate spatial information, an incredible variety of real-world and projected past or future data can be analyzed, interpreted and represented. GIS accuracy depends upon source data, and how it is encoded to be data referenced. Land surveyors have been able to provide a high level of positional accuracy utilizing the GPS -derived positions. In developing a digital topographic database for a GIS, topographical maps are the main source, and aerial photography and satellite imagery are extra sources for collecting data and identifying attributes which can be mapped in layers over a location facsimile of scale.

The scale of a map and geographical rendering area representation type [ clarification needed ] are very important aspects since the information content depends mainly on the scale set and resulting locatability of the map's representations. A quantitative analysis of maps brings accuracy issues into focus. The electronic and other equipment used to make measurements for GIS is far more precise than the machines of conventional map analysis. GIS data represents real objects such as roads, land use, elevation, trees, waterways, etc.

Real objects can be divided into two abstractions: Traditionally, there are two broad methods used to store data in a GIS for both kinds of abstractions mapping references: Points, lines, and polygons are the stuff of mapped location attribute references. A new hybrid method of storing data is that of identifying point clouds, which combine three-dimensional points with RGB information at each point, returning a " 3D color image ".

GIS thematic maps then are becoming more and more realistically visually descriptive of what they set out to show or determine. There are a variety of methods used to enter data into a GIS where it is stored in a digital format. Existing data printed on paper or PET film maps can be digitized or scanned to produce digital data. A digitizer produces vector data as an operator traces points, lines, and polygon boundaries from a map. Scanning a map results in raster data that could be further processed to produce vector data.

Survey data can be directly entered into a GIS from digital data collection systems on survey instruments using a technique called coordinate geometry COGO. A current trend in data collection gives users the ability to utilize field computers with the ability to edit live data using wireless connections or disconnected editing sessions. This eliminates the need to post process, import, and update the data in the office after fieldwork has been collected.

This includes the ability to incorporate positions collected using a laser rangefinder. New technologies also allow users to create maps as well as analysis directly in the field, making projects more efficient and mapping more accurate. Remotely sensed data also plays an important role in data collection and consist of sensors attached to a platform. Sensors include cameras, digital scanners and lidar , while platforms usually consist of aircraft and satellites.

Aircraft measurement software, accurate to 0. Helikites are inexpensive and gather more accurate data than aircraft. Helikites can be used over roads, railways and towns where unmanned aerial vehicles UAVs are banned. Recently aerial data collection is becoming possible with miniature UAVs. The majority of digital data currently comes from photo interpretation of aerial photographs. Soft-copy workstations are used to digitize features directly from stereo pairs of digital photographs.

These systems allow data to be captured in two and three dimensions, with elevations measured directly from a stereo pair using principles of photogrammetry. Analog aerial photos must be scanned before being entered into a soft-copy system, for high-quality digital cameras this step is skipped. Satellite remote sensing provides another important source of spatial data. Here satellites use different sensor packages to passively measure the reflectance from parts of the electromagnetic spectrum or radio waves that were sent out from an active sensor such as radar.

Remote sensing collects raster data that can be further processed using different bands to identify objects and classes of interest, such as land cover. When data is captured, the user should consider if the data should be captured with either a relative accuracy or absolute accuracy, since this could not only influence how information will be interpreted but also the cost of data capture. After entering data into a GIS, the data usually requires editing, to remove errors, or further processing.

For vector data it must be made "topologically correct" before it can be used for some advanced analysis. For example, in a road network, lines must connect with nodes at an intersection. Errors such as undershoots and overshoots must also be removed.


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For scanned maps, blemishes on the source map may need to be removed from the resulting raster. For example, a fleck of dirt might connect two lines that should not be connected. Data restructuring can be performed by a GIS to convert data into different formats. For example, a GIS may be used to convert a satellite image map to a vector structure by generating lines around all cells with the same classification, while determining the cell spatial relationships, such as adjacency or inclusion. Since digital data is collected and stored in various ways, the two data sources may not be entirely compatible.

So a GIS must be able to convert geographic data from one structure to another. In so doing, the implicit assumptions behind different ontologies and classifications require analysis.

The earth can be represented by various models, each of which may provide a different set of coordinates e. The simplest model is to assume the earth is a perfect sphere. As more measurements of the earth have accumulated, the models of the earth have become more sophisticated and more accurate. In fact, there are models called datums that apply to different areas of the earth to provide increased accuracy, like NAD83 for U.

GIS spatial analysis is a rapidly changing field, and GIS packages are increasingly including analytical tools as standard built-in facilities, as optional toolsets, as add-ins or 'analysts'.

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In many instances these are provided by the original software suppliers commercial vendors or collaborative non commercial development teams , while in other cases facilities have been developed and are provided by third parties. The increased availability has created a new dimension to business intelligence termed " spatial intelligence " which, when openly delivered via intranet, democratizes access to geographic and social network data.

Geospatial intelligence , based on GIS spatial analysis, has also become a key element for security. GIS as a whole can be described as conversion to a vectorial representation or to any other digitisation process. Slope can be defined as the steepness or gradient of a unit of terrain, usually measured as an angle in degrees or as a percentage. Aspect can be defined as the direction in which a unit of terrain faces. Aspect is usually expressed in degrees from north.

Slope, aspect, and surface curvature in terrain analysis are all derived from neighborhood operations using elevation values of a cell's adjacent neighbours. The following method can be used to derive slope and aspect: The elevation at a point or unit of terrain will have perpendicular tangents slope passing through the point, in an east-west and north-south direction.

The gradient is defined as a vector quantity with components equal to the partial derivatives of the surface in the x and y directions. The calculation of the overall 3x3 grid slope S and aspect A for methods that determine east-west and north-south component use the following formulas respectively:. Zhou and Liu [24] describe another formula for calculating aspect, as follows:. It is difficult to relate wetlands maps to rainfall amounts recorded at different points such as airports, television stations, and schools.

Progress in Spatial Analysis by Antonio Páez

A GIS, however, can be used to depict two- and three-dimensional characteristics of the Earth's surface, subsurface, and atmosphere from information points. For example, a GIS can quickly generate a map with isopleth or contour lines that indicate differing amounts of rainfall. Such a map can be thought of as a rainfall contour map. Many sophisticated methods can estimate the characteristics of surfaces from a limited number of point measurements. A two-dimensional contour map created from the surface modeling of rainfall point measurements may be overlaid and analyzed with any other map in a GIS covering the same area.

This GIS derived map can then provide additional information - such as the viability of water power potential as a renewable energy source. Similarly, GIS can be used to compare other renewable energy resources to find the best geographic potential for a region. Additionally, from a series of three-dimensional points, or digital elevation model , isopleth lines representing elevation contours can be generated, along with slope analysis, shaded relief , and other elevation products.

Watersheds can be easily defined for any given reach, by computing all of the areas contiguous and uphill from any given point of interest. Similarly, an expected thalweg of where surface water would want to travel in intermittent and permanent streams can be computed from elevation data in the GIS. A GIS can recognize and analyze the spatial relationships that exist within digitally stored spatial data. These topological relationships allow complex spatial modelling and analysis to be performed.

Topological relationships between geometric entities traditionally include adjacency what adjoins what , containment what encloses what , and proximity how close something is to something else. Geometric networks are linear networks of objects that can be used to represent interconnected features, and to perform special spatial analysis on them. A geometric network is composed of edges, which are connected at junction points, similar to graphs in mathematics and computer science.

Just like graphs, networks can have weight and flow assigned to its edges, which can be used to represent various interconnected features more accurately.


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Geometric networks are often used to model road networks and public utility networks, such as electric, gas, and water networks. Network modeling is also commonly employed in transportation planning , hydrology modeling, and infrastructure modeling. GIS hydrological models can provide a spatial element that other hydrological models lack, with the analysis of variables such as slope, aspect and watershed or catchment area.

Slope and aspect can then be used to determine direction of surface runoff, and hence flow accumulation for the formation of streams, rivers and lakes. Areas of divergent flow can also give a clear indication of the boundaries of a catchment. Once a flow direction and accumulation matrix has been created, queries can be performed that show contributing or dispersal areas at a certain point. One of the main uses of hydrological modeling is in environmental contamination research.

Other applications of hydrological modeling include groundwater and surface water mapping , as well as flood risk maps. Dana Tomlin probably coined the term "cartographic modeling" in his PhD dissertation ; he later used it in the title of his book, Geographic Information Systems and Cartographic Modeling Tomlin used raster layers, but the overlay method see below can be used more generally.

Operations on map layers can be combined into algorithms, and eventually into simulation or optimization models. The combination of several spatial datasets points, lines, or polygons creates a new output vector dataset, visually similar to stacking several maps of the same region. These overlays are similar to mathematical Venn diagram overlays. A union overlay combines the geographic features and attribute tables of both inputs into a single new output.

An intersect overlay defines the area where both inputs overlap and retains a set of attribute fields for each. A symmetric difference overlay defines an output area that includes the total area of both inputs except for the overlapping area. Data extraction is a GIS process similar to vector overlay, though it can be used in either vector or raster data analysis.

Rather than combining the properties and features of both datasets, data extraction involves using a "clip" or "mask" to extract the features of one data set that fall within the spatial extent of another dataset. In raster data analysis, the overlay of datasets is accomplished through a process known as "local operation on multiple rasters" or " map algebra ", through a function that combines the values of each raster's matrix.