Spatial Analysis and Modeling

1. Spatial Analysis and Modeling Vector Analysis Raster Analysis

2. Modeling Spatial World A model is a representation of reality Models are created as a simplified, manageable view of reality Models help you understand, describe, or predict how things work in the real world Data Models. Representation models. Process models. to explain the difference of grid, image, and tin, I want to show the data in arcgis/ArcTutor/3DAnalyst/Exercise1, or Exercise2to explain the difference of grid, image, and tin, I want to show the data in arcgis/ArcTutor/3DAnalyst/Exercise1, or Exercise2

3. Representation Models Represent the objects of real world through a sets of layers (Data Models) Common data models/descriptive models. Spatial relationships within an object (the shape of a building). Between the other objects in the landscape (the distribution of buildings). Model the attributes of the objects (who owns each building).

4. Process Models Describe the interaction or processes of the objects of real world, which are modeled in the representation model, by using map calculation

5. Creating a conceptual model to solve a spatial problem (1)

6. Through spatial analysis you can interact with a GIS to answer questions, support decisions, and reveal patterns. Spatial analysis is in many ways the crux of a GIS, because it includes all of the transformations, manipulations, and methods that can be applied to geographic data to turn them into useful information. While methods of spatial analysis can be very sophisticated, they can also be very simple. The approach this course will take is to regard spatial analysis as spread out along a continuum of sophistication, ranging from the simplest types that occur very quickly and intuitively when the eye and brain look at a map, to the types that require complex software and advanced mathematical knowledge. There are many ways of defining spatial analysis, but all in one way or another express the fundamental idea that information on locations is essential. Basically, think of spatial analysis as "a set of methods whose results change when the locations of the objects being analyzed change." For example, calculating the average income for a group of people is not spatial analysis because the result doesn't depend on the locations of the people. Calculating the center of the United States population, however, is spatial analysis because the result depends directly on the locations of residents. Types of spatial analysis vary from simple to sophisticated. In this course, spatial analysis will be divided into six categories: queries and reasoning, measurements, transformations, descriptive summaries, optimization, and hypothesis testing. Queries and reasoning are the most basic of analysis operations, in which the GIS is used to answer simple questions posed by the user. No changes occur in the database and no new data are produced. Measurements are simple numerical values that describe aspects of geographic data. They include measurement of simple properties of objects, such as length, area, or shape, and of the relationships between pairs of objects, such as distance or direction. Transformations are simple methods of spatial analysis that change data sets by combining them or comparing them to obtain new data sets and eventually new insights. Transformations use simple geometric, arithmetic, or logical rules, and they include operations that convert raster data to vector data or vice versa. They may also create fields from collections of objects or detect collections of objects in fields. Descriptive summaries attempt to capture the essence of a data set in one or two numbers. They are the spatial equivalent of the descriptive statistics commonly used in statistical analysis, including the mean and standard deviation. Optimization techniques are normative in nature, designed to select ideal locations for objects given certain well defined criteria. They are widely used in market research, in the package delivery industry, and in a host of other applications. Hypothesis testing focuses on the process of reasoning from the results of a limited sample to make generalizations about an entire population. It allows us, for example, to determine whether a pattern of points could have arisen by chance based on the information from a sample. Hypothesis testing is the basis of inferential statistics and forms the core of statistical analysis, but its use with spatial data can be problematic. Through spatial analysis you can interact with a GIS to answer questions, support decisions, and reveal patterns. Spatial analysis is in many ways the crux of a GIS, because it includes all of the transformations, manipulations, and methods that can be applied to geographic data to turn them into useful information. While methods of spatial analysis can be very sophisticated, they can also be very simple. The approach this course will take is to regard spatial analysis as spread out along a continuum of sophistication, ranging from the simplest types that occur very quickly and intuitively when the eye and brain look at a map, to the types that require complex software and advanced mathematical knowledge. There are many ways of defining spatial analysis, but all in one way or another express the fundamental idea that information on locations is essential. Basically, think of spatial analysis as "a set of methods whose results change when the locations of the objects being analyzed change." For example, calculating the average income for a group of people is not spatial analysis because the result doesn't depend on the locations of the people. Calculating the center of the United States population, however, is spatial analysis because the result depends directly on the locations of residents. Types of spatial analysis vary from simple to sophisticated. In this course, spatial analysis will be divided into six categories: queries and reasoning, measurements, transformations, descriptive summaries, optimization, and hypothesis testing. Queries and reasoning are the most basic of analysis operations, in which the GIS is used to answer simple questions posed by the user. No changes occur in the database and no new data are produced. Measurements are simple numerical values that describe aspects of geographic data. They include measurement of simple properties of objects, such as length, area, or shape, and of the relationships between pairs of objects, such as distance or direction. Transformations are simple methods of spatial analysis that change data sets by combining them or comparing them to obtain new data sets and eventually new insights. Transformations use simple geometric, arithmetic, or logical rules, and they include operations that convert raster data to vector data or vice versa. They may also create fields from collections of objects or detect collections of objects in fields. Descriptive summaries attempt to capture the essence of a data set in one or two numbers. They are the spatial equivalent of the descriptive statistics commonly used in statistical analysis, including the mean and standard deviation. Optimization techniques are normative in nature, designed to select ideal locations for objects given certain well defined criteria. They are widely used in market research, in the package delivery industry, and in a host of other applications. Hypothesis testing focuses on the process of reasoning from the results of a limited sample to make generalizations about an entire population. It allows us, for example, to determine whether a pattern of points could have arisen by chance based on the information from a sample. Hypothesis testing is the basis of inferential statistics and forms the core of statistical analysis, but its use with spatial data can be problematic.

7. Vector Spatial Analysis Map Overlay Union, Intersect, Identity, Erase, Symmetrical Difference, Update Extract Point in Polygon, Line in Polygon, Polygon on Polygon Clip, Select, Split, Table Select Proximity Buffer, Multiple Ring Buffer, Near, Point Distance Statistics Frequency, Summary Statistics

8. Map Overlay Tools Intersect Union Identity Erase Symmetrical Difference Update

9. Intersect This tool builds a new feature class from the intersecting features common in both feature classes. Available with any ArcGIS license

10. Intersect How Intersect (Analysis) works The Intersect tool calculates the geometric intersection of any number of feature classes and feature layers. The features or portion of features that are common to (intersect) all inputs will be written to the Output Feature Class. Intersect does the following: Determines the spatial reference for processing. This will also be the Output Feature Classes' spatial reference. For details on how this is done, see Spatial Reference. All the input features are projected into this spatial reference for processing. Cracks and clusters the features. Cracking inserts vertices at the intersection of feature edges; clustering snaps together vertices that are within the cluster tolerance. Discovers geometric relationships (intersections) between features from all the feature classes or layers. Writes these intersections as features (point, line, or polygon) to the output. To explicitly control the output spatial reference (coordinate system and domains), set the appropriate environments, the Output Z Aware, and Output M Aware. The inputs can be any combination of geometry types (point, multipoint, line, polygon). The output geometry type can only be of the same geometry or a geometry of lower dimension as the input feature class with the lowest dimension geometry (point = 0 dimension, line = 1 dimension, poly = 2 dimension). Specifying different OUTPUT TYPE will produce different types of intersection of the input feature classes. These are not a different representation of the same intersections; they are intersections that can only be represented by that geometry type (point, line, or polygon). Intersect can run with a single input. In this case, instead of discovering intersections between the features from the different feature classes or layers, it will discover the intersections between features within the single input. This can be useful to discover polygon overlap and line intersections (as points or lines).

11. Union This tool builds a new feature class by combining the features and attributes of each feature class. Available with any ArcGIS license.

12. Union How Union (Analysis) works Union calculates the geometric intersection of any number of feature classes and feature layers. All inputs must be of a common geometry type and the output will be of that same geometry type. This means that a number of polygon feature classes and feature layers can be unioned together. The output features will have the attributes of all the input features that they overlap. Union does the following: Determines the spatial reference for processing. This will also be the output spatial reference. For details on how this is done, see Spatial Reference. All the input feature classes are projected (on the fly) into this spatial reference. Cracks and clusters the features. Cracking inserts vertices at the intersection of feature edges; clustering snaps together vertices that are within the cluster tolerance. Discovers geometric relationships (overlap) between features from all feature classes. Writes the new features to the output. To explicitly control the output spatial reference (coordinate system and domains), set the appropriate environments, the Output Z Aware, and Output M Aware as desired. Note that the spatial reference used during processing is the same as the output spatial reference; therefore, all Input Features must be within the X, Y, Z, and M domains. Union can run with a single input feature class or layer. In this case, instead of discovering overlap between the polygon features from the different feature classes or layers, it will discover the overlap between features within the single input. The areas where features overlap will be separated into new features with all the attribute information of the input feature. The area of overlap will always generate two identical overlapping features, one for each of the features that participates in that overlap. 

13. Identity This tool combines the portions of features that overlap the identity features to create a new feature class. Requires an ArcInfo license.

14. Identity How Identity (Analysis) works Identity calculates the geometric intersection of the input and identity feature classes and feature layers. Identity does the following: Determines the spatial reference for processing. This will also be the output spatial reference. For details on how this is done, see Spatial Reference. All the input feature classes are projected (on the fly) into this spatial reference. Cracks and clusters the features. Cracking inserts vertices at the intersection of feature edges; clustering snaps together vertices that are within the cluster tolerance. Discovers geometric relationships (overlap) between the input features and the identity features. Input Features or portions of Input Features that do not overlap Identity Features are written to the output. Input features or portions of Input Features that overlap Identity Features get the attribute information from the Identity Feature and are written to the output. To explicitly control the output spatial reference (coordinate system and domains), set the appropriate environments, the Output Z Aware, and Output M Aware as desired. Note that the spatial reference used during processing is the same as the output spatial reference; therefore, all Input Features and Identity Features must be within the X, Y, Z, and M domains.

15. Erase This tool creates a feature class from those features or portions of features outside the erase feature class. Requires an ArcInfo license.

16. Symmetrical Difference This tool creates a feature class from those features or portions of features that are not common to any of the other inputs. Requires an ArcInfo license.

17. Update This tool updates the attributes and geometry of an input feature class or layer by the Update feature class or layer that they overlap. Requires an ArcInfo license.

18. Point in polygon Uses the Intersect or Union Command with a polygon and a point feature class Returns a point feature class with attributes from the points and polygons

19. Line in Polygon Uses the Intersect or Union Command with a polygon and a line feature class Returns a line feature class with attributes from the lines and polygons

20. Extract Tools Clip Select Split Table Select

21. Clip Extracts those features or portions of features from an input feature class that overlap with a clip feature class. The Clip tool is similar to the Intersect tool, however, the Clip tool does not transfer any attributes from the clip feature class to the output. Available with any ArcGIS license.

22. Select Extracts features from an input feature class or input feature layer and stores them in a new output feature class. The output feature class may be created with a subset of features based on a Structured Query Language (SQL) expression.

23. Split The spatial extraction of features by clipping portions of the input feature class into multiple feature classes. Requires an ArcInfo license.

24. Table Select Extracts selected attributes from an input table based on an attribute query and stores them in the output table. Available with any ArcGIS license.

25. Proximity Tools Buffer Multiple Ring Buffer Near Point Distance

26. Buffer The construction of area features by extending outward from point, line, or polygon features over a specified distance. Available with any ArcGIS license.

27. Multiple Ring Buffer Creates a new feature class of buffer features using a set of buffer distances. The new features may be dissolved using the distance values or as a set of individual features. Available with any ArcGIS license.

28. Near Computes the distance from each point in a feature class to the nearest line or point in another feature class. Requires an ArcInfo license.

29. Point Distance Computes the distances between point features in one feature class to all points in a second feature class that are within the specified search radius. Requires an ArcInfo license.

30. Statistics Tools Frequency Summary Statistics

31. Frequency Produces a list of the unique code occurrences and their frequency in an output table for a specified set of fields from an input feature class or table. Optionally, summary items may be totaled for each unique code combination�for example, the total area for unique combinations of zoning and land use. Requires an ArcInfo license.

32. Summary Statistics Generates summary statistics for fields from an input table or feature class and saves them in an output table. This tool contains the following statistics types: sum, mean, minimum, maximum, standard deviation, range, first, and last. Available with any ArcGIS license.

33. Raster Spatial Analysis Local, Focal, Zonal, and Global Functions Map Algebra Terrain Analysis Hydrologic Functions

34. Local Functions

35. Focal Functions Focal, or neighborhood, functions produce an output raster dataset in which the output value at each location is a function of the value at a location and the values of the cells in a specified neighborhood around that location Dem_blur = focalmean(dem, circle, 3)

36. Zonal Functions Zonal functions compute an output raster dataset where the output value for each location depends on the value of the cell at the location and the association that that location has within a cartographic zone. ZONALMEAN (<zone_grid>, <value_grid>, {DATA | NODATA})

37. Global Functions Global functions compute an output raster dataset in which the output value at each cell location is potentially a function of all the cells in the input raster datasets. There are two groups of global functions Euclidian Distance and Weighted Distance

38. Raster calculator

39. Terrain Analysis Contour Slope Aspect Hillshade Viewshed Cut/fill

40. Performing surface analysis: Contours Contours are polylines that connect points of equal value, such as elevation, temperature, precipitation, pollution, or atmospheric pressure.

41. Slope

42. Aspect

43. Hillshade

44. Viewshed Viewshed identifies the cells in an input raster that can be seen from one or more observation points or lines. It is useful for finding the visibility. For instance, finding a well-exposed places for communication towers

45. Cut/Fill Understanding cut/fill volumetric analysis Related topics Cut/Fill summarizes the areas and volumes of change between two surfaces. It identifies the areas and volume of the surface that have been modified by the addition or removal of surface material. Learn how to calculate cut/fill using the Spatial Analyst toolbar Learn how to calculate cut/fill using the cut/fill tool By taking two surface rasters of a given area from two different time periods, the Cut/Fill function will produce a raster displaying regions of surface material addition, surface material removal, and areas where the surface has not changed over the time period. Negative volume values indicate areas that have been filled; positive volume values indicate regions that have been cut. Taking river morphology as an example, to track the amount and location of erosion and deposition in a river valley, a series of cross sections need to be taken through the valley and surveyed on a regular basis to identify regions of sediment erosion and deposition.

47. Hydrologic Analysis Basin Creates a raster delineating all drainage basins within the analysis window. Fill Fills sinks in a surface raster to remove small imperfections in the data. Flow Accumulation Creates a raster of accumulated flow to each cell by accumulating the weight for all cells that flow into each downslope cell. Flow Direction Creates a grid of flow direction from each cell to its steepest downslope neighbor. Flow Length Calculates upstream or downstream distance along a flow path for each cell. Sink Creates a grid identifying all sinks or areas of internal drainage.

48. Hydrologic analysis Snap Pour Point Snaps selected pour points to the cell of highest flow accumulation within a specified neighborhood. SnapPour Snaps selected pour points to the cell of highest flow accumulation within a specified neighborhood. Stream Link Assigns unique values to sections of a raster linear network between intersections. Stream Order Assigns a numeric order to segments of a grid representing branches of a linear network. Stream To Feature Converts a raster representing a raster linear network to a feature class. StreamShape Converts a grid representing a raster linear network to a shapefile. Watershed Determines the contributing area above a set of cells in a grid.

49. Recalssification

51. GIS is not perfect A GIS cannot perfectly represent the world for many reasons, including: The world is too complex and detailed. The data structures or models (raster, vector, or TIN) used by a GIS to represent the world are not discriminating or flexible enough. We make decisions (how to categorize data, how to define zones) that are not always fully informed or justified. It is impossible to make a perfect representation of the world, so uncertainty is inevitable Uncertainty degrades the quality of a spatial representation

52. A Conceptual View of Uncertainty U1: 1. Spatial uncertainty. firstly, Tobler�s law: spatial autocorrelation, secondly, natural units of analysis: what is the measurement unit for a soil profile, how might we delimit an environmental impact of spillage from an oil tanker? (In nature, ecological phenomena or discrete features either influence neighbors, are influenced by neighbors, or both. The level of neighbor influence may vary with distance and other factors, making the autocorrelation function non-linear. In general, the closer the neighbors, the greater the level of correlation, which distorts statistical tests of significance in analyses such as correlation, regression, or analysis of variance (Cliff and Ord 1981). ) 2. Vagueness. can exist both in the positions of the boundaries of a zone and its attributes. how many oak trees in a forested zone can label as oak woodland? how far from ABQ to Socorro 3. Ambiguity. many objects are assigned different labels by different national or cultural groups. this is inherently ambiguous. second, imperfect indicators of phenomena cause ambiguous. For example, detail household income figures, provide direct indicator of demand for goods and services; rates of multiple car ownership might provide indirect indicator for household income data. U2: 1. Measurement & Representation objects and fields: raster and vector are characterized by different uncertainties: vector requires a priori conceptualization of the nature and extent of geographic individuals and the ways in which they nest together into higher-order zones. raster defines square or rectangle cells, with boundaries that bear no relationship at all to natural features. furthermore, the measurement process can actually introduce uncertainty. 2. error and accuracy Digitizing error, GPS accuracy U3:U1: 1. Spatial uncertainty. firstly, Tobler�s law: spatial autocorrelation, secondly, natural units of analysis: what is the measurement unit for a soil profile, how might we delimit an environmental impact of spillage from an oil tanker? (In nature, ecological phenomena or discrete features either influence neighbors, are influenced by neighbors, or both. The level of neighbor influence may vary with distance and other factors, making the autocorrelation function non-linear. In general, the closer the neighbors, the greater the level of correlation, which distorts statistical tests of significance in analyses such as correlation, regression, or analysis of variance (Cliff and Ord 1981). ) 2. Vagueness. can exist both in the positions of the boundaries of a zone and its attributes. how many oak trees in a forested zone can label as oak woodland? how far from ABQ to Socorro 3. Ambiguity. many objects are assigned different labels by different national or cultural groups. this is inherently ambiguous. second, imperfect indicators of phenomena cause ambiguous. For example, detail household income figures, provide direct indicator of demand for goods and services; rates of multiple car ownership might provide indirect indicator for household income data. U2: 1. Measurement & Representation objects and fields: raster and vector are characterized by different uncertainties: vector requires a priori conceptualization of the nature and extent of geographic individuals and the ways in which they nest together into higher-order zones. raster defines square or rectangle cells, with boundaries that bear no relationship at all to natural features. furthermore, the measurement process can actually introduce uncertainty. 2. error and accuracy Digitizing error, GPS accuracy U3:

53. Map representation error

54. The ecological fallacyThe ecological fallacy is the mistake of assuming that an overall characteristic of a zone is also a characteristic of any location or individual within the zone.  The Modifiable Areal Unit Problem (MAUP)The results of data analysis are influenced by the number and sizes of the zones used to organize the data. The Modifiable Area Unit Problem has at least three aspects: The number, sizes, and shapes of zones affect the results of analysis. The number of ways in which fine-scale zones can be aggregated into larger units is often great. There are usually no objective criteria for choosing one zoning scheme over another. - An example of the influence of the number of zones on analysis is the 1950 study by Yule and Kendall which found that the correlation between wheat and potato yields in England changed from low to high as the data were grouped into fewer and fewer zones (starting with 48 and ending with 2). - An example of the influence of zone shape is gerrymandering, in which voting district boundaries are manipulated in order to engineer a desired election outcome.

57. Living with uncertainty uncertainty is inevitable and easier to find, use metadata to document the uncertainty sensitivity analysis to find the impacts of input uncertainty on output, rely on multiple sources of data, be honest and informative in reporting the results of GIS analysis. US Federal Geographic Data Committee lists five components of data quality: attribute accuracy, positional accuracy, logical consistency, completeness, and lineage (details see www.fgdc.gov)