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Prof. Qiming Zhou Spatial Analysis Spatial Analysis

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**Spatial Analysis Analysis or modelling?**

Prof. Qiming Zhou Spatial Analysis Analysis or modelling? Vector GIS analysis capabilities Raster GIS analysis capabilities Geographical analysis procedure Spatial Analysis Spatial Analysis

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**Map analysis and modelling**

Prof. Qiming Zhou Map analysis and modelling “What distinguishes a GIS from other types of information systems are its spatial analysis functions. These functions use the spatial and non-spatial attribute data in the GIS database to answer questions about the real world”. Aronoff, 1989, pp 189. Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Analysis or modelling? The advantage a GIS can provide is the capability for transforming the original spatial data to answer user’s questions. Such transformations are often referred to as “data analysis” capabilities in GIS. However, most so-called “analysis” capabilities of today’s GIS are in fact data manipulation and maintenance functions, very rare of them are actually tell us something by “analysing” spatial data. Spatial Analysis Spatial Analysis

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**Definitions What is “analysis”?**

Prof. Qiming Zhou Definitions What is “analysis”? Analysis specifies data transformations which are analytical. “Analysis” is the process to resolve and separate the reference system into its parts to illuminate their nature and interrelationships, and to determine general principles of behaviour. What is “modelling”? Modelling specifies data transformations which involve the synthesis of information. The “synthesis” is the process to put together expressions of general principles with representations of parts of the reference system so as to form a replica that exhibits behaviour similar to that of the reference system. Spatial Analysis Spatial Analysis

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**Analysis versus modelling**

Prof. Qiming Zhou Analysis versus modelling A theory is the product of analysis. A model is the product of syntheses, using theory. Spatial Analysis Spatial Analysis

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**Spatial analysis and GIS**

Prof. Qiming Zhou Spatial analysis and GIS Geographical analysis allows the study of real-world processes by developing and applying models. A GIS enhances this process by providing tools which can be combined in a meaningful sequences to develop new models. These models may reveal new or previously unidentified relationships thus increasing our understanding of the real world. Results of geographical data analysis can be communicated with maps, reports, or both. Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Geographical model A GIS database is a model of the real world that can be used to mimic certain aspects of reality. A model must represent certain entities and relationship among them. A model may be represented in words, in mathematical equations, or as a set of spatial relations presented by maps or GIS. Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou The nature of models Models are designed to mimic only selected aspects of reality. A more complex model may or may not provide “better” answer. A model can be tested and manipulated more conveniently at a faster (or slower) rate and less expensively than the condition it mimics. Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou The use of models Models are used when it is more convenient or it is not possible to collect the information directly. e.g. It is convenient to measure road distance on a map. e.g. The height a forest will reach in 100 years time is impossible to measure directly. A model is used to understand what happened in the past and to present scenario on what consequence might be with the present conditions. Spatial Analysis Spatial Analysis

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**Organising geographical data for analysis**

Prof. Qiming Zhou Organising geographical data for analysis Data layers A data layer consists of a set of logically related geographical features and their attributes Representations of a data layer Raster grid, overlay (grid cells) Vector coverage (point, line, polygon) Spatial Analysis Spatial Analysis

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**GIS analysis functions**

Prof. Qiming Zhou GIS analysis functions A GIS provides analysis and modelling capability by means of its analysis functions. GIS analysis functions are capable of processing spatial and attribute data together. Based on GIS data model, GIS analysis functions can be categorised into vector and raster analysis functions. Spatial Analysis Spatial Analysis

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**Vector analysis functions**

Prof. Qiming Zhou Vector analysis functions Geographical query (introduced previously) Data manipulation Topological overlay Buffering Terrain analysis (to be introduced later) Network Analysis (to be introduced later) Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Data manipulation Mostly for manipulate spatial data to fit into application specifications. For example, in working with area objects to aggregate areas based on attributes: Commonly a three-step procedure is used: Reclassify areas by a single attribute or some combination; Dissolve boundaries between areas of same type by delete the arc between two polygons if the relevant attributes are the same in both polygons; Merge polygons into large objects by recording the sequence of line segments that connect to form the boundary and assigning new ID numbers to each new object. Spatial Analysis Spatial Analysis

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**Reclassify, dissolve and merge**

Prof. Qiming Zhou Reclassify, dissolve and merge Ad Bd Cf Bf Cd Reclassify Dissolve & merge A B C A B C Soil types A, B and C with growth potentials d and f Soil types A, B and C Soil types A, B and C Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Topological overlay Suppose individual layers have planar enforcement, when two layers are combined (overlaid or superimposed), the result must have planar enforcement as well. New intersection must be calculated and created wherever two lines cross and a line across an area object will create two new area objects. When topological overlay occurs, spatial relationships between objects area updated for the new, combined map. Spatial Analysis Spatial Analysis

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**Point in polygon Fast food restaurant Towns ID Restaurant 1 McDonald 2**

Prof. Qiming Zhou Point in polygon Fast food restaurant Towns 1 2 3 4 5 ID Restaurant 1 McDonald 2 Pizza Hut 3 KFC 4 5 Berger King A B C ID Town A Shi Qi B Gang Kou C San Jiao ID Town Restaurant 1 Shi Qi McDonald 2 Gang Kou Pizza Hut 3 KFC 4 San Jiao 5 Berger King 1 2 3 4 5 Spatial Analysis Spatial Analysis

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**Line on polygon Roads Geology Spatial Analysis Prof. Qiming Zhou**

ID Road No. 1 35 2 22 3 4 60 5 6 7 82 8 1 2 3 4 5 6 7 8 A B C ID Geology A Granite B Sandstone C Sand ID Original Road No. Geology 1 2 22 Granite Sandstone 3 35 4 5 60 6 7 8 9 Sand 10 82 11 1 2 3 4 5 6 7 8 9 10 11 Spatial Analysis Spatial Analysis

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**Polygon on polygon Watershed County Spatial Analysis Prof. Qiming Zhou**

1 2 3 4 A B C ID Watershed County 1 A 2 B 3 4 5 6 7 C 8 1 2 3 4 5 6 7 8 Spatial Analysis Spatial Analysis

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**Buffering A buffer can be constructed around a point, line or area.**

Prof. Qiming Zhou Buffering A buffer can be constructed around a point, line or area. Buffering algorithm creates a new area enclosing the buffered object. The application of this buffering algorithms fundamentally addresses the creation of zones around the target. e.g. protected zone around lakes, reservoirs or streams zone of noise pollution around highways or airports service zone around bus route groundwater pollution zone around waste site Spatial Analysis Spatial Analysis

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**Buffering on point, line and area**

Prof. Qiming Zhou Buffering on point, line and area d Buffering a point e.g. area within 1km to a hospital. d Buffering a line e.g. area within 100m to a road. d Buffering an area e.g. area within 100m to a building. Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Buffering example Spatial Analysis Spatial Analysis

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**Raster analysis functions**

Prof. Qiming Zhou Raster analysis functions Local functions (point functions) Zonal functions (regional functions) Focal functions (neighbourhood functions) Global functions Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Local functions Local functions operate on the values of all the attributes relating to each cell (location). The operations are independent of the effects of attribute values from neighbouring cells. A local function results in a new grid as a function of one or more input grids. Spatial Analysis Spatial Analysis

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**The generic form of local functions**

Prof. Qiming Zhou The generic form of local functions U = f (X1, X2, …) For example: new_map = old_map_1 + old_map_2 Spatial Analysis Spatial Analysis

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**Spatial context of local functions**

Prof. Qiming Zhou Spatial context of local functions Z A B U = f (A, B) Y U X Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Average 3.0 3.0 2.5 1.5 1 1 1 2 5 5 4 1 2.0 3.0 3.0 2.0 1 1 2 2 3 5 4 2 = mean , 2.5 3.0 2.5 2.5 1 2 3 3 4 4 2 2 3.0 2.5 3.0 2.0 2 2 3 3 4 3 3 1 Eg. outgrid = mean(ingrid_1, 2 * ingrid_2, (ingrid_3 + ingrid_4)) Spatial Analysis Spatial Analysis

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**Merge , = merge Eg. outgrid = merge(ingrid_1, ingrid_2, …)**

Prof. Qiming Zhou Merge 1 1 1 1 1 1 1 N 5 5 4 1 1 1 4 2 1 1 N N 3 5 4 2 = merge , 1 4 3 3 1 N 3 3 4 4 2 2 4 3 3 3 N N 3 3 4 3 3 1 If X1 == NODATA then U = X2 else U = X1 Eg. outgrid = merge(ingrid_1, ingrid_2, …) Spatial Analysis Spatial Analysis

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**Maximising = max , U = max (X1, X2, …)**

Prof. Qiming Zhou Maximising 5 5 4 2 1 1 1 2 5 5 4 1 3 5 4 2 1 1 2 2 3 5 4 2 = max , 4 4 3 3 1 2 3 3 4 4 2 2 4 3 3 3 2 2 3 3 4 3 3 1 U = max (X1, X2, …) Eg. outgrid = max (ingrid_1, ingrid_2) Spatial Analysis Spatial Analysis

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**Minimising = min , U = min (X1, X2, …)**

Prof. Qiming Zhou Minimising 1 1 1 1 1 1 1 2 5 5 4 1 1 1 2 2 1 1 2 2 3 5 4 2 = min , 1 2 2 2 1 2 3 3 4 4 2 2 2 2 3 1 2 2 3 3 4 3 3 1 U = min (X1, X2, …) Eg. outgrid = min (ingrid_1, ingrid_2) Spatial Analysis Spatial Analysis

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**Reclassification – arbitrary**

Prof. Qiming Zhou Reclassification – arbitrary X U 1 2 3 5 4 Lookup table 1 1 1 2 5 5 5 4 1 1 2 2 5 5 4 4 1 2 3 3 5 4 2 2 2 2 3 3 4 4 2 2 Given a1, a2, …, an and b1, b2, …, bn if X == a1 then U = b1 else if X == a2 then U = b2 … else U = X Eg. If (ingrid == 1) outgrid = 5 else if (ingrid == 2) outgrid = 4 else if (ingrid == 3) outgrid = 2 endif or outgrid = con(ingrid == 1, 5, ~ con(ingrid == 2, 4, 2)) Spatial Analysis Spatial Analysis

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**Reclassification – Boolean**

Prof. Qiming Zhou Reclassification – Boolean 1 1 1 2 5 5 5 2 Given a1, a2, …, an; b1, b2, …, bn; c1, c2, …, cn if X1 == a1 and X2 = b1 then U = c1 else if X1 == a2 and X2 == b2 then U = c2 … else U = NODATA 1 1 2 2 3 5 5 2 1 2 3 3 3 3 2 2 2 2 3 3 3 3 3 2 Boolean Coding scheme ingrid2 ingrid1 1 2 3 2 3 5 1 - 3 4 - - - - - 3 3 3 4 Eg. If (ingrid1 == 1 & ingrid2 == 2) outgrid = 1 else if (ingrid1 == 2 & ingrid2 == 2) outgrid = 4 else if (ingrid1 == 1 & ingrid2 == 5) outgrid = 3 endif N 3 N 4 N N N N N N N N Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Zonal functions Zonal functions operate on properties of the region (or zone) to which a given cell belongs. These properties might be: length, area or shape number of locations having a certain attribute value on one grid that occurs within the area defined by a region on another grid. Spatial Analysis Spatial Analysis

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**Characteristics of zonal functions**

Prof. Qiming Zhou Characteristics of zonal functions Do not change boundaries of regions Change attribute values for each region (or zone) according to its statistics or user’s specification Useful for understanding spatial distribution of objects, quantitative measurement of shapes, statistical properties of objects and spatial associations Spatial Analysis Spatial Analysis

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**Outcome of zonal functions**

Prof. Qiming Zhou Outcome of zonal functions Reclassify Statistic Tables Summarising properties of regions Spatial correlation Spatial Analysis Spatial Analysis

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**Reclassification – statistical**

Prof. Qiming Zhou Reclassification – statistical Slice Divide range values into in either equal intervals or equal areas Slice in equal intervals Slice in equal areas Outgrid = slice(ingrid, ~ EQAREA | EQINTERVAL, ~ nzones, base_zone#, ~ in_min, in_max) Spatial Analysis Spatial Analysis

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**Zonal statistics Zonal Area = zonalarea**

Prof. Qiming Zhou Zonal statistics Zonal Area Reassign the value to each region according to the area measurement 2.0 2.0 2.0 0.5 4 4 4 1 0.75 2.0 2.0 0.75 3 4 4 2 = zonalarea 2.0 2.0 0.75 0.75 4 4 2 2 2.0 0.75 0.75 0.5 4 3 3 1 Unit: km2 Database definition: 1 cell = 2,500 m2 (based on 50x50m grid cell size) Outgrid = zonalarea (ingrid) Spatial Analysis Spatial Analysis

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**The focal and global functions**

Prof. Qiming Zhou The focal and global functions The focal functions relate a cell to its neighbours. These are functions that explicitly make use of some kind of spatial associations in order to determine the value for the locations on the new output grid. Spatial Analysis Spatial Analysis

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**Focal function parameters**

Prof. Qiming Zhou Focal function parameters Every focal function requires at least three basic parameters: Target location(s) (neighbourhood focus) A specification of the neighbourhood around each target A function to be performed on the elements within the neighbourhood Spatial Analysis Spatial Analysis

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**Problem addressed by focal functions**

Prof. Qiming Zhou Problem addressed by focal functions Question: What is the number of residential buildings within 5km to the given fire station? Target: fire station Neighbourhood: the area within 5km radius Function: count the number of residential buildings Fire station Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Spatial search Compute an attribute value for each target cell as a function of attribute values of its neighbourhood in an existing grid. Target: target cell(s) on focal grid Functions: sum, mean, standard deviation, etc. Neighbourhood: circular, square or “ring-shape” Spatial Analysis Spatial Analysis

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**Focal statistics Focal grid Focal mean Result grid Data grid**

Prof. Qiming Zhou Focal statistics Focal grid Focal mean Result grid 1 1 2 5 2 3 1 5 4 5 3 6 8 2 2 2 3 1 1 2 6 3 2 2 3.5 5 1 7 2 4 5 4 6 Data grid 6 2 5 4 3 1 3 5 3 1 5 5 1 1 2 7 3.8 1 1 2 5 2 3 1 5 2 2 4 6 7 4 1 3 4 5 3 6 8 2 2 2 2 6 7 8 8 3 2 2 3 1 1 2 6 3 2 2 5 1 7 2 4 5 4 6 6 2 5 4 3 1 3 5 3 1 5 5 1 1 2 7 2 2 4 6 7 4 1 3 2 6 7 8 8 3 2 2 Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Contiguity Uniquely identifying individual contiguous groups or “clumps” of cells on an existing grid The output grid has every polygon (or group of cells) uniquely numbered ranging from 1 to n, where n is the total number of polygons found in the grid. Spatial Analysis Spatial Analysis

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**Contiguity analysis outcome**

Prof. Qiming Zhou Contiguity analysis outcome 1 1 1 2 2 3 3 3 1 1 1 2 2 3 3 3 1 5 3 2 2 2 2 2 1 4 5 2 2 2 2 2 5 5 3 2 2 3 3 3 4 4 5 2 2 6 6 6 5 1 1 2 4 3 1 4 4 7 7 2 8 6 9 10 1 1 1 4 3 1 4 4 7 7 7 8 6 9 10 10 2 1 5 5 1 1 1 4 11 7 12 12 9 9 9 10 2 2 4 5 4 4 1 1 11 11 13 12 14 14 9 9 2 4 5 5 5 4 2 2 11 13 12 12 12 14 15 15 Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Proximity Compute an attribute value for each cell according to the length of the shortest path between that cell and the target location or area. The distance can be measured in Euclidean distance or “cost distance” (or “weighted distance”). The least-cost path is the route between two targets where the cost distance is the minimum. In many cases, the cost distance is different from the Euclidean distance. Spatial Analysis Spatial Analysis

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**Proximity analysis variables**

Prof. Qiming Zhou Proximity analysis variables A 1 2 3 4 5 6 7 B The effect of a partial barrier (friction) on travel zones A 1 2 3 4 5 6 7 B Absolute Barrier 8 9 A 1 2 3 4 5 6 7 B 8 9 Travel zones defined by Euclidean distance The effect of an absolute barrier on travel zones Spatial Analysis Spatial Analysis

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**Spatial analysis procedure**

Prof. Qiming Zhou Spatial analysis procedure Establish the objectives and criteria for the analysis. Prepare the data for spatial operations. Perform the spatial operations. Prepare the derived data for tabular analysis. Perform the tabular analysis. Evaluate the interpret the results. Refine the analysis as needed. Spatial Analysis Spatial Analysis

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Prof. Qiming Zhou Summary One most significant advantage for GIS is the capability for geographical analysis. GIS analytical capabilities are closely related to its data model. Vector data analysis functions include, e.g., geographical query, manipulation, topological overlay, buffering, terrain analysis and network analysis. Raster data analysis functions include, e.g., local, zonal, focal and global functions. Spatial Analysis Spatial Analysis

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