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Copyright, 1998-2012 © Qiming Zhou GEOG3600. Geographical Information Systems Spatial Analysis

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2 Analysis or modelling? Vector GIS analysis capabilities Raster GIS analysis capabilities Geographical analysis procedure

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Spatial Analysis3 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.

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Spatial Analysis4 Analysis or modelling? The advantage a GIS can provide is the capability for transforming the original spatial data to answer users questions. Such transformations are often referred to as data analysis capabilities in GIS. However, most so-called analysis capabilities of todays GIS are in fact data manipulation and maintenance functions, very rare of them are actually tell us something by analysing spatial data.

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Spatial Analysis5 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.

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Spatial Analysis6 Analysis versus modelling A theory is the product of analysis. A model is the product of syntheses, using theory.

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Spatial Analysis7 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.

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Spatial Analysis8 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.

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Spatial Analysis9 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.

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Spatial Analysis10 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.

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Spatial Analysis11 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)

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Spatial Analysis12 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.

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Spatial Analysis13 Vector analysis functions Geographical query (introduced previously) Data manipulation Topological overlay Buffering Terrain analysis (to be introduced later) Network Analysis (to be introduced later)

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Spatial Analysis14 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. Data manipulation

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Spatial Analysis15 Reclassify, dissolve and merge Soil types A, B and C with growth potentials d and f Soil types A, B and C Ad BdCf Bf Cd Ad A B B C C A A B C A Reclassify Dissolve & merge

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Spatial Analysis16 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.

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Spatial Analysis17 Point in polygon IDRestaurant 1McDonald 2Pizza Hut 3KFC 4McDonald 5Berger King IDTown AShi Qi BGang Kou CSan Jiao IDTownRestaurant 1Shi QiMcDonald 2Gang KouPizza Hut 3Gang KouKFC 4San JiaoMcDonald 5San JiaoBerger King Fast food restaurantTowns 12 3 4 5 12 3 4 5 A B C

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Spatial Analysis18 Line on polygon IDRoad No. 135 222 335 460 5 635 782 835 IDGeology AGranite BSandstone CSand IDOriginalRoad No. Geology 1222Granite 2222Sandstone 3135Sandstone 4335Sandstone 5460Granite 6460Sandstone 7560Sandstone 8635Sandstone 9635Sand 10782Sand 11835Sand RoadsGeology 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 10 11 A B C

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Spatial Analysis19 Polygon on polygon IDWater shed County 11A 21B 33B 42A 52B 64B 72C 84C WatershedCounty 1 2 3 4 A B C 1 2 3 4 56 78

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Spatial Analysis20 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

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Spatial Analysis21 Buffering on point, line and area d d d Buffering a point e.g. area within 1km to a hospital. Buffering a line e.g. area within 100m to a road. Buffering an area e.g. area within 100m to a building.

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Spatial Analysis22 Buffering example

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Spatial Analysis23 Raster analysis functions Local functions (point functions) Zonal functions (regional functions) Focal functions (neighbourhood functions) Global functions

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Spatial Analysis24 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.

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Spatial Analysis25 The generic form of local functions U = f (X 1, X 2, …) For example: new_map = old_map_1 + old_map_2

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Spatial Analysis26 Spatial context of local functions X Y Z A B U U = f (A, B)

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Spatial Analysis27 Average 3.0 2.5 2.0 3.0 2.5 3.0 2.5 3.0 2.5 3.0 1.5 2.0 2.5 2.0 1 2 1 1 1 2 2 1 1 3 3 2 2 3 3 2 5 4 4 3 5 3 4 5 4 3 2 4 1 1 2 2 = mean, Eg. outgrid = mean(ingrid_1, 2 * ingrid_2, (ingrid_3 + ingrid_4))

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Spatial Analysis28 Merge 1 4 1 1 1 3 4 1 1 3 3 4 1 3 3 2 1 N 1 1 1 N N 1 1 3 3 N N 3 3 N 5 4 4 3 5 3 4 5 4 3 2 4 1 1 2 2 = merge, Eg. outgrid = merge(ingrid_1, ingrid_2, …) If X 1 == NODATA then U = X 2 else U = X 1

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Spatial Analysis29 Maximising 5 4 4 3 5 3 4 5 4 3 3 4 2 3 3 2 1 2 1 1 1 2 2 1 1 3 3 2 2 3 3 2 5 4 4 3 5 3 4 5 4 3 2 4 1 1 2 2 = max, Eg. outgrid = max (ingrid_1, ingrid_2) U = max (X 1, X 2, …)

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Spatial Analysis30 Minimising 1 2 1 1 1 2 2 1 1 3 2 2 1 1 2 2 1 2 1 1 1 2 2 1 1 3 3 2 2 3 3 2 5 4 4 3 5 3 4 5 4 3 2 4 1 1 2 2 = min, Eg. outgrid = min (ingrid_1, ingrid_2) U = min (X 1, X 2, …)

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Spatial Analysis31 Reclassification – arbitrary 1 2 1 1 1 2 2 1 1 3 3 2 2 3 3 2 5 4 5 5 5 4 4 5 5 2 2 4 4 2 2 4 Given a 1, a 2, …, a n and b 1, b 2, …, b n if X == a 1 then U = b 1 else if X == a 2 then U = b 2 … else U = X XU 123123 542542 Lookup table 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))

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Spatial Analysis32 3 N N N 3 N N 3 3 N N N 4 N N 4 1 2 1 1 1 2 2 1 1 3 3 2 2 3 3 2 5 3 3 3 5 3 3 5 5 3 2 5 2 2 2 2 Given a 1, a 2, …, a n ; b 1, b 2, …, b n ; c 1, c 2, …, c n if X1 == a 1 and X 2 = b 1 then U = c 1 else if X1 == a 2 and X 2 == b 2 then U = c 2 … else U = NODATA 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 Coding scheme ingrid2 ingrid1 123123 235235 1-34-----1-34----- Boolean Reclassification – Boolean

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Spatial Analysis33 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.

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Spatial Analysis34 Characteristics of zonal functions Do not change boundaries of regions Change attribute values for each region (or zone) according to its statistics or users specification Useful for understanding spatial distribution of objects, quantitative measurement of shapes, statistical properties of objects and spatial associations

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Spatial Analysis35 Outcome of zonal functions Statistic Tables Reclassify Summarising properties of regions Spatial correlation

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Spatial Analysis36 Reclassification – statistical Slice Divide range values into in either equal intervals or equal areas Outgrid = slice(ingrid, ~ EQAREA | EQINTERVAL, ~ nzones, base_zone#, ~ in_min, in_max)

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Spatial Analysis37 Zonal statistics 2.0 0.75 2.0 0.75 2.0 0.75 2.0 0.5 0.75 4 4 4 3 4 3 4 4 4 3 2 4 1 1 2 2 = zonalarea Database definition: 1 cell = 2,500 m 2 Unit: km 2 Zonal Area Reassign the value to each region according to the area measurement Outgrid = zonalarea (ingrid) (based on 50x50m grid cell size)

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Spatial Analysis38 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.

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Spatial Analysis39 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

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Spatial Analysis40 Problem addressed by focal functions Fire station 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

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Spatial Analysis41 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

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Spatial Analysis42 Focal statistics 1 4 3 5 6 3 2 2 1 5 1 1 2 1 2 6 2 3 1 7 5 5 4 7 5 6 2 2 4 5 6 8 2 8 6 4 3 1 7 8 3 2 3 5 1 1 4 3 1 2 2 4 3 2 1 2 5 2 2 6 5 7 3 2 3.5 3.8 1 4 3 5 6 3 2 2 1 5 1 1 2 1 2 6 2 3 1 7 5 5 4 7 5 6 2 2 4 5 6 8 2 8 6 4 3 1 7 8 3 2 3 5 1 1 4 3 1 2 2 4 3 2 1 2 5 2 2 6 5 7 3 2 Focal mean Focal grid Data grid Result grid

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Spatial Analysis43 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.

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Spatial Analysis44 Contiguity analysis outcome 1 1 5 5 1 2 2 2 1 5 5 1 1 1 2 4 1 3 3 1 1 5 4 5 2 2 2 2 4 5 5 5 2 2 2 4 3 1 4 5 3 2 3 3 1 1 4 4 3 2 3 1 4 1 1 2 3 2 3 4 4 4 1 2 1 1 4 4 7 11 1 4 4 7 7 7 13 1 5 5 7 7 12 13 12 2 2 2 2 8 2 2 2 8 6 9 14 12 3 2 6 6 9 9 14 3 2 6 9 10 9 9 15 3 2 6 10 9 15

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Spatial Analysis45 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.

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Spatial Analysis46 Proximity analysis variables A 12345 6 7 B A 12345 6 7B Absolute Barrier 8 9 A 12345 6 7B 8 9 Travel zones defined by Euclidean distance The effect of an absolute barrier on travel zones The effect of a partial barrier (friction) on travel zones

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Spatial Analysis47 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.

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Spatial Analysis48 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.

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