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Cartographic modelling. Day 1: cartographic modelling. Principles Mathematical and logical functions Overlay and distance functions Local, focal, zonal and global functions Spatial Analyst and ArcGrid. Principles. Mathematics applied to raster maps Map algebra or ‘mapematics’
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Day 1: cartographic modelling • Principles • Mathematical and logical functions • Overlay and distance functions • Local, focal, zonal and global functions • Spatial Analyst and ArcGrid
Principles • Mathematics applied to raster maps • Map algebra or ‘mapematics’ • e.g. combination of maps by: • Addition • Subtraction • Multiplication • division, etc. • operations on single layers • operations on multiple layers
Principles • “A generic means of expressing and organising the methods by which spatial variables and spatial operations are selected and used to develop a GIS model”
5 7 4 Principles 4 • A simple example... 1 3 2 3 6 4 2 2 6 1 2 3 Input 1 6 3 3 4 2 1 6 2 + 4 6 4 3 1 3 2 4 Input 2 7 7 6 6 13 5 7 7 = 6 10 8 5 2 10 5 5 Output
Maths and logic • Mathematical operators • Addition, subtraction, multiplication, division • Square, squareroot, logarithms, exponents, etc. • Trigonometry, etc. • Logical operators • Boolean (AND, OR, NOT, XOR) • Relative (maximum, minimum, etc.) • Combinatory • Etc.
Overlay and distance • Overlay is achieved mathematically • e.g. in raster calculator
Overlay and distance • Distance functions • calculate the linear distance of a cell from a target cell(s) such as point, line or area • use different distance decay functions • linear • non-linear (curvilinear, stepped, exponential, root, etc.) • use target weighted functions • use cost surfaces
Some examples Overlay and distance input source output = eucdistance(source) output = eucdirection(source) output = costdistance(source, input)
COSTPATH example Overlay and distance
Local, focal, zonal and global • Four basic categories of functions in map algebra: • local • focal • zonal • global • Operate on user specified input grid(s) to produce an output grid, the cell values in which are a function of a value or values in the input grid(s)
Local functions Local, focal, zonal and global • Output value of each cell is a function of the corresponding input value at each location • value NOT location determines result • e.g. arithmetic operations and reclassification • full list of local functions in GRID is enormous • Trigonometric, exponential and logarithmic • Reclassification and selection • Logical expressions in GRID • Operands and logical operators • Connectors, statistical, and other local functions
5 7 4 Local functions Local, focal, zonal and global input 25 49 16 output = sqr(input)
Some examples Local, focal, zonal and global input output = reclass(input) output = log2(input) output = tan(input)
Focal functions Local, focal, zonal and global • Output value of each cell location is a function of the value of the input cells in the specified neighbourhood of each location • Type of neighbourhood function • various types of neighbourhood: • 3 x 3 cell or other • calculate mean, SD, sum, range, max, min, etc.
5 7 4 Focal functions Local, focal, zonal and global input 11 16 output = focalsum(input)
Some examples Local, focal, zonal and global input output = focalvariety(input) output = focalstd(input) output = focalmean(input, 20)
Neighbourhood filters Local, focal, zonal and global • Type of focal function • used for processing of remotely sensed image data • change value of target cell based on values of a set of neighbouring pixels within the filter • size, shape and characteristics of filter? • filtering of raster data • supervised using established classes • unsupervised based on values of other pixels within specified filter and using certain rules (diversity, frequency, average, minimum, maximum, etc.)
1 2 1 3 4 1 1 2 3 1 2 4 5 1 2 2 1 2 4 1 1 2 4 5 2 Old class New class Supervised classification Local, focal, zonal and global
diversity 1 3 4 modal 2 4 5 1 2 4 minimum maximum mean Unsupervised classification Local, focal, zonal and global 5 4 1 5 3
Zonal functions Local, focal, zonal and global • Output value at each location depends on the values of all the input cells in an input value grid that shares the same input value zone • Type of complex neighbourhood function • use complex neighbourhoods or zones • calculate mean, SD, sum, range, max, min, etc.
5 7 4 Zonal functions Local, focal, zonal and global input Zone 2 zone Zone 1 9 7 7 7 9 7 7 7 9 9 9 7 output = zonalsum(zone, input) 9 9 9 7
Some examples Local, focal, zonal and global input Input_zone 535.54 127 6280 766.62 160 10800 output = zonalmax(input_zone, input) output = zonalperimeter(input_zone) output = zonalthickness(input_zone)
Global functions Local, focal, zonal and global • Output value of each location is potentially a function of all the cells in the input grid • e.g. distance functions, surfaces, interpolation, etc. • Again, full list of global functions in GRID is enormous • euclidean distance functions • weighted distance functions • surface functions • hydrologic and groundwater functions • multivariate.
5 7 4 Global functions Local, focal, zonal and global input 6 7 8 9 5 6 7 8 4 5 6 7 output = trend(input) 4 5 6 6
Practical exercise • Hands-on Exercise #3 • Cartographic modelling in ArcMap