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 * All of these are encapsulated in tools and various selection processes

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”

Principles A simple example... 5 4 7 6 3 2 1 13 10 8 Input 1 + Input 2 = Output

Maths and logic Mathematical operators Logical 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)

Overlay and distance COSTPATH example

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, focal, zonal and global Local functions 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

Local, focal, zonal and global Local functions 25 16 5 4 7 49 input output = sqr(input)

output = reclass(input) Local, focal, zonal and global Some examples input output = tan(input) output = reclass(input) output = log2(input)

Local, focal, zonal and global Focal functions 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.

output = focalsum(input) Local, focal, zonal and global Focal functions 5 4 7 16 11 input output = focalsum(input)

output = focalstd(input) output = focalvariety(input) Local, focal, zonal and global Some examples input output = focalstd(input) output = focalvariety(input) output = focalmean(input, 20)

Neighbourhood filters Local, focal, zonal and global Neighbourhood filters 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.)

Supervised classification Local, focal, zonal and global Supervised classification 1 2 3 4 5 Old class New class

Unsupervised classification Local, focal, zonal and global Unsupervised classification 1 3 4 2 5 diversity modal minimum maximum mean

Local, focal, zonal and global Zonal functions 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.

output = zonalsum(zone, input) Local, focal, zonal and global Zonal functions 5 4 7 input output = zonalsum(zone, input) zone Zone 1 Zone 2 9

Local, focal, zonal and global Some examples input Input_zone 535.54 766.62 127 160 output = zonalmax(input_zone, input) output = zonalperimeter(input_zone) 6280 10800 output = zonalthickness(input_zone)

Local, focal, zonal and global Global functions 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.

Local, focal, zonal and global Global functions 5 4 7 input output = trend(input) 9 8 6

Cartographic modelling in ArcMap Practical exercise Hands-on Exercise #3 Cartographic modelling in ArcMap Demo