Geographical Information Systems Pavel Hrubeš

Department of Transport Telematics Rehearsal Model of the Earth Sphere Elipsoid/Spheroid Geoid Projections Plane Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Modelling - Introduction GIS provides: comprehensive set of tools for spatial data management limited spatial analysis functionality but does provides framework of application limited spatial analysis functionality may be addressed by linking models into GIS Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Spatial modelling issues Model problems: most models do not provide tools for data management and display, etc. many models are aspatial GIS provides: framework of application allows user to add spatial dimension (if not already built into the model) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics Modelling guidelines In order to ensure that model results are as close to reality as possible the following guidelines apply: ensure data quality beware of making too many assumptions match model complexity with process complexity compare predicted results with empirical data where possible and adjust model parameters and constants to improve goodness of fit use results with care! Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Basics of cartographic modelling Mathematics applied to raster maps often referred to as map algebra or ‘mapematics’ e.g. combination of maps by: addition subtraction multiplication division, etc. operations on single or multiple layers Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics A definition “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” Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics A simple example… 1 4 3 2 5 4 7 6 3 Input 1 2 4 2 1 2 3 6 + 6 3 3 4 2 1 6 2 Input 2 4 6 4 3 1 3 2 4 = 7 7 6 6 7 7 13 5 Output 6 10 8 5 2 5 5 10 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics Question… How determine topological relationships? i.e. Boolean: AND, NOT, OR, XOR What is the arithmetic equivalent? Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Building spatial models It is (in theory) surprisingly simple: algebraic combination of: OPERATORS and FUNCTIONS rules and relationships inputs (and outputs) interfaces run at the command line/menu interface batch file embedded in system macro/script ‘hard’ programmed into system Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Problems in model building Knowledge systems and processes relationships and rules Compatability input data available outputs required Quality issues data quality (accuracy, appropriateness, etc.) model assumptions and generalisation confidence and communication Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics Modelling 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) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics 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 Other local functions Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics Local functions 5 4 7 input 25 49 16 output = sqr(input) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

output = reclass(input) Some examples input output = tan(input) output = reclass(input) output = log2(input) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics 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. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics Focal functions 5 4 7 input 11 16 output = focalsum(input) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Some examples input output = focalmean(input, 20) output = focalstd(input) output = focalvariety(input) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

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.) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Supervised classification 1 2 3 4 5 Old class New class Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Unsupervised classification 1 3 4 2 5 diversity modal minimum maximum mean 5 4 1 5 3 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics 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. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics Zonal functions 5 4 7 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 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Some examples input Input_zone 535.54 127 6280 766.62 160 10800 output = zonalthickness(input_zone) output = zonalperimeter(input_zone) output = zonalmax(input_zone, input) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics 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. Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics Global functions 5 4 7 input 6 7 8 9 5 6 7 8 4 5 6 7 output = trend(input) 4 5 6 6 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics Distance functions Simple 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 Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Some examples input source output = eucdistance(source) output = eucdirection(source) output = costdistance(source, input) Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics COSTPATH example Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics

Department of Transport Telematics Conclusions Linking/building models to GIS Idea of maths with maps surprisingly simple, flexible and powerful technique basis of all raster GIS Fundamental to spatial interpolation, distance and neighbourhood functions Czech Technical University in Prague - Faculty of Transportation Sciences Department of Transport Telematics