Spatio-temporal models Involve a least a three dimensional representation of one or more key attribute variation in planar (X-Y) space and through time. (a 4 th dimension could also be use, like Z for modeling a vertical direction) Continuous fields - e.g. temperature, soil ph Discontinuous objects e.g. land cover type Process based e.g. hydrologic cycle Purely fit model Spatio-temporal models Deterministic Same output from same input Stochastic Some random generation process, to capture chaos in systems Spatio-temporal hydrologic models Predicting fluctuation in soil moisture, lake/ stream levels or discharge over time Often depends on DEM information (slope, aspect) to determine flow direction Examples of other data: Precipitation, solar radiation, surface evaporation, transpiration, infiltration, vegetation, etc Mathematical functions describing cell-specific precipitation and discharge could be combined to predict the flow quantity at points in the network Example spatio-temporal model
Individual Process Models (Agent-based Models) Behavior of a set of agents are coded, and respond to a spatial neighborhood Spatial environment created, typically through a stack of GIS layers Model runs identify the impact of various behavioral relationships or rules on individual and aggregate action Output may be analyzed statistically, to identify important emergent properties, or as a decision support tool Sortie Spatially explicit, stochastic model of forest dynamics Individual light interactions drive growth Growth drives gap mortality and gap formation Gaps affect reproduction Pacala, 1993; 1995 8
Cellular Automatons - Raster Automata in a Vector Domain
Mobile Automata - Rules of Movement and Action Random walk with variation in X Directed movement with spatial behavior Mobile Automata on a Variable Surface http://www.youtube.com/watch?v=cnar8bfzcx0 Traffic: http://vwisb7.vkw.tu-dresden.de/~treiber/microapplet/ Boids: http://vimeo.com/1794249 Summary for 2-D Spatio-temporal Models Statistical, point models applied spatially to estimate continuous surface (e.g., USLE erosion). Process models, in both continuous and discrete forms, with interacting neighborhoods (WEPP erosion and transport) Discrete, individual focus models in continuous or discrete spatial domains
Lecture Ques*ons Discussion A.) Have County File and a polluted well point file; What county is the Well in? Name: What B.) Have road file and stream file; What roads are within 10 meters of a stream? C.) Have Orthophoto of park area; what is the length of paved roads in park? D.) Have dwelling loca*ons polygon files for both 1950 and 2009; how many houses were build aper 1950? E.) Have classified landcover file of a county and also a city boundary file; How much green space is in each city? F.) Have DEM and a landcover file showing dominant tree species; Where should you look for very slow growing White or Black Spruce trees? Discussion A.) Have County File and a polluted well point file; What county is the Well in? B.) Have road file and stream file; What roads are within 10 meters of a stream? C.) Have Orthophoto of park area; what is the length of paved roads in park? D.) Have dwelling loca*ons polygon files for both 1950 and 2009; how many houses were build aper 1950? E.) Have classified landcover file of a county and also a city boundary file; How much green space is in each city? F.) Have DEM and a landcover file showing dominant tree species; Where should you look for very slow growing White or Black Spruce trees? What Opera1on (s) to Intersect Buffer roads, buffer streams; intersect Digi*zed paved roads and calculate geometry Create binary fields in both files, union and find the in 2009 not in 1950 Union, reclassify & summarize by city Calculate slope & aspect; select steep & north slopes; intersect, convert to polygon; reclassify landcover and dissolve; intersect with north slopes