El model SLEUTH. Un Automatisme Cel lular aplicat al creixement urbà. Conceptes Bàsics. Robert Colombo June 6th, 2005

Transcription

1 El model SLEUTH. Un Automatisme Cel lular aplicat al creixement urbà. Conceptes Bàsics Robert Colombo June 6th, 2005

2 What is all about? Sleuth is a Cellular automata model based on Monte Carlo methods (random values), that uses Brute Force calibration methods to derive a set of coefficients to predict future states based on known situations as reference. Cellular automata are mathematical models for complex natural systems containing large numbers of simple identical components with local interactions (Wolfram, 1984). 2

3 What Does SLEUTH mean? SLEUTH is the acronym for Slope, (Pendent) Land use, (Ús del sol) Exclusion, (Exclusio) Urban extent, (Extensio urbana) Transportation, (Transportation) Hill shade, ( Sombrejat) 3

4 Who created the Model? The model was created in 1992 from an early research work of Dr Clarke (University of California, Santa Barbara, Department of Geography) while visiting USGS as a research scientist SLEUTH is written in C+ language and uses standard gnu libraries. The model works under UNIX systems The model has been applied in Cities around the world but basically in USA. Organizations such as NASA use this software for their predictions 4

5 A CA system usually consists of four basic elements: Cells. Set of states (occuppied/free, on/off, ). Neighborhoods defined by cells. Rules. Time periods. 5

6 Cells are the smallest units which must manifest some adjacency or proximity. Cells can be Pixels from Raster images. The cell state is updated considering the close environmental situations and states, not only a particular theoretical rule (Automata). 6

7 The state of a cell can change according to transition rules which are defined in terms of neighborhood functions (Xia &Gar 1998 ). This transition between one pixel state to another takes place in discrete time steps according to fixed rules (Wolfram 1986). 7

8 Neighborhoods can be configured in several ways : agglomerations of adjacent distance-defined cells clusters of cells Von Neumann (5 cell) 5 x 5 Moore 3 x 3 Moore 8

9 Each time step in a model could be called Cycle or Iteration or Generation. A simulation is just a sum of Cycles that determine a simulation for a specific time period. 9

10 The SLEUTH model SLEUTH is composed of 2 modules Urban Growth Model: prediction on how an urban area will grow (extension and development) prediction of the land cover change Land Use Deltaron The LCD: land use/cover transition model (Alive/dead cells) 10

11 Every Growing Cycle in SLEUTH is based in : Rules: they will allow the model to develop following certain patterns, using the assigned coefficients. Coefficient: set by the user every time but acquired using statistical methods, represent the metrics of a concrete behaviour (probaility, frequency, ) If the results of this performance reach the Critical high or Critical low values (selected by the user), the self modification procedure will be applied to make the growing model more real, adapted to a reality not always linear. 11

12 Growing Cycle in SLEUTH Initial conditions Computing Work Seed Number (1,..) + COEFFICIENTS Diffusion (User defined Start-Step-Stop) Breed (User defined Start-Step-Stop) Spread (User defined Start-Step-Stop) Slope (User defined Start-Step-Stop) Road Gravity (User defined Start-Step-Stop) Road gravity sensitivity (Definition optional) Slope sensitivity (Definition optional) Critical Low (Definition optional) Critical High (Definition optional) Critical Slope (Definition optional) Boom (Definition optional) Bust (Definition optional) IMAGES (GIF) Slope Land Use (optional) Excluded land Urban Extent Transportation network Hill shade + + N Growing cycles = Completed simulation 12

13 Growth Rules: A set of decisions, or growth, rules applied to the data to simulate urban driven land cover change. The Exclude land and Slope input layers limit the areas suitable for urbanization The UGM model works with 4 basic growth dynamics Spontaneous Growth New Spreading Centers Edge Growth Road-Influenced Growth 13

14 Spontaneous Growth: Defines the occurrence of random urbanization of land. Any cell from the un-urbanized category has a certain probability of becoming urban. Existent Urban cells Spontaneous Growth cell 14

15 New Spreading Center Growth: Determines if a new urban center born from a spontaneously growth, can become a center for future urban spreading center (determined by the Breed coefficient) Existent Urban cells New spreading center cell Newly urbanized cells from a new spreading center cell 15

16 Edge Growth: if there is a urban cell that has at least three free neighbor ready to urbanize cells, it has a probability (controlled by the Spread coefficient and the slope coefficient) to become urban. Non urbanized cells (no edge growing procedure) (t+1) Urbanized cells. Edge growing centers Urban cells product of Edge Growing 16

17 Road-Influenced Growth: If a road is found in a radius (road gravity coeff) of a new urbanized cell (Breed coef), a temporary urbanized cell is placed in the point where the road network is close to the urban cell. This temporary cell randomly moves across the urban network (moves defined by Dispersion coeff). The final location of this new urban cell then acts as a new urban spreading center. Possible in more than one cell at the time 17

18 Self modification rules: The coefficient values in a simulation do not have to remain static. Due to rapid or to low growth rates the coefficients may be increased or decreased by the system. The limits Critical high and Critical Low have effect in three of the growth control parameters: dispersion, breed, and spread, increasing or decreasing the values. Quoted from Project Gigalopolis Website 18

19 Coefficient: Affect how the growth rules are applied. These values are calibrated by comparing simulated land cover change to a study area's historical data. (reference input images). Dispersion Breed Spread Slope resistance Road gravity 19

20 Dispersion coefficient: In spontaneous growth type, controls the number of times a pixel will be randomly selected for possible urbanization. Possibly influenced by Road weighting, controls how many "steps", or pixels, make up a random walk along the transportation network on a road trip. 20

21 Breed coefficient: In New spreading center growth type: determines the probability of a spontaneous growth pixel becoming a new spreading center. In Road influenced growth the breed coefficient determines the number of times a road trip will be taken. 21

22 Spread coefficient: In Edge growth type: determines the probability that any pixel that is part of a spreading center (a cluster of urban pixels > 2 in 3x3 neighborhood) will generate an additional urban pixel in its neighborhood. 22

23 Slope coefficient: Building in lower slopes is easier than in higher slopes. The Critical Slope coefficient shows where building it s impossible. The proportion of flatland has a very big influence of the pressure to build in upper slopes. The slope coefficient acts as a multiplier. If the slope coefficient is high, increasingly steeper slopes are less likely to urbanize. 23

24 Road gravity coefficient: In Road influenced growth type the maximum search distance for a road from a pixel selected for a road trip is determined as some proportion of the image dimensions. (Project Gigalopolis USGS

25 Coefficient Selection: Subjectivity aspect in the SLEUTH results due to the coefficient selection methods used. The coefficient values are derived from the intensive calibration process in which each coefficient is tested individually 25

26 Coefficient Selection: Example of UNIX terminal message while computing Sleuth. Example of statistical results obtained in SLEUTH in original format (txt file, and treated in Office-like program. Brute force method means All possible combination will be tried, even if they are non realistic Lee Salee Weighted sum Best Run Diffusion Breed Spread Slope Road Gravity Best Run Diffusion Breed Spread Slope Road Gravity Corase Fine Final Different results obtained using 2 different Coefficient value selection 26

27 Coefficient Selection: file name created in mode flag dependent LOG_# T, C, P yes avg.log T, C, P yes coeff.log T, C, P yes control_stats.log T, C no restart_file.data# T, C, P no std_dev.log T, C, P yes List of available statistical output files available in Sleuth T=Test C=Calibration P=Prediction Metrics available in the control_stats.log statistical files, used for coefficient selection and for image information. 27

28 Model Inputs Images: The input images for SLEUTH need to follow some requirements to be analyzed in the model: Grey scale images (8 bit ranging from a pixel value of 0 to 255 where 0 means no-data and 255 means data filled ). Same number of rows and columns and pixel size for all images. Named following certain rules. Gif format. 28

29 The model needs to work at least 9 layers: 4 Urban extent layers (one for a different time period, derived for classified satellite images). 1 Excluded land layers (locate the non urbanizable areas) 2 Transportation network layers (from two different years) 1 Slope layer (derived from a DEM), 1 Hill shade layer (Derived from a DEM), Naming rules for GIF images and example for Project Atlanta Urban data GIFs format: <location>.urban.<date>.[<user info>].gif Atlanta200.urban.1983.gif Atlanta200.urban.1987.gif Atlanta200.urban.1992.gif Atlanta200.urban.1997.gif Road data GIFs format: <location>.roads.<date>.[<user info>].gif Atlanta200.roads.1992.gif Atlanta200.roads.1997.gif Landuse data GIFs format: <location>.landuse.<date>.[<user info>].gif Atlanta200.landuse.1983.gif Atlanta200.landuse.1997.gif Excluded data GIF format: <location>.excluded.[<user info>].gif Atlanta200.excluded.gif Slope data GIF format: <location>.slope.[<user info>].gif Atlanta200.slope.gif Background data GIF format: <location>.hillshade.[<user info>].gif Atlanta200.hillshade.gif *Atlanta 200: Input origin folder 29

30 Input image Examples a b c d e f Three sets of urban layers 1983, and *100 b)200*200 c)400*400 all of them reduced to the same size (not used in SLEUTH) 30

31 Excluded Hillshade Roads Slope Input data layers used in the Atlanta metro area. The colors are exaggerated. Note the binary code. 31

32 Excluded Hillshade Roads Original Layers with original color codes. Slope 32

33 Model Application Scenario Files: The Scenario files are regular text files that contain a specific commands, basically coefficient ranges, image layer paths, color legend patterns, output image file flags (numeric or alphanumeric choosing values), and all the basic information for a SLEUTH model. 33

34 SLEUTH simulation Scheme: 1 Model inputs Test phase Error Correct 2 Calibration phase Coarse Calibration Fine Calibration Final Calibration Deriving Calibration Prediction phase 3 Error Correct END 34

35 Model Phases and modes: Test: The phase was created as a way to generate a set of historical data simulations, for a single coefficient set without requiring a Start or Stop coefficients to be set. It s now use, as the name shows to run simple simulations to test the images 35

36 Model Phases and modes: Calibration: The user will have to set the coefficients and refine the selection for them several times to acquire finally some coefficient values valid for prediction mode, using Brute force methods. 36

37 Model Phases and modes: Calibration: Coarse: the range of the coefficient values to derive is set to the maximum values (0-100) using large increments (typical steps of 25). The resolution of the data is normally ¼ of the total resolution. Fine: The selection of the values comes from the control_stats.log from the coarse calibration output folder. The value range will be narrowed. The data used will be ½ of the total resolution (the resolution is being incremented). 37

38 Model Phases and modes: Calibration: Final: using the best fit values from the control_stats.log in the fine calibration, the range of coefficients will be narrowed again. Derive: with the coefficients obtained from the final calibration another calibration process will be run to obtain more robust coefficients for prediction phase. The number of Monte Carlo iteration for this calibration method is set to 100 or greater. 38

39 Model Phases and modes: Prediction: This phase will lead to predict how an urban area will grow with the coefficients derived from the Calibration process. All the previous phases are just processed to be able to get the coefficient values for this final step 39

40 Model Phases and modes: Coefficients obtained from calibrations for Project Atlanta Test Coarse Fine Final Derive Image Resolution Seed Monte Carlo Iterations Diffusion Start Diffusion Step Diffusion Stop Breed Start Breed Step Breed Stop Spread Start Spread Step Spread Stop Slope Resistance Start Slope Resistance Step Slope Resistance Stop Road Gravity Start Road Gravity Step Road Gravity Stop Time 0.5h 18h 25h 40h 0.25h Example of coefficient result, time of computation and data used in every phase for the 1st Colombo simulation of the Atlanta MA. 40

41 SLEUTH simulation Scheme: Model inputs Test phase Error Correct Calibration phase Coarse Calibration Fine Calibration Final Calibration Deriving Calibration Correct Prediction phase Error END 41

42 Results: Depending on the coefficient selection the results of the simulation will vary. Also the method of coefficient selection during the calibration process can derive on false values The model can help when trying to predict future situations and scenarios not only related on land consumption but taking care of human effects on newly developed areas, (transportation, water demand, ) 42

43 Results: The possible output available contains: Graphic images Growth type Land use change Urban Growth probability Deltatron Aging image Statistical files (derived from images) file name created in mode flag dependent LOG_# T, C, P yes avg.log T, C, P yes coeff.log T, C, P yes control_stats.log T, C no restart_file.data# T, C, P no std_dev.log T, C, P yes 43

44 Results: Coefficients Used Colombo Yand&Lo Samples Diffusion Bread Spread Slope Road Grav Gif images resulting from the different SLEUTH simulations a) 1st Colombo b) Samples, c) Yang&Lo coefficients The images can be easily imported in a GIS software to analyze the results 44

45 Graphic Output: Output image representing, prediction of urban growth in 2015 for Atlanta Metro. A succession of images creating an animation is also available. 45

46 1,600,000 New Urban pixels 1,400,000 1,200,000 1,000, , , ,000 3rdColombo coef 1st Colombo coeff. Samples coeff Yang&Lo coeff 200,000-1st Colombo Yang&Lo Samples 2nd Colombo 3rd Colombo Diffusion Breed Spread Slope Road Gravity

47 Questions and Future job to develop: Is SLEUTH a valid model for European urban structures? Is it valid for the Barcelona Metro Area? How does the urban planning need to be referred in the model? Can we predict real and complex scenarios (planning, economic crisis, demographic explosion, )? Can de model be suitable for Regressive urban areas? What is the weight of Public transport in models? 47

48 Questions and Future job to develop: Are there other types of dynamic growth not represented in the present model? Can the coefficient selection method be improved? Is this model useful for small urban areas. What's the best resolution to use in the input layers. Comparative analysis between SLEUTH and other CA (Dinamica framework, DUEM, ). 48

49 References and further reading (selection): Xiaojun Yang, (2000) Integrating image analysis and dynamic spatial modeling with GIS in a rapidly suburbanizing environment, Thesis (Ph. D.)--University of Georgia, Dir. C.P. Lo Yang, X., and Lo, C.P Modeling urban growth and landscape change in the Atlanta metropolitan area. International Journal of Geographical Information Science 17: Torrens, P M & O'Sullivan, D, 2001, "Cellular automata and urban simulation: where do we go from here?", Environment and Planning B Dietzel, Ch. and Clarke K. (2004)Determination of Optimal Calibration Metrics through the use of Self-Organizing Maps. Presentation for the Integrated assessment of the land system: The future of land useinstitute for Environmental Studies, Amsterdam October 30th, 2004 Clarke K. and Dietze Ch.l (2005)A Decade of SLEUTHing: Lessons Learned from Applications of a Cellular Automaton Land Use Change Model, Department of Geography, University of California,Santa Barbara, USA Benenson, I. & Torrens, P.M. (2004). "Geosimulation: object-based modeling of urban phenomena". Ed Wiley. 49

50 Web sites: Gracies!! 50