Geoinformatics FCE CTU 2011


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Application of GRASS fuzzy modeling system:
estimation of prone risk in Arno River Area

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Geoinformatics FCE CTU 2011

  1. 1. Geoinformatics FCE CTU 2011 Prague, Czech Republic, 19-20 May 2011 Application of GRASS fuzzy modeling system: estimation of prone risk in Arno River Area Jarosław Jasiewicz Margherita Di Leo Adam Mickiewicz University, Geoecology and Department of Environmental Engineering Geoinformation Institute and Physics (DIFA), Dzięgielowa 27, 60-680 Poznań, Poland University of Basilicata & via dellAteneo Lucano, 10, 85100 PotenzaUniversity of Cincinnati, Department of Geography, Italy Space Informatics Lab 401 Braunstain Hall, 45221 Cincinnati OH
  2. 2. Fuzzy system● Fuzzy logic belongs to multiple-valued logic and deals with approximate reasoning rather than exact results.● In contrast with "Boolean logic", where binary sets have two-values: true or false, fuzzy logic variables may deal with partial truth with membership degree between 0 and 1, where the truth value may range between completely true and completely false.● Fuzzy logic uses linguistic variables (TERMS) which may be managed by specific functions.● Fuzzy systems steam from fuzzy set theory by Lotfi Zadeh.
  3. 3. Classic problem: who is old, who is young?
  4. 4. What is the inference process?● Fuzzy inference systems are applied in numerous fields such as automatic control, data classification, decision analysis, expert systems, or computer vision.● The most common fuzzy inference method is based on Mamdanis methodology (1975).● Fuzzy inference is a mapping process from a given input to an output. The process of fuzzy inference involves following steps:
  5. 5. Fuzzy inference process parameters DATA IMPLICATION from FUZZYFICATION FUZZY LOGIC antecedent AGGREGATION DEFUZZYFICATION(membership grades) OPERATION to consequent RESULT Fuzzy map Fuzzy map Fuzzy rules definition definition
  6. 6. GRASS Fuzzy SystemFuzzy system is powerful and easy-to-use modelingsystem for GRASS GIS.It consists of three modules: ✔ r.fuzzy.set: modeling membership in the fuzzy set ✔ r.fuzzy.logic: fuzzy logic operation ✔ r.fuzzy.system: fuzzy inference system
  7. 7. When this approach can be useful?● Every time there are no transparent rules of reasoning (use heuristics instead of procedures)● Where data are incomplete or of poor quality● Where boundaries in data clusters are uncertain or fuzzy● When we want to improve simple overlay models based on binary logic
  8. 8. The main difference between boolean and fuzzy reasoning: If elevation_above_river is <5m and distance_to_river is <400m then flood_risk is 95% We assume here we know the rules of river behavior according long term monitoring or precise modeling. If not, we still can use heuristic: If elevation_above_river is “low” and distance_to_river is “near” then flood_risk is “high”
  9. 9. What does it mean?● We do not know precise notion of TERM LOW but we can assume that it is something below 3m (absolutely yes) between 3m and 5m (maybe) and above 5m (absolutely no) 1.2 1 0.8 MEMBERSHIP NO 0.6 fuzzy boolean 0.4 YES 0.2 0 0 1 2 3 4 5 6 7 8 ELEVATION ABOVE STREAM
  10. 10. Study area: Arno river basinDigital elevation model ofArno areaArea = 8830 km2Elev. Range = 0 ~ 1650 m a.s.l.
  11. 11. DEM derivatives AA)Elevation above water coursesB)Distance to streamsC)Modified topographic indexD)Minimum curvature C B D
  12. 12. River Network● Created with using Montgomerys approach with exponent=2 accumulation threshold=30000 and deleting streams shorter than 15 cells elevation=DEM40 accumulation=ACCUM threshold=30000mexp=2 stream_length=10 stream_rast=STREAMS stream_vect=streamsM direction=DIRSM● Elevation above and distance to streams have been calculated with following line command: stream=STREAMS dirs=DIRSM elevation=DEM40 method=downstream distance=DISTANCESTREAMS difference=ELEVATIONDIFF
  13. 13. River Network
  14. 14. Minimal curvature● Minimal curvature (suitable to detect channels) was calculated as follows: r.param.scale input="DEM40" output="MINCURV" s_tol=1.0 c_tol=0.0001 size=5 param="maxic"
  15. 15. MTI Topographic Index ● MTI has been calculated according Manfreda 2007 ((acc+1)⋅cellsize)n MTI=log tan(slope+0.001) ● MTI has been proven (Manfreda et al. 2011) to be strongly related to flood prone areasr.param.scale input=DEM40 output=SLOPE size=5 param=sloper.watershed -a -b elevation=DEM40 accumulation=ACCUM convergence=2r.mapcalc MTI = log((exp(((ACCUM+1)*40),0.087))/(tan(SLOPE+0.001)))
  16. 16. Fuzzyfication● Fuzzyfication is a process which in most fuzzy logic systems creates a lot of intermediate or even resulting maps● GRASS fuzzy system can use r.fuzzy.set to visualize/analyze results of fuzzyfication process (however this stage is not necessary)
  17. 17. Minimal curvature exampleMinimal curvature TERM concave TERM convex
  18. 18. Distance to streams example TERM near TERM far
  19. 19. Graphical User Interface
  20. 20. Definition of fuzzy sets (MAP file)%MTI● $ low {right; 3,5; sshaped; 0; 1}● $ moderate {both; 3,5,7,9; sshaped; 0; 1}● $ high {left; 7,9; sshaped; 0; 1}%ELEVATIONSTREAMS● $ low {right; 2,4; sshaped; 0; 1}● $ moderate {both; 2,3,5,6; sshaped; 0; 1}● $ high {both; 5,6,7,8; sshaped; 0; 1}● $ veryhigh {left; 7,8; sshaped; 0; 1}%DISTANCESTREAMS● $ near {right; 100,300; sshaped; 0; 1}● $ far {both; 100,300,500,600; sshaped; 0; 1}● $ veryfar {left; 500,600; sshaped; 0; 1}%CURVMIN● $ concave {right; -0.007,-0.003; sshaped; 0; 1}● $ flat {both; -0.007,-0.003,0,0.0001; sshaped; 0; 1}● $ convex {left; 0,0.0001; sshaped; 0; 1}
  21. 21. Definition of fuzzy sets (MAP file)%MTI● $ low {right; 3,5; sshaped; 0; 1} Output map defines the values for output resulting map.● $ moderate {both; 3,5,7,9; sshaped; 0; 1}● $ high {left; 7,9; sshaped; 0; 1} THIS IS NOT PROBABILITY%ELEVATIONSTREAMS (in percentage). This is only a number defining the membership in following set. For example● $ low {right; 2,4; sshaped; 0; 1} value 71 means that it is both normal and high● $ moderate {both; 2,3,5,6; sshaped; 0; 1} risk● $ high {both; 5,6,7,8; sshaped; 0; 1}● $ veryhigh {left; 7,8; sshaped; 0; 1} #output map %_OUTPUT_%DISTANCESTREAMS● $ near {right; 100,300; sshaped; 0; 1} ● $ none {both; 0,20,20,40; linear; 0;1}● $ far {both; 100,300,500,600; sshaped; 0; 1} ● $ low {both; 20,40,40,60; linear; 0;1}● $ veryfar {left; 500,600; sshaped; 0; 1} ● $ normal {both; 40,60,60,80; linear; 0;1}%CURVMIN ● $ high {both; 60,80,80,100; linear; 0;1}● $ concave {right; -0.007,-0.003; sshaped; 0; 1}● $ flat {both; -0.007,-0.003,0,0.0001; sshaped; 0; 1}● $ convex {left; 0,0.0001; sshaped; 0; 1}
  22. 22. Definition of fuzzy rules (RUL file) There are four rules which determine flood risk: they are stored in separate file arno.rul● $ none {(CURVMIN=convex & ELEVATIONSTREAMS=high) | ELEVATIONSTREAMS=veryhigh} areas where is no risk are defined as: all convex areas lying high above watercourses OR lying very high above watercourses● $ low {MTI=low & ELEVATIONSTREAMS~veryhigh} the area of low probability are defined as area of low values of topographic index AND (but) not very high. It usually means higher areas in deeply dissected mountain valleys● $ normal {MTI = moderate | ELEVATIONSTREAMS=moderate | CURVMIN = concave} two types of areas has been qualified as area of moderate risk: area with moderate MTI OR lying not very high above watercourses (lowlands) OR in concave valleys (mountains)● $ high {(ELEVATIONSTREAMS = low & MTI = high) | (ELEVATIONSTREAMS = low & DISTANCESTREAMS = near)} also two type of areas: low lying with high MTI for flats like Arno delta and low lying and nearby watercourses for rest of areas
  23. 23. Other parameters● Fuzzy logic family several fuzzy logic family (es. Zadeh, Lukasiewicz, Fodor, Hamacher etc.)● Implication method product or maximum● Universe resolution (precision of analysis)● Defuzzyfication method several methods including centroid and bisector
  24. 24. Final result : flood risk mapFlood risk:HighNormalLowNone
  25. 25. Validation of results Risk map obtained byRisk map obtained by accurate hydrological-fuzzy logic model hydraulic models (by Arno River Basin Authority)
  26. 26. Validation of results Underestimation (area of no risk inside ARNO RISK area according to our model in yellow)Overlay of the two risk maps Overestimation (area of low and higher risk outside ARNO RISK area according to our model in yellow)
  27. 27. Conclusions✔ The model is suitable to detect flood prone areas only on the basis of DEM derivatives.✔ Thanks to fuzzy logic it was possible to build the model without quantify all the variables involved in the process, only using linguistic variables.✔ The approach can be applied to many other different contests✔ r.fuzzy.system is very easy to apply without advanced knowledge on fuzzy logic.
  28. 28. License of this document This work is licensed under a Creative Commons License. 2011, Margherita Di Leo, Italy dileomargherita@gmail.comLicense details: Attribution-ShareAlike 3.0:You are free: * to Share — to copy, distribute and transmit the work * to Remix — to adapt the workUnder the following conditions: * Attribution — You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). *Share Alike — If you alter, transform, or build upon this work, you may distribute the resulting work onlyunder the same, similar or a compatible license.With the understanding that: * Waiver — Any of the above conditions can be waived if you get permission from the copyright holder. * Other Rights — In no way are any of the following rights affected by the license: o Your fair dealing or fair use rights; o The authors moral rights; o Rights other persons may have either in the work itself or in how the work is used, such as publicity or privacy rights.