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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 dell'Ateneo Lucano, 10, 85100 Potenza
University of Cincinnati, Department of Geography,                        Italy
               Space Informatics Lab
    401 Braunstain Hall, 45221 Cincinnati OH
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.
Classic problem: who is old, who is
              young?
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 Mamdani's methodology (1975).
●   Fuzzy inference is a mapping process from a given
    input to an output. The process of fuzzy inference
    involves following steps:
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
GRASS Fuzzy System

Fuzzy system is powerful and easy-to-use modeling
system 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
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
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”
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
Study area: Arno river basin




Digital elevation model of
Arno area

Area = 8830 km2
Elev. Range = 0 ~ 1650 m a.s.l.
DEM derivatives
                                  A
A)Elevation above water courses
B)Distance to streams
C)Modified topographic index
D)Minimum curvature

                         C




       B                              D
River Network
●   Created with r.stream.extract using Montgomery's
    approach with exponent=2 accumulation
    threshold=30000 and deleting streams shorter than
    15 cells
      r.stream.extract elevation=DEM40 accumulation=ACCUM threshold=30000
mexp=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:
          r.stream.distance stream=STREAMS dirs=DIRSM elevation=DEM40
      method=downstream distance=DISTANCESTREAMS difference=ELEVATIONDIFF
River Network
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"
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 areas

r.param.scale input=DEM40 output=SLOPE size=5 param=slope

r.watershed -a -b elevation=DEM40 accumulation=ACCUM convergence=2

r.mapcalc MTI = log((exp(((ACCUM+1)*40),0.087))/(tan(SLOPE+0.001)))
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)
Minimal curvature example
Minimal curvature         TERM concave




                          TERM convex
Distance to streams example




 TERM near            TERM far
Graphical User Interface
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}
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}
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
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
Final result : flood risk map




Flood risk:

High


Normal


Low


None
Validation of results




                       Risk map obtained by
Risk map obtained by   accurate hydrological-
fuzzy logic model      hydraulic models (by
                       Arno River Basin
                       Authority)
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)
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.
License of this document

            This work is licensed under a Creative Commons License.
                   http://creativecommons.org/licenses/by-sa/3.0/

                                   2011, Margherita Di Leo, Italy
                                           dileomargherita@gmail.com


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Geoinformatics FCE CTU 2011

  • 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 dell'Ateneo Lucano, 10, 85100 Potenza University of Cincinnati, Department of Geography, Italy Space Informatics Lab 401 Braunstain Hall, 45221 Cincinnati OH
  • 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. Classic problem: who is old, who is young?
  • 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 Mamdani's methodology (1975). ● Fuzzy inference is a mapping process from a given input to an output. The process of fuzzy inference involves following steps:
  • 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. GRASS Fuzzy System Fuzzy system is powerful and easy-to-use modeling system 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. 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. 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. 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. Study area: Arno river basin Digital elevation model of Arno area Area = 8830 km2 Elev. Range = 0 ~ 1650 m a.s.l.
  • 11. DEM derivatives A A)Elevation above water courses B)Distance to streams C)Modified topographic index D)Minimum curvature C B D
  • 12. River Network ● Created with r.stream.extract using Montgomery's approach with exponent=2 accumulation threshold=30000 and deleting streams shorter than 15 cells r.stream.extract elevation=DEM40 accumulation=ACCUM threshold=30000 mexp=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: r.stream.distance stream=STREAMS dirs=DIRSM elevation=DEM40 method=downstream distance=DISTANCESTREAMS difference=ELEVATIONDIFF
  • 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. 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 areas r.param.scale input=DEM40 output=SLOPE size=5 param=slope r.watershed -a -b elevation=DEM40 accumulation=ACCUM convergence=2 r.mapcalc MTI = log((exp(((ACCUM+1)*40),0.087))/(tan(SLOPE+0.001)))
  • 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. Minimal curvature example Minimal curvature TERM concave TERM convex
  • 18. Distance to streams example TERM near TERM far
  • 19.
  • 21. 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}
  • 22. 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}
  • 23. 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
  • 24. 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
  • 25. Final result : flood risk map Flood risk: High Normal Low None
  • 26. Validation of results Risk map obtained by Risk map obtained by accurate hydrological- fuzzy logic model hydraulic models (by Arno River Basin Authority)
  • 27. 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)
  • 28. 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.
  • 29. License of this document This work is licensed under a Creative Commons License. http://creativecommons.org/licenses/by-sa/3.0/ 2011, Margherita Di Leo, Italy dileomargherita@gmail.com License details: Attribution-ShareAlike 3.0: You are free: * to Share — to copy, distribute and transmit the work * to Remix — to adapt the work Under 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 only under 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 author's 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.