Application of GRASS fuzzy modeling system:

estimation of prone risk in Arno River Area

Geoinformatics FCE CTU 2011Prague, Czech Republic, 19-20 May 2011

Jarosław Jasiewicz Adam Mickiewicz University, Geoecology and

Geoinformation InstituteDzięgielowa 27, 60-680 Poznań, Poland

&University of Cincinnati, Department of Geography,

Space Informatics Lab401 Braunstain Hall, 45221 Cincinnati OH

Margherita Di LeoDepartment of Environmental Engineering

and Physics (DIFA), University of Basilicata

via dell'Ateneo Lucano, 10, 85100 Potenza Italy

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

FUZZYFICATION(membership grades)

FUZZY LOGIC OPERATION

IMPLICATION from

antecedent to

consequent

AGGREGATION DEFUZZYFICATION

RESULT

DATA

Fuzzy mapdefinition Fuzzy rules

parameters

Fuzzy mapdefinition

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”

0 1 2 3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

1.2

fuzzyboolean

ELEVATION ABOVE STREAM

ME

MB

ER

SH

IP

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)

YES

NO

Study area: Arno river basin

Digital elevation model of Arno area

Area = 8830 km2

Elev. Range = 0 ~ 1650 m a.s.l.

DEM derivativesA)Elevation above water courses

B)Distance to streams

C)Modified topographic index

D)Minimum curvature

A

DB

C

River Network

● Created with r.stream.extract using Montgomery's approach with exponent=2 accumulation threshold=30000 and deleting streams shorter than 15 cells

● Elevation above and distance to streams have been calculated with following line command:

r.stream.extract elevation=DEM40 accumulation=ACCUM threshold=30000 mexp=2 stream_length=10 stream_rast=STREAMS stream_vect=streamsM direction=DIRSM

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

● 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)))

MTI=log((acc+1)⋅cellsize)n

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 exampleMinimal curvature TERM concave

TERM convex

Distance to streams example

TERM near TERM far

Graphical User Interface

%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)

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}

Output map defines the values for output resulting map.

THIS IS NOT PROBABILITY

(in percentage). This is only a number defining the membership in following set. For example value 71 means that it is both normal and high risk

#output map

%_OUTPUT_

● $ none {both; 0,20,20,40; linear; 0;1}

● $ low {both; 20,40,40,60; linear; 0;1}

● $ normal {both; 40,60,60,80; linear; 0;1}

● $ high {both; 60,80,80,100; linear; 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 familyseveral 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 fuzzy logic model

Risk map obtained by accurate hydrological-hydraulic models (by Arno River Basin Authority)

Validation of resultsUnderestimation (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, Italydileomargherita@gmail.com

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