EstimationMethodofInundationExtentBasedon …downloads.hindawi.com/journals/mpe/2019/7825831.pdf · 2019-11-07 · ResearchArticle EstimationMethodofInundationExtentBasedon MathematicalMorphology

Research ArticleEstimation Method of Inundation Extent Based onMathematical Morphology

Jianxun Li 1 Kin Keung Lai 2 and Paul Safonov 3

1School of Economics and Management Xirsquoan University of Technology Xirsquoan 710048 China2College of Economics Shenzhen University Shenzhen 518060 China3Herberger Business School St Cloud State University St Cloud MN 56301 USA

Correspondence should be addressed to Kin Keung Lai mskklaioutlookcom

Received 16 June 2019 Revised 30 August 2019 Accepted 23 September 2019 Published 16 October 2019

Academic Editor Ioannis Kostavelis

Copyright copy 2019 Jianxun Li et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Estimation of inundation extent is critical for the flood control system It helps decision-maker determine the scope of damage tosave residentsrsquo lives and property In this paper we analyzed the drawbacks of two kinds of methods of inundation estimationhydrodynamic method and space-filling method and divided inundation extent into water-body extent and water-invasion extentfor the purpose of enhancing estimation accuracy Based on Mathematical Morphology an inundation estimation methodsuitable for flood mapping around natural and artificial lakes was put forward by integrating remote sensing (RS) data and digitalelevation model (DEM) datais method consists of three aspects including the subdivision of water-body extent the deductionof water-invasion extent which is viewed as the expansion of water-body extent and the smoothing the boundaries of water-invasion extent With subdividing DEM data horizontally into cross sections to build equiangular subsets the expansion op-eration was implemented by structuring elements which were established based on set operations and scalar flexibilities uswater-invasion extent was easily described by the structuring elements under given water volume so that inundation extent wasconveniently estimated by spatial data e experiment results show that the method has the advantages of high accuracy andexpressiveness and low time consumption It had been used to analyze the inundation caused by the water conservancy projectnamed Hanjiang-to-Weihe RiverWater Transfer Project in Chinaemethod served as decision support for building an efficientemergency response mechanism and helped implement flood disaster forecast and simulation

1 Introduction

Inundation is result from flood and tsunami and even fromthe construction of hydraulic projects that cuts off river tobuild a dam Viewed as a distinct model of catastropheinundation usually poses threats to mankindrsquos existence anddevelopment e United Nations Office for Disaster RiskReduction (UNDRR) reports that inundation accounts forover 30 of all natural disaster losses Inundation appears tobe a particular serious problem in crowded China due to itslong time span wide range unexpected frequency andtremendous devastation Statistically China has long beenharassed by inundations and is confronted with catastrophicflood every two years Approximately 28 of arable land and46 of the population nationwide are subject to the det-rimental effect of inundations thus hampering the

sustainable development of economy and society In theprocess of recovering from these damages inundation es-timation plays a significant role in analyzing the affectedextent and the loss amount It forecasts inundation extentmarks the flood-stricken region and gives emergency re-sponse instructions

For the convenience of analysis and estimation we di-vided the inundation extent into water-body extent andwater-invasion extent Water-body extent inundating low-lying region below water surface elevation is related to theregional terrain and water volume Water-invasion extentnamely the region adjacent to water-body extent is gen-erally determined by water surface elevation terrain andgeological conditions Considering the inaccuracy of mostwater-body extent estimations and the difficulty in water-invasion extent measurement we regarded water-invasion

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 7825831 10 pageshttpsdoiorg10115520197825831

extent as the expansion of water-body extent due to the factthat water-invasion extent produced by capillary rise is thesaturated portion of the soil surrounding water-body extenten a more accurate estimation method combining space-filling method and RS data was proposed for inundationestimation by introducing the Mathematical Morphologye method is mainly suitable for flood mapping aroundnatural and artificial lakes We has implemented the methodonDigital Earth platform and formulated a prototype systemwhich could analyze the affected extent in real time

e remainder of the paper is organized as followsSection 2 briefly reviews related work on inundation esti-mation Section 3 presents an estimation method for in-undation depth and inundation extent based onMathematical Morphology In Section 4 an experimentenvironment with the Digital Earth platform is built to verifythe effectiveness of the method Section 5 concludes thepaper and provides remarks

2 Literature Review

e estimation method of inundation extent is currentlydivided into two categories One is hydrodynamic methodwhich simulates the depth distribution of water mobilityresolves continuity equations and motion equations andthen estimates inundation extent by the evolution of un-steady flow is method requires calculating partial dif-ferential equations with multiple parameters e other oneis space-filling method which takes DEM as basic data Withthe help of GIS or RS it employs a differential method todecompose the research area into lots of differential units inthe light of certain elevation e water of these units isdynamically accumulated until the discrepancy betweencumulative result and water volume is less than the specificthreshold representing the estimation accuracy

21 Hydrodynamic Method Hydrodynamic method in-tegrates hydrology and hydrodynamics to build a model offlood routing by using equations of continuity and motionsIt takes into account the characteristics of water trans-mission river bed evaluation roughness coefficient andturbulent viscosity coefficient erefore the unsteady flowand its variation occurred at different inundating time iseasily simulated Based on hydrodynamics Horritt et al [1]constructed an assessment method involving spatial scale Itprovided prototype solutions for inundation estimationCombining the flood extent information derived from RSimagery and hydrodynamic simulations Nguyen et al [2]proposed a model for estimating inundation depth andspatially distributed water level e model provided moreeffective assessment for local-scale pluvial flood Due to itsstrong feasibility hydrodynamic model has fully been ap-plied to the assessment of inundation extents eg Bates et al[3] and Podhoranyi et al [4] In recent years researchersmainly studied on the estimation accuracy computationspeed and simulation environment of inundation As to theestimation accuracy Ilorme [5] discussed the influence ofthe inaccuracy of hydrological data and the insufficiency of

hydrometrical stations based on the investigation into thehomogeneity in inundation extent For quickly estimatinginundation at hyperresolutions Follum et al [6] put forwarda routing application for parallel computation of dischargewhich can be applied quickly over very large spatial extentsIn order to build a simulation environment Murphy et al[7] introduced a hydraulic and hydrologic modeling soft-ware Infoworks ICM (Integrated Catchment Modelling)into flood inundation e software used unstructured tri-angular mesh and advanced numerical scheme which im-proved the simulation speed and calculation accuracy Inaddition there have been several studies aiming at thesubproblem of inundation estimation by hydrodynamicmethod For example Gobeyn et al [8] took LISFLOOD-FPmodel as an explicit forward difference scheme for com-puting the shallow water wave over the floodplain Patel et al[9] carried out a simulation work under the 1D2D couplehydrodynamicmodeling in low-lying areas Faghih et al [10]applied nonparametric bootstrap sampling to simulate in-undation with different flow rates which provided a ref-erence for the uncertainty analysis of inundation

Above all under the conservation laws of specific watervolume hydrodynamic method fully demonstrates hydro-logical characteristics and serves as an accurate estimationmodel to estimate inundation extent Relying on partialdifferential equations the method obtains a relatively preciseestimation of inundation extent and provides a vivid ex-pression of water-body extent furthermore clearly de-scribing the dynamic features of inundation However themodel usually contains plenty of parameters and complexequations proved hard to solve [11] In particular mostexisting studies fail to take into consideration the boundaryterrain soil conditions vegetation and the water absorptionby the earth in water-invasion extent estimation

22 Space-Filling Method Space-filling method approxi-mately simulates the ultimate equilibrium of inundation byviewing the water surface as a plane Based on the overlandrunoff model this method estimates inundation extent aswell as inundation depth [12] such as the automatic in-tegrated estimation approach by Noman et al [13] Sincespace-filling method is implemented by simple mathemat-ical calculations with large errors the research mainly fo-cuses on improving the estimation accuracy Dewan et al[14] earlier used airborne laser altimetry for analyzing in-undation extent It leads researchers to introduce geospatialdata into space-filling method Geospatial data such as GISRS and DEM can offer more possibilities for increasing theaccuracy of inundation estimation One of the representativemethods was proposed by Mason et al [15] who adopted RSdata to rectify the traditional estimation model With thecombination of flooding data and RS data Kamontum [16]applied Landsat and IRS images to inundation extentanalysis further improving the estimation of inundationboundary Recently scholars conducted in-depth researchon the estimation model of DEM data or cellular automataapproach [17 18] Saksena and Merwade [19] consideredthat vertical accuracy is related to the spatial resolution

2 Mathematical Problems in Engineering

errors of DEM properties Teng et al [20] developed andimplemented a floodplain inundation model that uses high-resolution DEM to derive floodplain storages and connec-tivity between them at different river stages Moreover withthe support of interpolation techniques Sopelana et al [21]proposed a continuous simulation method for the estima-tion of extreme inundation in coastal river reaches It en-hanced the effectiveness and practicability of space-fillingmethod in inundation estimation

To sum up space-filling method is not as accurate ashydrodynamic method but convenience to calculationDepending on digital elevation the method uses total watervolume and elevation data to conduct alignment analysise accuracy of space-filling method could be considerablyenhanced when the digital elevation has high accuracy andthe connected regions become easy to identify Howeverdue to the lack of the ability to make full use of spatial datathe method fails to manifest the terrain factors and calculatewater-invasion extent e inundation extent estimated bythe method is usually smaller than the actual extent since itdoes not distinguish between inundation extent and water-invasion extent

Except the two categories of hydrodynamic methodand space-filling method there are some other methodsmentioned by researchers such as empirical methodsimplified method [22] and Bayesian statistical method[23] However looking at the results of existing re-searches they mostly ignore the estimation of water-invasion extent and only regard water-body extent asinundation extent because it is difficult to describe water-invasion extent which is related to the boundary of waterterrains and landforms us incorporating the Math-ematical Morphology [24] we proposed an inundationestimation method by combined space-filling methodand RS data e method divided inundation extent intowater-body extent and water-invasion extent with hightimeliness and accuracy It is worth mentioning thatVernieuwe et al [25] have put forward a MathematicalMorphology approach for a qualitative exploration ofdrought events in space and time is study demon-strates that the expansion operation and erosion oper-ation of Mathematical Morphology can be used toanalyze water-related problems More importantly Liet al [26] have presented an inundation estimationmethod using the Mathematical Morphology algorithmbut they adopted simple structuring elements and lackthe consideration of water-invasion issues erefore theaccuracy of inundation extent analysis still has a chanceto be improved

3 Inundation Estimation Based onMathematical Morphology

As a theory for obtaining intrinsic characteristics bystructuring elements Mathematical Morphology is widelyused in image processing artificial intelligence shapeanalysis and topology research It can extract the shape ofthe object and explore the morphologic changes under avariety of conditions thus providing a basic evolutionary

method tool between different structures In this paperwe divide the inundation extent into water-body extentand water-invasion extent Water-invasion extent ab-sorbing certain portion of water by soil and vegetation isthe expansion of water-body extent Due to the com-plexity of water-invasion process we introduced Math-ematical Morphology so as to obtain more accurate water-invasion extent and relatively high calculate speed Cor-respondingly we estimated water-body extent by themodified space-filling method and horizontally sub-divided it for conveniently implementing expansionoperation

31 Introduction of Mathematical MorphologyMathematical Morphology derives from set theory Itgives up traditional ways of mathematical analysis andmodeling and carries out data interpretation from theperspective of aggregation Moreover it probes intogeometry data by using structuring element which sup-plies various data such as direction size and chrominanceDue to its capacity of describing geometrical morphology weused the geometrical description to analyze the topographicelements of inundation extent Here inundation extent wasregarded as a binary image set and water-invasion extent wasaccordingly considered as the expansion of water-body extentbased on local landforms Geographically water-invasionextent is formed by the capillary rise of the soil surroundingwater-body extent e capillary rises in different landformsare respectively expressed as different evolutions of geo-metrical structures erefore we described the expansioncaused by capillary rise in a way of original image processingby structuring elements so that the relationship betweenwater-body extent and water-invasion extent was establishedby Mathematical Morphology and inundation extent wasprecisely estimated based on the operations of structuringelements such as horizontal panning crossing and merging

Suppose A denotes the binary digital image set of water-body extent and AC the complementary set of A en thetranslation action A[X] according to vector X and the re-flection action minus A according to coordinate origin are shownas follows

A[X] a + x | a isin A

minus A minus a | a isin A (1)

Based on these definitions of Mathematical Morphologythe erosion operation of contraction process in water-in-vasion extent is described by

AΘB x |B + x subA cap A minus b |b isin B capbisinB

A[minus b] (2)

Here B is a structuring element or a contraction tem-plate of water-invasion extent and the points in AΘB in-dicate the templatersquos original location gained by panning B

in A In other words AΘB means the result of intersectionoperation through panning A by minus b b isin B As an inverseoperation of erosion operation expansion operation isdefined as

Mathematical Problems in Engineering 3

AoplusB x |(minus B + x)capAneΦ1113864 1113865 cup A + b | b isin B

cup a + b | a isin A b isin B cupbisinB

A[b](3)

e expansion operation expands the specific areas ofthe binary image by adding pixels to the perceivedboundaries and satisfies the following equation

(AoplusB)C

ACΘ(minus B)

(AΘB)C

AC oplus (minus B)

(4)

where AoplusB is obtained through panning A by minus b b isin B which facilitates the expansion of A by B

us water-invasion extent corresponding to water-body extent A can be estimated by expansion operation ifappropriate structuring elements are chosen Besides erosionoperation and expansion operation there is another im-portant action named opening operation in MathematicalMorphology e opening operation is a quadratic formu-lation combining erosion operation and expansion opera-tion defined as

A ∘B (AΘB)oplusB cup B + X | B + X sub A (5)

It is acquired by structuring elements that fill in theinterior of water-invasion extent image e opening op-eration as a geometric process in water-invasion extent isused to delete useless structuring elements smooth extentoutline cut off narrow connection and eliminate tiny orprojecting part at is to say opening operation canconnect neighboring fields or smooth borders and improvethe expressiveness of inundation extent

In addition the erosion operation and expansion operationin Mathematical Morphology not only have the monotonicitycharacteristics of (Aprime subeA⟹Aprime ΘBsubeAΘB Aprime oplusBsubeAoplusB)and the expansibility characteristics of (AΘBsubeAsubeAoplusB) buthave translation invariance

A[X]ΘB (AΘB)[X]

A[X]oplusB (AoplusB)[X]

AΘB[X] (AΘB)[minus X]

AoplusB[X] (AoplusB)[X]

(6)

It indicates that water-body extent or templates usedfor conducting erosion operation and expansion opera-tion can change the position instead of the shape of water-invasion extent us we can use a template expandingwater-body extent to water-invasion extent as long asdifferent locations share the same terrain properties Moreimportantly the expansion operation conforms to com-mutative law AoplusB BoplusA and associative law Aoplus(BoplusC) (AoplusB)oplusC and the large-scale structuring el-ements D can be decomposed to D1 oplusD2 oplus oplusDn thusmaking it possible for small-scale structuring elements toreplace large-scale ones Moreover the expansion oper-ation also has scale flexibility when the scalar product istA ta | a isin A for any real number t there are five setoperations as

t(AoplusB) tAoplus tB

t(AΘB) tAΘ tB

(AcapB)oplusC (AoplusC)cap(BoplusC)

(AcupB)oplusC (AoplusC)cup(BoplusC)

Aoplus(BcupC) (AoplusB)cup(AoplusC)

(7)

is indicates further that the expansion operation ofwater-body extent can be divided into different subset op-erations conducted by structuring elements e function ofsubset operations is to carry out morphological processingindependently and achieve eventual results through setoperations

32 Subdivision of Water-Body Extent e estimation ofwater-body extent is only subject to the water volume ininundation extent and the landform of the underlyingsurfaceWith DEM data space-filling method is usually usedto estimate the region (water-body extent) obviously coveredwith water It vertically subdivides the research area intocubic columns with different depths However water-in-vasion extent as the expansion of water-body extent is ahorizontal and outward operation in size and range so theexisting methods hardly describe the relevance of water-invasion extent to water-body extent Due to the invarianceof water-body subdivided vertically or horizontally we use across-section set X to horizontally subdivide water-bodyextent As shown in Figure 1 if Δh and H represent theelevation interval and the depth of water-body extent thecross-section set can be denoted as X X0 XΔh1113864

X2Δh XλΔh where water-body extent is subdivided byλ HΔh times If λ is big enough the water volume Vm inwater-body extent in fact is the accumulation of those crosssections us we have

Vm 1113946H

0S X

η( 1113857dη asymp 1113944

lfloorHΔhrfloor

i0S X

iΔh1113872 1113873Δh (8)

where Xη denotes the specific cross section of water-bodyextent at depth η e area of Xη is represented as S(Xη)where S(middot) is an area operator Since the cross-section set X

is a series of intersections between the horizontal planes withdepth 0Δh 2Δh λΔh and DEM data we can easilyobtain water-body extent as long as we find depth H thatsatisfies equation (8) In other words water-body extent isequal to the area of intersection between DEM data andhorizontal planes at depth H Here dichotomy is a simpleway to get the suitable depth H when the water volume Vm isgiven which is as same as traditional space-filling method

Usually water-body extent is over several square kilo-meters Its border is too large to directly deduce for water-invasion extent byMathematical Morphology So we dividedwater-body extent into different subset operations that wereeasily implemented by structuring elements Here struc-turing elements are the template components used to expandwater-invasion extent from water-body extent e shape ofstructuring elements is related to landform factors such asgeological condition soil vegetation and boundary of


water-body extent Obviously it is difficult to constructstructuring elements directly on account of the influence ofthese factors A relatively comprehensive method is to collectthe data of landforms and test the water absorption abilitythrough experiments is method helps to establishstructuring elements with high accuracy but lots of ex-perimentation with various types of boundaries and land-forms lead to a great amount of prework which significantlyincreases time consumption For improving the responsespeed of Flood Control Decision Support System we assumethat two neighboring landforms with sufficiently smallboundaries shared homogeneous properties since the geo-logical conditions in the sufficiently small region are similarand water bodies usually do not cross different geologicalbelts us the typical structuring elements under differentelevations can be obtained according to the boundaries andlandforms of water-body extent Suppose the landformfactors denote φi φ1

i φ2i φμ

i1113864 1113865 gained from RS datathen φi can be normalized to ψi ψ1

i ψ2i ψμ

i1113864 1113865 and theaggregation of all landform factors by OWG operator isfi 1113937

μj1[ϕ

ji ]ωj

where ψji indicates φj

i 1113936ni0φ

ji ϕ

ji denotes

the j biggest data of ψi and ω1ω2 ωμ1113864 1113865 is the weightssatisfied with 1113936iωi 1 According to Mathematical Mor-phology the similar set Ei Eij1113966 1113967 will be the structuringelements related to the expansion operation from water-body extent to the water-invasion extent whereEij sim(fi fj) fi middot fj(|fi||fj|) is the similarities ofvectorial angle cosine is morphology operation bystructuring element is different from the 8-directionstructuring element method merely used to implement theexpansion It can also be applied to different elevationsthough it is worth noting that higher pressure can lead tomore water invasion and absorption at the boundaries ofwater-body extent

33 Morphological Estimation of Inundation Extent Sinceinundation extent is composed of water-body extent andwater-invasion extent there are three steps needed for theestimation of inundation extent based on morphologyexpanding water-body extent into water-invasion extentestimating the depth of inundation extent based on the givenvolume of water and smoothing the boundaries of water-invasion extent to improve the visualization effect of in-undation simulation

(i) Suppose Yη denotes the water-invasion extent cor-responding to water-body extent Xη at depth ηAccording to the characteristics of morphologyoperations Xη and Yη can be subdivided intoequiangular subsets Xη X

η1cupX

η2 cupXη

n andYη Y

η1cupY

η2 cupYη

n in polar coordinate systemwhere X

ηi and Y

ηi share the equal angles In Math-

ematical Morphology the structuring elements forexpansion operation from X

ηi to Y

ηi can be repre-

sented by a set Cη Cη1cupC

η2 cupCη

n Let Ei definedin Section 32 denote the expansion structuring el-ements under the condition of homogeneousproperties then C

ηi and C

ξi ξ isin 0Δh λΔh is

described as aηEi and Cξi C

ηi aξaη where

aη k 1113938η0 S(Xη)dη is the osmotic pressure generated

by water body at depth η and k is the coefficientdenoting the osmotic pressure per unit of watervolume e coefficient k is related to the bulkdensity porosity and infiltration of the soil sur-rounding the water-body extent Due to the simi-larity of geological conditions in a small region thevalue of k does not change in a certain area and canbe obtained from the soil property dataset Mean-while the water-invasion extent can be deducedaccording to set operations and scalar flexibilities ofexpansion operation In other words Yη

cupi(Xηi oplusC

ηi ) aη cupi(X

ηi oplusCi) is the water-invasion

extent corresponding to water-body extent Xη(ii) Assume the depth of inundation is H and the co-

efficient integrating permeability and absorptionrates (namely the water volume per unit area ofwater-invasion extent) is b Since the depth of water-body extent water-invasion extent and inundationextent are the same the water-body below depth H

can be represented by the aggregation of the watervolume of water-body extent Vm 1113938

H

0 S(Xη)dη andthat of water-invasion extent

Vx b 1113946H

0S Y

η( 1113857dη

b

aη 1113946H

0aξS cup

iX

ξi oplusCi1113872 11138731113874 1113875dξ

b

1113938η0 S cupi Xη( 1113857dη

1113946H

01113946ξ

0S X

η( 1113857dη1113888 1113889S cup

iX

ξi oplusCi1113872 11138731113874 1113875dξ

(9)

∆h

Inundation extent

Water-body area

Water-invasion extent

Horizontal subdivision

DEM

RSStructuring

elements

∆h

sum

Maximum depth of

inundation extent

Water volumeEquiangular

subset

Figure 1 Subdivision of water-body extent


us the water volume of inundation extent is asfollows

VH Vm + Vx asymp 1113944

lfloorHΔhrfloor

j

S XjΔh

1113872 1113873Δh +b

1113936[ηΔh]

j S cupi XjΔh( 1113857Δh

middot 1113944

lfloorHΔhrfloor

j

1113944

lfloorξΔhrfloor

m

S XmΔh

1113872 1113873Δh⎛⎝ ⎞⎠S cupi

XjΔhi oplusCi1113872 1113873Δh1113874 1113875

(10)

Apparently VH is a function of H simply denoted asVH F(H) It is easily to get the numerical solution 1113954H

of this equation by dichotomy Here 1113954H is the depth ofinundation extent which is also the depth of water-body extent and water-invasion extent e water-bodyextent XH is approximately the corresponding cross-section XlfloorHΔhrfloorΔh within the set X And water-invasionextent YH expanding from XH is approximately de-scribed as follows

YlfloorHΔhrfloorΔh

cupi XlfloorHΔhrfloorΔhi oplusC

ηi1113874 11138751113936lfloorHΔhrfloorm0 S XmΔh( 1113857Δh

1113936lfloorηΔhrfloorj0 S XjΔh( 1113857Δh

(11)

(iii) Usually the estimation results of water-invasionextent are applied in analogue simulation or dy-namic display However the lack of smoothnessoccasionally occurs at the boundaries becauseYlfloorHΔhrfloorΔh is gained by point set thus decreasing theeffect of representation e issue can be handled byopening operation of Mathematical MorphologySpecifically we select the smallest structuring ele-mentMin[S(C

ηi )] of set C

ηi as the opening operation

conducting on YlfloorHΔhrfloorΔh which eliminates thepointy part of water-invasion extent removesnarrow connections and enhances the effect ofvisualization e opening operation for smoothingwater-invasion extent is as follows


YlfloorHΔhrfloorΔh ∘Min S C

ηi( 11138571113858 1113859

YlfloorHΔhrfloorΔhΘMin S C

ηi( 11138571113858 11138591113874 1113875oplusMin S C

ηi( 11138571113858 1113859

(12)

4 Experiments and Analyses

In order to test the estimation method of inundation extentbased on Mathematical Morphology an experiment envi-ronment based on the Digital Earth platform was built withMODIS tile-pyramid RS images GIS basin data 06m ofQuickBird high-definition RS images and 25m of26368times 26368 DEM grid DEM data and RS data weremerged under the projection of EPSG4326 so the imageunits and projection of DEM and RS were unified in thesame coordinate system In the experiment environmentcombining topographic map and thematic map DEM data

were horizontally subdivided in accordance with Δh 1mIt created 986 DEM cross sections by the Kriging in-terpolation approach Meanwhile vegetation index soilmoisture index and evaporation index obtained from RSdata were aggregated to establish 412 equiangular subsets inthe light of homogeneous properties

Using the estimation method based on MathematicalMorphology and three other typical methods we calculatedthe inundation extent caused by the water conservancyproject Hanjiang-to-Weihe River Water Transfer Project inChina is project built a reservoir named SanhekouReservoir with a total storage capacity of 681times 109m3 andthe adjusted storage capacity of 55times109m3 e mainfunction of the reservoir is to regulate the inflow from theZiwu River and transfer the inflow from the Han Riverthrough pumping stations During the construction processof the Sanhekou Reservoir the riverway closure led to waterlevel increasing and lots of land submerged e influenceinvolves Shidunhe County Shimudi County Meizi CountyTongchewan Town and Heba Town More than 200 millionyuan was considered to invest in the establishment ofresettlement sites and the compensation for residents in thereservoir areas Obviously accurate inundation estimationwill help to determine the amount of project investment sowe make the following estimates and analyses

41 Accuracy Analysis For the purpose of analyzing theaccuracy of different methods we estimated the inundationdepth and inundation extent caused by the SanhekouReservoir at water volume of 1910times106m3 and2349times106m3 as shown in Table 1 HD represents the hy-drodynamic method proposed in the literature [2] SF is thespace-filling method put forward in the literature [20] LM isthe method of simple expansion indicated in the literature[25] andMM represents the method proposed in this paper

(i) When the water volume was 1910times106m3 or2349times106m3 the area of inundation extent esti-mated by the HD SF and LM was all less thanmeasurements as shown in Table 1 After estimatedthe inundation extents under another 8 differentwater volumes we found that the results obtainedby the traditional methods of HD SF and LM werealways lower than the actual result e reason isthose methods fail to take into account the water-invasion process that plays a significant role ininundation estimation As shown in Figure 2 thedark blue extent represents the water-body extentand the adjacent blue-green extent denotes thewater-invasion extent Apparently the traditionalmethods estimated inundation extent according toVm + Vx with the impact of water invasion ignoredIn other words the inundation extents obtained bythe HD SF and LM were often larger than thewater-body extent by the MM since the MM cal-culated water-body extent according to Vm How-ever inundation extent actually includes water-invasion extent and water-body extent In geogra-phy the mixture of water and soil causes more


inundation than the water itself so the water Vx

invading the soil surrounding water-body extentenlarges the inundation extent at is to saycorresponding to the water Vx the inundationextent estimated by the traditional methods issmaller than that estimated by the MM us theinundation extents estimated by the HD SF andLM were smaller than that (including water-in-vasion extent and water-body extent) estimated bythe MM

(ii) e MM method proposed in this paper showedrelatively higher estimation accuracy than the othermethods Its absolute error of inundation estima-tion of the MM method was less than 005 km2 andthe relative error of that was less than 08 eerrors of the MM method were only half that of theother methods Unlike the methods of HD SF andLM the inundation extent and inundation depthobtained by the MM method were a little bit largerthan actual measurements is suggests that theintroduction of Mathematical Morphology im-proves the accuracy of inundation estimation eMM method approximated to the result of theactual measurement is superior to the others andprovides more safe projections to avoid under-estimating the damage of inundation

(iii) After the smoothing of opening operation wasadopted in the water-invasion extent the area ofinundation extent under those two different watervolumes became 6398 km2 and 7835 km2 mani-festing a further increase in error Although more

error reduced the estimation accuracy it was lessthan 0005 km2 which only accounts for 008 of thearea of inundation extent and can be ignoredHowever the smoothing of opening operationmakes the inundation extents match well with theboundaries and RS data It improves the effect ofvisualization when simulating the inundation pro-cess or displaying the inundation extent

(iv) e HD method took 45 s for calculation whichmade it impossible to carry out real-time simula-tion In contrast although the MM method spenttwice as much time as the SF method did it was ableto control the time consumption within the limit of1 s It was clear that the MMmethod possessed hightimeliness for multiple-frame inundation simula-tion and great efficiency for dynamic simulation

42 Influential Factor Analysis e MM method imple-mented by horizontal subdivision and equiangular subsetsestimates inundation extent under given water volume withDEM data erefore the estimation accuracy largely de-pends on the factors including water volume the number ofhorizontal subdivisions and the number of equiangularsubsets

421 Water Volume As for the HD SF and LM methodsthe larger the water volume is the more influences theunderlying surface and landforms would impose therebyleading to more errors As shown in Figure 3 the absoluteerrors increased with the increase in water volume erelative error surpassed 2 at the water volume of2880times106m3 which barely met the accuracy need of disasterevaluation Particularly the exceeding amount of watercomplicated the HD method and dramatically made theanalogue simulation less effective By contrast the MMmethod is based on the expansion of water body so thesubdivision of the expansion process will be more compactas the water volume increases us equiangular subsetswith more homogeneous properties were generated whichpartially reduced the impact of environmental factors andhelped to acquire more accurate results As shown in Fig-ure 4 the effect of water volume on accuracy was not sig-nificant when the MM method was adopted

Table 1 Accuracy comparison of different methods

Method (watervolume (106m3))

Inundationextent(km2)

Inundationdepth (m)

Absolute error ofinundation extent

(km2)

Relative error ofinundationextent ()

Absolute error ofinundation depth

(m)

Relative error ofinundation depth

()

Timeconsumed

(ms)HD (1910) 6310 601672 0071 1113 2665 0441 45912SF (1910) 6219 600743 0162 2539 3594 0595 481LM (1910) 6353 601856 0028 0439 2481 0411 566MM (1910) 6395 606128 0014 0219 1791 0296 832HD (2349) 7643 618977 0139 1786 4952 0794 51150SF (2349) 7560 617263 0222 2853 6666 1068 526LM (2349) 7693 619849 0089 1144 4080 0654 601MM (2349) 7831 625201 0049 0630 1272 0204 908

Figure 2 Experiment environment based on the Digital Earthplatform


422 Number of Horizontal Subdivisions Its influence onthe MM method appeared as a concave curve shown inFigure 5 Excessively large number of horizontal sub-divisions enlarged the differences between structuring ele-ments while small subdivisions led to inadequate use of thedata resources of landforms Both of them resulted to lowerestimation accuracy erefore in order to ensure sufficienttimeliness and simulation accuracy DEM data have to reachhigh enough grid accuracy e optimal number of sub-divisions is the minimum extent difference of two neigh-boring cross sections divided by Δh ie mininej(|XiΔh minus

XjΔh|)Δh so as to make sure that the minimum differencecan be recognized

423 Number of Equiangular Subsets e equiangularsubsets are derived from aggregating influential factors oflandforms According to the MMmethod too small numberof equiangular subsets results in fewer structuring elementsand fewer templates available for the expansion operation

Consequently it gives rise to insufficient expansion oper-ation with homogeneous properties reduces the expansionabilities from water-body extent to water-invasion extentand then diminishes estimation accuracy On the contraryexcessive number of equiangular subsets increases thecomputational load and the number of structuring elementsthus leading to redundant expansion operation of the sameregion erefore the estimation result was much largerthan the actual measurement as shown in Figure 6

5 Conclusion

Inundation estimation is an important work of disasteranalysis which determines the scope and magnitude of thedisaster Focusing on the problem of insufficient accuracy ofinundation estimation we proposed an estimation methodbased on Mathematical Morphology e method takesinundation extent as the sum of water-body extent andwater-invasion extent With DEM data water-body extentwas calculated by space-filling method but it adoptedhorizontal subdivisions rather than vertical subdivisionsWater-invasion extent was expanded from water-body ex-tent by structuring elements and calculated with equiangularsubsets e experimental results show that the MMmethodproposed in this paper has higher accuracy than the typicalhydrodynamic method and space-filling method e esti-mation accuracy of the MMmethod is largely relative to thefactors including water volume the number of horizontalsubdivisions and the number of equiangular subsets Al-though the MM method gives estimations of inundation

Rela

tive e

rror

of

inun

datio

n ex

tent

()

000

090

180

270

360

450

28802680234919101420856Water volume (106 m3)

HDSF

LMMM

Figure 4 Relative errors under different water volumes

200 400 800 1000 1200 1400 1600e number of vertical subdivisions of DEM

Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110

Figure 5 Relative errors under different horizontal subdivisions856 1420 1910 2349 2680 2880

Abs

olut

e err

or o

fin

unda

tion

exte

nt(1

06 m

3 )

Water volume (106 m3)

HDSF

LMMM

0

005

01

015

02

025

03

035

Figure 3 Absolute errors under different water volumes

100 200 300 400 500 600 700 800e number of equiangular subsets

Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110

Figure 6 Relative errors under different equiangular subsets


extent and inundation depth with a little bit larger thanactual measurements it avoids underestimating the damageof inundation It is worth mentioning that the expansionoperation of water-invasion extent relies on the equiangularsubsets and structuring elements created by RS data whichreflecting landform features so the improvement of accu-racy of RS image data can further improve the estimationresult

Data Availability

e program code and data that support the plots discussedwithin this paper are available from the correspondingauthor upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

Jianxun Li gratefully acknowledges the support of the BasicResearch Project of Natural Science (Research and Imple-mentation of Assistant Decision-making for Immigrant ofWater Conservancy Projects under the 3S Technology no2014JM9365) Shaanxi Province China

References

[1] M S Horritt D C Mason and A J Luckman ldquoFloodboundary delineation from synthetic aperture radar imageryusing a statistical active contour modelrdquo International Journalof Remote Sensing vol 22 no 13 pp 2489ndash2507 2001

[2] N Y Nguyen Y Ichikawa and H Ishidaira ldquoEstimation ofinundation depth using flood extent information and hy-drodynamic simulationsrdquo Hydrological Research Lettersvol 10 no 1 pp 39ndash44 2016

[3] P Bates C Sampson A Smith et al ldquoValidation of a globalhydrodynamic flood inundation model against high resolu-tion observation data of urban floodingrdquo in Proceedings of theEGU General Assembly Conference Abstracts vol 17 pp 2ndash8Vienna Austria April 2015

[4] M Podhoranyi S Kuchar and A Portero ldquoFlood evolutionassessment and monitoring using hydrological modellingtechniques analysis of the inundation areas at a regionalscalerdquo IOP Conference Series earth and Environmental Sci-ence vol 39 no 1 Article ID 012043 2016

[5] F Ilorme Development of a Physically-Based Method forDelineation of Hydrologically Homogeneous Regions and FloodQuantile Estimation in Ungauged Basins via the Index FloodMichigan Technological University Houghton Michigan2011

[6] M L Follum A A Tavakoly J D Niemann and A D SnowldquoAutoRAPID a model for prompt streamflow estimation andflood inundation mapping over regional to continental ex-tentsrdquo JAWRA Journal of the American Water ResourcesAssociation vol 53 no 2 pp 280ndash299 2017

[7] A T Murphy B Gouldby S J Cole R J Moore andH Kendall ldquoReal-time flood inundation forecasting andmapping for key railway infrastructure a UK case studyrdquo E3SWeb of Conferences vol 7 2016

[8] S Gobeyn A Van Wesemael J Neal et al ldquoImpact of thetiming of a SAR image acquisition on the calibration of a flood

inundation modelrdquo Advances in Water Resources vol 100pp 126ndash138 2017

[9] D P Patel J A Ramirez P K Srivastava M Bray andD Han ldquoAssessment of flood inundation mapping of Suratcity by coupled 1D2D hydrodynamic modeling a case ap-plication of the new HEC-RAS 5rdquo Natural Hazards vol 89no 1 pp 93ndash130 2017

[10] M Faghih M Mirzaei J Adamowski J Lee and A El-ShafieldquoUncertainty estimation in flood inundation mapping anapplication of non-parametric bootstrappingrdquo River Researchand Applications vol 33 no 4 pp 611ndash619 2017

[11] S Afshari A A Tavakoly M A Rajib et al ldquoComparison ofnew generation low-complexity flood inundation mappingtools with a hydrodynamic modelrdquo Journal of Hydrologyvol 556 pp 539ndash556 2018

[12] S Cohen G R Brakenridge A Kettner et al ldquoEstimatingfloodwater depths from flood inundation maps and topog-raphyrdquo JAWRA Journal of the American Water ResourcesAssociation vol 54 no 4 pp 847ndash858 2018

[13] N S Noman E J Nelson and A K Zundel ldquoReview ofautomated floodplain delineation from digital terrainmodelsrdquo Journal of Water Resources Planning and Manage-ment vol 127 no 6 pp 394ndash402 2001

[14] A M Dewan T Kumamoto andM Nishigaki ldquoFlood hazarddelineation in greater Dhaka Bangladesh using an integratedGIS and remote sensing approachrdquo Geocarto Internationalvol 21 no 2 pp 33ndash38 2006

[15] D C Mason P D Bates and J T DallrsquoAmico ldquoCalibration ofuncertain flood inundation models using remotely sensedwater levelsrdquo Journal of Hydrology vol 368 no 1ndash4pp 224ndash236 2009

[16] S Kamontum Fusion of Landsat-7 IRS-1D and Radarsat-1Data for Flood Delineation University of Florida GainesvilleFl USA 2009

[17] F Dottori and E Todini ldquoDevelopments of a flood inundationmodel based on the cellular automata approach testing dif-ferent methods to improve model performancerdquo Physics andChemistry of the Earth Parts ABC vol 36 no 7-8pp 266ndash280 2011

[18] R Charrier and Y Li ldquoAssessing resolution and source effectsof digital elevation models on automated floodplain de-lineation a case study from the Camp Creek WatershedMissourirdquo Applied Geography vol 34 pp 38ndash46 2012

[19] S Saksena and V Merwade ldquoIncorporating the effect of DEMresolution and accuracy for improved flood inundationmappingrdquo Journal of Hydrology vol 530 pp 1ndash52 2015

[20] J Teng J Vaze D Dutta and SMarvanek ldquoRapid inundationmodelling in large floodplains using LiDAR DEMrdquo WaterResources Management vol 29 no 8 pp 2619ndash2636 2015

[21] J Sopelana L Cea and S Ruano ldquoA continuous simulationapproach for the estimation of extreme flood inundation incoastal river reaches affected by meso- and macrotidesrdquoNatural Hazards vol 93 no 3 pp 1337ndash1358 2018

[22] J Teng A J Jakeman J Vaze B F W Croke D Dutta andS Kim ldquoFlood inundation modelling a review of methodsrecent advances and uncertainty analysisrdquo EnvironmentalModelling amp Software vol 90 pp 201ndash216 2017

[23] J F Rosser D G Leibovici and M J Jackson ldquoRapid floodinundation mapping using social media remote sensing andtopographic datardquo Natural Hazards vol 87 no 1 pp 103ndash120 2017

[24] M O Sghaier S Foucher and R Lepage ldquoRiver extractionfrom high-resolution SAR images combining a structuralfeature set and mathematical morphologyrdquo IEEE Journal of


Selected Topics in Applied Earth Observations and RemoteSensing vol 10 no 3 pp 1025ndash1038 2016

[25] H Vernieuwe B De Baets and N E C Verhoest ldquoAmathematical morphology approach for a qualitative explo-ration of drought events in space and timerdquo InternationalJournal of Climatology no 6 pp 1ndash14 2019

[26] F W Li X N Zhang and C W Du ldquoStudy on floodsubmergence based on GIS and mathematical morphologyrdquoAdvances in Science and Technology of Water Resourcesvol 25 no 6 pp 14ndash24 2005


Hindawiwwwhindawicom Volume 2018

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Dierential EquationsInternational Journal of

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Submit your manuscripts atwwwhindawicom

extent as the expansion of water-body extent due to the factthat water-invasion extent produced by capillary rise is thesaturated portion of the soil surrounding water-body extenten a more accurate estimation method combining space-filling method and RS data was proposed for inundationestimation by introducing the Mathematical Morphologye method is mainly suitable for flood mapping aroundnatural and artificial lakes We has implemented the methodonDigital Earth platform and formulated a prototype systemwhich could analyze the affected extent in real time

e remainder of the paper is organized as followsSection 2 briefly reviews related work on inundation esti-mation Section 3 presents an estimation method for in-undation depth and inundation extent based onMathematical Morphology In Section 4 an experimentenvironment with the Digital Earth platform is built to verifythe effectiveness of the method Section 5 concludes thepaper and provides remarks

2 Literature Review

e estimation method of inundation extent is currentlydivided into two categories One is hydrodynamic methodwhich simulates the depth distribution of water mobilityresolves continuity equations and motion equations andthen estimates inundation extent by the evolution of un-steady flow is method requires calculating partial dif-ferential equations with multiple parameters e other oneis space-filling method which takes DEM as basic data Withthe help of GIS or RS it employs a differential method todecompose the research area into lots of differential units inthe light of certain elevation e water of these units isdynamically accumulated until the discrepancy betweencumulative result and water volume is less than the specificthreshold representing the estimation accuracy

21 Hydrodynamic Method Hydrodynamic method in-tegrates hydrology and hydrodynamics to build a model offlood routing by using equations of continuity and motionsIt takes into account the characteristics of water trans-mission river bed evaluation roughness coefficient andturbulent viscosity coefficient erefore the unsteady flowand its variation occurred at different inundating time iseasily simulated Based on hydrodynamics Horritt et al [1]constructed an assessment method involving spatial scale Itprovided prototype solutions for inundation estimationCombining the flood extent information derived from RSimagery and hydrodynamic simulations Nguyen et al [2]proposed a model for estimating inundation depth andspatially distributed water level e model provided moreeffective assessment for local-scale pluvial flood Due to itsstrong feasibility hydrodynamic model has fully been ap-plied to the assessment of inundation extents eg Bates et al[3] and Podhoranyi et al [4] In recent years researchersmainly studied on the estimation accuracy computationspeed and simulation environment of inundation As to theestimation accuracy Ilorme [5] discussed the influence ofthe inaccuracy of hydrological data and the insufficiency of

hydrometrical stations based on the investigation into thehomogeneity in inundation extent For quickly estimatinginundation at hyperresolutions Follum et al [6] put forwarda routing application for parallel computation of dischargewhich can be applied quickly over very large spatial extentsIn order to build a simulation environment Murphy et al[7] introduced a hydraulic and hydrologic modeling soft-ware Infoworks ICM (Integrated Catchment Modelling)into flood inundation e software used unstructured tri-angular mesh and advanced numerical scheme which im-proved the simulation speed and calculation accuracy Inaddition there have been several studies aiming at thesubproblem of inundation estimation by hydrodynamicmethod For example Gobeyn et al [8] took LISFLOOD-FPmodel as an explicit forward difference scheme for com-puting the shallow water wave over the floodplain Patel et al[9] carried out a simulation work under the 1D2D couplehydrodynamicmodeling in low-lying areas Faghih et al [10]applied nonparametric bootstrap sampling to simulate in-undation with different flow rates which provided a ref-erence for the uncertainty analysis of inundation

Above all under the conservation laws of specific watervolume hydrodynamic method fully demonstrates hydro-logical characteristics and serves as an accurate estimationmodel to estimate inundation extent Relying on partialdifferential equations the method obtains a relatively preciseestimation of inundation extent and provides a vivid ex-pression of water-body extent furthermore clearly de-scribing the dynamic features of inundation However themodel usually contains plenty of parameters and complexequations proved hard to solve [11] In particular mostexisting studies fail to take into consideration the boundaryterrain soil conditions vegetation and the water absorptionby the earth in water-invasion extent estimation

22 Space-Filling Method Space-filling method approxi-mately simulates the ultimate equilibrium of inundation byviewing the water surface as a plane Based on the overlandrunoff model this method estimates inundation extent aswell as inundation depth [12] such as the automatic in-tegrated estimation approach by Noman et al [13] Sincespace-filling method is implemented by simple mathemat-ical calculations with large errors the research mainly fo-cuses on improving the estimation accuracy Dewan et al[14] earlier used airborne laser altimetry for analyzing in-undation extent It leads researchers to introduce geospatialdata into space-filling method Geospatial data such as GISRS and DEM can offer more possibilities for increasing theaccuracy of inundation estimation One of the representativemethods was proposed by Mason et al [15] who adopted RSdata to rectify the traditional estimation model With thecombination of flooding data and RS data Kamontum [16]applied Landsat and IRS images to inundation extentanalysis further improving the estimation of inundationboundary Recently scholars conducted in-depth researchon the estimation model of DEM data or cellular automataapproach [17 18] Saksena and Merwade [19] consideredthat vertical accuracy is related to the spatial resolution














A[minus b] (2)






A[b](3)


(AoplusB)C

ACΘ(minus B)

(AΘB)C

AC oplus (minus B)

(4)






A[X]ΘB (AΘB)[X]




(6)



t(AΘB) tAΘ tB




(7)




Vm 1113946H

0S X

η( 1113857dη asymp 1113944

lfloorHΔhrfloor

i0S X

iΔh1113872 1113873Δh (8)






i φ2i φμ


i ψ2i ψμ


μj1[ϕ

ji ]ωj


i 1113936ni0φ

ji ϕ

ji denotes




η1cupX

η2 cupXη

n andYη Y

η1cupY

η2 cupYη


ηi and Y



ηi to Y

ηi can be repre-


η2 cupCη


ηi and C



ηi aξaη where



cupi(Xηi oplusC

ηi ) aη cupi(X





H


Vx b 1113946H

0S Y

η( 1113857dη

b

aη 1113946H

0aξS cup

iX

ξi oplusCi1113872 11138731113874 1113875dξ

b

1113938η0 S cupi Xη( 1113857dη

1113946H

01113946ξ

0S X

η( 1113857dη1113888 1113889S cup

iX

ξi oplusCi1113872 11138731113874 1113875dξ

(9)

∆h

Inundation extent

Water-body area



DEM

RSStructuring

elements

∆h

sum

Maximum depth of

inundation extent


subset





lfloorHΔhrfloor

j

S XjΔh

1113872 1113873Δh +b

1113936[ηΔh]


middot 1113944

lfloorHΔhrfloor

j

1113944

lfloorξΔhrfloor

m

S XmΔh

1113872 1113873Δh⎛⎝ ⎞⎠S cupi

XjΔhi oplusCi1113872 1113873Δh1113874 1113875

(10)







(11)


ηi )] of set C





ηi( 11138571113858 1113859


ηi( 11138571113858 11138591113874 1113875oplusMin S C

ηi( 11138571113858 1113859

(12)



















Inundationdepth (m)


(km2)



(m)


()

Timeconsumed








5 Conclusion


Rela

tive e

rror

of

inun

datio

n ex

tent

()

000

090

180

270

360

450

28802680234919101420856Water volume (106 m3)

HDSF

LMMM



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110


Abs

olut

e err

or o

fin

unda

tion

exte

nt(1

06 m

3 )


HDSF

LMMM

0

005

01

015

02

025

03

035



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110




Data Availability




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018




















A[minus b] (2)






A[b](3)


(AoplusB)C

ACΘ(minus B)

(AΘB)C

AC oplus (minus B)

(4)






A[X]ΘB (AΘB)[X]




(6)



t(AΘB) tAΘ tB




(7)




Vm 1113946H

0S X

η( 1113857dη asymp 1113944

lfloorHΔhrfloor

i0S X

iΔh1113872 1113873Δh (8)






i φ2i φμ


i ψ2i ψμ


μj1[ϕ

ji ]ωj


i 1113936ni0φ

ji ϕ

ji denotes




η1cupX

η2 cupXη

n andYη Y

η1cupY

η2 cupYη


ηi and Y



ηi to Y

ηi can be repre-


η2 cupCη


ηi and C



ηi aξaη where



cupi(Xηi oplusC

ηi ) aη cupi(X





H


Vx b 1113946H

0S Y

η( 1113857dη

b

aη 1113946H

0aξS cup

iX

ξi oplusCi1113872 11138731113874 1113875dξ

b

1113938η0 S cupi Xη( 1113857dη

1113946H

01113946ξ

0S X

η( 1113857dη1113888 1113889S cup

iX

ξi oplusCi1113872 11138731113874 1113875dξ

(9)

∆h

Inundation extent

Water-body area



DEM

RSStructuring

elements

∆h

sum

Maximum depth of

inundation extent


subset





lfloorHΔhrfloor

j

S XjΔh

1113872 1113873Δh +b

1113936[ηΔh]


middot 1113944

lfloorHΔhrfloor

j

1113944

lfloorξΔhrfloor

m

S XmΔh

1113872 1113873Δh⎛⎝ ⎞⎠S cupi

XjΔhi oplusCi1113872 1113873Δh1113874 1113875

(10)







(11)


ηi )] of set C





ηi( 11138571113858 1113859


ηi( 11138571113858 11138591113874 1113875oplusMin S C

ηi( 11138571113858 1113859

(12)



















Inundationdepth (m)


(km2)



(m)


()

Timeconsumed








5 Conclusion


Rela

tive e

rror

of

inun

datio

n ex

tent

()

000

090

180

270

360

450

28802680234919101420856Water volume (106 m3)

HDSF

LMMM



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110


Abs

olut

e err

or o

fin

unda

tion

exte

nt(1

06 m

3 )


HDSF

LMMM

0

005

01

015

02

025

03

035



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110




Data Availability




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018










A[b](3)


(AoplusB)C

ACΘ(minus B)

(AΘB)C

AC oplus (minus B)

(4)






A[X]ΘB (AΘB)[X]




(6)



t(AΘB) tAΘ tB




(7)




Vm 1113946H

0S X

η( 1113857dη asymp 1113944

lfloorHΔhrfloor

i0S X

iΔh1113872 1113873Δh (8)






i φ2i φμ


i ψ2i ψμ


μj1[ϕ

ji ]ωj


i 1113936ni0φ

ji ϕ

ji denotes




η1cupX

η2 cupXη

n andYη Y

η1cupY

η2 cupYη


ηi and Y



ηi to Y

ηi can be repre-


η2 cupCη


ηi and C



ηi aξaη where



cupi(Xηi oplusC

ηi ) aη cupi(X





H


Vx b 1113946H

0S Y

η( 1113857dη

b

aη 1113946H

0aξS cup

iX

ξi oplusCi1113872 11138731113874 1113875dξ

b

1113938η0 S cupi Xη( 1113857dη

1113946H

01113946ξ

0S X

η( 1113857dη1113888 1113889S cup

iX

ξi oplusCi1113872 11138731113874 1113875dξ

(9)

∆h

Inundation extent

Water-body area



DEM

RSStructuring

elements

∆h

sum

Maximum depth of

inundation extent


subset





lfloorHΔhrfloor

j

S XjΔh

1113872 1113873Δh +b

1113936[ηΔh]


middot 1113944

lfloorHΔhrfloor

j

1113944

lfloorξΔhrfloor

m

S XmΔh

1113872 1113873Δh⎛⎝ ⎞⎠S cupi

XjΔhi oplusCi1113872 1113873Δh1113874 1113875

(10)







(11)


ηi )] of set C





ηi( 11138571113858 1113859


ηi( 11138571113858 11138591113874 1113875oplusMin S C

ηi( 11138571113858 1113859

(12)



















Inundationdepth (m)


(km2)



(m)


()

Timeconsumed








5 Conclusion


Rela

tive e

rror

of

inun

datio

n ex

tent

()

000

090

180

270

360

450

28802680234919101420856Water volume (106 m3)

HDSF

LMMM



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110


Abs

olut

e err

or o

fin

unda

tion

exte

nt(1

06 m

3 )


HDSF

LMMM

0

005

01

015

02

025

03

035



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110




Data Availability




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018









i φ2i φμ


i ψ2i ψμ


μj1[ϕ

ji ]ωj


i 1113936ni0φ

ji ϕ

ji denotes




η1cupX

η2 cupXη

n andYη Y

η1cupY

η2 cupYη


ηi and Y



ηi to Y

ηi can be repre-


η2 cupCη


ηi and C



ηi aξaη where



cupi(Xηi oplusC

ηi ) aη cupi(X





H


Vx b 1113946H

0S Y

η( 1113857dη

b

aη 1113946H

0aξS cup

iX

ξi oplusCi1113872 11138731113874 1113875dξ

b

1113938η0 S cupi Xη( 1113857dη

1113946H

01113946ξ

0S X

η( 1113857dη1113888 1113889S cup

iX

ξi oplusCi1113872 11138731113874 1113875dξ

(9)

∆h

Inundation extent

Water-body area



DEM

RSStructuring

elements

∆h

sum

Maximum depth of

inundation extent


subset





lfloorHΔhrfloor

j

S XjΔh

1113872 1113873Δh +b

1113936[ηΔh]


middot 1113944

lfloorHΔhrfloor

j

1113944

lfloorξΔhrfloor

m

S XmΔh

1113872 1113873Δh⎛⎝ ⎞⎠S cupi

XjΔhi oplusCi1113872 1113873Δh1113874 1113875

(10)







(11)


ηi )] of set C





ηi( 11138571113858 1113859


ηi( 11138571113858 11138591113874 1113875oplusMin S C

ηi( 11138571113858 1113859

(12)



















Inundationdepth (m)


(km2)



(m)


()

Timeconsumed








5 Conclusion


Rela

tive e

rror

of

inun

datio

n ex

tent

()

000

090

180

270

360

450

28802680234919101420856Water volume (106 m3)

HDSF

LMMM



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110


Abs

olut

e err

or o

fin

unda

tion

exte

nt(1

06 m

3 )


HDSF

LMMM

0

005

01

015

02

025

03

035



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110




Data Availability




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018










lfloorHΔhrfloor

j

S XjΔh

1113872 1113873Δh +b

1113936[ηΔh]


middot 1113944

lfloorHΔhrfloor

j

1113944

lfloorξΔhrfloor

m

S XmΔh

1113872 1113873Δh⎛⎝ ⎞⎠S cupi

XjΔhi oplusCi1113872 1113873Δh1113874 1113875

(10)







(11)


ηi )] of set C





ηi( 11138571113858 1113859


ηi( 11138571113858 11138591113874 1113875oplusMin S C

ηi( 11138571113858 1113859

(12)



















Inundationdepth (m)


(km2)



(m)


()

Timeconsumed








5 Conclusion


Rela

tive e

rror

of

inun

datio

n ex

tent

()

000

090

180

270

360

450

28802680234919101420856Water volume (106 m3)

HDSF

LMMM



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110


Abs

olut

e err

or o

fin

unda

tion

exte

nt(1

06 m

3 )


HDSF

LMMM

0

005

01

015

02

025

03

035



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110




Data Availability




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018



















Inundationdepth (m)


(km2)



(m)


()

Timeconsumed








5 Conclusion


Rela

tive e

rror

of

inun

datio

n ex

tent

()

000

090

180

270

360

450

28802680234919101420856Water volume (106 m3)

HDSF

LMMM



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110


Abs

olut

e err

or o

fin

unda

tion

exte

nt(1

06 m

3 )


HDSF

LMMM

0

005

01

015

02

025

03

035



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110




Data Availability




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018












5 Conclusion


Rela

tive e

rror

of

inun

datio

n ex

tent

()

000

090

180

270

360

450

28802680234919101420856Water volume (106 m3)

HDSF

LMMM



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110


Abs

olut

e err

or o

fin

unda

tion

exte

nt(1

06 m

3 )


HDSF

LMMM

0

005

01

015

02

025

03

035



Rela

tive e

rror

of

inun

datio

n ex

tent

()

050

060

070

080

090

100

110




Data Availability




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018









Data Availability




Acknowledgments


References






































Journal of












Journal of







Volume 2018






Volume 2018



















Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Documents

EstimationMethodofInundationExtentBasedon …downloads.hindawi.com/journals/mpe/2019/7825831.pdf · 2019-11-07 · ResearchArticle EstimationMethodofInundationExtentBasedon MathematicalMorphology