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Yongbo LiuDepartment of Geography, University of Guelph,50 Stone Road East, Guelph, Ontario, N1G 2W1,Canada. Email:[email protected]

Syed Tauseef Mohyud-DinDepartment of Mathmatics, COMSATS Instituteof Information Technology, Islamabad, PakistanEmail: [email protected]

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Vol.Vol.Vol.Vol. 2,2,2,2, No.No.No.No. 1111 2012201220122012

CONTENTSCONTENTSCONTENTSCONTENTS

Characterizing Snow Redistribution in SWAT for Simulating Spatially Distributed SnowmeltRunoff in Cold Regions

Y.B. Liu, W.H. Yang, B. Gharabaghi, J.Z.Liu, H.Wu, J. Yarotski----------------- 1-8

Spatial and Temporal Distribution of Temperature and Precipitation in the Lancang RiverBasin from 1971 to 2000

Y.N. Guo, X.H. Yang, Y. Mei, C.L. Di, Z.H. Dong----------------------------------9-14

Fuzzy Decision-Making Model Based on Dynamic Programming and Its Application in FloodControl

Q.L. Gu, X.H. Yang, S.S.Yang, T.B. Zhao--------------------------------------------15-22

Flood Forecasting Using Improved Evolution Algorithm Based on Chaos Memory OperationY.Q. Li--------------------------------------------------------------------------------------23-26

Ecological Risk Assessment Based on AHP-TOPSISZ.H. Dong, X.H. Yang, X.J. Chen----------------------------------------------------- 27-32

New Refining Stratification Method for Logging CurveS.S. Yang, X.H.Yang, G.D. Lv----------------------------------------------------------33-40

Y.B. Liu, W.H. Yang, B. Gharabaghi, et al., Nonlinear Science Letters C, Vol. 2, No.1, 2012, 1-8

Copyright © 2012 Asian Academic Publisher Ltd. Journal Homepage: www.NonlinearScience.com

1

CharacterizingCharacterizingCharacterizingCharacterizing SnowSnowSnowSnow RedistributionRedistributionRedistributionRedistribution inininin SWATSWATSWATSWAT forforforfor SimulatingSimulatingSimulatingSimulating SpatiallySpatiallySpatiallySpatiallyDistributedDistributedDistributedDistributed SnowmeltSnowmeltSnowmeltSnowmelt RunoffRunoffRunoffRunoff inininin ColdColdColdCold RegionsRegionsRegionsRegions

Y.B.Y.B.Y.B.Y.B. LiuLiuLiuLiu1,2,1,2,1,2,1,2,****,,,, W.H.W.H.W.H.W.H. YangYangYangYang1111,,,, B.B.B.B. GharabaghiGharabaghiGharabaghiGharabaghi3333,,,, J.Z.J.Z.J.Z.J.Z. LiuLiuLiuLiu2,42,42,42,4,,,, H.H.H.H.WuWuWuWu2,42,42,42,4,,,, J.J.J.J. YarotskiYarotskiYarotskiYarotski5555

1Department of Geography, University of Guelph, Guelph, ON, N1G2W1, Canada2State Key Laboratory of Environmental Information System, Institute of Geographic Sciencesand Natural Resources Research, CAS, Beijing 100101 China3 School of Engineering, University of Guelph, Guelph, ON, N1G2W1, Canada4University of Chinese Academy of Sciences, Beijing 100049, China5 Agriculture and Agri-Food Canada, Regina, SK S4P 4L2, Canada

AbstractAbstractAbstractAbstract

This paper presents the development of a conceptual mass balance approach incorporated into theSWAT model for simulating spatial snow redistribution and snowmelt at a watershed scale in coldregions. The approach takes account of the impacts of climate including precipitation, temperature,wind speed and wind direction, topography including aspect, slope, and curvature, and land cover onsnow redistribution and is able to estimate snow cover variations of each computation unit at a dailytime step within a watershed. A case study in a Canadian prairie watershed demonstrates that therevised model can achieve a much improved performance of predicted flow at both watershed outletand inside stations. The developed approach is helpful for simulating spatial variation of snowmeltrunoff, and particularly for assessing the impact of land management practices on hydrology in snowdominated areas.

Keywords:Keywords:Keywords:Keywords: Snow redistribution, Snowmelt runoff, SWAT, Hydrologic modeling

1.1.1.1. IntroductionIntroductionIntroductionIntroduction

Under cold climate condition, snow is subject to significant redistribution during and after snowfallas a result of wind drift. In agriculture dominated landscapes, snow is typically drifted from uplandand short vegetation areas to local depressions, tall vegetation areas, and river valleys. This wouldcause a non-linear and non-uniform distribution of snow cover before snowmelt, thus result in a spatialvariations of snowmelt runoff over the watershed. In hydrologic modelling, the ability to providerealistic spatial simulations of snow cover and snowmelt runoff is critical for simulating the energyand water budget of watershed hydrology, and in particular for evaluating the spatial impact ofbeneficial management practices (BMPs) at a field scale in cold regions.Snow redistribution is a very complex process governed by spatial patterns of climate (e.g. snowfall,

temperature, wind speed and direction), topography (e.g. slope, aspect, and curvature), and vegetationduring snow accumulation process (Hiemstra et al., 2006). These complexities cause difficulties onmodeling snow redistribution and accumulation on landscapes. For simplification purposes, snowcover properties are typically estimated from their empirical relationships to topography and landcover variables (Lapen and Martz, 1996). In SWAT (Soil and Water Assessment Tool, Neitsch et al.,2011), snow cover is simulated as a function of a user defined threshold snow depth over which snowcoverage is extended to 100% of the HRU (Hydrologic Response Unit) area, and below which thefraction of HRU area covered by snow is allowed to decline non-linearly based on a natural logarithmdepletion curve. However, because each HRU is an independent computation unit, snow redistribution

* Corresponding Author: [email protected]


ISSN 2078-2322 Nonlinear Science Letters C: Nano, Biology and Environment2

among different HRUs is not accounted for in the model simulation. This would limit the use of SWATto study snow related hydrologic processes at small scales.Several modeling studies have been conducted to simulate snow redistribution at different spatial

and temporal scales. Durand et al. (2001) developed an operational parameterization for snowredistribution over mountainous terrain. MacDonald et al. (2009) developed an approach forcalculating snow redistribution in subarctic mountains with moderate topographic roughness and ran ablowing snow model to estimate snow accumulation quantities. Pomeroy et al. (2007) and Fang andPomeroy (2008) developed a Cold Region Hydrological Model (CRHM), in which the processes ofsnow drift and snow accumulation as well as snow energy and water budget were simulated in muchdetail. However, these models require high resolution climate and geospatial data and predict snowaccumulation at site-specific level, which are difficult to be applied to data limited areas and are overmeticulous to be embedded into SWAT type watershed management models. For the purpose of BMPassessment, it would be more appropriate to incorporate a relatively simple but effective method into awatershed model for simulating snow redistribution processes.The objective of this paper is to present a module developed to simulate the variation of non-linear

snow distribution among different HRUs in SWAT and to simulate the spatial snowmelt runoff over awatershed. The method is verified by comparing the modeling output with field snow cover and flowmeasurement, and satisfactory results have been achieved. The advantages and limitations of thismethod are also discussed in this paper.

2.2.2.2. MethodologyMethodologyMethodologyMethodology

To simplify the hydrologic processes in the module, we assume that snow has a similar distributionpattern inter annually controlled mainly by the amount of snow, topography, and land cover, while theaverage wind speed and wind direction in winter period change slightly from year to year. The snowmass balance at watershed scale is maintained as:

outintt SASASASA −+= −1 (1)

Where SAt and SAt-1 are snow water equivalent (SWE) over the watershed after and beforeredistribution (mm), and SNin and SNout are snow blown into and out of the watershed duringredistribution (mm). For a large watershed SNin can be assumed equal to SNout, and SA2 = SA1. Thisimplies that snow is redistributed internally among the HRUs within the watershed, and the totalamount of snow is not changed within the watershed after redistribution. For a small watershed or awatershed with unique land use and landscape, SNin can be less or greater than SNout. In such a case,SA2 can be estimated by SA2= kblow*SA1, where kblow is a correction factor subjected to modelcalibration.The impact of a land cover on snow accumulation is mainly controlled by its snow holding capacity(SHC). The relative impact of land cover on snow redistribution in comparison to cropland can beexpressed as:

⎪⎩

⎪⎨

⎧

≥

<⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

i

iic

it

c

i

i

SHCSWEwhen

SHCSWEwhenSHCSHCSHCSA

SHCSHC

WL1

1* (2)

where WLi is the land cover weighting factor of the HRU, SAt is the SWE over the watershed (mm),and SHCiand SHCc are the snow holding capacity of the land cover i and the cropland (mm). Thecropland SHC is served as a denominator because the model is intended to be applied in agriculturalwatersheds. Based on literature SHC values (e.g. Prasad et al., 2001; Liston and Elder, 2006), theSHCi/SHCc can be estimated. The land cover of impervious and open water areas performs differentlycompared to other land covers because of their very small resistance to the snow. A constant ratio, 0.15,

Y.B. Liu, W.H. Yang, B. Gharabaghi, et al., Nonlinear Science Letters C, Vol. 2, No.1, 2012, 1-8 3

is assigned to these two land covers for estimating the land cover weight factor.Topographic properties such as elevation, aspect, slope, and curvature play important roles in theprocess of snow redistribution (Winstral and Marks, 2002). Topographic factors typically affect thedistribution of wind speed over the watershed. The method of quantifying topographic effects using aweighting factor (Liston and Sturm, 1998) is adopted in the study as:

iii CkSkWT 210.1 ++= (3)

Where WTi is a weighting factor to quantify the impact of topographic features on snowredistribution of the HRUi, Si and Ci are slope and curvature calculated along the wind direction of theHRU i, and k1 and k2 are empirical coefficients identifying the importance of slope and curvaturerespectively.Temperature affects the cohesive regime of snow and therefore affects the process of snowredistribution significantly. The threshold value of wind speed over which blowing and drifting snowwill initiate varies with temperature. The empirical equation proposed by Li and Pomeroy (1997)based on data collected in Canadian prairies is used in this study as:

( )20 27.270033.0 ++= TUU TT (4)

where UT is the threshold wind speed (m/s) at air temperature T (oC), and UT0is a constant(m/s).At nearly 0 oC, the threshold wind speed is 9.43 m/s over which snow blowing and drifting wouldinitiate. To further simply the temperature and threshold wind speed effects on snow redistribution, atemperature weighting factor, which is a snow redistribution decay coefficient, is proposed in thisstudy as:

( )⎪⎩

⎪⎨

⎧

≥−<−≤−

<−=

0

00

10

00

UUUwhenUUUwhenUUU

UUwhenWW

T

TT

T

i (5)

where WWi is a wind speed and temperature weighting factor of the HRU over the time step, U isthe average wind speed (m/s), and U0 is the wind speed at which the decay coefficient is 1 (m/s). U0 isan empirical coefficient and can be adjusted during calibration.At each time step, the potential snow drift or deposit of the HRU can be estimated as:

1,1

1 )**(/*** −=

− ∑ −= ti

N

iiiiiiti SAAWLWTAWLWTSAPSR (6)

Where PSRi is the potential snow redistribution of HRU i (mm), N is the number of HRUs, Ai and Aare areas of the HRU and the watershed (ha), and SAi,t-1 and SAt-1 are the SWE of the HRU and thewatershed at time t-1 (mm). The first part on the right-hand side of the equation represents thepotential SWE of the HRU after snow redistribution accounting for topographic and land cover factors.The actual snow redistribution of the HRU, SRi, over the time step can be estimated by multiplying theclimate weighting factor.

iii WWPSRSR *= (7)

Where SRi<0 for drift, SRi>0 for deposition, and SRi=0 for no redistribution. The SWAT snow massbalance of the HRU over time step is modified as:

iiiititi SMSESRPSASA −−−+= −1,, (8)


Where Pi is the precipitation over the time step (mm), and SEi and SMi are snow sublimation andsnowmelt over the time step (mm) calculated using the SWAT approach. Based on the setup, thevariations of snow redistribution and SWE of each HRU can be estimated by taking account oftopographic, land cover, and climate factors into the system. The three additional spatial parametersincluding slope and curvature of the HRU along the dominant wind direction and the SHC of eachHRU, can be prepared using GIS based on the SWAT project HRU distribution information prior tomodel execution.

3.3.3.3. CaseCaseCaseCase StudyStudyStudyStudy

The 75km2 South Tobacco Creek (STC) watershed located in southern Manitoba of Canada isselected to apply the snow redistribution module. The STC watershed has a three-tier topography withan average slope of 5.6% (Figure 1). Elevation ranges from 306m at the watershed outlet to 506m atthe hilltop. Approximately 71%of the watershed area is under cultivation (Figure 2). The remaining29% are comprised of non-cultivated grasslands, trees, water bodies, and road allowances. Thecultivated soils in the STC watershed are largely Orthic-Dark-Gray loam and clay loam developedfrom a mixed till of shale, limestone and granite. The watershed has a semi-arid climate with apronounced seasonal variation. Differences in terrain result in a slight variation in average annualtemperature of 2.0 to 4.0°C and annual precipitation from 590 to 500mm above and below theescarpment. About 75% of this precipitation occurs as rainfall from April to October while theremainder falls as snow during winter months. The average annual daily discharge at the watershedoutlet is 0.16 m3/s ranging from 0.01m3/s to 0.41m3/s (1964-2010), and the average annual runoff is69.4mm with an average runoff coefficient of 0.125. More than 80% of the runoff and most of theannual peak discharges are observed in spring because of snowmelt. Therefore, snow and snow relatedprocesses play a dominant role in the STC hydrologic modeling and watershed management.

Figure 1. Elevation and stream network of the STC watershed

The GIS data of LiDAR DEM (1×1 m), soil type, land use, and stream network used for modelsetup are obtained from the Agriculture and Agri-Food Canada (AAFC)). Climate data of precipitation,temperature, wind-speed, and wind-directionare available at the stations of Miami Orchard, Deerwood


and the Twin watershed from 1991 to 2011. Flow data at 16 stations are available for model validationof which two are Environment Canada stations on the mainstream (1995-2011) and 14 are AAFCmonitoring stations at field edges and small subbasins(2005-2011). In addition, field data of153 SWEsamples collected during the period of 9-23/2/2011 covering areas with various topography and landuses within the watershed are obtained (Figure 2). These snow data together with the flow data at 16flow stations are used to calibrate and validate the developed snow redistribution module in SWAT.

Figure 2. Land use, flow stations and snow sampling sites in the STC watershed

Based on the STC spatial data of DEM, soil, and land use, 82 subbasins and 348 HRUs aredelineated with the SWAT model. In addition to climate inputs, the actual field management datacollected from 1991 to 2010 including crop type, seeding and harvest, fertilizer, manure, tillage, andresidual management are used to setup the SWAT. For purpose of running the snow redistributionmodule, the spatial parameters of SHC, the slope and curvature along the dominant wind direction inwinter period (Northwest for the STC watershed) are calculated for each HRU using GIS. The SHCvalues for forest, shrub, grass, crop, impervious, and open water are set to 0.50, 0.10, 0.05, 0.02, 0.003,and 0.003 m in SWE respectively corresponding to zero slope and zero curvature based on literaturevalues (Prasad et al., 2001; Liston and Elder, 2006). The parameters of k1, k2, UT0, and U0in modellingsnow redistribution are assigned to 60, 145, 6.98, and 11 respectively after model calibration bycomparing the SWAT HRU SWE output with field SWE measurement and comparing the SWAT reachoutput with actual flow rates measured at mainstream and field flow stations. The calibration andvalidation of the SWAT are not a focus of this paper, and therefore not discussed in detail herein.Figure 3 shows the average observed and modelled SWE at HRU scale on 23/2/2011. The sampling

SWE is grouped and averaged for each land use and is compared with the modeled HRU SWE on thedate average for the land use. A perfect match is obtained between the two lines with R2=0.98.However, significant differences of SWE is also found for a few crop and forest HURs suggestingfurther data analysis and model calibration are required. Figure 4(a) shows a variation of simulatedSWE accumulation for selected crop, grass, and forest HRUs before and after snow redistribution in1996-1997. Without snow redistribution, the SWE variations of the three HRUs are almost the same asdemonstrated in the red line. After snow redistribution, more snow is accumulated in the forest HRUs,and less snow distributed in the crop and grass HRUs which is evident from the field survey data.


Simulated snowmelt from selected conventional till, zero till, and woodland HRUs in spring 1997 isshown in Figure 4(b). The peak of conventional till HRU is slightly higher than that of the no-till HRU,while the depth of snowmelt runoff of the two HRUs is almost the same suggesting the SWE values ofthe two HRUs are very close when the SWE values are greater than their SHCs. A much highersnowmelt amount is found from the forest HRU because of the snow redistribution. No snowmeltoccurred in late February from the forest HRU because of the lower snow temperature simulated in themodel.

Figure 3. Average observed and modelled SWE at HRU scale on 23/2/2011

Figure 4.(a) Simulated SWE variation for different HRUs in 1996-1997, and (b) Simulated snowmeltfrom conventional till, zero till, and wooded HRUs in spring 1997

The coefficient of Nash–Sutcliffe model efficiency (Nash and Sutcliffe, 1970) is calculated at eachflow station to evaluate the model performance. Because majority of flow is generated from springsnowmelt, the evaluation result can be an indicator on model performance for simulating snowmeltrunoff. Before snow redistribution, the daily flow Nash coefficient is 0.73for the outlet station, Miami,and 0.70 for another station, HYW240, in the middle of mainstream for the period from 1996 to 2010after model calibration. However, the mean daily flow Nash coefficient is 0.17 for the rest 14 field andsmall subbasin monitoring sites for the period from 2005 to 2010. After snow redistribution, the Nashcoefficient is 0.75 at Miami, and 0.71 at HYW240, while the mean Nash coefficient increases to 0.45for the rest 14 stations. This pattern demonstrates that the SWAT could provide good snowmelt flowestimation at larger scales in the STC watershed, but poorly predict snowmelt flow at small scales. Therevised model after incorporating snow redistribution processes within the watershed has considerablyimproved the performance of model predictions at all stations, and therefore is able to simulate moreprecisely the spatial variation of snow processes and spatial pattern of snowmelt runoff in the STCwatershed.The mass balance approach is implemented in this study to simulate snow redistribution over the

watershed. Therefore, it represents an average condition for different combinations of slope, curvature,


land cover, wind speed, and temperature. The algorithm does not take the location of different landcover over the watershed into account for simplification purposes. This coincides with the SWAT HRUalgorithm, and is therefore suitable to be implemented in the SWAT for simulating snow redistributionamong different HRUs, but may not predict accurately the snow depth or SWE at a particular site andat a specific time. Calibration of the model parameters is required if field measurement data areavailable. Equation 2 simplifies the process of snow redistribution among different land covers in afunction of accumulative snow depth under the same topographic conditions, and therefore wouldgreatly save the computation time and data requirement. For a small snow accumulation, all landcovers play a role in the snow redistribution. When snow accumulation goes higher, the SHC of forestwould become a key parameter to control snow redistribution at the end. The area proportions of theland cover are also accounted for in the equation. For a certain amount of snow accumulation, thesnow depth in the forest would be less if majority of the land is covered by forest, and is higher ifmajority of the land is covered by crop.

4.4.4.4. ConclusionConclusionConclusionConclusion

In this study, we have developed a conceptual approach to simulate snow redistribution process inthe SWAT. The method takes accounts for the impact of land use, topographic, and climate factors onsnow exchange among different HRUs, and is able to simulate the spatial and temporal SWEvariations during snow accumulation and snowmelt periods. The algorithm has a strong physical basisas all major controlling factors are involved in the simulation of snow redistribution in a simple butrealistic way. A case study in the STC watershed demonstrates that the revised model could provide areasonable estimation of spatial SWE patterns, and improve the snowmelt flow predictionconsiderably at filed and small subbasin stations inside the watershed. This will make the estimation ofspatial snowmelt runoff and the evaluation of BMPs more precisely at small scales with a much higherspatial resolution, and also make the scale up of the model more reliable for policy making. Furthermodel validation is required when continuous spatial SWE data, such as the high resolution opticaland active radar remotely sensed data sources, become available.

AcknowledgementsAcknowledgementsAcknowledgementsAcknowledgements

This paper is supported by the Canadian AAFC WEBs project and the Sino-German CooperationGroup “Climate Change, Floods and Droughts” project (GZ 412). We thank Dave Kiely of AAFC forthe project management, and the Deerwood Soil and Water Management Association for the field datacollection.

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9

SpatialSpatialSpatialSpatial andandandand TemporalTemporalTemporalTemporal DistributionDistributionDistributionDistribution ofofofof TemperatureTemperatureTemperatureTemperature andandandand PrecipitationPrecipitationPrecipitationPrecipitationinininin thethethethe LancangLancangLancangLancang RiverRiverRiverRiver BasinBasinBasinBasin fromfromfromfrom 1971197119711971 totototo 2000200020002000

Y.Y.Y.Y. N.N.N.N. Guo,Guo,Guo,Guo, XXXX.... H.H.H.H. YangYangYangYang****,,,, YYYY.... Mei,Mei,Mei,Mei, C.C.C.C. L.L.L.L. Di,Di,Di,Di, Z.H.Z.H.Z.H.Z.H. DongDongDongDongState Key Laboratory of Water Environment Simulation, School of Environment, BeijingNormal University, Beijing, 100875, China


The spatial and temporal distribution of temperature and precipitation in the Lancang River Basinfrom 1971 to 2000 are studied in this paper. Both the trend and mutability of the time series arediscussed based on the Mann–Kendall method. As a result the spatial distribution of temperature andprecipitation of Lancang River Basin present the steeped distribution along the basin. And thetemporal distribution of temperature and precipitation of Lancang River Basin are uptrend, of whichthe temperature is significant uptrend with 0.020℃/a increasing rate, the precipitation is notsignificant with 1.8375mm/a increasing rate from 1971 to 2000 year. Besides, the 1988 and 1993 yearsare the mutability years of temperature, and the 1992, 1994, 1996 and 1999 years are the mutabilityyears of precipitation.

Keywords:Keywords:Keywords:Keywords:Mann–Kendall method, Lancang River Basin, Temperature, Precipitation


Climate change has become an increasing important issue to the utilization and management ofwater resources which is concerned by the whole world (Chen et al., 2009). Climate change willchange the present situation of the hydrologic cycle, causing spatial-temporal redistribution of waterresources. There already many studies to research the trend of climate change, however, a few worksto analyze the mutability of the time series. The Mann–Kendall test method is widely used in thetrends test of precipitation, temperature and runoff (Kumar et al., 2009; Sheng and Cavadias, 2002; Xuet al., 2010; Zhang et al., 2006). The temperature and precipitation are the main factors of the climate.In this paper , the Mann–Kendall test method is used to analyze the spatial and temporal distribution ofprecipitation and temperature of Lancang River Basin.

2.2.2.2. MannMannMannMann ---- KendallKendallKendallKendall MethodMethodMethodMethod

The Mann–Kendall method is first proposed by Mann and Kendall (Mann, 1945; Kendall, 1975)which is widely used in the trends test of precipitation, temperature and runoff. The time series used inthe Mann–Kendall method do not ask for following a certain distribution and some abnormal valuewill not influence the results of the method. Thus, the Mann–Kendall method is an effective method toanalyze the non-normal distribution data, such as hydrology and meteorological data.In the Mann–Kendall method, the null hypothesis oH is a time series ),...,,( 21 nxxx , the sample

includes the independent and random variables with the same distribution. Alternative hypothesis 1H isa bilateral inspection. All of the njk ≤, , jk ≠ and the distributions of kx , jx are different. The

test statistic variable S is calculated by the following formula.

)sgn(1

1 1∑ ∑−

= +=

−=n

k

n

kjkj xxS (1)

app:ds:spatial

app:ds:and

app:ds:temporal

app:ds:distribution

app:ds:spatial

app:ds:and

app:ds:temporal

app:ds:distribution

app:ds:mutability

app:ds:spatial

app:ds:distribution

app:ds:temporal

app:ds:distribution

app:ds:mutability

app:ds:mutability

app:ds:mutability

app:ds:ask

app:ds:for

app:ds:abnormal

app:ds:value



Where

⎪⎩

⎪⎨

⎧

<−−

=−

>−

=−

01

00

01

)sgn(

kj

kj

kj

kj

xxxxxx

xx (2)

S is normal distribution, the mean value is 0 and the variance is18/)52)(1()( +−= nnnSVar . When 10>n , the statistic variable of the normal distribution

Z is calculated as follows:

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

<+

=

>−

=

0)(

100

0)(

1

SsVar

SS

SSVar

S

Z (3)

In the given confidence levelα , if 2/1 α−≥ ZZ , the null hypothesis cannot accept which states the

time series have an obvious up or down trend (if 0>Z , it is up trend, otherwise is down trend).The Mann–Kendall method can further test the mutability of the time series. The statistic variable is

different Z which should define a rank series as follows.

),....,4,3,2(1

1

nkSk

i

i

jijk == ∑∑

=

−

α (4)

)1(0

1ij

xxxx

ji

jiij ≤≤

⎪⎩

⎪⎨⎧

≤

>=α (5)

The new statistic variable kUF is defined by the following formula:

),....,2,1()()(

nkSVarSES

UFk

kkk =

−= (6)

Where, 72/)52)(1()(;4/)1()( +−=+= kkkSVarkkSE kk .Reverse the time series order to attain a new time series and again to calculate the statistic variablekUB based on the Equation 6.At the same time:

),...,2,1(1

nkknk

xxUFUB jikk =⎩⎨⎧

−+=

>−=(7)

If there are intersections of kUF and kUB , and the intersections are between the Critical lines,they are the mutational points.

3.3.3.3.ApplicationApplicationApplicationApplication andandandand ResultsResultsResultsResults

The Mann–Kendall method is applied in Lancang River Basin. In this study, we collect 45 stationsprecipitation and temperature data from 1971-2000. According to the basis meteorological data, thetrends of temperature and precipitation of the Lancang River Basin are analyzed.

app:ds:variance

app:ds:mutability

app:ds:mutational



11

3.13.13.13.1 TrendsTrendsTrendsTrends ofofofof TemperatureTemperatureTemperatureTemperature

3.1.13.1.13.1.13.1.1 TheTheTheThe temporaltemporaltemporaltemporal distributiondistributiondistributiondistribution ofofofof temperaturetemperaturetemperaturetemperature

According to the analysis of the temperature trends of Lancang River Basin based on the basistemperature data from 1971-2000, the annual average temperature of the Lcancang River Basin is16.5℃, the annual maximum temperature is 15.8℃ and the annual minimum temperature is 19.8℃.Figure 1(a) is the annual temperature anomaly of each year which states the trend of the temperature isuptrend. And the Z statistic value based on the Mann–Kendall method is 2.4442. If the Z statistic valueis greater than 1.64 (the Z of the 95% confidence), the temperature has an obvious change trend. Thus,the Lancang River Basin is significant uptrend with 0.020℃/a increasing rate.

(a)The annual temperature anomaly (b) The mutability testFig.1 The analysis of temporal distribution of temperature based on Mann-Kendall method

To further analyze the temporal distribution of the temperature of Lancang River Basin, themutability of the time series is tested based on Mann–Kendall method. The annual averagetemperatures of Lancang River Basin have two mutability years: 1988 and 1993years just as shown inFigure 1(b). Both of the two mutability years are the uptrend begin times and the increasing rate of1988 year is bigger than 1993year. Besides, all of the UF statistic values are positive which state thetemperature is uptrend. Therefore, the analysis result is in accordance with the above.

3.1.23.1.23.1.23.1.2 TheTheTheThe spatialspatialspatialspatial distributiondistributiondistributiondistribution ofofofof temperaturetemperaturetemperaturetemperature

To analyze the spatial distribution of temperature of Lancang River Basin, the upstream, middlestream and downstream are respectively discussed. And 45 weather stations from upstream todownstream are also studied in this paper.

(a) The average temperature and Z statistic values (b)The Z statistic values of 45 weather stationsFig. 2 The analysis of spatial distribution of temperature based on Mann-Kendall method

The average temperatures of upstream, middle stream and downstream are 11.5℃,16.4℃and

app:ds:temporal

app:ds:distribution

app:ds:mutability

app:ds:mutability

app:ds:mutability

app:ds:spatial

app:ds:distribution



19.5℃ which present the downstream temperatures of the Lancang River Basin is higher than theupstream. From the Figure 2(a) we can also see the Z statistic value based on the Mann–Kendallmethod, of which the Lancang River Basin is 2.4442, the upstream is 1.6235, the middle stream is2.3372 and the downstream is 3.8180. The Lancang River Basin is significant uptrend with 0.020℃/aincreasing rate, and the increasing rate of the temperature has a stepped distribution along the Basin:the downstream(0.015℃/a) >the middle stream(0.020℃/a)>the upstream(0.033℃/a). The Figure 2(b)is the Z statistic value of 45 weather stations (from upstream to downstream) which shows about total26 stations have significant uptrend and the downstream stations have the obvious uptrend than theupstream.

3.23.23.23.2 TrendsTrendsTrendsTrends ofofofof PrecipitationPrecipitationPrecipitationPrecipitation

3.2.13.2.13.2.13.2.1 TheTheTheThe temporaltemporaltemporaltemporal distributiondistributiondistributiondistribution ofofofof PrecipitationPrecipitationPrecipitationPrecipitation

The precipitation trends of Lancang River also discussed based on the basis temperature data from1971-2000, the annual average precipitation of the Lcancang River Basin is 1218.3mm, the annualmaximum precipitation is 1048.0mm and the annual minimum precipitation is 1399.4mm. The annualprecipitation anomaly of each year is shown in Figure 3(a) which states the trend of the precipitationhas no significant uptrend. And the Z statistic value based on the Mann–Kendall method is1.3559<1.64,that is the Lancang River Basin is a little uptrend with 1.8375mm/a increasing rate butnot significant.

(a)The annual precipitation anomaly (b) The mutability testFig. 3 The analysis of temporal distribution of precipitation based on Mann-Kendall method

To further analyze the temporal distribution of the precipitation of Lancang River Basin, themutability of the time series is also tested based on Mann–Kendall method. The annual averageprecipitation of Lancang River Basin has four mutability years: 1992, 1994, 1996 and 1999years justas shown in Figure 3(b). All of the four mutability years are the uptrend begin times, but the increasingrate of 1992, 1994 and 1996 years are small, the increasing rate of 1999 year is bigger than the others.Besides, before 1996 year, most of the UF statistic values are negative which present the precipitationis downtrend and after 1996 year, the precipitation is uptrend with a small increasing rate.

3.2.23.2.23.2.23.2.2 TheTheTheThe spatialspatialspatialspatial distributiondistributiondistributiondistribution ofofofof precipitationprecipitationprecipitationprecipitation

To analyze the spatial distribution of precipitation of Lancang River Basin, the upstream, middlestream and downstream are respectively discussed. And 45 weather stations from upstream todownstream are also studied in this paper.

app:ds:temporal

app:ds:distribution

app:ds:mutability

app:ds:mutability

app:ds:mutability

app:ds:negative

app:ds:spatial

app:ds:distribution



13

(a)The average precipitation and Z statistic values (b) The Z statistic values of 45 weather stationsFig. 4 The analysis of spatial distribution of precipitation based on Mann-Kendall method

The average precipitation of upstream, middle stream and downstream are 1101.3mm, 1092.1mmand 1523.9mm which present the downstream precipitation of the Lancang River Basin is bigger thanthe upstream. The trend is accordance to the temperature which has the stepped distribution along theBasin. Figure 4(a) shows that the Z statistic value based on the Mann–Kendall method, of which theLancang River Basin is 1.0348, the upstream is 1.3559, the middle stream is 1.231 and thedownstream is -0.21419. The precipitation of Lancang River Basin is a little uptrend with 1.8375mm/a increasing rate, the upstream (3.7875mm/a) > the middle stream (3.5583 mm/a), and thedownstream with downtrend (-0.9500mm/a). The Figure 4(b) is the Z statistic value of 45 weatherstations (from upstream to downstream) which shows only 1 station has significant uptrend, about 35stations have a little uptrend and 9 stations have a little downtrend which 6 stations belong to thedownstream. Thus, the downstream stations have a little downstream.

4.4.4.4. ConclusionsConclusionsConclusionsConclusions

The Mann–Kendall method is used to analyze the spatial and temporal distribution of temperatureand precipitation of the Lancang River Basin. The main conclusions can be drawn as follows:(1)The annual temperature of Lancang River Basin is significant uptrend with 0.020℃/a increasing

rate from 1971 to 2000 years. And1988 and 1993 years are the mutability years which are the uptrendbegin times and the increasing rate of 1993 year is bigger than 1988 year.(2)The annual temperature of downstream is obviously higher than the upstream which is steeped

distribution along the basin. Besides, the increasing rates of temperature of different part of basin arepresent a certain rule. The downstream is bigger than upstream: the downstream(0.015℃/a) >themiddle stream(0.020℃/a)>the upstream(0.033℃/a). The downstream have the obvious uptrend thanthe upstream.(3)The annual precipitation of the Lancang River Basin is uptrend but not significant with

1.8375mm/a increasing rate from 1971 to 2000 year. There are four mutability years: 1992, 1994,1996 and 1999 years. All of the four mutability years are the uptrend begin times, but the increasingrate of 1992, 1994 and 1996 years are small, the increasing rate of 1999 year is bigger than the others.(4) The annual precipitation of downstream is obviously higher than the upstream which is steeped

distribution along the Basin. However, the upstream and middle-stream are uptrend, the downstream isdowntrend: the upstream (3.7875mm/a) > the middle stream (3.5583 mm/a), and the downstream withdowntrend (-0.9500mm/a).The study of the spatial and temporal distribution of temperature and precipitation of Lancang River

Basin is significant for understanding the climate change over the years. It has practical significancefor water resources allocation and management in the future.

app:ds:spatial

app:ds:and

app:ds:temporal

app:ds:distribution

app:ds:mutability

app:ds:mutability

app:ds:mutability

app:ds:and

app:ds:temporal

app:ds:practical

app:ds:significance




This work was supported by the Project of National Natural Science Foundation of China (No.50939001, 51079004), the National Basic Research Program of China (No. 2010CB951104), theFunds for Creative Research Groups of China (No. 51121003), theSpecialized Research Fund for the Doctoral Program of Higher Education (No. 20100003110024), andthe National Commonweal Research Project of Ministry of Water Resources (No. 201201020).


Chen YN, Xu CC, Hao XM, Li WH, Fifty-Year Climate Change and Its Effect on Annual Runoff inthe Tarim River Basin, China, Quaternary International, 208(2009) 53–61.

Kendall MG, Rank Correlation Methods, Griffin, London, 1975.Kumar S, Merwade V, Kam J, Thurner K, Streamflow Trends in Indiana: Effects of Long Term

Persistence, Precipitation and Subsurface Drains, Journal of Hydrology 374(2009) 171–183.Mann HB, Nonparametric tests against trend, Econometricam,13(1945) 245–259.Xu ZX, Liu ZF, Fu G, Chen YN, Trends of Major Hydroclimatic Variables in the Tarim River Basin

during the Past 50 Years, Journal of Arid Environments 74(2010) 256–267.Yue S, Pilon P, Cavadias G, Power Of The Mann-Kendall and Spearman's Rho Tests for Detecting

Monotonic Trends in Hydrological Series, Journal of Hydrology 259(2002) 254–271.Zhang Q, Liu CL, Xu CY, Jiang T, Observed Trends of Annual MaximumWater Level and Streamflow

during Past 130 Years in The Yangtze River Basin, China. Journal of Hydrology 324(2006),255–265.

Q.L. Gu, X.H. Yang, S.S. Yang, T.B. Zhao, Nonlinear Science Letters C, Vol. 2, No.1, 2012, 15-22


15

FuzzyFuzzyFuzzyFuzzy Decision-MakingDecision-MakingDecision-MakingDecision-Making ModelModelModelModel BasedBasedBasedBased onononon DynamicDynamicDynamicDynamic ProgrammingProgrammingProgrammingProgramming andandandandItsItsItsIts ApplicationApplicationApplicationApplication inininin FloodFloodFloodFlood ControlControlControlControl

Q.L.Q.L.Q.L.Q.L. GuGuGuGu1111,,,, X.H.X.H.X.H.X.H. YangYangYangYang2,2,2,2,**** ,,,, S.S.S.S. S.S.S.S. YangYangYangYang3333,,,, T.T.T.T. B.B.B.B. ZhaoZhaoZhaoZhao4444

1 School of Mathematical Sciences, Shandong Normal University, Jinan,250038,China2 State Key Laboratory of Water Environment Simulation, School of Environment, BeijingNormal University, Beijing, 100875, China3 School of Mathematical Sciences, Beijing Normal University, Beijing, 1008754 School of Mathematical Sciences, Beijing University of Posts and Telecommunications,Beijing, 100876


Fuzzy decision-making can be used on flood control. In this work, we firstly introduce a dynamicprogramming method to solve parallel reservoir flood control problem. Then a fuzzy aggregationmethod is used as a proper way to solve the multi-attribute decision problem. This paper shows amethod that is not only able to be adopted in flood control but also in other fuzzy decision-makingproblem.

Keywords:Keywords:Keywords:Keywords: Flood control; Decision-making; Dynamic programming; Aggregation; Fuzzy-set theory


Fuzzy decision-making is of vital importance in systems engineering, management science andoperational research nowadays. While making decision, lots of aspects are needed to be considered.Some aspects cannot be measured in an accurate way. As the development of fuzzy-set theory in recentyears, we have got some new approaches to solve this problem.

Flood control is a complex practical problem. During the past decades, traditional optimizationtechniques have been the primary approaches for this problem. (Needham Et Al, 2000) broughtdynamic programming into flood control operation.However as is pointed out by (Cheng & Chau,2001) that traditional optimization techniques are hard to adapt to these situations, for decision makingof flood control is effective only for a constrained periods. (Yeh, 1985) also presented a in-depth andexcellent review of reservoir management and operation model which indicated that a gap may stillexist between theories and applications particularly in the area of real time flood operations. At thesame time, the use of fuzzy decision-making in water resource management has gain greatachievement. Bender and Simonovic (Bender & Simonovic, 2000) describe a fuzzy compromiseapproach to water resources systems planning under uncertainty. (Despic & Simonovic, 2000) presenta general methodology for the numerical evaluation of complex qualitative criteria based on the theoryof fuzzy sets. This method has been developed as a suitable aggregation operator for the qualitativeevaluation of flood control.

Suppose that there is a set of alternatives

1 2{ }nA A A A= , , ,…

that we can choose from and a set





1 2{ }mO O O O= , , ,…

which indicates the m attributes we must consider. Then we transform the characteristic value of theseobjects to member functions and compute the corresponding weight of these objects. The evaluation ofan alternative can be obtained by a fuzzy aggregation method.

For multi-reservoir problem, it is much more complex than a pure fuzzy decision making problem.The collaboration of different reservoirs must be taken into consideration, so it is necessary to find away to figure out the comprehensive evaluation of the whole system. By considering parallel reservoirflood control problem, a fuzzy dynamic program method is provided here to select a properalternative.

2.2.2.2. ParallelParallelParallelParallel ReservoirReservoirReservoirReservoir FloodFloodFloodFlood ControlControlControlControl BasedBasedBasedBased OnOnOnOn DynamicDynamicDynamicDynamic ProgrammingProgrammingProgrammingProgramming

In our daily lives, the reservoirs not only protect the people from disasters but bring the regioneconomical benefits such as electricity generation, agricultural irrigation and fiseries. Consider thehypothetical reservoir system used by (Larson, 1968), a kind of dynamic programming method wereapplied to this system, a number of earlier methods were also applied to it. However, these methodsare seldom feasible since they neglect some important characteristics of flood control operation.

Suppose a reservoir network with n reservoirs. To make it easier, it is assumed that they are onlyparallelly connected. The whole network are located in the same block of the river. Assume that themax flow that the river can load is a constant number maxQ , and the flow of the river itself Q is

constant. Define the release of the ith reservoir at time t is itR .So the outflow that the reservoirsrelease corresponds to the following constrains:

1

n

it omaxi

omax max

R Q

Q Q Q=

≤

= −

∑ (1)

where omaxQ is the maximum flow that the reservoirs can release. Define the water level of reservoir

i at time t as ith .Then the corresponding reservoir storage ( )i itS h and outflow itR can be obtained.Under constant outflow the following equation is established:

1 ( )t t t tS S I R t+ = + − ∆ (2)

where tI is the inflow at time t .In the model, there are n reservoirs discharging water at the same time in order to meet our goal of

flood control and impounding. When some regions receive precipitation forecast, the relativereservoirs must enlarge their outflow in preparation for flood control. At this time, the outflow of otherreservoirs must be restrained so that the river flow is lower than the capacity of the river.

In practical, for the sake of downstream navigation and agricultural activities, the outflow of areservoir should change as little as possible. So reservoir decision making can be seen as a decision fordischarge hole status and constant outflow, for which it is possible to treat I and R in equation (2)as constant in a period, and available alternatives are finite. For the ith reservoir, define the set of allfeasible alternatives as

1 2{ }ii i inA A A= , , ,…iiiiAAAA

and the set of possible status as



17

1 2{ }ii i inS S S= , , ,…iiiiSSSS .

To each alternative, the set of attributes are

1 2{ }mO O O= , , ,…OOOO .

With each reservoir being considered as a stage of this model, the feasible alternatives of current stagecan be obtained by the status, and the attribution of given alternatives. Finally, an optimizedcombination is found.

Suppose the status of the 1i th− stage is 1iS − and the cumulative number of the kth attribute

of the jth alternative is 1ijkx− after the decision of the first i-1 stages is made, and there are 1ip −

(alternatives that satisfies constrain condition 1iG − . After the decision of the ith stage iD is made,

define the objective of the kth attribute of the jth alternative as 1( )jk i if S D− , . The matrix ofalternative is:

1

1

1

11 1 12 1 1 1

21 1 22 1 2 11

1 1 2 1 1

( ) ( ) ( )

( ) ( ) ( )( )

( ) ( ) ( )

i

i

i

i i i i p i i

i i i i p i ii i

m i i m i i mp i i

f S D f S D f S D

f S D f S D f S DS D

f S D f S D f S D

−

−

−

− − −

− − −−

− − −

, , ,⎡ ⎤⎢ ⎥

, , ,⎢ ⎥, = ⎢ ⎥⎢ ⎥

, , ,⎢ ⎥⎣ ⎦

…

…

⋮ ⋮ ⋱ ⋮…

FFFF (3)

Define operator ⊗ , which is +,∨ or ∧ . In different situations ⊗ may represents differentoperation. Given Matrix

1 1

1( )i i

iS jk m px− −

−×=XXXX (4)

Then ( )iSXXXX can be obtained by:

1

1

1 1

1 1

11 1 1 1

1 1

1 1 1

1 111 1 11 1

1 11 1

( ) ( )

( ) ( ) ( )( ) ( )

i

i

i i

i i

h hi i p i i

i i i ih h

m i i mp i i

i i ip p

i i im mp m mp

f S D f S D

S S D Sf S D f S D

x x x x

x x X x

−

−

⎡ ⎤⎢ ⎥⎢ ⎥− −⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢⎢⎢⎢− −⎣ ⎦

− −

− −

− −

− −⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥

− −⎢ ⎥⎢ ⎥⎣ ⎦

⎡ ⎤, ,⎢ ⎥

= , ⊗ = ⎢ ⎥⎢ ⎥, ,⎣ ⎦

⊗ =

X XX XX XX X

… …

… …

…

⋮ ⋱ ⋮…

⋮ ⋱ ⋮ ⋮ ⋱ ⋮

FFFF

⎥⎥⎥⎥

(5)

Let

1 1 1( , ) ( , ) ( , ) ( , )i p i i i i p pS S S D S D S D− + −= …X F F FX F F FX F F FX F F F ,

and it is not hard to get out the following equation:

1( ) ( ) ( ) 1p i i pS S S S i p−= ⊗ , , < <X X XX X XX X XX X X (6)

where ( )i pS S,XXXX is the cumulative number from stage i to stage p.

Define ( ( ))j iSµ XXXX be the evaluation of the jth alternative at stage i. By equation (6), we have



( ( )) ( ( ) ( )) 1j i j q j q iS S S S q iµ µ= ⊗ , , < <X X XX X XX X XX X X .

Let 1 2( , , , )nD D D…GGGG be the function of the constrains of the problem. Then the goal ofoptimization is turned into an equation:

1 2

( ( )). . ( , , , )

n

n

max Ss t D D D

µ∈

XXXX…G GG GG GG G

(7)

in which G is the constrain of function 1( )nG D D, ,… . An optimized solution can be found outby the follow steps:

SSSSteptepteptep 1:1:1:1:Let 2 1i j= , = , calculate 1S and 1 1( )SXXXX

SSSSteptepteptep 2:2:2:2:Calculate 1 1( ) ( ) ( )j

j i i i j iS S D S− −= , ⊗X F XX F XX F XX F X , and abandon the alternatives that are notsatisfied with constrains

SSSSteptepteptep 3:3:3:3:Using the same method, calculate 1( )j i nS S+ ,XXXX , such that 1( ( ))j i nS Sµ + ,XXXX is the

maximum among all possible choicesSSSSteptepteptep 4:4:4:4:Let 2 nj p= ,..., , we get all 1( )j i nS S+ ,XXXX , and select the best value

1 1 1( ( )) ( ( ) ( ))j n j i j i nS S S S S Sµ µ +, = , ⊕ ,X X XX X XX X XX X Xsuch that it not only satisfies with the constrains but also is a maximum.StepStepStepStep 5:5:5:5:

The decision combination 1 … npD D, , we get is what we are looking for.

3.3.3.3. FuzzyFuzzyFuzzyFuzzyAggregationAggregationAggregationAggregation MethodMethodMethodMethod ForForForFor FloodFloodFloodFlood ControlControlControlControl

The evaluation of flood control objectives can be given by fuzzy aggregation method. Given anmulti-objective matrix ( )ij m nR r ×= , in which ijr is a fuzzy number that implies the normalized

relative membership degree of the ith attribute and the jth alternative. It is given by the followingformulae:

1

1 1

nij ijj

ij n nij ijj j

x xr

x x=

= =

−=

−∧

∨ ∧(8)

1

1 1

nij ijj

ij n nij ijj j

x xr

x x=

= =

−=

−∨

∨ ∧(9)

1max

ij iij

j ij i

x xr

x x

∗

∗

| − |= −

| − |(10)

where ijx is value of the ith attribute of the jth alternative, “∧ ” is the minimum operator and “∨ ”is the maximum operator. Then we can get the ideal alternative and the nonideal alternative



19

{1 1 1}{0 0 0}

MM

+

−

= , , ,= , , ,

……

(11)

After all these, the weighted distance between alternative iA and ideal alternative is

2

1

[ ( )] 1 2n

i j j ijj

D w M r i m+

=

= − , = , , ,∑ … (12)

and for nonideal alternative it is

2

1

[ ( )] 1 2n

i j ij jj

d w r M i m−

=

= − , = , , ,∑ … (13)

where w is the weighting vector, 1 2{ }mw w w w= , , ,… , and

1

1 0 1 2m

j jjw w j m

=

= , > , = , , ,∑ …

the In most conditions, alternatives M + and M − are impossible. So the most satisfactoryalternative is considerably far from nonideal alternative and close to ideal alternative. We define themembership degree of the ith alternative is iµ , define

2 2 2 2( ) (1 ) 1 2i i i i i if w D d i nµ µ µ, = + − , = , , ,… (14)

Let1 1 2 2( ) ( ( ) ( ) ( ))n nf u w f w f w f wµ µ µ, = , , , , , ,… ,

then the goal function is constructed as

1 1 2 2

1

{ ( ) ( ( ) ( ) ( ))}

1 0 1 2

0 1 1 2

n n

m

j ij

i

min f u w f w f w f w

w w i ms t

i n

µ µ µ

µ=

, = , , , , , ,

⎧= , > , = , , ,⎪. .⎨

⎪ < < , = , , ,⎩

∑

…

…

…

(15)

Let λ be the Lagrangian multiplier, then equation 16 can be solved by its Lagrange function

1

( ) ( ) ( 1)m

i i i i jj

L w f u w wµ λ λ=

, , = , + −∑ (16)

when

0 0i i

i

L Lµ λ∂ ∂

= , =∂ ∂

(17)

we obtain2

2 2 1 2ii

i i

d i nd D

µ = = , , ,+

… (18)

4.4.4.4.ApplicationApplicationApplicationApplication

Suppose the alternatives of three parallel reservoirs are as follows:



Table 1 Alternatives of three parallel reservoirsReservoir Alternative Criterion 1 Criterion 2 Criterion 3 Criterion 4

1 1 900 302.49 302.21 3.102 1100 302.07 301.59 3.75

2 1 1400 301.53 300.70 4.662 1600 301.20 300.10 5.27

3 1 1800 300.87 300.00 5.372 2000 300.59 300.00 5.37

By our description above, there are three stages, and the total alternatives are:

1

2

3

900 302 49 302 21 3 101100 302 07 301 59 3 75

1400 301 53 300 70 4 661600 301 20 300 10 5 27

1800 300 87 300 00 5 372000 300 59 300 00 5 37

X

X

X

. . .⎡ ⎤= ⎢ ⎥. . .⎣ ⎦

. . .⎡ ⎤= ⎢ ⎥. . .⎣ ⎦

. . .⎡ ⎤= ⎢ ⎥. . .⎣ ⎦

and they are guided by the following constrains:3

114500i

ix∗=

≤∑the four successively operators ⊗ are +,∧,∧ , and + .The 2th and the 3rd should benormalized so that the standard is unified. So the six alternatives are represented as:

11

12

21

22

31

32

[900 0 0 3 10][1100 1 1 3 75][1400 0 0 4 66][1600 1 1 5 27][1800 0 1 5 37][2000 1 1 5 37]

AAAAAA

= , , , .= , , , .= , , , .= , , , .= , , , .= , , , .

There are four possible combinative alternatives, that are:

11 31 11 32 12 31 12 32{ ( ) ( ) ( ) ( )}A A A A A A A A, , , , , , ,X X X XX X X XX X X XX X X X

To 11 31( )A A,XXXX , there are two possible decisions: 11 21 31( )A A A, , and 11 22 31( , , )A A A .Their finalstatus are:

11 21 31

11 22 31

( ) [4100 0 0 13 13]( ) [4500 0 0 13 74]A A AA A A

, , = , , , ., , = , , , .

XXXXXXXX

and the membership degree matrix is:

1 0 0 10 0 0 0

R∗ ⎡ ⎤= ⎢ ⎥⎣ ⎦



21

Suppose the weight vector (0 4 0 3 0 2 0 1)W = . , . , . , . and we obtain their relative membership

degrees {0 5667 0}µ∗ = . , , so 11 31 11 21 31( ) ( )A A A A A, = , ,XXXX XXXX .After computing orderly, we get all feasible alternatives:

11 21 31

11 21 32

12 21 31

12 21 32

( ) [4100 0 0 13 13]( ) [4300 0 0 13 13]( ) [4300 0 0 13 78]( ) [4500 0 0 13 78]

X A A AX A A AX A A AX A A A

, , = , , , ., , = , , , ., , = , , , ., , = , , , .

and the membership degree matrix is:1 0 0 10 5 0 0 10 5 0 0 00 0 0 0

R

⎡ ⎤⎢ ⎥.⎢ ⎥=⎢ ⎥.⎢ ⎥⎣ ⎦

After calculating the relative membership degrees, we get to know that 11 21 31( )A A A, , is the bestalternative.


This paper presents an algorithm to solve fuzzy decision-making problem for parallel reservoirs. Inthis method, the reservoirs are treated as stages firstly, so the problem turns into a multi-objectivemulti-stage decision making problem. Then a fuzzy dynamic programming is adopted, and all feasiblealternatives are taken into comprehensive consideration. Finally, a considerably optimized method israised to solve this problem. To every reservoir, they are able to develop their alternatives in arelatively independent way. The method is easy to be understood by operators and can be applied toother multi-attribute decision-making problems.


This work was supported by the National Basic Research Program of China (No. 2010CB951104),the Project of National Natural Science Foundation of China (No. 50939001, 51079004), the Funds forCreative Research Groups of China (No. 51121003), the Specialized Research Fund for the DoctoralProgram of Higher Education (No. 20100003110024), and the National Commonweal ResearchProject of Ministry of Water Resources (No. 201201020).


Cheng Chuntian, 1999:Fuzzy optimal model for the flood control system of the upper and middlereaches of the Yangtze River, Hydrological Sciences Journal, 44:4, 573-582

Houck, M.H., 1982. Real-Time Reservoir Operations by Mathematical Program. Water ResourcesResearch 18(5):1345-1351.

Needham, J.T., D.W. Watkins, Jr., J.R. Lund, and S.K. Nanda, 2000.Linear Programming for FloodControl in the Iowa and Des Moines Rivers. Journal of Water Resources Planning andManagement 126(3):118-127.

Cheng C. and K.W. Chau, 2001. Fuzzy Iteration Methodology for Reservoir Flood Control Operation.Journal of the American Water Resources Association 37(5):1381-1388.

Despic, O. and S.P. Simonovic, 2000. Aggregation Operators for Soft Decision Making in WaterResources. Fuzzy Sets and Systems 115:11-33.



Bender, M.J. and S.P. Simonovic, 2000. A Fuzzy Compromise Approach to Water Resource SystemsPlanning Under Uncertainty. Fuzzy Sets and Systems 115:35-44.

Yeh, W. W-G., 1985. Reservoir Management and Operations Models: A State-of-the-Art Review.Water Resources Research 21(12):1797-1818.

YU, YI-BIN, BEN-DE WANG, GUO-LI WANG and WEI LI, 2004, Multi-Person MultiobjectiveFuzzy Decision-Making Model for Reservoir Flood Control Operation.Water ResourcesManagement 18: 111-124.

Larson, R. E.: 1968, State Increment Dynamic Programming, Elsevier, New York, U.S.A.Janusz Kacprzyk,Augustine 0.Esogbue,1996.Fuzzy dynamic programming: Main developments and

applications.Fuzzy Sets and Systems 81:31-45.

Y.Q. Li, Nonlinear Science Letters C, Vol. 2, No.1, 2012, 23-26


23

FloodFloodFloodFlood ForecastingForecastingForecastingForecasting UsingUsingUsingUsing ImprovedImprovedImprovedImproved EvolutionEvolutionEvolutionEvolutionAlgorithmAlgorithmAlgorithmAlgorithm BasedBasedBasedBased ononononChaosChaosChaosChaos MemoryMemoryMemoryMemory OperationOperationOperationOperation

Y.Q.Y.Q.Y.Q.Y.Q. LiLiLiLi11111School of Geography and Remote Sensing Science,Beijing Normal University,Beijing 100875,P.R.China


To improve the computational accuracy for flood forecasting, an improved evolution algorithm basedon chaos memory (IEACM) is proposed, in which initial population are generated by chaotic mappingand searching range is automatically renewed with the excellent individuals by chaos memoryoperation. Its efficiency is verified by application of flood forecasting for seven rainfall events.Compared with standard binary-encoded genetic algorithm (SGA), chaos algorithm (CA), randomsearch algorithm (RSA), IEACM has higher precision and rapider convergent speed. It is good for theglobal optimization in the practical flood forecasting.

Keywords:Keywords:Keywords:Keywords: Flood forecasting, Precision, Evolution algorithm, Memory operation, Optimization


Flood forecasting is very important in basin and urban planning. Muskingum models are oftenused in flood forecasting. The parameters of these models are usually estimated from historical datausing artificial intelligent techniques, such as, genetic algorithm (GA) (Mohan, 1997), differentialevolution algorithm (Xu & Zhong, 2008). The parameter optimization of the complicated models isintractable mathematically with traditional optimization methods. Once an objective function hasmany local extreme points, the traditional optimization methods may not obtain the globaloptimization efficiently (Yoon & Padmanabhan, 2003; Yang et al., 2005; 2008).

In this paper, an improved evolution algorithm based on chaos memory (IEACM) is introduced toreduce computational amount and to improve the calculation precision. It gradually directs to anoptimal result with the excellent individuals obtained by memory operation. Its efficiency is verifiedby application of flood forecasting for seven rainfall events.

2.2.2.2. FloodFloodFloodFlood forecastingforecastingforecastingforecasting modelsmodelsmodelsmodels watershedwatershedwatershedwatershed

In this paper, Muskingum flood calculation models are used. The flow conditions of Muskingummodels at two locations on a river can be related by the following continuity equation

)1()1(~

QQ = , (1)

niiQciIciIciQ ,...,2),1()1()()(~

321

~=−+−+= , (2)

txktkxc∆+−

∆+−=

5.0)1(5.0

1 ,txk

tkxc∆+−

∆+=

5.0)1(5.0

2 ,txktxkc

∆+−∆−−

=5.0)1(5.0)1(

3 (3)

3,2,1,0 =≥ ici , (4)



in which andk x are the Muskingum parameters, and )(~iQ and )(iQ represent the calculated

outflow discharges and observed outflow discharges at time t , respectively. )(iI represents theinflow discharge at time interval it . n is the total time number, 21 ,cc and 3c are the Muskingumparameters in equation (2). In order to estimate the parameters of the above Muskingum models, weadopt the following the objective function of mean relative errors (MRE):

)()1/()|)1()(|(),(min2

2121 iQnriIciIcccfn

i−+−+= ∑

=

,

r = )()1()1(~

21 iQiQcc −−−− (5)

3.3.3.3. DescriptionDescriptionDescriptionDescription ofofofof IEACMIEACMIEACMIEACM

Here we construct an improved evolution algorithm based on chaos memory (IEACM) forparameter optimization in flood forecasting.Consider the following optimization problem,

min )(cf (6)

pjjcjcjcts ul ~1),()()(.. =≤≤ ,

where { }pjjcc ~1),( == , )( jc is a parameter to be optimized, f is an objective function, therange of the parameter )( jc is the interval )](),([ jcjc ul .The procedure of IEACM is shown asfollows.

StepStepStepStep 1111. Real-valued encoding. Consider the following linear map

))()(()()()( jcjcjxjcjc lul −⋅+= (7)

Suppose the jth parameter range is the interval )](),([ jcjc ul .The real-valued code array of the jthparameter is denoted by the logistic chaotic variable )( jx .

StepStepStepStep 2222. Create chaotic initial population. To cover homogeneously the whole solution space and toavoid individuals entering into the same region, large chaotic population is created in this algorithm bychaotic mapping (Yang et al., 2008).

StepStepStepStep 3333. Evaluate fitness value of each individual. Substitution of )( jc into Eq.(6) produces theobjective function )(if . The smaller the value )(if is, the higher the fitness of its correspondingi th chromosome is. So the fitness function of i th chromosome is defined:

ε+= 2)]([

1)(if

iF

StepStepStepStep 4444. Selection. Select chromosome pairs randomly depending on their fitness value (using roulettewheel method) from the initial population. And n -chromosomes )~1;~1(,),(1 nipjijx == aregotten.

StepStepStepStep 5555. Crossover. Perform crossover on each chromosome pair ),(),,( 21 ijxijx according toprobability cp to generate one offspring )~1;~1(,),(2 nipjijx == by linearly combining themrandomly.

Y.Q. Li, Nonlinear Science Letters C, Vol. 2, No.1, 2012, 23-26


25

StepStepStepStep 6666. Adaptive mutation. A new offspring )~1;~1(,),(3 nipjijx == can be computed by a

random adaptive mutating probability )(ipm . The operator of chaotic mutation is as follows:

)(),(3 juijx = ， mu < )(ipm ；

),(),(3 ijxijx = ， mu ≥ )(ipm .

Where )~1(),( pjju = is random variable, mu is the uniformity random variable within theinterval of [0, 1].

StepStepStepStep 7777. Chaos memory operation. Some better points in the previous phase are memorized in thememory operation, which will be further searched by chaos algorithm (Yang et al., 2005; 2008). Thenew better points will be inserted to replace the worst ones in the previous phase. Repeat step3 to step7 until the evolution times Q is met.

StepStepStepStep 8888. Rapid cycle. The parameter ranges of m excellent individuals obtained by Q-times of thepattern search evolution alternating are regarded as the new ranges of the values, and then the wholeprocess back to the real valued-encoding (Yang et al., 2005). The IEACM computation is over until thealgorithm running time gets to the design T times or there exists a chromosome fitc whose fitness

satisfies a given criterion. In the former case the fitc is the fittest chromosome or the most excellent

chromosome in the population. The chromosome fitc represents the solution.

The parameter design of IEACM is as follows: n =300, cp =0.5, 01.0=ε , m =10, Q =2.

4.4.4.4. PracticalPracticalPracticalPractical exampleexampleexampleexample

Example.Example.Example.Example. Flood forecasting with IEACM for seven rainfall events.

In this paper, Muskingum models are used in flood forecasting. IEACM is used for the parameterestimation of Muskingum models. Time interval ht 5=∆ . The observed inflow and outflowdischarges for four practical rainfall events are shown in Fig. 1. The detail data can be seen in theYang’s reference (Yang et al., 2008).

Fig. 1. The figure of the observed inflow discharges I and outflow discharges Q

The parameters 1c and 2c are required in this model. The significance of these parameters can beseen in Eqs. (1)-(4). In this work, these two parameters are estimated with respect to one criterion,



namely the mean relative error. The form of the objective function is described as Eq. (5).

The optimal parameters 1c =0.47, 2c =0.03, the mean relative error (MRE) f is 3.4990 withIEACM.

For IEACM, the evaluation number of the objective function is 2400. The computational results of theabove model are given in Table 1.

For SGA (standard binary-encoded genetic algorithm), the evaluation number of the objective functionis 3000, 1c =0.43, 2c =0.13, and the MRE f is 3.6073.

For random search algorithm (CA) (Yang et al., 2008), the evaluation number of the objective functionis 3000, 1c =0.41, 2c =0.03, and the MRE f is 5.0990.

For random search algorithm (RSA) (Steven & Raymond, 2000), the evaluation number of theobjective function is 3000, 1c =0.39, 2c =0.05, and the MRE f is 5.6251.

Table 1 gives the errors comparison of several methods. From table 1, we can see that the resultsachieved with our IEACM are satisfactory in global optimum and convergent speed. In terms ofminimizing the objective function, IEACM has shown to be capable for Muskingum models.

Table 1 Comparison with several methods in flood forecasting calculationMethods Evaluation number of the objective function MRE f

IEACM 2400 3.4990SGA 3000 3.6073CA 3000 5.0990RSA 3000 5.6251


In this paper, an improved evolution algorithm based on chaos memory search (IEACM) ispresented for the parameter optimization of flood forecasting models. The circulating mechanism ofIEACM has been studied. Because the operations of real-encoding, the chaos initial population andrapid cycle based on memory are adopted, the efficiency and accuracy of IEACM are very highcompared with SGA, CA, RSA for seven rainfall events in flood forecasting calculation. This paperprovides a good optimal algorithm for the parameter optimization of the practical water environmentalforecasting.


Mohan S, Parameter estimation of nonlinear Muskingummodels using genetic algorithm, Journal ofHydraulic Engineering, ASCE, 2(1997) 137-142.

Xu XJ, Zhong XX, Differential Evolution for Parameter Estimation of Muskingum Model, ComplexSystems and Complexity Science, 3(2008) 85-91.

Yoon J, Padmanabhan G, Parameter estimation of linear and nonlinear Muskingum Routing Models, J.Water Resour. Planning Mgmt, 5(1993) 600–610.

Yang XH, Yang ZF, Shen ZY, GHHAGA for Environmental Systems Optimization, Journal ofEnvironmental Informatics, 1(2005) 36-41.

Yang XH, Yang ZF, Yin XA, Li JQ, Chaos gray-coded genetic algorithm and its application forpollution source identifications in convection–diffusion equation, Communications in NonlinearScience and Numerical Simulation, 8( 2008) 1676-1688.

Steven CC, Raymond PC, Numerrical Methods for Engineers, McGraw-Hill Companies,Inc.2000.

Z.H. Dong, X.H. Yang, X.J. Chen, Nonlinear Science Letters C, Vol. 2, No.1, 2012, 27-32


27

EcologicalEcologicalEcologicalEcological RiskRiskRiskRiskAssessmentAssessmentAssessmentAssessment BasedBasedBasedBased ononononAHP-TOPSISAHP-TOPSISAHP-TOPSISAHP-TOPSIS

Z.H.Z.H.Z.H.Z.H. DongDongDongDong1111,,,, XXXX.H..H..H..H. YanYanYanYangggg1,1,1,1,****,,,, X.J.X.J.X.J.X.J. ChenChenChenChen11111State Key Laboratory of Water Environment Simulation, School of Environment, BeijingNormal University, Beijing, 100875, China


In order to evaluate the ecological risk of Haihe River, this paper established an index system ofecological risk, which included three risk sources and twelve risk indexes. Also the evaluation criteriawas divided into five levels: slight risk, low risk, moderate risk, high risk and extreme risk. Analytichierarchy process (AHP) and TOPSIS (AHP-TOPSIS) is introduced, which AHP was used to calculatethe weights of the indexes and TOPSIS was adopted to evaluate current ecological risk in Haihe Riverwatershed. The results showed that the ecological risk in Haihe River was belonging to moderate risk,which was consistent with the actual situation.

Keywords:Keywords:Keywords:Keywords: Ecological risk assessment(ERA), TOPSIS, AHP, Haihe River


Ecological risk assessment(ERA), which has grown and evolved since 1980s, has caused abundantattentions and become a significant part in environmental fields(Bruce,2006). By evaluating thelikelihood that adverse ecological effects caused by some possible eco-environmental hazard mayoccur(Suter II,2007), ERA has become a favorable tool to environmental management and decision.However, most research paid close attention on the ecological risk caused by single harmful factor,such as heavy metals, natural disaster and human activities, while the ecological risk is connected withall of them. So current ecological risk assessment is evolving from single factor to multifactorevaluation. Ecological risk assessment included four main parts: hazard assessment, exposureassessment, reception analysis and risk characterization, which was rely mostly on the toxicologyexperiment, geographical information system(GIS) and model simulation(Guillaume, et al,2011).Therefore, this paper adopted a method, which determined the risk by establishing index system(SuterII,2001) and calculating with AHP-TOPSIS(Chen&Tsao,2008), to assess the ecological risk in HaiheRiver watershed.

2.2.2.2.AHP-TOPSISAHP-TOPSISAHP-TOPSISAHP-TOPSIS MethodMethodMethodMethod

To evaluate the ecological risk of the river, it need to establish evaluation criteria of ecological risk,which must take the actual situation of the river into account. Also Analytic Hierarchy Process(AHP)and Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)(Wang&Taha,2006) wereadopted to evaluate current ecological situation of the river. So the evaluation result can be found outby the follow steps.

Step 1: Determine the evaluation criteria of ecological riskTo establish the evaluation criteria of the ecological risk for a river(Yang,et al,2011), it is primarily

to make sure the ecological situation of it. Then the related risk sources, which are identified as themain interference for ecological risk, should be chosen out to represent the risk. The indexes standingfor the sources should be determined, also the grading of the evaluation criteria.





Step 2: Determine the evaluation criteria matrix X and the normalized decision matrix R .The decision matrix X, which consists of the minimum of each level of all risk indexes, is

described by Eq.(1):.,,2,1;,,2,1,][ njmiwithxX nmij ⋯⋯ === × (1)

Where, m is the levels of the ecological risk, and n represents the number of the risk indexes.For the partitioning method of risk indexes have different standards and the data have various

sources, it is necessary to normalize the data to form the dimensionless matrix. The normalizeddecision matrix is expressed as Eq.(2):

.,,2,1;,,2,1,][ njmiwithrR nmij ⋯⋯ === × (2)In general, the indexes can be divided into two types: benefit index and cost index. The normalized

value ijr is calculated as Eq.(3) for benefit indexes, and Eq.(4) for cost indexes:

Benefit index: .,,2,1;,,2,1)x-(x)x-(x minij

maxij

minijij njmirij ⋯⋯ === (3)

Cost index: .,,2,1;,,2,1)x-(x)x-(x minij

maxijij

maxij njmirij ⋯⋯ === (4)

where,maxijx is the maximum of the

thj index for thethi level in ecological risk assessment, and

minijx is the minimum of the

thj index forthi the level.

Step 3: Determine the weights of the risk indexes with AHP method.In order to obtain scientific evaluation results, the weight of the risk indexes should be made sure

firstly. It can be calculated in many ways, such as Entropy method, Factor Analysis method andAnalytic Hierarchy Process. In this work, the weights are calculated by Analytic Hierarchy Process(AHP)(Metin,et al,2009).

Step 4: Calculate the weighted normalized decision matrix VThe normalized decision matrix V can be calculated with the normalized decision

matrix R obtained in step 1 and the weight matrix W described by step 3, as shown in Eq (5).( ) .,,2,1;,,2,1, njmiwithvV

nmij ⋯⋯ ===×

.,,2,1;,,2,1 njmiwithwrv ijij ⋯⋯ === (5)

Step 5: Determine the ideal solutions+jv and negative-ideal solutions

−jv

.,,2,1,,, 21 njwithvvvV j ⋯⋯ == ++++ ）（ (6)

.,,2,1,,, 21 njwithvvvV j ⋯⋯ == −−−− ）（ (7)

Step 6: Calculate the separation measures+iS and

−iS

The Euclidean distances from each alternative to the ideal solution+iS and to the negative-ideal

solution−iS , are respectively expressed as Eq. (8) and (9):

( ) .,,2,11

2 miwithvvS n

j jiji ⋯=−= ∑ =++

(8)

( ) .,,2,11

2 miwithvvS n

j jiji ⋯=−= ∑ =−−

(9)Step 7: Calculate and rank the relative closeness to the ideal solution

( ) .,,2,1 miwithSSSC iiii ⋯=+= −+− (10)

where, iC means the distance from each alternative to the ideal solution.



29

To rank the alternatives according to the relative closeness to the ideal solution. The bestalternative is the one with the greatest relative closeness to the ideal solution.

3.3.3.3.ApplicationsApplicationsApplicationsApplications

The method described above is applied to the ecological risk assessment of Haihe River whichlocated in northeast China, between 30°-43°N and 112°-120°E. For locating in social and economicrapid development area, the ecological and environment health of Haihe River has been influencedstrongly, which finally lead to some ecological risk.

The index system of the ecological risk in Haihe River have been established, and the risk sourceshave been divided into three parts: natural sources, anthropogenic sources and engineering sources.Also each source is represented by four risk indexes, which is showed in Table 1.

Table 1 The index system of ecological risk in Haihe RiverRisk Source Risk Index Description

NaturalSources(RS1)

Change rate of runoffcoefficient(%)(RI1)

Variation for ten years/runoff coefficientten years ago ×100%

Guarantee rate of river channelecological flowrequirements(%)(RI2)

River channel ecological water use/riverchannel ecological flow requirements×100%

Vegetation coverage rate(%)(RI3)

The area of vegetationcoverage/watershed area ×100%

Change rate of fishspecies(%)(RI4)

Variation for ten years/fish species tenyears ago ×100%

Anthropogenic Sources

(RS2)

Water utilization rate(%)(RI5) Water utilization amount/total waterresources×100%

Ratio of soil loss area(%)(RI6) Soil loss area/watershed area×100%Standard-reaching rate of waterquality(%)(RI7)

The length of the river meeting Ⅰ,Ⅱ,Ⅲlevel of water quality standard in China/total river length×100%

Water utilization ratio ofliving,producing andecology(RI8)

Domestic water /productionwater/ecological water

EngineeringSources(RS3)

Change rate of flood carryingcapacity(%)(RI9)

Variation for ten years/flood carryingcapacity ten years ago ×100%

Effective rate ofnon-engineering flood controlmeasures(%)(RI10)

The number of effective measures/totalnon-engineering flood control measures×100%

Effective rate of engineeringflood control measure (%) (RI11)

The number of effective measures/totalengineering flood control measures×100%

Change rate of runoff sedimentconcentration(%)(RI12)

Variation for ten years/runoff sedimentconcentration ten years ago ×100%

According to evaluation criteria and the related data from 2001 to 2010 in Haihe River which wasshown in Table 2, the decision matrix X can be determined, also the normalized decision matrix R canbe calculated.



Table 2 The evaluation criteria of ecological risk in Haihe River

Risk Source Risk IndexRisk level Haih

eRive

r

Slight Low Modera

te High Extrema

NaturalSources(RS1)

Change rate of runoffcoefficient(%)(RI1)

<10 10~20 20~30 30~40 >40 20

Guarantee rate of instreamecological flowrequirements(%)(RI2)

>90 70~90 50~70 30~50 <30 85

Vegetation coverage rate(%)(RI3)

>90 70~90 50~70 30~50 <30 74

Change rate of fishspecies(%)(RI4)

>60 50~60 40~50 30~40 <30 44

Anthropogenic Sources

(RS2)

Water utilizationrate(%)(RI5)

<20 20~35 35~50 50~65 >65 64.6

Ratio of soil lossarea(%)(RI6)

<5 5~20 20~35 35~50 >50 31.1

Standard-reaching rate ofwater quality(%)(RI7)

>75 60~75 45~60 30~45 <30 36.3

Water utilization ratio ofliving,producing andecology(RI8)

>0.6 0.4~0.6 0.2~0.4 0.05~0.2 <0.05 0.11

EngineeringSources(RS3)

Change rate of floodcarrying capacity(%)(RI9)

<20 20~30 30~40 40~50 >50 28

Effective rate ofnon-engineering floodcontrol measures(%)(RI10)

>90 80~90 70~80 60~70 <60 80

effective rate of floodcontrol structural measure(%) (RI11)

>90 80~90 70~80 60~70 <60 85

Change rate of runoffsedimentconcentration(%)(RI12)

<10 10~15 15~25 25~40 >40 35.5

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

5.3585802811.03.361.316.6944748520400050005065000402560604005.030355030303030157070302.045203540505020108080204.060520507070100909006.075006090900

6

5

4

3

2

1

XXXXXX

X

where, ),,,,( 54321 XXXXX stands for five levels of the evaluation criteria, 6X is the actual datain Haihe River.

The weights for the natural, anthropogenic and engineering sources, calculated with AHP method,

are )1571.0,5936.0,2493.0(1 =W ; While the weights for twelve risk indexes to related sources are



31

all defined as 0.25. So the weights of the evaluation criteria are shown as:

]0393.0,0393.0,0393.0,0393.0,1484.0,1484.0,1484.0,1484.0,0623.0,0623.0,0623.0,0623.0[=W

Following the Eq.(5) to (10), the separation measures+iS ,

−iS and the relative closeness to the

ideal solution iC can be calculated, also the outcome of ecological risk assessment in Haihe Riverhas been obtained.

[ ]2322.03314.02425.01646.00821.00=+iS

[ ]1453.001028.01755.02564.03314.0=−iS

[ ]3848.002976.05161.07573.00000.1=iC

Ranking the alternatives according to the relative closeness to the ideal solution iC , it is clear that

1C is best choose, while 5C is the worst alternatives to the ecological risk assessment in Haihe River.So it is clear that the ecological risk in Haihe River 6C is belonging to moderate level.

546321 CCCCCC ≻≻≻≻≻


This paper presents an evaluation criteria to assess ecological risk, also applies AHP and TOPSISmethod to determine the ecological risk level in Haihe River. The result of assessment reveals that theecological risk in Haihe River is belong to moderate level, which is consistent with the actual situation.So the method is suitable to the ecological risk assessment for all rivers. To meet current ecologicalsituation of different rivers, the risk sources and risk indexes should be changed, also the classificationof the standard.


This work was supported by the National Basic Research Program of China (No. 2010CB951104),the Project of National Natural Science Foundation of China (No. 50939001, 51079004), the Funds forCreative Research Groups of China (No. 51121003), the Specialized Research Fund for the DoctoralProgram of Higher Education (No. 20100003110024), and the National Commonweal ResearchProject of Ministry of Water Resources (No. 201201020).


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S.S. Yang, X.H. Yang, G.D. Lv, Nonlinear Science Letters C, Vol. 2, No.1, 2012, 33-40


33

NewNewNewNew RefiningRefiningRefiningRefining StratificationStratificationStratificationStratification MethodMethodMethodMethod forforforfor LoggingLoggingLoggingLogging CurveCurveCurveCurve

S.S.S.S. S.S.S.S. YangYangYangYang1111,,,, X.H.X.H.X.H.X.H. YangYangYangYang2,2,2,2,**** ,,,, G.G.G.G. D.D.D.D. LvLvLvLv3333

1 School of Mathematical Sciences, Beijing Normal University, Beijing, 1008752 State Key Laboratory of Water Environment Simulation, School of Environment, BeijingNormal University, Beijing, 100875, China3 Faculty of Education, Beijing Normal University, Beijing, 100875


In this paper, we firstly combine the Walsh transformation and fuzzy mathematics to accomplish thestratification of logging curve. First, we utilize the Walsh transformation to find the rough position ofthe boundary; after that we find the precise position of the boundary based on the method of fuzzymathematics. Comparing the outcome of our model with artificial stratification, we ascertain that theprecision of the model established in the paper is high. The outstanding feature of the model is that wecombine two methods of automatic stratification of logging curve so that the reliability of the newmodel is ensured.

KeyKeyKeyKey wordswordswordswords: automatic stratification, median filter, Walsh transformation, fuzzy mathematics, LoggingCurve


In the field of geophysical prospecting, researchers need to use the log information to accomplishsome fundamental work such as lithology identification, logging facies analysis(Yin et al., 1999) andreservoir classification. However, the stratification of the logging curve, to make the logging curveinto rectangular curve, is the most basic work (Feng et al., 1991). The purpose of the stratification is toascertain the goals of the research according to the characteristics of different stratum, the stratum thatshould be studied carefully, and the research range of different wells.

Recently, researchers mainly stratify the logging curves according to the method of manualinterpretation. This method is not only time-consuming, but also easily affected in the samplingprocess of because of the experience and proficiency of the researchers. Besides, due to the differentpersonal standard of different researchers, the stratification results may not be precise.

With the increase in the number of regional wells, people hope to utilize the data and the featuresof different stratum as the control point, combining the data of logging curve of different wells so thatthey can realize the automatic stratification. The basic idea and the methods of automatic stratificationis a process of constant development, researchers should constantly compare the results betweenautomatic stratification and manual stratification, improving the precision of automatic stratification inorder to find the optimal method.

In this paper, we aim to solve the following problems:According to the data of standard well, we build the mathematical model to accomplish the

automatic stratification of other wells and we compare the results with that of manual stratification.After that, we make judgments of the precision of the model.

Ascertain the proper mathematical model to stratify the wells and analyze the results.





2.2.2.2. RefiningRefiningRefiningRefining stratificationstratificationstratificationstratification methodmethodmethodmethod

2.12.12.12.1 SelectionSelectionSelectionSelection ofofofof logginglogginglogginglogging curvescurvescurvescurves

Each well contains plenty of data of logging curves, which represent the features of the well.However, after our analysis, we find that not all logging curves can show the features of the wellperfectly, and we should firstly select the logging curves which can represent the features of the wellsideally.

In this paper, we adopt the method of median filtering and all the logging curves of Well 1 aredealt by such method. The interference of the peak of logging curves is eliminated, and we select thelogging curves with high resolution and small noise as the ones used to build the mathematical model.

2.22.22.22.2 MedianMedianMedianMedian filteringfilteringfilteringfiltering

Supposed that a logging curve has the sample series xi ( i = 1，2……N), when the number of thewindows is 2n+1, then the procedures of filtering are:

(1) Sorting the data which has 2n+1 points with the ith point as the center;(2) Selecting the median after sorting the data as the value of filtering of the ith point(3) Calculating the value of each point by top-down and iterative algorithm.When i<n or i>N-n, let n=i-1 and N-i respectively in order to keep the sample size be N after

filtering (Ji et al., 2007).Taking Well 1 for example, we find its density (DEN) logging curve become smoother after

median filtering as figure 1 shows:

200 300 400 500 600 700 800 9002.3

2.4

2.5

2.6

2.7After median filtering

depth

DEN

200 300 400 500 600 700 800 900 10001

1.5

2

2.5

3

depth

DEN

Before median filtering

Fig. 1 Change of den logging curve of Well 1 after median filtering

We take this method to deal all the logging curves of Well 1 and select the curve which is



35

smoother and has higher resolution as the logging curve used to build the mathematical model. In thisrule, we select the spontaneous potential (SP) and density (DEN)logging curve of Well 1 toaccomplish the stratification.

2.22.22.22.2 UnitizationUnitizationUnitizationUnitization processingprocessingprocessingprocessing

Since different logging curves have different scale and dimension, when westratify the wells, weshould unify the data of different logging curves into [0,1]in order to rule out the effect brought bydifferent scale and dimension.

In this paper, we let

(1)

Where Xi is the logging value corresponding to its certain depth; Xmax and Xmin are themaximum and minimum in the logging value respectively; Xi′ is the unified value of thecorresponding depth.

2.32.32.32.3 StratificationStratificationStratificationStratification bybybybyWalshWalshWalshWalsh transformationtransformationtransformationtransformation

Walsh transformation has a primary function which consists of an orthogonal function familywhich only has the value “+1” or “-1”.

Via Walsh transformation, the logging data can be transferred to square wave data and thecatastrophe point of square wave can be regarded as the demarcation point in the process of roughstratification.

The definition of the Walsh function of the first kind is

(2)

where ; is the mantissa of the k when k is expressed inbinary system;

(3)

The expressions of the first eight Walsh function are

(4)(5)(6)(7)(8)(9)(10)

. (11)

The functional images of them are shown in figure 2:



0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1-2

0

2w a l(0 , t )

0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1-2

0

2w a l1 , t )

0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1-2

0

2w a l(2 , t )

0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1-2

0

2w a l(3 , t )

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1-2

0

2w a l ( 4 , t )

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1-2

0

2w a l ( 5 , t )

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1-2

0

2w a l ( 6 , t )

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1-2

0

2w a l ( 7 , t )

Fig. 2 The functional image of Walsh function

For the logging data which mainly consists of discrete points, we should unify the discrete points asshown in formula (4):

(12)where is the ith unitization point; is the value of the ith point; is thenumber of thepoints. Then we make Walsh transformation for the unitization points:

; (13)

After that, n discrete coefficients are generated. The coefficients should be dealt by inverse Walshtransformation (Wang ZW et al., 2003; Wang P et al., 2008):

(14)

where N is the cut-off frequency and represents the number of stratum we need to sort.Now we have got the Walsh transformation coefficients, so we can transfer the logging curve to theform made by some Walsh functions.

2.42.42.42.4 RefiningRefiningRefiningRefining StratificationStratificationStratificationStratification methodmethodmethodmethod bybybyby fuzzyfuzzyfuzzyfuzzy mathematicsmathematicsmathematicsmathematics

According to the meaning of fuzzy, there will be a most undimmed point near the demarcation



37

point got in Section 2.2 and the depth corresponding to the point is the demarcation point.Provided that there are m log parameters, and the sample number of each parameter is M, then we

can get a matrix , where represents the value of the jth points in the ith logging curve.

According to the analysis of the law of the change of the logging curve, we decide the number ofsampling points is 2n+1. For the ith logging curve, in the 2n+1 (2n+1 M) sampling points, theaverage is and the variance is .

Utilizing the formula (9)-(13), we can get the ambiguity of each point and then we can find thedemarcation point which is the most dimmed(Li et al., 1992).

(15)

(16)

, (17)

(18)(19)

Where, represents the membership； represents the ambiguity;

; . (20)

Via calculation, we find the most undimmed point near the demarcation point got in the model ofWalsh transformation, as it stated in part 2.3, we know that such most undimmed point is thedemarcation point.

3.3.3.3. ApplicationApplicationApplicationApplication

As it shown in part 2.1, we select the DEN and SP logging curve of Well 1 to build the model.After unifying the data and making the coupling curve of the unified data of DEN and SP, we get theoutcome of the stratification of Well 1 by Walsh transformation shown in figure 3.

As figure 3 shows, the position of fault in the figure is the separation. According to the formula (1),we can get the outcome of the rough stratification shown in table 1.

Table 1 The automatic rough and manual stratification of Well 1Stratum Automatic (rough) ManualLong 31 293.55 294Long 32 334.675 330Long 33 375.8 368Long 41 416.925 410Long 42 458.050 453.8Long 61 499.175 495.3Long 62 540.3 530.2Long 63 581.425 575Long 71 622.550 614.7Long 72 663.675 654.5Long 73 704.8 697Long 81 745.925 736.3Long 82 787.050 771.8Long 91 828.175 814



Long 92 869.3 857.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Unified depth'

Unifiedloggingdata

Coupling logging curve of Well 1

Fig.Fig.Fig.Fig. 3333 TheTheTheThe automaticautomaticautomaticautomatic stratificationstratificationstratificationstratification ofofofofWellWellWellWell 1111 bybybybyWalshWalshWalshWalsh transformationtransformationtransformationtransformation

Compared with the outcome of manual stratification, we found that the precision of the methodWalsh transformation need to be improved.

According to the formula (9)-(13), we get the ambiguity of each point of the Well 1 (part) shownin figure 4.

There will be the most undimmed point and the point is the demarcation point. As it shown infigure 5, we found that the demarcation point is at the depth of 293.8.

In this method, we get the outcome of refined stratification shown in table 2.Table 2 The outcome of automatic refined and manual stratification of Well 1

Stratum Automatic (refined) ManualLong 31 293.55 294Long 32 329.3 330Long 33 366.8 368Long 41 412.9 410Long 42 452.2 453.8Long 61 496.4 495.3Long 62 534.3 530.2Long 63 579.4 575Long 71 612.5 614.7Long 72 657.3 654.5Long 73 701.8 697Long 81 736.9 736.3Long 82 773.2 771.8Long 91 819.1 814



39

Fig.Fig.Fig.Fig. 4444AmbiguityAmbiguityAmbiguityAmbiguity curvecurvecurvecurve ofofofofWellWellWellWell 1111

Compared with rough stratification, the precision of refined stratification has been apparentlyimproved, so the rationality of the model is guaranteed.


We transfer the image of the data to the square wave signal by Walsh transformation and we canget the rough outcome of the stratification. Since the step has the same length, the error of roughstratification is comparatively high. However, this method is very easy to some extent and it isconvenient to be utilized.

By using the method of fuzzy mathematics, we can find the most undimmed point near the roughdemarcation point and we assume that such undimmed point is the refined demarcation point. For thismethod, the precision of the outcome has been improved; however, since the outcome is based on thefeature of the curve observed by people, the complexity is relatively high.

By combining the two methods, we build the model to get the outcome of stratification. Thedisadvantage of each method has been overcome to some extent by such combination. The precisioncan be improved by using fuzzy mathematics, and the complexity of singly using fuzzy mathematicscan be overcome by utilizing Walsh transformation.


This work was supported by the National Basic Research Program of China (No. 2010CB951104),the Project of National Natural Science Foundation of China (No. 50939001, 51079004), the Funds forCreative Research Groups of China (No. 51121003), the Specialized Research Fund for the DoctoralProgram of Higher Education (No. 20100003110024), and the National Commonweal Research

Long 92 863.3 857.8



Project of Ministry of Water Resources (No. 201201020).


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JiRongyi, Fan Honghai, Yang Xiongwen, Yang Jieping, Design and Application of Well LogCurves Automatic Sorting in Layers.Petroleum Drilling Techniques, 2007, 2(35):24-25.

Wang Zhuwen, Liu Jinghua, Application of Walsh Transform for the Identification of RockBoundaries with Logging Data.2003,4(39):81:83.

Wang Ping, ZangYuwei, Ma Gang, Liu Danhong, Stratifying algorithm of electric well logs basedon Walsh transform. 1001- 9081( 2008) S2- 0366- 03.

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