Multiob Optimization of Pollutant Loads from Sources in Watershed

Catchment Systems Systems Association Association (JRCSA) {JRCSA)

Japan Rainwater JapanRainwaterCatchment

Optimization of Pollutant Loads from Nonpointjective Sources in Watershed Considering Surface and Subsurface Flows Multiob

[[bshihiko Kawachi3

Alok Kumari, Shigeya Maeda2and

from allocatethe pollutant load emitted fiows. ArcView GIS (Geographic in flowlengthand InformatiollSystem)software is used to include the effect of geographical variations unit subsurfbce geology for each 1and management (LMU),which is a grid of regular identicalsize, of the through surface and subsurfhce fiows is differentiatedbased watershed. The process of selfpurification total The objective function in the rnodel maximizes on the data of subsurface geology foreach LMU. to the constTaints allowable discharged loadsfrom LMUs and promotes equal allocation of them, subject types relation among mean eMuellts from different of eMuent limitationat an outlet of sub-watershed, and minimum and subsurface fiow in each LMU of LMUs, relation between eMuents through overland to demonstrate the model's applicability, the formulated model is limit of eMuent in each LMU. In order applied to a sub-watemshed of the Yasu river basinin Shigaprefecture,Japan, to determine the optimum from differentkinds of LMUs present in the sub-watershed. allocation of discharged loadsof total nitrogen of water reseurces. This model could be helpful to arrive at policiesrelated to sound management Keyzvords: Norrpoint sources; Multiebj'ective optimization; GISi PVater qualitv;Ibtal nitrogen; Sudece and subsuf:foce Subsurfoce geotogy flows; A

Abstract: nonpoint

in

1 Introduction A considerable amount

a

is

model

multiobjective

sources

watershed

developed to

considering

surfhce

needed

loads from

of

towards proper

management

pollutant

of

et (Erisman

2001; Arheimer and Brandt, 2000). Nonpoint sources have wide spatial distribution and are infiuenced by unhydrologic and varying certain geological features. Hence, it has been diMcult to manage pollutant loads originating frornthese sources and (Novotny Chesters, 1981). Estimating maximum allowable discharged load of nonpoint source pollutantfrom each unit area in a watershed is essential fbr emnonpoint

sources

al,,

water ploying policies concerning quality preservation and Solomon, 1998; Culver et al., 2002), The issues relating water quality conservation in waand use of these water resources for ecoter bodies

(Jarvie

nomic

and

development are in conflict. advantageous to decide man-

agricultural

Therefore, it is often plans

agemeni]

A

to unit

(Kumar

et al.,

has been de-

model

total allowabledischargedpol-

catchment

areas

theory,

optimization

optimization

maximize

lutantloadin a those

the

using

multiobjective

velopod

using

considering optimizatlon

2002), In the

equity

among

GIS

theory and

abovementioned

work,

IPostgraduate Student, Graduate School of Agricultural SakyoScience,Kyoto University,Kitashirakawaroiwake-cho,

ku, Kyoto, 6008502

and

subsurface

into grids polygon of land use was discretized area arrd each was treated as having the same grid

each

pollutant loads to the water bodies originates from nonpoint sources. In order to control the negative impact of these pollutant loads on the quality of water bodies, efibrts are

optimally

Japan

2Instructor,

Graduate Scheo] of Agricultural Science, Kyoto UniversitM Kitashirakawa-oiwake-cho, Sakyo-ku, Kyoto, s 60e8502 Japan 3Professor, Graduate School of Agricultural Science,Kyote Kitashirakawaroiwake-cho, Sakyo-ku, Kyoto, 606University, 8502 Japan

JOURNAL

land management total pollutast] load from a separate as

a whole

and

a single

unit

each LMU

(LMU).However, was

considered

of watershed-wide

value

(A)

self

for the formulapurification coeMcient tion of optimization model, In contrast, in this study, is considthe pollutant load flow from each LMU components. ered to includeoverland and subsurface Hence, the data on subsurface geology foreach LMU isused to discriminatethe processof selFpurification fiows and the optithrough overland and subsurface was

used

The forproblem is modified accordingly. is applied to a selected area ofinterest mulated model discharged in Yasu river basin to allocate optimum mization

load of [[btalNitrogen (T-N) from each LMU. The with the optimum values of result is also compared without discriminating the dischargedloadsobtained loads intooverland and subsurface flows, 2 Methodology 2.1 Sub-watershed

and

land

management

units

is A method of defininga sub-watershed of interest is delineated,from describedat first.A watershed 1arger elevation data) of a relatively DEM (digital the SpatialAnalyst module of ArcView area, using 1996). The process of watershed delinGIS (ESR[[, determiriation ef the flow eation involvessubsequent and direction, fiow aceumulation, stream networks finally the outlet of watershed. The flow direction slope to one of is determined basedon the steepest the eight neighboring Then flow accumulagrids.

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LMU

j, L

::･

frem 1,/oPvO:lul tanndt ooawd

flt

LP,'S.O,il

)rom

t,a..t,ioAg

Figure 1: Schematicdiagrainof LMU tant load fiow

and

pellu-

flow direction

tion is computed using the values of in each grid. Based on the value of ficrwaccumulation, the stream networks isextracted and thus the

is also determined. The delineated watershed isfurtherfragmented into a number Then out of these deof smalIer sub-watersheds,

outlet

rived

of

watershed

sub-watersheds,

one

sub-watershed

drains into a permanent

outlet

whose

S ¢ rensen, 1998). The occurrence ratio of pollutantload flow in each LMU also depends on soil types. Based on study of Skop and S ¢ rensen (1998), it isassumed that in loamy soils, 41% of load istransflow and 59% of load by subsurported by overland for sandy soils the corresponding faceflow,whereas values are 1096 and 90%, respectively. Hence, in order to different]iate the ratio of overland and subsurin each LMU, the data of subsurfacefiowsoccurring from face geology isused. These data are obtained the GIS source data. and

of river,

so that the effect of the smal1 transport of pollutants in the sub-watershed stream

sen

interest, is cho-

fiow on can be

2.3 Optimization model model The objective function of the optimization one for presented below includes two objectives, loads in maximizing the total dischargedpollutant the

sub-watershed

another

and

forminimizing

the

deviation of discharged pollutant load load for each LMU type, to hEwe eqall LMUs. Taking into consideration

maximum

from mean uity axnong the above

points, the objective function and confor the optimization of discharged pollutant

straints

load from nonpoint

sources

are

formulatedas:

neglected.

The

sub-watershed

consists

normally

of a

number

differentland use. These polygons are furtherfragmented into regular gridsof the same size using the SpatialAnalyst module of ArcView area are treatedas GIS.These grids having identical individualLMUs. polygons

of

of

2.2 Decay process and flow discrimination model, the data on [[b formulate the optimization fiow length from each LMU to the outlet of selected sub-watershed is required. The value of fiow length for each LMU isdetermined using the SpatialAnalystmodule from the DEM data based on the value of flow direction foreach LMU. The discharged loads from nonpoint sources first the

reach

streams

flow

overland

and/or

sub-

are latertransported along the In this study, pollutarrt load from is considered to includetwo components each LMU fiow in Figure 1, as shown pollutant load by overland flow. These loads and load by subsurface pollutant normally reduce in amount due to selfipurification

surface stream

fiow

by

or

processes denitrification,volatilization and retention by biomass and sediment in the case of totalnitrogen. reduction rate unit length can be assumed The per of dischamgedpolto be proportional to the amount such

of watershed

as a result

of

as

lutantload from sources (dLldx -AL), and can Loe-A=, where be integrated to have the form L L = dischargedload reaching the outlet, Lo pollutantload disehargedfrom emission point, A == selF length of flow path and x purficatien coeMcient et al., 1998). The values of A isconsidered to be (Ha different foroverland fiow and subsurface flow (Skop =

=

=

:=

81JOURNALOF

Ij

+ L,b.,) =j Z(L,e.,

wi

i=1

Z](Li l](1) [m,ax( lj

+-2

>I]

(Li +

Ljb'i)

'

LJb',)flj'

i=1

to:

subject

1, Effluentlimitationat the

outlet

of a

watershed

Iti2

L,b,)s L + E(e-XOXotL,O, eJAbxsi

j'

(2)

i=1

between eenuents through 2, Relations flowand subsurface flow in each LMU

overland

and

river.

characteristics

-

Minimize

= LjO-,:LJb･, 41:59

forj'ion loamy

soils

LsO･,:Lob･. 10:90

for2'ion

soils(3)(4)

=

3, Relat･ions among types of LMUs

mean

effluents

l.

from different

Id

2(Lg,

+ Lg,)!ib

cM

-

+ LZ. )Iid Z(LZ.

(5)

i=1

i=1

lp

Ic

Z(LS.

+ Lg,)Iib

-

6E(LZ,

+ L2,)!i.

(6)

i=1

i=1

4. Lower limitof

sandy

effluent

L,O., + L,b-, -> Ll. jiVi

in

each

LMU

i==1,2,...,I}

(7)

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p, d, and

where

c

indices deneting paddy

=

fields, and

upla:nd

(JRCSA) {JRCSA)

･i

cities, respectively,

fields, identifip, d,

=

(j'

of LMU on LMU type j' = 1,2,,..,b･), total nuinber of LMU on LMU type i LjO･, dischargedpollutant load by Ljb･, overland flow from LMU o'i flow from discharged pollutant load by subsurface cation

number

and

i

c,

With the modifications tive functioncan be

G･

Minimize -

+ L9. )+ Eji=12(L,O, 2

wi

=

(glmonthlgrid), =:

w2

objec-

w,

(14)

j･

The linearprogramming

problem formulatedabove, is solved to determine the optimum amount of discharged pollutant load through flow overland flow and through subsurface ) that can be allocated to ea £ h LMU,

(2)-(7) (11)-(14), == LMU ji (g/monthlgrid), xj, length of flow path for LMU j'itQ the outlet (m),AO = basin-wideself (LjO･, ) flow (m-i), Ab purification coeMcient foroverland basin-wide selfpurification coeMcient forsubsurface fiow (m-i), L eanuent standard value of pollutant 3 Application at the outlet of the watershed LS･. lower (gfmonth), limitof pollutant load in LMU j'i (glmonth!grid), 3.1 Selected area, flow length =

the

as:

Ij

=

=

introducedabove, rewritten

and

(Lsb･.

=

=:

wi

and

w2

given to the 1), and a and

weights

=

+ w2 jectives (Lvi ,B of landuse type. The values preference =

w2

=

for

weights of

wi

and

be decided by the decision-maker based on weightage isto be given to each objective.

can

how The

ob-

corresponding

much

values

of a

5 depend

and

LMU

on

type in the

a

decision-maker's of mean load

preference discharged from an unit area, To convert the absolute functionpresent in into linearone, the fo11owingvariables are introducedfor all i and o': of

sense

(1)

Ij

+ L9.,)

(L,o.,

y;,-i(

+ Le,)1!}･ E(L,O･, i=1

)

Jp'

+ L,b,)Iib 2(L,O･,

)-

+(L ,O.,+ Li

i=1

yj'i =

Ij

;(

+ L,b.,)fl)z(L,o.,

+ Le.,)(L,o,,

i=1

((L

)]

I,-

-

+ L,b,)/Ib )-E(L,O･.

L,b. ,o,,+

i=1

Further a

variable

wj

isintroducedsuch

-

+ L,b,,)

(LS.,

m,ax(

+ L,b,)!ib 2(L,O., i=1

=

m,a.x{y

Consequently, for

all

straints

added

are

newly

vj'

e'･,+s(ji,}

i

(9)

that

lj

w,

(8)

J, the fo11owingconto the optimization prob-

lem:

{O

Cll)

lj

- yi y,+.,

-

+ L,b..) + L,b.)fi} (12) (L,O., E(L,O. i=1

wj- >- o Yo+',, Z{j-･,:

soil

cate-

the formulated basin in Shiga having an area of 6.3 krn2, is seprefecture(Japan), leetedas the amea of interest. The runoff from the se lectedarea drainsdirectlyintothe Yasu river. Flow length foreach LMU in the study area iscalculated a

model,

using

an

application

subwatershed

ArcView GIS and

of

of

Yhsu

elevation

river

data whose

source

is map 50m grid(elevation)' produced by the 1997. It is assumed, GeologicalSurvey Institutein forsimplicity, that fiowlengthsforsurfaee flow and subsurface flow are the same f6r each LMUs. The land use pattern in the area isshown in Figure 2, It the LMU al$o shows grids (50m× 50m) fbr which optimization isconsidered in this study. The LMUs under foresthave been excluded beeauseit is relatively diMcult to control the discharged loads from these LMUs. Therc are altogether 1,156 LMUs in177 units of cities, cluding 802 units of paddy fields, and 177 units of upland fields in the selected area. The subsurface geology foreach LMU in the area source is is shown in Figure 3. These data whose `Subsurface map' by the Land produced geological Agency are for a soil from the soil surface to 3040 meters below. Since the data forpToportions of are only available for fiowas overla[rid and subsurface loamy and sandy soils, all the LMUs are either placed into sandy or loamy category based on the subsurface in that LMU. Those LMUs type dominant geolog}r type as loamy sand and having subsurface geology as sandy coarse fragment (Figure 3) are considered having subsurface type LMUs, whereas other LMUs clay and silty loam type as limestolle, silty geology are considered as loamy type, for simplicity. [Digital

}(10)

and

Yj+'T+Yi -Wj

gory [[b demonstrate

and

3.2 Parameter determination The fbrmulated model is applied for the optimal T-N in the selected area, Based allocation of and Sptrensen the on the study of Skop (1998), flow is eonsidered as value of A for overland flow is taken O,OO and that for subsurface (Ab) value of as O.OO085. The eMuent standard polcan be lutant at the outlet of watershed

(AO)

(L)

(13)

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N

g･month-i

grit

-l

v

3S70

tllSSSSS-3ss32S2S.4S89S

e

g -

leet

loDo

leoom

e!!!!!!!!!!

10eem

Figure 2: Map showing the study area and grids forwhich optimization is considered

Figure 5: Optimum dischargedT-N loadforwi == O.05 and w2 = O,95 without flow discrilnination

N

N.-l"(..

g,tuonth'i,grid'i

SubellTfacesofitypeoneaganysandcfragment

/

2914199.177SS-3112

O s

tOOe

e s

i-eO Meters

Figure 3: Subsurfaeegeologyforthe

stndy

.grva -1

month'1

2oscm

Figure 6: Optirmim surface tvi = O.05and w2

area

N

looo

component =

ofload

for

O,95

-1

Nw9elF-E

g-tuonth-1.10-11-31.42-E3 grld 3Sro142S44-17740().3220S

.11S5SSSS-M966"66

e

s

loeo

2ooom o

Figure 4: Optimum dischargedT-N load forwi

O,05and and

1OIJOURNAL

w2

=

O.95considering

subsurface

OF RAINWNER

s

2ooem

=

overland

floweomponents

CMCHMENT

looo

Figure7:Optimum subsurface forwi

SYSTEMS

==

O.05and

w2

component] ==

ofload

O,95

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decidedby

a river

quality

water

management

allowed

model.

isnot available forthe region at present. Therefore,L is calculated using value of the unit loading factor(Soumiya, 2000) foreach land use type: O.38 glm21month O.77 (paddyfields), fields) and O.11 glm21month (upland glm21menth and the area of eaeh LMU. The calculated (cities) value of L used here is 1,151,300g!month. The However,

values

such

fiare

of a and

spectively,

considered

as

the preference

assuming

O.5

2,

and

111,587 land load as their use category are allocated an optimum function definedvalue ef lower limit. The objective takes a value of -2,098,729 glmonth, in this case.

become:

L;, + Lg,

The

i=1,2,...,802

L:, + LZ,

69>

i=1,2,...,177

Lz. + L2,

10

i=1,2,...,177

vaJues

justas

of

wi

and

an example

w2

as

O.05 and

O.95,

the solution

and

method

obtained

using

the

arately, model

overland

i.e., by

and

subsurface

among

is shown

(Kumar et

al,,

components

sep-

previously developed 2002),is also presented in Fig-

operating

our

5, taking the same values of wi and w2 and considering the value of watershed-wide selfpurification coeMcient A as O,OO085. In Figure 5, 35 LMUs ure

upland fieldare allowed a discharged load of 458,980 glmonth/grid, 103 LMUs of paddy fieldare of

JOURNALOF

of

al-

for optimum

model

allocation

nonpoint

sources

of

discharged polis developed to

total loads considering equity The process of pollutant load transfer flows is differthrough the overland and subsurface entiated by taking differentvalues of selfpurification coeMcients. The occurrence ratio of these flews isassigned to each LMU bascd on soil category, which is determined by the data on subsurface geology,

the

in Figure 4. In the optimization, in Figure 4, each of 78 LMUs out of 177 LMUs of upland fieldisallocated an optimum load of 32,207 g/monthlgrid and the remaining 99 upland fieldLMUs are restricted to their lower limitload of 69 glmonth/grid, Similarly, out of 802 paddy fieldLMUs, 205 LMUs get an optimum alloeation of 27,739 glmonthlgrid each and the remaining field LMUs are allocated paddy lower limitof loads as 34 gfmonthfgrid. Out of the 177 LMUs of city, 44 LMUs are aJlo ¢ ated an optimum Ioad of 14,283 g!month/grid each and the rest of city LMUs are allocatedtheir lower limitvalues as 10 glmonthlgrid. The value of objective function in this case is -395,919 g/month. The optimum solutionforoverland and subsurface flow components, forthis case, isalsopresented separately in Figures 6 and 7. The optimum solution obtained without considering

overestimation

4 Conclusion

maximize

problem is solved

each

(56,509,O15

The

results

optimization

of

of

(e.g.,

lutantloads from

above

simplex

taken

LMUs

that the LMUs with higher fiow length values are allocated higher optimum loads in each land use type and LMUs with loads, lower flow lengthget lower values of optimum In Figure 4, however, due to the flow discrimination based on subsurface pregeology,in the model LMUs sented here, the tendency is broken on some LMUs within circles in Figure 4). [[btal persub-watershed is 8,855,529 mitted load in the whole is smaller than that in in Figure 4, which glmonth This is because, in Figure 5 g!month). the newly developedmodel, only 90% of load istransperted as subsurface fiowin sandy LMUs and 59% in Ioamy ones for which the value ofA is higher. It can be said that differentiating the flow msing subsurface

geologydata results in avoiding lowableT-N load.

calculation,

3.3 Optimization The

are

load

a

allocated

remaining

(15)(16)(17)

34>

>

are

3.4 Discussion In Figure 5, it is observed

re-

field2) Paddy field3) Cityi'.It is practically not possible to haye LMU dischargingzero levelof pollutant load, Therefbre,optimization is carried out by defininglower limitvalues of discharged pollutant load in (7).The lower limitvalues are calculated simply using the values of unit loading factors. The values of lower limit,LS,,Lk,, and LL, are taken as O.O136 glm21month fields), O.0276 (paddy fields) and O.O04 gfm21month (upland g!m2/month respectively, Therefore,the constraints in (cities),

(7)in this case

load of 353,327 glmonthlgrid

optimum

and

Upland

`Ll)

order

an

36 LMUs of city glmonthlgrid. The

a model

The

allowable

LMUs.

ArcView GIS is incorporatedto delinand to compute the flow length subfrom each LMU to the outlet of the selected watershed. The model can be used fbr optimally in allocating dischargedpollutani] loads from LMUs a catchment on the gridbasisfor a set of weightage values to the two objectives and for a defined (bl) preference order of Iand use type,based on the need In addition, this of decision-makeror model-users. model can be helpfu1foreMuent trading between or among the different kinds of pollutant sources, as is being practiced in some countries, More studies will be required to establish a more reliable data on par rameters likebasin-wideself-purification coeMcients use

of

eate

sub-watersheds,

and

proportions of flow

forother types

of soil

as

overland

and

subsurface

geology.

Acknowledgements data for the Yasu This study uses the GIS source river basin,which has been provided by Department of Lake Biwa and the Environment, Shiga Prefecwould like tural Government, Japan. The authors

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to

extend

Catchment Systems Systems Association Association (JRCSA) {JRCSA)

their appreciation and gratitude to the re forthis contribution and kind far

latedorganization vor.

References

[1]Arheimer, modelling

landto

B.

the

and

Brandt, M.

(2000):Watershed

lossesfrom amable Swedishcoast in 1985 and 1994, Ecolqg-

of

nonpoint

nitrogen

icalEngineering, 14, pp.389-404. T,R., Potts, A.L., Zhang, H.X., Neeley, K.A. and YU, S.L. (2002): Case study of impact of total maximum daily load allocations on nitrate leaching, Joutveal of LVater Resottrces Planning and Mdnagement, 128(4), pp.262-270. ArcVieu,Spatiat Analyst - Advanced [3]ESR[[ (1996): SPatialAnalysis USing Raster and I,leetor Data, Environmental Systems ResearchInstituteInc., CA, USA. Erisman, J.W.,de Vries, W,, Kros, H., Oenema, O., [4] van der Eerden, L., van Zeljts,H. and Smeulders, S. (2001): An outlook for a national integrated nitrogen policy, Environmental Scienceev Policy, 4,

[2]Culver,T.B., Naperala,

pp.87-95,

[5]Ha,

S.R., Jung, D.I. and Ybon, C.H. (1998): A renmodel for spatial analysis of pollutant runoff loads in agricultural watershed, Wtiter Science and flechnology,38(10), pp.207-214. Point-nonpoint [6]Jarvie,M. and Selomon, B, (1998): eMuent trading in watersheds: A review and critique, Environ7nental 1mpact Assess7nent Review, 18(2),pp.135-157. Kumar, A,, Maeda, S, and Kawachi, T, (2002): [7] Multiobjective optimization of discharged pollutant loads from non-point seurces in watershed, Thansactions of the JswRE, (inPress). Handbook of [8]Novotny, V. and Chesters, G. (1981): Nbnpoint Pollution - SouTz)es and Management, Van Nostrand Reinhold Company, New Ybrk, USA. [9]Skop, E. and Sojrensen,P.B. (1998):GtS-based modelling of solute fluxes at the catchment scale: ovated

a

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of

nitrogen

Denmark,

the

agricultural

contribution

EcotqgicalModelling, 106, pp.291-

310.

Soumiya, [10]

I. (2000): Lahe Biwa- The Environment PVIiterQuatity, Gihodo Publications,p.155 (in Japanese). and

[Discussion open

12IJOURNAL

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te the

loadingin the Vejle Ejord catch-

until

June 30, 2003]

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