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BulletinofGlaciologicalResearch22（2005）19−29◎JapaneseSocietyofSnowandIce

AnalogoussimulationoftheannualrunofFofHeiheRiver（China，Qilianshan）

VIadimirKONOVALOVlandMasayoshiNAKAWO2
1InstituteofGeography，Moscow，Russia．

2ResearchInstituteforHumanity and Nature，Kyoto602rO878Japan．
（Received September29，2003；RevisedmanuscriptreceivedNovemberll，2004）

Abstract
Analogous simulation modelwas developed and used to calculate annualrunoff of the Heihe

River，locatedinwesternChinawithlimitedhydrologicaldataavailable．Theanalogywasdrawnwith

the Naryn Basin having similar hydrographic and climate characteristics．The runoffand climate
CharacteristicsofKeriaandYurungkaxriverbasinsinwesternChinawerealsotakenintoconsidera−tion．Simulated annualrunoffisconsidered asrathersatisfactory．

1．lntroduction
Glaciers are one of the most important water

resources，in particular，in the arid region extending
OVerCentralEurasia．Itisofimportance，therefore，tO

estimatethechangesofannualriverrunofffromgla−
Cierized area，Since the river wateris of significance

2．Statementofa problem
Variousoncomplexitymathematicalmodelsand

COmputer PrOgramS（e．g，Borovikova et alリ1972；
Abbottetal．，1986a，1986b；Bergstrom，1995；Bevenetal．，
1995；Vinogradov，1982；Konovalov，1985；Seibert，

1999）use at present for description and calculation

forlocalpeopletouseforirrlgation，drinking，andtherunoff process of mountain rivers with undistorted
Other daily use．The Heihe River，One Of the rivers
seasonalcourse．One ofthe basicconditionsfordevel−
OriginatingfromglaciersinQinghai，GansuProvinces，Opment and application methods of mathematicalandInnerMongolia，China，StartStOflowfromQilian modelinginhydrologyisavailabilityofthelong−termMountains，runningtowardnorth，anddisappearsina Climaticinformation，and alsodatafordetermination
lake：atyplCalinlandriver．Thelengthisroughly400 parameters of a basin，COefncients of empiricalequa−

kmin total．
The famous Silk Road locates through the basinin the east and west direction．At the same time，anomadic route in the north and south direction also
penetratingthroughthebasin，CrOSSingwiththe Silk

Road．Thebasinisconsidered hencethemostimpor−tant areain thelong history，because manyfights
have taken place between nomads and agrarians in
the basinin some era，and they arein harmonyin
Otherera．Therunoffvariationofthebasinisofgreat
importance forinterpreting the historicalevents，
Sincethepeoplehavebeendependentontheavailabil−
ityofwaterevenin the historicaltime．
Forestimatingthehistoricalvariationoftherivertions and dependences used to simulate components

OfhydrologlCalcycle．Afterestimating，thevolumeof

information available now for Heihe river basin，We
COme tO the conclusion，that any of thelisted above
models can not be used because of the absence oflong−termdataonrunoff，Whicharenecessaryfirstof

allforcalibrationand testingamodel．
InthissituationitisexpedienttofitupforHeihebasinananalogouswatershedwithasimilarcomplex
Of parametersinfluencing on formation and along−term reglme Ofannualrunoff．The method of runoff
Calculation fora basinTanalogueshouldallowitscer−tain even indirect confirmation or testing besides of
Substantialutilizationin Heihe basin．

runoff，however，aVailabledataareverylimited．Asa
firsttrialoftheestimation，therefore，Wehavetriedto
3．Criteriasimilarityofriverbasins

estimatetherunoffchangesinthelastseveraldecades
byintroducingtheanalogoussimulationmethod．

The following criteria were accepted as parame−ters of similarity between Heihe watershed and a
Certain basinTanalogue．
1．Close enough values of area and averageBulletinofGlaciologicalResearch2（フWeightedaltitudeofbothbasins．

ズ（z）＝∬（zo）［1＋豊（z一之o）

2．The same maJOr factors of runoffformation，

having similar relative contributions to theriverfeeding．

3．Similarseasonaldistributionofmonthlyaver−aged air temperature and monthly sums ofprecipitationattheaverageweightedaltitude（3）＋去怒（z一之D）2］・

Functionx（zo）couldbedefinedbymeansofanalyticalexpression approximating dependence of precipita−

tionfromaltitude，Whichbasedonlong−termaVerage
4．Similarseasonaldistributionofrunoff，Which data．In the most common caseitis
Of a watershed．

have to be resulted after realization of theズ（zo）＝αZ呂＋∂zo＋c．

above three conditions．

ThefirststagetodetermineareaofHeiheriverbasin
WaS bounding this watershed on topographic map．

（4）

Then

Theisoline1500ma．s．1wasacceptedasthelowborder
Closing basin area．Geographicalcoordinates−longi−

ズ（之）＝（αZ呂＋わzo＋c）

tude and latitude were further determined for all

2αZo＋わαZ呂＋∂zo＋c

（z之o）

（5）

αZ呂＋∂zo＋c

POintsformingclosedcontourofthewatershed．Thenboundary of the basin was overlaid on the Earth

Itfollowsfrom thisequation，that

digitalelevation model−GTOPO30，prepared by US
GeologicalSurvey（1997）．Contour of this basin was

finally updated by means of GTOP030 DEM model
Wherelongitude，1atitude and elevation above sea
levelare known for each pixelof rasterimage and

2αZo＋∂ゐ2＝（6）

αZ呂＋∂zo＋c

andtheir size corresponds to the map ofl：100000scale．

ゐ3＝

（7）

αZ呂＋わzo＋c■

Valuesofareaandaverageweightedelevationwithin
the boundaryofHeihe watershed wereestimated bymeansofappropriatesoftwaremodulesofGISIDRISIOf precipitation，their averagelayer芳forsome basin

determined that area of Heihe basin at outlet limited

ingexpression−

Inthecaseofratherhomogeneousspatialdistribution

322nd version（Eastmen，2001）．As a result，it was
byisoline of1500m a．s．l．is9900km2，and average
Weightedelevationforthisareaequalsto3671ma．s．l．

WithareaFcouldbeobtainedbymeansofthefollow−（8）

Zmax 貢＝去Jズ（z）雷dz・．■＝川I

4．Determination averagevaluesofclimatefac− Substitutingx（Z）according to Eq．（1）intotheexpres−Sionfor貢Weget：to「S芳＝乎ァ［1＋ゐ2（z−之。）＋ゐ3（z之。）2］雷d乙（9）ZxAverage weighted altitude is one of the basic
geometricalparameters of a mountain river basin，
Wherespatialvariabilityofthe mainclimaticfactors

Zmln

Of runoff formation（precipitation，air temperature
andits humidity，SOlar radiation，etC．）essentially de−pendingonelevationofaregion．

Analysis performed by Denisov（Borovikova et al．，
1972）has shown，that for extrapolation data on pre−CipitationxalongelevationzthemostcommonformAt theintegrating procedurein Eq．（9）we willtake
into consideration that
Zmax 2＝‡Jz雷ね

（10）

Zmin

is mean weighted elevation for the basin area F
bounded byaltitudesZmlnandZm。X，and Eq．（11）−Ofdependencex＝X（z，t）isanonlinearfunction：
ズ（z）＝ズ（zo）［1＋た2（z一之o）＋ゐ3（z一之o）2］，（1）

Wherex（z）andx（zo）areaccordinglysumsofprecipita−tion on the elevations z and zo，k2and k3，empiricalCOefhcients．Following to the method，SuggeSted by
Borovikova etal．（1972），decomposition of functionx（z）at the point zo to the Taylor seriesis used for

determination theparametersk2andk3：

ズ（z）＝ズ（zo）＋＝zo）（z一之o）＋実字（z一之o）2・（2）Bringingx（zo）outofparenthesis，WeObtain：

Zmax 仇2＝去J（z−2）2雷dz・

（11）

Zmin

representsvarianceofaltitudeswithinthisarea．Ulti−mately for determination averagelayer of precipita−
tionforareaFwithinthealtitudesZminandZm。XWegOt
equation：
芳＝ズ（zo）［1＋ゐ2（貞Zo）＋が（2之o）2］＋ズ（zo）ゐ3戎，（12）

where the first term in the right part represents
amount of precipitation at the average weighted ele一
vation2．

ニリ

Konovalov eJαJ．

Tablel．Long−term aVerage Values of air temperature and annualpreclpitation by the data of
meteorologicalstationslocatedwithin93．0104．00Eand36．0−43．00N．

Alt， BegYear BegYear TOc

Lat

Long

HaMi

42．82

93．52

738

1951

1951

9．8

25．4

36

EjinQi

41．95

101．07

941

1960

1960

8．4

25．1

36

Guaizinhu

41．18

103．27959

Dunhuang

40．15

94．68

1139

1938

1951

9．3

23．5

38

Anxi

40．53

95．77

1171

1939

1951

8．7

23．3

47

Minqin38．63

103．08

1367

1953

1953

8．0

21．9

JiuQuan

39．77

98．52

1477

1934

1934

7．2

20．5

88

ZhangYe

38．93

100，58

1483

1937

1937

7．0

20．3

128

Abagaql

39．22

101．68

1510

97．03

1526

MstTitle

Yumenzhen

40．27

ma．s．1（T）

TOc
P（P） MeanI−XII MeanVI−ⅤIII Ⅰ−ⅩⅠⅠ，mm

1960

38

112

1960
1953

6．9

20．6

Wuwei

37．92

102．671532

1960

Yema］1e

41．58

96．88

1963

1958

4．1

18．2

ⅩiNing36．62

101．77

2261

1936

6．0

16．4

Lengh

38．83

93．38

2733

1957

2．7

15．9

Golmud

36．42

94．90

2808

1956

4．6

16．6

Gonghe36．27

100．62

2835

1953

3．6

14．3

Delingha

37．37

97．37

2982

1955

3．8

15．6

Dulansi

37．02

98．77

2985

1957

4．3

15．3

1953

Wushaoling

37．20

102．87

3045

1951

1951

UulanCaka

36．78

99．08

3088

1956

1956

DaQaidam

37．85

95．37

3173

391

1．7

13．1

209

1957

1．4

14．0

2．9

13．7

0．1

9．8

380

9．1

288

36．30

98．10

3191

1940

Gangca37．33

100．13

3301

1957

1960

98．42

3361

1957

1957

38．82

−0．2

322

10．1

Dulan

QilianTuole

162

−3．0

Note：T−isairtemperature，Prispreclpitation

Itfo1lowsfromEq．（12）thatifk3＝0，meanValueof

linear function z from z equals to its value at the

averageweightedelevationofabasin，i．e．貢＝X（2）．This

mulaeforthesedependenceshavethefollowingform：
P 点−＝0．125z＝75．15，

important conclusion wi11be repeatedly usedin theforannualsumofpreclpitationand

Allavailable data from different openinter−national sources of meteorological information

T7クエ川〜＝29．15−0．0053z，

further research．

（13）

（14）

for average summer air temperature．The fo1lowing（Guterman（ed．），1968；Kaiseretal，1997；Lebedevand
dimensionswereusedinEqs．（13）and（14）：elevationz，Kopanev（eds），1975；WMO／OMM，1996）were col− in m a．s．1．，preCipitationin mm，airtemperatureinOc．

lectedforobtaininglocaldependencesofprecipitation
andair temperature from elevationin Heihe basin．
List of meteorologlCalstations，Within the mountainarea Nanshan including Qilianshan ridge and Heiheriver basinis glVenin Tablel．Location of these

Stationscould beseenon Fig．1．

This set of meteorological data and altitude of
Stationsabovesealevelallowedustogetrepresenta−
tive dependences both annual sums of precipitation

PlX．i＝f（Z）andaveragesummerairtemperatureTL，i iiE＝f（z）from elevationz above sealevel．Empiricalfor

Theindex ofdetermination orsquared coefhcientof

COrrelation wasO．85forPiXii＝f（z），and O．93for T乙，iVtii＝／（z）．

Since dependence Pl，li＝f（2z）for the territory
Nanshan within 93．0−104．00E and 36．0−43．00N foundOutlinear（i．e．k3＝0），itisnecessary todetermineonly
parameter k2in Eq．（1）using the Denisov s method（Borovikovaetal，1972）．EmpiricalformulaeofEq．（13）andEq．（15）wereusedforthispurpose．Thefollowing
formofEq．（15）wasobtainedfromcommonEq．（6）for
ゐ2at（‡＝0：Bu11etinofGlaciologicalResearch

22

争ざ

鮪

タ7

対

き争

†郎

†￠†

†○〜

Iの

Fig．1．Sites of meteorologicalobservation（marked by star）within Nanshan region．Near to the mark ofmeteorologicalstationisits elevationin m a．s．1．

ゐ2＝わ／（わzo＋c）．

（15）

Here，followingtoEq．（13），parameterbfortheconsid−
ered region equals to O．125，and c＝−75．15，but zo

equals to elevation of the meteorologlCalstation，
which data on precipitation will be extrapolated totheaverageweightedelevationofHeihebasin．Wide−Spreadlinearextrapolatingformulais usedforcalcu−

1atinglong−termrangeOfTl，VlllValuesattheaverage

WeightedelevationofHeiheriverbasin：
T（2，f）＝T（zo，f）−γ（2一之o），

latedconclusionsforunderstandingconditionsofrun−
0ffformationinHeiheriverbasin，andforsearchofa
WaterShedwithasimilarhydrologlCalregime．

㊥IntraTannualdistributionofmonthlyprecipi−
tation has a welldefined maximumin theSummerperiod（thelargestmonthlysumisin

July）andaminimuminthewinter（thesmall，
est monthly sumisin December−January）．

Thisfeatureistypicalfora11consideredmete−
OrOloglCalstations．

㊥ Thelargest values of average monthly air

temperature also take placeinsummertime（16）

Whereγ1SVerticallapserateofairtemperature，andT（zo，t）is known air temperature at the elevation zo
Where certain meteorologlCalstationlocates．It foト
lows from Eq．（14），that the parameterγfor calcu−

1ations of average summer air temperature at the
average weighted elevation of Heihe basin equals to

5．30ckml．Thustheconsideredmethodofcalculation
TuiVLiLandPlXLiattheaverage weightedelevation蔓and Eqs．（1），（13），（14）and（16）allowed us to obtain

annualsumsofpreclpitationandsummerairtemperaL

ture as mean values for the whole area of Heihe river
basin．

Ranges of observation on precipitation and air（June−August）withamaximuminJuly．Reg−

ular decreasing of air temperatureis ob−
served in all months of a year depending on

theelevationofthereglOn．OnFig．2itiswell

Visible that according to fallingairtempera−
tureatmeteorologicalstations，theheightof
a set of bars gradually decreases within themarkedlimits of each month on a time or
abscissa axis．Hereitis necessary to notice
thatthedescribedspatialandtemporaldistri−butionofairtemperatureisthecommonpro−
Perty for many river basins of the Central

Asia（Amudarya，Syrdarya，Tarim，Indus，Ganges，Brahmaputra，HuangHeandothers）．

temperaturefor1960−19930n anetWOrk ofthemete− Theanalysisdescribedaboveallowedformulatingthe
orologicalstationslocatedwithin93．0−104．00Eand36．O following characteristic attributes in order to select−43．00N were used for revealing the features of sea−basin−analogueforHeiheriverwatershed．

SOnalcourse of these elements．Good representation
OnSpatialandtemporalvariabilityofclimatecharac−
teristics for the considered territory can be received

from Fig．2and3．Basingon thesegraphs，Weformu−

1．Theareaofabasinlocatedin theCentralAsia
isaround oflOOOOkm2．
2．Theaverage weighted elevation ofabasinis
within3500−3700m a．s．1．

Konovalov efαJ．

）l

J

M

IV

V

VI

23

VIJ

V l

lX

X

XI

X

monthsFig．2．Intra−annualcourse of relative monthly preclpitation within Nanshan reglOn．Each verticalbar on the graphrelatedtothedataatseparatemeteorologicalstation．

笠
O
L
D
O
P
U

■
︑
︶

○

・5

・10

−15
−20
＿25
month＄
Fig．3．Intra−annualcourse of monthly airtemperature within Nanshan reglOn．Eachverticalbaron thegraph related tothedataatseparate meteorologlCalstation．

3．Thereisclearcharacteristics ofsummer maxT
imum and winterminimumofprecipitation．

4．Long−term year−rOund runoffdata are avail−ablemeasuredathydro10gicalgorgingsite．

5．LongTterm year−rOund data of precipitation，

temperatures and humidity of air are avail−able measured at meteorologicalstations，
WhosenumberisenoughforobtainingreglOn−

ally representative dependences of thelisted
Climatic characteristics from elevation above
Sealeveland／orotherspatialcoordinates．
6．Thereisprevalenceofsnoworsnow−raintype
Of runoffformation．

BulletinofGlaciologlCalResearch

24

Table2．SometopographicalcharacteristicsofYurungkaxandKeriariverbasins．
Mean weighted

Basin

Area，km2

Mean weighted
elevationof

Yurungkax

17046

4416

3581

5582

Keria

13249

4417

738

5929

glaciers，ma．S．1

CatChment，ma．S．1

Note：1．Function ofareadistributionalongaltitudeforYurungkax riverbasinis
γ＝0．0196二r4−0．0131∬3＋0．1081ズ2＋0．323ズ＋0．436．
2．FunctionofareadistributionalongaltitudeforKeriariverbasinis
ッ＝−0．0439こr4−0．0628二r3＋0．1957二r2＋0．43批＋0．383．
Hereyisintegralfunctionofxdistribution Std−isstandarddeviation．

tions of runoffandits climatic factorsin the other

5．Selection basin−analogue

WaterShedofCentralAsia−Narynriverbasin．

There are some grounds to assume that condi−
tions of runoff formation for right tributaries ofTarim Riverandoverthe territory bounded by coor−

6．NarYn river basin as anaIoguefor calculation
Of Heihe river annualrunoff

dinates93．0104．00E and36．0−43．00N，may have com−

mon features because they located close enough toeachother．Thisassumptionprovestobetruethatonamapofdistributiontheannualsumofprecipitation

CentralTien Shan mountain areaislocated up−
StreamOfNarynriverbasin，anditrelatestotherivers

Ofsnow−glacialtypeofrunoffformation（Shul ts，1965）．

The considered regionincludes BoIshoiNaryn andMalyiNaryn watersheds．Number of parameters forfor China territory（http：／／www．1ib．utexas．edu／
estimating topographical similarity of Naryn andmaps／middleeaStandaSia／chinapreCip．jpg）andfor the Asian continent（GPCC，0ffenbach，Germany Heihe basinsis givenin Table3．The sources of hy−
Wetter Dienst）both areas areinside the same zone
intervalofprecipitationscale．
From the number of right tributaries of Tarim，
themostvarioussetofthehydrometeorologlCalinfor−
mation is available for Keria and Yurungkax river
basins．Geometricalparameters of these basins are
glVenin Table2．AllareaandaltitudinalcharacterisT
ticsin Table2were obtained by reconnaissance forthe contours of watersheds and glaciers on topo−

graphicalmaps，definitions of geographicalcoordi−

nates of these contours and utilization of the proper

drographicandglaciologlCaldataforNarynriverba−
Sin are glVenin USSR，Main Administration on

Hydrometeorology（1967；1974）and Vinogradov andKotlyakov（1973r1977）．Figures4a，4b and5present
averagelong−termintra−annualdistributionsformon−
thlysumsofprecipitation，aVeragemOnthlytempera−
tures of air and Naryn river runoff，reSpeCtively．

Quantitative similarity estimations of topographicalparameters for Heihe and otherbasinsare presented
in Table4．

ConsideringdatainTable4，WeSeethatclosenesssoftwaremodulesofGISIDRISI32，Ⅴ．2forcalculation of topographical parameters between Heihe andOftherequiredparameters．

AnalysIS Of theintra−annualdistributions of cli−

maticfactorsofrunoffinYurungkaxandKeriabasins
Showedthatinbothbasinsmaximumofmonthlysum
Of precipitationisinJune，but notinJuly asin

Naryn basinsis very good and thisis a ground to
COnCludethatbothrivers haveidenticaltypeoffeed−
ing since the size of the basins and their average
Weightedelevationsessentiallyinfluencetotherunoff

regime as Shul ts（1965）has shown．One more confir−Nanshan area．Nevertheless，itis possible to assume， mation of analogousness between Naryn（at gp
Naryn）andHeihebasinsonintra−annualdistributionthat distribution of runoff in Nanshan area and

YurungkaxandKeriabasinscanhavesimilarfeatures．

of the runoff and its climatic factors follows fromtirelyusedfordecisionofthegivenproblem，ifwewi11
takeintoaccountallcriteriaaccepted forsearchanaT

MaximumofmonthlysumofpreclpitationisobT
SerVedinJuly for Naryn basin，and their seasonal

Ofgeometricalcharacteristicsandinsufficientnumberof meteorological stations for getting dependences

ral course of average monthly air temperature could
be noted also both at the average weighted altitude，
andin allrange of elevations for Naryn and Heihe

However neither Yurungkax，nOr Keria can be en−logue−WaterShed．Thereisrathernoticeabledifference

from elevation z above sealevelas for the annual

SumSOfprecipitationPiXii＝f（z），andaveragesummer

COmparisonofFigs．2，3，4aand4b．

minimuminDecember−February．Similarityoftempo−

basins．Thus，We COnCluded the analogousness of to−airtemperature T‖2，iii＝f（z）．

pographical parameters for Naryn and Heihe riverafter performing analysIS Ofintra−annualdistribu−

basic climatic factors．This conclusionis a necessary

Essentiallymoreacceptableresultswerereceived

basins，intra−annualdistributionoftheirrunoffandits

25

Konovalov efαJ．

Table3．SomecharacteristicsofNarynand Heiheriverbasins．
Area，

Basin

Glaciers
area，km2

Mean weighted
elevation of

Fb。S，km2

elevation，Naryn（gpNaryn）

10500

3570

716

4208

Heihe（above1500ma．s．l．）

9900

3671

64

4556

ma．s．1glaciers，ma．S．1

Note：1．Function ofareadistribution alongaltitudeforNaryn riverbasinis
γ＝一0．0064ズ4−0．0283ズ3＋0．0395ズ2＋0．359ズ＋0．477．
2．Functionofareadistribution alongaltitudeforHeiheriverbasinis
γ＝rO．0058ズ40．0295ズ3＋0．0331二r2＋0．365二ー＋0・485・

Hereyisintegralfunctionofxdistribution，，Std−isstandarddeviation．

Table4．Relativedifferences（in％）between parametersofHeiheandotherbasins．
Meanmoduleofrelativedifference
Meanweighted elevation betweencoefficientsinF（z）equations

Area

Basin

（seeTables23）

Naryn

6．1

2．8

7．4

Yurungkax

72．2

20．3

108．4

Keria

33，8

methodical substantiation for elaborating method to
CalculatelongTtermSeriesofNarynriverannualrun−

S00
450

0ff，Whichshouldprovideanadequatequalityofrun−

400

∈
∈
ご i50
○
葛 0
亘 0
− 駒
0
川
0
﹂ 8
d
2
ゝ
て 2
■
○
ゝ

◆◆ ●ヽ′

／

◆
◆
√

◆ 一′
◆

◆ ■■′ ◆◆ノitin mind．

わ

7．CalcuIationannualrunoffofNaryn riverbasin
On equation ofwaterba（ance
List of meteorological stations for Naryn basin

罵
﹂
○
∈
∈
コ
叫
u
冨
王

5

（b）

＼

2 0

■
−

and adjoining territoryincludes 51points（USSR，
Main Administration on Hydrometeorology，1966，1968）．The empiricaldependences（Fig．5）and equa−tions below TL．i1，，l，＝f（z）andPl＿，lil＝f（z）were received

bythesematerials．

ヽむ

■
〇

▲

1 〇

一
5

＼．

1000

2000

（17）

（18）

tionoftheaverageairtemperatureinsummerseason：

▲

3000

4000

劇titudo，m a．S．l．
Fig．4．（a）Dependence of yearly precipitation and（b）

mean summer air temperature from elevation．By
data of meteorologicalstationslocated within

Naryn river basin and adjacent territory（USSR，
Main Administration on Hydrometeorology，1967，
1974；1966，1968），

T〜ノg己′7g〜＝26．37−0．0061z，
Pト班＝0．196z−158．5．

Herezisgivenin m a．s．l．，TvL7，tii，inOc，PiXibin mm．
TakingintoaccounttheseformulaandEqs．（1），（6）and（7），We Obtain empiricalEqs．（19）and（20）for calcula▲
U0

has different relative contribution in feeding Naryn

eredasnegliblebutnotintheNarynandwewillbear

2．5−

0ffsimulationin the Heihe river basin．Glacier runoff

andHeiherivers．IntheHeihebasinitcouldbeconsid−

A州tudo，kmabov080alov0l
∽
万
一
冒
p
U
〇
．
〇
﹂
コ
一
巴
O
d
∈
○

260．6

−20．3

T〃トと，∫〜∫（2，f）＝Tv．v．1．（zo，f）−0．0061（2之o）， （19）and annual sum of precipitation on the average
Weighted elevationofNaryn basin：P．∫∫〜（2，f）＝君∫∫〜（zo，J）［1＋0．503（2一之o）］． （20）

Empiricalparameter k2＝0．503in Eq．（29）was deterT

mined，prOVided thatelevations2andzoexpressedin

km，andbasicpointofobservationP巨頭（zO，t）ismeteLBulletin ofGlaciologlCalResearch

2∂

．
u
O
篭
−
亘 急
菖 亘
﹂ u
d 0
p 2
u 0
巾 d
望
P
噂

For determining temporalvariability of co−efncientRC，letuspresentitasastochasticfunction

5
2

Of some climatic factors of runoff：

○

0
5
1

1

︻
︺

1

■
■

2 0

0

2

O
J
n
l
巴
O
d
∈
○
毒

5

盲
弓
0

1 2 3 4 5 ￠ 丁 8 9 10 1112
Month8■0

Runo†lhoight
Procip触tionm8tK011yu−1−Ajrtemperaturern＄tTien・Shanrm l‥こ＝＝二＝二：こ：猫用

Fig．5．Intra−annualdistribution of monthly values ofrunoffanditsclimaticfactorsin Naryn riverbasin（averaged for1952988）by datagorgingsiteNaryn，meteorologlCal stations Tienshan and Koilyu（Bodo，2000；USSR，Main Administration on Hydro−
meteorology，1967，1974；1966，1968）．

尺C＝′（P，T，ガ）．

（24）

HereP T andHarevaluesofpreclpitation，tempera−ture and humidity of air by data of meteorologlCal

observations for characteristicintervals of time．Un−

doubtedlythelistofargumentsintherightpartofEq．

（24）canbeexpanded．Asonemaysee，Eq．（24）presents
generalform of mathematicalmodel，described tem−poralvariability coefncientofan annualrunoff．Con−

crete form of this model is multifactor equation ofregression．Allarguments of Eq．（24）should be ex−

trapolatedtotheaverageweightedelevationofNarynbasin taking into account the further application ofthisequationin Heihe basin．
Duringtheoptimizationofthestructureofmodel

OfEq．（24），itwasrevealedthatthepairdependenceRC＝f（P）is nonlinear．Finally，the following practicalformulawasreceivedforcalculationoflong−termVar−

iability of annualrunoff coefncientin Naryn river
basin：

月C＝0．891げ」2．4439＋2．148β，（25）

OrOloglCalstationKoilyuforspatialandtemporalex−

Wheref2isarelationofannualsumofprecipitationat

dataalmostdonotdeviatefrom the received relation−

age summer temperatureini−th year to the average

trapolationofannualsumofprecipitation．Thismete− the2，aVerageWeightedelevationofNarynini−thyear
OrOlogicalstationlocates within Naryn basin andits
totheiraveragelong−termnOrm，OisrelationofaverT
Ship PlXli＝f（z）．After substituting the average
Weighted elevation of Naryn basin（3．57km）and thealtitude of meteorologicalstations Koilyu（2．80km）
andTien Shan（3．614km）intoEq．（19）and Eq．（29），We

gotfinalformulastocalculateaveragevalueofmete−

OrOloglCalvariables for Naryn basin atz＝2．Namely，

airtemperatureofsummer：

Tl，ト乙′∠∫よ（乏，f）＝T7ノト再烏（zo，f）＋0．27，（21）

and annualsum ofpreclpitation：P′エ汀（2，J）＝君∫∫ （zo，f）1．39．

（22）

long−termnOrm Tu，Ui，i（2）attheaverageweightedele−
Vation of Naryn．The coe踊cient of determination ofEq．（25）equalstoO．72．Before normalization，Valuesof

airtemperature at the average weightedelevationof
Naryn were transformed from Celsius scale to the
Kelvin scalein order to avoid operations with num−bers of different sign or equaled to zero．Numericalpresentation modelof Eq．（24）as function ofnormal−
ized argumentsis necessary，in relation to forthcom−
inguseofEq．（25）inHeihebasinwithotherrangesof

precipitation and air temperatures at the average
Weightedelevation．

Thus，based on the measured annualvalues of
WegotonemoreempiricalEq．（26）afterincluding
precipitationandrunoff，Wedetermine thecoe踊cient Water VaPOr PreSSure u tO thestructureofthe model
Of the annualrunofffor Naryn（gp Naryn）basin，aC−
OfEq．（24）．Inthiscasethecoefficientofdetermination
COrdingtothewe11−knownequationofwaterbalance： was O．77．
斤C＝月／［P−（E±lγ）］，

月C＝0．988922．619日十2．408β0．33払（23）

WhereRCisacoefBcientofannualrunoff，Risrunoff，（26）

Thus，eXpanSion of the structure ofmodelofEq．（24）allowsmorepreciselydescribinglong−termVariability

OfcoefncientRC．However，Eq．（26）doesnotintendfor
applicationin Heihe river basin，because of the ab−
ValuesRC，CalculatedbysimplifiedversionofEq． SenCeOflong−term dataon watervaporpressure．

Eis evapotranspiration，Wis dynamic storage ofwaterin a basin．

（23），i．e．RC＝R／／′君 are quite realistic for the givenbasin and meet well to characteristic values of thisindexfortheriversofCentralAsia，Which havebeen
revealedbyShul

ts（1965）．ItisaroundO．6atthemean

Weighted altitude3．5km a．s．1．

Let us denote measured annual layer of NarynriverrunoffasRlandcalculatedonebyEq．（25）asR2．

Series of Rland R2are related to the19521985time
intervaland thesedatawere used togetdistribution
Of statisticalprobabilities forbothvariables．Further

Konovalov efαJ．

wecalculatedrelativedeviationsD（in％）ofsimulated

ValuesR2from the measured ones．
Theequation

27

basic meteorologicalstation，i．eリPト油（zo，t）．

As wellasin Naryn river basin，the reglOnal

dependencesof Eq．（13）forPl血＝f（z）and Eq．（14）for

β＝100（月1一月2）／月1．

T乙′l一〃，l＝f（z），and also Eqs．（15）and（16）were used for

WaSaPpliedforthesecalculations．AnalysisofDmod− definition empiricalcoe踊cientsin Eqs．（27）and（28）．
ules showed that their averaged absolute value（i．e．，
Values of TvL ui，L（えt）andP巨頭（2，t）were transformed
modD）is5．5％foryearswhoseprobabilityofrunoff
further，in the same way asit was made for Naryn．
deviates fromlong−term aVerage Valueno more thanFinally，long−term Seriescoefhcientsofannualrunoff
25％．
inHeihebasinRC2WaSCalculatedbyEq．（25）．Substan−

ValueofDforlowandhighwateryearsequalsto

18．1％．The abnormalon waterflow yearsarerelated

tothecases，Whenintegralfunctionofdistributionof

runoffisinthelimitsfromP（X±0．674（7Ⅹ）tillP（X±2
CTX）．HereXis mean valueof the range，CTrisstandard
deviation of the variablex．

Annualrunoff of Naryn river，Calculated bytiatedusingthisequationforHeiheriverbasinisthe
importantresultobtainedbymeansofprovensimilar−
ityofthewatershedstopographyandclimatefactors
for runoff formation between Naryn and Heihe river
basins．

Layersofannualrunoffduringof1957−1993were
computed after multiplication of the annual sum of
preclpitation at the average weighted elevation ofmeans of empiricalEq．（25）and equation of waterbalance，Should be considered as satisfactory，taking Heihe watershed on the coefhcient of runoff．Long−

into account not so highcoefncientdetermination of

the Eq．（25）and essentialenough errors of measured
Waterdischargesand precipitationin high−mOuntain−
OuSbasins．Itisnecessarytoaddsomenewindepend−
entvariablesinmodelofEq．（24）ortodescribespatial

Variabilityofclimaticfactorsofrunoffformationby
Other methods and make better the convergence be−term serie ofHeiheriverannualrunoff，COmputed on
the basis of equation of water balance，is the main
resultofthe presentresearch．
Certain indirect methods were used to estimate

quality of calculatedlong−term Serie，because of ab−

sence of sufficient sample of direct measurements ofrunoff．Particularly Fi女．6illustrates temporalfluctu−
tweentimeseriesRl（t）andR2（t），．Oncemoreopportu− ations of an annualrunoffof Yurungkax and Heihe
nity toimprove results of・Simulation Naryn river
rivers during1957−1990．Itis established earlier，that
runoffis the estimation of glaciers runoffin Eq．（23）
COnditions of runoffformationin these two river ba−
butin this case we refused to doitin order to elabo−
Sinshavesomesimilarproperties．Analysisoftempo−

rateslightlysimplifiedsolutionforHeihebasinwhereralchangesoftheannualrunoffofbothriversallows
concluding on synchronism of low and high water
yearsinmostcasesforthecomparedwatersheds．This
COnClusion confirms the acceptable quality of simu−

relativeglaciersareaisonlyO．7％．

8．Modeling annualrunoff of Heihe river bymeansof basin−analogue
Selection of the meteorologicalstation，Whosedata on precipitation and／Or temPerature Of air will
beextrapolatedontheaverageweightedelevation ofa basin and substitutedin Eq．（25）is undoubtedly

crucial stage of application of the method of waterbalance and the empiricalEq．（25）in Heihe basin．

High−mOuntainous meteorologlCalstations having
longest ranges of climatic observations within
Nanshan territory were preliminary selected for
decisionofthisproblem．
Dataonprecipitationandairtemperatureatthese
Stations were extrapolated to the average weighted
elevationofHeiheriverbasinand norm andstandard

deviation values were received for each time series．

Extrapolations were performed by means of the fol−lowingequations：
T．トⅧ摘（2，′）＝T】…〜′よ（zo，J）＋0．27，（27）

for average summer air temperature when data of

Qilianmeteorologicalpoint，SerVedasTl，i iii（zo，t）and君∫∫〜（乏，f）＝P巨頭（zo，f）1．39，

forannualsumofprecIPitationwhenGongheusedas（28）

1ated annualrunoffof Heihe river．

Onemorewaytotestresultsofcalculatedannual
runofffor Heihe basinisindependentdetermination
Ofannualevapotranspirationforitsareaandsolving

equation of water balance．EmpiricalEq．（29），Sug−
gestedbyRomanenko（1961），WaSappliedforcalculat−

ingpotentialevaporationE．

E＝0．0018（25＋T）2（100−仇）．

（29）

Here TisairtemperatureinOc，助isrelativehumid−
ity ofairin％．Analysis and controIvariousmethods
OfcalculationEhaveshown（ⅩuandSingh，1998）that
results obtained by Romanenko s formula are rather
Close to the data of evaporimeter．Itis obvious，thatthe values of air temperature and relative humidity
Should bedetermined at theaverageweighted eleva−
tion for Heihe basinin order to get meanlayer of
evaporationforthiswatershed．

EmpiricalEq．（30）was used forcalculation ofair

temperatureTyaveragedforyearattheelevation3671
m a．s．1∴

1．＝9．30．9×106z2＋0．0004z，Whereziselevation ofreglOnin ma．s．1．

（30）Bulletin ofGlaciologicalResearch

2g

l

420

∈
∈

鼻

白

古 320

■
．1：
＝

220

120

望＼

「、

∧

1

0

∈
∈
．
×
巾
一
ひ
u
コ
L
⊃
ト

1 2 0

ト． か
In＋＋lnOI O〉 ▼■

▼■

▼
岩
−

父
冨
−

盟
岩
−

ト
￠
￠
︻

の
▼−
tO ト ト■￠￠01 仇 ▼●

▼■

▼■

M V〉
ト■

t■

ト
ト
○
▼

助
卜
仇
︻

−
∞
の
一

M
O
仇
−

的
∞
￠
−

ト
○
￠
−

空
茶
−

￣ yurungkax■■−−■ −Hoiho
Fig．6．Temporalcourseofmeasuredandcomputedyearlylayerofrunoff．YurungkaxandHeiherivers．

midity of air Hm（l，il）WaS Studiedin order to deter−

Spatialvariabilityofaverageannualrelativehu，

doubtedlyevenlessiftoaddrunofffrommeltinglCe
andfirn on glaciers areain Heihe basin totheinput

tory of China and bounded by mountain ranges：

Waterbalanceisan additionalconfirmationofrepre−

processedfordeterminingparametersofmultiplelin−

9．Conclusion

minethismeteorologicalelementontheelevation2＝

partofwaterbalance．Thus，almostidealconvergence3671m．ThereglOnunderresearchincludesplainterri− between input and output parts of the equation ofNanshan，Kunlun，Tien Shan，PamirandHinduKush．
Sentatively simulatedlong−termSeriesofannualrun−
Dataofobservation（Titov，1976；Pertziger，1996；Kaiser
0ffin Heihe river basin．
etal，1997）basically for25to30yearsintervalwere
earregressionofEq．（31）：l．Method to determine components of waterbalance equationin the Heihe river basin was elabo，Hereスand甲arelongitudeandlatitudeindegrees，and ratedandrealizedforsimulatingatemporalrangeof
Ziselevationinma．s．l．ComplexcoefBcientofcorrela− annualrunoffinthiswatershed．Thefollowingstages
tionforEq．（31）equalsO．73，andaveragestandarderror Werefulfi11edin ordertogetacceptableresults．
伽（ト∫∫り＝47．7＋0．175Å0．754￠0．0038z．（31）Ofcalculation was7．1％．AftersubstitutioninEq．（31）mean weighted elevation and geographicalcoordi−

natesofHeihe basin，it wasfound thataveragelong−term relative humidityequalsto52％．
Values7t，andHm（iXii），reCeived by Eqs．（30）and（31），Were uSedin Eq．（29）for estimating potential
annuallayer of evaporation Ein Heihe basin．Ulti−matelyEwasdeterminedas572mm．Thesearchedfor
evapotranspiration ET presents production of the
COmPuted value E on the coefncient describing soil
moistureKsm thatis
gT＝片肌丘．

（32）

WeacceptedKsm＝0．4asapproximateestimation，

based on measured evaporation in Yurungkax river

basin（UjihashiandKodera，2000）．
As a result of application of the Romanenko s
method and calculations by Eqs．（30）and（32），itwas
revealed that the averagelong−term Value of evapo−transplrationinHeihebasinwasupto229mm．Hence，
SOlving equation of waterbalance，We reCeived，that
the difference betweeninput（precipitation）and out−put（runoff＋evapotranspiration）parts of this equa−tionequals to6％only．Thisdistinction becomesun−

・ Revealing characteristic features ofintraTannualdistribution of precipitation and airtemperature forHeihe riverbasin by dataof
meteorologlCalstationslocatedwithinof93．0−104．00Eand36．0−43．00N．

・ Determination the following morphometry

parameters of the Heihe river watershed：area of the basin，its average weighted alti−

tude，function of the basin area distribution
in relation with elevation above sealevel，
glaciers area andits average weighted alti−

tude．

・ De点nitionofthecriteriaforriverbasinssimi−

1arity on conditions ofrunoffformation anditsintra−annualdistribution．
・ Analysis of mean weighted elevation of a

WaterShed as characteristiclevelfor deter−mining values of preclpitation，air tempera−ture or another meteorologlCalvariable，Which equaled to their average meaning for
the whole glVen area Of a river basin．Thus
Calculating climate factors at the mean wei−
ghted elevation ofa watershed allowsappli−

cation of water balance method for simulat−

KonovalovβJαJ．

2タStreams of the former Soviet Union［FSU］．Toronto，Canada．http：／／www．dss．ucar．edu
Borovikova，L．N．，Denisov，Yu．M．，Shentsis，Ⅰ．D．and T
・ Revealing basin−analogy for modelinglong−
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term range of annualrunoffof Heihe river．
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Naryn river basin was adopted as basin−
Eastmen，R．］．（2001）：IDRISI32Release2．Guide to GIS andanalogy forHeihe watershed．
Image Processing．Clark Labs．Clark University．Idrisi
・ Preparation digitalarchive oflong−term Cli−
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tistical Characteristics of Meteorological Elements in
43．00N，Yurungkax and Keria river basins
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HydrometeoizdatPublish．House，317p．（in Russian）．
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Zhang Qingyun（1997）：Two Long−TermInstrumentalarchiveincludesalsorunoffdataforthelisted
Climatic Data Bases of the People s Republic of China．
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tainedforcalculationsannualsumofprecipi−
mationAnalysisCenter，OakRidgeNationalLaboratory，
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Konovalov，Ⅴ．G．（1985）：Meltingandglacialrunoffprocesses
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HydrometeoizdatPublish．House，236p．（in Russian）．
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House，448p．（inRussian）．
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3．Long−termrangeOfHeiheriverannualrunoff
Sive Summaries of Uppsala Dissertations from the Fac−
for1957r1993wassimulatedastheresultsofapplylng
ulty ofScienceand Technology436，52p．
Water balance method and equation for calculating
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