GEOPHYSICAL RESEARCH LETTERS, VOL. 22, NO. 24, PAGES 3529-3532, DECEMBER 15, 1995
Anthropogenicimpacton globalgeodynamics
due to reservoir
water impoundment
BenjaminFongChao
Geodynamics
Branch,NASA GoddardSpaceFlightCenter,Greenbelt,Maryland
Abstract. Water impoundedin artificial reservoirssince of the gravitationalpotential field. These are the specific
N1950is by far thelargestanthropogenic
hydrologicalchange geodynamicquantitieswe will compute.
in terms of the mass involved. This mass redistribution
Chao [1988] has computedthe polar motion excitation
contributesto geodynamicchangesin the Earth'srotationand producedby a hostof major hydrologicalchangesincluding
gravitational
field thathavebeencloselymonitoredby modern thosedueto majorartificialreservoirsin theworldcompleted
spacegeodetictechniques.
We computetheeffectof 88 major before 1986. Buildinguponthe latter,we will in thispaper
reservoirson length-of-day,polar motion, and low-degree computeand discussnot only the polar motionexcitationbut
gravitational
coefficients.On an individualbasismuchsmaller alsoLOD andlow-degreegravitationalchangesdueto a more
than geophysical signals in scale and magnitude, these completeandup-to-datelist of major reservoirs.
anthropogenic
effectsproveto be non-negligible
cumulatively,
especiallywhenconsidering
the factthatourresultsrepresent
Data and Computation
underestimates
of thereality. In particular,reservoirwaterhas
contributed
a significant
fractionin the total observedpolardrift
We havecompileda tally of 88 majorreservoirsthatexceed
overthelast40 years.
10km3in capacity
fromfourdifferent
sources.
Twoofthem,
Introduction
atmosphericmoistureor equivalentto 10 times the Earth's
Van der Leeden[1975] and U.S. Departmentof the Interior
[1983], led to 53 major reservoirs previously listed and
employedby Chao [1988]. Two additionalsources,U.S.
Department of the Interior [1988] andInternational Water
Power & Dam ConstructionHandbook [1993], provide
supplementary
aswell asmoreup-to-datetally. Figure 1 shows
theirgeographical
distributionandrelativesizesin logarithmic
scale. The correspondingcumulativewater impoundmentis
shownin Figure2. The growthof theamountof waterovertime
is virtuallylinearsince1950,showingno signof slowingdown.
The computations
conductedbelow in thispaperpertainto
these major reservoirs. The water mass redistribution is
modeledas an instantaneous
additionof a pointmassequalto
the full capacityat the reservoir location in the year of its
completion,minusan accompanyingeustaticdrop in the sea
biological
water,
andgreatly
exceed
the1,900km3compiled
by
level to conservethe total water mass (see the inside scale of
Humanactivitieshavegreatlyalteredtheliving environment
throughout
history.One of the mostsignificantalterationsis
watermanagement
thathasbeenadministered
on land.Among
various types of water managementprojects,the artificial
reservoirs
areby far thelargestin termsof the amountof water
involved[e.g., Chao, 1991].
Ever sincethe early 1950s, the world has seenintensive
constructionof artificial reservoirs.In a study of the
anthropogenic
impacton sealevel, Chao [1991] estimatedthat,
growingessentially
linearly,theamountof waterimpounded
in
thesereservoirsby the early 1990shavereachedas muchas
10,000
km3,or 1016kg.Thisisasmuch
waterasthere
istotal
Sahagianet al. [1994] whichhasbeenconsidered
asa gross Figure 2). The formulae for computingchangesof the
quantitiesdue to the additionof a pointmass rn at
underestimate
[Chao, 1994; Rodenburg,1994]. Ultimately geodynamic
removedfrom the ocean,it hasloweredthe sealevel by about location(latitude0, longitude)•) areof thegeneralform:
3 crn,equivalent
to an averagerateof sealevel dropof 0.7 mm
per yearoverthepast40 years.
AQ = q(0,)•) m / (massof Earth)+ [oceancorrection]. (1)
The water mass redistribution due to the artificial reservoirs
alsohasimpacton globalgeodynamics
in two distincteffects: The functionq(O,•,)is the geographical
weightingfunction
It changesthe momentof inertia,andhencethe rotationof the dependingon theparameterin question.
Earth under the conservationof angularmomentum.It also
For thechangein thenormalizedharmoniccoefficientsof the
changesthe externalgravitationalfield accordingto Newton's gravitational
field,or the(complex)Stokescoefficients
Ctm+
gravitational
law. The Earthrotationalchangeis conveniently /S•m
ofdegree
l andorderm,q =[(1+k[)/(21+1)]Ptm(O)exp(im30
expressed
in termsofitsmagnitude,
or thelength-of-day
(LOD) [e.g., Chao and O'Connor, 1988], wherePlmis the 4nvariation, and its orientationin the terrestrialreferenceframe,
normalized
Legendre
function,
andthefactor1+kt' (wherekl' is
or the polar motionexcitation.The gravitationalchangesare
theloadLovenumber,e.g.,ka' = -0.31,k3'= -0.20,k4'= -0.13,
expressed
in termsof the variationof the harmoniccoefficients
etc.) accountsfor the elasticyieldingeffectof the Earth under
loading.In particular,theun-normalizedzonal"f' coefficients
Thispaperisnotsubject
toU.S.copyright.
Published
in1995bytheAmerican
Geophysical
Union.
aregiven
byJt= -(2/+1)• Cto.
The LOD changein unitsof Its canbe directlyevaluatedby
multiplying
1.96x 1011
tothechange
inJ2.Thisisbecause
the
Papernumber95GL02664
twochanges
are proportionalto eachotheraslong as the mass
3529
3530
CHAO: GLOBAL GEeDYNAMICS EFFECTSOF RESERVOIRS
World Meier Reservoirs
Figure 1. The geographical
distributionof 88 majorreservoirsandtheirrelativesizesin logarithmicscale.
redistribution
occurs on the surface of the Earth which can be
well approximated
by a spherical
shell(sothatthe changein the
trace of the inertia tensorvanishessubjectto the conservation
of mass,see Chao and O'Connor [1988]). Here it is assumed
thatthefluidcoreis decoupledfrom the mantlein the excitation
process
thatis rapidcomparedto the characteristic
time for the
Earth'svisco-elasticresponses.
Thepolarmotionexcitation
is oftenexpressed
in the complex
quantity
•F = •Fx + i•, wherex andy axespointto the
andpolar motionexcitationsto accountfor the decouplingof
thecore).The oceancorrectionis typicallyno morethana tenth
of the point-masscontribution,becausethe water distribution
involvedis wide spreadand henceless effectivethan point
masses.In addition, the actual motion of the (water) mass
transportalsoexcitesEarth rotationalvariations.However, this
contributionin our present case is negligible as the motion
(from oceanto thereservoirs)is a relativelyslowprocess.
As a rule of thumb from Equation (1), a point mass
to 100km3 of water(aswiththeverylargest
GreenwichMeridian andthe 90øE longitudein the terrestrial equivalent
coordinatesystem.Its geographicalweightingfunctionis q = reservoirs)will onlyproducea LOD changeon the orderof 1
-1.12sin0cos0exp(i)•)/ J2, proportional
tothechange
in the gs, a polar motionexcitationon the order of 1 milliarcsecond
Stokescoefficientsof degree2 and order 1. The point-mass
(mas),
andaJ2change
ontheorder
of10-•. Weshall
examine
excitation is most effective at the 45 ø latitudes and zero at the
the cumulativeeffects computedsimply by sequentially
summing
up the88 individualcontributions
overtime: AQ(t) =
polesandtheEquator,whereastwo equalmasseslocatedon the
samelatitudebut 180ø apartin longitude,suchasCanadaand
•"•QiH(t-ti),
where
H indicates
theHeaviside
function
and
ti
Siberia (cf. Figure 1), will canceleachother.The factor1.12
is the completiontime (in nominalyear) of the ith reservoir.
takesintoaccountthe elasticyieldingeffectandthe decoupling
of the core. The polar motion excitation enjoys the
magnification
bythefactor
1/J2(where
J2= 1.083x 10-3isthe
Results and Discussion
Earth'sdynamicoblateness),becausethe system"inertia"that
it needsto overcomeis only the differencebetweenthe axial
We computethe changesinducedby the 88 reservoirsin the
and equatorialmomentsof inertia of the Earth (as opposedto
threedegree-1Stokescoefficients
(C•o, Ci•, • ), the five
the axial moment of inertia itself in the caseof the LOD).
(J2,C2•,S2•,•2, •2 ), andthe
An ocean correctionterm is invoked in Equation (1) to degree-2Stokescoefficients
of degree3 and4 (J3,J4). As stated,the
conserve
watermass.It is assumedthat the waterimpoundedin zonal coefficients
change
in
LOD
is
proportional
to that of J2, andthe polar
reservoirsultimatelycomesfrom the ocean(by way of the
is proportional
to thechangein C2•+ iS2•'
atmosphere),resultingin an instantaneous,uniform eustatic motionexcitation
dropof sealevel.Thistermis computedaccordingto Chao and Higher harmonic changes, which tend to be smaller in
magnitudebecauseof geographicalcancellations,are of less
O'Connor[1988] (an extrafactor of 1.12 is introducedto LOD
interestasthey are not subjectto directobservations.
Figure3 showsthereservoir-induced,
cumulativechangesin
• 30oo
•
C•o,C•pandS•, converted
todistance
(inmm)bymultiplying
_••
the Earth'smean radius and inverting the sign. Respectively
they representthe z, x, and y componentsof the shift of the
"geocenter"
location.The centerof massof thetotalsystemof
[solidEarth + reservoirs]remainsunchangedas the reservoirs
•
i r-"
I
0,,40
,;80
ooo are filled, of course.Therefore, the center of mass of the solid
Earth, or geocenter,shiftsin the oppositedirectionto the net
Figure 2. The cumulativeimpoundmentof reservoirwater watermassshift(which is towardthe northernhemisphereand
over time. The insidescalegivesthe equivalenteustaticsea- thepositivex direction).The geocentershiftcanbe detectedby
level drop.
spacegeodeticmeasurements
madeat geodeticstations,which
•n
ß2ooo
sealeveldrop
.•.r-,
-J-I-F'
3am
CHAO: GLOBAL GEODYNAMICS
EFFECTS OF RESERVOIRS
i
0.6
3531
!
i
i
i
J4
0.4
-0.5
J3
x
-1
-0.2
-1.5
-0.4
20O0
Figure 3. Geocentershiftdueto world'smajorreservoirs.
Figure 4. Changesin the Earth'szonalgravitationalcoefficientsJ2,J3,andJ4dueto world'smajorreservoirs.
are fixed w.r.t the solid Earth. The total reservoir-induced shift
of about3 mmis comparable
in magnitudeto thermscenter-of- skatersdrawingher arms towardher body, the Earth spins
mass fluctuationscausedby the seasonalatmosphericmass faster under the conservationof angularmomentum(hence
redistribution
[R. S. Nerem,personalcommunication,
1995].
shorter
LOD), andthekineticenergyof thespinincreases
in the
Figure4 showsthecumulative
changes
in thezonalJ2,J3, process.The ultimatesourceof thisenergyis thesolarenergy
andJ4.In particular,
thereservoirs
caused
theEarth'sdynamic transferred
by way of themeteorological
heatengine.It is easy
oblateness
J2todecrease
attherateofabout
-1.0x 10-•2per to show[Chaoand Gross,1995] thatthe averagerate of this
year since N1950. This quasi-secularrate is an order of
magnitudelarger than the earthquake-induced
counterpartat
about-0.2
x 10-•2peryearaveraged
over1977-1993
[Chaoet
al., 1995]. In comparison,
the observedsecularrate of J2
determinedfrom laserrangingto Lageossatelliteis about-26
x 10-•2peryear,whereas
thermsseasonal
fluctuation
ofJ2is
even
larger
atabout
200x 10-•2[e.g.,Nerem
etal., 1993].The
formerhasbeenattributed
to the post-glacialreboundandpolar
icesheetvariations,
andthe latteris primarilya consequence
of
atmosphericmass redistributions.Similarly, the 'overall
reservoir-induced
variationin J3 is two ordersof magnitude
smallerthanthat observedby Lageos.
spinenergyincrease
is +10•8 joulperyear,or about30
gigawatt,equivalentto about3% of the total humanpower
consumption.
In comparison,the averagerate of seismicwave
energyreleaseduring1977-1993is about5 gigawatt.
Figure 7 shows the polar motion excitation function •F.
Despitea considerable
geographicalcancellation,bothx andy
componentsshow a quasi-seculartrend. Thus, the filling of
major reservoirsover the past 40 yearshas causedthe mean
rotationalpole to drift some20 mas, amountingto an average
of 0.5 masper year,towardN130øW. The observedpolar drift
overthesameperiodis estimatedto be 3.2 masper year in the
direction of 81øW [R. S. Gross, personalcommunication,
1994]. The reservoirshave thus contributeda significant
fractionin theobservedpolardrift, in roughlythe samegeneral
Figure5 givesthecumulative
changes
in J22and•22,defined
by J22exp(i2([}22)
= C22+ i/•2' As shownby Liu and Chao
[1991], J22isa normalized
positivedifference
betweenthetwo direction. This should be taken into consideration in studies
equatorialprincipalmomentsof inertia,while •22 is the with respectto the geophysicalcausesof thepolar drift.
longitude
of the (equatorial)principalaxisof theleastmoment
of inertia. Their changescan be easily evaluatedfrom the
o
i
i
i
i
Earth's
existing
C22andS22andchanges
thereof.Thereservoir- -o.o5
induced
J22shows
a decreasing
trendattherateofabout-0.6x -: -o.1-
10-•2
peryear
forthelast40years.
LikeJ2,thisrateisanorder"" -0.15
of magnitudelarger than the earthquake-induced
counterpart
during
1977-1993.
The
reservoir-induced
change
intheangle
• -0.2•22 has,to date,revertedto its originalvalueafterpeakedat
-0.25
some 1.4 arcseconds in the 1970s.
_
1.5
Thereservoir-induced
LODchange
isproportional
tothatof
J2.Thecumulative
change
is shownin Figure6, displaying
an
o
average
rateof about-0.2 Its (in eachday)per yearfor thepast
40 years.Although
hardlynoticeable
evenin modern •o.5
measurements,
thisrateis abouttwice thatdueto earthquakes
2000
during1977-1993[Chaoand Gross,1995].It is interesting
to
o 1940
1950
1960
1970
1980
examinethephysics
of theprocess.The net watertransporthas
in theEarth'sequatorialmomentsof inertia
beentowardhighlatitudes
(cf. Figure1);J2reduces
asa result Figure5. Changes
andsodoestheEarth'saxial momentof inertia.Like a spinning dueto world'smajor reservoirs.
3532
CHAO' GLOBAL GEODYNAMICS
!
i
i
i
i
i
EFFECTS OF RESERVOIRS
forLOD andthe zonalgravitationalharmonicsconsideringthe
zonal nature of human activities, than for the polar motion
o
excitation
o
-10
i
i
i
i
i
1940
1950
1960
1970
1980
i
1990
2000
Figure 6. Changesin thelength-of-day
dueto world'smajor
reservoirs.
Discussions
and Summary
because
of the east-west
cancellation
mentioned
above.The second,and potentiallymore important,reasonis
that we have only consideredthe "visible" part of the water
impoundment
andignoredthe water that is storedunderground
in anartificially
elevated
watertable [Chao, 1991].The amount
ofthis"invisible"watercan oftenbe comparableif not significanflylargerthanthe visiblepart [D. Sahagian,personalcommunication,
1995],although
theeffectis oftenpartiallyoffsetby
the fact that the reservoirsare not alwaysfilled to the design
capacity.A more realistic accountfor this effect is pending
betterknowledgeaboutthe local geologyandreservoirhistory.
The water impounded
in artificialreservoirsis by far the Acknowledgments.
I thankD. Sahagian
forencouragement
and
largest anthropogenichydrologicalchangein terms of total discussions,
and Y. S. Changfor graphicsupport.This studyis
watermassinvolved.
It notonlyrepresents
a significant
element supported
byNASAGeophysics
Program.
in the global hydrological and sea level budget, but also
contributesto geodynamicchangesin the Earth'srotationand
gravitational
field thathavebeencloselymonitoredby modem
space
geodetic
techniques.
Wehavecompiled
alistof88major References
reservoirs
thatexceed
10km3 in capacity,
andcomputed
the
effect
oftheassociated
watermass
redistribution
onlength-of-Chao,B. F., Excitation
of theEarth's
polarmotion
dueto mass
day, polarmotion,andlow-degreegravitationalcoefficients.
variations
in majorhydrological
reservoirs,
J. Geophys.
Res.,93,
The mass redistribution is modeled as an instantaneous addition
13811-13819, 1988.
ofapointmass
minusanaccompanying
eustatic
dropin thesea Chao,
B.F.,andW.P.O'Connor,
Effectofa uniform
sealevelchange
leveltoconserve
thetotalmass.
In termsofmagnitude,
these ontheEarth's
rotation
andgravitational
field,Geophys.
J.,93,
anthropogenic
geodynamic
signals
fromindividual
reservoirs191-193,
1988.
arebarely
detectable.
However,
thecumulative
effects
showChao,
B.F.,Man,
water,
and
sea
level,
EOS,
Trans.
Amer.
Geophys.
Union, 72, 492, 1991.
non-negligible, quasi-secular behavior (as opposed to Chao,B. F., Man-madelakesandglobalsealevel,Nature, 370, 258,
characteristics
of a randomwalk process)
due to non- 1994.
randomness
in thereservoirs'
geographical
distribution.
In Chao,
B.E,and
R.S.Gross,
Changes
oftheEarth's
rotational
energy
particular,the reservoirs
accountfor a significantfractionin the
observedpolar drift.
Finally, we shouldpoint out that our computedresultsonly
representunderestimates
of the reality,for two reasons.First,
themajorreservoirs
underconsideration
accountfor about40%
of the totalwaterimpoundmentin the world to date [cf. Chao,
1994].Smallerreservoirs
aremorenumerous;individuallythey
areindeedentirelynegligible.But their collectivecontribution
maynotbe negligible.This omissionis presumablymore severe
inducedby earthquakes,
in press,Geophys.
J. Int., 1995.
Chao,B. F.,R. S. Gros.s,
andD. N. Dong,Globalgravitational
energy
changesinducedby earthquakes,
in press,Geophys.J. Int., 1995.
International Water Power & Dam ConstructionHandbook, ed. R.
M. Taylor, ReedBusinessPub.,Surrey,1993.
Liu, H. S., andB. F. Chao,The Earth'sequatorialprincipalaxesand
momentsof inertia,Geophys.J. Int., 106, 699-702, 1991.
Nerem, R. S., B. F. Chao, A. Y. Au, J. C. Chan, S. M. Klosko, N. K.
Pavlis,andR. G. Williamson,Temporalvariationsof the Earth's
gravitational
fieldfromsatellite
laserrangingto LAGEOS, Geophys.
Res. Lett., 20, 595-598, 1993.
Rodenburg,E., Man-madelakesand globalsealevel,Nature, 370,
258, 1994.
Sahagian, D. L., F. W. Schwartz, and D. K. Jacobs,Direct
anthropogeniccontributionsto sea level rise in the twentieth
century,Nature, 367, 54-56, 1994.
U.S. Department of Interior, Major Dams, Reservoirs, and
HydroelectricPlants,Bureauof Reclamation,Denver,1983.
U.S. Departmentof Interior,The World'sMajor Dams,Manmade
Lakes,andHydroelectricPlants,1980:1988 Updating,Bureauof
•-10
o
o
o
.•
.o
•
5
0
Reclamation, Denver, 1988.
o
VenderLeeden,F., WaterResources
of the World,WaterInformation
Center, Inc., New York, 1975.
o
n -10
-15
1930
i
1940
i
1950
i
1960
i
1970
i
1980
I
919
0
2000
B. F. Chao, Geodynamics
Branch,NASA GoddardSpaceFlight
Center,Greenbelt,Maryland 20771, USA.
Figure7. Polarmotionexcitation
by world'smajorreservoirs (Received:March7, 1995' revised:May 11, 1995;
accepted:July20, 1995)
(they component
offsetverticallyby anarbitraryamount).