JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 99, NO. D7, PAGES 14,415-14,428, JULY 20, 1994
A simplehydrologicallybasedmodelof land surfacewater and
energyfluxesfor generalcirculationmodels
Xu Liang andDennisP. Lettenmaier
Department
of Civil Engineering,
Universityof Washington,
Seattle
Eric F. Wood
Department
of Civil Engineering
andOperations
Research,
Princeton
University,Princeton,
New Jersey
StephenJ. Burges
Departmentof Civil Engineering,
Universityof Washington,
Seattle
Abstract. A generalization
of the singlesoillayervariableinfiltrationcapacity(VIC) land surface
hydrological
modelpreviouslyimplemented
in the Geophysical
FluidDynamicsLaboratorygeneral
circulationmodel(GClVOis described.The new modelis comprised
of a two-layercharacterization
of
the soil column,andusesan aerodynamicrepresentation
of the latentand sensibleheatfluxesat the land
surface.The infiltrationalgorithmfor theupperlayeris essentially
the sameasfor the singlelayer VIC
model,while the lower layer drainageformulationis of the formpreviouslyimplementedin the MaxPlanck-InstitutGCM. The modelpartitionsthe areaof interest(e.g., grid cell) into multipleland surface
covertypes;for eachland covertype the fractionof rootsin the upperandlower zoneis specified.
Evapotranspiration
consists
of threecomponents:canopyevaporation,evaporation
from bare soils,and
transpiration,
whichis represented
usinga canopyandarchitectural
resistance
formulation.Oncethe
latentheatflux hasbeen computed,the surfaceenergybalanceis iteratedto solvefor the land surface
temperatureat eachtime step. The modelwastestedusinglong-termhydrologicandclimatologicaldata
for KingsCreek,Kansasto estimateandvalidatethehydrological
parameters,
andsurfaceflux datafrom
threeFirst InternationalSatelliteLand SurfaceClimatologyProjectField Experimentintensivefield
campaigns
in the summer-fallof 1987to validatethe surfaceenergyfluxes.
1. Introduction
BATS and SiB, is that they have a high level of vertical
resolutionand structure,but a low level of horizontalresolution
The problemof how to representthe land surfacein general [Wood, 1991]. In addition,most SVATS use a "flat Earth"
circulationmodels (GCMs) used for climate simulationand
numericalweatherpredictionhas drawnthe interestof climate
modelers, and increasingly, hydrologists and systems
ecologists.Manabe [1969] used Budyko's"bucket"model to
representland surface hydrology at the global scale, and
representationof the land surface. Topography can
significantlyaffect large scalesoil moisturedynamics,runoff
production,andsurfaceenergyfluxes(J.S.FamigliettiandE.F.
Wood, Application of multiscalewater and energybalance
model on a tall grassprairie, submittedto Water Resources
variations of the bucket model have been used in most GCMs.
Research, 1993, herein after referred to as Familglietti and
Recent improvementsin GCM land surfacerepresentations
Wood, submittedpaper1).
have beenprimarily in the area of soil-vegetation-atmosphere
An alternativeline of investigationis to developsimpler
transfer schemes(SVATS) which seek to representthe
land surfacemodelsthat still incorporateimportantfeaturesof
interactions of vegetation with the soil column and the
the governinghydrologicalprocessesin both the vertical and
atmosphereas they affect surface energy fluxes, especially
horizontal. For example,Xue et al. [1991] simplifiedSiB by
latent heat. Among the best known SVATS are biospherereducingthe numberof parametersfrom 44 to 21, apparently
atmosphere
transferscheme(BATS) [Dickinsonet al., 1986]
with negligible loss of accuracy. Ducoudre et al. [1993]
and simplebiospheremodel (Si_B)[Sellerset al., 1986]. A
developeda new set of parameterizations
of the hydrologic
distinguishingfeature of SVATS, which is evident in both
exchanges
(SECHIBA) at the land/atmosphere
interfacewithin
a GCM which representsvegetation, as does a recent
modificationto the land surfaceschemeof the EuropeanCenter
Copyright1994by the AmericanGeophysical
Union.
for MediumRangeWeatherForecasting.
In
Papernumber94JD00483.
0148-0227/94/94JD-00483505.00
addition
to
the
above-noted
initiatives
in
SVATS
modeling,investigationsof subgridscalevariability associated
14,415
14,416
LIANG ET AL.' HYDROLOGICALLY
BASED LAND SURFACE FLUX MODEL
with terrain, soil and vegetationheterogeneitieshave been
motivatedby studiessuchas that of Avissat and Pielke [1989]
who showedthat spatialheterogeneityin vegetationcan have
significanteffectson temperatureandprecipitation.Entekhabi
and Eagleson[1989] examinedthe effectsof subgridspatial
variability of soil moisture and storm precipitation via
statisticallyderivedexpressions
for the hydrologicfluxesbased
on the assumedsubgridsoil andprecipitationvariability. J.S.
Famiglietti and E.F. Wood (Multiscalemodelingof spatially
variable water and energy balanceprocesses,submittedto
WaterResources
Research,1993) developeda modelof water
and energybalancebasedon the conceptof a topographic
index,which allowsthe local fluxes of eachgrid elementto be
aggregatedby statisticalintegrationof the local fluxes over
theirrespectivespatialprobabilitydensityfunctions.
In this paperwe describea land surfacehydrologicalmodel
suitablefor incorporationin GCMs that is a generalization
of
the variable infiltration capacity(VIC) model describedby
Woodet al. [1992] and implemented
in the Geophysical
Fluid
DynamicsLaboratory(GDL)-GCM by $tarnrnet al. [1994].
The soil moisture algorithm is a generalizationof the Arno
model [Francini and Pacciani, 1991] in which the infiltration,
evaporation,soil moistureandrunoff generationvary within an
area (or within a grid cell in GCMs). Simplificationsof the
Arno model, usingthe traditionalbeta functionrepresentation
of evapotranspiration,
have previouslybeen incorporatedin
GCMs [$tarnrn et al., 1994; Damenil and Todini, 1992].
However, there are major differencesbetweenthe two-layer
VIC modeldeveloped
hereandthe earlierversionsincorporated
in the GFDL and Max-Planck-Institut(MPI) GCMs. Both of
the earlier schemeshave a single soil layer, and neither
explicitly representsvegetationin the surface energy flux.
$tarnrnet al. [1994] concludedthat "... the resultsover North
American and Eurasia [suggest]the need to representthe
surfacehydrologywith a two layersoil system..."
The current model is comprisedof a simple two-layer
soilsof varyinginfiltrationcapacities.It allowsdifferenttypes
of vegetationto be presentsimultaneously.It doesnot, at
present,accountfor the spatialvariabilityin precipitation.
2. Model Description
The modelcharacterizes
the subsurface
as consisting
of two
soil layers. The surfaceis described
by N+I landcovertypes,
where n = 1, 2, . . . , N representsN differenttypes of
vegetation,and n = N+I representsbare soil. There is no
restrictionon the numberof vegetationtypes,but in the interest
of modelparsimony,N will almostalwaysbe lessthan 10. The
vertical
and
horizontal
characterizations
are
shown
schematically
in Figure 1. The land covertypesare specified
by their leaf area index (LAI), canopyresistance,andrelative
fraction of roots in each of the two soil layers. The
evapotranspiration
from eachvegetationtype is characterized
by potential evapotranspiration,together with canopy
resistance,aerodynamicresistanceto the transferof water, and
architectural resistance.
Associated with each land cover class
is a singlecanopylayer,soillayer1 (upperzone)andsoillayer
2 (lower zone). The upperlayer (soil layer 1) is designedto
represent
the dynamicbehaviorof the soilcolumnthatresponds
to rainfall events,andthe lowerlayer(soil layer2) is usedto
characterizethe slowly varying between-stormsoil moisture
behavior. The lower layer only responds
to rainfallwhenthe
upperlayeris wettedandthuscanseparate
the subsurface
flow
from stormquick response. Rootscan extendto layer 1 or
layers1 and2, depending
on the vegetation
andsoiltype. For
thebaresoilclass,thereis no canopylayer. In thepresentform
of the model,the soil characteristics
(thatis, the distribution
of
waterholdingcapacities,
as described
below)are the samefor
all land coverclasses.However,eachcoverclassmay have
different soil moisture distributionsat each time step.
Infiltration, drainageof moisturefrom layer 1 to layer 2,
surfacerunoff and subsurface
runoff are computedfor each
characterization
of the soil columnand usesan aerodynamic
representation
of the latentand sensibleheat fluxesat the land
surfacebasedon a simplifiedSVATS-typerepresentation
of
vegetationcover. The infiltrationalgorithmin the VIC model
cover type. The total latent heat flux transferredto the
atmosphere,total sensibleheat and groundheat fluxes, the
effectivesurfacetemperature,
andthe total surfacerunoff and
subsurface
runoffare then obtainedby summingoverall of the
canbe interpreted
withinthe contextof a spatialdistribution
of
surface cover classes.
E1
Ec
Et
P
Canopy
Od
3
2
Layer 1
cover
n - N+I
class
n- 1
Q12
4
c
Layer 2
N
W2
Ob
Figure 1. Schematic
representation
of thetwo-layerVIC model.
(Bare
LIANG ET AL.: HYDROLOGICALLY
BASED LAND SURFACE FLUX MODEL
2.1. Evapotranspiration
14,417
Following
Louis[1979],Fw[n] is defined
as
Three types of evaporationare consideredin the model.
They are evaporationfrom the canopylayer of eachvegetation
class,transpirationfrom each of the vegetationclasses,and
evaporationfrom bare soil. Total evapotranspiration
over the
F,•[n]
=1- 9'4RiB[n]
1+c.IRi[nll
'/2'RiB[nl
<0 (4C)
1
gridcelliscomputed
asthesumofthecanopy,
vegetation,
and
F,•[n]
=(1+4.7RiB[n])
2' 0_<
RiB[n
]_<
0.2 (4d)
bare soil components,
weightedby the respectivesurfacecover
areafractions(equation(23)).
The maximumcanopyevaporation
for the nth surfacecover where
RiB[n
] is thebulkRichardson
number,
andc is expressed
class,
E•[nJ,
isspecified
as
W•[n]
)2/.•
r•[n]
E:[n]
=((Wire[n]
Erin]
r,•[n]
+r0[n
]
as
(1)
C49.82xa2[n]xlZ2[n]
=
z0[n]
,
(4e)
In Louis'representation,
the dragcoefficients
for waterandheat
In equation(1), the argumentn refersto the vegetationsurface
are takento be equal,but they canbe differentfrom the drag
coverclassindex. Throughoutthe remainderof the paperthe coefficient for momentum.
dependenceof many of the surface and subsurface
Basedon the formulationof Blondin[1991] andDucoudreet
characteristics
on surface cover class is implied by this
al. [1993],transpiration
is estimatedas
argument
evenif notnotedspecifically.
Wi[n
] is theamount
of
intercepted
waterin storage
in thecanopy
layer,Wim[n
] is the
maximumamountof water that the canopylayer can intercept;
thepower
of2/3isused
according
toDeardorff[1978].
Ep[n]
is
=
-
kWire[n]
Ep[n]
r,•[n]+ r0[n
] + rc[n
]
the potentialevaporationfrom a surfacebasedon the PenmanMonteith equationwith the canopyresistanceset to zero
] isthecanopy
resistance
givenby
[Shuttleworth,
1993]. The architectural
resistance
thatis dueto whererc[n
the variationof the gradientof specifichumiditybetweenthe
roc[n]gsm[
n]
leavesandtheoverlying
airin thecanopy
layeris r0[n] [Saugier
r,[n] =
andKaterji,1991], andrw[n
] is theaerodynamic
resistance
to
LAI[n,m]
(5)
(6)
the transferof water. The form of equation(1) is sometimes
referredto as a "beta"representation.
In equation
(6),roc[n
] istheminimum
canopy
resistance,
go•m[n]
The maximum amountof water interceptedby the canopy is a soil moisture stress factor dependingon the water
canbe calculatedusing[Dickinson,1984]
availabilityin the rootzonefor the nth surfacecoverclass. It is
expressedas
W•m[n
] = KœxLAI[n,m]
(2)
g;m•[n]
= 1,
W•'[n]
>_W;r
(7a)
where LAI[n,m] is leaf area index for the nth surfacecover
classin monthm, andKL is a constant,
takento be 0.2 mm
followingDickinson[1984].
The aerodynamicresistanceto the transfer of water is
calculatedas [Monteithand Unsworth,1990]
g;m•
[n]=
Wa.[n
]
gjm•[nl
= 0,
r,•[n]
=C,•[n]u,(z2)
1
Wf < W•.[nl
< Wjcr
W•[n]
< Wf
(7b)
(7C)
(3) whereWj[n]isthesoilmoisture
content
inlayer
j, j=l, 2. •j.cr
is the critical value abovewhich transpirationis not affectedby
whereUn(Z2)
is thewindspeed
overthenthsurface
coverclass themoisture
stress
in the soil,and•'• is the soilmoisture
at levelz2[n], andCw[n
] is thetransfercoefficient
for water contentat permanentwilting point. Water can be extracted
whichis estimatedtakinginto accountthe atmospheric
stability fromlayers1 and/or2 depending
onthefractions
of roots
f• [n]
[Louis,1979] as follows:
andf2[n] in eachlayer.
Thereis no soilmoisturestress,
i.e., gsm[n]=lin equation
(4a) (6), if either(i) W2[n
C•[nl=l.351xa2[n]xF,•[n]
] is greater
orequalto W2
*r, andf2[n]>_0.5
or (ii) Wl[n] is greater
or equalto •,r, andf• [n]>_0.5.
In case
(i), thetranspiration
is supplied
bylayer2 withno soilmoisture
where
a2[n]=
stress,
i.e.,Et[n]=E•[n
] (regardless
&wateravailability
inlayer
(4b) 1); in case(ii), the transpirationtakeswater from layer 1, i.e.,
Et[n]=E([n],
alsowithout
anysoilmoisture
stress.Otherwise,
z0[n]
[l•z2[n]-do[n]12
transpirationis
is the dragcoefficientfor the caseof near-neutralstability,K is
Et[n] = f•[n].E([n]+f2[n]-E•[n]
(8)
yonKarman's
constant,
whichwe takeas0.4;do[n
] is thezero
fromlayer1 andlayer
planedisplacement
height,andz0[n] is the roughness
length. whereE•[n], E•[n] arethetranspiration
14,418
LIANG ET AL.: HYDROLOGICALLY
BASED LAND SURFACE FLUX MODEL
2, respectively,computedusingequation(5). If the rootsonly
i-im [1-(1 -A)l/bi)]
extend
tolayer1,thenEt[n]=E•[n
] withf2[n]
= 0.
For the case of a continuous rainfall with a rate lower than the
canopyevaporation,it is importantto considerevaporation
from the vegetationwhenthereis insufficientintercepted
water
to supplythe atmospheric
demandwithin onetime step. In this
case,theevaporation
fromthecanopy
layer,Ec[n], is
E•[n]= f[nl.Ej[n]
(9)
whereJln] is the fractionof the time steprequiredfor canopy
evaporationto exhaustthe canopyinterceptionstorage. It is
givenby
f[n]
=mill,
W/[n]
+P.
At
(10)
whereP is the precipitationrate, and At is the time stepwhich
is taken as 1 hour in the model calculation. The transpiration
duringthe time stepis then
0 As
1
Fraction
Erin]
=(1.Of[n])Ev[n
]
of Area
Figure 2. Schematic
representation
of the computation
of
r,•[n]+ro[n]+rc[n]
evaporationfrom bare soil.
(11)
r,•[n]+ro[n]+r•[n]
As
1
E1=Ep[N+I]
dA+
.ira
1--(;2A)
1/•'
dA
(14)
wherethe first term represents
the fractionof the time stepfor
which no evaporationoccurs from the canopy interception
the contribution
of
storage,andthe secondterm represents
the fractionof the time In equation(14), the first integralrepresents
step for which both evaporationfrom the canopy and the saturatedarea,which evaporatesat the potentialrate. Since
there is no analytical expressionfor the secondintegral in
transpirationoccur.
Evaporationfrom bare soil is extractedonly from layer 1;
equation
(14),E• is obtained
through
apowerseries
expansion:
baresoilevaporation
fromlayer2 (E2)is assumed
to be zero.
When layer 1 is saturated,it evaporatesat the potentialrate
=
E1
Ev[N+l]{As+t½(1
As)[l+
b•(1
=
+
lm
- .4,)
'+
-
l+b,
-.4,)
- .4,1 '+...
'+
(15)
whenit is unsaturated,
it evaporates
at rateE• whichvaries
within the bare soil area due to the inhomogeneitiesin
This approachaccountsfor the subgridvariability in soil
infiltration,
topography
andsoilcharacteristics.
E• is computed moisturewithin the areacoveredby baresoil.
using the evaporationformulationof Francini and Pacciani
[ 1991]. This formulationusesthe structureof the Xinanjiang 2.2. Canopy Layer Water Balance
model [Zhao et al., 1980] (see also Woodet al. [1992]) and
The water balancein the canopylayer (interception)canbe
assumes
that the infiltrationcapacityvarieswithin an areaand described
by
canbe expressedas
i=im[1-(1-A)
•/b'
]
(13)
clW,[n]
• dt = P -Ec[n]-Pt[n],0 < W•[n]
< Wim[n
]
(16)
of precipitation
whichoccurs
wherei and im are the infiltrationcapacityand maximum wherePt[n] is the throughfall
when
Wim[n
]
is
exceeded
for
the
nth
surface
cover
class.
infiltrationcapacity,respectively,A is the fractionof an area
for whichtheinfiltration
capacity
is lessthani, andbi is the 2.3. Surface Runoff From Bare Soil
infiltration
shape
parameter.
LetA, represent
thefraction
ofthe
baresoilthatis saturated,
andio represent
the corresponding Surface rimoff is computed using the formulation for
The Xinanjiang
pointinfiltration
capacity.Then,assuggested
by Figure2, E• infiltration given by equation (13).
canbe expressedas
formulation,
whichis described
in detailby Woodet al. [1992],
LIANG
ET AL.:
HYDROLOGICALLY
BASED
LAND
SURFACE
FLUX
MODEL
14,419
x•2+3
is assumed
to hold for the uppersoil layer only. The maximum
soilmoisture
content
of layer1, W•
c, is relatedto imandbi as
(20)
follows:
im
whereKs.is the saturated
hydraulic
conductivity,
Or is the
W•*
=1•-bi
(17)residual
moisture
content,
andBpistheporesizedistribution
index.
The Xinanjiang model effectively assumesthat runoff is
generatedby thoseareasfor whichprecipitation,when addedto 2.4. Subsurface Runoff From Bare Soil
soil moisture storageat the end of the previoustime step,
The formulationof subsurface
runoff(baseflow) followsthe
exceedsthe storagecapacityof the soil. The directrunoff from Arno model conceptualization
[Franciniand Pacciani, 1991],
theseareasis Qa[N+I], whereN+I indicates
thebaresoilclass. which is appliedonly to the lower soil layer (drainagefrom
In integratedform, the resultis
layer 1 goesonly to layer 2, and doesnot contributeto runoff).
Baseflow is givenby
Qa[N+I].At=P.M-W[ +W•-[N+I],
io+P.At>i m
+ =v.v.
(18a)
+q,
0 < W2-[N
+1]< W,W2*
(21a)
Qa[N+1].At= P.At- W•*
+W•-[N
+1]
Qb[N
+1]=D'D'n
W2-[N
+1]
+W•[1
_i0
+P.
At]
l+b'
'
,
i0 + P. At < im
+(D.
w,
whereW•-[N+I] is the soil moisturecontentin layer 1 at the
w: -w,w:
'
(2lb)
beginningof the time step. Note that, for the bare soil class,
there is no canopystorage,hence "throughfall"is equal to
whereQb[N+I]is thesubsurface
runoff,Dmis themaximum
precipitation
P. For baresoil,thewaterbalancein layer 1 is
Wt+[N
+1]= W•-[N
+ 1]+
(P-Qa[N+1]- QI2[N
+1]-E•).At
(19)
subsurface
flow,Ds is a fraction
of Din,W2
c is themaximum
soilmoisture
content
of layer2, Wsis a fraction
of W2
* , withDs
< Ws, and W2-[N+I] is the soil moisture
contentat the
beginningof the time stepin layer 2. Equations(21a) and
(2lb) describea recessionthat is linear below a threshold
whereW•+[N+I]is the soilmoisturecontentin layer 1 at the (equation(21a)), andnonlinearat highersoil moisturevalues
endof eachtimestep,andQ•2[N+I]isthedrainage
fromlayer (equation(2lb)) asshownin Figure3. Thenonlineardrainage
1 to layer 2. Assumingthat the drainageis drivenby gravity, is requiredto representsituationswhere substantialsubsurface
we use the Brooksand Corey [1964] relationto estimatethe storm flow occurs. Equations (21a) and (2lb) have a
hydraulicconductivity,and thus we can expressthe drainage continuous first derivative at the transition from the linear to
nonlineardrainageas shownin Figure3.
from layer 1 to layer 2 as
DsDm
o
wsw
Layer 2 Soil Moisture,W2
Figure 3. Schematic
representation
of Arnononlinearbaseflow.
14,420
LIANG ET AL.: HYDROLOGICALLY
BASED LAND SURFACE FLUX MODEL
Using equations (21a) and (2lb), and the notation that
W2+[N+I]is the layer2 soilmoisturecontentat the endof the
currenttime, the water balanceis
W2+[N
+1]=
+ 1]
+(Q12[N
+1]-Qb[N
+1]-E2).At
(22a)
whereRn[n
] is thenetradiation,
H[n] is thesensible
heatflux,
Pwis the densityof liquidwater,Le is the latentheat of
vaporization,
PwLeE[n]
isthelatentheatflux(e.g.,withunitsof
Wm'2 ), andG[n]is theground
heatflux. Fora surface
thatis
relatively flat and homogeneous,
the energybalanceequation
for a layer of the air columnboundedby the groundsurfaceat
the bottom and a surfaceof given height in the atmosphere
above,canbe expressed
as
whenW2-[N+I]+ (Q12[N+11
- Qb[N+I]- E2)'At< W2
c, in
whichcaseQbisgivenbyequation
(21a)or(2lb).
(27)
P•[n]= H[n]+ p,•LeE[n
] +G[n]+
In the caseW2-[N+ 1]+ (Q12[N+l]- Q;[N+ 11 - E2).At
>W2
c, (whereQ•[N+ 111is givenbyequation
(21a)or(2lb)),
wherez•r/s[n
] is the change
in the energystorage
in thelayer
W2+[N
+ 1]= W2
*
(22b)
and
per unit time, per unit area. The sensibleandlatentheatfluxes,
aswell asthe net radiation,are associated
with the top surface
of the air layer, andthe groundheatflux with the bottomof the
layer. The rate of heatenergystoragein the layer is
Q'2[N
+I] = W2-[N
+I]
A/-/$[n]
=Pacp(T•+[n]T•-[n])za[n]
+(Q12[N
+1]- Q•[N+1]-E2).At-W2
•
(28)
2•
When equation(22b) applies,the total subsurface
runoff from
Paandcparethemass
density
andspecific
heatofairat
layer2 is givenby Q,[N+11
= Qi[N+11+ Q;IN+l]. In where
constant
pressure,
T•+[n] and T•-[n]arethe surface
temperature
practice,this conditionoccursrarely.
2.5.
Surface
and Subsurface
of the bottom surface of the layer at the end and at the
beginning
of a timestep,respectively,
andza[n]istheheightof
thetopsurface
of thelayerwhichis usedonlywhenz•r/s[n
] is
Runoff
From Soil With Vegetation Cover
The equationsfor surfaceand subsurface
flow andthe water
balance in each layer are the same for cover classeswith
vegetation
asfor thebaresoilcase,exceptthatP, El, andE2
are changed
to Pt[n], El[n], and E•[n], respectively,
in
equations(18), (19), and(22), to reflectthe vegetationclass.
The total evapotranspiration
E, and the total runoff Q can be
thenexpressed
as
considered
to be significant.
The net radiationis givenby
R,[n]:
(1-at[nl)R•
+8[n].
(R•- oT•4
[n])
(29)
whereat[n]isthealbedoof thenthsurface
coverclass,
Rsisthe
downwardshortwaveradiation,a[n] is the emissivityof the nth
surfacecoverclass,RL is the downward
long-wave
radiation,
N
E = Z Cv
In]'(E,[n]
+Et[n])+
Cv[N
+1].E1
n=l
(23)
obtainedfrom equation(26). The sensible
heatflux is givenby
N+I
Q= Y,Cv[n].(Q,•[n]+Qb[n])
n=l
and o is the Stefan-Boltzmannconstant. The latent heat flux,
which is the link betweenthe water and energybalances,is
(24)
,[n]=p•cp
(T•[n]T•[n])
(30)
whereCv[n
] is thefractionof vegetation
coverforthenth(n=l,
2....
, N) surfacecoverclassof interest,Cv[N+I] is the where T,[n] is the surfacetemperature,
T•[n] is the air
fraction
of
the
bare
soil
covered
area, temperature,
and
rh[n
]
is
the
aerodynamic
resistance
to heat
N+I
flow. We takerh[n] to be equalto rw[n
] in equation
(3). The
and •Cv[n I = 1.
groundheat flux G[n] is estimatedusing two thermal soil
n=l
layers.Forthefirstsoillayer,withdepthD1 (subsequently
2.6. Aerodynamic Flux Representation
assumed
to be 50 mm), we have
The two-layerhydrologicalmodel describedaboveis usedin
conjunctionwith the energybalanceat the land surfaceandthe
(31)
thermalpropertiesof soilsto calculatethe surfacetemperature,
andsimultaneously,
the fluxesof sensibleheatandgroundheat
andT1[n]isthesoil
which dependon surfacetemperature. The energybalance whereK[n]isthesoilthermalconductivity,
at depthD 1. Forthe second
soillayerwith depth
equationfor an ideal surfaceof the nth surfacecover classcan temperature
D2, at whichthe bottomboundary
condition
is constant
soil
be expressedas
temperature,
the law of energyconservation
(assuming
that the
G[n]
=KD•(T•[n
]-Tl[n])
R•[n]= H[n]+PwLeE[n]
+G[n]
(25)
with
E[n]= E,[n]+Et[n], n= 1,2.... , N
(26a)
heatstorage
in thefirstsoilthermallayeris negligible)
gives
C•[n]'(T•+[n]
- Tl-[n])
G[n]
r[n].(rl[n]-(32)
=•
2. At
D2
D22
(26b) whereCs[n
] is the soilheatcapacity,
Tl+[n]andT•-[n]arethe
LIANG
ET AL.:
HYDROLOGICALLY
BASED
LAND
soiltemperature
at depth
D• attheendandthebeginning
of a
timestep,respectively,
andT2 is the constant
temperature
at
Month
functionsof the soilwatercontent(althoughsuchan adjustment
would be straightforward),
and are taken to be the samefor
both soil thermallayers. From equations(31) and (32), the
groundheatflux G[n] canbe expressed
as
K[n]
(Ts[n]_
T2
)+C•[n]'D2(Ts[n]T,[n])
D2
FLUX
MODEL
14,421
Table1. Average
MonthlyNDVIsatFWE
depth
D2. At present,
Cs[n
] andK[n]arenotconsidered
to be
1+D•+C•[n]'D•'D2
SURFACE
(33)
2.At.tin]
ForthecasewhereA/-/•[n]canbeignored,
theenergy
balance
equationfor anidealsurface(equation(25)) canbe usedinstead
of equation
(27). Fromequations
(29), (30), (33), andequation
(26) (scaledby thelatentheatof vaporization
andthedensityof
liquidwater),the sensible
heatandgroundheatfluxesandthe
surface
temperature
for the nthcoverclasscanbe obtained.In
the casewhereA/-(s.[n]
is negligible,
the surface
temperature
Ts[n
] isiteratively
solved
usingequation
(34):
r[n]+
%[n].
D2
e[n]•T•[n]+
pacv•22-
NDVI
Jail.
53
Feb.
58
March
66
April
89
May
132
June
147
July
145
Aug.
136
Sept.
122
Oct.
84
Nov.
66
Dec.
62
T,[n]is determined
in the samemannerasfor equation
(34).
Theeffectivesurface
temperature
T,, sensible
heatfluxH, and
groundheatflux G canthenbe obtainedas
rh[n]
•2-2
+
+1+-•-•--•[n•D2''T•[
n]
=(1- o•[n])R•
+e[n]-Rr,
+rl,[n
pacv
T•rnqp,•LeE[n
]
] [•
N+I
rs= ZCv[n].rs[n]
n=l
(36)
N+I
H = ZCv[n]'H[n]
tin].T2 C•[n].
D2ßT•-[n]
n=l
--+
.D2
i+D•+ Cs[n].D,
D2
(34)
(37)
N+I
G = ZC•[n]'G[n]
2' At.K[n]
n=l
(38)
Theiterativeprocedures
for computing
the surfacetemperature
ForthecasewhereAHs[n
] cannot
beignored,
equations
(27)to T,[n]is asfollows:
(30), and(33) are combinedto give
e[n]•(Tf[n])
4[P•C
p•cvz
•[n]
+
1o+
D2 2./Xt rf[n]
2. At.K[n]
(1-o•[n]).
Rs+g[n].
Rr,+
QaCp
T•[n]-pwLeE[n]
PaCvz•[n]'Tf[n
] + D2
2.At
2.At
1+ D, + Cs[n].D,.D:
D2
formulation.
2. Iterate equation(34) or (35) to solvefor the surface
2.At.<[n]
equation(34) or (35). The surfacetemperature
obtainedfrom
this stepis thenconsidered
to be the surfacetemperature
at the
farsttime stepof themodelsimulation.
5. For subsequent
time steps,use the surfacetemperature
from the previoustime stepto calculatethe bulk Richardson
number,vaporpressuredeficit, and net radiation,then repeat
steps2-4.
gin].T2 Cs[n].D2ßT•-[n]
•+
-[
Penman-Monteith
3. Use the surfacetemperatureobtainedfrom step(2) to
calculatethe bulk Richardsonnumber,vaporpressuredeficit,
andnet radiationagain.
4. Recalculatethe surfacetemperatureiteratively using
D• + Cs[n].D• .D2
D2
radiation
thatareneeded
in estimating
Ep[n]through
the
temperature.
r[n] Cs[n].D
2
1+
1. Setthe surfacetemperature
to the air temperature
at the
farsttime step. Thisallowscomputation
of the initialvaluesof
the bulk Richardson
number,the vaporpressuredeficitandnet
(35)
It shouldbe mentionedthattheproceduredescribed
aboveis
not iterativein the samesenseas the procedureusedto solve
for the surfacetemperature
from equation(34) or (35), sincethe
stepsare only repeatedonce. The use of a singleiterationis
justifiedby the relativelysmoothvariationusuallyobservedin
14,422
LIANG ET AL.: HYDROLOGICALLY
BASED LAND SURFACE FLUX MODEL
10 .I
lO
observed
.......
modeled
a
4
2
Oct Dec Feb Apr Jun Aug
Oct Dec Feb Apr Jun Aug
Water Year 1983
Water Year 1984
Figure4. Predicted
(dottedline)andobserved
(solidline)streamflow
for KingsCreekfor calibration
years
1983-1984.
surfacetemperaturesdue to the thermal inertia of the soil term climatalogicaldata at nearby Manhattan,Kansas,which
column. Of course,multipleiterationscouldbe performedif allows for validationof the hydrologicalportion of the VIC
required. Such an approachin fact implies two nested model. The overall strategyfor validationof the modelwas to
iterations;oneto solveequation(34) or (35), andthe otherto
Table 2. Model Parameters
determinethe bulk Richardsonnumberand related quantities
Parameter
Value
neededto computethe surfaceenergyfluxes.
2.7.
Snow
bi
0.008
When snowis present,the model is coupledwith a singlelayer, energy- and mass-balancesnow accumulationand
ablation model [Wigmostaet al., 1994]. At the snow-air
interface,the energyexchangeis describedby the net radiation,
sensibleheat, evaporationfrom the water in the snowpackand
Din,mm/h
0.34
Ds
7.7x10
'5
Ws
0.96
sublimation or condensation, and the heat advected to the
Bp
0.16
Ks,,mm/h
6.44
W[, m
0.25
w2
•, m
1.25
Wf, m
O.lS• •
Wfr,m
0.46 Wf
0
0.5
to[1], s/m
2.0
snowpackby rainfall. The snow-ground
interfaceis assumedto
be a zero energyflux boundary. Snow albedois determined
basedon snowage. The presentversionof the snowmeltmodel
doesnot considerfractionalsnowcoverage;it is assumedthat
the entire area is coveredby a uniform depth of snow if a
snowpackis present.
3. Parameter
Estimation
The test location for the model was the FIFE (First
InternationalSatellite and Land SurfaceClimatologyProject
FieldExperiment)sitein centralKansas.TheFIFE experiment
is described
in detailby Sellerset al. [1992]. The siteis a 15x
15km2region
ontheKonzaPrairie,
a nativegrassland
preserve
nearManhattan,Kansas.It hasa fairly homogeneous
tall grass
cover,and thusthe numberof vegetationtypesN was takento
be 1, withCv[N+I]=O.O.
TheKingsCreekcatchment,
of area
11.7km2, lieswithintheFIFE site. TheFIFE siteis of interest
because of the detailed measurements
of surface fluxes that
were collectedin the summerof 1987. DuringtheperiodMayOctober 1987, four intensivefield campaigns(IFCs) were
conductedat the site, duringwhich tower-basedmeasurements
of latent, sensible,and ground heat fluxes were made. In
addition,throughout
the summerof 1987,a networkof portable
automatedmesonet(PAM) stationswas operated,from which
measuredvalues of incoming solar and long-wave radiation,
andothermeteorological
dataare available. Furthermore,
longterm streamflowdata exist for Kings Creek, alongwith long-
roc[1],s/m
100.0
do[1],m
0.25
Zo[1],m
0.07
Cv[1]
1.0
fl[l]
1.0
f2111
0.0
T2,øK
293.6
•[1]
0.2
r[1], W m'1 K'1
0.514
Cs[l],Jm-3K-1
2.13x106
LIANG ET AL.'
HYDROLOGICALLY
BASED LAND SURFACE FLUX MODEL
14,423
10
observed
modeled
15
.......
10
,
Oct
Dec
Feb
Apr
Water
Year
Jun
Oct
Aug
Dec
Feb
Apr
Jun
,
,
Aug
Water Year 1987
1 986
Figure 5. Predicted(dotted)andobserved
(solid)streamflow
for KingsCreekfor verificationyears19861987.
Surfacemeteorological
and surfaceflux data at the FIFE site
are limited to selectedperiodsduringthe summerof 1987.
Data from the PAM stationsinclude surfacepressure(p),
estimatethe hydrologicalparametersusingprecipitationand
streamflowdatafor part of the long-termKingsCreekrecord,
and to evaluate its hydrological performance using the
remainingpart of the record. The model's surfaceflux
algorithms were then parameterizedand validated using
wind speed(u) measured
at 5.4 m abovegroundlevel, surface
measuredfluxes observedduringthe summer1987 IFCs.
temperature
(T,), ground
soiltemperatures,
T•0andTs0,at 10
mixingratio(t0) andair temperature
(Ta)at the2-m leveland
Daily precipitationand temperaturemaximum/minimum cm and 50 cm below the surface,respectively,and downward
data have been collected at Manhattan, Kansas,which is about short- and long-wave radiation. Radiation data were also
11 km from the centroidof the Kings Creek catchment,which collectedfrom flux stations(eddycorrelationandBowenratio).
has been gaugedsincethe late 1800s. Daily averagestream Data from both PAM stationsand flux stationswere averaged
dischargedata for Kings Creek (U.S. GeologicalSurveyNo. for each date and time amongall the stationsby Betts et al.
analysisof the radiation
06879650,11.7 km2) havebeencollected
sinceabout1980. [1993]. Theyfoundfrom consistency
6OO
......
400
observed
modeled
3oo
500
400
v
x
200
300
"-'
100
200
..c
0
IO0
.9_ -100
•
0
30
2
4
6
8
-200
10
30
2
4
6
8
10
30
2
4
6
8
10
20O
15o
100
50
-•
310
,-
300
E
0
•
290
•
280
i
io•
,
-5o
(..9
-100
30
2
4
6
8
10
Figure 6. Comparison
of predicted(dotted)andobserved
(solid)surfacefluxesandsurfacetemperature
at the
FIFE sitefor June30-July11, 1987 (IFC 2).
14,424
LIANG ET AL.' HYDROLOGICALLY BASED LAND SURFACE FLUX MODEL
datathat the flux datawere more self-consistent
internallythan
the PAM data basedon the comparisonof the calculatedand
the same mean as the Penman-Monteithestimates,using an
measured net radiation.
1.64 with a standarddeviationof 0.70 over the 35 days. The
scaledHamonestimateswere usedfor the long-termhydrologic
water balancecomputations,
exceptduringthe IFC periods,
whenthe dataneededfor computation
of the Penman-Monteith
Therefore we used the radiation data
from the flux stationsand the atmosphericdata from PAM
stationsto test our model surfaceflux and surfacetemperature
predictions.Data for 35 dayscommonto the two datasetsin
the summerof 1987 were used. They are June 30-July 11,
August9-20, and October6-16.
The model parameterscan be classifiedinto hydrological
parametersand atmosphericallyrelated parameters. The
hydrologicalparametersincludethe infiltrationshapeparameter
adjustment
factorke,whichwasdetermined
to havea meanof
Ep[1] wereavailable.
During
theIFCperiods,
Ep[1] andrw[
1]
were estimatedby the Penman-Monteithmdthod and by
equation(3), respectively.
For the 35 days of the IFCs, we calculatedan average
aerodynamic
resistance
(equalto the inverseof the productof
bi (equation
(13)),thesoilporesizedistribution
index
Bp,the the drag coefficientfrom equation(4b) and the wind speed
residual moisture content 0r, the saturatedhydraulic under the assumptionthat the resistanceto the transferof
conductivity
K, (equation
(20)), the threebaseflow related momentumand water are equal). This averageaerodynamic
parameters
D•, Din,andWs (equation
(21)),themaximum
soil resistancewas then used for the purposeof estimatingthe
moisturecontentsW[ and W2
• in layers1 and2, respectively hydrologicalmodel parameters,and for computingthe soil
(equations(17) and (21)), the soil moisturecontentat the moistureat the beginningof the first IFC and betweenIFCs
wiltingpointWf andat the criticalpointWf• (/'=1,2)in (but not for validationof the energyfluxesduringthe IFCs
resistance
equation (7). Atmosphericallyrelated parametersinclude reportedin section4). The averageaerodynamic
architectural
resistance
ro[n] (equation
(1)), minimumcanopy overthe 35 dayswas40.8 s/mwith a standarddeviationof 29.7
resistance
roc[n
] (equation
(6)), leafareaindexLAI[n,rn](n=l, s/m. This value is within the rangegiven for shortgrassand
2, . . . , N; rn=l, 2....
, 12) for each surfacecover class cropsby Monteithand Unsworth[1990]. Sincethe roughness
as wind speedincreases,
the
(equation(6)), the zero plane displacement
heightdo[n], lengthof many cropsdecreases
resistance
is approximately
a constant
roughness
lengthZo[n
] (equation
(4a)),andtherelativefraction inverseof aerodynamic
of rootsin eachof thetwosoilzones
f• In] andf2[n] (equation overa rangeof low wind speeds.The dailyaveragewind speed
(8)). We classify
f•[n] andf2[n] as atmospherically
related during the 35 days was 2.38 m/s, and the aerodynamic
(40.8 s/m)wastakenasconstant
for the estimation
of
parameters because they determine the canopy resistance resistance
the
three
hydrological
parameters.
In
addition,
we
did
not
(equations(6)-(8)).
Amongthehydrological
parameters,
onlythree(bi,D.eand correct for atmospheric stability, primarily to assure
ofEp[1]
between
theIFCsandduring
thelonger
Ws)wouldbestbe estimated
usingstreamflow
dataif theyare compatibility
waterbalancesimulation,
whenthedata
available(it shouldbe notedthatbothA•.andio in equations periodof hydrological
(15) and (18) are not modelparameters,
they are evaluatedat
eachtime step). The other hydrologicalparameterscan be
estimatedusing,for instance,soil characteristics.Clearly, for
application in GCMs, global parameter estimation using
streamflowdata is infeasible;for GCM applicationsDamenil
needed to make the correctionswere not available. However,
the stability correctiongiven by equations(3) and (4) was
appliedto the energyflux computations
performedfor the
modelvalidationsreportedin section4.
At theFIFE site,the depthsof layer 1 (upperzone)andlayer
2
(lower zone) are about 0.5 m and 2.5 m, respectively
andTodini[1992]havesuggested
valuesforbi,Ds,andWs. An
(Famiglietti
and Wood, submittedpaper 1). Sincethe soil
ongoingresearch
topic,whichwill be investigated
in the Global
ProtectionAgency
Energyand Water ExperimentContinentalScaleInternational textureat FIFE is silt loam [Environmental
•
Project(GCIP), is to developregionalrelationships
for GCM (EPA), 1991],the porositywastakento be 0.5, andthusW•
• =1.25m,andWf andWfr areabout
26%and
hydrologicalparameters. However,becausestreamflowdata =0.25m andW2
were availablefor Kings Creek,we madeuse of the observed 46% of the total water that the soil can hold. However,Smithet
al. [1993]reportedthat evapotranspiration
wasnot observed
to
datatoestimate
bi,D•, andWs.
be
limited
by
soil
moisture
in
the
20%-30%
range,
and
they
In orderto estimate
bi, Ds, andWs through
calibration,
we
needto knowE [1] andrw[1], in addition
to otherparameterstook 18% as the wilting point instead,which we alsousedas
ourestimate.In this studywe used70% of field capacityasour
Zo[1],ro[1],roe[l],andLAI[1,m](m=l, 2, . . . , 12). At the criticalpoint(we foundvia sensitivityanalysisthat almostthe
like
Wf,Wf,4cr(J':l,
2),Ks,B,,0r,
f•[ll,f2[1
],Un(Z2),
do[1
],
FIFEsite,thedatarequired
to estimate
Ep[1]bythePenman-sameresultswere obtainedwhen the criticalpoint was 75% of
Ks.
, Bp,Or weretaken
as6.44mm/h,
0.16,and
Monteith
method
andrw[1
] by equation
(3) areavailable
only fieldcapacity).
duringthe IFCs. Thereforefor the purposesof estimatingthe
hydrologicalparameters,we usedHamoffsmethod[Hamonet
al., 1954; Hamon, 1961] which requires only daily air
0.01 m, respectively, following Famiglietti and Wood
(submittedpaper 1). Sincethe vegetationis dominatedby
grass,we assumed
thatall therootsarein the upperzone(i.e.,
).
temperature
andlatitude
to estimate
Ep[1]. During
summerf•[1]=l.0 andf211]=0.0
1987 we also used E [1] via the Hamon method for the
between-IFCperiodsto allow continuous
computation
of soil
moisture(neededas initial valuesduringthe IFCs). The daily
Becausethe wind speed from the PAM stationswas
measuredat 5.4 m abovethe groundsurface,and the other
Ep[1]computed
using
theHamon
formula
wascompared
with
thedailyEp[1]obtained
using
Penman-Monteith's
equation
for
surface,thewind speedwasconverted
to the 2 m levelthrough
a logarithmicvelocityprofile. Sugitaand Brutsaert[1990]
meteorological
dataweremeasured
atz211
]=2 m above
ground
thezeroplanedisplacement
heightdo[1
]=26.9m, and
the 35 daysof the 1987 FIFE IFCs. The comparison
indicated estimated
thatthe HamonequationgivessmallerE_[1] estimates,
but the thesurface
roughness
length
Zo[1]=l.05
m atFWEbyanalyzing
pattern over the 3S-day period was ramilar for both E [1] neutralwind velocityprofilesmeasuredby radiosondes.They
estimates. Therefore we scaled the Hamon estimates to have
foundthat a logarithmicvelocityprofile only holdsover the
LIANG ET AL.: HYDROLOGICALLY
BASED LAND SURFACE FLUX MODEL
heightrangesbetween50 m + 19 m and 202 m+ 101 m above
14,425
surface temperatureagainst with the measuredones. The
thegroundsurface.However,theirvaluesshouldbe interpreted albedo c•[1] was taken as 0.2 during the IFCs following
in the contextof the Flint Hills region,which is characterized Famiglietti and Wood (submittedpaper 1). The thermal
by relief of about25 m betweensteepridgesandvalleys. By conductivity
•:[1] andsoilheatcapacity
Cs[1
] in equation
(33)
contrast,Smith et al. [1992a] usedmuch smallerlocal valuesof wereestimated
to be 0.514W m-• K-• and2.13x106J m-3K-1,
do[1]=0.25
m, andZo[1]=0.07
m. Theirvaluesfall between respectively,followingSmithet al. [1992b, 1993]. The depth
uncutgrassandlonggrass/crops
for a relativelyflat area[Arya, D2wastakentobe0.45m, andthetemperature
T2 (i.e.,T5o
) in
1988]. Sincethe FIFE siteis only a smallpart of the Flint Hills equation(33) was prescribedas 293.6 øK, which was the
regionwhichcoversa 50- to 80-km-widenorth-south
stripin averageof T5ofor the selected
35 daysof the IFCs. The
Kansas from Nebraska to Oklahoma, we decided to use the
standard
deviation
of T5oforthe35 dayswas3.1 øK. All the
relatedmodel
smallervaluesfor do[1]andZo[1
], andassumed
a logarithmic valuesof the hydrologicallyandatmospherically
velocityprofile locally. The 2-m wind speedcan then be
estimated as
parametersare listed in Table 2. We comparedthe surface
energybudgetscomputedusingbothequation(25) andequation
(27), and found that there was almost no differencein the
results
whenwetookza[1]=z211
]=2m.
u,(z2)= u,(z•)
(39)
4. Model
Validation
Figures 5a and 5b showpredictedand observedstreamflow
for 1986 and 1987, 2 years not in the calibrationperiod.
wherez•[1]=5.4m, andun(z•)is thecorresponding
measuredGenerally, the results are consistentwith those of the
windspeed.Thevalueof to[1] forgrassland
istakenas2.0 s/m calibration period: the dry period flows are fairy well
[Ducoudreet al., 1993]. Monteith and Unsworth[1990] represented,as is the timing of the major peaks, but the
suggest
thatfor grassland
roe[1]=100s/m. Smithet al. [1993] magnitudesof the peaks,especiallythe largestones,are subject
foundthatbothroe
[1]=100s/mandroc
[1]=125s/mareamong to major errors. In this study,streamflowpredictionis not a
thebestvaluestheyobtained
throughan optimization,
with the goalper se, instead,our purposein evaluationof the predicted
is to provideevidencethat the modelis producing
latterslightlybetter. Thuswe takeroc[1]=100
s/m. The hydrographs
a
reasonable
soilwaterbalance.To this extent,the hydrograph
monthlyaverageLAI[ 1,m](re=l, 2,..., 12)werederivedfrom
werejudgedadequate.
the averagenormalizeddifferencevegetationindex (NDVI) simulations
After estimatingthehydrologicalmodelparameters,
we used
givenbyEPA[1991
] withLAImax=6.0
andLAIm•=0.1
which
the
FIFE
surface
fluxes
and
meteorological
measurements
for
areconsistent
withthevaluesusedby Smithet al. [1993],
the summerof 1987 to test the modelpredictionsof latentheat,
sensible heat and ground heat fluxes, and the surface
LAI[1,m]
=0.1+0.0628(NDVI
l- 53.0) (40) temperature.
We usedthe Kings Creek precipitationnetwork,
The averagemonthlyNDVIs for 1986, 1987, and 1988 at FIFE as well as the precipitation,air temperature,and downward
are listed in Table 1.
solarand long-waveradiationcompositedfrom the PAM and
Thehydrological
parameter
Dmcanbe eitherestimated
by flux stationsby Bettset al. [1993] to testthe modelheatfluxes
identifyingextendeddry periodsduringthe calibrationinterval andsurfacetemperature.Resultsare shownin Figures6, 7, and
1982-1985 using the precipitationdata, and recessionrates 8 for partsof the June,July,August,andOctoberIFCs.
inferred from the observedKings Creek stream
flows during
Figure 6 showspart of IFC 2 (from June 30 - July 11).
these periods; or by multiplying saturated hydraulic Therewere precipitationeventson June30 and July 7. On the
conductivityby an average soil slope. We used the first rest of the days, there was little or no rainfall. During this
approach,
whichgaveDm = 8.2 mm/d. The hydrologicalperiod,the latentheatflux for dry dayswastypicallyabout400
thelatentheatandsensible
heat
parameters
bi andDs,andWs,wereestimated
usingstream
flow W m-2 . Themodelpredicted
at Kings Creek, and precipitation,and maximum/minimum fluxes fairly well, exceptthat it somewhatunderpredicted
the
temperaturedata at Manhattan,Kansasfrom 1982-1985. The July 9, 10, and 11 latent heat fluxes and overpredicted
the
calibration
gavebi=0.008,
Ds=7.7x10-5,
andWs=0.96.It sensibleheat fluxes on the same days. These days were
shouldbe mentionedthat the one-layersnowmeltmodelwas characterizedby relatively high winds, high potential
not usedto obtainthe abovemodelparameters,sincenot much evaporation,and high soil moisture. The surfacetemperatures
snowoccursin the KingsCreekcatchment.Hydrographs
for agreewith the observedonesquite well, but the magnitudeof
on
two of the calibrationyears (1983 and 1984) are shownin the diurnalcycleof the groundheatflux wasunderpredicted
Figures4a and 4b. The model reproducesthe streamflow someof the days.
Figure7 showspredictedand observedlatent,sensible,and
reasonably
well; discrepancies
areattributed
to (1) the distance
of the precipitationgagefrom the KingsCreekcatchment;
(2) groundheat fluxes, and surfacetemperature,for the August 9the inability of a singlegageto representspatialvariationsin 20, 1987,portionof the third IFC. RainfalloccurredonAugust
precipitation;(3) the use of a daily time stepfor a relatively 12, 13 and 18. Before the August 12-13 storm,the soil was
small catchment whose time of concentration is of the order of
moderatelydry. During this period, the observedlatent heat
an hour or less;and(4) small-scaleheterogeneities
whichcan
fluxeswerelessthan300 W m-2. After the rainfall,the latent
stronglyaffect runoff productionin small catchmentsand are
not capturedby a macroscale
modelsuchasVIC.
heatfluxesincreased
to about400W m-2. Duringthisperiod,
With the parametersdescribedabove,togetherwith the
parameters
c•[1], •:[1], Cs[1], D2,andT2,wethenusedthePAM
and flux data to test our model-predicted
surfacefluxes and
the model predictedthe latent heat and sensibleheat fluxes
quitewell, exceptduringthe nightsof August14 and 15, when
the latentheat fluxeswere overpredicted
and the sensibleheat
fluxes were underpredicted.This is mainly due to the high
14,426
LIANG ET AL.' HYDROLOGICALLY BASED LAND SURFACE FLUX MODEL
600
......
400
observed
modeled
500
3O0
400
200
300
100
20O
0
100
o
-100
-200
9
11
13
15
17
19
2OO
150
100
5O
•.-
310
,-
300
E
0
-50
•
290
•
280
-leo
9
11
13
15
17
19
9
11
13
15
17
19
Figure7. Comparison
ofpredicted
(dotted)
andobserved
(solid)
surface
fluxes
andsurface
temperature
atthe
FIFE siteforAugust9-20,1987(IFC 3).
potential evaporation obtained during that time.
From
equations
(1) and (5), it can be seenthat large evaporation
wouldbe obtainedif the potentialevaporation
is large,even
5. Conclusions
We have describeda land surfacemodel designedfor
though
therw[n
] andrc[n] arereasonable.
Duringthisperiod, application
within coupledland-atmosphere-ocean
GCMs. The
thegroundheatfluxeswerepredicted
reasonably
well, although modelis formulatedto be appliedasa fully coupled
waterand
therewas a tendencyto underestimate
the magnitudeof the energybalancesystem. The land surfacehydrologyis a
diurnalcycle. Thesurface
temperatures
werewell predicted
in generalization
of theVIC (variableinfiltrationcapacity)
model
general.
whichincorporates
a two-layerdescription
of the soil column,
Figure8 showsthe energyfluxesandsurfacetemperature
for in whichthe upperlayer is characterized
by the usualVIC
October6-16, 1987, a portionof IFC 4 whichwas characterized spatialdistributionof soil moisturecapacities,
andthe lower
by low soil moisture. Duringthis period,the observedlatent layer is spatiallylumped,and usesthe Arno [Franciniand
heatfluxeswere about100 W m-2 or less,while the sensible Pacciani,1991] drainageterm. The modelpartitionsthe area
heatfluxesincreased
to about300W m-2 (fromabout200 W of interest(e.g.,gridcell) intoN+I landsurfacecovertypes;for
m-2 in JulyandAugust).Themodelpredicts
thelatentand eachlandcovertypethefractionof rootsin theupperandlower
sensible
heatfluxes,andsurfacetemperature,
reasonably
well, zone is specified. Evaporation and transpirationare
butit overpredicts
the groundheatfluxesonmostof the days parameterizedby a Penman-Monteith
formulation,applied
duringthisperiod.
separately
to bare soil and vegetationclasses. Evaporation
In general, the model performedquite satisfactorily, fromwaterintercepted
by thevegetation
is alsorepresented.
In
especiallygiven its simplicity. There are some caveatsin addition, the model contains an energy-basedsnow
interpretationof the results. First, the FIFE site is a native accumulation
andablationparameterization.
grassland,
whichis characterized
by a singlevegetation
type.
Althoughthe model is formulatedfor a fully coupled
Therefore
theportionof themodeldealing
withheterogeneousapplication
within a GCM, it canalsobe run "off-line"using
vegetationwas not exercisedin these tests, so the effects of observedenergy and water fluxes (or their surrogates,
certain associatedsimplificationsare not reflected in the especiallyin the caseof radiationforcings)as forcings. The
results. A second,related limitation is that since the FIFE
importance
of off-line simulationfor this particularmodelis
vegetation
is all grassland,
the algorithms
dealingwith trees, that it allowsthat hydrologicparametersto be calibratedso as
whichusuallyextractmoisturefromthe lower,ratherthanthe to maintain long-term, observedwater balances. This was
upper,soilmoisturezonehavenot beenexercised.We have, accomplished,
in the absenceof long-term(multipleyear)
however,implemented
the model for a tropicalforest radiationdata,usingsurfaceair temperature
asa surrogate
(via
application
in connection
withtheProject
forIntercomparison
Hamoffsmethod)to estimatethepotentialevapotranspiration.
of Land-surface
Parameterization
Schemes
[Pitman
etal., 1993; With estimates
of potentialevapotranspiration,
the landsurface
Lianget al., 1993],andthemodelresults
werecomparable
to hydrologyparameterscan be estimatedusing observed
thoseof mostof theparticipating
models.
precipitation
and streamflow.This approach
is an important
LIANG ET AL ß HYDROLOGICALLY
600
......
500
BASED LAND SURFACE FLUX MODEL
14,427
4OO
observed
modeled
300
400
300
100
2O0
0
100
-100
-200
0
6
8
10
12
14
16
6
8
10
12
14
16
6
8
10
12
14
16
2OO
310
150
100
300
50
290
0
-50
280
-lOO
6
8
10
12
14
16
Figure8. Comparison
of predicted
(dotted)andobserved
(solid)surface
fluxesandsurfacetemperature
at
FIFE site for period of extremely dry soil moisture during October 6-16, 1987
(IFC 4).
stepto applicationof improvedland surfaceschemes
wittfin References
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