Calibration approaches for distributed hydrologic models in poorly gaged basins

28 Pages·2015·6.06 MB·English

Hydrol.EarthSyst.Sci.,19,857–876,2015
www.hydrol-earth-syst-sci.net/19/857/2015/
doi:10.5194/hess-19-857-2015
©Author(s)2015.CCAttribution3.0License.
Calibration approaches for distributed hydrologic models
in poorly gaged basins: implication for streamflow
projections under climate change
S.Wi1,Y.C.E.Yang1,S.Steinschneider1,A.Khalil2,andC.M.Brown1
1DepartmentofCivilandEnvironmentalEngineering,UniversityofMassachusettsAmherst,USA
2TheWorldBank,Washington,DC,USA
Correspondenceto:S.Wi([email protected])
Received:10August2014–PublishedinHydrol.EarthSyst.Sci.Discuss.:17September2014
Revised:13January2015–Accepted:20January2015–Published:10February2015
Abstract. This study tests the performance and uncertainty equifinality does emerge. The results suggest that increased
ofcalibrationstrategiesforaspatiallydistributedhydrologic (excessive)parametercomplexitydoesnotalwaysleadtoin-
model in order to improve model simulation accuracy and creased predictive uncertainty if structural uncertainties are
understandpredictionuncertaintyatinteriorungagedsitesof present. The largest uncertainty in future streamflow results
asparselygagedwatershed.Thestudyisconductedusinga fromvariationsinprojectedclimatebetweenclimatemodels,
distributed version of the HYMOD hydrologic model (HY- whichsubstantiallyoutweighsthecalibrationuncertainty.
MOD_DS) applied to the Kabul River basin. Several cali-
bration experiments are conducted to understand the bene-
fits and costs associated with different calibration choices,
including (1) whether multisite gaged data should be used 1 Introduction
simultaneously or in a stepwise manner during model fit-
ting,(2)theeffectsofincreasingparametercomplexity,and Inanefforttoadvancehydrologicmodelingandforecasting
(3) the potential to estimate interior watershed flows using capabilities, the development and implementation of physi-
only gaged data at the basin outlet. The implications of the callybased,spatiallydistributedhydrologicmodelshaspro-
different calibration strategies are considered in the context liferated in the hydrologic literature, supported by read-
of hydrologic projections under climate change. To address ily available geographic information system (GIS) data and
the research questions, high-performance computing is uti- rapidly increasing computational power. Distributed hydro-
lized to manage the computational burden that results from logicmodelscanaccountforspatiallyvariablephysiographic
high-dimensionaloptimizationproblems.Severalinteresting properties and meteorological forcing (Beven, 2012), im-
resultsemergefromthestudy.Thesimultaneoususeofmul- proving simulations compared to conceptual, lumped mod-
tisite data is shown to improve the calibration over a step- elsforbasinswherespatialrainfallvariabilityeffectsaresig-
wise approach, and both multisite approaches far exceed a nificant (Ajami et al., 2004; Koren et al., 2004; Reed et al.,
calibration based on only the basin outlet. The basin out- 2004;Khakbazetal.,2012;Smithetal.,2012)andfornested
let calibration can lead to projections of mid-21st century basins(Bandaragodaetal.,2004;Brathetal.,2004;Korenet
streamflowthatdeviatesubstantiallyfromprojectionsunder al., 2004; Safari et al., 2012; Smith et al., 2012). The ben-
multisitecalibrationstrategies,supportingtheuseofcaution efits of distributed modeling have been recognized by the
whenusingdistributedmodelsindata-scarceregionsforcli- U.S. National Oceanic and Atmospheric Administration’s
matechangeimpactassessments.Surprisingly,increasedpa- National Weather Service (NOAA/NWS) and demonstrated
rameter complexity does not substantially increase the un- in the Distributed Model Intercomparison Project (DMIP)
certainty in streamflow projections, even though parameter (Reed et al., 2004; Smith et al., 2004, 2012, 2013). Impor-
tantly,distributedhydrologicmodelscanevaluatehydrolog-
PublishedbyCopernicusPublicationsonbehalfoftheEuropeanGeosciencesUnion.
858 S.Wietal.:Implicationforstreamflowprojectionsunderclimatechange
icalresponseatinteriorungagedsites,abenefitnotafforded let gage (which is often all that is available in developing-
by lumped models. The use of distributed hydrologic mod- country river basins). In the case of significant spatial vari-
eling for interior point streamflow estimation is particularly abilityinthebasinpropertiesthatinfluencerunoffgeneration
relevant for poorly gaged river basins in developing coun- (e.g., permeability, vegetation, and slope), accurate runoff
tries, where reliable predictions at interior sites are often predictions are unlikely at interior locations based only on
required to inform water infrastructure investments. As in- thelumpedinformationobtainedatthebasinoutlet(Ander-
ternational development agencies begin to integrate climate sonetal.,2001;Caoetal.,2006;Breueretal.,2009;Leratet
change considerations into their decision-making processes al.,2012;Smithetal.,2012;Wangetal.,2012).Theextent
(e.g., Yu et al., 2013), these investments need to be robust of this error and uncertainty is not well understood for het-
underbothcurrentclimateconditionsandpossiblefuturecli- erogeneousbasinsduetothecomputationalexpenserequired
materegimes. toexplorethisissue.Finally,rarelyhavetheimplicationsof
Despitetheirrootsinphysicalrealism,distributedhydro- these calibration issues been explicitly examined for possi-
logicmodelscansufferfromsubstantialuncertainty.Amajor ble future climate conditions, which is required in climate
source of uncertainty originates from the proper identifica- change impact studies. This question has been explored for
tionofparametervaluesthatvaryacrossthewatershed,espe- lumped, conceptual models (Wilby, 2005; Steinschneider et
ciallywhenobservedstreamflowdataisonlyavailableatone al.,2012),buthasbeendifficulttoevaluateforcomputation-
orafewpoints(Exbrayatetal.,2014).Parameterscanbedis- allyexpensivedistributedmodels.
cretizedacrossthewatershedinseveralways(Flugel,1995; Thisstudyaddressestheaboveresearchchallengesbyfo-
Efstratiadisetal.,2008;Khakbazetal.,2012):uniquelyfor cusingonthefollowingfourquestions:(1)howdoescalibra-
eachgridcellorhydrologicresponseunit(fullydistributed), tion procedure for using multisite data affect the accuracy
based on sub-basins whose boundaries do not necessarily and uncertainty of distributed models used for streamflow
ensure homogenous characteristics (semi-distributed) or, in predictionsatungagedsites;(2)whateffectsdoesincreased
the simplest case, a single parameter set for all model grid parameter complexity have on distributed model calibration
cells (lumped). With limited data, the parameter identifica- andprediction;(3)howmuchdegradationinmodelaccuracy
tion problem, particularly for the fully distributed case, can anduncertaintycanbeexpectedforinteriorflowestimation
be impractical or infeasible (Beven, 2001). The parameteri- based on a calibration procedure using only the basin out-
zation challenge has spurred substantial advances in under- let; and (4) how do different calibration formulations for a
standing appropriate calibration techniques for distributed distributedmodelalterprojectionsofstreamflowatungaged
hydrologic models. Many studies have attempted to reduce sites under climate change conditions? These questions are
thedimensionalityofthecalibrationproblemtoalleviatethe considered in an application of a distributed version of the
issue of equifinality (Beven and Freer, 2001), which is the daily HYMOD hydrologic model to the Kabul River basin
phenomenon whereby multiple parameter sets produce in- inAfghanistanandPakistan.Toaddresstheseresearchques-
distinguishablemodelperformance.Thisworkhasfoundfa- tions,high-performancecomputingisutilizedtomanagethe
vorable results when the parametric complexity of the dis- computational burden that often hinders such explorations
tributedmodelisalignedwiththedataavailableforcalibra- (LaloyandVrugt,2012;Zhangetal.,2013).
tion (Leavesleyet al.,2003; Ajami etal., 2004;Eckhardt et
al., 2005; Frances et al., 2007; Zhu and Lettenmaier, 2007;
ColeandMoore,2008;PokhrelandGupta,2010;Khakbazet 2 Studyarea
al.,2012).Therehasalsobeenextensiveresearchexploring
theuseofmultipleobjectivesanddifferentoperationalproce- The Kabul River basin (67370km2) is a plateau sur-
durestounderstandparameterestimationtradeoffsandiden- rounded by mountains located in the eastern central part of
tifiability for distributed model calibration, with great suc- Afghanistan (Fig. 1). It is the most important river basin of
cess (Madsen, 2003; Efstratiadis and Koutsoyiannis, 2010; Afghanistan, containing 35% of the country’s population.
Lietal.,2010;Kumaretal.,2013). While it encompasses just 12% of the area of Afghanistan,
Despitetheseadvances,importantquestionsstillpersist.It the basin’s average annual streamflow (about 24 billion cu-
stillremainsdifficulttocomparetheuncertaintythatemerges bic meters) is about 26% of the country’s total streamflow
from different operational calibration procedures for mul- volume(WorldBank,2010).
tisite applications (i.e., whether gages in series should be WaterresourcesfromthebasinaresharedbyAfghanistan
usedsequentiallyorsimultaneouslyforcalibration)andun- andPakistanandserveasawatersupplysourceformorethan
der different levels of parametric complexity. Due to the 20millionpeople.Theshareduseoftransboundarywaterbe-
computationalburdenrequiredtocalibratedistributedmod- tweenthesetwocountriesiscentralinestablishingregional
els, this uncertainty is problematic to explore. Furthermore, waterresourcesdevelopmentforthisarea(Ahmad,2010).It
inpoorlygagedbasins,itischallengingtoquantifythelost iscrucialtodeveloptoolsthatcansupportengineeringplans
accuracy and increased uncertainty for interior flow estima- forexistingandpotentialwaterinfrastructuretotakefullad-
tion when a distributed model is calibrated only at an out- vantageofthewaterresourcesinthebasin.Thegovernment
Hydrol.EarthSyst.Sci.,19,857–876,2015 www.hydrol-earth-syst-sci.net/19/857/2015/
S.Wietal.:Implicationforstreamflowprojectionsunderclimatechange 859
Figure1.KabulRiverbasin.
of Afghanistan has developed comprehensive plans for new 70%ofannualprecipitation(475mm)fallsduringthewin-
hydropowerprojectsontheKabulRiverowingtoitsadvanta- terseason(November–April).Whilethedominantsourceof
geous topographyfor the developmentof waterstorage and streamflowinwinterisbaseflowandwinterrainfall,glaciers
hydropower (IUCN, 2010), and recently reached an agree- and snow cover are the most important long-term forms of
ment with the Pakistan government to work on a 1500MW water storage and, hence, the main source of runoff during
hydropowerprojectontheKunarRiver(oneofmajortribu- theablationperiodforthebasin(Shakiretal.,2010).Into-
taryintheKabulRiverbasin)aspartofthejointmanagement tal, 2.9% (1954km2) of the basin is glacierized based on
ofcommonriversbetweenthetwocountries(DAWN,2013). the Randolph Glacier Inventory version 3.2 (Pfeffer et al.,
ThestreamflowregimeoftheKabulRivercanbeclassifiedas 2014). The meltwater from glaciers and snow produce the
glacial with maximum streamflow in June or July and min- majority(75%)ofthetotalstreamflow(Hewittetal.,1989).
imum streamflow during the winter season. Approximately Table 1 provides the climates and geophysical properties of
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860 S.Wietal.:Implicationforstreamflowprojectionsunderclimatechange
Table1.StreamflowgagingstationsintheKabulRiverbasin.
Dataperiod Physiographicproperty Basinclimate
Datasource Station River Start End Drainage Glacier Mean Mean Mean Mean
name area(km2) area(%) elev.(m) annual annual annual
Prcp. mean flow
(mm) Temp.(◦C) (mm)
USGS/ Dakah Kabul 2/1968 7/1980 67370 2.9 2883 418 7.7 282
GRDC
USGS/ Pul-i-Kama Kunar 1/1967 9/1979 26005 7.3 3446 446 5.6 573
GRDC
USGS Asmar Kunar 3/1960 9/1971 19960 9.4 3716 483 4.1 651
GRDC Chitral Kunar 1/1978 12/1981 11396 14.4 4126 518 2.1 698
USGS Gawardesh Landaisin 5/1975 6/1978 3130 2.1 3707 555 4.5 521
USGS/ Chaghasarai Pech 2/1960 2/1979 3855 0.4 3141 482 7.4 535
GRDC
USGS/ Daronta Kabul 10/1959 9/1964 34375 0.3 2722 350 8.0 165
GRDC
eachsub-watersheddelineatedbythestationslocatedinside the Supplement). Thus, the APHRODITE precipitation was
the Kabul Basin (Fig. 1). Two different climate patterns are bias-correctedbytheprecipitationproductfromtheUniver-
distinguishableacrossthesub-basins.Thesub-basinsonthe sityofDelawareglobalterrestrialprecipitation(UD)dataset
Kunar River tributary (Kama, Asmar, Chitral, Gawardesh, (LegatesandWillmott,1990).Dailyseriesofbias-corrected
andChaghasarai)receivemoderateannualprecipitationand APHRODITEprecipitationwerecoupledwithAPHRODITE
arehighlyaffectedbysnowandglaciercovers.Allofthese temperature for 160 0.25◦C grid cells to produce a climate
sub-basinshavehighratiosofmeanannualflowtomeanan- forcingdatasetforthedistributeddomainoftheKabulRiver
nualprecipitation,withtheratiosfortheKama,Asmar,Chi- basinmodel.
tral, and Chaghasarai sub-basins larger than 1. Conversely, This study used the set of global climate change simula-
the Daronta sub-basin contains only minimal glacial cover, tions from the World Climate Research Programme’s Cou-
and is relatively dry. Daronta is also much less productive, pled Model Intercomparison Project Phase 5 (CMIP5) mul-
with annual streamflow far below the other sub-basins with timodel ensemble (Talyor et al., 2012). Monthly climate
anaverageofonly165mmyr−1. outputs of GCMs (general circulation models) were down-
IssuesofsharedwaterresourcesbetweenAfghanistanand scaledtoadailytemporalresolutionand0.25◦Cspatialres-
Pakistan in the Kabul River basin are becoming complex olution based on the bias-correction spatial disaggregation
duetotheimpactsofclimaticvariabilityandchange(IUCN, (BCSD)statisticaldownscalingmethodintroducedbyWood
2010). The vulnerability of glacial streamflow regimes to etal.(2004).
changesintemperatureandprecipitation(Stahletal.,2008; Monthly streamflow observations for seven locations in
Immerzeeletal.,2012;Radicetal.,2014)highlightstheneed theKabulRiverbasin(Fig.1)weregatheredbetweencalen-
toassesstheimpactofclimatechangeonfuturewateravail- dar years 1960 and 1981 from two data sources: the Global
abilityinthisarea. RunoffDataCentre(GRDC)databaseandtheUnitedStates
Geological Survey (USGS) database (Table 1). Streamflow
datawerenotcollectedinAfghanistanafterSeptember1980
3 Dataandmodels
untilrecentlybecausestreamgagingwasdiscontinuedsoon
aftertheSovietinvasionofAfghanistanin1979(Olsonand
3.1 Data
Williams-Sether,2010).Thoughmeasurementsweretakenat
adailytimestep,dataareonlymadeavailableforpublicuse
Griddeddailyprecipitationandtemperatureproductswitha
spatialresolutionof0.25◦Cweregatheredbetweencalendar at monthly aggregated levels, calculated using the mean of
thedailyvalues.Theavailablemonthlystreamflowobserva-
years 1961 and 2007 from the Asian Precipitation Highly
tionsateachstationwereusedforcalibratingandvalidating
Resolved Observational Data Integration Towards Evalua-
thedistributedhydrologicmodel(Fig.2).KamaandAsmar
tion(APHRODITE)dataset(Yatagaietal.,2012).Therehas
stationsaretreatedasungagedsitesbecausetheyalignwith
been some concern regarding underestimation of precipita-
the potential dam project on the Kunar River tributary. The
tion in APHRODITE for some regions of Asia (Palazzi et
two gage stations are left out of the processes of multisite
al., 2013); our preliminarily data analysis (intercomparison
calibrationsinordertoevaluatethemodel’sabilitytopredict
of precipitation products between five different databases)
streamflowatinteriorungagedsites.Furthermore,halfofthe
confirmedthisfortheKabulRiverbasin(showninFig.S1in
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S.Wietal.:Implicationforstreamflowprojectionsunderclimatechange 861
sentsoilmoistureaccounting,evapotranspiration,snowpro-
cesses, glacier processes and flow routing. The model op-
erates on a daily time step and requires daily precipitation
andmeantemperatureasinputvariables.Theoverallmodel
structure of the HYMOD_DS and its 15 parameters are de-
scribedinFig.3andTable2,respectively.Furtherdetailsare
providedbelow.
The HYMOD conceptual watershed model has been ex-
tensively used in studies on streamflow forecasting and
model calibration (Wagener et al., 2004; Vrugt et al., 2008;
Kollat et al., 2012; Gharari et al., 2013; Remesan et al.,
2013). The HYMOD is a soil moisture accounting model
based on the probability–distributed storage capacity con-
Figure2.Streamflowdatausageforthemodelcalibrationandval- ceptproposedbyMoore(1985).Thisconceptualizationrep-
idation. resents a cumulative distribution of varying storage capaci-
ties(C)withthefollowingfunction:
recordattheDakahstation,locatedatthebasinoutlet,isalso (cid:18) C (cid:19)B
F(C)=1− 1− 0≤C≤C , (1)
max
usedforvalidationpurposes. C
max
The Randolph Glacier Inventory version 3.2 (RGI 3.2)
where the exponent B is a parameter controlling the degree
dataset(Pfefferetal.,2014)wasusedtoextractglacialcov-
of spatial variability of storage capacity over the basin and
erage in the Kabul River basin, which totaled 5.7% of the
C isthemaximumstoragecapacity.Themodelassumes
max
basin area (Fig. S2). In the hydrological modeling process,
that all storages within the basin are filled up to the same
themodelneedstobeinformedbyreliableestimatesonvol- criticallevel(C∗(t)),unlessthisamountexceedsthestorage
ume of water retained in glaciers, especially for future sim-
capacityofthatparticularlocation.Withthisassumption,the
ulationsunderwarmingconditions.Wefollowedthemethod
totalwaterstorageS(t)containedinthebasincorrespondsto
proposedinGrinsted(2013),whichusesmultivariatescaling
relationships to estimate glacier and ice cap volume based C (cid:18) C∗(t)(cid:19)B+1!
onelevationrangeandarea.Specifically,thescalinglawin- S(t)= max 1− 1− . (2)
B+1 C
max
cludingareaandelevationrangefactorswasappliedtoesti-
mateglacier/icecapvolumewhentheglacierdepthexceeded Consequently, two parameters are introduced for the runoff
10m.Otherwise,glacier/icecapvolumewasestimatedwith generationprocesswithtwocomponents:
the area–volume scaling law. The elevation range spanned
 P(t)+C∗(t−1)−C ifP(t)
byeachindividualglacierisestimatedusingtheglobaldig-  max
Runoff = +C∗(t−1)≥C , (3)
ital elevation model (DEM) from the shuttle radar topog- 1 max
 0ifP(t)+C∗(t−1)<C
raphy mission (SRTMv4) in 250m resolution (Jarvis et al., max
2008).Densityofice(0.9167gcm−3)isappliedtocalculate

glacier/icecapvolumeinmetersofwaterequivalent. (P(t)−Runoff )+(S(t)−S(t−1))
 1
The database for land covers and soil types of the Kabul Runoff = ifP(t)−Runoff ≥S(t)−S(t−1) , (4)
2 1
River basin (Fig. 1) are provided by the Food and Agricul-  0ifP(t)−Runoff <S(t)−S(t−1)
1
tureOrganizationoftheUnitedNations(Lathametal.,2014)
where P(t) is precipitation, Runoff is surface runoff, and
and United States Department of Agriculture – Natural Re- 1
Runoff issubsurfacerunoff.Aparameter(α)isintroduced
sources Conservation Service Soils (USDA-NRCS, 2005), 2
torepresenthowmuchofthesubsurfacerunoffisroutedover
respectively.
thefast(Q )andslow(Q )pathway:
fast slow
3.2 DistributedHydrologicModel(HYMOD_DS) Q =Runoff +α·Runoff , (5)
fast 1 2
Q =(1−α)·Runoff . (6)
slow 2
InthisstudythelumpedconceptualhydrologicalmodelHY-
MOD (Boyle, 2001) is coupled with a river routing model The potential evapotranspiration (PET) is derived based on
to be suitable for modeling a distributed watershed system. the Hamon method (Hamon, 1961), in which daily PET in
WenameitHYMOD_DSdenotingthedistributedversionof millimetersiscomputedasafunctionofdailymeantemper-
HYMOD. Snow and glacier modules have been introduced atureandhoursofdaylight:
to enhance the modeling process for glacier and snow cov-
(cid:16) (cid:17)
ered areas within the Kabul River basin. The HYMOD_DS 0.611·exp 17.27·(T+2T73.3)
is composed of hydrological process modules that repre- PET=Coeff·29.8·Ld· T +273.3 , (7)
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862 S.Wietal.:Implicationforstreamflowprojectionsunderclimatechange
Table2.HYMOD_DSparameters.
Feasiblerange
Parameter Lower Upper
name Description bound bound
Coeff Hamonpotentialevapotranspirationcoefficient 0.1 2
Cmax Maximumsoilmoisturecapacity(mm) 5 1500
B Shapeforthestoragecapacitydistributionfunction 0.01 1.99
α Directrunoffandbaseflowsplitfactor 0.01 0.99
Ks Releasecoefficientofgroundwaterreservoir 0.00005 0.001
DDFs Degreedaysnowmeltfactor(mm◦Cday−1) 0.001 10
Tth Snowmelttemperaturethreshold(◦C) 0 5
Ts Snow/raintemperaturethreshold(◦C) 0 5
r Glaciermeltratefactor 1 2
Kg Glacierstoragereleasecoefficient 0.01 0.99
Tg Glaciermelttemperaturethreshold(◦C) 0 5
N Unithydrographshapeparameter 1 99
Kq Unithydrographscaleparameter 0.01 0.99
Velo Wavevelocityinthechannelrouting(ms−1) 0.5 5
Diff Diffusivityinthechannelrouting(m2s−1) 200 4000
Figure3.DistributedversionoftheHYMODmodel(HYMOD_DS).
whereL isthedaylighthoursperday,T isthedailymean glacialareaandrunofffromglacialareasisregardedassur-
d
air temperature (◦C), and Coeff is a bias correction factor. faceflow.Therunofffromeachareaisweightedbyitsarea
The hours of daylight is calculated as a function of lati- fractionwithinthebasintoobtaintotalrunoff.
tudeanddayofyearbasedonthedaylightlengthestimation Thetimerateofchangeinsnowandglaciervolumegov-
model(CBMmodel)suggestedbyForsytheetal.(1995). erned by ice accumulation and ablation (melting and subli-
The HYMOD_DS includes snow and glacier modules mation) is expressed by the degree day factor (DDF) mass
with separate runoff processes, i.e., the runoff from the balancemodel(Moore,1993;Stahletal.,2008).Thedomi-
glacierizedareaiscalculatedseparatelyandaddedtorunoff nantphaseofprecipitation(snowvs.rain)isdeterminedby
generated from the soil moisture accounting module cou- atemperaturethreshold(T ).ThesnowmeltM andglacier
th s
pledwiththesnowmodule.Theimplicitassumptionhereis meltM iscalculatedas
g
thatthereisnointerchangeofwaterbetweensoillayersand
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S.Wietal.:Implicationforstreamflowprojectionsunderclimatechange 863
outlet (Dakah), should be approached with caution. Given
thatamajorityofthegagesexaminedinthisstudyareonan
Ms=DDFs×(T −Ts), (8) underdevelopedbranchoftheKabulRiver,issuesofhuman
M =DDF ×(cid:0)T −T (cid:1), (9) interferenceoncalibrationaresomewhatmitigated.
g g g
withDDF (T )andDDF (T )appliedseparatelyforsnow
s s g g
andglaciermodules,respectively.Toaccountforthehigher 4 Methods
melting rate of glaciers than snow owing to the low albedo
(Konz and Seibert, 2010; Kinouchi et al., 2013), we intro- The purpose of this study is to explore the implications
ducedaparameterr>1toconstrainDDF tobelargerthan of different calibration strategies and choices for a compu-
g
DDF (i.e., DDF =r×DDF ). For the rain that falls on tationally expensive distributed hydrologic model. A vari-
s g s
theglacierizedarea,theglacierparameterK determinesthe ety of calibration experiments are conducted, with the re-
g
portionofrainbecomingsurfacerunoffasamultiplierforthe sults from preceding experiments informing choices made
rainfall.Theremainingrainfallisassumedtobeaccumulated forsubsequentones.Allcalibrationapproachesaretestedin
totheglacierstore. terms of their ability to predict flows at interior site gages
The within-grid routing process for direct runoff is rep- that were left out of the calibration process. In all cases,
resented by an instantaneous unit hydrograph (IUH) (Nash, the genetic algorithm (GA) introduced by Wang (1991) is
1957), in which a catchment is depicted as a series of N used as an optimization method for model parameter cali-
reservoirseachhavingalinearrelationshipbetweenstorage bration, and the objective function is based simply on the
and outflow with the storage coefficient of K . Mathemati- Nash–Sutcliffe efficiency (NSE) (Nash and Sutcliff, 1970),
q
cally,theIUHisexpressedbyagammaprobabilitydistribu- which is by far the most utilized performance metric in hy-
tion: drological model applications (Biondi et al., 2012). A mul-
tisite average of the NSE is used when evaluating perfor-
u(t)= Kq (cid:0)K t(cid:1)N−1exp(cid:0)−K t(cid:1), (10) manceacrossmultiplesites.Wefullyrecognizethattheuse
q q
(cid:48)(N) of one objective, such as the NSE, is inferior compared to
multiobjective approaches that can identify Pareto optimal
where(cid:48)isthegammafunction.Thewithin-gridgroundwater
solutions that provide good model performance across dif-
routingprocessissimplifiedasalumpedlinearreservoirwith
ferent components of the flow regime (Madsen, 2003; Efs-
thestoragerecessioncoefficientofK .
s
tratiadisandKoutsoyiannis,2010;Lietal.,2010;Kumaret
Thetransportofwaterinthechannelsystemisdescribed
al.,2013).However,inthisparticularstudydailyhydrologic
using the diffusive wave approximation of the Saint-Venant
model simulations can only be compared against available
equation(Lohmannetal.,1998):
monthly streamflow records, reducing the number of viable
∂Q ∂Q ∂2Q objectivesagainstwhichtocalibrate.Thatis,statisticsrepre-
+C −D =0, (11) sentingpeakflows,extremelowflows,andotherdailyflow
∂t ∂x ∂2x2
regimecharacteristicsoftenusedinmultiobjectiveoptimiza-
whereCandDareparametersdenotingwavevelocity(Velo) tionapproachesareunavailable.Webelievethattheuseofa
anddiffusivity(Diff),respectively. monthlyNSEvalueasasingleobjective,whilecoarse,does
Similartomostotherhydrologicalmodels(Efstratisdiset not inhibit our ability to provide insight into the research
al.,2008),HYMOD_DSisnotdesignedtomodelwaterab- questions posed. In addition to the NSE, the Kling–Gupta
stractions for agricultural lands and dam operations within efficiency (KGE) (Gupta et al., 2009) is adopted as an al-
the basin. According to the World Bank (2010), water de- ternative model performance metric, which equally weights
mand for agricultural use is about 2000 million cubic me- modelmeanbias,variancebias,andcorrelationwithobser-
ters,orabout8.3%ofthetotalannualflow.TheNagludam vations.
(Fig.1)upstreamoftheDarontastreamflowgageformsthe Inthisstudy,threelevelsofparametercomplexityarecon-
largestandmostimportantreservoirinthebasin,withanac- sidered: lumped, semi-distributed, and fully distributed for-
tive storage of 379 million cubic meters. In our hydrologic mulations (Fig. 4). The different levels of parameter com-
modeling process, the water consumed by irrigated crop- plexity are defined according to the spatial distribution of
lands is implicitly accounted for by the evapotranspiration unique hydrologic model parameters. In the lumped formu-
module. We note that the degree of irrigation impact dur- lation a single parameter set is applied to the entire basin.
ingthetimeframeusedforcalibration(1960–1981)islikely In the semi-distributed formulation, a unique parameter set
muchsmallerthanthecurrentlevel.Wealsoexpectthatusing is assignedto each sub-basin, defined basedon the location
monthlydataforcalibrationsomewhatreducesthebiasfrom of available streamflow gaging sites. The fully distributed
human interference, particularly the daily operations of the parameter structure follows the spatial discretization of cli-
Nagludam.Nevertheless,thecalibrationresultsforthegage mateinputgrids,allowingforauniqueparametersetforeach
below this dam (Daronta), and to a lesser extent the basin gridcell.Nomattertheparameterizationscheme,themodel
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864 S.Wietal.:Implicationforstreamflowprojectionsunderclimatechange
Figure4.Modelstructurebasedonclimateinputgridsandthreedifferentparameterizationconcepts.
structure follows the climate input grids; i.e., the hydrolog- andpooledapproach.Inthestepwisecalibration,parameters
icalwatercyclewithineachgridcellismodeledseparately. arecalibratedforupstreamgagedsub-catchmentsandsubse-
We note that a lumped model structure (i.e., no gridded or quentlyfixedduringcalibrationofdownstreampoints,while
sub-unit structure) has often been considered as a baseline forthepooledapproach,parametersarecalibratedformulti-
model formulation in the assessment of distributed model- plesub-catchmentssimultaneously.Bothapproachesareas-
ing frameworks (e.g., see Smith et al., 2013). However, the sessed for the semi-distributed formulation. The better of
focus of our study is on ungaged interior site streamflow the two methods is identified for use in the second experi-
estimation, making this formation somewhat inappropriate. ment, where the effects of increased parameter complexity
Furthermore, preliminary tests comparing streamflow sim- aretestedintermsofstreamflowpredictionaccuracyandun-
ulations at the basin outlet (Dakah) between a gridded and certainty. In the third experiment, we consider the situation
basin-averagedstructure,bothwithalumpedparameterfor- where there is only data at the basin outlet for calibration.
mulation, support the use of the distributed grid structure Here,themodeliscalibratedagainsttheoutletgageunderall
(Fig.S3). levels of parameter complexity and is compared against the
Theparametercomplexitywillvarydependingonthecal- bestcombinationofcalibrationstrategy(stepwiseorpooled)
ibration experiment being conducted but, for each exper- andparametercomplexity(lumped,semi-distributed,orfully
iment regardless of the parameterization, the optimization distributed)identifiedinthepreviousexperiments.Finally,a
is implemented 50 times using the GA algorithm to ex- subset of the calibration approaches deemed worthy of fur-
plorecalibrationuncertainty.Theconsiderablyhighcompu- therinvestigationarecomparedintermsoftheirprojections
tational cost required to perform a large number of calibra- offuturestreamflowunderclimatechangetohighlighthow
tions is managed using the parallel computing power pro- modelcalibrationdifferencescanaltertheresultsofaclimate
videdbytheMassachusettsGreenHigh-PerformanceCom- change assessment for water resources applications. These
putingCenter(MGHPCC),fromwhichseveralthousandsof experimentsaredescribedinfurtherdetailbelow.
processorsareavailable.
Inthefirstmodelingexperiment,weexploretwocalibra-
tionstrategiesforusingmultisitestreamflowdata,astepwise
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S.Wietal.:Implicationforstreamflowprojectionsunderclimatechange 865
searchestheentireparameterspaceatoncetomaximizethe
averageNSEacrossallsites.Thisoperationalfeaturereduces
the processing time spent on the GA implementation com-
paredtothestepwisecalibrationstrategy.Toidentifythebet-
ter of the two multisite calibration approaches, the compar-
ison focused on their ability to predict streamflow and cal-
ibration uncertainties at two interior site gages (Kama and
Asmar)thatwereassumedtobeungaged(Fig.5),aswellas
forvalidationdataatthebasinoutlet.
It is important to note that the evaluation of these multi-
sitecalibrationstrategiesissomewhatweakenedbecauseof
thelackofoverlappingdataperiodsamongmostofthesta-
tions(Fig. 2).Thisdrawbackprevents thecalibrationmeth-
odsfromaccountingforsimultaneousinformationfromdif-
ferenttributaries,which,ifavailable,wouldbetterenablethe
calibration methods to account for heterogeneity of hydro-
logicalprocessesacrossthesub-basins.
4.2 Increasedparametercomplexity
In the second experiment, the better of the two approaches
Figure5.(a)Sub-basinscorrespondingtofivegagingstationsare
(stepwiseorpooled)identifiedinthefirstexperimentisfur-
usedforthemultisitecalibrations.(b)Twosub-basins(Kamaand
thertestedwithrespecttothethreedifferentlevelsofparam-
Asmar)areassumedtobeungagedandusedforevaluatingthecal-
ibrationapproaches. eter complexity. In addition to the semi-distributed param-
eter formulation considered in the first experiment, lumped
and fully distributed parameter formulations are calibrated
fortheselectedapproachtoinvestigatethegainorlossaris-
4.1 Multisitecalibration:stepwiseandpooled
ingfromdifferentlevelsofparametercomplexity.Sincethe
approaches
hydrologicmodelHYMODemployedinthisstudyinvolves
15parameters,thelumpedversionoftheHYMOD_DScon-
Inthefirstexperiment,thesemi-distributedparameterization
tainsasingle,15-memberparametersetappliedtoallmodel
concept is compared under alternative multisite calibration
grid cells. The semi-distributed conceptualization of HY-
strategies, the stepwise and pooled calibration approaches.
MOD_DS contains a single parameter set for each sub-
To conduct the stepwise calibration, a nested class of sub-
basin, totaling 75 parameters. In the distributed parameteri-
basins is defined corresponding to multiple gaging stations.
zationthenumberofparametersincreasesdramatically.With
In the first step of the stepwise calibration, the optimiza-
160 0.25◦C grid cells, the number of parameters requiring
tionprocessiscarriedoutwithnestedsub-basinsatthelow-
calibration reaches 2400. As the number of parameters in-
est level (i.e., the most upstream sites). Once parameters of
crease across the parameterization schemes, calibration be-
nested sub-basins are determined, the parameters are fixed,
comes increasingly computationally expensive. The num-
andthecalibrationprocedureproceedswithnestedbasinsat
ber of model runs used in the GA optimization algorithm
upper levels until parameters for the entire basin are deter-
forthelumped,semi-distributed,anddistributedparameter-
mined.InthisparticularapplicationtotheKabulRiverbasin,
ization schemes are 15000 (150 populations×100 gener-
fivegagedsub-basinswereselectedandthestepwisecalibra-
ations), 75000 (750×100), and 480000 (2400×200), re-
tion procedure for those sub-basins followed this direction:
Chitral→Gawardesh→Chaghasarai→Daronta→Dakah spectively.Thesepopulation/generationsizesweresupported
usingconvergencetestsforeachcalibration.Again,50sep-
(Fig.5).Thestepwisecalibrationapproachinvolvesanum-
arateGAoptimizationswereusedtoexplorecalibrationun-
berofGAimplementationscorrespondingtothenumberof
certaintiesforeachparameterizationscheme.Togiveasense
gagingsites.TheGAoptimizationwascarriedoutatotalof
ofthecomputationalburdenofthisexperiment,wenotethat
250timesinthisapplication,with50optimizationrunscon-
50trialsoftheHYMOD_DScalibrationunderthedistributed
tainingGAimplementationsforfivesub-basinregions.
conceptualization required 1000 processors over 7 days on
Thepooledcalibrationstrategyinvolvescalibratingallpa-
theMGHPCCsystem.
rameters of the model domain simultaneously against mul-
tiple streamflow gages within the watershed. This approach
aims at looking for suitable parameters that are able to pro-
duce satisfactory model results at all gaging stations in a
single implementation of GA optimization. That is, the GA
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866 S.Wietal.:Implicationforstreamflowprojectionsunderclimatechange
4.3 Basinoutletcalibration the model performance evaluated with the NSE, as well as
analternativemetric,theKGE.
The third experiment considers the situation where there is
only gaged data at the basin outlet (Dakah) for calibration, 5.1 Pooledcalibrationvs.stepwisecalibration
a common situation when calibrating hydrologic models in
data-scarce river basins. Here, we evaluate the potential of This section reports the results from the first experiment
the basin outlet calibration to estimate interior watershed comparing the stepwise and pooled calibration approaches
flows in terms of both accuracy and precision at all gaging for the semi-distributed model parameterization. Figure 6
stations. All levels of parameter complexity are considered showsthecomparisonbetweentheSemi-StepwiseandSemi-
forthiscalibration.Themainpurposeofthisexperimentisto Pooled with box plots representing the 50 trials of calibra-
comparetheveracityofadistributedhydrologicmodelcali- tion.Underthestepwisecalibrationtheresultsforfoursub-
bratedonlyusingbasinoutletdatawithresultsfrommultisite basins (Chitral, Gawardesh, Chaghasarai, and Daronta) are
calibrations to better understand the degradation in model optimal because there is no interaction between those sub-
performance under data scarcity. Other than the use of an basins. However, the calibrated parameter sets of each sub-
NSEobjectiveonlyatthebasinoutlet,allotherGAsettings basinactasconstraintsinthelaststepoftheSemi-Stepwise
for each level of parameter complexity are identical to the resulting in the degradation of model skill at the basin out-
settingsusedinthesecondexperiment. let(Dakah)andtwoleft-outgages(AsmarandKama).This
becomesapparentwhencomparingtheSemi-Stepwisetothe
4.4 Climatechangeprojectionsofstreamflow
Semi-Pooledresults.ThemodelskillundertheSemi-Pooled
issimilartothatfromtheSemi-Stepwisewithrespecttothe
The fourth experiment investigates how the choice of cali-
four upstream sub-basins, but it outperforms at the verifi-
bration approach can alter the projections of future stream-
cation gages. This is particularly true for the Asmar gage,
flowunderclimatechange.Toexplorethisquestion,stream-
which exhibits a downward bias and substantial variability
flowsimulationsforthe2050s,definedasthe30-yearperiod
in performance under the Semi-Stepwise. The Semi-Pooled
spanning from 2036 to 2065, are carried out using climate
results suggest that small sacrifices of model performance
projectionsfromtheCMIP5(Talyoretal.,2012).Atotalof
atcertainsitescanimproveandstabilizebasin-wideperfor-
36differentclimatemodelsrunundertwofutureconditions
mance.ExpectedvaluesofKGEfrom50calibrationsarealso
ofradiativeforcing(RCP4.5and8.5)areused.Streamflow
provided(valuesinparenthesisinthebottomofFig.6)and
projections are developed for the basin outlet (Dakah) and
this performance metric also leads to the same conclusion.
twointeriorgagesleftoutofthecalibration(KamaandAs-
Therefore,theSemi-Pooledwasselectedasthebettermulti-
mar).Byusing36differentGCMsand50optimizationtrials
sitecalibrationstrategyandisconsideredforfurtheranalyses
for each calibration scheme, this analysis compares the un-
inthefollowingsections.
certainty in future streamflow projections originating from
uncertainty in different hydrologic model parameterization
5.2 Pooledcalibrationwithalternative
schemesandunderalternativefutureclimates.
parameterizations
Streamflow projections are considered under all three
parameterization schemes (lumped, semi-distributed, and
Here we examine results for the three levels of parameter
fully distributed) for both the basin outlet model and the
complexity applied to the pooled calibration approach. Fig-
best multisite calibration approach (stepwise or pooled).
ure 7 shows the comparison of the pooled calibrations. Un-
Multiple streamflow characteristics are evaluated, includ-
surprisingly, streamflow predictions from the Lump-Pooled
ing monthly streamflow, wet (April–September) and dry
have the lowest accuracy and largest uncertainty at the cal-
(October–March) season flows, and daily peak flow re-
ibration sites, particularly for the Chaghasarai and Daronta
sponse. The differences and uncertainty in these metrics
sites. This demonstrates the well-known difficulty in rep-
across calibration approaches will highlight the importance
resenting flow characteristics of a spatially variable system
ofcalibrationstrategyforevaluatingfuturewateravailability
withahomogenousparameterset(Beven,2012).Thepooled
andfloodrisk.
calibration substantially improves with increasing parame-
tercomplexityatthecalibrationsites.BoththeSemi-Pooled
5 Results and Dist-Pooled produce NSE values above 0.8 for all cal-
ibration sites; however, the Dist-Pooled shows a somewhat
For the remaining part of the paper, we introduce the higherperformance,undoubtedlyfromitsgreaterfreedomto
following shorthand: Lump, Semi, and Dist indicate the overfittothecalibrationdata.However,theadvantageofthe
lumped,semi-distributed,andfullydistributedparameteriza- Dist-Pooledwithrespecttostreamflowpredictionsatvalida-
tion schemes, and Outlet, Stepwise, and Pooled correspond tionsitesbecomeslessclear.OnlytheDist-PooledatKama
tobasinoutlet,stepwise,andpooledcalibrations.Thecom- showsmarginallybetterpredictions,whiletheresultsaream-
parison between different calibration strategies is based on biguous at Dakah and Asmar. Overall, this likely suggests
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