Land surface assimilation March 2001 · Land surface assimilation March 2001 By Jean-François Mahfouf and Pedro Viterbo Table of contents ... based on Monin-Obukhov theory; the crucial

Land surface assimilation

1 Meteorological Training Course Lecture Series

ECMWF, 2002

Land surface assimilationMar ch 2001

By Jean-François Mahfouf and Pedro Viterbo

Table of contents

1 Introduction

2 Design of land surface parametrizations

2.1 General features

2.2 Surface fluxes

3 Introduction to land surface assimilation

4 Simple land surface initialisation methods

5 Soil moisture initialisation using SYNOP observations

5.1 The ECMWF method

5.2 Possible improvements

6 Other techniques to initialise soil moisture

6.1 Methods based on precipitation data

6.2 On-site observations and methods based on satellite imagery

7 Initialisation of other land surface quantities

7.1 Snow mass

7.2 Deep soil temperatures

7.3 Vegetation properties

8 Conclusions

REFERENCES

Abstract

This lecturenoteprovidesa review of techniquesrecentlydevelopedfor initialising the prognosticvariablesof land surfaceparametrizationsin numericalweatherpredictionmodels.The importanceof soil moistureinitialisation is emphasizedsincethe evolution of the boundarylayer is very sensitive to its specificationandthe associatedtime scalesaremuchlongerthanthoseof mediumrangeforecasts.The analysisof snow massis alsodescribed,usingthe ECMWF methodasan illustrativeexample.Differentmethodsanddataavailablefor theinitialisationof otherslowly varyingcomponentsat thesurface,suchassoil temperature, vegetation fraction, leaf area index and albedo, are described at the end.

1INTRODUCTION

Theimportanceof landsurfaceprocesseshasbeenrecognisedfor alongtimeby theclimatemodellingcommunity,

in orderto describein aconsistentwayall thecomponentsof thewaterandenergy cycleover longperiodsof time.



ECMWF, 2002

As aconsequenceavarietyof schemeshavebeendevisedrangingfrom thesimplebucketmodelof Manabe(1969)

to the complex soil-vegetation SiB (Simple Biosphere) model ofSellers et al. (1986).

Although a numberof sensitivity studieshave shown that land surfaceprocessescanalsoaffect mediumrange

weatherforecasts(Rind 1982;RowntreeandBolton 1983;Yehet al. 1984;Rowell andBlondin 1990;Beljaarset

al. 1996),the parametrizationof the interactionsbetweencontinentalsurfacesandthe lower atmosphereis still

rather crude in most numerical weather prediction models.

Recentfield experiments,suchasHAPEX-MOBILHY 86,FIFE87or BOREAS94,haveenabledthedevelopment

andthevalidationof landsurfaceschemesdescribingthemostimportantprocessesgoverningthewater, heatand

momentumexchangeswhile remainingsimple enoughto be includedin operationalweatherforecastsmodels

(NoilhanandPlanton1989;ViterboandBeljaars1995).Suchparametrizationscanimprovesignificantlythequal-

ity of the forecastsof weatherelements(Bougeaultet al. 1991;Lanzinger1995).Initialisationof theprognostic

soil variablesatglobalscaleis animportantissuegiventheverydifferenttimescalesof evolutionbetweentheat-

mosphericandthesoil systems.Realisticschemesappearto besensitive to thespecificationof initial soil temper-

aturesandwatercontents(JacqueminandNoilhan1990;Bouttieret al. 1993a,1993b).Theincreasein realismof

otherphysical parametrizations(clouds,radiation,convection)in numericalweatherpredictionmodelshasalso

madeerrorsin thesurfacerepresentationeasierto identify. Theimportanceof positive feedbacksbetweenthesur-

faceandtheatmospheremustbeunderlined: realisticmechanismsshouldberepresented(which is not possible

whensurfaceboundaryconditionsarefixed),but spuriousones,resultingfrom systematicerrorsin therepresenta-

tion of somecomponentsof theenergy andwatercycles,shouldberemovedwith anappropriateinitialisationpro-

cedure.

In thefollowing, wewill startin Section2 by describingthebasicfeaturescommonto mostsurfaceschemes.Spe-

cial featuresof thelandsurfaceassimilationareidentifiedin Section3, in termsof dataavailability andits relation

to modelvariables.Section4 reviewstheproblemsof simplesurfaceinitializationprocedures.Methodsfor thein-

itialisation of soil water in numericalmodelsusingnear-surfacetemperatureandhumidity observationsarede-

scribedin Section5, while Section6 explainsthedrawbacksof on-sitesurfaceobservationsof soil moistureand

discussestheneedfor remotesensing.Finally, Section7 reviewstheinitialisationof otherslowly varyinglandsur-

face variables, such as snow mass, deep soil temperatures and vegetation characteristics.

2DESIGN OF LAND SURFACE PARAMETRIZA TIONS

2.1 General features

Theaimof landsurfaceschemesis to computetemperatureandspecifichumidityat thelowerboundaryof atmos-

phericmodels.Thesetwovariablesarerequiredin theestimationof heat,waterandmomentumexchangesbetween

the continental surfaces and the lower atmosphere.

The surface temperature is derived as the solution of the surface energy balance written as:

(1)

whereRn is thenetradiationflux convertedin latentheatflux , sensibleheatflux andgroundheatflux .

The ground heat fluxG depends upon deep soil temperatures and soil thermal properties.

The surface specific humidity can be written formally as :

�sk

�n

�� + +=

��


Meteorological Training Course Lecture Series

ECMWF, 2002 3

(2)

where representsthevalueof specifichumidityat thelowestmodellayer. Thequantities and (described

with moredetailsin the next paragraph)dependuponsoil moisture which is obtainedby solving the surface

water budget :

(3)

whereP is the precipitation flux,E the total evaporation flux andR the surface runoff.

Thisbrief descriptionshowsthatalandsurfaceschememustmanageat leasttwo prognosticequationsfor thetem-

perature and soil moisture in the soil. Heat and water transfers are governed by the following diffusion laws :

(4)

(5)

Thediffusivity D andconductivity K coefficientsarenon-linearfunctionsof soil moisturecontent.Thediffusion

equationsaregenerallydiscretizedover2 to 4 layersin orderto dealwith timescalesrangingfrom daysto months.

2.2 Surface fluxes

Thelink betweensoil andatmosphericvariablesis providedthroughtheexpressionof thesurfacefluxes,usually

basedon Monin-Obukhov theory;thecrucialvariablehereis theevaporationflux becauseits magnitudedepends

explicitly uponsurfaceproperties.Recentlandsurfaceschemesrepresentdifferentlythegrid boxfractionscovered

by: a) baresoil, with evaporationcontrolledby soil moisturein a shallow top soil layer;b) vegetation,with tran-

spirationcontrolledby soil moisturein the root zoneaffecting the magnitudeof stomatalresistance;c) snow or

interceptionreservoir, evaporatingat thepotential(maximum)rate.Thesetwo lastcomponentsrequiretheexist-

ence of model prognostic equations for snow mass and interception reservoirs.

Evaporation from bare soil can be written as (seeMahfouf and Noilhan 1991 for a review) :

(6)

Theefficiency of theturbulenttransfersis accountedfor throughtheaerodynamicresistance , while thecontrol

by thesurfacesoil moisture is representedby thesurfacerelative humidity [ and in

Equation(2)]. A typical variationof is presentedon the left panelof Fig. 1 . Evaporationtakesplaceat

the potential rate above a threshold value (field capacity) (defined from soil texture) up to the saturation .

Transpiration from vegetation canopy writes similarly:

(7)

Theanalogywith Equation(2) leadsto and . Watertransfersfrom the

�s

� �sat×�

sk( ) �L×+=

�L

� θ

dθd------ � �

–�

–=

∂�

s

∂ ---------∂

∂�------ ��∂�

s

∂�--------- –

∂θ∂ ------

∂∂�------ θ

∂θ∂�------

∂ � θ

∂�----------+=

�g ρ

�� sat�

sk( ) ��–�a

---------------------------------------=

�a

θs

��θs( )

� ��= 0=��

θs( )θf c θsat

�tr ρ

�sat

�sk( ) ��–�

c

�a+

--------------------------------=

� �a

�c

�a+( )⁄= �

c

�c

�a+( )⁄=



ECMWF, 2002

root zoneto theatmospheredependbothonbiologicalandphysicalcontrols.Plantslimit theirwaterlossesin un-

favorableenvironmentalconditionsdeterminedby soil moisturein therootzone,atmosphericwatervapourdeficit,

solarradiation,air temperatureandcarbon-dioxideconcentration.A typical dependency of thecanopy resistance

with soilmoistureisshownontherightpanelof Fig.1 . Below athresholdvalueoftendefinedasthepermanent

wilting point , it is assumedthat plantsareunableto pumpwaterfrom the root zoneto the stomatalcells,

correspondingto arapiddecreaseof transpiration(increasein ). As for baresoils,it if oftenassumedthatabove

the field capacity the plant transpiration is not controlled by soil moisture.

Figure 1Surface relative humidityhu as a function of the surface volumetric water content (left) and canopy

resistanceRc as a function of the mean volumetric water content (right). (FromMahfouf 1991).

3INTRODUCTION TO LAND SURFACE ASSIMILA TION

Themajorproblemof landsurfaceassimilationis the lack of routineobservationsof soil moistureandsoil tem-

perature.This is speciallytruein thecaseof soil moisture,wherecurrentmethodscannotprovideglobalcoverage

routinely(seeSubsection6.1 for moredetails).Furthermore,soil moistureobservationsshow largevariability in

smallspatialscales(seee.g.WetzelandChang1988);not all scalesareof relevancefor theatmosphere,andthe

assimilationmethodhasto take thatinto account.For soil temperaturetheclimatenetwork exists,with acoverage

similar to theSYNOPstationsandwith mostof thestationsperformingobservationsat leastdaily; unfortunately,

thoseobservationsarenot exchangedroutinelyat thetime of measurement,so in practicethey canonly beused,

in delayed mode, for verification purposes.

Thenatureandavailability of theobservationsimposestheuseof proxyvariablesfor soil moisture.Theamountof

waterin the root zoneimpactson theevaporative fraction,which in itself determines,for a givenamountof net

radiation,middaysummerscreenlevel temperatureandhumidity (seeprevioussectionandthereview by Bettset

al. 1996).On theotherhand,the time evolution of soil waterdependson therainfall intensityandon its timing.

Threemaintypesof datahavebeenusedin thepastto infer soil moisture:(a)Screenlevel atmospherictemperature

andhumidity; (b) Rainfall rates;and(c) Radiometricsurfacetemperature(infrared,microwave).Notethat,since

thoseobservationsalreadyrepresent,to acertainextent,theimpactof soil moistureontheatmosphereabove,they

have already filtered out the smaller scales in soil water.

Therearetwo aditionaldifficulties in the assimilationof land surfaceobservations.First, theseobservationsare

non-linearlyrelatedto soil moistureandsoil temperature(throughtheequationsof thelandsurfacescheme).Sec-

ondly, thestatisticsof forecasterrors,usedto spatiallydistributethelocal incrementsin atmosphericanalyses,are

�c

θpwp �c



ECMWF, 2002 5

not known for soil variables.

4SIMPLE LAND SURFACE INITIALISA TION METHODS

Dueto thedifficultiespresentedabove,soil variablesareinitialisedempiricallyin mostoperationalforecastsmod-

els.

A first methodfor initialising soil variablesis to settheanalysedsoil variablesto climatologicalvalueswithout

usingany modelinformation(throughthefirst-guess).In practice,this is doneby addinga relaxationto climatol-

ogyto theprognosticequationsof thelandsurfacescheme(Blondin1991).Theunderlyingideaof this termis that

simplesurfaceschemescanonly describecorrectlythevariableshaving a shorttime scaleevolution, like thesur-

facesoil temperature,andthatvariableshaving a time scalelongerthana few daysmustbeprescribed.Problems

arisefrom thespecificationof climatologicalsoil valueswhicharebasedonindirectatmosphericobservationsand

very simplifed transfermodels.Theseproducts,like thesoil moistureclimatologyof Mintz andSerafini(1992),

haveahigh level of uncertaintyasshown by ViterboandBeljaars(1995).Anotherpotentialproblemis thatwith a

relaxationof deepvariablestowardsclimatology, seasonalanomaliescannotbe forecasted.An exampleof such

deficiency hasbeenshown by Beljaarset al. (1996)with two versionsof the ECMWF model for the 1993US

floods.

Theotherapproachto initialisesoil variablesis to settheanalysedvaluesto thefirst-guess.In thatcontext, anab-

soluteconfidenceis givento thelandsurfaceschemefor evolving its prognosticvariablesandnocontrolexiststo

prevent thelandsurfaceschemefrom drifting to anunrealisticstate.Suchdrifts canoccurthroughpositive feed-

backswith theatmosphere,in situationswheretheschemeexperiencessystematicerrorsin theatmosphericforcing

(toomuchradiation,toomuchrainfall, ...) or from amisrepresentationof somelandsurfaceprocesses.Thesecond

point canbecheckedwith stand-alonesimulationswheretheatmosphericforcing is prescribed.An exampleof a

drift of thecurrentECMWF landsurfaceschemewithin thedataassimilationsystemis describedin thenext sec-

tion.

5SOIL MOISTURE INITIALISA TION USING SYNOP OBSERVATIONS

5.1 The ECMWF method

Thelandsurfaceschemedevelopedby Viterbo andBeljaars(1995)wasintroducedoperationallyin August1993

andall soil prognosticvariableswereinitialized to first-guessvalues.Oneof themaindifferenceswith respectto

thepreviousECMWFlandsurfacescheme(Blondin1991)is theabsenceof climatologicalrelaxationfor deepsoil

temperatureandwatercontent.During May-June1994,thesoil reservoirs weredrying out, leadingto surfaceair

temperatureerrorsincreasinglypositive,andin comparisonwith othermodels,suchastheGermanWeatherServ-

ice(constrainedby climatologicalsoil moisture),forecastskill wasdeteriorating(ViterboandCourtier1995).The

downwarddrift of soil moistureappearsto belinkedto excessincomingsolarradiationprimarily causedby under-

predictionof clouds.Furthermore,theexcessive warmingat thelower troposphereaffectedtheforecastperform-

ance,asshown in Fig. 2 . The500hPageopotentialday2 forecastaveragedoverEuropeis presentedfor April to

June 1994. The ECMWF forecast (dashed line) has a positive bias from late April onwards.



ECMWF, 2002

Figure 2Bias of the 500 hPa geopotential height, averaged over Europe, for the day 2 ECMWF (dashed) and

DWD (solid) forecast.

Analysisincrementsof specifichumidityat thelowestmodellevel duringMay 1994show positivevaluesoverEu-

ropewith maximareaching2.5g/kg.Theatmosphericanalysistriesto compensatefor themodelbiasby moisten-

ing andcoolingthelower atmosphere.Therefore,thelow level humidity incrementscanbeusedto identify areas

wherethesoil is toodry. Knowing theanalysisincrementof specifichumidity , thecorrectionof soil

moisture to be applied the root zone is assumed to be proportional :

(8)

with ∆ t = 6 hours,andthesubscriptsaandf referto analysisandforecastvalues,repsectively. Therelaxationco-

efficientD is constantin spaceandtimeandcorrespondsto aspecifichumidityanalysisincrementof 1.5g/kgfill-

ing 150mm of waterin thesoil in 9 days.Thefractionof vegetation in theabove formulaguaranteesthatthe

schemeis notactiveoverdeserts.No incrementsareproducedin thepresenceof snow, andtheanalysedsoil mois-

turecontentsθa arelimited by thefield capacityandpermanentwilting point thresholds.Theintegratedsoil water

incrementsaredistributedin eachof thethreesoil layersfollowing themodelrootextraction.Thisnudgingscheme

wasimplementedoperationallyin December1994.It suppliessoil moistureto maintainevaporationin areasof ex-

cessive radiationat thesurface,caused,amongotherfactors,by insufficient cloudcover. Fig. 3 comparestheday

3 forecasterrorsin screenlevel daytime temperatureandhumidity, averagedoverEurope.Threeexperimentsare

compared:Operations,FWDC,whereno initialisationof soil wateris appliedandthediagnosticcloudschemeis

used;IWDC, initial soil watermethodusingthetechniquedescribedabove,diagnosticcloudscheme,and;IWPC,

initial soil watermethodandprognosticcloudscheme.Theerrorsin bothtemperatureandhumidity aredramati-

cally reducedwhenthe initialization of soil wateris used,andthey arereducedeven furtherwhenthe radiation

forcing at thesurfaceis improvedby theuseof theprognosticcloudscheme.Notethatthesoil waterwasresetto

field capacityat3 July, in aquickeffort to correctthelargesystematicerrorsin themodel;thisexplainsthemuch

reducedoperationalerrorsafterthatdate.Thereductionof nearsurfacewarmdry biasremovesthebiasat thetrop-

osphericgeopotential,impactingfavourablyon theroot meansquare(rms)of thetroposphericgeopotentialover

EUROPE LAT 35.000 TO 75.000 LON -12.500 TO 42.500MEAN ERROR FORECAST

500hPa GEOPOTENTIAL FORECAST VERIFICATION

M’�

MA = 5 Day Moving Average�

1�APRIL�

1994�3� 5� 7� 9� 11 13 15 17 19 21 23 25 27 29 1�

MAY� 3� 5� 7� 9� 11 13 15 17 19 21 23 25 27 29 31 2�JUNE

4 6! 8" 10 12 14 16 18 20 22 24 26 28 30 2�-15

-10

-5

0

5

10

15

20

ECMWF 12Z T+ 48 MA

OFFNB 12Z T+ 48 MA#

∆ � �a�

f–=

∆θ θa θf–=

θa θf– $ v ∆ � a�

f–( )=

$ v



ECMWF, 2002 7

land areas.Examplesfor the geopotentialrms at 500 hPa over Europeandat 200 hPa over North Americaare

shown in Fig. 4.

Figure 3Averaged European bias (model minus observations) in the 2m temperature (left) and the humidity

(right) for theday3 forecastverifying at12UTC. FWDC:Control;IWDC: Nudgingof water;IWPC:Nudgingof

water and prognostic cloud scheme.

Similar techniquesareusedoperationallyat Météo-France(Coiffier et al. 1987)andat theCanadianMeteorolog-

ical centreMailhot et al. 1997).Recently, Yanget al. (1994)haveproposedto improve this methodby usingboth

informationsof temperatureandspecifichumidity. previousforecasterrorswith coefficientsdependingonvegeta-

tion type.Unfortunatelythemethodproposedis biased,becauseacorrectionof soil moistureis appliedevenif the

forecast of atmospheric low level parameters is perfect; this may lead to a long term drift.

Figure 4Averagedgeopotentialrootmeansquareerrorfor the20 forecastswith initial datesbetween940601and

940620, for 500 hPa Europe (top) and 200 hPa North America (bottom); experiment names as in Fig 3. For all 3

experiments the root mean square is computed against the operational analysis.

5.2 Possible improvements

Mahfouf (1991)andBouttieretal. (1993a,1993b)haveproposedanoptimalinterpolationschemefor theassimi-

lation of soil moistureusinginformationof both temperatureandrelative humidity at two metres,which canbe

formaly written:

1-Jun% 11-Jun% 21-Jun% 1-Jul% 11-Jul& 21-Jul& 31-Jul& 10-Aug'-1.0

0.0

1.0

2.0

3.0

4.0

5.0

(K)(

2m Temperature Europe)T + 72*

FWDCIWDCIWPC

1-Jun% 11-Jun% 21-Jun% 1-Jul% 11-Jul& 21-Jul& 31-Jul& 10-Aug'-2.5

-1.5

-0.5

0.5

(g/k

g)

Specific Humidity Europe+-,T + 72

0. 1/ 20 31 42 53 64 75 86 97 10Forecast Day80

20

40

60

80

100

120

140

160

180M9 DATE1=940601/... DATE2=940601/... DATE3=940601/...

AREA=EUROPE TIME=12 MEAN OVER 20 CASESROOT MEAN SQUARE ERROR FORECAST

500 hPa GEOPOTENTIALFORECAST VERIFICATION

FWDC

IWDC

IWPC

0. 1/ 20 31 42 53 64 75 86 97 10Forecast Day80

20

40

60

80

100

120

140

160

180M9 DATE1=940601/... DATE2=940601/... DATE3=940601/...

AREA=N.AMER TIME=12 MEAN OVER 20 CASESROOT MEAN SQUARE ERROR FORECAST

200 hPa GEOPOTENTIALFORECAST VERIFICATION

FWDC

IWDC

IWPC



ECMWF, 2002

(9)

Theoptimalcoefficientsα andβ minimisetheanalysisvarianceandarerelatedto theforecasterrorstatistics.They

aremodeldependentandthesuccessof themethoddependsontheiraccurateestimation.Mahfouf(1991)hasused

a Monte-Carlotechniquewith a one-columnmodel,wheresoil moistureis perturbedrandomlyin a rangeof pos-

siblevalues.Oneconclusionof this studyis that thecoefficientsα andβ stronglydependuponthediurnalcycle

(informationon soil moisturefrom atmosphericparameterscanbeextractedmoreeasilyduringdaytime in clear

sky conditions)anduponthevegetationcover (over baresoil, correctionsareappliedto thesuperficialreservoir

andwhenthevegetationcover is importantsoil correctionsareappliedover thewholeroot zone).Bouttieret al.

(1993a)proposeda first parametrizationof the optimumcoefficients,recentlygeneralizedby Giard andBazile

(2000).In orderto beused,this initialisationmethodrequiresananalysisof temperatureandrelative humidity at

two metres(Navascues1997);theanalysisincrementsshouldbezeroin thosesituationswhereparametersin the

boundarylayerarenot informativeaboutsoil moisture,e.g.strongadvection,andlow radiative forcingat thesur-

face.

Oncetheoptimalcoefficientsarederived,thesequentialassimilationcaneasilybeimplementedin currentopera-

tionaldataassimilationsystems;however, it assumeslinearrelationshipsbetweenatmosphericincrementsandcor-

rectionsto be appliedin the soil which is not a goodapproximationfor mostof the physical parametrizations.

Anotheroptionis thevariationalmethod,which seemsa priori moresuitableto theanalysisof soil moisturedue

to thenon-linearitiesof theproblemandto theimportanceof thetime distribution of observations(surfacevaria-

blesarestronglyaffectedby thediurnalcycle).Mahfouf (1991)andmorerecentlyCalliesetal. (1998)useda1D-

Var approachto estimatetheinitial soil moistureof a one-columnmodelthatbestfit observationsof temperature

andrelative humidity duringa diurnalcycle.Thevariationalmethodwasappliedby Rhodinet al. (1999)to a re-

gionalweatherforecastmodelover a five-dayspringperiod.Theoptimal soil moistureminimisesthe following

cost-function:

(10)

In theaboveformula , , and , represent,respectively, thescreenlevel temperatureandrelativehu-

midity, andtheirassumedobservationalerrors,andthesubscriptsoi andfi representtheobservationi andthefore-

castvalueinterpolatedto thepoint i; thesummationisdoneoverthetotalnumberof observationobservationpoints,

N. Mahfouf(1991)hasvalidatedthetwo methodsdescribedabovewith aone-columnversionof theMétéo-France

forecastmodelusingdatafrom theHAPEX-MOBILHY 1986field experiment.Datafrom thiscampaignprovided

at variouslocationssimultaneousinformationaboutsoil moisturecontentandlow-level atmosphericparameters,

i.e.temperature,relativehumidity, windspeed.Whenusingobservationsof temperatureandrelativehumidity, both

the sequentialandvariationaltechniqueconverge towardsthe neutronprobeestimatesof soil moisture,starting

from arbitrary initial values of soil moisture (Fig. 5).

θa θf– α�

a

�f–( ) β

�:�a

�;�f–( )+=

<θ( )

�o= �

f =–

σ�---------------------- 2

�;�o= �;�

f =–

σ >@?---------------------------------- 2

+= 1=

A∑=

� �B�σ� σ >-?



ECMWF, 2002 9

Figure 5Evolution of the surface (left panel) and root (right panel) soil moisture contents during the sequential

assimilationon4-5July1986.Dottedcurvesindicatetheobservedvalues.Thesiteis HAPEX-MOBILHY. (From

Mahfouf 1991).

Mahfouf (1991)assumedthatthereis a priori no usefulinformationin thefirst-guesswhich is certainlyincorrect

with anoperationalmodelof someskill; in realisticapplicationsa backgroundtermshouldbeaddedto thecost-

function.

Resultsshow that for clear-sky situationsbothmethodsretrieve soil moisturecontentscloseto eachotherandto

theobservations.Thevariationalmethodis moreefficientbut non-linearitiesof theproblemmaketheefficiency of

theconvergencedependenton the initial startof theminimisation.Whenthe fractionof vegetationis large,soil

moisturein therootzoneis retrievedmoreaccuratelythansurfacesoil moisture.Theexaminationof thecost-func-

tion (Fig. 6 ) showstheexistenceof asecondaryminimum(correspondingto ambiguityin theresponse,thesame

surfaceevaporationcanbeobtainedwith totally differentswatercontentsin thesoil reservoirs)aswell asaplateau

wheresurfaceevaporationis notsensitiveto modificationsin soil moisture(abovefield capacity, evaporationis as-

sumed to take place at a potential rate, therefore it is no more controlled by the surface).



ECMWF, 2002

Figure 6Variations of the cost function with soil moisture for 4-5 July 1986. (A) represents the dry guess

( ), (B) represents the moist guess ( ), and the square is the searched state (reference).

(FromMahfouf 1991).

6OTHER TECHNIQ UES TO INITIALISE SOIL MOISTURE

6.1 Methods based on precipitation data

Two methodshave beenintroducedto initialise soil moisturefrom precipitationdata,bothof themrequiringthe

availability of measurementsover large areasandan algorithmto performa precipitationanalysisbeforehand.

They have only been applied over areas with a good observational coverage like the US or the UK.

Thefirst techniqueis anuncoupledinitialisationwherea landsurfaceschemeis forcedwith conventionalmeteor-

ologicalobservations(temperature,humidity, wind,radiationandprecipitation)toprovideanestimateof soilmois-

ture.Feasibilitystudieshave beenundertakenin variouslimited areamodelsby Smithet al. (1994),Macpherson

(1996)andMitchell (1994).Theimprovementof theforecastsof screenlevel humidity whensoil wateris initial-

izedwith sucha method,usingtheUK Met Office waterbudgetscheme,is shown on Fig. 7 (from MacPherson

1996) for all UK stations.

θ 0.30θsat= θ 0.70θsat=



ECMWF, 2002 11

Figure 7Screenlevel relativehumidityverificationof forecastsfrom 28June199500UTC, with differentinitial

soil moisture:Operational(OP)with freecycling moisture,climatological(CLIM); MORECS(S)andMORECS

(R) refer to a smoothed and raw version, respectively, of the soil moisture initialisation using oberved

precipitation. (FromMacPherson 1996).

Anothertechniquemakesuseof bothobservedprecipitationratesandmodelfirst-guess.Assuminga rainfall rate

increment over a 6-hour period:

(11)

This quantityis convertedin soil moistureincrementby usingthetangentlinearmodelof a soil moisturebudget

scheme:

(12)

whereE is themeanevaporationrateandθ themeansoil moisturecontentduringthe6-hourassimilationperiod

(trajectory).Then,thesoil moistureincrement∆ θ is addedto thesuperficialreservoir. Studieshave beenunder-

takenatECMWFby Vasiljevic (1989,personalcommunication)andatUKMO by JonesandMacpherson(1995).

Sucha methodis sensitive to thespecificationof surfacerun-off andcanconvergeslowly whenbiasesin theroot

zone are large.

6.2 On-site observations and methods based on satellite imagery

Existingtechniquesfor groundbasedobservationsof soil moisture(seerecentreviews in Schulinetal. 1992;Wei

1995)aretimeconsumingandnormallyrequirehumanintervention.Therepresentativenesserrorof theon-sitees-

timatesis bestavoidedby deploying several instrumentswithin a relatively small area( 100m2), increasingthe

costof themeasurements.In spiteof its problems,on-sitesoil moisturedataarevery usefulfor regionalesimates

for climaticstudies,essentialto closethewaterbudgetin large-scalehydrologicexperiments(CuencaandNoilhan

1991;Goutorbeet al. 1989;Mahfouf 1990)andto calibrateremotesenseretrieval techniques(Georgakakosand

Baumer 1996).

Thereisnoprospectof obtainingreal-timeglobalestimatesof soilmoisturebasedonexistingtechnologyof ground

basedinstruments.For this reason,severalalgorithmshavebeendevelopedto infer soil moisturefrom satelliteob-

3C

6D

9E

12 1815

fForecast time (hours)

2G

0 CH

LIM

10

5I0J

15

-5

-10

-150J

mea

n er

ror

(%)

20

fForecast time (hours)

15

10

5I

0J

3C

6D

9E

12 15 18

rms

erro

r (%

)

MORECS(S)MORECS(R)OK

P

∆� � a � f–

∆ ------------------=

d∆Θd-----------

∆θθ

-------�

– ∆�+=



ECMWF, 2002

servations,althoughnoneof themis currentlyusedin anoperationaldataassimilationsystem.Threetypesof tech-

niqueshave beenproposed(seereviews in Paloscia1996; Schulin et al. 1992; Wei 1995) basedon infrared

measurements,passive microwave and, more recently, active microwave (radar) instruments.

In theinfraredchannels,thesensitivity of thediurnalcycle of surfacetemperatureto soil moisturehasbeenused

to definemethodsbasedon the observed changeson the infraredskin temperature(which avoid the problemof

absolutecalibrationof thesatellitesensor).For reviewsof applicationsseeCarlson(1991),SchmuggeandBecker

(1991),andSchulinetal. (1992).Geostationarysatellitesallow for abettertemporalsampling(Wetzeletal. 1984

; McNideretal.1994).Thesemethodscanonly beappliedin clearsky conditionsbut provideaninformationabout

soil moisturein therootzoneovervegetatedareas.Bastianssen(1995)developedrecentlya techniqueto estimate

regionalevaporationoverheterogeneousterrain,basedonaseparateestimateof theevaporationof unstressedpix-

els,basedon potentialevaporation,andfully stressedpixels,basedon the infrareddiurnal cycle technique.The

evaporationof theremainingcloud-freepixelscanbeobtainedby interpolationbetweenthewetpixelsandthedry

pixels.vandenHurk etal. (1997)hasappliedthis techniqueto initialize thesoil waterof a limited areamodelover

the Iberianpeninsula.Themodelsoil moistureis the linearizedsolutionof a variationalproblemthatminimizes

the difference between model and satellite estimates of evaporative fraction ).

Microwavechannelscanbeusedto infer soil moisturedueto theimportantvariationsof thedielectricconstantof

asoil with volumetricwatercontentfor frequenciesbetween1 and5 GHz(SchmuggeandJackson1994).Passive

microwavetechniquesusethefactthatsoil emissivity changeswith its watercontent.In activemicrowavesensors

(radar)thesignalis emittedby anartificial sourceandtheintensityof thebackscatteredradiation,afterreflection

by thesurface,is measured.Thereflectivity of thesoil changeswith its watercontents,hencetheintensityof the

reflectedsignalcanberelatedto thesoil moisture.Activemicrowavesystemsallow, for thesamewavelength(same

maximumpenetrationdepth),a finer horizontalresolution,becausethegroundcanbescannedwith anangularly

confinedbeam.Oneof thedrawbacksof microwaveretrievalsis thatthesurfaceemissivity/reflectivity is alsosen-

sitiveto thesurfaceroughnessandthewatercontentsof thevegetationcanopy. Nevertheless,it appearsthatsimple

estimatesof surfaceroughnessof broadvegetationclassesaresufficienttocorrectthesoilmoistureestimate(Njoku

andEntekhabi1996).Ontheotherhand,theoppacityof thevegetationlayerincreaseswith its watercontent,mak-

ing thecorrectionsdueto vegetationincreasinglyunreliablefor moistsoils.Perhapsthemajordrawbackof micro-

wave estimatesis thedepthof penetrationof thesignal,limited to thetop layerof thesoil (2 to 10 cm,depending

on thewavelength).However, for specificsoil hydrologicalandatmosphericconditions,thesoil watercontentsof

theroot layer is correlatedwith thetop soil water. Recentstudiesshow that it is possibleto infer, in a physically

consistentway, thewholeprofileof soil waterfrom its valuesat thetoplayer(e.g.Njoku andEntekhabi1996;Cal-

vet et al. 1997).

Wehaveshown in thissectionthatground-basedestimatesof soil moisture,althoughveryimportantfor calibration

purposesandin intensive field efforts, cannotgive a nearreal-timeglobalstimateof soil moisture.Satelliteesti-

matescanachieveglobalcoverage,but arelimited to clear-sky conditions(infraredchannels)or senseonly thetop

few centimetresof soil (microwavechannels).Thefuturereliesonphysicallybasedestimatesof soil moisturefrom

a combinationof satellitemeasurementsandmodelshort-termforecasts,usinga variationaltechniquein orderto

find the soil water contents that fits best the satellite signal.

7INITIALISA TION OF OTHER LAND SURFACE QUANTITIES

7.1 Snow mass

Themethodsusedto analysesnow massarerelatively crudewhencomparedto analysisschemesfor theatmos-

phericvariables(Lorenc1986)andcould easilybe improved. In this section,the ECMWF snow analysisis de-

� � ��+( )⁄



ECMWF, 2002 13

scribed. The methodology used in other operational centres is very similar.

Figure 8Snow depth(cm) for January(top)andApril (bottom).Theclimatologyusedin theECMWFanalysisis

shown on the left, differences to the US Air Force climatology is shown on the right. The linear snow density

formulaof Verseghy(1991),varyingbetween188kg m-3 and450kg m-3, is usedto convert thesnow massvalues

of the analysis climatology into snow depth.

Every 6 hours a snow analysis is performed in three steps:

20ON

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snow depth (cm) (EC AN - USAF) climate 01

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snow depth (cm) EC AN climate 04S

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ECMWF, 2002

1) Snowfall analysis:From SYNOPreportsof temperatureandprecipitationrate,a snowfall rate is

estimatedat the observation points, and then a spatial interpolation is done by a successive

correction method.

2) Snow massbackgroundfield: A very simplesnow modelevolution is usedto build thebackground

from the analysedsnowfall , the previous analysisof snow mass(persistence) , a snow

climatological mass , and an empirical melting function M basedon the 2m temperature

forecast:

(13)

or in a discretized form:

(14)

3) 3) Snow massanalysis:a sucessive correctionmethodis appliedto thesnow massincrements(the

differencebetweenthebackgroundfield in (2) andtheobservationsof snow depth,suitablyscaled

assuming a fixed snow density of 250 kg m-3).

Themainshortcomingsarethatinformationsfrom themodel(first-guess)arenottakeninto accountin theanalysis

processandthat thesnow massclimatology, towardswhich theanalysisis relaxedandin fact thedominantterm

in datavoid regions,is ratherpoor. Thesnow climatology(BrankovicandvanMaanen1985,BvM85) hasbeen

constructedby runningto equilibriumanempiricalsnow massmodelforcedby precipitationmonthlyclimateval-

uesandadjustedfor meltingusingatemperatureclimatology;noticethatnosnow observationswereusedandthat

thespatialresolutionis ratherpoor( ). Fig. 8 shows BvM85 climatologyfor JanuaryandApril, andcom-

paresits valueswith the USAir Force(USAF)climatology(FosterandDavy 1988),thelattertakinginto

considerationanextensivecollectionof regionalandglobalsurveysof groundbasedsnow depthobservations.Note

that,sincetheUSAFis aclimatologyof snow depth,BvM85 snow massvalueshave to beconvertedusinganem-

pirical specificationof snow density:Eq(48)of Verseghy(1991),thattakesintoaccountthepackingof snow under

its own weight,wasused.It is clearthat in January, theBvM85 valuesextendtoo far southin Asia,overestimate

thesnow depthin southSiberia,MongoliaandeasternEurope,northwesternandeasternCanada,andunderesti-

matethe snow depthin northernSiberia,Iraq, Iran, westernEuropeand CentralCanada.BvM85 valuesover

GreenlandaremuchlargerthanUSAF, partlybecausetheUSAFrepresentsaclimatologyof seasonalsnow depth,

while BvM85 snow massvalueshave beenassignedthearbitrarily high valueof 10 m, "to avoid unrealisticmelt-

ing" (BvM85). In springBvM85 overestimatesthesnow depthvirtually everywhere,but for theeuropeanvalues

(e.g. the Alps and Pyrenees), where a small underestimation is detected.

MeanmonthlyJanuaryandApril snow depthvaluesof theECMWFreanalysisareshown in Fig. 9 , togetherwith

theirdifferenceto theUSAFclimatology. Theoverallpatternsin theright panelsof Figs.8 and9 areverysimilar,

indicatingthat theBvM85 climateinfluencesstronglythereanalysisvalues.Nevertheless,it is alsoclearthat the

informationfrom observationsin Januaryis effectively used(valuesof top panelof Fig. 9 aresmallerthanthe

correspondingvaluesin Fig. 8 ), especiallyfor EuropeandwesternAsia.Substantialerrorsin theBvM85 clima-

tology in springleadto largeanomaliesof the reanalysismeanvalues.As a further illustrationof the reanalysis

informationbroughtby theuseof observations,themonthlydeviationsof snow massfrom theBvM85 valuesis

shown ontheleft panelsof Fig.10 , while theright panelsshow thestandarddeviationof themonthlymeanvalues

of analysedsnow mass.Sincewearedealingexclusively with snow massvalues,therewasnoneedto usetheden-

sity relationin thisfigure.ThenortheasternAsianvaluesof snow in winteraresimilar to BvM85, andthestandard

deviationis small.A separateanalysis(Corti etal.2000)showsthataverylargenorthernAsianareacorresponding

Ug � s

UpU

c

dU

d------- � s

V–

Uc

U–

τ----------------+=

UXW1 λ–( )

Up λ

Uc ∆ Y� s

V–( )+ +=

5° 5°×1° 1°×



ECMWF, 2002 15

to theformerSoviet Union hasa datacover very inhomogeneousin time: thenumberof observationsfrom 1979

to 1992are10to 30timessmallerthanin 1993.Valuesfor themonthof May (notshown) displaylargerdifferences

to theclimateandlargervariability in northernlatitudes.Thisis dueto interannualvariability in theratesof melting

implictely usedin thesnow analysisalgorithm(Eq.(14)), andcontrolledby thefirst-guesstwo-metretemperature.

Figure 9AsFig. 8, but for the reanalysis mean January value (top left) and the mean April value (bottom left).

Right panels show the difference between these values and the US Air Force climatology.

20OZN

40OZN

60ON

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90OW

45OW 0O45OE

90OE

135O[E

snow depth (cm) EC AN climate 01\

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135O[E


20ON

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snow depth (cm) EC AN climate 04\

20ON

40ON

60ON

80ON

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90OZW

45OZW 0O

45OE

90OE

135OE




ECMWF, 2002

Figure 10Snow mass(mm)differencebetweenthereanalysismeanmonthlyvaluesandtheanalysisclimatology

(left), and standard deviation of the monthly mean reanalysis values (top row, January; bottom row, April).

20OZN

40ON

60ON

80OZN

180OZ

135OZW

90OW

45OW 0O45OE

90OE

135O[E

snow mass (mm) (ERA - EC AN) climate 01

20ON

40ON

60ON

80ON

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90OW

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90OE

135O[E

std snow mass (mm) ERA 01

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snow mass (mm) (ERA - EC AN) climate 04

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std snow mass (mm) ERA 04



ECMWF, 2002 17

Figure 11Dailysnow mass(mm)valuesfrom 1 August1981to 31July1991for apointover theFrenchAlps (47

N, 6 E, altitude1100m). Thesolid line representsaproxy for thetruth,estimatedwith Martin (1996)model(see

text for more details), the dashed line shows reanalysis values.

Theanalysisalgorithmhasbeenfurtherevaluatedby Martin (1996),andresultsfor snow massaredisplayedin Fig.

11 . Thevaluesof the reanalysis(labelledERAin thepicture)arecomparedwith thoseproducedby anoff-line

integrationof adetailed,physicallybasedsnow model,CROCUS(Brunetal. 1989;1992),forcedby ERA values

of screenlevel temperature,wind speedandhumidity, precipation,andsemi-empiricalderivedvaluesfor incoming

radiation.Thepictureshows daily values,from 1 August1981to 31July 1991,for apoint in theFrenchAlps (47

N 6 E), wherethemodelelevationis similar to thestationheight(1100m). Thereanalysissnow massvaluescap-

turewell the interannualvariability, with maximumvaluesfor theyears81/82and83/84,andminimafor 82/83,

88/89and89/90.However, thereanalysisvaluesaresystematicallytoohighfor theaccumulationperiod,with ERA

overshootingCROCUSvaluesat times.Themeltingperiodcomestooearly, althoughthereanalysismeltingrates

aresometimessimilar to valuesfrom CROCUS.Thesnow analysis(step3 above) requiresthespecificationof a

snow densityto convert theobserveddepthof snow in equivalentwaterdepths(massvalues)which arethequan-

tities managedby thelandsurfacescheme.A fixedvalueof 250kg m-3 is assumedwhich appearsto betoo high

for freshsnow, explainingtheoverestimationduringtheaccumulationperiod.In thereanalysisvalues,therelaxa-

tion coefficient towardstheBvM85 climatologyis λ = 0.02which correspondsto a time scaleof τ = 12.5days.

PoorspatialresolutionovertheAlps mightresultin lackof dataandarelaxationto theunderestimatedclimatolog-

ical values (see bottom right panel ofFig. 8 over the Alps).

Possibleimprovementsof this techniquecouldbeto useanupdatedsnow massclimatologybasedondirectobser-

vationsandavailableataresolutionon1 degreecompatiblewith thecurrentECMWFmodelresolution(Sellerset

al. 1996).Thelandsurfaceschemecouldbeimprovedto provideamorereliablefirst-guess.With theintroduction

of thesnow densityasa prognosticvariable(Douville et al. 1995)it shouldbepossibleto performananalysisin

termsof snow depths,theobservedground-basedvariable,insteadof snow waterequivalent(sincesnowfall can

Aug]Sep^ Oct_

Nov` Dec^Jana Feb^

Marb Aprc

MayJun]

Jul]

100

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(mm

)

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(mm

)

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(mm

)

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)

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m)

Aug]Sep^ Oct_

Nov` Dec^Jana Feb^

Marb Aprc

MayJun]

Jul]

CROCUSERA

81/82d

82/83d

83/84d

84/85d

85/86d

86/87d

87/88d

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90/91e



ECMWF, 2002

easilybeconvertedknowing densityof freshsnow). Remotelysensedinformationshouldbeused,sinceweekly,

andmorerecentlydaily, snow cover chartsarepreparedby NOAA/NESDIS (BruceRamsay, personalcommuni-

cation,seealsoSellersetal.1996)basedonacombinationof visible,infraredandmicrowaveimagery. Microwave

valuescouldbeusedto obtainsnow massandsnow density, usingthedependency of thesignalon frequency and

polarization(seereview in Hallikainen1996a;1996b);theavailablealgorithmsaremoreaccuratefor dry snow,

andhaveproblemsfor wetsnow or whentherearelargevariationsof theroughnessin thefield of view. Thevalues

of ECMWF analysisof snow massshouldbe routinelycomparedwith the US Air Forcedaily analysisof snow

depth, based on ground observations and satellite imagery.

7.2 Deep soil temperatures

Figure 12Soil temperature profiles averaged for a number of stations over northern Germany for 10 April 1997.

The solid (red) line represents the mean observed profile at 14 UTC, the dashed (blue) line represents the

interpolated short-term forecast values verifying at 15 UTC.

Sincedeepsoil temperaturesevolveover timescalesmuchlongerthanshortandmediumrangeforecasts,thelack

of initialisationfor thesevariablescanleadto potentialdrifts astheoneobservedfor soil moisturein theECMWF

model.ExperienceatECMWFduringthewinter95/96hasshown thatthisproblemcanoccurin winter, whenthe

atmosphericforcing over thesurfaceis weaker, andthethermalinfluenceform thesoil deeperlayersis moreim-

portant.Thecombinationof amisrepresentationof somephysicalprocessesin thelandsurfacescheme(soil water

freezing),excessive radiative cooling,andinsufficient downwardsheattransferin very stableboundarylayersled

-200

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soil

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th [

cm]

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00g 2h 4i 6j 8k 10 12 14

soil temperature [C]l

0g 2h 4i 6j 8k 10 12 14

Germany (10001-10999) 137 stationsFC: 97041012 t + 3h / OBS: 97041014

Vertical soil temperature profiles

OBS MODEL



ECMWF, 2002 19

to excessivecoolingof thesoil, andlargenegativebiasesin screenlevel temperature.Nevertheless,theproblemis

lesscritical thanthesummersoil moisturedrift sincein winter thestablestructureof theboundarylayerdecouples

the atmosphere from the surface below and prevents surface errors from propagating into the mid-troposphere.

Unlike soil moisture,routinemeasurementsof profilesof temperaturein thesoil areperformedby mostmeteoro-

logical offices.Unfortunately, only very few of thesemeasurementsaretransmittedin theGTS,andthereforeno

globalor evencontinentalcoverageexistsin realtime.A handfulof europeancountriessendsdaily valuesto EC-

MWF, andthoseareusedregularly for validationandmonitoringthemodelvalues.An examplein Fig.12 , where

anaverageprofileof soil temperaturefor stationsin northernGermany is comparedwith thecorrespondingmodel

values,for a recentdate.Themodeldeeptemperaturesshow acoldbias,but it is interestingto notethatthemodel

gradientis compareswell with observations.Thismight indicatereasonablygoodsoil thermalproperties(they de-

terminetheverticalgradient),but comparatively pooratmosphericforcing in thepreviousweeks(determiningthe

rateof coolingof thewholesoil slab).Theresultsareconsistentwith thewell known systematicunderestimation

of longwave downwardsurfaceradiationof theECMWF modelandothermodels(Wild et al. 1995;Garrattand

Prata 1996).

Theonly existing methodfor initialising soil temperaturehasbeenproposedby Coiffier et al. (1987)whereana-

lysedincrementsat2 m arereporteddirectly in thesoil.Thissub-optimalmethodcouldbeimprovedby anoptimal

interpolation following the methodology ofMahfouf (1991).

7.3 Vegetation properties

Xueetal. (1996)have recentlyshown thatthespecificationof theseasonalvariationsof vegetationpropertiescan

haveasignificantimpacton thesimulationof monthlymeantemperaturesnearthesurfaceover theNorthAmeri-

cancontinent.Thesesonalevolution of thevegetationcanbeof importanceover areaswith agriculturalpractices

(mid-latitudecontinents,tropical regions).Vegetationpropertiesarecurrentlyeitherfixedspatially, asin theEC-

MWF model(Viterbo andBeljaars1996),or canvary from monthto monthaccordingto correspondencetables

(Mahfoufetal. 1995).In anoperationalcontext, theuseof satellitedatalikeGlobalVegetationIndexes(GVI) (see

Gutman1994)couldbeabetterwayto captureseasonallityandinter-annualvariability of thevegetation.Thema-

jor difficulty is to relatesatellitereflectancesto input parametersof the land surfacescheme(leaf areaindex,

albedo,vegetationcover,...).However, variationaltechniquesalreadyusedfor theretrieval of atmosphericvertical

profiles from satellite radiances appear promising (Eyre et al. 1993).

8CONCLUSIONS

During thelastfive years,theinitialisationof prognosticanddiagnosticsurfacevariableshasbeenrecognisedas

animportantissuefor numericalweatherprediction.Weaknessesof initialisationsbasedeitheronfirst-guessonly

or climatologyhave beenclearlyidentified.As a consequence,soil moistureis currentlyinitialisedin variousop-

erationalweathercentresusingsub-optimalanalysismethodsandobservationsfrom SYNOPreports(ECMWF,

UKMO, CMC, Météo-France,HIRLAM). Thesetechniquescouldbebeimprovedby usinganalysismethodsal-

readytestedfor atmosphericvariableslikeoptimuminterpolationin thesequentialframework and4D-Var (which

is ratherappealingby betteraccountingfor thenon-linearitiesof theproblemaswell asthetemporaldistribution

of observations).

Theotherlandsurfaceprognosticvariablesarestill crudelyinitialised.Concerningsnow massanalysisatECMWF,

thecurrentschemecouldbeimprovedby usingamorerecentclimatologyandamorerealisticobservationoperator

if snow density can be computed by the land surface parametrization.

Areasnotyetexploredconcerntheinitialisationof deepsoil temperaturesfor which thetimescaleof evolution is



ECMWF, 2002

alsomuchlongerthanshortrangeforecasts,andthespecificationof vegetationpropertieshaving aseasonalcycle

(suchasthealbedo,thevegetationcoveror theleafareaindex). Remotesensedatathatcouldbeusefulin thatcon-

text include quantities such as satellite skin temperatures or the normalized difference vegetation indices (NDVI).

Finally, theexamplesshown in thepaperillustratethefactthattheinitializationandparametrizationmethodshave

to bedevelopedtogether. Realisticmodelsareneededto supportindirectmeasurementstechniques,e.g.,forecast

snow densityallows a betteruseof snow depthmeasurementsto initialise snow mass.On theotherhand,refine-

mentsin thelandsurfaceparametrizationusedby numericalmodelsmightbeneededin orderto extractfrom new

measurement techniques its full information content.

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Land surface assimilation March 2001 · Land surface assimilation March 2001 By Jean-François Mahfouf and Pedro Viterbo Table of contents ... based on Monin-Obukhov theory; the crucial