Agricultural and Forest Meteorology 151 (2011) 607619

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Agricultural and Forest Meteorology

journa l homepage: www.e lsev ier .com/

The effect of temporal aggregation of weather inpresults

L.G.J. van ta,d

a Plant Product etherlb Netherlands Ec Earth System 12 Pod University of nn, Gee Plant Researc agenin

a r t i c l

Article history:Received 7 August 2009Received in revised form20 November 2010Accepted 10 January 2011

Keywords:Spring wheatWeather geneTemperatureRadiationCrop growth mClimate chang

Weather data are essential inputs for crop growth models, which are primarily developed for eld levelapplications using site-specic daily weather data. Daily weather data are often not available, especiallywhen models are applied to large regions and/or for future projections. It is possible to generate dailyweather data from aggregated weather data, such as average monthly weather data, e.g. through a linearinterpolation method. But, due to the nonlinearity of many weathercrop relationships, results of sim-

1. Introdu

In recenfrom the plincluding mstudy the etivity (Ewequantitativegrowth moon plot andIttersum etseason or a

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ulations using linearly interpolated data will deviate from those with actual (daily) data. The objectiveof this study was to analyse the sensitivity of different modelling approaches to the temporal resolu-tion of weather input data. We used spring wheat as an example and considered three combinationsof summarized and detailed approaches to model leaf area index development and associated radiationinterception and biomass productivity, reecting the typical range of detail in the structure of most mod-els. Models were run with actual weather data and with aggregated weather data from which day-to-dayvariation had been removed by linear interpolation between monthly averages.

Results from different climatic regions in Europe show that simulated biomass differs between modelsimulations using actual or aggregated temperature and/or radiation data. In addition, we nd a rela-tionship between the sensitivity of an approach to interpolation of input data and the degree of detail inthat modelling approach: increasing detail results in higher sensitivity. Moreover, the magnitude of theday-to-day variability in weather conditions affects the results: increasing variability results in strongerdifferences between model results. Our results have implications for the choice of a specic approach tomodel a certain process depending on the available temporal resolution of input data.

2011 Elsevier B.V. All rights reserved.

ction

t years, crop productivity assessments have extendedot and eld scale to the regional or even global scaleuch longer time horizons (100 years or more), e.g. toffects of global climate change on global crop produc-rt, 2004; Leemans, 1997). The only suitable tools forassessment of future global crop productivity are crop

dels. Early crop growth models mainly concentratedeld scale (Hansen et al., 2006; Monteith, 2000; Vanal., 2003) for assessments covering time-horizons of ayear. Due to the change in the scale of crop produc-

ding author at: Plant Production Systems Group, Wageningen Uni-search Centre, P.O. Box 430, 6700 AK, Wageningen, The Netherlands.7 482141; fax: +31 (0) 317 484892.ress: Lenny.vanBussel@wur.nl (L.G.J. van Bussel).

tivity assessments, crop growth models, with varying degree ofdetail, are increasingly applied at the continental or global scale,for example: LPJmL (Lund Potsdam Jena managed Land; Bondeauet al., 2007), DAYCENT (Stehfest et al., 2007), GEPIC (Liu et al., 2007),GLAM (Challinor et al., 2004), GAEZ (Tubiello and Fischer, 2007),and WOFOST (Reidsma et al., 2009).

If crop growthmodels are applied at large scales, problems arisewith respect to missing input data (Nonhebel, 1994) and lack ofparameter values for different regions with regard to e.g. speciccultivar characteristics. Applying models in regions with missinginput data or in regions beyond the domain for which they weredeveloped and validated, may lead to unreliable results (Ewertet al., 2005; Irmak et al., 2005).

Field-scale crop growth models are typically based and vali-dated on site-specic daily weather input data. Historical globaldaily weather data sets are available, see e.g. Shefeld et al. (2006)and Hirabayashi et al. (2008), with spatial scales of 1 1 and0.5 0.5 grid cells, respectively. For climate change scenarios,

see front matter 2011 Elsevier B.V. All rights reserved.agrformet.2011.01.007Bussela,b,, C. Mllerb,c, H. van Keulena,e, F. Ewerion Systems Group, Wageningen University, P.O. Box 430, 6700 AK, Wageningen, The Nnvironmental Assessment Agency, P.O. Box 303, 3720 AH, Bilthoven, The NetherlandsAnalysis, Potsdam Institute for Climate Impact Research (PIK), P.O. Box 60 12 03, D-144Bonn, Institute of Crop Science and Resource Conservation, Katzenburgweg 5, 53115 Boh International, Wageningen University and Research Centre, P.O. Box 616, 6700 AP, W

e i n f o a b s t r a c tlocate /agr formet

ut data on crop growth models

, P.A. Leffelaara

ands

tsdam, Germanyrmanygen, The Netherlands

608 L.G.J. van Bussel et al. / Agricultural and Forest Meteorology 151 (2011) 607619

some global circulation models (GCMs) provide daily weather data(LLNL, 1989), however, GCM performance at this level of temporaldetail has hardly been evaluated; posing considerable limitationson the use of daily weather data from GCMs in climate changeimpact studclimatechasets. Missinture, can thweather dafrom aggre(a) simple lapplied in tand the GLAweather coto the monDAYCENT (Sbe disaggreas stochastiparametricsemi-paramet al., 2010)

Crop grbetween wspecic cro2006; Semethesis, showrates if temcal developin temperattemperaturrange of thbe the resuextremely ha high num1993). Thesin various w

Generatassumptionday-to-daytures are elweather geious shortcdaily weath(stochasticdistributedet al., 2010)tested for sapplicabilit

Althougate daily wto be carefuimplementconsiderablPorter, 199variability,deviations fresults are lability. As emore freque2000; Salinthis aspect

Temporahave differgrowth moand radiatiin modellin

to temporally aggregated data. Our hypothesis is that a detailedmodel is more sensitive to the use of aggregated data than a moresummarized model. A detailed model is dened in this study asa more explanatory model, i.e. a model that contains most of the

tionarizeed rin thmmterisrelatientale varrallytionreforrop mtion oup-scal levm) avelotivitling ae dus onclimSouspor

s. Toeshots, anectsmo

ationultse then, bo

teria

rop ginin

ilizatotosylden

combradiaf depproa ind

ss prea inch, astreselowm ett obsial goncluble tthrerive

fy thies. Alternatively, monthly weather data aggregates forngescenariosareavailable fromlarge-scale climatedatag daily weather data, such as radiation and tempera-en be generated on the basis of these average monthlyta (Nonhebel, 1994; Soltani et al., 2004). Conversiongated, monthly data to daily data can be achieved byinear interpolation between monthly averages, as e.g.he LPJmL model (Bondeau et al., 2007; Sitch et al., 2003)M model (Challinor et al., 2004) or (b) assuming that

nditions for all days within one month are identicalthly averages, as e.g. applied in a global application oftehfest et al., 2007). In addition, monthly averages cangated to daily values using weather generators, suchc weather generators (e.g. applied by Semenov, 2009),weather generators (e.g. applied by Liu et al., 2009), oretricweather generators (e.g. applied by Apipattanavis.owth is the result of nonlinear, dynamic relationseather, soil water and nutrients, management, andp characteristics (Hammer et al., 2002; Hansen et al.,nov and Porter, 1995). Some processes, e.g. photosyn-

continuous and mainly nonlinear changes in theirperature changes. Other processes, such as phenologi-ment, show a much more linear change with variationure. Finally, crops also respond to absolute changes ine, i.e. if a crop experiences temperatures outside theose typically experienced, signicant yield losses maylt (Porter and Semenov, 2005), e.g. a short period ofigh temperatures near anthesis in wheat can result inber of sterile orets (Ferris et al., 1998; Mitchell et al.,e relationships are implemented in crop growthmodelsays, with different levels of abstraction being used.

ed weather data, based on linear interpolation or on theof identical weather conditionswithin onemonth, lackvariability in weather patterns, e.g. extreme tempera-iminated, in contrast to weather data generated by anerator. However, weather generators suffer from var-omings, such as lack of available observed site-specicer data in order to calibrate the weather generatorand semi-parametric weather generators) or normal-data (parametric weather generators) (Apipattanavis. Moreover, so far, weather generators have only beenpecic regions or sites, which leaves doubt about theiry at the global scale.h linear interpolation is a pragmatic method to gener-eather data at the global scale, its applicability needslly examined, because of the nonlinear relationships

ed in crop growth models, which can bias model resultsy (Hansen et al., 2006; Nonhebel, 1994; Semenov and5). Especially in regions with high day-to-day weatherlinearly generated weather data will show substantialromactualweather. Consequently, differences inmodelikely to be largest in regions with high day-to-day vari-xtreme weather events have been projected to occurntly in the future (Beniston et al., 2007; Easterling et al.,

ger et al., 2005), the use of interpolateddatawill excludeof climate change from impact studies.l aggregation of temperature and radiation data will

ent effects on different processes considered in cropdels, as these differ in their sensitivity to temperatureon. Moreover, the degree of detail taken into accountg specic processes may determine their sensitivity

interacsummsimplicessesand sucharaclinearcontinlate thtemposimula

Theity of cresoluin theregionaestivuarea deproducmodeldamagimpactfuture2010;the temmodelple thrdata sethe effgrowthinform

Resanalyslocatioered.

2. Ma

In cdetermand utthe phVan Dethreemodelrange otivity aleaf arebiomaleaf arapproawatergiven b

AdaagainspotentTheycwere a

Thewere dquantis and elements important for the system. In contrast, ad model is in general more descriptive, it often containsepresentations of the complicated interactions andpro-e system. The difference in sensitivity between detailedarized models is expected due to differences in theirtic times (or reaction rates) and in their number of non-onships considered. Crop growth models applied at theor global scale differ in their level of detail to simu-

ious processes of crop growth. Consequently, the use ofaggregated weather data may have different effects onresults among global crop growth models.e, the objective of this study is to examine the sensitiv-odels with different modelling detail to the temporal

f weather input data. This should provide more insightaling of important crop growth processes from eld toel for global applications.Weuse springwheat (Triticums an example and analyse two important processes, leafpment, to simulate radiation interception, and biomassy. For each process a summarized and a more detailedpproach is used. None of the models used here coverse to extreme weather events such as heat stress. Thesecrop yields are of increasing concern due to expectedate changes (Battisti and Naylor, 2009; Long and Ort,sana et al., 2010) and are likely to be very sensitive toal resolution of input data if included in crop growthexamine the possible impacts, we have tested a sim-ld model with daily observed and monthly aggregatedddiscuss the implications formodelling. Consequently,of temporal resolution of input data on results of cropdels have to be studied, as data aggregation leads tolosses.

are presented for nine locations across Europe, toeffects under different climatic conditions. For eachth fully irrigated and rainfed conditions were consid-

l and methods

rowth models, two processes play an important role ing biomass dynamics: radiation interception by leavesion of the intercepted radiation to produce biomass vianthesis process (Gabrielle et al., 1998; Monteith, 1977;et al., 2001; Yin et al., 2000). In this study we appliedinations of summarized and detailed approaches totion interception and biomass productivity, reecting atail in model structure: a summarized biomass produc-ach was combined with a summarized and a detailedex approach (Fig. 1a and b, respectively) and a detailed

oductivity approach was combined with a summarizeddex approach (Fig. 1c). For each biomass productivityspecic water balance was used to simulate effects of

s. Details of the approaches and water balances used areand in Appendix.al. (2011) evaluated the different model combinations

erved data for a wide range of climatic conditions underrowing conditions, using observed daily weather data.ded that, after calibration, all threemodel combinationso reproduce observed yields within reasonable limits.e model combinations to calculate crop productivityn by both actual and interpolated weather data. Toe sensitivity, the average relative differences (Bd, %)

L.G.J. van Bussel et al. / Agricultural and Forest Meteorology 151 (2011) 607619 609

Fig. 1. Schemaefciency, and

between toson with inweather da

Bd =9

k=1

1absolute va

2.1. Radiati

2.1.1. DetaiA relativ

m2 m2)dyand was ap(LINTUL) inpotatoes (SLINTUL (wiapproachesOijen and E

Growthstage, or untic overview of the different model combinations: (a) summarized leaf area index with r(c) summarized leaf area index with Farquhar photosynthesis.

tal standing biomass at the end of the growing sea-terpolated weather data (Bi, g Cm2) and with actualta (Ba, g Cm2) over the nine stations were calculated:

BikBak

19 100% (1)lues were used to avoid cancelling out of results.

on interception

led leaf area index approachely detailed approach to model leaf area index (LAI,namics isdescribedbySpitters andSchapendonk (1990)plied in the light interception and utilization modelseveral case studies of maize (Farr et al., 2000) and

pitters and Schapendonk, 1990). Adapted versions ofth the same LAI approach, but different assimilation) were used for spring wheat (Ewert et al., 1999; Vanwert, 1999).of LAI is divided into two phases. During the juveniletil a certain LAI threshold is reached (LAIj, m2 m2),

expansionthrough itsoccurs, incrbetween ac

Beyondsupply of aof increaseincrementfraction of bcic leaf areof water strweight is reportionallyself-shadin(Rd-ag, d1)

2.1.2. SummAmore s

the conceptet al., 2005point in timleaf area inadiation use efciency, (b) detailed leaf area index with radiation use

of LAI is exponential. It is governed by temperatureeffect on cell division and extension. If water stress

ease in LAI is reduced by a water stress factor: the ratiotual and potential transpiration.the juvenile stage, LAI expansion is restricted by thessimilates and is calculated using the simulated ratein leaf weight, which is based on the total biomass

multiplied with a partitioning coefcient, dening theiomass allocated to the leaves, andwith a constant spe-a of new leaves (SLA, m2 gC1). To account for the effectess on LAI beyond the juvenile stage, the increase in leafduced through the water stress factor. Leaves die pro-to their weight with a relative death rate, as a result ofg (Rd-sh, d1) and, in the post-anthesis stage, from aging, which is affected by temperature (Fig. 2).

arized leaf area index approachummarizedapproach tomodel LAIdynamics is basedonof the SWAT (Soil and Water Assessment Tool, Neitsch

) model and is applied in the LPJmL model. LAI at anye is calculated as a fraction of a predened maximumdex (LAImax, m2 m2). This fraction is calculated by a

610 L.G.J. van Bussel et al. / Agricultural and Forest Meteorology 151 (2011) 607619

Fig. 2. The relused in the de

forcing functions. Potenthe calculatpre-anthesition for LAIratio of acturadiation usspiration raconditions,potential evwith theFar2.2.1.

The maistrong feedthe detailedsummarizeis dependeduced biomof developmcalculate LAunfavourabperiod mayfeedback mlow biomasthe leavesimplies agagrowing coas leaf areaproduction(Eq. (A.12))

2.2. Biomas

2.2.1. DetaiA detaile

chemical psimplicatisynthesis, Cof plant eninterceptedenzymeRubfrom currenusing Beertion betwee

empecentrar phot

raturynthhesistheber otraticalcunancbaset ofuntase ostomnt COrate (2003balaninglay

ation, see

Summore

is thops,ative death rate of leaves (d1) as a function of temperature (C), astailed leaf area index approach.

tion, dened in terms of sigmoidal and quadratic func-tial LAI is reduced if the required biomass to supported LAI is not available. To account forwater stress, in thesphase awater stress factor is included in the rate equa-growth. The water stress factor is either based on theal and potential transpiration (in combination with thee efciency approach), or based on the maximum tran-te that can be sustained under optimum soil moisturesoil moisture content, potential canopy conductance,apotranspiration, and a scaling factor (in combinationquharphotosynthesis approach)asdescribed inSection

n difference between the two LAI approaches is theback between biomass production and LAI growth inLAI approach, while this feedback is weaker in the

d LAI approach. Growth of LAI in the detailed approachnt on so-called allocation factors, i.e. the daily pro-ass is allocated to the different organs in dependenceent stage. Biomass allocated to the leaves is used toI using SLA. This implies that, in the detailed approach,le growing conditions in the beginning of the growinghave strong effects on nal yield levels. A negativeay occur: unfavourable growing conditions result ins production, therefore little biomass is allocated toand this results in low radiation interception, whichin low biomass production. The effect of unfavourable

Fig. 3. TCO2 conFarquha

tempephotostosyntshowsa numconcen

Tomaintethesis,amounto acco

In cof theambietheticet al.,watercontainof bothevapordetails

2.2.2.A m

tivityFor crnditions is less strong in the summarized LAI approach,is only reduced if water stress occurs or if biomassis insufcient to sustain the root and leaf biomass

.

s productivity

led biomass productivity approachd approach to model biomass productivity is the bio-hotosynthesis model of Farquhar et al. (1980) withons by Collatz et al. (1991). In the process of photo-O2 is converted into carbohydrates through activationzymes by light. Photosynthesis is either limited byradiation (Je, g Cm2 h1) or by the availability of theisco (Jc, g Cm2 h1). Intercepted radiation is computedt LAI and a constant light extinction coefcient (k, ),

s law. Daily gross photosynthesis is the gradual transi-n the two limiting rates and is inuenced by ambient

cepted radithe RUE vof photosy1990). Thecomputedcient, usig Cm2 d1

cepted radiMJm2 d1

synthetical(A.34)).

In the astant; withpotential trthrough a wple bucket,downwardlayer is updrature response of the daily net rate of photosynthesis, at an ambienttion of 350ppm and various radiation intensities, as simulated withosynthesis.

e, CO2 concentration, and radiation intensities.Dailynetesis (And, g Cm2 d1) is calculated as daily gross pho-minus the dark respiration (Rd, g Cm2 d1); Fig. 3

effect of temperature on daily net photosynthesis forf (constant) radiation intensities and a (constant) CO2on of 350ppm by volume.late daily net primary productivity (NPP, g Cm2 d1),e respiration is subtracted from daily net photosyn-d on tissue-specic C:N ratios, temperature, and thebiomass per organ. The remainder is reduced by 25%for growth respiration.f water stress, the model simulates a limited openingata, causing a change in ratio between intercellular and2 concentrations, which results in a reduced photosyn-Gerten et al., 2004; Haxeltine and Prentice, 1996; Sitch). Water available for the crop is calculated through ace, in which the soil is represented by a simple bucket,two layers, each with a xed thickness. Water contenters is updated daily, taking into account transpiration,, runoff, and percolation through the layers (for moreGerten et al., 2004 and Appendix).

arized biomass productivity approachsummarized approach to model biomass produc-

e radiation use efciency (RUE, g CMJ1) approach.a linear relation exists between accumulated inter-

ation and accumulated biomass, the slope representingalue (Monteith, 1977), which combines the effectsnthesis and respiration (Goudriaan and Monteith,daily fraction of intercepted radiation by the crop isfrom current LAI and a constant light extinction coef-ng Beers law. Daily net primary productivity (NPP,) is calculated by multiplying the fraction of inter-ation with: daily incoming short-wave radiation (Rdr,), 0.5 (to convert short-wave radiation into photo-ly active radiation), and radiation use efciency (Eq.

bsence of water stress, radiation use efciency is con-water stress, it is reduced by the ratio of actual andanspiration. Water available for the crop is calculatedater balance, in which the soil is represented by a sim-consisting of single layer that increases in thickness indirection with the growing roots. Water content of theated daily, taking into account transpiration, evapora-

L.G.J. van Bussel et al. / Agricultural and Forest Meteorology 151 (2011) 607619 611

Table 1Location-specic crop phenological parameters.

Location (country, latitude (), longitude ()) Day of emergence (day of year) Temperature sum until anthesis (Cd) Temperature sum until maturity (Cd)

UK (5221 , 007) 56 1185 1693Denmark (57 1577The Netherla 1924Germany (48 1383France (cent 1657France (sout 2149Spain (centr 2022Spain (south 2200Italy (4225 2044

Source: Boons- ity of spring barley are representative for spring wheat.

tion, runoffFarr et al. (

The maity approacincoming rbiomass prapproach isthe detailedbalance schuse efciencentrations

Table 1 seters; otherand biomas(Table 2).

2.3. Weathe

Weathera databaselocations indata forminincoming stion (P, mmms1). Dailtion intercefrom minimvarious Eur

We concpolation ofdisaggregatsoilwaterprocesses osoilwateraggregatingmostly disathe basis ointerpolatioprecipitatio

2.3.1. LineaActual d

weather stafor temperwere assignMDi=2 = 46)polated daMJm2 d1

Xk = Xi +D

M

Xi and Xi+1 are monthly averages of weather variable X (C2 d1) at the middle day of month MDi and MDi+1, respec-

and DOYk is the kth day of the year (Sitch et al., 2003; Soltani004). The sameprocedurewas applied toderive interpolatedmax values (C).a measure for the day-to-day variability in weather condi-he average annual difference (for temperature or radiation)orMJm2 d1) between linearly interpolateddata (Wi, Cor

2 d1) and actual data (Wa, C or MJm2 d1) was computed:

365

k=1

Wik Wak 1365 (3)rger difference indicates larger day-to-day variability.

Occuremeh thafteday

ov (2tempnthersdif993

ractioere06 , 951) 95 1104nds (5206 , 510) 85 134707 , 1142) 91 968re) (4758 , 145) 69 1160h) (4337 , 122) 41 1504e) (4027 ,333) 36 1470) (3725 , 552) 36 1540, 1412) 36 1431

Prins et al. (1993), assuming that sowing dates and temperature sums until matur

, and percolation through the layer (formore details, see2000) and Appendix).in difference between the two biomass productiv-hes is the dependence of the detailed approach onadiation, CO2 concentration, and temperature, whileoductivity calculated according to the summarizedonly dependent on incoming radiation. Furthermore,approach includes a coupled photosynthesis-water

eme, which allows for accounting for changes in watercy, under changing temperatures or at higher CO2 con-.hows the location-specic (phenological) crop param-crop parameters with regard to radiation interceptions productivity are kept constant across the locations

r data

input data for the model runs were extracted fromdescribed by Van Kraalingen et al. (1991), for variousEurope (Fig. 4), for the year 1982. It contains daily

imumandmaximumtemperature (Tmin, Tmax, C), dailyhort-wave radiation (Rdr, MJm2 d1), daily precipita-

d1), vapour pressure (e, kPa), and wind speed (u,y average temperature (Taverage, C), used in the radia-ption and biomass production approaches, is calculatedum and maximum temperatures. Data were used fromopean weather stations (see Table 1).entrated in this study on the effects of linear inter-temperature and radiation data only, as effects of

ion of precipitation data strongly depend on themodel considered. We here focus on crop growthnly and do not compare different levels of detail inmodels, that would allow addressing the effects of dis-precipitation data. Besides, monthly precipitation is

ggregated to daily values in crop growth models onf precipitation generators rather than through linearn (e.g. Bondeau et al., 2007; Liu et al., 2007). Therefore,n is given as daily values in all simulations.

r interpolation of temperature and radiation data

whereor MJmtively,et al., 2daily T

Astions, t(Wd, CMJm

Wd =

A la

2.3.2.Ext

througalreadyas oneSemenimumafter acultivaet al., 1xed fDays waily temperature and radiation values from the ninetions were used to derive interpolated daily values

ature and radiation. Average monthly values, whiched to the middle of each month (e.g. MDi=1 = 15 and

, were calculated from the actual weather data. Inter-ily values for weather variable at day k (Xk, C or) were calculated as:

OYk MDiDi+1 MDi

(Xi+1 Xi) (2)Fig. 4rrence of high temperaturesly high temperatures may strongly inuence yieldseir effects on grain set, since harmful effects occurr exposure to high temperatures for durations as short(Saini and Aspinall, 1982). In line with a study by

009),we summed the number of dayswith a dailymax-erature exceeding 27 C and 31 C during the ten dayssis; two threshold temperatures were used, as wheatfer in their tolerance to extreme temperatures (Mitchell; Porter and Gawith, 1999). Anthesis was dened as an (0.7) of the temperature sum till maturity (Table 1).

summed for the nine locations, based on the data-sets. Locations of the nine weather stations used in this study.

612 L.G.J. van Bussel et al. / Agricultural and Forest Meteorology 151 (2011) 607619

Table 2Most important parameters for the different model approaches and their values.

Symbol Parameter Value and unit Source

Parameters for the summarized leaf area index approachfLAI1 and fLA areafTsum1 and fT eaf arfTsum a nce stSLALAImaxParameters fRgLAIifTjfTsum aLAIjTbaseSLARd-shmxLAIcParameters fRUEkParameters fK25 and Q10 r for aKCKOC3bC3mC3PO2CmasskCqcamaxgmgmin

a Kiniry et ab Van Keulec Haxeltined Sitch et al.e Gerten et

with (1) acdaily Taverag

3. Results

3.1. Weathe

Day-to-dorder to examodel resural resolutiovariability iest in southin weatherthe Unitedvariability isouthern Sp

Duringexceeded a27 C in allcentral FraItaly, actuatemperaturpolated daiI1 Fraction of leaf area index at the rst and second inexion points on the leafsum2 Fraction of temperature sum at the rst and second inexion points on the l

Fraction of the total temperature sum when anthesis is reached and senesceSpecic leaf area of leavesMaximum leaf area index

or the detailed leaf area index approachMaximum relative growth rate of leaf area indexInitial leaf area indexFraction of temperature sum when juvenile stage endsFraction of temperature sum when anthesis startsThreshold leaf area index when juvenile stage endsBase temperatureSpecic leaf area of leavesMaximum death rate due to shadingCritical leaf area index above which self-shading is assumed to start

or the radiation use efciency approachRadiation use efciency based on total daily radiationLight extinction coefcient

or Farquhar photosynthesis approach (C3 plants)The value of the parameter at 25 C and the relative change in the parameteMichaelis constant for CO2Michaelis constant for O2CO2/O2 specic ratioC3 quantum efciencyRd/Vm ratio for C3 plantsOptimal ci/ca for C3 plantsAtmospheric pressurePartial pressure of O2Molar mass of carbon

Light extinction coefcientConversion factor for solar radiation at 550nm from MJm2 d1 to mol photonsmAmbient mole fraction CO2Co-limitation parameterMaximum PriestleyTaylor coefcientScaling conductanceMinimum canopy conductance, which accounts for water stress not directly relate

l. (1995).n and Seligman (1987).and Prentice (1996).(2003).

al. (2004).

tual daily Tmax, (2) interpolated daily Tmax, (3) actuale, and (4) interpolated daily Taverage.

r data

ay variability in weather conditions was calculated inmine its correlation with possible differences betweenlts due to the use of input data with different tempo-ns. Among the considered study locations, day-to-day

n weather conditions was highest in Germany and low-ern Spain (Fig. 5 and Table 3). Day-to-day variabilityconditions in Denmark, The Netherlands, France, andKingdom was comparable to that in Germany, whilen Italy and in central Spain was comparable to that inain (Table 3).the ten days following anthesis, actual daily Tmaxt least during one day the threshold temperature oflocations, except those in the United Kingdom and innce. In The Netherlands, southern France, Spain, andl daily Tmax also exceeded at least once the thresholde of 31 C in the ten days following anthesis. If inter-ly Tmax data were used, only in southern France, Spain,

and Italy TmTmax exceeused than wlated) neve(Table 4).

3.2. Total bdata

Sensitivtion of inpuradiation setemperaturferences beweather dastations (se

The modferent typeare in genethe combinUsing the Faapproach, uof 15% (avebiomass bedevelopment curve 0.05 and 0.95 ()ea development curve 0.05 and 0.45 ()arts 0.70 ()

0.053m2 (gC)1

5.0m2 m2

0.0108 (Cd)1

0.025m2 m2

0.15 ()0.70 ()0.75m2 m2

0 C a

0.053m2 (gC)1

0.03d1 b

4.0m2 m2 b

1.38 gC MJ1

0.5 () c

10 C change in temperature, respectively30 Pa (Q10 = 2.1) c

30103 Pa (Q10 = 1.2)2600molmol1 (Q10 = 0.57)0.08molmol1 c

0.015 (gCm2 d1)/(g Cm2 d1) c

0.8 PaPa1 d

100103 Pa c20.9103 Pa c12gCmol10.5 () c2 d1 4.6103 mol photonsMJ1

molmol1

0.7 () c1.391 () e3.26mms1 e

d with photosynthesis 0.5mms1 e

ax exceeded 27 C, Tmax never exceeded 31 C. However,ded 27 C on more days if interpolated daily Tmax wasith actual daily Tmax. Daily Taverage (actual and interpo-

r exceeded 27 C during the ten days following anthesis

iomass for actual and linearly interpolated weather

ity of the different model combinations to interpola-t data was tested for interpolation of temperature andparately and for the combination of both interpolatede and radiation. Fig. 6 shows the average (relative) dif-tween simulated total standing biomass with actualta andwith interpolatedweather data based on the ninee Eq. (1)), for irrigated and rainfed conditions.els respond differently to the interpolation of the dif-s of input data. Differences under rainfed conditionsral larger than under irrigated conditions, especially foration of both interpolated radiation and temperature.rquhar photosynthesismodelwith the summarized LAInder rainfed conditions, results in an average differenceraged over the nine stations, Fig. 6) in simulated totaltween simulationswith actual and simulationswith the

L.G.J. van Bussel et al. / Agricultural and Forest Meteorology 151 (2011) 607619 613

Fi

combinatioa maximumcombinedwresults in aactual andradiation damarized corainfed conbetween simture and int

Table 3Day-to-day va

Location

UKDenmarkThe NetherlaGermanyFrance (centFrance (soutSpain (centrSpain (southItalyg. 5. Actual and interpolated (daily) temperature (C) and radiation (MJm2 d1) from w

n of both interpolated temperature and radiation, withof 38% in Germany (Fig. 7). Using the RUE approachith the detailed LAI approach, under rainfed conditions,n average difference of 9% between simulations withsimulations with interpolated temperature and actualta, with a maximum of 30% in the UK. The most sum-

mbination (RUE and summarized LAI approach), underditions, results in the lowest average difference (4%)ulations with actual and those with actual tempera-

erpolated radiation,with amaximumof 9% inDenmark.

riability in weather conditions.

Average annual deviationbetween actual andaverage temperature (C)

Average annual deviationbetween actual andaverage radiation (MJm2)

2.22 3.122.19 3.15

nds 2.28 3.132.61 3.42

re) 2.40 3.16h) 2.19 3.22e) 1.80 2.68) 1.66 2.30

1.80 2.71

The effelocations: slow day-to-Spain, showtemperaturconditions.such as Ger

Table 4Number of daydata sets; Taver

Location

United KingDenmarkThe NetherlGermanyFrance (centFrance (soutSpain (centrSpain (southItalyeather stations in Germany and southern Spain in 1982.

cts vary among locations as shown for two contrastingouthern Spain and Germany (Fig. 7). Locations with aday variability in weather conditions, such as southernsmall differences as a result of the use of interpolated

e and/or radiation data, for both irrigated and rainfedIn contrast, locationswith a high day-to-day variability,many, especially the use of the Farquhar photosynthe-

s when Tmax exceeded a certain threshold temperature for two inputage (actual daily and interpolated daily) never exceeded 27 C.

Days with actualdaily Tmax above

Days withinterpolated dailyTmax above

27 C 31 C 27 C 31 C

dom 0 0 0 02 0 0 0

ands 4 1 0 01 0 0 0

re) 0 0 0 0h) 5 1 3 0e) 9 3 10 0) 6 3 10 0

6 2 10 0

614 L.G.J. van Bussel et al. / Agricultural and Forest Meteorology 151 (2011) 607619

Fig. 6. Averagcompared to t

sis approachdata for botwe show thweather varesults withthe model cIt is evidentive linearin weatherproductionday-variabiresults for t(not shown

The usetions in a sone day chTherefore,to simulatealmost exclperiod.

4. Discussi

The objecrop modeldifferent detion of weabiomass deand/or radie differences (%) based on all nine locations in simulated total biomass at the end of the use of interpolated data, for irrigated and rainfed conditions. The error bars indicate th

results in large differences of up to 37%, if interpolatedh temperature and radiation are used (Fig. 7). In Fig. 8e relationship between the day-to-day variability in

riables (see Eq. (3)), and the difference between modelactual and interpolated weather data (see Eq. (1)), forombination with the detailed biomass model (Fig. 1c).t that for this model combination a systematic posi-relationship exists, i.e. a higher day-to-day variabilityconditions results in a larger difference in biomass

between input data sets. Relationships betweenday-to-lity in weather conditions and differences in simulationhe other combinations of approaches are less distinct).of aggregated temperature data results for several sta-mall change in the timing of anthesis and in at mostange in the simulated length of the growing season.differences in simulated biomass are not attributabled differences in length of the growing period, but areusively due to weather variability during the growing

on and conclusions

ctive of this study was to analyse the sensitivity ofling approaches, representing growth processes, withtail, in response to changes in the temporal resolu-ther input data. Our results show that the simulatedpends on whether actual or interpolated temperatureation data are used. This is in line with earlier results of

Nonhebel (ied locationand found oa result of usignicantdataat the lfor crop grothe presentinterpolatiothe day-to-ingdetail incombinatiobiomass wilated inputcombinatio

The larggatedweathapproach cthe assimilathe lack ofdata, tempegrowth, resmore lineadifferencessis approacvariability ibiomass beinterpolatehigh day-tohe growing season, using actual temperature and actual radiatione maximum and minimum differences.

1994) and Soltani et al. (2004). Nonhebel (1994) stud-swithhighday-to-dayvariability inweather conditionsverestimates of 515% for simulated potential yields assing average weather data. Soltani et al. (2004) found

over-estimates of yield with linearly interpolated inputocationswithoptimalor supraoptimal air temperatureswth and a high day-to-day variability. Importantly, instudy, we nd in addition, that the sensitivity to then of input data not only depends on the magnitude ofday weather variability, but also increases with increas-theprocessmodelling. For themost summarizedmodeln, the difference at a particular site between simulatedth actual and simulated biomass with linearly interpo-data is at most 10%, while for the most detailed modeln it is 37%.e differences (higher simulated biomass with aggre-er data) in themodelwith the Farquhar photosynthesis

an be explained by the nonlinear temperature effect ontion rate incorporated in that approach (Fig. 3). Due today-to-day variability in linearly interpolated weatherratures are more often at or near optimum values forulting in higher photosynthetic rates. In contrast, ther nature of the other approaches resulted in smaller. Furthermore, we found for the Farquhar photosynthe-h a positive linear relationship between the day-to-dayn weather conditions and the differences in simulatedtween simulations driven with actual and with linearlyd input data (Fig. 8). This indicates that in locationswith-day variability in weather conditions, and therefore

L.G.J. van Bussel et al. / Agricultural and Forest Meteorology 151 (2011) 607619 615

Fig. 7. Differefor southern S

large differedata, differeare large.

The requmodel to ason crop groinclude thethresholds2010). Our rcannotbe siif calibratedthat threshoaggregatedbe re-param(interpolatethermore, wto crops candepends onstatistical dglobal set owhich is be

In additito ozone poEwert and Pas it is not aever, it is lidata with aapplied in tnces (%) in simulated total biomass at the end of the growing season using actual tempepain and Germany for rainfed conditions.

nces between actual and linearly interpolated weathernces due to the use of linearly interpolated input data

ired structure, parameter values and input data for asess effects of extreme weather events, e.g. heat waves,wth are not yet fully understood. Existing models thatse effects, often apply threshold approaches, as e.g. Tmaxfor heat stress (Challinor et al., 2005; Teixeira et al.,esults, however, suggest that current threshold modelsmplyappliedwith temporally aggregatedweatherdata,with more detailed weather data. We cannot concludeldmodels are generallyunsuitable in combinationwithdata, but at least current threshold values will have toeterized if weather data with different characteristicsd vs. actual; mean vs. maximum) are being used. Fur-hether threshold temperaturemodels for heat damagebe applied with interpolated monthly data also largelythe local day-to-day temperature variability and theiristribution characteristics. An in-depth analysis of af daily temperature measurements would be required,yond the scope of this study.on to heat stress, effects such as yield reductions duellution are also simulated using threshold values (e.g.orter, 2000). This effect has not been considered here,ddressed in any global-scale crop growth model, how-kely that re-parameterization is also advisable if inputdifferent temporal resolution are being used, than thathe original model.

Based onof the provated througby global ciweather daators, are cu2009), whicglobal scaledata shouldsites. Resultmates, espeto assess thmay requirditions of h

Our hypaggregatedmodelling aobservationto model aresolutionuncertaintycombined wevaluation.resolution oand model aof a (globabe (re-)evainput data,rature and actual radiation compared to the use of interpolated data

the results presented here, we stress the importanceision of daily weather data. Such data may be gener-h weather generators, in combination with or directlyrculation models. However, site-specic observed dailyta, which are often required to calibrate weather gener-rrently unavailable for large parts of the Earth (Liu et al.,h hampers the application of weather generators at the. For that reason, we stress that observed daily weatherbe made available for more regions and measurements ofweather generators should be tested for various cli-cially for climates with extreme temperatures, in ordereir applicability in climate impact assessments, whiche rather detailed crop growth models, at least for con-igh day-to-day weather variability.othesis that model sensitivity to the use of temporallydata increases with an increasing degree of detail in thepproach, is supported by the results of this study. Thishas implications for the choice of a specic approachcertain process, which thus depends on the temporalof the available input data. However, whether modelis unnecessarily increased if detailed approaches areith temporarily sparse weather data, needs further

Nevertheless, we suggest that the available temporalf the input data and the implications for model resultspplicability need to be taken into account in the design

l) crop growth model. More detailed models need toluated or re-parameterised if driven with less detailedwhile more summarized models may prove to be

616 L.G.J. van Bussel et al. / Agricultural and Forest Meteorology 151 (2011) 607619

Fig. 8. Relatiovariability of tthe combinati

unsuitableday weathe

Acknowled

The autanonymousversion of t

Appendix A

A.1. Radiati

A.1.1. DetaiDuring t

m2 m2), thby tempera

dLAIdt

= LAI

Teff = max(

where Rg (((C) the effedaily avera(Tbase, C), abetween acn between the average annual difference between actual and interpolated weather datahe weather variables, Eq. (3)), and the difference between model runs driven by actual aon of the Farquhar photosynthesis and the summarized leaf area index approach.

for studies addressing the effects of changes in day-to-r patterns, such as studies on weather extremes.

gements

hors are grateful for the valuable comments of tworeviewers,who proposed useful revisions to a previous

his paper.

.

on interception

led leaf area index approachhe juvenile stage or until a certain LAI threshold (LAIj,e rate of increaseof LAI is exponential andmainlydriventure, through its effect on cell division and extension:

Rg Teff Wf (A.1)

0, [Taverage Tbase]) (A.2)

Cd)1) is the maximum relative growth rate of LAI, Teffctive temperature, calculated as thedifference betweenge temperature (Taverage, C) and a base temperaturend Wf () a water stress factor, derived from the ratiotual and potential transpiration.

Beyond

dLAIdt

= dWdt

where dW1weight andleaves.

The sene

dLAIdt

= rdwith

rd = max(R

Rd-sh = max

where Rd-agture and thtakes placeshading, wshading onrelative sen

A.1.2. SummBefore s

maximum l

fLAImax =fTon the one hand (x-axis, indicating the magnitude of the day-to-daynd interpolated weather data on the other hand (y-axis, Eq. (1)); for

the juvenile stage:

1 SLA Wf (A.3)

/dt (g Cm2 d1) is the simulated rate of increase in leafSLA (m2 (gC)1) is a constant specic leaf area of new

scence rate is described by:

LAI (A.4)

d-ag, Rd-sh) and (A.5)[0,min

(Rd-shmx, Rd-shmx

LAI LAIcLAIc

)](A.6)

is an exogenously dened relation between tempera-e relative death rate due to aging (Fig. 2), which onlyafter anthesis. Rd-sh is the relative death rate due to

here LAIc (m2 m2) is the critical value above whichly takes place and Rd-shmx (d1), the maximum possibleescence rate due to shading.

arized leaf area index approachenescence starts, the fraction of an exogenously denedeaf area index (fLAImax, ) is calculated as:

fTsum

sum + exp(l1 l2 fTsum)(A.7)

L.G.J. van Bussel et al. / Agricultural and Forest Meteorology 151 (2011) 607619 617

l1 = ln(

fTsum1fLAI1

fTsum1)

+ l2 fTsum1 (A.8)

l2 =ln[(fTsum /fLAI ) fTsum

] ln

[(fTsum /fLAI2) fTsum

]

where fTsumperature sutemperaturlated fromthe fractionnously denFollowing t

fLAImax = ((1

where fTsumsenescence

Potentiaan exogeno(LAImax, m2

LAIp = fLAImLAIp is reduleaf area ind

LAI = min(L

where Bt aning root bio2005).

To accouscaler (Ws,is either ba(in combinacombinatio

Ws =(Eq

where S iswtial evapotrgp potentiaet al., 2004)

A.2. Biomas

A.2.1. DetaiDaily ne

gradual traRubisco-lim

And =(

Je +

where is aand Rd (g C

Je =C1 AP

Jc = C2 Vm24where APAactive radia

solar radiation, with:

C1 = TC3 Cmass C3 pi

pi + 2 , (A.17)

i + K

, thef:

ca, the

P, the

O2] per

5 Q

the nmpe,C3presoptiractilisMnt foer KC2 d

1b

)

C2

b,

rk r

Vmb is aaseconasas ofynth

nd +

resse

l (

gc (m1) th

loss nts fovapoom gpres1 1 1 2 2

fTsum2 fTsum1(A.9)

() is the fraction, on a specic day, of the total tem-m required to reach maturity (based on the effectivee), and l1 () and l2 () are shape coefcients, calcu-the fractions of leaf area index (fLAI1, ; fLAI2, ) ands of the temperature sum (fTsum1 , ; fTsum2 , ) at exoge-ed inexion points on the leaf area development curve.

he onset of senescence, fLAImax is calculated as:

1 fTsum)2

fTsum a)2(A.10)

a () is the fraction of the total temperature sum whenstarts.l leaf area index (LAIp, m2 m2) is calculated fromusly dened crop-specic maximum leaf area indexm2) and fLAImax:

ax LAImax (A.11)

ced if the biomass required to support the calculatedex is not available:

AIp, [Bt Br] SLA) (A.12)

d Br (g Cm2) are standing total biomass and stand-mass, respectively (Bondeau et al., 2007; Neitsch et al.,

nt for water stress, in the pre-anthesis phase a water) is included to reduce LAIp. This water stress scalersed on the ratio of actual and potential transpirationtion with the radiation use efciency approach), or (inn with the Farquhar photosynthesis model) as follows:

S

max)/(1 + (gm/gp)

) (A.13)ater supply (see Eq. (A.30),mmd1), (Eq max) poten-anspiration (mmd1), gm a scaling factor (mms1), andl canopy conductance (see Eq. (A.29), mms1) (Gerten.

s productivity

led biomass productivity approacht photosynthesis (And, g Cm2 d1) is calculated as thensition between the light-limited (Je, g Cm2 h1) andited (Jc, g Cm2 h1) conditions:

Jc

(Je + Jc)2 4 Je Jc2

) dl Rd

(A.14)

co-limitation parameter (), dl (hd1) the day length,m2 d1) the dark respiration, with:

AR Cqdl

(A.15)

(A.16)

R (MJm2 d1) is daily absorbed photosyntheticallytion and Cq (mol photonsMJ1) a conversion factor for

C2 =p

pi (Pa)the lea

pi = pa (Pa)

pa = ca* (Pa)

= [2the tem

Ki = K2where() a tecarbonpartialundermole fMichaeconstaKi eith(gCm

Vm =(

with

=[1

s = 24dl

the da

Rd = bwhere

In ccanopytrationin termphotos

Adt = A

or exp

Adt =d

where(mms

wateraccounwatersion frdl is expi C

(1 + ([O2]/KO)

) , (A.18)partial pressure of CO2 in the intercellular air spaces of

P and (A.19)partial pressure of ambient CO2:

(A.20)

CO2 compensation point:

, and (A.21)

ature dependent parameters KC, KO, and :

(T25)/1010 (A.22)

umber 24 (hd1) is the number of hours per day, TC3rature stress factor, Cmass (gmol1) the atomic mass oftheC3quantumefciency (molmol1), [O2] (Pa) thesure of oxygen, (Pa Pa1) the ratio of pi to pa (=maxmal water conditions), ca (molmol1) the ambienton of CO2, P atmospheric pressure (Pa), KC (Pa) theenten constant for CO2, K0 (Pa) the MichaelisMenten

r O2, (molmol1) the CO2/O2 specicity ratio, with, KO or , and Q10 the accompanying Q10 values, and Vm1) the maximum daily rate of photosynthesis:

(

C1C2

) [(2 1) s (2 s C2) ]

APAR Cq (A.23)

C2 s s

]1/2, (A.24)

and (A.25)

espiration (Rd):

(A.26)

constant Rd/Vm ratio ().of water stress, the photosynthesis rate is related toductance through the diffusion gradient in CO2 concen-result of thedifference inpi andpa. This canbeexpressedtotal daytime net photosynthesis. Total daytime net

esis (Adt, g Cm2 d1) is calculated as:(1 dl

24

) Rd (A.27)

d in terms of canopy conductance:

gc gmin)1.6

[ca (1 )] (A.28)

ms1) is average daytime canopy conductance, gmine minimum canopy conductance, which accounts forot directly related with photosynthesis, the factor 1.6

r the difference in the diffusion coefcients of CO2 andur; in Eq. (A.28) Adt is expressed in mmd1 (the conver-Cm2 d1 to mmd1 is based on an the ideal gas) andsed in s.

618 L.G.J. van Bussel et al. / Agricultural and Forest Meteorology 151 (2011) 607619

gc is calculated by rearranging Eq. (A.28):

gc = gmin +1.6 Adt

[ca (1 )] d1(A.29)

Maximuthesis rateaccordinglyAPAR=PAR,gives themimum poten

Water sthan waterdaily transp(Emax, mmd(Wr, m3 m

S = Emax The soil

each with aThe soil waaccount trathe layers.Wtwo soil layspecic layea fraction ofdifference bthewater bGerten et al

Demandis wet (w,based on tparameter g

D = (1 w)

Water stEqs. (A.20)tion methoconditions.

Finally, nas:

NPP = And where R (g Cage organs aC:N ratios,rate, and Rg

Rg = max(0A more d

Haxeltine a

A.2.2. SummNet prod

NPP = RUEwhere R

(MJm2 d

light extincradiation)

wave radiaa water streration. Poteequation (Pon its potenand soil cha

the basis of a soil water balance, calculated for one layer. The thick-ness of the layer increases with increasing root extension. Newlyexplored soil is assumed to be at eld capacity. Water content ofthe soil is updated daily, taking into account precipitation, transpi-

evapo theore d

nces

., Vanodelliatic conaviss andeorol.D.S., Nrecede, M.,naes,007. Fate m, A., Se-Camcultur. 13, 6rins, E-specmunir, A.J.,optimMeteor, A.J.act of180G.J., Blationincludg, D.R. Clim207., Vanessess in E247.., Portt-term. Chan., 2004er chavelopt Prodersitytute f., Rouariosivity.r, G.GheticVan Orent i., Ellis,thesi316

e, B., Ddevel222.

D., Schandwel. J. Han, J.,ght inr, G.L.mod

ding g1.J.W., Ccasts ie, A.,el bastion amashi,8200m (non-water limited) daily net potential photosyn-is calculated with help Eq. (A.28) with =max, and, applying Eq. (A.29) and Eq. (A.14) with =max andi.e. all available photosynthetically active radiation,

aximumaveragedaytimecanopy conductance, i.e.max-tial canopy conductance (gp, mms1).

tress occurs when water supply (S, mmd1) is lowerdemand (D, mmd1). Supply is given by the maximumiration rate possible under well-watered conditions1) and the relative soil moisture in the rooting zone

3):

Wr (A.30)

is represented by a simple bucket containing two layers,xed thickness and a xed fraction of the roots present.ter content of each layer is updated daily, taking intonspiration, evaporation, runoff, andpercolation through

r is calculatedby summing the soilwater content of theers, which are multiplied by the fraction of roots in theranddividedby its thickness. Finally,Wr is expressedasWmax,which is a soil-specic parameter, indicating theetween eld capacity andwilting point. Initialisation ofalance is obtained by a spin-up run (formore details, see., 2004).is dependent on the fraction of the daytime the canopy

), potential evapotranspiration ((Eqxmax), mmd1),he PriestleyTaylor equations, gp, and an empiricalm (mms1):

(Eq max)1 + (gm/gpot)

(A.31)

ress results in a lower canopy conductance, therefore,and (A.33) are solved simultaneously, using a bisec-d, to obtain values of And and under water-limited

et primary production (NPP, g Cd1 m2) is calculated

Rr Rso Rp Rg (A.32)m2 d1) is the maintenance respiration of roots, stor-nd a reserve pool, respectively, based on tissue-specic

temperature, the amount of biomass, and a respirationthe growth respiration:

,0.25 And Rr Rso Rp) (A.33)etailed description of the functions used is provided bynd Prentice (1996) and Sitch et al. (2003).

arized biomass productivity approachuctivity (NPP, g Cm2 d1) is calculated as:

Rdr 0.5 (1 ekLAI) Wf (A.34)UE (g CMJ1) is the radiation use efciency, Rdr

1) daily incoming short-wave radiation, and k () thetion coefcient, the number 0.5 (MJ PAR (MJ short-wave1) is used, because half of the daily incoming short-tion is photosynthetically active radiation, and Wf ()ss factor, i.e. the ratio of actual and potential transpi-ntial transpiration is calculated based on the Penmanenman, 1948), actual transpiration is calculated basedtial value, but also on soil water content (Wc, m3 m3)racteristics.Water available for the crop is calculated on

ration,fed int(for m

Refere

Adam, Mof mclim

ApipattaatorMet

Battisti,unp

BenistonHalsK., 2clim

BondeauLotzagriBiol

Boons-PCropCom

ChallinoandFor.

Challinoimp135,

Collatz,reguthat

Easterlin20002068

Ewert, Fprocyear231

Ewert, FshorGlob

Ewert, Fund dePlanUnivInsti

Ewert, Fscenduct

Farquhasynt

Farr, I.,diffe

Ferris, Rat an82, 6

Gabriellarea209

Gerten,tionmod

Goudriaon li

Hammecropstan153

Hansen,fore

Haxeltinmodpeti

Hirabay(194oration, runoff and percolation. Initial water content,model, is used for initialisation of the water balance

etails, see Farr et al., 2000).

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The effect of temporal aggregation of weather input data on crop growth models resultsIntroductionMaterial and methodsRadiation interceptionDetailed leaf area index approachSummarized leaf area index approach

Biomass productivityDetailed biomass productivity approachSummarized biomass productivity approach

Weather dataLinear interpolation of temperature and radiation dataOccurrence of high temperatures

ResultsWeather dataTotal biomass for actual and linearly interpolated weather data

Discussion and conclusionsAcknowledgementsRadiation interceptionDetailed leaf area index approachSummarized leaf area index approachBiomass productivity

Detailed biomass productivity approachSummarized biomass productivity approachReferences

References