A photothermal model of leaf area index for greenhouse crops

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A photothermal model of leaf area index for greenhouse crops

R. Xu a, J. Dai a, W. Luo a,*, X. Yin b, Y. Li a, X. Tai a, L. Han a, Y. Chen a, L. Lin a, G. Li a, C. Zou a, W. Du a, M. Diao a

a College of Agriculture, Nanjing Agricultural University, No.1 Rd Weigang, Nanjing Jiangsu 210095, PR Chinab Centre for Crop Systems Analysis, Department of Plant Sciences, Wageningen University, P.O. Box 430, 6700 AK Wageningen, Netherlands

1. Introduction

Leaf area index (LAI) is one of the most important cropparameters that determine radiation intercepted by the cropcanopy, and therefore has strong impacts for the calculation ofcrop canopy photosynthesis (which in turn affects the CO2 balanceinside a greenhouse) and transpiration (which in turn affectsenergy and water balances inside a greenhouse). Measuring ormodelling LAI is either time-consuming and/or complicated andrequires special equipment and skills which hampers their use incommercial production settings (Serdar and Demirsoy, 2006). Inthe existing photosynthesis-driven greenhouse crop models, LAIis calculated using either SLA (Dayan et al., 1993; Heuvelink, 1996;Gijzen et al., 1998) or growing degree days (GDD) (Marcelis andGijzen, 1998). Crop leaf growth is not only affected by tempera-ture, but also by photosynthetically active radiation (PAR)

(Heuvelink and Marcelis, 1996). Since temperature inside thegreenhouse, especially when the greenhouse has to be heated andcooled or when there is artificial supplementary light inside thegreenhouse, does not follow solar radiation as closely as for a fieldcrop, using GDD to predict crop leaf area for greenhouse growncrops does not give as good predictive results as it does for fieldgrown crops (Marcelis et al., 1998). When using SLA to estimatecrop leaf area, SLA is usually assumed to be a constant (Lieth andPasian, 1991) or simulated as a function of plant age (Leutscherand Vogelezang, 1990) or season (Heuvelink, 1996). Since thesimulated LAI is very sensitive to SLA which is strongly influencedby crop developmental stage and water, nitrogen and radiationlevels, small error in predicting SLA values can result inunacceptable error for simulating LAI and crop biomass produc-tion (e.g. Kropff et al., 1994; Yin et al., 2000). In addition, SLA canonly be obtained by destructive measurements. This limits theapplication of SLA-based model to greenhouse crop and climatemanagement, because of limited available plant material relativeto that of field crops. A model for predicting LAI based on easilyobtained morphological traits of leaves such as the number of

Agricultural and Forest Meteorology 150 (2010) 541–552

A R T I C L E I N F O

Article history:

Received 12 May 2009

Received in revised form 17 January 2010

Accepted 25 January 2010

Keywords:

Temperature

PAR

Leaf elongation rate

Leaf area index

Leaf rank

A B S T R A C T

Leaf area index (LAI) is an important variable for modelling canopy photosynthesis and crop water use. In

many crop simulation models, prediction of LAI is very sensitive to errors in the value of parameter

‘‘specific leaf area’’ (SLA), which often relies on destructive measurements to determine. In this study, we

present a model for predicting LAI of greenhouse crops based on the quantification of easily measured

morphological traits as affected by temperature and radiation. Our model predicts LAI based on canopy

light interception as a function of node development rate along with specific leaf size and elongation

rates characteristics defined on a leaf number basis. Growth studies with five greenhouse crops

(cucumber, sweet pepper, chrysanthemum, tulip and lilium) were conducted in different greenhouses

and different sites during 2003 to 2009. The model was evaluated, in comparison with two commonly

used methods for predicting LAI – the growing degree days (GDD) based model and SLA based model,

using independent data from other experiments. The coefficient of determination (r2) and the root mean

squared error (RMSE) between the predicted and measured values using our photothermal method are

0.99 and 0.95 (r2, RMSE) for leaf number, 0.98 and 0.01 m for specific leaf length, and 0.98 and

0.13 m2 m�2 for canopy LAI. For the GDD-based model, the r2 and RMSE are 0.93 and 4.23, 0.82 and

0.04 m, 0.87 and 0.48 m2 m�2 for the three traits, respectively. For the SLA-based model, the r2 and RMSE

for canopy LAI is 0.81 and 1.24 m2 m�2 when using the estimated SLA data as input or 0.94 and

0.25 m2 m�2 when using the measured SLA data as input. So, our model better predicts LAI for

greenhouse crops at different latitudes and a range of planting densities and pruning systems. Although

calibrations for specific light regime, pruning practices and cultivars are needed, the fact that production

conditions in commercial greenhouse production are often well controlled and production practices are

often rather standardized implies a general applicability of our model.

� 2010 Elsevier B.V. All rights reserved.

* Corresponding author. Tel.: +86 25 84399100; fax: +86 25 84399100.

E-mail address: [email protected] (W. Luo).

Contents lists available at ScienceDirect

Agricultural and Forest Meteorology

journal homepage: www.e lsev ier .com/ locate /agr formet

0168-1923/$ – see front matter � 2010 Elsevier B.V. All rights reserved.

doi:10.1016/j.agrformet.2010.01.019


leaves per plant and the length of individual leaf may overcomesuch problem caused by the difficulty in obtaining reliable SLAinformation.

Recently, there is an increased interest in developingfunctional-structural models for crop simulation (Prusinkiewicz,1998; Pan et al., 2000; Vos et al., 2007; Kang et al., 2008). A keycomponent of functional-structural modelling is to integrateoutput parameters from functional modules into structural ones.The output of the existing leaf area models, however, only givesthe total area of one plant or of the whole-crop stand (Kahlen,2006). A model for predicting LAI based on some underlyingmorphological traits of leaves would facilitate the link betweenconventional crop simulation models and functional-structuralcrop models.

The objective of this study is to develop a model for predictingcanopy LAI of greenhouse crops based on simple morphologicaltraits such as leaf number and specific leaf length as affected bytemperature and PAR. For this purpose, experiments at differentsites and different types of greenhouses were conducted during2003 to 2009 to collect data for development and validation of aphotothermal LAI model.

2. Materials and methods

Growth studies for five greenhouse crops – cucumber, sweetpepper, chrysanthemum, tulip and lilium were conductedduring 2003 and 2009. Detailed information about the experi-mental sites, periods, crop cultivars, planting density, type ofsubstrate and greenhouses is given in Table 1. In theseexperiments, cucumbers of experiments 1 to 6 were prunedto a single stem and one flower (fruit) was kept at each nodefrom the sixth node onwards, only one fruit was kept per fruitcluster. Sweet peppers of experiment 7 and 8 were pruned totwo stems at the 11th node. Leaf rank of sweet pepper wascounted according to the sequence of leaf appearance on bothstems. Standard commercial crop management practices wereused for growing the five crops.

In each experiment, three plants were sampled every 7 days tomeasure leaf area and dry matter accumulation and dry matterpartitioning. Ten additional plants were randomly selected fornon-destructive measurements. For these plants, leaf number, leaflength of each leaf node, and senesced leaves were measured every3 days. Minimum thresholds values used for leaf appearancesmeasurements were 20, 25, 50 and 35 mm for cucumber and sweetpepper, chrysanthemum, tulip and lilium, respectively. Leaf lengthwas measured from leaf tip to the point of petiole intersectionalong the midrib.

Air temperature at 1.5 m above the ground and PAR (LI190SB,LI-COR, Lincoln, Nrebaska, USA) above crop canopy inside thegreenhouses was monitored automatically and 30 minutes aver-age data were saved using a datalogger (CR1000, CampbellScientific Inc, Logan, Utah, USA).

Leaf net photosynthetic rate (Pn) in response to PAR wasdetermined, using Li-6400 (LI-COR) system at a CO2 concentrationof 370 � 20 mmol mol�1, on the newly fully-expanded leaves. Themeasurements were carried out during 9:00 to 12:00 for 3 successivesunny days at each development stage for cucumber, and at flowerbud break stage for other crops.

Data of the first experiment of each crop (i.e. experiments 1, 7, 9,11, 13, see Table 1) were used for model development. Those of thenine remaining experiments were used for model validation.

3. The photothermal model

3.1. Model structure

The overall model structure is shown in Fig. 1. In brief, usingdata of experiment 1, the photothermal index (PTI) was firstcalculated using greenhouse air temperature at 1.5 m aboveground and the intercepted PAR, which is dependent on theincoming PAR above canopy and the planting density. Secondly,using the accumulated PTI and the leaf number on the plantingdate, the number of appeared leaves per plant and the meanelongation rate of each leaf rank were calculated. Thirdly, the

Table 1Experimental period, crop and types of substrate, greenhouse and irrigation.

Exp# Location Cultivar Planting date

(dd-mm-yyyy)

Planting density

(pl m�2)

Type of

substratec

Type of

greenhoused

Type of

irrigatione

Cucumber (Cucumis Sativus)1a Shanghai (31.3 oN, 121.4 oE) Deltastar 16-12-2003 2.8 perlite I A

2 Shanghai (31.3 oN, 121.4 oE) Shenlu 72 31-03-2004 3.1/2.1b 1 II A

3 Shanghai (31.3 oN, 121.4 oE) Deltastar 04-05-2005 2.2 1 II A



6 Shanghai (31.3 oN, 121.4 oE) Deltastar 05-10-2007 2.2 Perlite I A

Sweet pepper (Capsicum annuum L)7a Shihezi (44.1 oN, 86 oE) Mandy 24-04-2005 3.3 2 III A

8 Shanghai (31.3 oN, 121.4 oE) Huangoubao 10-08-2005 3.3 2 II A

Chrysanthemum (Chrysanthemum morifolium)9a Beijing (39.7 oN, 116.6 oE) Jinba 30-09-2007 57 3 III A

10 Shanghai (31.3 oN, 121.4 oE) Jinba 08-09-2005 62 3 III A

Tulip (Tulip Gesneriana)11a Lianyungang (34.7 oN, 119.5 oE) Golden Parade 05-12-2007 80 Soil III B

12 Lianyungang (34.7 oN, 119.5 oE) World Favorite 06-01-2008 100, 120 Soil III B

Lilium (Lilium Oriental hybrids)13a Lianyungang (34.7 oN, 119.5 oE) Sorbonne 28-08-2008 28 Soil III B

14 Nanjing (32 oN, 118 oE) Sorbonne 26-03-2009 36 3 IV A

a Data from this experiment were used for model development, and those from remaining experiments were used for model validation.b Planting density before/after flowering (05-05-2004).c Type of substrate: 1 peat: perlite (1:1); 2 vermiculate: perlite (2:1); 3 sand: turf: soil (2:1:1).d Type of greenhouse: I is Venlo-type glasshouse, composed of 44 spans; II is Venlo-type plastic greenhouse, composed of 24 spans; III is solar greenhouse; IV is plastic

greenhouse, composed of 2 spans.e Type of irrigation: A is drip irrigation with system; B is furrow irrigation.

R. Xu et al. / Agricultural and Forest Meteorology 150 (2010) 541–552542


actual leaf length at different leaf ranks was quantified. Finally, LAIwas calculated according to the relationship between leaf area andleaf length. Details of this model approach are outlined below, withall equations given in Appendix A and all variables in the equationslisted in Appendix B.

3.2. Calculation of the normalized thermal time and the photothermal

index

The first step to obtain PTI is to calculate the normalizedthermal time for leaf growth (TTT). To this end, we used values of Pn

under saturated PAR (2000 mmol m�2 s�1) (Pn,max), derived fromthe PAR response curve of Pn. Temperature response curve of Pn,max

was constructed by fitting eqn (1) in Appendix A to data of Pn,max

obtained at different air temperatures, and an example is shown inFig. 2 for cucumber. Assuming that the minimum (Tmin), optimal(To) and maximum temperature (Tmax) for leaf growth are similarto those for leaf Pn, thermal time for leaf growth can be calculatedbased on eqn (1). We define TTT as the ratio of the growth rate at anactual temperature to that at To. So, TTT is calculated using Tmin, To

and Tmax according to eqn (2) in Appendix A, using the hourly airtemperature data of experiments 1, 7, 9, 11 and 13.

The PTI is defined as the daily average TTT multiplied by thedaily total PAR intercepted by the crop canopy. The value of PTI onday j (PTI[j]) can be calculated according to eqns (3) and (4), andthe accumulated PTI (PTIsum) during a certain growth period,which lasts for m days, is then calculated according to eqn (5)(Appendix A).

3.3. Calculation of the number of appeared leaves per plant

Values of PTIsum obtained in the last step can be used to quantifythe number of appeared leaves per plant (N). It was shown that

Fig. 1. Conceptual framework of the photothermal-based leaf area index model.

Fig. 2. Relationship between leaf net photosynthetic rate of cucumber under

saturated PAR (Pn,max) and air temperature at 1.5 m above ground (values at the

time when the PAR response curve of Pn is measured) inside the greenhouse. (

Pn,max values derived from the measured PAR response curve of Pn; — Fitted curve).

Fig. 3. Relationship between the numbers of appeared leaves per plant (a: cucumber, sweet pepper, chrysanthemum; b: tulip and lilium) and the photothermal index (PTIsum)

accumulated since planting date. (Measured data: cucumber; � sweet pepper; chrysanthemum; tulip; lilium; — Fitted curve).

R. Xu et al. / Agricultural and Forest Meteorology 150 (2010) 541–552 543


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there was a linear relationship between N and post-planting PTIsum

generally in two phases (Fig. 3). Let PTIsum(x) denote the momentfor the transition between the two phases, which representsdifferent developmental stage of different crops – the start of fruitsetting for cucumber and sweet pepper, but the start of flower budbreak for chrysanthemum, tulip and lilium. The relationshipsbetween N and PTIsum can then be summarised as eqn (6)(Appendix A). Using data of experiments 1, 7, 9, 11 and 13,coefficients in eqn (6), r1, r2 and PTIsum(x), were estimated for thefive crops (Table 2). For chrysanthemum, tulip and lilium, leaves donot appear after the flower bud break; so after flower bud break thenumber of leaves appeared per plant is a constant and the rate ofleaf appearance is zero in these three crops (Fig. 3). For these threecrops, the coefficient r2 was therefore set as zero (Table 2).

3.4. Calculation of the mean elongation rate of each leaf rank

The mean elongation rate of the leaf at rank n (RL[n]), countedupward from the first leaf, is defined as the ratio of its maximumleaf length (Lmax[n]) to the PTIsum over the period from the date ofits first appearance to the date when the leaf reaches its maximallength (DPTIsum). RL(n) then can be calculated as eqn (7)(Appendix A).

Values of both DPTIsum(n) and Lmax(n) depend on leaf rank perse (Fig. 4). A negative exponential model was found to be mostsuitable for describing DPTIsum(n) as a function of leaf rank n

(Fig. 4a, eqn (8) in Appendix A). A similar negative exponentialmodel was found to describe Lmax(n) development during the firstgrowth stage, after which a slight linear decline needs to be taken

Fig. 4. Effect of leaf node number on accumulated photothermal index from the date when the leaf appears to the date when the leaf reaches its maximal length ( PTIsum) (a:

cucumber, sweet pepper and chrysanthemum; b: tulip and lilium) and the maximum leaf length (c: cucumber, sweet pepper and chrysanthemum; d: tulip and lilium).

(Measured data: cucumber; � sweet pepper; chrysanthemum; tulip; lilium; — Fitted curve).

Fig. 5. Relationship between individual leaf area and leaf length (a: cucumber; b: sweet pepper; c: chrysanthemum; d: tulip; e: lilium). ( Measured value; — Fitted curve)



into account (Fig. 4b, eqn [9] in Appendix A). Using the data ofexperiments 1, 7, 9, 11 and 13, their coefficients (r3, r4, and r5) wereestimated (Table 2).

3.5. Calculation of actual leaf length at different leaf ranks

The actual leaf length at leaf rank n on day j (L[n,j]) can then becalculated using eqns (10) and (11) (Appendix A). For thiscalculation, an input variable PTIsum(j) was already described,i.e. be calculated using eqns (1) to (5) in Appendix A, and therequired leaf rank n can be calculated using eqn (6).

3.6. Determination of the relationship between individual leaf area

and leaf length

For our model methodology to calculate LAI based on individualleaves, it is necessary to establish the relationship between thearea of a leaf and its corresponding length. We found a simpleallometric equation, eqn (12) in Appendix A, to adequately capturethis relationship. The empirical coefficients C of the equation forcucumber, sweet pepper, chrysanthemum, tulip and lilium wereobtained from curve-fitting using data of experiments 1, 7, 9, 11and 13, respectively (Fig. 5). Values of coefficient C for these cropsare summarized in Table 2.

3.7. Calculation of canopy leaf area index

Using the aforementioned relationships, canopy LAI on day j

(LAI [j]) can be calculated based on the leaf area per plant on day j

(LA[j]) and the crop planting density (d), according to eqns (13) to(16) in Appendix A.

4. Comparison with GDD- and SLA-based models

To compare our model approach with the existing GDD- andSLA-based models, the same experiments used for the modeldevelopment and validation were also used to develop and validatethe latter two models.

In principle, the above relationships established for ourphotothermal model can be used for the GDD-based model,provided that PTI-related variables are now replaced with GDD-

related variables. Thus, using the data of experiments 1, 7, 9, 11 and13, the relationship between number of appeared leaves per plantand accumulated GDD (GDDsum) was determined as eqn (17)(Fig. 6a,b). The accumulated GDD here is calculated using theminimum temperature for leaf growth (Tmin) of each crops listed inTable 2 as the base temperature. Then, the mean elongation rate ofthe leaf at rank n (R’L[n]) can be calculated as eqn (18). Thedependence of Lmax(n) on leaf rank n is the same as eqn (9). Inanalogy with eqn (8), the dependence of DGDDsum(n) (Fig. 6c,d) onleaf rank n is determined as eqn (19) using the data ofexperiments 1, 7, 9, 11 and 13. The actual leaf length at leaf rankn on day j (L[n,j]) can be calculated as eqns (20) and (21). For theGDD-based model, canopy LAI on day j (LAI [j]) still can becalculated using eqns (12) to (16). The estimated values of thecoefficients of the GDD-based model are also given in Table 2.

For the SLA-based LAI calculation, the SUCROS crop model(Goudriaan and van Laar, 1994) was used by assuming a maximumleaf photosynthetic rate of 32 kg CO2 ha�1 leaf h�1 for cucumber(equivalent to 20 mmol m�2 s�1) (Fig. 2), 32 kg CO2 ha�1 leaf h�1

for sweet pepper, 37 kg CO2 ha�1 leaf h�1 for chrysanthemum,35 kg CO2 ha�1 leaf h�1 for tulip, and 29 kg CO2 ha�1 leaf h�1 forlilium according to our experimental data. In this crop model, cropcanopy was divided into three layers to calculate canopyphotosynthesis using the three-point Gaussian integration meth-od. For the detailed description on the calculation of crop biomassproduction (BIOMASS), readers are referred to Goudriaan and vanLaar (1994).

Because SLA was measured as the average value of standingleaves in the canopy, we slightly changed the original formulationin SUCROS, in which the partitioning was meant for the incrementof photosynthetic assimilates. Here, for our illustration of the SLA-based model, we define the shoot dry matter partitioning index asthe ratio of the accumulated shoot dry weight to the accumulatedtotal biomass, and the leaf dry matter partitioning index as theratio of the accumulated leaf dry weight to the accumulated shootdry weight. Values of these partitioning indices were calculated aseqns (22) and (23), using the data of experiments 1, 7, 9, 11 and 13(Fig. 7). The canopy LAI can then be calculated as eqns (24) and(25).

To evaluate the three model methods, the commonly usedcoefficient of determination of the simple linear regression (r2) and

Fig. 6. Relationship between the numbers of appeared leaves per plant and GDD accumulated since planting date (a: cucumber, sweet pepper and chrysanthemum; b: tulip and

lilium) and the dependence of GDD accumulated from the date when the leaf appears to the date when the leaf reaches its maximal length ( GDDsum) on leaf node number

(c: cucumber, sweet pepper and chrysanthemum; d: tulip and lilium). (Measured data: cucumber; � sweet pepper; chrysanthemum; tulip; lilium; — Fitted curve).



root mean squared error (RMSE) between the predicted andmeasured values (see eqns [26] and [27]) are calculated.

5. Results

5.1. Validation of the photothermal model

Data of experiments 2 to 6, 8, 10, 12 and 14 were used tovalidate the model. Using the greenhouse air temperature at 1.5 mabove ground and PAR above canopy, planting date, the leafnumber on the planting date, planting density, and the number ofremoved old leaves as input, our photothermal model (eqns [1] –[16]) gave satisfactory predictions of the number of leavesappeared per plant, individual leaf length at each rank, and thecanopy LAI of all the five greenhouse crops (Fig. 8). The overallcoefficient of determination (r2) and the RMSE of the five cropsbetween the predicted and measured results were 0.99 and 0.95,respectively, for the number of leaves appeared per plant, 0.98 and0.01 m for individual leaf length and 0.98 and 0.13 m2 m�2 for LAI.

Measured LAI of cucumber and sweet pepper were smaller thanthat of chrysanthemum, tulip and lilium (Fig. 8) due to the lowerplanting density and the removal of senesced leaves of the plants ofthese two crops. The number of appeared leaves per plant ofcucumber and sweet pepper and the maximum leaf length of all

the crops except tulip fluctuated with the changes of the sink-source ratio induced by new fruit (flower) appearing, fruitabortion, and fruit (flower) harvesting after fruit setting or budbreak. Therefore, the prediction accuracy of the number of leavesappeared per plant, individual leaf length and canopy LAI ofcucumber in the late growing season was somewhat lower thanthat in the early season.

5.2. Comparison of the photothermal model with the GDD- and

SLA-based models

For the GDD-based model, the r2 and RMSE between thepredicted and measured results in the validation experiments are0.93 and 4.23, respectively, for the number of leaves appeared perplant (Fig. 9a), 0.82 and 0.04 m for the leaf length (Fig. 9b), and 0.87and 0.48 m2 m�2 for LAI (Fig. 9c). The number of appeared leavesper plant and the canopy LAI were overestimated (in experiments 4and 6) or underestimated (experiments 2, 3 and 5) by the GDD-based model. This can be attributed to the fact that inside thegreenhouse, sometimes PAR does not synchronize with thetemperature inside the greenhouse. For example, the accumulatedPAR of cucumber of experiment 1 was lower than that ofexperiments 2, 3 and 5 but higher than that of experiments 4and 6 (Fig. 10).

Fig. 8. Comparison between the predicted and measured number of appeared leaves per plant (a), individual leaf length (b) and LAI (c) using our photothermal model.

( cucumber; � sweet pepper; chrysanthemum; tulip; lilium; — 1:1 line).

Fig. 9. Comparison between the predicted and measured number of appeared leaves per plant (a), individual leaf length (b) and LAI (c) using the GDD-based model.

( cucumber; � sweet pepper; chrysanthemum; tulip; lilium; — 1:1 line).

Fig. 7. The relationship between dry matter partitioning index of shoot (PISH) (a) and dry matter partitioning index of leaf (PIL) (b) and GDD accumulated since planting date.

(Measured data: cucumber; � sweet pepper; chrysanthemum; tulip; lilium; — Fitted curve).



To further investigate the reason why the photothermal modelgave better predictions than the GDD-based model, the keyparameters of both models were estimated using the data of thevalidation experiments, i.e. experiments 2 to 6, 8, 10, 12 and 14(Table 3). Table 3 shows that the key parameters of thephotothermal model (DPTIsum[nFS], r1-r5) are much more conser-vative than those of the GDD-based model (DGDDsum[nFS], r6 andr7) among the cultivars and planting densities used in this study. Inthe photothermal model, the consistency of the model parametersacross the experiments can be attributed to the fact that the PARintercepted by crop canopy that is dependent on LAI or plantingdensity is also taken into account by the model.

For comparison between the photothermal model and the SLA-based model, both the measured SLA data and the estimated SLAdata (seasonal time course of SLA in the experiments for modeldevelopment) were used to predict the LAI of experiments 2 to 6, 8,10, 12 and 14 using the SLA-based model (Fig. 11). The r2 and RMSEbetween the predicted and measured LAI were 0.81 and1.24 m2 m�2, respectively, when using the estimated SLA (data

of experiments 1, 7, 9, 11 and 13) as input (Fig. 11a), and 0.94 and0.25 m2 m�2 when using the measured SLA data of experiments 2to 6, 8, 10, 12 and 14 as input (Fig. 11b). The SLA-based model gavethe poorest predictions of LAI when using the SLA data set formodel development as input (Fig. 11a) due to the large variation ofSLA among different growing seasons (Fig. 12 shows this variationfor the case of cucumber). The SLA-based model gave betterpredictions of LAI when using the measured, experiment-specificSLA data as inputs (Fig. 11b). The SLA data, however, can only beobtained by destructive measurements. This limits the applicationof the SLA-based model to greenhouse crops and climatemanagement practices. Compared with the SLA-based model,our photothermal model can not only give satisfactory predictionsof LAI, but also predict the leaf appearance and individual leaflength and area at each rank satisfactorily.

6. Discussion and conclusions

Although both temperature and PAR are important climatefactors affecting leaf growth, many studies mainly focus oninvestigating the effect of only temperature on leaf growth such asleaf number (Baker et al., 1986; Villalobos and Ritchie, 1992;NeSmith, 1997) and leaf elongation rate (Ong, 1983a, 1983b,1983c). Analysis of our experimental data further demonstratesthat only using temperature as an input parameter, the GDD-based model did not accurately describe leaf growth (number perplant, individual leaf length) and canopy LAI for greenhouse-grown crops (Fig. 9) because temperature did not synchronizewith PAR (Fig. 10). Compared with the GDD-based model, theadvantage of our photothermal model lies in the consistency ofthe model parameters across different production settings andcrops (Table 3). Based on this it appears that the photothermalmodel is more universally applicable than the GDD-based modelbecause the effects of planting density on leaf appearance andgrowth were taken into account by using the PAR intercepted bycrop canopy.

Fig. 10. Seasonal time course of accumulated GDD (a) and accumulated PAR (b). ( experiment 1, for model development;� experiment 2; experiment 3; experiment 4;

experiment 5; experiment 6).

Fig. 12. Seasonal time course of the specific leaf area (SLA) of cucumber crops.

( experiment 1, for model development; � experiment 2; experiment 3;

experiment 4; experiment 5; experiment 6).

Fig. 11. Comparison between predicted LAI and measured LAI by the SLA-based model using estimated SLA values (a) and measured SLA data (b) as inputs. ( cucumber; �sweet pepper; chrysanthemum; tulip; lilium; — 1:1 line).



In principle, the effects of both temperature and interceptedPAR on leaf growth are taken into account in photosynthesis-driven crop simulation models. However, prediction of LAI usingthis type of simulation models is to a large extent affected by SLAvalues that are being used (Kropff et al., 1994; Yin et al., 2000).These SLA-values in turn, are very sensitive to environmentalconditions (Poorter et al., 2009), implying that SLA may not be thecause of LAI but simply be the consequence of different responsesof leaf area and biomass to environmental factors. In general, it ishard to obtain accurate SLA values, since model-predicted valuesare often flawed while values required destructive measurements.

Most crop models predict LAI, considering individual leaves asuniform group of separate entities based on leaf mass (e.g. inSUCROS, Goudriaan and van Laar, 1994) or from canopy leaf-nitrogen content (Yin et al., 2003). Alternatively, canopy LAI can beconsidered to be dependent on number of leaves per plant, area ofindividual leaf and planting density. Individual leaf area can be easilyestimated using leaf length (Serdar and Demirsoy, 2006; Peksen,2007; Kandiannan et al., 2009). Based on current results, we proposean approach to predict LAI by quantifying the number of leaves perplant and the length of individual leaf, as affected by temperatureand PAR. Using temperature and PAR as driving variables, our modelgave robust predictions of canopy LAI of different greenhouse cropsgrown in different site, seasons and planting densities (Fig. 8). Zezgin(2006) used a similar approach to predict leaf numbers before fruit-set of tomato crops. In Zezgin’s study, temperature and light wereintegrated by means of multiple regression analysis. The regressioncoefficients used in the model, however, have little biologicalmeaning; hence limit the model application for crops andconditions other than those used during model development. Inour model, the variables and parameters are more directlylinked to biological processes. Compared to LAI-based models,our photothermal model, though empirical, can not only givebetter predictions of LAI, but also predict the morphologicaltraits of leaves satisfactorily. Hence, our model has a potential tobe integrated with a functional-structural model for greenhousecrops grown under conditions without stresses.

Our model adequately predicts LAI for greenhouse-growncrops at different latitudes (from 31.3 oN to 44.1 oN, from 86 oE

to 121.4 oE) and a range of both planting densities (from2.08 pl m�2 to 120 pl m�2) and pruning system (single stem forcucumber and two stems for sweet pepper). By calibrating thevariety- and pruning type-dependent parameters (Table 2),our model can be applied to other crops or varieties and pruningtypes. Therefore, our model can be integrated with photosyn-thesis driven crop growth models to solve the problemcaused by the difficulty in obtaining reliable SLA information,and with canopy transpiration models that need canopy LAI asinput.

A number of areas, however, have been identified to furtherimprove our model approach. First, leaf nitrogen concentration(e.g. Yin et al., 2003) and soil water potential (e.g. Reymond et al.,2003) are known to have an impact on leaf growth; and theireffects with regard to prediction of LAI should be considered in thenext step within our model framework. Secondly, Marcelis (1994)and Bertin (1995) have shown that after fruit setting, the growth ofleaves (the rate of leaf appearing, individual leaf elongation) isaffected by the changes of the sink and source strength due to newfruit appearing, fruit abortion and harvesting. Quantifying theeffects of sink-source strength on the growth of plant leaves afterfruit setting is the key step to further improve the predictionaccuracy of our photothermal model. To this end, more experi-ments for the crops like cucumber and sweet pepper with widerange of fruit loads (e.g. various ways of fruit pruning andfrequencies of fruit harvesting) are needed to quantify the effects ofthe changes of the sink-source ratio on leaf growth after fruitsetting. Lastly, there is a need to make an effective calibrationprocedure if our model is to be used widely. For this purpose,development of an optimization routine, such as that in DSSAT,that makes calibrating our model more effectively, is another stepto take in future.

Acknowledgements

This research was funded by the Natural Science Foundation ofChina (NSFC) (30771262), the Chinese High-tech Program 863(2006AA10Z218), and the Jiangsu Natural Science Foundation(JSNSF) (BK2007720).

Table 3Some key models parameters in photothermal model and GDD-based model, estimated from all different experiments.

Key parameters used for photothermal model Key parameters used for GDD-based model

Exp# PTIsum(x)

MJ m�2

r1 leaves

(MJ m�2)�1

r2 leaves

(MJ m�2)�1

DPTIsum(max)

MJ m�2

Lmax(max)

m

r3

MJ m�2

r4

mm

r5

mm

DGDDsum(max)oC

r6 leavesoC�1

r7oC

1 33 0.59 0.21 72 0.30 8.5 80 2 789 0.038 67

2 34 0.53 0.19 74 0.29 8.6 80 2 524 0.040 62

34 0.53 0.19 74 0.29 8.1 80 2 524 0.059 65

3 32 0.65 0.22 73 0.30 8.2 80 2 778 0.051 74

4 32 0.64 0.22 74 0.30 8.2 80 2 793 0.034 81

5 33 0.56 0.19 72 0.29 8.3 80 2 803 0.043 72

6 34 0.57 0.21 73 0.30 8.2 80 2 652 0.018 62

7 88 0.30 0.21 83 0.20 14.0 44 4 840 0.036 130

8 91 0.30 0.00 88 0.19 11.9 45 4 1008 0.040 98

9 293 0.19 0.00 180 0.11 15.0 21 2 1910 0.027 152

10 289 0.19 0.00 188 0.10 14.7 20 2 2083 0.027 152

11 16 0.26 0.00 11 0.26 12.3 150 – 36 0.018 23

12 17 0.24 0.00 11 0.24 11.8 140 – 53 0.016 18

18 0.22 0.00 10 0.23 11.6 140 – 49 0.020 18

13 41 0.85 0.00 55 0.14 5.5 28 3 520 0.029 44

14 43 0.85 0.00 54 0.14 5.4 28 3 581 0.028 51


xurui

高亮


Appendix A. Equations for different steps of our photothermal model and those for the GDD- and SLA-based models

Equations Unit Number

Calculation of the normalized thermal time and the photothermal index

Pn;max Tð Þ ¼

0 T < Tminð Þ

Pn;max Toð Þ � sinp2� T � Tmin

To � Tmin

� �Tmin � T < Toð Þ

Pn;max T0ð Þ � sinp2� Tmax � T

Tmax � To

� �To � T � Tmaxð Þ

0 T > Tmaxð Þ

8>>>>>><>>>>>>:

mmol m�2 s�1 (1)

TTT= Pn;max Tð ÞPn;max Toð Þ – (2)

PTI jð Þ ¼ 124

X24

i¼1

TT i; jð Þ !

� PARint jð Þ MJ m�2 d�1 (3)

PARint (j) =PAR (j) � (1-exp (-k � LAI (j-1))) MJ m�2 d�1 (4)

PTIsum ¼Xmj¼1

PTI jð Þ MJ m�2 (5)

Calculation of the number of appeared leaves per plant

N ¼ n0 þ r1 � PTIsum PTIsum � PTIsumðxÞnx þ r2 � PTIsum � PTIsum xð Þð Þ PTIsum > PTIsumðxÞ

�– (6)

Calculation of the mean elongation rate of each leaf rankRL(n)=

Lmax nð Þ�La p

DPTIsum nð Þ m (MJ m�2)�11 (7)

DPTIsum(n)= DPTIsum maxð Þ � 1� exp � r3�nDPTIsum maxð Þ

� �� MJ m�2 (8)

LmaxðnÞ ¼ Lmax maxð Þ � 1� exp � r4 � n

Lmax maxð Þ

� �� n � nmaxð Þ

Lmax maxð Þ � r5 � n� nmaxð Þ n>nmaxð Þ

8<: m (9)

Calculation of actual leaf length at different leaf ranks

L n; jð Þ ¼ RL nð Þ �DPTIsum n; jð Þ þ La p L n; jð Þ< Lmax nð ÞLmax nð Þ L n; jð Þ� Lmax nð Þ

�m (10)

DPTIsum (n,j) = PTIsum (j)-PTIsum (n) MJ m�2 (11)

Determination of the relationship between individual leaf area and leaf lengthLA(n,j) =C � (L (n,j)) 2 m2 (12)

Calculation of canopy leaf area indexLAI(j) = LA(j) � d – (13)

LAð jÞ ¼ ðXN

n¼1

LAðn; jÞÞ � LAoð jÞ m2 (14)

LAoð jÞ ¼XNoð jÞ

n¼1

ðC � ðLmaxðnÞÞ2Þ m2 (15)

LAI(0)=Xn0

n¼1

C � L p nð Þ� �2

� �� d – (16)

Comparison with GDD-based modelN = n0 + r6 � GDDsum – (17)

R’L(n)=Lmax nð Þ�La p

DGDDsum nð Þ m oC�1 (18)

DGDDsum(n)= DGDDsum maxð Þ � 1� exp � r7�nDGDDsum maxð Þ

� �� oC (19)

L n; jð Þ ¼ R0L nð Þ �DGDDsum n; jð Þ þ La p L n; jð Þ< Lmax nð ÞLmax nð Þ L n; jð Þ� Lmax nð Þ

�m (20)

DGDDsum (n,j) = GDDsum (j)-GDDsum (n) oC (21)

Comparison with SLA-based modelPISH(j) = PISHmax � a1 � exp �GDDsum jð Þ

a2

� �– (22)

PIL jð Þ ¼ PILmin þPILmax�PILmin

1þ10�a3� a4�GDDsum jð Þð Þ – (23)

LAI(j)= WSH(j) � PIL(j) � SLA(j) – (24)

WSH(j) =BIOMASS(j) � PISH(j) g m�2 (25)



References

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Appendix A (Continued )

The method of model validation

r2=P

x�xð Þ y�yð Þð Þ2Px�xð Þ2

Py�yð Þ2

– (26)

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXb

i¼1

OBSi�SIMið Þ2

b

vuuut– (27)

Appendix B. List of all variables used in the models and their units.

Variable Definition Unit Eqn#

b Number of samples – (27)

BIOMASS(j) Accumulated total biomass production on day j g m�2 (25)

d Planting density plants m�2 (13), (16)

GDDsum Accumulated GDD oC (17)

GDDsum (n) GDDsum from the planting date to the date when leaf at rank n (here n = N) appears oC (21)

GDDsum (j) GDDsum from the planting date to day j oC (21), (22), (23)

DGDDsum(n) GDD accumulated from the date of the leaf (at rank n, here n = N) appearance to the date

when the leaf reaches its maximal length

oC (18), (19)

DGDDsum (n,j) GDD accumulated from the date when leaf at rank n (here n = N) appeared today j oC (21)

L(n,j) Actual leaf length at leaf rank n (here n = N) on day j m (10), (12)

Lmax(n) The maximum length of the leaf at rank n (here n = N) m (7), (9), (15)

LA(j) Leaf area per plant on day j m2 plant�1 (14)

LA(n,j) Leaf area at rank n (here n = N) on day j m2 plant�1 (14)

LAo(j) Area of the removed old leaves per palnt till day j m2 plant�1 (14), (15)

LAI (j-1) Canopy leaf area index on day j-1 – (4)

LAI (j) Canopy leaf area index on day j – (13), (24)

LAI(0) Initial leaf area index on the planting date – (16)

Lp(n) Leaf length at rank n on the planting date m (17)

N Number of appeared leaves per plant plant�1 (6)

No(j) Number of removed old leaves per plant till day j plant�1 (15)

n Leaf rank counting upward from the first leaf – (8), (9)

n0 Number of appeared leaves per plant on planting date plant�1 (6)

OBSi Measured data – (27)

PAR (j) Daily total PAR above the canopy on day j MJ m�2 d�1 (4)

PARint(j) Daily total PAR intercepted by the cucumber crop canopy on day j MJ m�2 d�1 (3), (4)

PISH(j) Dry matter partitioning index of shoot on day j – (22), (25)

PIL(j) Dry matter partitioning index of leaves on day j – (23), (24)

Pn,max(T) Leaf net photosynthesis rate under saturated PAR at temperature T mmol m�2 s�1 (1), (2)

PTI(j) Value of PTI on day j MJ m�2 d�1 (3), (5)

PTIsum Accumulated PTI MJ m�2 (5), (6)

PTIsum(j) PTIsum from the planting date to day j MJ m�2 (11)

PTIsum(n) PTIsum from the planting date to the date when leaf appeared at rank n (here n = N) MJ m�2 (11)

DPTIsum(n) PTI accumulated from the date when the leaf at rank n (here n = N) appeared to the date

when the leaf reaches its maximal length

MJ m�2 (7), (8)

DPTIsum (n,j) Accumulated PTI from the planting date to day j minus the accumulated PTI from the date

when the leaf at rank n (here n = N) appeared

MJ m�2 (11)

RL(n) Mean elongation rate of the leaf at rank n (here n = N) based on PTI m (MJ m�2)�1 (7), (10)

R’L(n) Mean elongation rate of the leaf at rank n (here n = N) based on GDD m oC�1 (18), (20)

SIMi Predicted data – (27)

SLA(j) Specific leaf area on day j m2 g�1 (24)

TT(i,j) Normalized thermal time at hour i on day j – (3)

TTT Normalized thermal time at temperature T – (2)

WSH(j) Accumulated shoot dry weight on day j g m�2 (25)

x Measured value – (26)

x Mean values of the measured variables – (26)

y Predicted value – (26)

y Mean values of the predicted variables – (26)



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A photothermal model of leaf area index for greenhouse crops

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