A Simulation Model for Predicting the Development of Cut Lily Based on Photo-Thermal Index

A Simulation Model for Predicting the Development of Cut Lily Based on Photo-Thermal Index

Corresponding author: Dr. Yongyi Dong, No. 996 (west), Sila Mulun Street, Tongliao, Inner Mongolia, China, Tel: 0475-8314809,13947516684; Email: dongyong74@126.com


In order to provide accurate prediction of the development stages of cut lily, which is crucial for decision-making of the market schedule, a simulation model based on photo-thermal index was developed to estimate the phenophase days during greenhouse production. Three experiments of Lilium Oriental Hybrids cv. ‘Sorbonne’ with different planting date were conducted in PC multi-span greenhouse in Nanjing from March 2009 to January 2010 for data collection used to model construction and validation. The results showed the relative prediction error (rRMSE) between the observed days and the simulated days for each development stage were 1.58 d, 2.23 d, 2.54 d, 1.58 d, respectively. The coefficient of determination (r2) between the predicted and the measured phenophase days were 0.97 with the error remained in three days, which is more accurate than GDD based model. The model developed in this study gave satisfactory predictions of phenophase days, hence, can be used for anthesis control in Sorbonne production

Keywords: Cut Lily, Photo-Thermal Index, Development Stages, Phenophase Days, Model


Lilium (liliaceae), one of five popular cut flowers in the world, is deemed as the king of flower bulbs. The produce area of Easter lily which occupies the most cultivated area increasing- ly extends in china due to its valuable and extensive use be- sides strong symbolic meaning. The price of lily depends on the scheduling to market and the post-harvest preservation during transportation, which requires the accurate develop- ment simulation and robust anthesis prediction to support the regulation of market scheduling.

The relationship between the temperature and the develop- ment of flower including the flower-bud size, weight and diam- eter from bud appearance to opening is well known in many studies [1,2]. The study of six cultivars suggests no significant between flowering and light intensity, but to temperature [3].

The model concentrated on the development rate under the function of temperature in chrysanthemum [4] and cactus [5]. Taking account into the involvement of the effects of the light on flowering result from the fact that light intensity affects the photosynthesis and dry matter production which actually al- ter the time to flower [6], daily light integral was considered in modeling the chrysanthemum flower development [7] and supplementary lighting prevented lilly flower bud abortion [8]. The relationship between the photo-thermal ratio and the poinsettia quality has been confirmed [9]. Considering the sit- uation that the irradiance and temperature are not synchro- nized unlike the field condition, a new photo-thermal index was developed to solve this problem [10,11].

In order to provide concrete support to measure and control the marketing schedule, the research used Oriental Lily Sor- bonne as experimental material, established a model of anthesis prediction based on the new photo-thermal index with different planting dates.

Materials and Methods

Plant Material and Greenhouse Environment

The circumference of seed bulb Sorbonne, imported from Netherlands, was 14-16 cm and the plant density was 36 plants per square meter. The substrate of potting plant was 2:1:1 for sand, grass carbon and soil, respectively. The volumetric weight, pH and EC value were 1.08 g·cm-3, 6.5, and 0.76 mS·cm-1, respectively.

The experiment was taken in a PC multi-span greenhouse of Nanjing Agricultural Science Research Institute from March synthesis Pn,max (μmol.CO2.m-2.s-1) was measured with saturate light intensity (1500 μmol.m-2.s-1) with 3 replications in each stage.

The software SPASS v19.0 was used to statistical analysis and curve-fitting the data.

Model Description

The irradiation and temperature effects were described as PARint(j) and TT(i,j), respectively. The photo-thermal index (PTI) was defined as relative thermal effect (RTE) multiplies the total PAR intercepted by the plant canopy [10]. It can be given from equations (1) ~ (3):

2009 to January 2010. The green house was east-west trend

PTI j    1 24 TT i, j   PAR



with the length 28 m and two 8 m spans. The height of eaves

 24 i 1

 int

and ridge was 3 m and 5 m, respectively. The length, width and height of nursery bed were 25 m, 1.7 m, 1 m, respectively. The heating pipes circled in the greenhouse ware used in winter. The wet curtain and fan cooling system was used in summer.

Experiment Design



j  PARj 1 exp k LAIj 1

TTT Pn, maxT

Pn, maxT 0



The experiment I was conducted from Mar. to Jun. 2009 with the planting date and collection date at 26th Mar. and 15th Jun., respectivesity. The experiment II was conducted from Apr. to Jul. 2009 with the planting date and collection date at 20th Apr. and 4th Jul., respectivesity. The experiment III was conducted from Sep. 2009 to Jan. 2010 with the planting date and collec- tion date at 27th Sep. and 21th Jan., respectively. The planting date and collection period of three experiments were, Jun 15, July 4, Jan 21, respectively. The data from the Exp I were used to establish the model. The independent data required from the Exp II and Exp III were used to validate it.

Where PTIsum is the accumulated PTI (MJ.pl-1) from the first day to the day m, PARint(j) is the total PAR (MJ.m-2.d-1) inter- cepted by the canopy at day j, TT(i,j) is RTE at time i (i=1- 24h) during the day j, k is the extinction coefficient of the canopy (the value 0.702 is used in this study), LAI(j-1) is the LAI at day j-1, TTT is the RTE at the temperature T, defined as the ratio of Pn,max at actual temperature (T) to optimal T (T0).

According to our environmental data collection (Figure. 1), the relationship between leaf net photosynthesis rate and envi- ronment temperature (Figure. 2), can be described as equation (4):


The whole phenophase has been divided into four periods:

 0

P T  sin

  • T Tmin 

T Tmin


planting stage (from planting to sprouting), seedling stage P

T   

n,max o

 2 To


  • Tmin 

min o


(from sprouting to basic three leaves unfolding completely),



    • T

P T  sin

  • max 


leaf-expansion stage (from the basic three leaves unfolding to

the first visible bud), bud stage (from the first visible bud to the harvest). The days from the beginning to the end of each

n,max o

 2 Tmax


  • To

o max

T Tmax

stage was recorded.

The greenhouse environment data were automatically collect- ed by CR1000 (Campbell Scientific Inc) with the frequency 10 min, average value including PAR (LI200X, Li-Cor Inc) above the canopy and air temperature at the height of 1.5 m above the nursery bed were recorded each 30 min.

The net photosynthesis Pn (μmol.CO2.m-2.s-1) of the leaves from the first to third under the first flower bud were measured

Where T is the temperature within the greenhouse, Pn,max(T) is the Pn,max at air temperature Toc; Tmin, To and Tmax are the minimum limit, optimum and maximum limit temperature of lily growth, respectively, and their values are 5oc, 20oc and 30oc, respectively.

Then the accumulated PTI from day 1 to day m was defined as

PTIsum(MJ.m-2) calculated by equation (5):


and used to make light response curve (the CO2 concentration



PTI( j )


above the canopy was 380±20 μmol.mol-1, the measurement operated from 9:00 to 10:30). The maximum leaf net photo2A



1.5 32

Daily total PAR (MJ·m-2)

Daily average air temperature (℃)




0 20 40 60 80

Days since sprouting date (d)





0 20 40 60 80

Days since sproting date (d)

Figure 1. The daily total PAR (A) and daily average air temperature (B) inside the greenhouse since sproting – Measured data for Experiment I, Measured date for Experiment II…Measured data for Exp. III.

18 is the mean value of measured and predicted data.

The maximum leaf net photosynthetic rate (μmolCO2·m-2·s-1)

rRMSE  1

1 













0 10 20 30 40

Air temperature at 1.5m above ground (℃)

Figure 2. Relationship between maximum leaf net photosynthetic

Where OBSi is the measured data, SIMi is the predicted data, n is the number of samples and M is the mean value of measured data.


By using the data from Exp I to calculate the accumulated PTI of cut Lilium at for each stage, the accumulated PTI of cut Lili- um are 0.00, 0.02, 9.42, 24.08 for planting stage, seedling stage, leaf-expansion stage and bud stage, respectively.

The independent data used in model validation was adopted from Exp II and III. According to the accumulated PTI from Exp

rate of Lilium ‘Sorbonne’ (P


) (values derived from the measured

I and the photo-thermal data from Exp II and III, the calculated

continuing days of each stage were used to estimate the start-

PAR response curve of Pn under saturated PAR conditions) and air temperature at 1.5m above ground inside the greenhouse.

ing and ending time. Comparing with the observed develop- ment time, the results showed an error in 3 days, which was

  • Pn,max

values derived from the measured PAR response curve of Pn

more accurate than the growing degree days (GDD) method we

tested with the same data (Table. 1). The relative prediction

Fitted Curve.

Model Validation

The coefficient of determination (r2) and the relative root mean square error (rRMSE) between the predicted and measured values (from Exp II and Exp III) are used for model validation and calculated as:

error (rRMSE) between the observed days and the simulated days for each stage with PTI and GDD method were 1.58 d, 2.23 d, 2.54 d, 1.58 d and 4.74 d, 3.54 d, 6.21 d, 5.38 d, respective- ly. The coefficient of determination (r2) between the predicted and the measured phenophase days were 0.97 and 0.91 for PTI and GDD method (Figure. 3).

GDD method has been comprehensively adopted in modeling

x xy y2

r 2   2  2

x x y y


the development rates of several field crop sand plants, namely rice, maize, spruce, etc [12,13]. The prediction of phenophase days of cut lily through GDD method showed a relatively bigger

Where x is the measured data, y is the predicated data , ȳ and

error due to the unsynchronized phenomenon between light and temperature caused by the artificial environmental

Phenophase Item Experiment II Experiment III PTI




Planting stage (d) Observed 8 14 1.58 4.74
Simulated 10 13
Error -2 1
Seedling stage (d) Observed 6 13 2.23 3.54
Simulated 7 16
Error -1 -3
Leaf-expansion stage (d) Observed 29 44 2.54 6.21
Simulated 27 41
Error 2 3
Bud stage (d) Observed 28 45 1.58 5.38
Simulated 30 46
Error -2 -1

Table 1. Simulated and observed phenophase days of different varieties of cut lily (d)


Predicted phenophase days (d )





0 15 30 45

Measured phenophase days (d)

Figure 3. Comparison between predicted and measured phenophase days of different phenophase of cut lily.

⧠ Measured data for Exp.II ◊ Measured data for Exp. III (PTI )

█ Measured data for Exp.II ⧫ Measured data for Exp.III (GDD)

—1:1 line

control in the greenhouse. Meanwhile, considering the growth hysteresis induced by high temperature, the relationship be- tween development rate and temperature in different range from the optimum to the upper or lower limit of temperature is not linear correlation [14]. Thus the single index of tempera- ture and the assumption of the linear relationship between de- velopment rate and temperature are not sufficient to calculate the phenophase days for greenhouse crops.

Other than temperature, both photoperiod and light integral affect the initiation and development. According to the study on grandiflorum and cyclamen, high light integral promoted flowering and decreased time to flower [15,16]. Science our lily material is not sensitive to photoperiod, the daily total PAR intercepted by the canopy was used to balance the effect of light integral on development rate. The relative photoperi- odic effect (RPE) should be considered if the plant material is sensitive to photoperiod [14]. Whether the planting density or different places affect the development process need to be tested, further research should concentrate on the model mod- ification under various water and fertilizer conditions.

  1. Roberts AN, Yin-Tung Wang, Moeller FW. Effects of pre-and post-bloom temperature regimes on development of Lilium longiflorum Thunb. Sci. Hortic. 1983, 18(4): 363-379.
  2. Halla AJ, Catleya JL, Walton EF. The effect of forcing tempera- ture on peony shoot and flower development. Sci. Hortic. 2007, 113(2): 188-195.
  3. Persson L, Larsen RU. Adapting a prediction model for flow- er development in chrysanthemum to new cultivars. Acta Hort. 1998, 456(16): 143-150.
  4. Hiden C, Larsen RU. Predicting flower development in green- house grown chrysanthemum. Sci. Hortic. 1994, 58(1-2) : 123- 138.
  5. Larsen RU, Birgersson A, Nothnagl M, Karlen H. Model- ling temperature and flower bud growth in November cactus (Schlumbergera truncata,Haw). Sci. Hortic. 1998, 76(3-4): 193-203.
  6. Genhua N, Royal DH, Arthur CC, William HC. Day and night temperatures, daily light integral, and CO2 enrichment affect growth and flower development of Campanula carpatica `Blue Clips’. Sci. Hortic. 2001, 87:93-105.
  7. Larsen RU, Persson L. Modelling flower development in greenhouse chrysanthemum cultivars in relation to tempera- ture and response group. Sci. Hortic. 1999, 80(1-2): 73-89.
  8. Jadwiga T. Effects of supplementary lighting on flowering, plant quality and nutrient requirements of lily ‘Laura Lee’ during winter forcing. Sci. Hortic. 2003, 98(1): 37-47.
  9. Liu B, Heins RD. Is plant quality related to the ratio of radiant energy to thermal energy? Acta Hort. 1997, 435(16): 171-182.
  10. Xu R, Dai J, Luo W, Yin X, Li Y, et al. A photothermal model of leaf area index of greenhouse crops. Agric. Forest Meteorol. 2010, 150(4): 541-552.
  11. Lu Lin, Wenwen Li, Jingqing Shao, Weihong Luo et al. Mod- elling the effects of soil water potential on growth and qual- ity of cut chrysanthemum (Chrysanthemum morifolium). Sci. Hortic. 2011, 130(1): 275-288.
  12. Francois T, Boris P. Modelling temperature-compensated rates of development (an alternative to growing degree days). CBP Part A: Molecular & Integrative Physiology 2009,Supple- ment 153(2): S226.
  13. Biing T.G, Chih-Hsin Cb, Shu-Tzong L, Chieh-Wen S. Quan- tifying height growth and monthly growing degree days rela- tionship of plantation Taiwan spruce. FOREST ECOL MANAG 2009, 257(11): 2270–2276.
  14. Yuan CM, Luo WH, Zhang SF, Dai JF, Jin L. Simulation of the development of greenhouse muskmelon. Acta Horticulture Si- nica. 2005, 32(2): 262-267.
  15. Nazrul Islam, Grete Grindal Patil, Hans Ragnar Gislerød. Ef- fect of photoperiod and light integral on flowering and growth of Eustoma grandiflorum (Raf.) Shinn. Sci. Hortic. 2005, 103(4): 441-451.
  16. Wook Oh, In Hye Cheon, Ki Sun Kim. Photosynthetic Daily Light Integral Influences Flowering Time and Crop Character- istics of Cyclamen persicum. HortScience. 2009, 44(2): 2341- 2344.

Be the first to comment on "A Simulation Model for Predicting the Development of Cut Lily Based on Photo-Thermal Index"

Leave a comment

Your email address will not be published.