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63
Rose Grow: A Model to Describe Greenhouse Rose Growth
E. Dayan, E. Presnov, and M. Fuchs J. Ben Asher
Agricultural Research Organization Ben Gurion University
Besor Exp. Stat. Israel 85400 Beer Sheva Israel
Keywords: models, morphology, roses, greenhouse
Abstract
This model is designed to help in the early testing of different climate control
regimes and morphological plant treatments in an attempt to predetermine that the
waves of flowering will appear at an economically propitious date. The model
describes the growth and development of the canopy in greenhouse roses by tracking
the changes in the weight and morphology of each of the lateral branches that make
up the canopy. The model uses a source-sink approach to allocate carbohydrate for
the growth of different organs. The sink demand for carbohydrates is calculated
using the template for the plants’ morphogenetic potential at each age.
INTRODUCTION
The highly competitive nature of the flower markets has winnowed out many
growers from this market leaving in place only the most knowledgeable and
technologically advanced growers. The knowledge required in order to survive at the
present competitive level includes the ability to control the flower quality–quantity
balance and market the crop at the most economically valuable production dates. (Kool,
1996) To achieve this goal, farmers are using sophisticated computers and a variety of
means to control the root system and microclimate conditions. In addition, a variety of
special plant treatments have been developed to reach these farmers’ goals. These plant
treatments include: bending, pruning, pinching, flower removal, de-budding, and de-
shooting.
The different possible combinations of methods provide a wide range of possible
plant responses. This leaves the greenhouse rose growers with a recognized need for a
combination of physical and biological models that will help them to determine the most
profitable combination of controlled variables, pre-test growth patterns for new varieties,
and predict responses to different harvesting regimes. In recent years, considerable effort
has been applied to provide models supporting the farmers’ endeavors (Fisher et al., 1997;
Lieth, 1999).
Using the model described here to help solve rose-growing problems, an attempt
was made to apply to rose growing some modified versions of ideas that have been tried
and tested in tomato growing using the TOMGRO model (Dayan et al., 1993).
MODEL DESCRIPTION
The model describes canopy growth and development for rose bushes grown in
greenhouses using the bending method. The model has three main sections: A:
Management and weather, B: Total dry weight accumulation, and C: Morphological and
phenological development and DM allocation. The simulations within parts A and B are
familiar procedures from known Dutch models. (Gijzen et al.,1998) and they will be
described briefly below.The third part, C, follows TOMGRO concepts (Dayan et al.,
1993) that have been modified with some unique procedures for this model. This part will
be described in greater detail below.
The model was designed to respond to dynamic changes in temperature, solar
radiation, and CO2 concentration throughout the day. For this purpose, time in the model
is updated by using two loops. The main loop employs time increments based on a daily
schedule and a fast loop that works on a 30 minute interval. Within the fast loop,
temperature, CO2, and light (PAR) are computed for the same instant in time at which
photosynthesis and respiration rates are computed. Plant growth is dealt with by the daily
Proc. 4th IS on Cropmodels
Eds. J.H. Lieth & L.R. Oki
Acta Hort. 593, ISHS 2002
64
loop where, at the end of the day, the plant’s state variable vectors are
updated.Management and Weather of this section in the model includes parameter and
data inputs such as: Planting dates and configuration, irrigation, climate and microclimate
control (Gijzen et al., 1998).
Dry Weight Accumulation of Carbohydrate availability for growth is based on
photosynthesis and respiration calculations that were used in TOMGRO. Photosynthetic
rate (Pg) is computed at each time increment within the fast loop for each branch. The
daily quantity available for growth (supply) is calculated by summing all of these
quantities and then subtracting the quantity required for maintenance respiration (Dayan
et al., 1993).
Morphological and Phenological Development and DM Allocation.
Descriptions of growth, development, and the distribution of dry matter in the canopy are
computed by tracking changes to the weight and morphology of each of the lateral
branches that together form the rose bush canopy as they occur along a time line.
The bending technique used in the experiment caused a further differentiation to
be made between two types of lateral branch on the plants: branches that develop flowers
(fl) and side branches that develop into a ‘skirt’ or side shoots (ss). The flowering
branches usually develop in the center of the planted bed. The growers remove side
shoots that arise from the flowering branches and, at a specific bud opening stage, are
harvested. The branches that make up the skirt are usually side-branches or alternatively,
flowers with abnormal development that have been bent to the edges of the bed. These
branches remain on the plant even after their development is complete. However, starting
with the leaves and continuing to the stalks, some of them do wither, die and fall off.
From time to time, the rose bush also produces basal shoots (bs) which are very vigorous
and very important for flower production (Kool, 1996)The growth patterns of the basal
shoots used for prediction of the potential growth in the model.
Three different parts are discerned for every branch of every type: stem, leaf and
bud. The characteristic sigmoid growth pattern for each part, from initiation to maturity,
is divided into a number of age stations. Each group of branches of the same type and
similar age is defined as an “age group” and described according to a number of state
variables that include information on the organs that make up the branch: stem numbers,
weight, and length; leaf numbers, weight, and length; the number, weight, and volume of
the flower buds developing along the branch. As time passes, there are changes to the
state variables for each age group for the following reasons:
Changes that Take Place Due to Branch Transition from One Age Group to
Another. These calculations are made by transporting the state variables through the age
stations using the Boxcar trains technique (De Wit et al., 1978.) The number of trains
involved is the number of state variables. The time that it takes for each branch to
complete the life cycle from initiation to flowering (G) is considered to be a genetic
parameter that is biased by environmental factors, and in the most part by temperature.
When the temperature is high, the cycle is shorter and when the temperature is low, the
cycle is longer. The residual time (RT), is the time spent at each age station and it is
determined according to the number of age stations (n) and the time required for the
nascent branch to complete the cycle RT=G/n. Rapid development shortens total lifetime
and hence the time spent in each age class. The general equation used to calculate the
changes (Qrx) caused by age for each state variable(Q): weight, number or length, area,
or volume of fl or ss:
() ( 1) () ()
*( )
iiii
Qrx RT Q Q Qrd
−
=−−
Eq -1
Where Q(i) = state variable in age class i.
Qrd(i)= death rate of items in age class i .
Additional Weight or Size or a Lack of Weight or Size at Each Age Station is
the result of assimilate and weight gain or the death of parts of the branch. The increase in
carbohydrates within each plant part (WGr(j,x,i), see Eq-5) is made of the assimilates pool
65
of the plant, based on the potential size for each organ at every age (see below) and on
transformation coefficients from dry matter to morphological size (Sx): specific stem
length (SSL) (m/kg), specific leaf area (SLA) (m2/kg), or specific bud volume (SBV)
(m3/kg). The potential size of state variables and transformation coefficients are thought
to be genetic traits dependent upon the age and type of branch. The transformation
coefficients are biased by environmental conditions. According to these parameters, the
plant processes dry matter (WGr) to form stems, leaves, and buds with a given length,
area, and volume (DGr):
( , ,) ( , ,) ( , ,)
*S'
jxi jxi jxi
DGr WGr= Eq -2
Calculations for the quantity of assimilates demanded by each organ on a branch
are performed with the help of the transformation coefficients mentioned above. Potential
changes to the size of the morphological template for each branch part can be calculated
by using a mathematical derivation from the graph that describes the template for
morphological growth of the plant’s organs divided by the transformation coefficient:
(,,) (,,)
(,,) '
()
/
jxi jxi
jxi
dPS
PWGr S
dt
= Eq -3
The absorbed material in each part and the relationships between the sink
strengths for carbohydrates in the stems, leaves and flower buds at any specific moment
in time are determined according to the relationships between the curves that describe the
morphological changes in each part of the branch. The ‘demands’ for assimilates made
by each branch are calculated using the demand schema for each of the branch organs.
The total sink of assimilates by the canopy (SD) is calculated using the demand schema
for all the organs at all ages in all the different types of branch:
(,,) (,,)
1*
n
jxi jxi
jxi
SD PWGr N
=
=∑∑∑ ,,;
,, ;
j leaf stem bud
x
flower sideshoot basalshoot
=
= Eq -4
The relationship between the source and the total sink demand is calculated by
dividing the supply value by the SD value: supply/SD. In the model, this relationship
characterizes the status of the assimilate economy as a whole and the strength of
competition within the plant. Using this relationship, the model calculates the quantity of
assimilates transported to each organ, the initiation and abortion rate for new branches,
and buds and the rate at which shoots wither. E.g: The calculation of the actual quantity
of assimilates transported to each organ:(WGr(j,x,i), see Eq-2) is made according the
potential organ size assuming that each existing organ monopolizes up to a maximum
amount of assimilates, according to its age, its potential size and the ratio of supply/SD.
(,,) (,,) (,,)
**
jxi jxi jxi supply
WGr WPGr N SD
= Eq -5
The model was written in the MATLAB-6 language. The model is divided into
modular sub-routines that can be replaced or modified.
MATERIALS AND METHODS
The measurements that were involved during model development included those
made to establish the climate database that is a required model input and others used to
calibrate the morphological and physiological parameters. The description of these
measurements and results were presented earlier (Gijzen et al., 1998). Quantities,
qualities, and timing of the measurements were made on the harvested crops quantities,
qualities, and process. These data made it possible to check the calculated results during
the model validation process. Some of these measurements will be presented.
The Experimental Systems: Information to validate the model was gathered from
a semi-commercial greenhouses in which an experiment was in progress to monitor the
effects of heating, cooling, shading, and CO2 enrichment on greenhouse rose ‘Long
Mercedes’ production. The experiments were conducted in multi-span greenhouses at the
Besor Experimental Station in Israel (31°16’N, 34°24’E). A detailed description of the
66
experiments in this greenhouse can be found in Fuchs et al. (1997).
Quantity and Quality: Flower quality and quantities for each treatment were
determined from the flowers picked from 250 plants in 19 containers lockated in the
center of the greenhouse span. The flowers were picked every two days, sorted into
groups according to stem length (40-50, 50-60, 60-70, 70-80 centimeters), and then
counted. Samples of buds from each group were plucked and their diameter, length, and
weight were measured. The total number, weight, and length of the flowers picked per
day (number, g, and cm per 2 per day) were considered quantity parameters. Daily
averages of flower length and weight (cm and g per flower) were considered stem quality
parameters and the daily average of the buds’ weight, diameter, and length (g, mm, and
mm per bud) were considered bud quality parameters. The average series were plotted
against time and the curves were statistically smoothed. A Smooth B-spl Fix, Order 8,
Knots 13 (SPSS, 1997) identified picking waves. The beginning, end, and duration of
each picking wave period were determined according to the inflections within these
smoothed curves.
Growth Rates and Morphological and Phenological Changes: At 10 fixed sites
in the center of the greenhouses in which the microclimate treatments were tested, vertical
measuring tapes were fixed in place from the plant bases and upward. The measuring
tapes were used to establish length, area, and volume for the stems, leaves and buds on
the 10 branches on the fixed sites. Measurements of each branch were taken every two
days, starting at initiation and ending with picking. Once the branch had been picked, a
new series of measurements was srarted for a newly initiated branch in the same location.
The different values that describe the branch measured were displayed on a common time
axis. Symmetrical sigmoid curves were adapted representing the changes of the branch
organs. This adaptation was made using the program Tablecurve 2D ( SPSS ,1997).
Growth start and end dates were established for each organ when the dimension
represented by the sigmoid curve reached 2%, (start) or 98% (end) of the asymptotic
value for that curve. Total growth time for the organ was calculated from the time
difference between the start and end dates. The maximum morphological rate of growth
for the organ was established as a derivative of the sigmoid curve at its central inflection
point. The growth start date for each organ and the total growth period for each organ
belonging to the branch are established in reference to the start date for stem
lengthening(Presnov et al., 2002). Flower shoots, side shoots and basal shoots were
measured. SSL,SLA,SBV and RT required for the model were calculated using the
analysis of the basal shoots sigmoid curves while the the flower and side shoots curves
were used for validation.
RESULTS
Figure 1 presents parameters that were not bold calculated according to the
morphological monitoring work covering increases in length, area and volume for the
stems, leaves and buds. Changes that take place along the time axis for each organ on a
basal shoot branch were described by using symmetrical sigmoid curves. It is possible to
discern the three periods: linear, logarithmic and senescence using these curves, during
the growth of each of the organs mentioned above. The stem is the first to begin linear
lengthening, and is followed a short time afterwards by linear leaf expansion. Linear bud
filling starts at the same time when stem senescence begins.
Validation Results
Figure 2.1 presents the rates at which flower quantities (expressed as the picked
flowers number per m2 per day) matured and the daily averages for the quality of the
picked flowers expressed as the average flower length during the 1996 – 1997 season.
The smoothed curves show that the flowers matured picking in waves. Until the middle of
the summer, the waves are shorter and more frequent (30 days). Approaching mid-winter,
the waves are longer and less frequent (70 days). The curves representing flower quality
also display a wave formation similar to the maturation curves. Flower quality changed in
67
waves with similar frequencies to the quantity waves, but they appeared in the opposite
phase. The flowers were shorter as the crop grew and became longer as the total quantity
harvested declined. The lowest point 0n the quantity wave did not appear at the same time
as the quality wave peak. The relationships between quality and quantity during one of
the picking waves (7 Jan 97 - 2 Mar 97) are described in figure 2.2.
After using trial and error to modify some of the model’s parameters, it became
possible to use the model to produce the calculated situations and trends for a portion of
the period between 7 Jan 97 and 02 Mar 97. More adjustment work is still required to get
a full agreement between multi-seasonal predictions and measurements.
The model helped to explain the relationships between flower quality and
quantity: The canopy produces a limited quantity of assimilates for plant use, that is lower
than the quantity necessary to satisfy the plant branch requirements. As the result of this
limitation, the plant organs compete for assimilates and each organ receives only a part of
the quantity that it required to reach its potential template. The allocation of dry matter is
carried out such that each organ draws from the limited overall quantity, a portion that is
relative to its sink strength in comparison to all the other organs in the plant. When the
plant is burdened with a large number of branches, the limited quantity of assimilates is
allocated amongst a large number of consumers and each branch receives only a small
quantity of assimilates, which then permits only a relatively small rise in the
morphological dimensions that describe flower quality, e.g. stem length or bud volume.
However, the dearth of assimilates also causes lower rates of initiation and fewer new
branches form. When only a small number of branches develop on the plant, the quantity
of assimilates is allocated amongst fewer consumers and each branch adds more size to its
stem, leaves and buds.
In terms of assimilate allocation and partitioning, the present model is similar to
many other models in which the allocation of dry matter is performed using source/sink
relationships as parameters that describe the competition for an insufficient quantity of
available assimilates (Gijzen et al. 1998).
Using morphogenetic parameters for modeling is alternative approach, Fisher et
al. (1998), Lieth (1999), and others created decision support models for greenhouse crops,
in these models morphological yardsticks are used as the means to identify how far the
plant is from its growth potential dimensions and to establish the methodology that should
be used in order to impel growth and development in the preferred direction.
Notwithstanding that fact, the model under consideration here is special in that it uses
morphological indicators and parameters. Forexample, e.g.: the morphological
dimensions of the ‘template’ for the potential plant or the transformation coefficients
between morphological dimensions and quantity of dry matter, to estimate and calculate
the strengths of physiological processes. The principal example for the manner in which
physiological processes are calculated according to morphological relationships is seen in
the way that the ‘sink’ of plant assimilates is calculated. The source/sink relationship is a
critical physiological parameter in the model and with this the model is able to deal with
the allocation of dry matter, shoot initiation, etc.
The combining of ecophysiological and architectural approaches that link the
structure and functioning of the plants is justified as a large number of rose researchers
have investigated the connection between morphological states, plant architecture, and
their physiological attributes (Kool, 1996; Morisot et al., 1996). Treatments such as
bending, pruning, pinching, flower removal, de-budding, de-shooting affect flower
production by influencing carbohydrate allocation, plant responses and energy balance
and must be adapted to the seasonal changes in carbohydrate patterns (Kool, 1996)
68
ACKNOWLEDGEMENT
The study was partially supported by the "Katif research center for coastal desert
development"
Literature Cited
Dayan, E., Van Keulen, H., Jones, J.W., Challa, H. 1993. Development, calibration and
validation of a greenhouse tomato growth model. I. Description of the model. Agric.
Syst. 43: 145-163.
Fisher, P.R., Lieth, J.H., Heins, R.D. 1998. Predicting variability in anthesis of Easter Lily
(Lilium longiflorum Thunb.) populations in response to temperature. Acta. Hort. 456:
117-124.
Fuchs, M., Dayan, E., Shmuel, D., Zipori, I., 1997. Effects of ventilation on the energy
balance of a greenhouse with bare soil. Agric. For. Met. 86: 273-282.
Gijzen, H., Heuvelink, E., Challa, H., Dayan, E., Marcelis, L.F.M., Cohen, S., Fuchs,M.,
1998. Hortisim: A model for greenhouse crops and greenhouse climate. Acta. Hort.
456: 441-450.
Kool, M.T.N. 1996. System Development of Glasshouse Roses. PhD. Thesis.
Landbouwunivesity, Wageningen, The Netherlands.
Lieth, J.H. 1999. Crop management models for decision support and automated
optimization. Acta. Hort. 507: 271-277.
Morisot, A. 1996. A first step to validating 'PP.Rose', an empirical model of the potential
production of cut roses. Acta. Hort. 417:127-138.
Presnov, E. Dayan, E., Fuchs, M., Plaut, Z. 2002. Coherence and synchronization of rose
development. The proceeding of the International ISHS symposium on “Product and
Process Innovation for Protect ed Cultivation in Mild Winter Climate.”. (Giuseppe,N.(
ed)). Ragusa Italy, 5-8 March 2002. (Preprint of Acta Hort. Accepted for publication).
SPSS. TableCurve2D. 1997. Chicago, SPSS Inc.
Wit, C.T.de., et al. 1978. Simulation of Assimilation, Respiration and Transpiration of
Crops. Pudoc, Wageningen.
Notation
DAP Days after planting
DGr Growth change of length, area, or volume
(cm m-2 day-1; cm2 m-2 day-1; cm3 m-2 day-1)
G Growth period (days)
n Number of age classes
(,,)jxi
N Number of items within age group (i). (Nu-2)
(,,)jxi
PWGr Potential growth rate of single item (Kg m-2 day-1)
(,,)jxi
PS Potential size: area, volume, or length
Q State variable: weight, number, length, area, or volume, (Kg m-2 day-1,
Nu m-2 day-1, cm m-2 day-1, cm2 m-2 day-1, cm3 m-2 day-1, respectively).
Qrx(i) Rate of Q transfer from age group class AC(i-1) to AC(i).
Qrd(i) Death rate
RT Residual time (days)
S’ Genetically specific transformation factor (SLA, SBV, SSL) biased by climate
factors. (area, volume, or length,: cm2 Kg-1, cm3 Kg-1, cm Kg-1, respectively
SD Crop sink demand. Integration of all developmental stages.
(Kg(DM) m-2 day-1)
WGr DM weight growth (Kg m-2 day-1)
Subscripts
j l (leaf), s(stem), or b(bud)
x fl(flower), ss(skirt shoot), or bs(basal shoot)
i Age group 1,2,3….n
69
Figures
0
100
200
300
400
500
1000 1010 1020 1030 1040 1050
0
2
4
6
8
10
St.Length
LA
Bud Vol.
1.1
0
10
20
30
40
50
1000 1010 1020 1030 1040 1050
0
1
2
3
4
5
1.2
Fig. 1. Monitoring height, area and volume for the stem, leaves and bud on a rose bush
branch in a greenhouse vs Days after planting (DAP).
1.1. Measured values and sigmoid curves were adapted for the data.
1.2. Rates for lengthening, expansion, and filling of the stem leaves and buds.
Mathematical derivatives from the sigmoid curve were adopted for these rates.
Stem Length (mm)
Leaf Area (cm2)
Bud Volume (cm3)
Leaf Extension Rate (cm2/day)
Stem Elongation Rate (cm/day)
Bud Filling Rate (cm3/day)
DAP (0=15-Sep-96)
70
0
1
2
3
4
5
6
7
0 100 200 300 400 50020
30
40
50
60
70
80
90
Length
Number
Summer 97
y = -4.86x + 62.28
R2 = 0.10
y = -15.53x + 80.55
R2 = 0.41
50
60
70
80
90
00.511.522.5
07.01.97-27.01.97
28.01.97-02.03.97
Fig. 2.1. The number of flowers picked and the average flower length on the picking dates
during 1996-97 season. The line curves have been adapted for the data. The
section between two vertical lines, was used for validation.
Fig. 2.2. The relationships between the rates at which flowers mature towards picking and
their average length during a picking wave that lasted from 7-1-97 – to 2-3-97.
Solid circles and solid line describe the relationships measured until 27-01.
Hollow circles and dashed line describe the relationships measured starting on
28-01. The curve marked with a dashed line is data calculated by the model.
Avg. Stem Length (cm/fl)
Pickin
g
rate (Nu/m2/da
y
)
DAP (0=15-Sep-96)
Picking Rates (Nu/m²,day)
Avg.Flower Length (cm/fl)
