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Author(s)
First Name
Middle Name
Surname
Role
Email
David
H
Fleisher
ASABE
member
David.fleishe
[email protected].
gov
Affiliation
Organization
Address
Country
USDA-ARS
10300 Baltimore Avenue /
Beltsville, MD 20705
USA
Author(s) – repeat Author and Affiliation boxes as needed-First Name
Middle Name
Surname
Role
Email
Dennis
J
Timlin
Coauthor
Dennis.timlin
@ars.usda.g
ov
Affiliation
Organization
Address
Country
USDA-ARS
10300 Baltimore Avenue /
Beltsville, MD 20705
USA
Author(s) – repeat Author and Affiliation boxes as needed-First Name
Middle Name
Surname
Role
Email
The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily
reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution
does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer
review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this
work should state that it is from an ASABE meeting paper. EXAMPLE: Author's Last Name, Initials. 2007. Title of Presentation.
ASABE Paper No. 07xxxx. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a technical
presentation, please contact ASABE at [email protected] or 269-429-0300 (2950 Niles Road, St. Joseph, MI 49085-9659 USA).
Yang
Yang
ASABE
member
Yang.yang@
ars.usda.gov
Affiliation
Organization
Address
University of Maryland
Country
Wye Research and Education
Center, University of Maryland,
Queenstown, MD
USA
Author(s) – repeat Author and Affiliation boxes as needed-First Name
Middle Name
V.R.
Surname
Role
Email
Reddy
Coauthor
VR.Reddy@
ars.usda.gov
Affiliation
Organization
Address
USDA-ARS
10300 Baltimore Avenue /
Beltsville, MD 20705
Country
Publication Information
Pub ID
Pub Date
073013
2007 ASABE Annual Meeting Paper
The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily
reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution
does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer
review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this
work should state that it is from an ASABE meeting paper. EXAMPLE: Author's Last Name, Initials. 2007. Title of Presentation.
ASABE Paper No. 07xxxx. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a technical
presentation, please contact ASABE at [email protected] or 269-429-0300 (2950 Niles Road, St. Joseph, MI 49085-9659 USA).
An ASABE Meeting Presentation
Paper Number: 073013
Simulation of Potato Gas Exchange Using SPUDSIM
David H. Fleisher
Crop Systems and Global Change, USDA-ARS, Beltsville, MD 20705 USA
Dennis J. Timlin
Crop Systems and Global Change, USDA-ARS, Beltsville, MD 20705 USA
Yang Yang
Wye Research and Education Center, University of Maryland, Queenstown, MD
V.R. Reddy
Crop Systems and Global Change, USDA-ARS, Beltsville, MD 20705 USA
Written for presentation at the
2007 ASABE Annual International Meeting
Sponsored by ASABE
Minneapolis Convention Center
Minneapolis, Minnesota
17 - 20 June 2007
Abstract. SPUDSIM is a new potato model derived from an older USDA-ARS model, SIMPOTATO,
developed to incorporate new advances in the knowledge of plant growth and development. Modifications
incorporated in SPUDSIM focus at simulating canopy growth and development at the individual leaf level and
include routines for individual leaf appearance rates and leaf expansion as a function of leaf physiological age
and plant assimilate status. Coupled sub-models for leaf level photosynthesis, transpiration, and stomatal
conductance were used to replace the older radiation use efficiency approach. A radiative transfer routine that
estimates intercepted photosynthetically active radiation for sunlit and shaded leaves was also added. During
each time increment, net photosynthetic rate is estimated for sunlit and shaded leaf area. Photosynthate is
partitioned among leaves in the canopy according to leaf age, potential expansion, and plant assimilate status.
Assimilate allocation to branches, roots, and tubers proceeds according to fixed partitioning coefficients defined
in SIMPOTATO. Remaining photosynthate is used to support the appearance of new leaves or branches in the
canopy according to predicted demand. Whole plant gas exchange and harvest data from SPAR (soil-plantatmosphere research) chamber experiments conducted at USDA-ARS Beltsville, MD were used to evaluate
SPUDSIM predictions. Results indicate that SPUDSIM accurately captures potato growth and developmental
responses over a wide range of temperatures and will be suitable for a variety of applications involving complex
soil-plant-atmospheric system relationships.
Keywords. Potato, Models, Simulation, Decision Support, Photosynthesis, Gas Exchange
The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the
official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not
constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by
ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is
from an ASABE meeting paper. EXAMPLE: Author's Last Name, Initials. 2007. Title of Presentation. ASABE Paper No. 07xxxx. St. Joseph,
Mich.: ASABE. For information about securing permission to reprint or reproduce a technical presentation, please contact ASABE at
[email protected] or 269-429-0300 (2950 Niles Road, St. Joseph, MI 49085-9659 USA).
Introduction
The United States is the 5th largest potato growing country in the world, producing 19.7 million metric
tons on 453,000 ha in 2006 (USDA, 2007). As with other agricultural crops, there are significant risks
and challenges involved in potato production due to uncertainties with climate, pests, and other pressures.
As operations increase in size and complexity, farmers are required to manage, interpret, and make
decisions upon large amounts of information. Fluctuating market prices, costs of fertilizers, pesticides
and irrigation, environmental impact concerns from agricultural practices, land-use pressures, and
projected climate change factors create additional demands on farmers, crop consultants, policy planners
and scientists. Over the past 40 years, mechanistic, process level computer models have been developed
that attempt to mimic crop responses to climatic and management factors. Complex, mechanistic crop
models are needed to encapsulate knowledge on the soil-plant-atmosphere system, test hypotheses,
evaluate the behavior of complex agricultural systems, and study alternative production scenarios under
different climactic, management, and geographic locations (Reddy and Reddy, 1998). These models are
typically integrated with computerized decision support systems to help manage and interpret large
amounts of complex information in order to help farmers reduce risk (Uehara and Tsuji, 1998; Timlin et
al., 2002; Wang et al., 2002). However, many crop models are still at an early stage of development and
do not necessarily include state-of-the-art science due to (a) lack of perceived need to incorporate this
new information, (b) lack of resources, or (c) other knowledge gaps that prevent adoption of new research
in the models. By including this new information into the models, more reliable predictions of growth
and development in response to climactic and nutritional stresses can be obtained.
Potato models generally simulate crop growth and development by using a ‘big-leaf’ approach. Increases
in total canopy leaf area are based on inputs for environment and plant nutritional status (e.g. International
Benchmark Sites Network for Agrotechnology Transfer, 1993; Kooman and Haverkort, 1995; Hodges et
al., 1992; Shaykewich et al., 1998). Daily gains in plant dry weight are obtained by multiplying an
estimate for canopy light interception (based on leaf area) by a conversion factor known as radiation use
efficiency (RUE, g carbohydrate (CHO) MJ-1 daily intercepted radiation). This value can be reduced by
additional empirical factors that approximate limiting effects of plant nutritional status, water content,
and temperature on growth rate. Conceptual carbon (C) pools for total leaf and stem dry mass are then
computed through the use of empirical partitioning coefficients as opposed to predicting individual leaf
appearance, expansion, and duration. RUE based models are popular and have been successfully applied
to a variety of studies for many crops. However, factors such as leaf nitrogen content, water stress,
senescence, elevated [CO2] and rising air temperatures play significant roles in influencing plant
photosynthetic rate at daily and shorter time-scales, and cannot be mechanistically accounted for with an
RUE approach (Demetriadeshah et al., 1992, 1994). In addition, such an approach can over-estimate
daily growth rate due to the nonlinearity of leaf response to light (Thornley, 2002).
Over the past few years, a new potato model, SPUDSIM, has been developed. SPUDSIM is based on a
series of modifications to an older ARS potato model, SIMPOTATO (also known as SIMGUI), that
follows the general RUE based modeling approach outlined above (Hodges et al., 1992). These
modifications primarily focus on replacing RUE and big-leaf method to simulate canopy growth and
development with an individual leaf level approach. Modifications include simulation of individual leaf
appearance on different stems in the canopy (Fleisher et al, 2006a), individual leaf expansion as a
function of leaf physiological age and plant assimilate status (Fleisher and Timlin, 2006), and
incorporation of a leaf-level coupled model for photosynthesis, transpiration, and stomatal conductance
(Soo and Lieth, 2003). This paper focuses on the details of these modifications, provides preliminary
comparison between model predictions with experimental gas exchange data, and discusses the future
modifications planned for the model.
2
Materials and Methods
i. Data
The majority of new modifications incorporated in SPUDSIM come from experiments conducted in daylit
soil-plant-atmosphere research (SPAR) chambers at USDA-ARS facilities in Beltsville, MD in 2003
through 2006. Data from field studies and literature have been used to validate modeling sub-components
where appropriate. Daylit SPAR chambers were constructed from clear acrylic, transparent to natural
sunlit, had a 1 m2 cross-sectional area, and a total chamber volume of 3360 L. Air temperature and
relative humidity were monitored and controlled with TC2 controllers (Environmental Growth Chambers,
Ohio USA). A dedicated Sun SPARC5 work station (Sun Microsystems, Mountainview, CA) logged
environmental data (air and soil temperatures, atmospheric CO2 concentration ([CO2]), and
photosynthetically active radiation (PAR, in µmol m-2 s-1)) every 300 s. Mass flow controllers in each
chamber were used to maintain [CO2] at desired levels during the day. Each chamber has a dedicated
infrared gas analyzer, permitting continuous monitoring of whole plant carbon dioxide fluxes at 5 minute
intervals during the course of the season. This permits calculation of gross and net canopy photosynthetic
rates. Additional details on SPAR chamber operation and related calculations can be found in Reddy et
al., (2001).
ii. SPUDSIM
SPUDSIM contains most of the same phenological components and carbon allocation routines as the
original SIMPOTATO model. SPUDSIM was coded in C++ and runs on an hourly time-step. The
model has been integrated with 2DSOIL, a modular, comprehensive two-dimensional soil simulator that
is specifically designed to be integrated with existing crop models (Timlin et al., 1996). 2DSOIL
modules can simulate water, solute, heat and gas movement as well as plant root activity in a twodimensional profile. Coupling SPUDSIM with 2DSOIL allows simulation of the soil-plant-atmosphere
continuum.
The basic weather data needed to run SPUDSIM include daily solar radiation, maximum and minimum
temperature, relative humidity and rainfall. Management inputs include planting and emergence date,
planting density and depth, seed reserve at planting, row spacing, cultivar, amount, type and incorporation
depth of crop residue, and in-season fertilization and irrigation information. Soil inputs include initial,
saturated, wilting and upper limit of field capacity volumetric water contents, mineral ammonium and
nitrate concentrations, and soil pH of each user defined soil horizon.
At each time-step, SPUDSIM reads in the appropriate input data and simulates plant development, gas
exchange, carbon allocation, and organ initiation as indicated in Figure 1. Routines that are different
between SPUDSIM and SIMPOTATO are shaded. The model keeps iterating until either harvest date,
maturity date, or other user-specified end point is reached. The frequency and type of model outputs can
be specified by the user and include, but are not limited to, dry weights of all organs, transpiration,
photosynthetic rate, assimilate status, leaf and lateral branch numbers, and leaf area index.
iii. Modifications
a. Leaf appearance rate
Data from the literature (Kirk and Marshall, 1992) and daylit SPAR and field experiments were used to
model leaf appearance rates on potato mainstem and lateral branches as detailed in Fleisher et al. (2006a).
Rates followed a nonlinear response with temperature and were modeling using a modified β distribution
3
function (Yan and Hunt, 1999), and take the form shown in equation (1). Rates accumulate at an hourly
basis in SPUDSIM using the previous 24 h average air temperature (°C).
 T T
r  Rmax  max
T T
opt
 max
 T

 T
 opt




Topt
Tmax Topt
,
r0
at
T 0
(1)
r  0 at T  Tmax
where:
r – leaf appearance rate (leaves plant-1 day-1)
Rmax – maximum leaf appearance rate (leaves plant-1 day-1); 0.96
Tmax – ceiling temperature where r = 0; 39.5°C
Topt – optimum temperature where r = Rmax; 27.2°C
T – average daily temperature from previous 24 h (°C)
A comparison with experimental data is shown in Figure 2. As implemented in the model, leaves can
appear on any lateral or mainstem branch – i.e., each branch accumulates leaf appearance rate separately,
as long as there is sufficient plant assimilate supply to support the new organ. The appearance of lateral
branches is assumed to have the same temperature response.
b. Leaf expansion
Individual leaf expansion rate was modeled using a modification of an organ expansion routine
introduced by Ng and Loomis (1984). The routine simulates individual leaf expansion primarily as a
function of genetic potential and temperature, with external factors for nutrient, water, and plant
assimilate supplies limiting the expansion (Fleisher and Timlin, 2006):
RA  A  RA max  f age  f T   f (C )
where:
RA
RAmax
A
f(age)
f(T)
f(C)
(2)
– rate of leaf expansion, [cm2 d-1]
– maximum relative rate of area expansion, [cm2 cm-2 d-1]; 10
– leaf area, [cm2]
– physiological age dependent expansion rate, [cm2 cm-2]; 0 to 1
– air temperature affect on cell division and expansion, [unit less, 0 to 1]
– affect of assimilate supply on potential leaf expansion, [unit less, 0 to 1]
It is assumed that all leaves have the same potential to expand to the same maximum size and at the same
potential rate, but are limited by nutrient, temperature, water, and plant assimilate supply. A comparison
of experimental and model predictions of individual leaf area versus time in potato are shown in Figure 3
(in this case, equation (2) was tested directly against experimental data). The expansion of each leaf is
tied to carbon demand through the use of specific leaf area (SLA, cm2 leaf g-1 dry weight). In SPUDSIM,
SLA decreases with physiological age of the leaf; thus, more carbon is required to support an equivalent
increase in area of mature versus newly initiated leaves.
c. Gas exchange
The RUE approach in SIMPOTATO was replaced with a leaf-level gas exchange routine that requires
inputs for [CO2], PAR, temperature, relative humidity, and wind speed. For estimating the fraction of
4
PAR incident at the leaf surface, the canopy is divided into sunlit and shaded leaf fractions, following the
descriptions in Sinclair et al. (1976) and Campbell and Norman (1998).
Photosynthetic rate and transpiration are estimated per unit leaf surface based on the work of Kim and
Lieth (2003) who coupled a biochemical model of photosynthesis for C3 leaves (de Pury and Farquhar,
1997; Harley et al., 1992; Farquhar et al., 1980) with a model of stomatal conductance (Ball et al., 1987)
and an energy budget equation at the leaf surface (Campbell and Norman, 1998). Separate carbohydrate
(CHO) assimilation rates are computed for sunlit and shaded leaves, and then multiplied by leaf area
index to provide the total carbon assimilate pool for the plant at the current time-step.
Respiration losses due to growth and maintenance for each organ are then substracted from the assimilate
pool at each time-step. Growth respiration is based on 30 to 40% of organ growth demand largely
following the work of Ng and Loomis (1984). Maintenance respiration is computed as a function of
temperature, organ type and mass, and metabolic activity. Carbon allocation and demand of various
organ classes is primarily a function of leaf expansion and tuber demand as defined in SIMPOTATO
(Hodges, 1992).
iv. Testing of SPUDSIM
Gas exchange and harvest data comes from a daylit SPAR chamber study conducted in 2004. Certified
potato (solanum tuberosum L. cv. Kennebec) seed tubers were planted in a 50:50 peat/vermiculite potting
medium in 15L pots at a depth of 5 cm. Plants were selected for uniformity based on main-stem leaf
count, thinned to a single main-stem at a density of 12 pots (12 stems) per chamber. SPAR chambers
were set to one of six different day/night temperature regimes: 14/10, 17/12, 20/15, 23/18, 28/23, and
34/29°C with a 16- and 8-h day / night thermoperiod. Plants were harvested at approximately 60 DAE
and dry weights were obtained for each organ class. Additional details can be found in Fleisher et al.
(2006b).
Results and Discussion
SPUDSIM predictions for daily assimilation during the course of the season were reasonably accurate.
Correlation coefficients for 1:1 comparisons of predicted versus measured data were 0.8 for 14/10°C, 0.7
for 17/12, 20/15, 23/18, and 28/23°C and 0.3 for the 34/29°C treatment. An illustration is provided for
the 17/12 and 28/23°C treatments (Figure 4). The dips in the gas exchange data at 151,152, 156, 157,
164, and 175 day of year were due to reduced daily PAR as a result of cloud cover. The poor correlation
in the 34/29°C treatment is discussed in more detail below.
The model also reproduces diurnal patterns of gas exchange. Figure 5 shows daily net photosynthetic rate
for the 23/18°C treatment at 20, 40, and 60 DAE. In the 20 and 40 DAE, the model shows an increased
sensitivity to high levels of PAR (greater than 1100 µmol m-2 s-1) which may indicate too high a response
of the gas exchange routines to high light levels.
Nonetheless, SPUDSIM does a reasonable job in simulating the biomass totals at harvest for most
temperature treatments (Table 1). The model reproduced the experimentally measured responses to
temperature, with the largest amounts of biomass (mostly attributed to tuber yield) occurring at the
coolest temperatures. Model predictions were within 15% of total and tuber dry mass values for all
temperatures except the 14/10 and 34/29°C treatments. At the 14/10°C treatment, the model overpredicted tuber yield response, most likely a function of too large an increase in leaf area at that
temperature (data not shown). Over-prediction of dry mass at the 34/29°C treatment was most likely a
result of the model lacking an insufficient response to high heat stress on leaf expansion, as the leaves
from the plants in this treatment were visually curled and stunted.
5
Table 1: Comparison of experimental (actual) dry mass (g plant-1) versus model predictions for
each organ type including senesced leaf mass. Standard deviations are provided.
Treatment Total
Tuber
Stem
Leaf
Senesced
(°C)
Actual
Model Actual Model Actual Model Actual Model Actual Model
14/10
93±18
112
75±16 93
2±1
4
12±3 11
0
0
17/12
103±20 92
80±19 78
3±1
4
15±1 8
1±2
0
20/15
103±21 101
79±18 82
5±2
5
13±3 11
3±2
4
23/18
87±30 84
51±22 63
8±4
5
11±4 12
5±5
4
28/23
64±17
59
24±10 23
10±5 6
17±3 20
5±3
4
34/29
13±3
20
0
0
9±4
9
3±3
6
5±4
2
The results presented here indicate SPUDSIM can provide accurate predictions of potato growth and
development over a wide range of temperature conditions. The responses to warmer environments
suggest SPUDSIM can also be used to simulate production in the tropics (Manrique et al., 1989).
However, the current simulations assume non-limiting nutrient and water. The incorporation of leaflevel canopy growth and development routines, and replacement of the RUE approach with a state-of-theart leaf-level gas exchange / energy balance approach, provides a basis to include more recent knowledge
on the response of various plant processes to nutrient and water stress. For example, our lab is currently
testing alternate theories on the response of stomatal conductance to drought stress as mediated by either
abscisic acid signaling from the root system or reduced bulk leaf water potential (Yang et al., 2007). In
either case, the effect of drought stress on gas exchange can directly be modeled. These changes, along
with methods to simulate nitrogen and water uptake, and their associated limiting effects on organ
expansion and initiation, are currently being incorporated into SPUDSIM.
The modifications incorporated into SPUDSIM update the previous potato model, SIMPOTATO, to
include more state of the art knowledge on plant response to the production environment. Once fully
validated, SPUDSIM will provide more accurate responses to the off-nominal growth conditions typically
encountered by farmers, improving the model’s importance as part of a computer based decision support
system. The integration of SPUDSIM with the 2DSOIL two-dimensional soil simulator will permit
evaluation of complex soil-plant-atmosphere system issues in a more in-depth basis. These include the
impact of climate change, cropping rotations, nutrient dynamics and movement in soil, and assessment of
conservation practices on soil health.
Conclusion
SPUDSIM is a new USDA-ARS potato model that incorporates recent advances in individual leaf
appearance, growth, and gas exchange. These modifications essentially replace the big leaf, radiation use
efficiency (RUE) approach used in older potato models with a more mechanistic depiction of canopy
growth and development. Specifically, routines for individual leaf appearance rates and individual leaf
expansion were developed using experimental data. A biochemical model of photosynthesis, stomatal
conductance, and transpiration were coupled and incorporated in SPUDSIM to predict photosynthetic rate
and transpiration for both shaded and sunlit leaves in the potato canopy. Preliminary analysis of
SPUDSIM results indicate the model predicts plant growth and development responses over a broad range
of temperatures. Planned additions to the model include components for water and nitrogen stress on gas
exchange, organ expansion, and initiation, and are expected to make the model suitable for simulating offnominal conditions typically experienced by farmers. SPUDSIM has been integrated with a twodimensional soil simulator in order to more effectively study impacts of climate change, crop rotations
nutrient dynamics, and evaluation of conservation and other management practices on soil quality.
6
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Yan, W., and L.A. Hunt. 1999. An equation for modeling the temperature response of plants using only
the cardinal temperatures. Ann. Bot. (London) 84:607-614.
Yang, Y., D. Timlin, D.H. Fleisher, and V.R. Reddy. 2007. Simulating Canopy Evapotranspiration and
Photosynthesis of Corn Plants Under Different Water Status Using a Coupled MaizeSim+2DSOIL Model.
In preparation.
8
Increment time step
Read in data:
-weather
-management
-soil status
Compute developmental rates:
-Whole plant phenology
-Branch appearance rate
-Leaf (nodal unit) appearance rate
-Tuber initiation / bulking rate
Compute canopy gas exchange:
-Estimate sunlit / shaded leaf area fraction
-Gross photosynthetic rate
-Transpiration rate
Subtract maintenance respiration costs
Is there sufficient CHO
to satisfy all organ
growth rates?
No
Reduce potential growth for all
organs based on developmental
stage and assimilate status
Yes
Allocate CHO to each organ:
-Give young leaves first priority
-Subtract growth respiration costs
Initiate new organs based on developmental
rate and availability of plant assimilate
Output data to file
Figure 1: General implementation of SPUDSIM. Shaded boxes represent major modifications to
SIMPOTATO.
9
1.2
Leaves plant-1 day-1
1.0
0.8
0.6
0.4
D1
D2
D0
KM
0.2
5
10
15
20
25
30
35
Observed average daily temperature (C)
Figure 2: Comparison of leaf appearance rates (with standard errors) versus observed average
daily temperature for three SPAR chamber experiments (D0, D1, D2) and data from Kirk and
Marshall (1992) (KM.) The nonlinear temperature response model based on the modified beta
distribution (equation (1)) is the solid line. Figure comes from Fleisher et al. (2006).
350
300
Leaf area (cm2)
250
200
150
34/29
28/23
23/18
20/15
17/12
14/10
100
50
o
C
C
o
C
o
C
o
C
o
C
o
0
0
10
20
30
40
50
60
Days after appearance
Figure 3: Measured (symbols) and simulated (lines) individual leaf area versus days after
appearance for a SPAR experiment with 6 different day/night temperatures.
10
1.6
1.4
Measured
SPUDSIM
1.2
1.0
0.8
mol CO2 m-2 d-1
0.6
0.4
0.2
0.0
1.6
1.4
Measured
SPUDSIM
1.2
1.0
0.8
0.6
0.4
0.2
0.0
130
140
150
160
170
180
190
Day of year
Figure 4: Comparison of daily net CO2 accumulation for the season between measured and
predicted (SPUDSIM) data for the 17/12 (top) and 28/23°C (bottom) treatments.
11
DAE 20
-1
DAE 60
3000
30
20
2000
10
1000
-2
40
4000
PPF (umol PAR m s )
-2
umol CO2 m s
-1
50
0
40
0
3:00
4000
DAE 40
3000
30
20
2000
10
1000
7:00
PPF (umol PAR m-2 s-1)
-2
umol CO2 m s
-1
-10
50
11:00
15:00
19:00
Time of day (hh:mm)
Measured
Spudsim
PAR
0
-10
0
3:00
7:00
11:00
15:00
19:00
Time of day (hh:mm)
Figure 5: Comparison of diurnal patterns in net photosynthetic rate between measured and
predicted data at 20, 40, and 60 DAE for the 23/18°C treatment.
12