Simulation modeling of the effects of short and long-term climatic
variations on carbon balance of apple trees
A. N. Lakso1, M.D. White2 and D. S. Tustin2
1
2
Dept. of Horticultural Sciences, NY State Agricultural Experiment Station, Geneva, NY 14456, USA
HortResearch, Private Bag 1401, Havelock North, New Zealand
Abstract
Effects of short- and long-term climatic variation and foliar pests were modeled with an improved version
of a simplified apple tree carbon balance model (Lakso and Johnson, Acta Hort. 276:141, 1990). New and
improved submodels were developed on (a) spring leaf area development and autumn leaf fall, (b)
partitioning of carbon to the organs of the tree, and (3) fruit growth and abscission based on carbon
balance. Simulations of known effects of low light and foliar pest damage on apple fruit growth and
abscission were realistic and similar to experimental results. Similarly, long-term simulations were run of
leaf area development, light interception, canopy photosynthesis and canopy respiration in different
climates using temperature and radiation data from New York, New Zealand and Washington State.
Simulations suggest that mid-to-late-season differences were the most distinguishing among climates, and
that early season differences were less when expressed as time after budbreak. Total canopy photosynthesis
over the season was estimated to be approximately 18, 23 and 25 kg fixed CO2 for a mature slender spindle
tree at 2000 trees/ha using NY, WA and NZ weather, respectively. Seasonal canopy respiration was
simulated to be about 13-15% of the fixed carbon for all climates. Simulations of short-term responses to
low light and foliar pests and the long-term climatic simulations suggest that the model in general is
behaving realistically.
Keywords: fruit abscission, fruit growth, leaf area development, photosynthesis,
radiation, respiration, temperature
Introduction
Apple orchard productivity varies greatly in different climates or different years in a one
climate, but it is difficult to determine the critical factors over such a range of climatic
conditions. Also, the large, perennial nature of apple trees limits classic growth analyses
on cropping trees in the field, although some have been done (Forshey et al., 1983;
Palmer, 1988). The lack of a great number of growth analyses in different climates
reduces our ability to understand and predict climatic effects on productivity.
Consequently, a sound model of short and long-term climatic effects on apple trees would
be helpful to integrate empirical data, and to help explain and ultimately predict tree
responses to the environment. Such results would help improve understanding, help
focus research on key principles, and provide specific hypotheses to test.
Over the past 25 years there have been several attempts to model apple productivity.
Some models have emphasized sunlight interception by different orchard designs
(reviewed in Jackson, 1980; Palmer, 1989; and Wagenmakers, 1991) and were helpful
in clarifying some important interrelationships of orchard design, light interception and
productivity. More complex physiologically-based models have been attempted
(Cervenka, 1977; Thorpe et al., 1978; Landsberg, 1979; Elfving et al., 1983) but these
were not well described or difficult to work with due to the complexity of their structure
and the computer programming used. Thus, the usefulness of these models has been
primarily limited to those who developed them.
One important use of a realistic, easy-to-use model of carbon balance would be to
compare the effects of varying climates with long-term weather data to try to
understand how much of the marked differences in yields among production regions is
related to environmental versus management effects on carbon balance. It is especially
interesting to elucidate the reasons why New Zealand has such high yields compared to
many other regions. Another goal is to understand the effects of short-term effects such
as low light or effects of foliar pests on fruit development and fruit abscission.
Description of the Model
The current model is a modification of the original daily time-step model of leaf
development, photosynthesis and respiration as described by Lakso and Johnson (1990)
using Stella® dynamic modeling software. The model begins at budbreak. The major
components of the model are: leaf area development/abscission, daily gross canopy
photosynthesis (from Charles-Edwards, 1982), respiration of organs, carbon partitioning,
and fruit development/abscission. Improvements were made to the original leaf area
development submodel. New submodels were added to simulate autumn leaf abscission,
partitioning of carbon among organs, and fruit growth and abscission.
The parameter values in the current model are based on summarized data on many
apple cultivars from the literature and our studies, but much of the data and the fruit
growth components are based on our studies of 'Empire' apples. The “standard” tree
simulated is a mature slender spindle 'Empire'/M9 at approximately 2000 trees/ha. This
was chosen since we have done considerable research on light interception, tree and fruit
development and physiology in such orchards and the chosen tree size and form is fairly
common in most apple production regions. Therefore, we can better evaluate whether the
simulation outputs are realistic.
Required inputs. There are two types of required inputs: tree descriptions and weather
data. To describe the tree, initial inputs are required of numbers of long and short shoots,
numbers of flowers, spacing, and wood surface area (from surface area-to-trunk cross
sectional area regressions). Default seasonal curves of photosynthesis and respiration can
be accepted, or modified to reflect cultivar or seasonal differences. The required weather
data is daily maximum and minimum temperatures and daily total radiation.
Leaf area development and abscission submodel. Leaf area development is driven by
accumulation of growing degree days, a leaf area expansion rate per degree day, total
shoot numbers and the fraction of shoots that are growing at any time. The original leaf
area development model used one growth function for all shoots and did not model leaf
abscission in the autumn. The current version divides the shoots into long extension
shoots (>5 cm) and short rosette-type shoots (spurs with bourse shoots <5 cm and short
lateral shoots from 1-year-old wood). Each shoot type has a different leaf area expansion
rate based on growth studies in 'Empire' and other apple cultivars. Shoot termination is
artificially constrained as we have not yet developed a good understanding of regulation
of shoot termination. Simulated spring leaf area development of pruned and unpruned
'Empire' trees fit published data (Lakso, 1984) reasonably well (Fig. 1).
The leaf abscission in the autumn is based on multiple-year leaf drop studies done in
New York and Hawkes Bay, New Zealand, representing a range of observed leaf area
durations. Since both locations have similar latitudes of 41-44˚, the differences were
primarily due to temperature differences. Based on these data and other observations
(Jonkers,1980), the leaf abscission submodel was based on an accumulation of daily
minimum temperatures below 5˚C in the autumn, similar to chill unit models.
2
Leaf area (m
/tree)
10
8
6
unpruned - actual
unpruned - simulated
pruned - actual
pruned - simulated
4
2
0
0
200
400
600
800
o
Growing dregree days after budbreak (base
C) 4
Figure. 1. Actual and simulated leaf area development on pruned and unpruned 'Empire'
apple trees (measured data from Lakso, 1984) as a function of degree-days above 4˚C.
Photosynthesis and respiration. The canopy photosynthesis equation of Charles-Edwards
(1982) and leaf, structural wood and fruit respiration components have remained the same
as in the original model. Current parameter values that have been improved or confirmed
by recent measurements of leaf photosynthesis or organ respiration rates.
Carbon Partitioning Submodel. After net CO2 exchange is calculated from canopy
photosynthesis - organ respiration, the partitioning of the accumulated fixed carbon is
adapted from Buwalda’s kiwifruit vine model (Buwalda, 1991). The total demand for
each type of organ is estimated from its numbers and estimated maximum growth rates
(typically estimated from growth studies under assumed optimum conditions for growth).
Shoot and fruit demands were estimated from growth studies, but root and wood demands
were mostly guesses. The total demand for an organ is equal to the maximum growth
demand (adjusted for temperature) times the number of active organs of that type. If
adequate carbon is available to fully support all organs , the carbon is partitioned equal to
the demands and maximum growth occurs for all organs. However, if the carbon supply
is less than the total demand, a prioritization was used. A “relative sink strength” (RSS)
factor was estimated for each type of organ, and the total of the RSS factors equal 1.0.
Based on review of the literature and our own studies, the relative sink strengths were
chosen to be in the following order: shoots>>fruits>roots=wood. This gave strong
priority to shoots so that early in the season when shoots are active, they receive a greater
proportion of their demand. Later, as shoots terminate growth, the partitioning shifts to
fruits and other organs even though the RSS values remain constant. This is consistent
with studies that indicated that shoot tips were very strong competitors for carbon in the
early season and that under low light conditions, carbon partitioning to fruit or fruit
growth suffered much more than did shoot growth (Quinlan and Preston, 1971; Corelli
Grappadelli et al., 1994; Bepete and Lakso, 1998). The actual amount partitioned to each
organ type depends on the individual demands, the number of actively-growing organs
(e.g. number of active shoots), and whether carbon is adequate or limiting.
The relative partitioning to a given organ (RPi) is estimated by:
RPi = DemandI - (DemandI (1-RSSi)(1 - (Carbon avail / Demand total)
The actual carbon partitioned then to each organ is:
Carboni = RPi (Carbon avail / ∑ RPi )
Fruit abscission and growth submodel. To simulate the effects of carbon supply on the
growth and abscission of the fruit, fruit abscission occurs if fruit growth rate is not
maintained above a critical rate. This relationship was based on several studies of growth
rates and abscission of different cultivars in response to different treatments such as
Naphthaleneacetic acid (NAA) thinning sprays or heavy shading. Although there was
variation, a consistent pattern of fruit abscission occurred if fruit growth rates were not
maintained above about 60% of the rate of the fastest-growing fruits in the population
(Fig. 2). We found that the relationship was more consistent if the growth rates were
expressed relative to the fastest-growing fruits in each study rather than to any specific
absolute growth rates. Whether further improvements will occur if relative growth rates
(RGR) are used is being explored.
Fruit abscission (%)
100
Delicious '91
Gala '91
Empire '91 - 20mm
Empire '93 - 7mm
Empire '93 - 18mm
Empire '86 - 10mm
Empire '86 - 24mm
80
60
40
20
0
0
20
40
60
80
100
Fruit growth rate as % of fruit with highest growth rate
Figure 2. The relationship between fruit abscission and fruit growth rate as % the fastest
growing fruits in a population in several NAA or shade studies (unpublished data of A.
Lakso).
The fruit growth/abscission model operates by comparing the amount of fruit growth
supported by the carbon partitioned to fruit each day with a 3-day running average (to
simulate the observed buffering of single day variations) to the maximum growth
expected on that day (based on a maximum growth rate curve and the number of fruits on
the tree at that time). The % of maximum growth supported is used to cause fruit
abscission as described above. As fruit abscise, the number of current fruit decreases for
the next daily cycle. The fruit growth that is supported is accumulated to give the total
crop weight and mean fruit weight.
Simulations of Short and Long-Term Climatic Variation
Climate Comparisons. Long-term mean daily weather data and average budbreak dates
were obtained for Geneva, NY (20 year mean, latitude 43˚ N), Prosser, Washington (4
year mean, latitude 46˚N courtesy of R. Wample) and Havelock North, New Zealand (4
year mean, 40˚ S latitude). The climate data was used to drive the model. It was decided
to use the "standard tree" to emphasize climate differences and to avoid the confounding
effects of different training systems or tree sizes, etc. The trees were constrained to stop
at the same final leaf area (about 14 m2/tree) and same final light interception (about 52%
at full canopy). It is recognized that apple trees may grow for longer periods in different
climates, but that aspect will be modeled later.
The climatic differences can be summarized as follows:
• New York (NY) had the shortest growing season, shortest leaf area duration (LAD) and
the lowest amount of total radiation available and intercepted. Temperatures were
intermediate among the 3 climates and showed less diurnal amplitude than in New
Zealand and Washington.
• New Zealand (NZ) allowed the longest LAD, the least extreme climate due to the
marine influence, and the coolest summer and warmest winter temperatures.
• Washington State (Wa) is a slightly longer season than NY, but shorter than NZ. There
are more clear days so there is higher radiation mid-season, with the warmest
maximum temperatures and cool minimums.
Since climate comparisons are begun at apple budbreak, the three climates are
surprisingly similar in the first 30-50 days since the tree development requires similar
temperatures to begin regardless of the rest of the growing season. The greatest
differences are in the length of the seasons and the amount of postharvest activity. This is
reflected in the simulated seasonal patterns of canopy photosynthesis and respiration (Fig.
3). They suggest that early-season differences are relatively small, but that mid and lateseason differences are quite large, reflecting the differences in LAD. Wünsche et al.
(2000) with whole canopy chambers reported similar results, except that they found much
higher NCE rates at 211 days after bloom than our model.
The seasonal cumulative light-period canopy photosynthesis (does not include lightperiod respiration by fruits, wood, etc.) was simulated to be about 18, 23 and 25 kg of
fixed CO2 per tree in NY, Wa and NZ respectively, a range of almost 40%. Seasonal
cumulative total respiration loss (24-hour fruit and wood plus dark leaf respiration) was
estimated at 13-15 percent of the fixed CO2 in all climates. This gave net cumulative
CO2 fixation per tree per year of about 16, 19 and 22 kg/tree in NY, Wa and NZ
respectively. The respiratory losses are very low compared to most plants (Amthor,
1989), but they are reasonable compared to our previous studies with direct measurement
by “balloon” chambers. We found night respiration rates of 5-20% of daily fixed CO2
following sunny days at different times of the season (Lakso and Piccioni, unpublished
data). Studies in NZ by Wünsche et al. (2000) found that night respiration in the cool
nights of NZ to give even smaller percentage respiratory losses.
2 /day)
Daily canopy photosynthesis (g
CO
180
150
120
90
NZ
60
NY
Wa
30
0
0
30
60
90 120 150 180 210 240 270 300
Days after budbreak
Figure 3. Simulated daily canopy photosynthesis of modeled 'Empire'/M.9 slender
spindle trees at 2000 trees/ha using long-term weather data from Geneva, NY, Prosser,
WA and Havelock North, NZ.
Simulations of short-term light effects. During the early period after bloom when final
fruit numbers are set and cell division occurs in the fruit, fruit abscission is known to be
quite sensitive to low light or high temperatures. Byers et al. (1991) showed that at 30
days after bloom fruit abscission could be increased by very low light if it occurred more
that 2 consecutive days, but that single days of low light had no effect. This general
effect was simulated by reducing the radiation input at a similar time of the season to 4
MJ/m2 (about 15% of that on a clear sunny day that reduced simulated canopy
photosynthesis by 73%) for 1, 2 or 3 days continuously or 2 and 3 days of low light
alternated with days of full sunlight. The simulations were realistic to the low light
treatments at that time with 1 day of low light causing no fruit abscission, 2 days causing
some abscission, and 3 days causing heavy abscission (Fig. 4). If alternated with sunny
days, 2 or 3 days of low light caused partial abscission. Byers, et al. (1991) found similar
experimental responses although our simulations indicated a stronger effect of 3
continuous days of low light.
Simulations of foliar pest effects. A second simulation test of the fruit development
model was to simulate the effects on fruit growth of a severe mid-season European Red
Mite infestation (cumulated mite-days of about 2000) as measured experimentally by
Francesconi et al. (1996). The model used long-term average NY weather and simulated
the mite effect by reducing the light-saturated leaf photosynthesis rate (Pmax) at 110 days
after budbreak by 40% as found in the actual study. The seasonal fruit growth curves of
our "standard" fully-cropped trees with and without the simulated leaf damage were found
to be quite similar to those found experimentally (Fig. 5). This suggests that the model is
realistic in modeling mid-to-late season fruit growth effects.
Fruit number as % of untreated
100
Byers et al., 1991
Simulated
80
60
40
20
0
None
1 Day
2 Day
3 Day
2/Alt
3/Alt
Low light treatments
Figure 4. Effects of 1, 2 or 3 days of continuous low light or 2 or 3 days of low light
alternated with sunny days on actual (Byers, et al., 1991) and simulated relative fruit
drop.
Mean fruit weight (g)
200
Actual - control
Simulated - control
Actual - 2000 cmd
Simulated - 2000 cmd
160
120
80
40
0
0
30
60
90
120
150
Days after bloom
Figure 5. Patterns of fruit growth as affected by a severe mid-season European Red Mite
infestation (2000 cumulative mite-days) as determined experimentally by Francesconi et
al. (1996) and simulated by reducing the leaf Pmax at 80 days after bloom by 40% as found
in the actual study.
Summary
We have developed an extended version of the simplified apple carbon balance model.
The results of the long-term climatic simulations and tests of short-term responses to low
light and foliar pests suggest that the model in general is behaving realistically. The
inclusion of a root growth and respiration components and the extension of the model to a
year-round cycle with carbon reserves are under development.
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