Agronomy Journal Journal of Natural Resources and Life Sciences Education
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via ISI Web of Science (9)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Green, S.
Right arrow Articles by Clothier, B.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Green, S.
Right arrow Articles by Clothier, B.
Agricola
Right arrow Articles by Green, S.
Right arrow Articles by Clothier, B.
Related Collections
Right arrow Heat Movement Models
Right arrow Crop Physiology & Metabolism
Right arrow Crop Models
Right arrow Plant Analysis
Right arrow Plant and Environment Interactions
Published in Agron. J. 95:1380-1387 (2003).
© American Society of Agronomy
677 S. Segoe Rd., Madison, WI 53711 USA

SYMPOSIUM PAPERS

Modeling Light Interception and Transpiration of Apple Tree Canopies

Steve Green*, Keith McNaughton, J. N. Wünsche and Brent Clothier

Environ. and Risk Manage. Group, HortResearch Inst., Private Bag 11-030, Palmerston North, New Zealand

* Corresponding author (sgreen{at}hortresearch.co.nz).

Received for publication November 6, 2002.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Sap flow in the trunk of two different-sized apple trees [Malus sylvestris (L.) Mill. var. domestica (Borkh.) Mansf. cv. Splendour/MM.106 and Braeburn/M.9] was measured using the compensation heat-pulse method. Supporting measurements were made of the total photosynthetic photon flux (QP) and the total all-wave radiation (QN) absorbed by each tree. These data were used to test the output from a three-dimensional model of light interception that approximated the orchard as an array of nonoverlapping, truncated ellipsoids, with each tree having a uniform density of green leaves that were randomly distributed within the canopy volume. Experimental observations, together with model predictions, were used to demonstrate how transpiration responds to changes in the aerial environment. Model testing was rigorous in the sense that the model was compared against complete and independent data collected on the same time scale. Agreement between measured and modeled values was generally very good; all correlation coefficients were large (r2 > 0.95), and the linear relationship between measurements and simulations of QP, QN, and transpiration has a slope that was within 5% of 1:1. A sensitivity analysis revealed that light interception was influenced most by changes in leaf area and leaf optical properties while transpiration was influenced most by changes in leaf area and leaf conductance. On a leaf-area basis, results from the Braeburn tree (leaf area = 8.65 m2) were very similar to those from the larger Splendour tree (leaf area = 35.5 m2). A smaller, more compact fruit tree is more efficient at intercepting the sun's energy, yet it may require more irrigation water per hectare to sustain productivity.

Abbreviations: PAR, photosynthetically active radiation • PPF, photosynthetic photon flux • QN, total all-wave radiation • QP, total photosynthetic photon flux • 3-D, three dimensional


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
ONE OF THE MAJOR environmental factors that influences transpiration and photosynthesis is the amount of light that is intercepted by the leaves. In general, the amount of light intercepted by an apple orchard system depends primarily on orchard design factors, such as planting system, tree spacing, tree shape, tree height, alley width, row orientation as well as leaf area index (ratio between the total area of all leaves per tree to the land area allocated to the tree) and the length of the growing season. These various factors have all been well researched over the past 20 to 25 yr (Jackson, 1980; Wagenmakers, 1991; Lakso et al., 2000).

Apple yields are generally well correlated with the total amount of intercepted sunlight, but due to the deleterious effects of canopy shading, optimum apple yields are normally achieved at about 60 to 70% light interception (Lakso, 1994; Wünsche and Lakso, 2000a). The relationship between yield and percentage light interception is expected to show a curvilinear response (Wünsche and Lakso, 2000b) that mimics the relationship between yield and leaf area (Wünsche et al., 1996). Adequate light distribution within the tree canopy is also needed to secure high fruit quality because shade causes a reduction in fruit weight and other symptoms of fruit immaturity such as decreased fruit color, fruit dry matter, fruit soluble solids, and increased fruit firmness (Doud and Ferree, 1980; Lakso, 1994; Robinson et al., 1983).

Computer models that can predict light interception and its distribution within the tree canopy offer the possibility of estimating the influence of canopy architecture and orchard layout on the transpiration and photosynthesis of individual trees and the potential productivity of the whole orchard system (Robinson and Lakso, 1991). Such computer models may also provide a tool to assist in the design of the optimum orchard system that consistently produces high yields of top quality fruit (Warrington et al., 1989; Wagenmakers and Callesen, 1995).

Even though several methods exist to estimate tree light interception by apple orchards (Wünsche et al., 1995), the Whirligig radiometer (HortResearch, Palmerston North, New Zealand) appears to be the only instrument that can provide a direct and continuous measure of light interception by individual trees at a fine time resolution (McNaughton et al., 1992). The Whirligig has been used, in the past, to understand the transpiration losses from single orchard trees and to estimate whole-canopy C exchanges using simple empirical models to interpret these Whirligig data (Green and McNaughton, 1997).

The task here is to use these single-tree data to test a model of light interception and utilization that accommodates the normal range of canopy dimensions, leaf areas, and orchard planting patterns. Experimental observations, together with model predictions, are used to illustrate how transpiration (kg s-1) responds to changes in the aerial environment and how tree size influences light interception and transpiration losses from a single tree and from the whole orchard. The paper will focus on a detailed and rigorous test of a three-dimensional (3-D) computer model of light interception using complete and independent data. Such testing at the single-tree scale is unprecedented outside of our work.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Experimental Site and Plant Material
The data sets used in this study came from two field experiments. One experiment examined a large apple tree (Malus domestica Borkh. cv. Splendour/MM.106) and was performed at the Massey University research orchard near Palmerston North, New Zealand (40°12' S, 175°24' E), for a 6-wk period in the summer of 1994–1995. The site and experimental data are described in Green and McNaughton (1997). The second field experiment examined a dwarf apple tree (M. domestica Borkh. cv. Braeburn/M.9) and was performed at the Nelson Research Centre, Motueka (41°6' S, 173° E), for a 3-wk period in the summer of 2000–2001. In both orchards, the trees were well irrigated, and the ground cover was in grass except for a 1-m-wide strip of bare soil in each tree row. The tree's total leaf area was measured at the end of each experiment by removing all of the leaves and passing a subsample (5% by weight) through a leaf area meter (Model LA3100, LI-COR, Lincoln, NE). The tree spacing, canopy dimensions, and leaf area of each tree are reported in Table 1.


View this table:
[in this window]
[in a new window]
  		Table 1. Parameter values used to calculate light interception and transpiration from the apple trees. Leaf conductance parameters (bi) are described in the text; S is the tree spacing; rX, rY, and rZ are the tree's ellipsoidal radii in the horizontal (x, y) and vertical (z) direction; zB is the basal height of the tree canopy; fD is the foliage density; and AT is the tree's total leaf area. Leaf optical properties were assumed to be typical of green leaves (Ross, 1981).

 
Sap Flow Measurements
Sap flow was measured using the compensation heat pulse technique (Green and Clothier, 1988). Two sets of probes, each consisting of a line heater of 1.8 mm diam. and two temperature probes also of 1.8 mm diam., were installed into parallel holes drilled radially into the trunk at heights of about 0.5 m above the ground. Sap velocity was measured at four radial depths (5, 10, 15, and 20 mm in the Braeburn; 5, 12, 21, and 32 mm in the Splendour) following the procedure of Green and Clothier (1988), using theoretical calibrations to account for the probe-induced effects of wounding (Swanson and Whitfield, 1981). Volume flow rates (L/h) were then calculated by integrating the radial profile of sap velocity over the sapwood cross section. A Campbell CR10 data logger (Campbell Sci., Logan, UT) was used to control the heat pulse equipment and to record the measurements once every 10 min. Details of the measurement system are described in Green et al. (2003).

Light Interception by the Leaf Canopy
The Whirligig radiometer was set up around a single apple tree to measure the total amount of visible light [photosynthetic photon flux (PPF)] and all-wave solar energy absorbed by the tree canopy (McNaughton et al., 1992). The Whirligig consists of a vertical circular frame that rotates at 3 rpm on a horizontal turntable. A set of eight net radiometers (Model Q*6, Radiation and Energy Balance Syst., Seattle, WA) and 16 photosynthetic light sensors (Biggs et al., 1971) were mounted at equal-spaced intervals on the circumference of the frame. As the Whirligig frame rotated, it described a sphere about the tree with each radiometer following a horizontal, circular path at fixed latitudes on the sphere. The total amount of radiant energy absorbed by the tree was approximated from the weighted sum of the radiation signals recorded by each sensor [see McNaughton et al. (1992) for details]. Two data loggers (CR21X, Campbell Sci., Logan, UT) were used to record signals from the radiometers once every second. A microswitch on the turntable was used to indicate the number of revolutions of the Whirligig. A total for the absorption of all-wave radiation, QN (W), and photosynthetically active radiation (PAR) radiation, QP (µmol s-1), was recorded after every 30 revolutions of the Whirligig (about 10 min). A 4-m-diam. frame was used for the large Splendour tree while a 2.4-m-diam. frame was used for the smaller Braeburn tree.

Meteorological Measurements
A meteorological station was installed on site to record 10-min averages of incoming radiation, wind speed, air temperature, and relative humidity using a Campbell CR10 data logger. The incoming streams of global short-wave radiation (W m-2), global PPF density (µmol m-2 s-1), and net all-wave radiation (W m-2) were measured respectively with silicon-cell pyranometers (Models LI200SB and LI190SB, LI-COR, Lincoln, NE) and a Q*6 net radiometer. A second pyranometer under a shadow band was used to monitor incoming diffuse short wave (W m-2). These instruments were mounted on a mast in the middle of the orchard, at a height of about 1 m above the tallest trees and well away from any shadows cast by the neighboring shelter trees. Air temperature and relative humidity were measured with a Campbell 207 probe, wind speed was measured with a sensitive three-cup anemometer, and a tipping-bucket rain gauge was used to monitor rainfall. These instruments were mounted on the same mast at a height of about 2.5 m above the ground. This was about midcanopy level in the apple orchard. Vapor pressure deficit of the air was computed using 10-min averages of air temperature and relative humidity.

Calculation of Leaf Transpiration
For the purpose of modeling, the tree canopy was divided into a number of subvolumes. The total leaf area within each subvolume was divided into a fraction of sunlit leaves that receive direct-beam and diffuse solar radiation and a complementary fraction of shaded leaves that receive only diffuse radiant energy. Uniform leaf properties were assumed for each class of leaves. Transpiration was modeled using a Penman–Monteith type equation of the form

[1]
following Jarvis and McNaughton (1986). The summation was made over a set of i uniform leaves, each being a fraction, ai, of the total leaf area, AT (m2), and having an associated leaf and boundary-layer resistance equal to rS,i and rB,i (s m-1), respectively. Here, EP represents the total transpiration flux (kg m-2 s-1) from all the leaves, RN,i is the net radiation flux density (W m-2) of the ith set of leaves, DA is the ambient vapor pressure deficit of the air (Pa), {lambda} is the latent heat of vaporization of water (J kg-1), s is the slope of the saturation vapor pressure curve (Pa K-1), {gamma} is the psychrometric constant (Pa K-1), {rho} is the air density (kg m-3 ), and cp is the specific heat capacity of air (J kg-1 K-1). The factor 2 on the bottom line of Eq. [1] arises because apple leaves are hypostomatous, with heat loss occurring from both sides of the leaf and transpiration occurring from just one side.

The mean leaf conductance, gS,i (=1/rS,i), was modeled using the simple empirical model of Jarvis (1976)

[2]
where RP,i is the incident PPF density on the leaf surface (µmol m-2 s-1) and DA is the ambient vapor pressure deficit of the air (Pa). The parameters have the following significance: b1 + b3 is the maximum conductance at full sunlight, b2 is the slope of the light response curve (i.e., dgL/dRP) approaching zero light, b3 is the corresponding conductance in zero light, and b4 expresses the DA effect. A porometer (Model LI-1600, LI-COR, Lincoln, NE) was used in the field to measure the leaf conductance, normally on six sunlit and six shaded leaves over the course of several full days. These data were then used to derive model parameters for Eq. [2], following the boundary-line method of Jarvis (1976). Values of RP,i and RN,i for the sunlit and shaded leaves were calculated using the 3-D light array model, as described below.

Leaf boundary-layer resistances, rB,i, were computed from the empirical relation derived by Landsberg and Powell (1973), which accounts for the mutual sheltering of clustered leaves as:

[3]
where d is a characteristic leaf dimension (leaf width, m) and U is the mean wind speed (m s-1) across the leaf surface, which was assumed to be the wind speed at mean canopy level. The parameter p is a measure of the foliage density seen by the wind, being the ratio of total leaf area to the area of foliage silhouette projected onto a vertical plane. Equal boundary-layer resistances were assumed for the sunlit and shade leaves.

A Three-Dimensional Light Interception and Utilization Model
A 3-D light array model was developed to investigate radiation interception and utilization by the tree canopy. The light model used here was similar to other published models (Charles-Edwards and Thornley, 1973; Norman and Welles, 1983; Wang and Jarvis, 1990) that consider light interception by a uniform canopy of green leaves that are randomly distributed within the canopy volume of a given geometrical shape. The coordinates of each tree were specified in three dimensions to allow the effects of different planting patterns to be investigated. Trees were individually referenced and represented by a truncated ellipsoid defined by a height, three elliptical radii, and the canopy length that extended from the base to the top of the tree. All leaves were distributed randomly with respect to orientation, inclination, and location. A uniform foliage density (m2/m3) was assumed, as defined by the one-sided leaf area per unit volume containing the foliage elements. Absorption by the fruit and branches was neglected, but this seems to be quite small ({approx}5%) in fully leafed apple trees (Palmer, 1977).

Theory for calculating the absorption of solar radiant energy was adopted from earlier models (Norman, 1979; Norman and Welles, 1983; Wang and Jarvis, 1990), and so only the salient details are presented here. First, the respective incoming direct-beam and diffuse components of solar radiation were calculated from measurements of global and diffuse short-wave radiation, plus net radiation recorded in the orchard (Green and McNaughton, 1997). From these incoming streams of solar radiation, the model calculated the absorption of beam radiant energy and sky diffuse radiant energy in the photosynthetically active waveband (400–700 nm) and in the near-infrared (700–3000 nm) wavebands. These wavebands were considered separately because the optical properties of the foliage (i.e., transmission, reflection, and absorption) depend strongly on wavelength. Palmer (1977) investigated the leaf transmission and optical properties of apple leaves (‘Cox’s Orange Pippin' and ‘Golden Delicious’) at different wavelengths. He found that apple leaves have similar optical properties compared with a range of other green leaves. Table 1 provides respective values used in the model to parameterize the leaf optical properties.

Model calculations were performed on a target tree whose canopy volume was divided into five horizontal layers with 24 subvolumes in each layer as represented by three radial depths and eight azimuthal orientations. All other trees within the orchard array were described with the same detail of 120 grid points although the neighboring trees could have had different dimensions and foliage densities. The amount of direct-beam radiation reaching the midpoint of each subvolume was calculated on the basis of the probability of interception (Monsi and Saeki, 1953),

[4]
that depends on the foliage density, {rho}F; the distance, S, that the beam traverses as it travels through the canopy; and the corresponding extinction coefficient, kS. A value of kS = 0.5 was assumed for a random distribution of leaves (Campbell and Norman, 1989). The distance S for an ellipsoidal canopy was calculated using the equations of Norman and Welles (1983) that consider the influence of all neighboring trees through which the light beams might pass.

The absorption of diffuse radiant energy that originates from the sky, other foliage, and the soil was treated by numerically averaging the transmission probabilities over the upper and lower hemispheres (Norman, 1979). Multiple scattering effects for solar radiant energy were calculated using an iterative approach where the diffuse radiation at a point F in the tree canopy was approximated by the equivalent point H in an infinite horizontal canopy having the same transmission probabilities in the upper and lower hemispheres (Norman and Welles, 1983). Leaf temperatures were calculated from the thermal long-wave balance (wavelengths >3000 nm) at each point F following the approach of Welles et al. (1979).

Transpiration losses from the tree were calculated using the Penman–Monteith equation (Eq. [1]). This calculation was based on a sunlit and shaded leaf area, ai, as well as the local PPF density, RP,i, and net all-wave radiation balance, RN,i, within each subvolume of the tree canopy. Values of leaf conductance were computed via Eq. [2] based on the incident PPF density at each point F in the tree canopy. Transpiration from the whole tree was then obtained by summing the contributions from each of the canopy subvolumes. For these calculations, the air temperature, wind speed, and the saturation vapor pressure of the air were assumed to be constant within the canopy.

Model output included values of absorbed radiant energy in the visible, near-infrared, and long-wave bands as well as the corresponding radiant fluxes at any point inside or outside of the tree canopy. Transpiration was calculated from different parts of the canopy and from the whole tree canopy. Output was synchronized with the sap flow and Whirligig measurements so that a direct comparison could be made. The model was written in FORTRAN, to run on a PC, and is available from the authors on request.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
The complete set of measurements on the Splendour tree lasted about 6 wk over the summer period. There was always a very good correspondence between the model output and the Whirligig measurements of QP and QN absorbed by the tree (Fig. 1 and 2) . In fact, it is very hard to distinguish visually between the two data sets. A linear regression analysis revealed a very good correlation (r2 > 0.95), with a slope close to 1.0 and a relatively small offset from zero (Fig. 3) . At solar noon, the Splendour tree absorbed between 15 and 20 mmol s-1 of PPF and about 5 kW of all-wave radiant energy. The corresponding transpiration rate during the middle of the day ranged between about 5 and 6 L h-1 on warm, sunny days and was reduced to 2 to 3 L h-1 on the cooler, cloudy days (Fig. 4) . Heat pulse measurements of sap flow were also in good agreement with model calculations of transpiration from the whole tree canopy (Table 2 and Fig. 4 and 5) .



View larger version (42K):
[in this window]
[in a new window]
  		Fig. 1. Total amount of photosynthetic photon flux (QP) radiation absorbed by the ‘Splendour’/MM.106 apple measured by the Whirligig radiometer and calculated using the three-dimensional array model.

 


View larger version (41K):
[in this window]
[in a new window]
  		Fig. 2. Total amount of all-wave radiation (QN) absorbed by the ‘Splendour’/MM.106 apple tree measured by the Whirligig and calculated using the three-dimensional array model.

 


View larger version (25K):
[in this window]
[in a new window]
  		Fig. 3. The relationship between model predictions and measured values of the total amount of all-wave radiation (QN) absorbed by the ‘Splendour’/MM.106 apple tree.

 


View larger version (41K):
[in this window]
[in a new window]
  		Fig. 4. Transpiration rate of the ‘Splendour’/MM.106 apple tree determined by the heat pulse method (data) and calculated using the three-dimensional array model (model).

 

View this table:
[in this window]
[in a new window]
  		Table 2. Comparison of model output and simulated values of the absorbed photosynthetic photon flux radiation (QP), the absorbed all-wave radiation (QN), and the transpiration rate (T) from a large ‘Splendour’ and a small ‘Braeburn’ apple tree. The slope, intercept, standard error (SE), and r2 values were derived from a least-squares linear regression between predicted and observed values.

 


View larger version (35K):
[in this window]
[in a new window]
  		Fig. 5. The relationship between model predictions and measured values of the transpiration rate (T) of the ‘Splendour’/MM.106 apple tree.

 
A sensitivity analysis was performed to examine the effects of a 20% change in input parameters on the simulated amounts of absorbed radiant energy and the transpiration. As expected, light interception and utilization by the Splendour tree was influenced mostly by changes in leaf area. A 20% increase in leaf area resulted in an average 6% increase in absorbed PAR, an average 8% increase in absorbed all-wave radiation, and an average 15% increase in transpiration (Table 3). Thus, any predictions of tree water use are only as reliable as the estimate of leaf area. Here, leaf area was measured from a destructive harvest at the end of the experiment, so there is good confidence in the total leaf area of the Splendour tree. Altering leaf absorption of PPF by 10% (and adjusting downwards the leaf reflectance) resulted in only a small change (average {approx}2%) in both the absorbed light and transpiration rates.


View this table:
[in this window]
[in a new window]
  		Table 3. Percentage change in the simulated values of absorbed photosynthetically active radiation (QP), absorbed all-wave radiation (QN), and the transpiration rate (T) from the ‘Splendour’ apple tree when model parameters are increased by 20% (or 10% for {alpha} values). The original parameter values are presented in Table 1. Values in parentheses represent a 20% reduction (or 10% for {alpha} values) in the model parameter.

 
Modeled rates of transpiration were also strongly influenced by changes in the leaf conductance parameters. A 20% increase in the leaf conductance parameter b1, yielded an average 10% increase in transpiration while a 20% increase in the b4 parameter, the vapor pressure deficit effect, gave a 14% decrease in transpiration. Although the leaf conductance parameters were derived from porometer data measured on neighboring trees during the course of the field experiment, variation between individual leaves in a similar light and humidity environment was often 20% or more. Green et al. (1995) show that the calculated values of gS for leaves on the Splendour tree were typically within the scatter of the porometer measurements.

Tree spacing, canopy dimensions, and foliage density are important operational factors that determine the energy balance and potential productivity of an apple orchard. These factors can be altered in the array model, and manipulated in real orchards, to optimize the amount of light that is intercepted by the whole orchard. Results from the Braeburn tree, which was a much smaller and more compact fruit tree, provided contrasting experimental data to test the model output and to confirm the influence of tree size on canopy and orchard processes.

At solar noon on 8 and 9 January (day of year 39 and 40), the Braeburn tree absorbed PPF at a rate of about 4 mmol s-1 (Fig. 6) . This represents just 20 to 25% of the PPF energy intercepted by the larger Splendour tree under a similar high-light environment. In terms of light interception by the whole orchard, the Braeburn tree absorbed slightly more of the incoming visible light ({approx}60% of the daily RP) compared with the Splendour tree ({approx}50% of the daily RP). The corresponding absorption of all-wave radiant energy peaked at about 1.5 kW (Fig. 7) , or about one-fourth of the total amount of all-wave energy intercepted by the Splendour tree. Small long-wave losses from the Braeburn tree at night varied between zero on the cloudy nights and about -0.2 kW on the clear nights. Model predictions for the Braeburn tree were always in very good agreement with the measured values of the radiant energy balance (Fig. 6 and 7) and the measured rates of sap flow (Fig. 8) . Once again, a linear regression between measured and modeled values yielded very high correlations (r2 > 0.95), with a slope close to 1.0 and a relatively small offset (Table 2).



View larger version (41K):
[in this window]
[in a new window]
  		Fig. 6. Total amount of photosynthetic photon flux (QP) radiation absorbed by the ‘Braeburn’/M.9 apple tree measured by the Whirligig radiometer (data) and calculated using the three-dimensional array model.

 


View larger version (39K):
[in this window]
[in a new window]
  		Fig. 7. Total amount of all-wave radiation (QN) absorbed by the ‘Braeburn’/M.9 apple tree measured by the Whirligig (data) and calculated using the three-dimensional array model.

 


View larger version (43K):
[in this window]
[in a new window]
  		Fig. 8. Transpiration rate of the ‘Braeburn’/M.9 apple tree determined by the heat pulse method (data) and calculated using the three-dimensional array model (model).

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
The two data sets presented here, from a large Splendour apple and a compact Braeburn apple, together provide a more complete test of whole-tree radiation and transpiration models than has been possible before. The two trees were very different in terms of their height (2x factor), planting density (3x factor), and total leaf area (4x factor). In addition, the evaporative demand from the two orchards was also different, with Nelson typically having a drier climate with more days that are warm and sunny days and with less rainfall than in Palmerston North.

The motivation for developing and testing a complex model of vegetation–atmosphere interactions was to eventually link fruit quality to aspects of orchard layout and the interior light level within the tree canopy. It is not possible to make such a link using a simple big-leaf model. The model presented here calculates transpiration by summing across different parts of the tree canopy, on the basis of a local energy balance and the average leaf conductance of the sunlit and shaded leaves. Because this summation depends on the amount of light that reaches each point F in the tree canopy, the good agreement between measured sap flow and modeled transpiration suggests the model may also have generated a reasonable light distribution within the tree canopy although there was no independent data for confirmation. Sap flow provided an independent check on calculated rates of transpiration in a way that previous measurement and modeling comparisons have not been able to test.

There was more scatter between measured and modeled rates of transpiration (Fig. 5) compared with the results for light interception (Fig. 3). One reason for the increased scatter could be because the heat pulse measurements respond to the instantaneous sap flow whereas the 3-d array model expresses the average transpiration over a 10-min period. Furthermore, a time lag might be expected between measured sap flow in the trunk and transpiration losses from the leaves because of changes in water storage within the other tree organs (e.g., branches, fruit, and stem). Some nocturnal sap flow was recorded in the Braeburn tree, typically on warm, windy nights when the vapor pressure deficit remained elevated. Sap flow at night that continues for several hours after evaporative demand has declined close to zero has often been attributed to a recharge of the tree's stored water (Milne, 1989; Holbrook and Sinclair, 1992). In the case of the Braeburn tree, these nocturnal flows were most likely to be induced by transpiration losses from the leaves because apple stomata do not close completely late in the growing season (Green and Clothier, 1988).

Several researchers have attempted to validate similar 3-D models of light interception against a variety of experimental data. For example, Wang and Jarvis (1990) worked in a uniform stand of Sitka spruce [Picea sitchensis (Bong.) Carrière] using a fixed array of light sensors located close to the ground. De Castro and Fetcher (1998) worked in a mixed forest stand using spot measurements from light sensors located in the lower parts of the canopy. Sinoquet and Bonhomme (1992) provided a partial validation for the reflection and transmission of solar radiation in a mixed-row intercropping systems using radiation sensors mounted above and below the crop. In each case, the model agreement with experimental data was generally found to be satisfactory and to yield a strong linear correlation (0.75 < r2 < 0.88). The measurement/modeling comparisons presented here for light interception are at least as good, and may even be better than, previous model validation studies.

For the large Splendour tree and the small Braeburn tree, all correlation coefficients were large (r2 > 0.95), and the slope of the linear relationship between measurements and simulations of QP, QN, and transpiration was within 5% of the 1:1 line. The model calculated almost exactly the same short-term dynamics of light interception as measured by the Whirligig. Thus, the model assumptions appear to be justified, at least in terms of total light interception and transpiration from the whole tree. The very good agreement was somewhat surprising since the calculations were based on quite a simple geometrical description and assumed uniform leaf areas within the tree canopy. Clearly the canopy had some large gaps within it, as well as some areas in the canopy where the foliage was of a more clumpy nature. While gaps in foliage do not contribute to the total light interception and transpiration of the tree canopy, they could, potentially, have a large influence on the light environment within the tree crown.

Cohen et al. (1995) used cluster analysis theory to show that leaves in the upper part of young apple trees are typically clustered around leafy shoots. They found that that the distribution of leaf area became more uniform deeper in the apple canopy where shoots would fill in the canopy space. Cohen et al. (1995) concluded that such variations in clumpiness would be critical for models attempting to map the light environment inside the canopy. Our results suggest that clumpiness is less important in the case of modeling total light interception and transpiration from the whole tree. Leaf area and planting density are both important scaling factors that help reduce the difference between the two trees that we have studied here. Over the course of a day, the large Splendour tree intercepted about 50% of the incident PPF energy while the smaller Braeburn tree intercepted closer to 60% of the incoming PPF energy. Daily water use of the Braeburn tree was less than 20 L d-1; this equates to a transpiration loss of some 4.5 mm per day when expressed on a unit ground area determined by the tree spacing. Corresponding transpiration losses from the larger Splendour tree exceeded 50 L d-1, yet this equates to only about 3 mm per day. The smaller, more compact fruit tree appears to be more efficient at intercepting the sun's energy, yet it may require more irrigation water per hectare to sustain productivity, given the same soil and weather conditions.

The current version of the 3-D array model has been successful in explaining the short-term dynamics of total light interception and transpiration from a single tree. The next step in model development will be to calculate whole-canopy photosynthesis and eventually link aspects of fruit quality to the interior light environment within the tree crown. Future experiments are planned to measure the light distribution within the tree canopy, thereby providing a more complete data set to test the model. The modeling framework can easily be modified to allow for variations in leaf density within the canopy, especially if future experiments show this to be an important factor in determining the light distribution.

On a less positive note, the additional data requirements to more precisely define the leaf area distribution within the canopy envelope will be more time consuming and difficult to obtain. It should be kept in mind that one of the most important goals in any modeling approach is the ability to predict unknown states of the system, in time and space. If the model requires parameters (such as leaf area distribution) that are much more difficult or time consuming to obtain than the variable the model predicts, then the model is of little use as a predictive tool. In that case, it may still be easier to measure total light interception with a Whirligig and to monitor sap flow using heat pulse. A modeling approach may be more useful in assessing rates of photosynthesis, where simple measurements are not easy to obtain from whole trees, and assessing the potential productivity of different canopy architectures in new orchard systems.

The work presented here indicates that experimental observations, together with model predictions, can now be used with confidence to predict how transpiration responds to changes in the aerial environment and how the different canopy architectures influence light interception and utilization. The small, compact fruit tree is more efficient at intercepting the sun's energy on a per-unit ground area basis. Knowledge of how and when to manipulate sunlight exposure to support optimal fruit development will allow targeted canopy management strategies to produce the desired canopy light levels for fruit at the proper time.


   ACKNOWLEDGMENTS
 
This research was conducted via coinvestment under FRST Contract C06X0004 "Knowledge Tools for Environmental Action." We acknowledge the assistance of John Palmer and Bill Dawson during the measurement campaign at Nelson.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 





This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via ISI Web of Science (9)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Green, S.
Right arrow Articles by Clothier, B.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Green, S.
Right arrow Articles by Clothier, B.
Agricola
Right arrow Articles by Green, S.
Right arrow Articles by Clothier, B.
Related Collections
Right arrow Heat Movement Models
Right arrow Crop Physiology & Metabolism
Right arrow Crop Models
Right arrow Plant Analysis
Right arrow Plant and Environment Interactions

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
The SCI Journals Crop Science Vadose Zone Journal
Journal of Natural Resources
and Life Sciences Education		 Soil Science Society of America Journal
Journal of Plant Registrations Journal of
Environmental Quality		 The Plant Genome