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Modeling of par interception and productivity by Opuntia ficus-indica
Agricultural and Forest Meteorology, 34 ( 1985 ) 145--162
145
Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
MODELING OF PAR INTERCEPTION AND PRODUCTIVITY BY OPUNTIA FICUS-INDICA VICTOR GARCIA de C O R T A Z A R and EDMUNDO ACEVEDO
Laboratoria Relaciones Suelo-Agua-Planta, Facultad de Agronom}a, Universidad de Chile, Casilla 1004, Santiago (Chile) PARK S. NOBEL*
Department of Biology and Laboratory of Biomedical and Environmental Sciences, University of California, Los Angeles, California 90024 (U.S.A.) (Received July 16, 1984; revision accepted October 11, 1984)
ABSTRACT Garcia de Cortazar, V., Acevedo, E. and Nobel, P.S., 1985. Modeling of PAR interception and productivity by Opuntia ficus-indica. Agric. For. Meteorol., 34: 145--162. A model is described that permits accurate calculation of radiation interception and shadows cast by a set of planar surfaces whose Cartesian coordinates are known. The model is applied to the calculation of interception of photosynthetically active radiation (PAR) by the cladodes (flattened stems) of the widely cultivated cactus, Opuntia ficusindica. Taking into account both direct and diffuse PAR, a PAR index is determined for both sides of the 27 cladodes on two plants. This index has a maximum value of 1.00 when net CO2 uptake by the cladodes is not limited by PAR. The product with similar indices for water status and temperature indicates the fraction of maximum net CO2 uptake expected under particular environmental conditions, the environmental productivity index (EPI). EPI is used to predict the net assimilation rate (NAR) of O. ficus-indica under field conditions in central Chile, where its NAR has been measured. The predicted NAR closely agreed with seasonal trends and average annual values, but underestimated measured NAR in the winter, presumably due to over-representation of the low NAR caused by isotropic diffuse radiation at this cloudy time of the year. Applying the PAR model to different plant spacings, the annual productivitYlPredicted for a stem area index (stem area per ground area) of 1.4 was 1.4 kg m -2 y- , which closely matched field measurements; maximal productivity nearly threefold higher was predicted at a stem area index of 7. The PAR model was also used to analyze a hypothetical plant with all cladodes in a plane so that the influence of cladode orientation on the PAR index at various times of the year for both clear and cloudy days could be determined. Besides indicating PAR distribution within the canopy of the platyopuntias, the PAR model can be used for other three-dimensional distributions of photosynthetic surfaces, especially those that have regularly repeating units in space, such as orchards and vineyards.
INTRODUCTION
Few Crassulacean acid metabolism (CAM) plants are extensively cultivated and relatively little is k n o w n a b o u t their productivity. One o f the m ost *Author for correspondence and reprint requests.
0168-1923/85/$ 03.30
© 1985 Elsevier Science Publishers B.V.
146 widely cultivated is pineapple (Ananas comosus), which can have a net assimilation rate (NAR) (Milthorpe and Moorby, 1979) of 2.0 g dry weight m -2 leaf area d -1 under optimal temperatures in the laboratory; also, it has been predicted to yield 1.2 kg carbohydrate m -2 ground area y- ~ (12 metric tons ha -1 y - l ) in the field in Hawaii when irrigated (Bartholomew, 1982). Field studies with Agave fourcroydes and other fiber-producing agaves in Mexico, Tanzania, and various other countries indicate a maximal productivity of about 1.0 kg leaf dry weight m -2 y-1 for these CAM plants (Smith, 1929; Lock, 1962). Consistent with this, the net productivity of A. deserti in California was 0 . 5 7 k g m -2 over a relatively wet 5-month period (Nobel, 1984). The cactus Opuntia ficus-indica is cultivated on a limited basis for both its fruit and its cladodes (flattened stems) in tropical and subtropical areas as well as in h o t regions of the temperate zone. Total biomass productivity of 5.0kg wet weight m -2 y-1 has been observed in North Africa (Le Houerou, 1970) and 9 . 3 k g wet weight m -2 y-1 in Brazil (Metral, 1965), with a fruit productivity of 1.6 kg wet weight m -2 y-1 measured in central Chile (Reflasco, 1976). Recently, a dry weight productivity of 1.0 kg m -2 y-1 for cladodes and 0 . 3 k g m -2 y-1 for fruit has been measured for O. ficus-indica in Chile (Acevedo et al., 1983). Whether this 1 . 3 k g m -2 y-1 approaches the maximal annual productivity of CAM plants is not known. Opuntia ficus-indica has also been studied under controlled laboratory conditions, and so the responses of net CO2 uptake to photosynthetically active radiation (PAR), air temperature, and soil water status are known. Most CO2 uptake by O. ficus-indica and other CAM plants occurs at night, and so net CO2 uptake is n o t easily related to the instantaneous value of PAR. Rather, it has proved useful to relate net CO2 uptake b y CAM plants to the total dally PAR. Although there is some dependence on PAR distribution during the day as well as on temperature, 90% PAR saturation for O. ficus-indica occurs near a total daily PAR of 2 0 m o l m -2 (Nobel and Hartsock, 1983, 1984), just as for many other CAM plants (Nobel, 1982a). Maximal net CO2 uptake over a 24-h period occurs for relatively low nighttime air temperatures of 11 to 1 2 ° C (Nobel and Hartsock, 1984); daytime temperatures are less important for net dally CO2 uptake by O. ficus-indica as well as by other CAM plants (e.g., Nobel and Hartsock, 1978). Under well-watered conditions, optimal temperatures, and saturating PAR, net CO2 uptake by O. ficus-indica over a 24-h period is 344 mmol m- 2 (Nobel and Hartsock, 1983, 1984). If this all were carbohydrate, it would correspond to a N A R of 10.3 g m -2 d- 1. However, NAR values measured in the field for O. ficus-indica averaged only 3.3 g m-2d -1 over 1.5-year period for plants initially 0.5 year old and 3.1 g m -2 d -1 for those initially 1.5 years old (Acevedo et al., 1983 and unpublished observations; initial age refers to when a mature cladode is placed in the ground for these vegetatively propagated plants). Since temperature and water status do not appear to be far from optimal in the commercial plantations of O. ficus-indica in Chile, especially since they are irrigated during the late spring/summer dry period,
147 the factor limiting productivity m a y be PAR. However, it has been difficult to estimate or model the PAR interception under field conditions, because of the complex three
Plant material and field site Opuntia ficus-indica (L.) Miller (Cactaceae) was studied at a commercial plantation in Til Til, Chile (33 °2'S, 70°54'W, 570 m above sea level) about 50 km north-northwest of Santiago. The two representative, adjacent field plants analyzed were 1.5 years old and had a total of 27 cladodes. Air temperatures and rainfall were obtained from the Rungue meteorological station (700 m elevation) located 10 km north-northeast of the study site. Annual rainfall was 467 m in 1980 and 326 m m in 1981, the two years when the net assimilation rate (NAR) was measured in the field. Additionally, the fields were irrigated three times during late spring/summer with a water depth of about 80 m m each time. Fractional attenuation of photosynthetically active radiation (PAR, 400 to 700 nm) by clouds was equated to the fractional attenuation of global shortwave radiation measured at the A n t u m a p u meteorological station in Santiago. PAR model A computer model was developed to predict the PAR intercepted by each side of all cladodes for two adjacent plants having a total of 27 cladodes. The morphology of the plants was described by the Cartesian coordinates of the proximal and the distal ends along the longitudinal axis of each cladode and of each side of the width at the widest place. The outline of the cladode surface was then generated from an empirical relation of relative width versus relative length along the longitudinal axis determined from 20 measurements along each of six cladodes of various sizes: width/widthmax = -- 3.24 (length/ lengthmax) 2 + 3.38 length/lengthmax + 0.11, r 2 = 0.89, where length was measured from the proximal end and hence lengthmax was the total length
148 along the longitudinal axis. C l a d o d e area f o r each planar side averaged 0 . 7 2 5 x lengthmax x widthmax and t h e lengthm~x/widthm~x ratio was 1.94 + 0.34 ( s t a n d a r d d e v i a t i o n f o r 27 cladodes). A r e c t a n g u l a r parallelepiped or " c e l l " just enclosing t h e t w o plants o c c u p i e d 0.89 m in t h e n o r t h - - s o u t h (x) d i r e c t i o n , 1 . 0 9 m in t h e e a s t - - w e s t ( y ) d i r e c t i o n , and 0 . 9 8 m in height (z d i r e c t i o n ) . T h e t o t a l area o f b o t h sides o f all 27 cladodes was 2.54 m 2 : b o t h sides m u s t be i n c l u d e d , since t h e c l a d o d e s are o p a q u e and h e n c e t h e c h l o r e n c h y m a o n each side relates t o a d i f f e r e n t surface f o r P A R interc e p t i o n . F o r t h e cell just enclosing the t w o plants, t h e g r o u n d area was 0.97 m 2 and h e n c e the stem area i n d e x S A I (total area o f b o t h sides o f cladodes per unit g r o u n d area) f o r t h e cell was 2.62. E a c h c l a d o d e surface was described b y a r e c t a n g u l a r a r r a y o f squares (Figure 1) 1 8 m m o n a side, the c e n t e r o f each square lying within t h e
C
B
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Fig. 1. Schematic illustration of a three-dimensional "cell" containing a plant with four cladodes. Cladode surfaces are divided into squares (actual model has an average of 145 squares for each cladode side). Direct solar irradiation is indicated by rays that are incident on a cladode (ray A), incident on the ground (ray B), and exiting the cell (ray C). The exiting ray enters an adjacent identical cell, which is equivalent to re-entering at the opposite side of the same cell (ray C'), and is intercepted by a cladode near the middle of the plant.
149 parabola defining the cladode outline (an average of 145 squares were used for each cladode surface). The direct solar beam was represented by 5000 equally spaced rays in a rectangular array orthogonal to the propagation direction, all such rays entering the t op of the cell. A particular ray was either intercepted by one of the squares of a cladode (ray A in Fig. 1), was incident on th e ground (ray B), or passed o u t of the side o f the cell (ray C). This latter ray could then enter a neighboring identical cell, which is equivalent to re-entering the opposite side o f the same cell (with suitable allowance for change in z if the cells are n o t adjacent), and perhaps strike a square in the surface of an underlying cladode (ray C' in Fig. 1). To determine how m uch o f each cladode surface was exposed to the sun at a particular time of day, a new c oor di nat e system was created having a rectangular grid of 5000 squares in the x ' - y ' plane (corresponding t o the 5000 rays) with the direct solar beam traveling along the z' axis. All the center points from the squares o f the cladode surfaces were placed in this new system and their location in the squares of the new rectangular grid noted. If points from different cladodes o ccurred in the same grid square, then the cladode with the highest z' intercepted the ray and the ot her or others were in its shadow. The direct PAR on a cladode surface was then calculated as the fraction o f the center points of a particular cladode surface intercepting rays times the PAR in a plane perpendicular to the direct solar beam times the cosine o f the angle between the normal to the cladode surface and th e direct solar beam (orientation of the normal to each of t he two sides o f a cladode was det er m i ned f r o m t he cross p r o d u c t o f a vector along the longitudinal axis with a vector f r om the cladode base to one of t he points o f the m a x i m u m width). Diffuse PAR f r o m the sky and reflected f r o m t h e ground was also determined for each cladode surface, assuming radiation from each source to be isotropic. Diffuse PAR from t he sky equaled the view factor of a cladode surface toward the sky corrected for occlusion by overlying cladodes times t h e diffuse PAR on an unshaded horizontal surface. The diffuse PAR on an unshaded horizontal surface for clear days was assumed to be 13% of total PAR when the sun was overhead, 16% for a sun elevation angle of 45 °, and 32% at 15 ~ (Goudriaan, 1977). For clear days the global shortwave irradiation (direct plus diffuse) in W m -2 for sun elevation angle ~ was set equal to 1360 sin f i e -°'30/sin~, corresponding to the locally measured atmospheric transmissivity o f e -°'3° or 0.74 for an optical air mass of uni t y (Castillo and Santibafiez, 1981). A shortwave irradiation of 1 . 0 0 M J was assumed to correspond to 2 . 0 2 m o l p h o t o n s from 400 to 700 nm (VarletGrancher et al., 1981). For a c o m p l e t e l y overcast day, PAR was entirely diffuse and based on local measurements was assumed to equal 22% of the radiation incident on t he earth's a t m o s p h e r e (Castillo and Santibafiez, 1981). Diffuse PAR reflected f r o m the ground was equat ed t o the view factor o f a particular cladode surface t ow a r d the ground times the total PAR on a horizontal surface (including effects of shading by cladodes) times the
150 measured reflectivity of the ground for PAR (0.11). Direct and diffuse PAR were calculated for b o t h surfaces of all 27 cladodes for hourly positions of the sun and integrated to give the total daily PAR for b o t h clear and overcast days.
Environmental productivity index Net CO2 uptake by O. fieus-indica in the field was predicted from its response to water status, temperature, and PAR measured under controlled conditions in the laboratory (Nobel and Hartsock, 1983, 1984). An index value was assigned to indicate the fraction of maximal net CO2 uptake expected for each factor individually (Nobel, 1984). For instance, when the soil water potential was above the chlorenchyma osmotic potential (-- 0.5 MPa) (Nobel and Hartsock, 1984), the water status index was assigned a value of 1.00, indicating that water was then not limiting net CO2 uptake. Since the soil particle size distribution and the water retention curve for soil from the field site (Acevedo et al., 1983) were similar to that for soil from a site in the western Sonoran Desert near Palm Desert, California (Nobel, 1976), the relation between rainfall and soil water potential (e.g., Nobel, 1977) from the latter site was used. The relation between drought length (number of days when ~so~ < _ 0.5 MPa in the r o o t zone) and the fraction of maximal net CO2 uptake determined with O. ficus-indica in the laboratory (Nobel and Hartsock, 1984) was used to calculate the water status index when ~so~ was below -- 0.5 MPa. Hence, an average water status index could be determined for the periods of interest. Since nighttime temperatures are more important for net CO2 uptake by desert CAM plants than daytime temperatures (Nobel and Hartsock, 1978), the temperature index was based on mean monthly minimum nighttime temperatures (Nobel, 1984). Field measurements indicated that the average nighttime cladode chlorenchyma temperature of O. ficus-indica was 2°C above the minimum nighttime air temperature at the Rungue meteorological station. Hence, the temperature status index was determined from the net CO2 uptake response to temperature determined for O. ficus-indica in the laboratory (Nobel and Hartsock, 1984) adjusted to a nighttime cladode chlorenchyma temperature 2°C above the m o n t h l y minimum nighttime air temperature obtained from the Rungue meteorological station. The temperature status index was 1.00 for a nocturnal chlorenchyma temperature of 14 ° C, higher or lower temperatures reducing net CO2 uptake. The total daily PAR incident on each side of each cladode was determined b y the PAR model. The PAR index representing the fraction of maximal net CO2 uptake by O. ficus-indica at saturating total daily PAR (Nobel and Hartsock, 1983) could then be determined for each cladode surface for both clear and cloudy days. Based on the measured m o n t h l y attenuation of global shortwave irradiation by clouds, the actual PAR index for each cladode surface was obtained by linearly interpolating between the
151
clear and the cloudy (overcast) conditions. This cladode PAR index times the corresponding cladode surface area summed over both surfaces of all cladodes and then divided by the total cladode surface area gives the PAR index for the plant. The product of the indices for water status, temperature, and PAR, the environmental productivity index EPI (Nobel, 1984), was assumed to reflect the influence of the physical factors of the environment on productivity. EPI times the maximum net CO2 uptake over a 24-h period under ideal conditions (344 mmol m-2; Nobel and Hartsock, 1983, 1984) indicates the predicted daily CO2 uptake per unit stem area. Assuming that such net CO2 uptake can be equated to carbohydrate gain, productivity in mass per unit stem area per unit time (i.e., NAR) can be calculated. This value times the stem area index indicates the productivity per unit ground area. RESULTS
Testing the PAR model Because determination of the shadows is crucial for predicting the PAR intercepted by cladodes of O. ficus-indica, the ability of the model to predict shadows for four geometrically simple objects at various orientations in space was tested first. The model closely predicted the percentage of the rectangles shaded over the entire range from no shading to complete shading (Fig. 2.). Next, the model was used to predict the area available for the tO0
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152 0.5 ~.__ E
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Fig. 3. Effective area of the cladodes directed toward the solar beam at various times during a day. The unshaded area of the cladodes was projected in the direction of the solar beam for the two plants with a total of 27 cladodes using the PAR model ( ~ ) and field measurements (-- ---~-- --) on 22 December 1983. i n t e r c e p t i o n o f d i r e c t P A R b y t h e t w o p l a n t s w i t h a t o t a l o f 27 cladodes. T h e area was p r o j e c t e d i n t o t h e d i r e c t i o n o f t h e d i r e c t solar b e a m a n d t h e n c o m p a r e d w i t h s u c h values m e a s u r e d in t h e field at h o u r l y intervals (Fig. 3). E x c e l l e n t a g r e e m e n t was o b t a i n e d b e t w e e n t h e m o d e l a n d m e a s u r e m e n t , t h e average h o u r l y d i s c r e p a n c y b e i n g o n l y 6% ( d i f f e r e n c e s a p p e a r to be r a n d o m a n d t h e m o d e l values w e r e a b o v e t h e m e a s u r e d values f o r 5 o f t h e 10 h o u r s a n d b e l o w f o r t h e o t h e r 5). T h e t w o - f o l d l o w e r values f o r t h e c l a d o d e area p e r p e n d i c u l a r t o t h e solar b e a m at n o o n c o m p a r e d t o d a w n (Fig. 3) is a c o n s e q u e n c e o f t h e a p p r o x i m a t e l y vertical o r i e n t a t i o n f o r t h e m a j o r i t y o f t h e c l a d o d e s t h a t o c c u r s f o r O. ficus-indica, as well as f o r o t h e r p l a t y o p u n t i a s (Nobel, 1982c).
P A R distribution Once the coordinates of the cladodes were known, the cladode surface a r e a at a n y p a r t i c u l a r h e i g h t interval c o u l d b e r e a d i l y d e t e r m i n e d b y t h e m o d e l (Fig. 4). T h e s u r f a c e area was s y m m e t r i c a l l y d i s t r i b u t e d vertically, with a maximum near the center of the canopy. Cladode surface area per h e i g h t interval d e c r e a s e d t o a p p r o x i m a t e l y zero at t h e t o p o f t h e c a n o p y (1 m ) a n d at g r o u n d level (Fig. 4). As w o u l d be e x p e c t e d f o r essentially v e r t i c a l l y o r i e n t e d surfaces, t h e p r e d i c t e d t o t a l daily P A R p e r u n i t c l a d o d e area was g r e a t e s t at t h e t o p of t h e c a n o p y a n d p r o g r e s s i v e l y d e c r e a s e d t o w a r d t h e g r o u n d as c l a d o d e - c l a d o d e shading increased (Fig. 5). C o m p a r e d to t h e t o p o f t h e c a n o p y , w h e r e t h e average t o t a l daily P A R o n t h e c l a d o d e s j u s t e x c e e d e d 20 m o l m - 2 d-1 at t h e s u m m e r solstice, t h e t o t a l daily P A R was a p p r o x i m a t e l y halved at
153
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Fig. 5. Average total daily PAR incident on cladode surfaces at various canopy heights. Height intervals correspond to those in Fig. 4. Simulations were done for clear days at the indicated times of the year. the 0.1-to-0.2 m height intervals for the summer solstice and the equinox. At t h e w i n t e r s o l s t i c e , w h e n t h e u n i f o r m l y d i s t r i b u t e d d i f f u s e P A R is o f g r e a t e r f r a c t i o n a l i m p o r t a n c e , p r e d i c t e d t o t a l d a i l y P A R was a t t e n u a t e d b y o n l y 36% f r o m t h e t o p t o t h e b o t t o m o f t h e c a n o p y (Fig. 5).
Environmental productivity index and field productivity The various components of the environmental productivity index were d e t e r m i n e d f o r a 1 9 8 0 / 1 9 8 1 p e r i o d f o r w h i c h field d a t a o n t h e N A R o f
154
O. ficus-indica are available. In the field the base cladodes were 0.5 m apart in the east--west direction (the basic " cel l " with the t w o plants having 27 cladodes considered above) and the base cladodes of t w o adjacent plants were 1 m away in the n o r t h - - s o u t h direction, forming a rectangular array of 4 plants. These arrays were repeated at 4 m intervals in the east--west direction and at 5 m intervals in the n o r t h - - s o u t h direction, and so for modeling purposes t w o identical cells each enclosing two of the four plants were similarly spaced at 4 m repeating distances in the east--west direction and at 5 m repeating distances in t he n o r t h - - s o u t h direction. Using the PAR model, the PAR incident on each surface of the 54 cladodes o f the f o u r plants was calculated. A PAR index was then assigned to each surface based on the response of daily net CO2 upt ake to PAR, and an overall PAR index value f or the four plants was det erm i ned (Fig. 6A). This index ranged f r o m a low of 0.15 near the winter solstice to a high of 0.56 near the summer solstice, indicating t hat PAR was varying considerably and indeed limiting the net CO2 upt a ke by O. ficus-indica under field conditions. Attenuation o f total daily PAR on a horizontal surface by clouds t ended to be less during th e s u mm e r (e.g., 20% in November 1980 and 17% in January 1981) i
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Fig. 6. S e a s o n a l p a t t e r n o f c o m p o n e n t e n v i r o n m e n t a l i n d i c e s a n d t h e overall EPI f o r n e t CO 2 u p t a k e . D a t a were c a l c u l a t e d f o r m o n t h l y values o f e n v i r o n m e n t a l p a r a m e t e r s averaged a t a p p r o x i m a t e l y t w o - m o n t h intervals c e n t e r e d o n t h e p o i n t i n d i c a t e d .
155
and greater during the late fall and winter (e.g., 49% in May 1980, 47% in May 1981, and 46% in July 1980). The water status index ranged from 0.70 to 0.98 (Fig. 6B); the relatively high value from November 1980 to February 1981 was a consequence of the three irrigations, since the rainfall in this late spring/summer period was only 27 mm. The least variation occurred in the temperature index, which ranged from 0.80 to 0.98 (Fig. 6C). During essentially the entire observation period, the m o n t h l y minimum nighttime temperatures and hence cladode temperatures were at or below the optimal temperature for net CO2 uptake, e.g., the monthly minimum air temperatures ranged from 1.3°C in July 1981 to 10.0°C in February 1981. The environmental productivity index EPI equals the product of the three individual indices in Fig. 6A--C. EPI (Fig. 6D) times the net daily CO2 uptake under ideal conditions (344 mmol m -2 d -1 ) indicates the net CO2 uptake predicted for field conditions, which can be converted to the units of N A R (g dry weight m -2 stem area d -1) by assuming that the CO2 is converted to carbohydrate. In this way, a predicted N A R can be compared to the NAR measured for O. ficus-indica in the field in the 1980/1981 period (Fig. 7). Although there were differences between predicted and measured NAR, the seasonal pattern was similar, i.e., the lowest values occurred in the winter and the highest in the summer. In the summer (here considered as November--February), the model predicted an average NAR of 5.03 g m -2 d -1 and the measurements yielded 5 . 1 0 g m -2 d -~ (Fig. 7). However, the average N A R for the winter (May--August) for 1980 and 1981 was predicted
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Fig. 7. N e t assimilation rate p r e d i c t e d f r o m the e n v i r o n m e n t a l p r o d u c t i v i t y i n d e x and measured in the field. Measured values were means f o r plants i n i t i a l l y 0.5 or 1.5 years old
(differences between two ages averaged 10%; Acevedo et al., 1983 and unpublished observations), which is comparable in age to the 1.5-year-old plants used to develop the PAR model.
156 t o b e 1.46 g m -2 d-1 w h e r e a s t h e m e a s u r e d average was 2 . 7 4 g m - 2 d-1. T h e average p r e d i c t e d N A R f o r J u l y 1 9 8 0 to J u l y 1981 was 3 . 1 6 g m -2 d -~, c o m p a r e d w i t h t h e average m e a s u r e d N A R f o r similarly s p a c e d p l a n t s o f a p p r o x i m a t e l y t h e s a m e size o f 3 . 3 2 g m -2 d- 1 (Fig. 7).
Predicted annual productivity versus stern area index T h e P A R m o d e l was n e x t used to v a r y t h e spacing o f cells and t h e r e b y to g e n e r a t e " f i e l d s " o f O. ficus-indica w i t h d i f f e r e n t s t e m area indices. T h e daily N A R was c a l c u l a t e d as f o r Fig. 7. T h e a n n u a l p r o d u c t i v i t y per u n i t g r o u n d area c o u l d t h e n b e p r e d i c t e d b y i n t e g r a t i n g daily N A R d e t e r m i n e d f o r c o n d i t i o n s a p p r o p r i a t e f o r J u l y 1 9 8 0 t o J u l y 1981 a n d m u l t i p l y i n g b y t h e SAI ( t h e l a t t e r t o c o n v e r t p r o d u c t i v i t y f r o m a s t e m area basis to a g r o u n d area basis). T h e m a x i m u m p r e d i c t e d a n n u a l p r o d u c t i v i t y o f 3.4 kg m - 2 y-1 o c c u r r e d n e a r an SAI o f 7 (Fig. 8). P r o d u c t i v i t y d r o p p e d o f f r a p i d l y at l o w e r SAI's, r e f l e c t i n g l o w e r s t e m areas available f o r CO2 u p t a k e . A t S A I ' s a b o v e 7, p r o d u c t i v i t y p e r u n i t g r o u n d area was r e d u c e d even t h o u g h t h e r e was m o r e s t e m area available (Fig. 8); t h e r e d u c t i o n o c c u r r e d b e c a u s e t h e P A R p e r u n i t s t e m area d e c r e a s e d , leading t o an even greater f r a c t i o n a l d e c r e a s e in n e t CO2 u p t a k e .
Angular dependence of P A R index T o see t h e e f f e c t o f c l a d o d e o r i e n t a t i o n o n P A R i n t e r c e p t i o n a n d h e n c e o n t h e P A R i n d e x f o r n e t CO2 u p t a k e , t h e P A R m o d e l was used to a n a l y s e a h y p o t h e t i c a l flat p l a n t w i t h 13 c l a d o d e s o f t h e s a m e t o t a l a r e a as t h e average f o r t h e t w o p l a n t s in t h e field ( 1 . 2 7 m 2 ; Fig. 3). Such p l a n a r p l a n t s w e r e s p a c e d 2 m a p a r t in r o w s w i t h all o f t h e i r c l a d o d e s vertical a n d aligned along t h e row. R o w s w e r e s p a c e d 0.5 m a p a r t , a n d so t h e s t e m area i n d e x was 1.27. /
6'c
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Fig. 8. Annual productivity predicted for fields of different stem area indices. SAI's greater than 2.62, a value obtained by placing the cells just enclosing the 27 cladodes on the 2 plants adjacent to each other, were created by stacking such cells on top of each other. NAR data were obtained for time intervals of two months for environmental conditions appropriate for July 1980 to July 1981 (Fig. 7) and then integrated to obtain annual values.
157 ~'~-- 0.5 m - - I ~
/
Fig. 9. H y p o t h e t i c a l p l a n t w i t h all 13 c l a d o d e s in a single, vertical plane. T h e 9 t e r m i n a l c l a d o d e s were 36 c m l o n g ( m a x i m u m w i d t h was h a l f t h e l e n g t h for all t h e cladodes), t h e 3 i n t e r m e d i a t e c l a d o d e s were 40 c m long, a n d t h e base c l a d o d e was 46 c m long w i t h half b e l o w g r o u n d level. T o p a n d base c l a d o d e s are indicated.
PAR indices were calculated for three times of the year (winter solstice, equinox, and summer solstice) for five angles of rotation ranging from 0 ° (plants and hence cladodes facing east--west) to 90 ° (cladodes facing north-south) for both clear days and cloudy days. The total daily PAR calculated by the model for an unshaded horizontal surface was 5 5 . 9 m o l m -~ on the summer solstice, 3 8 . 5 m o l m -2 on the equinox, and 1 6 . 7 m o l m -2 on the winter solstice for the clear days and 19.0, 14.0, and 7 . 5 m o l m -2, respectively, for the cloudy days. For a clear day on the summer solstice, the PAR index averaged for both surfaces of all cladodes decreased nearly fourfold as the plants were rotated from facing east--west to facing north--south (Fig. 10A). A gradual decrease occurred for such rotation on a clear day at the equinox (Fig. 10C), while s u c h rotation from facing east--west to north--south on the winter solstice increased the PAR index about 2-fold (Fig. 10E). Indeed, facing north--south on a clear day at the winter solstice led to a higher PAR index than facing north--south on the summer solstice. For cloudy days represented by isotropic diffuse PAR, the PAR index was independent of direction; it averaged 0.24 on the summer solstice (Fig. 10B), 0.12 on the equinox (Fig. 10D), and only 0.01 on the winter solstice (Fig. 10F). The low value for the winter solstice on cloudy days was a consequence of the low PAR, averaging only 3.8 mol m -2 over the cladode surface, which is essentially the light compensation value for net COs uptake by O. ficus-indica (Nobel and Hartsock, 1983). On both clear and cloudy days at the three times of the year considered, the PAR index for the t o p m o s t central cladode (Fig. 9) was always above the average for the plant and that of the base cladode was always below the average (Fig. 10). The effect of shadows accounts for the increase in PAR index of the base cladode upon rotation of these geometrically regular plants from 0 ° to 22.5 ° at the summer solstice on clear days and its substantial decrease for this rotation on an equinox (Fig. 10A and C).
158
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Fig. 10. I n f l u e n c e o f angle of r o t a t i o n o f vertical cladodes for plant in Fig. 9 on the P A R index p r e d i c t e d for three different times of the year for clear and c l o u d y days. The solid lines represent the average for all 13 cladodes o f the plant in Fig. 9, the dashed lines are for the t o p cladode, and the d o t t e d lines are for the base cladode. An angle of r o t a t i o n of 0 ° corresponds to facing east-west and 90 ° to facing north-south. DISCUSSION
The PAR model incorporating the trajectory of 5000 equally spaced rays in a rectangular grid proved extremely accurate for calculating the shadows from b o t h geometrically simple and also complex shapes. Using the coordinates at the proximal and distal ends and at the t w o extremes of the width for each of 27 obovate cladodes of Opuntia ficus-indica, a three-dimensional architecture was created that determined which portions of underlying cladodes were in shadow for various times of the day. The direct PAR incident on each surface of each cladode plus the diffuse PAR from the sky and reflected from the ground, including the effects of occlusion by other cladodes, allowed determination of the total PAR intercepted over an entire day. For example, the model showed that the PAR intercepted by the cladodes decreased most rapidly with height near midcanopy, where the greatest cladode surface area per unit height occurred (Fig. 4). From the predicted PAR interception and the influence of total daily PAR on net CO2 uptake by O. ficus-indica (Nobel and Hartsock, 1983, 1984), a PAR index was determined that together with those for water status and temperature (Nobel, 1983) allowed the prediction o f the net assimilation rate of O. ficus-indica under field conditions. The predicted N A R agreed quite favorably with
159 previously measured N A R (Acevedo et al., 1983 and unpublished observations) with respect to seasonal trends and average values. However, the predicted N A R tended to underestimate the measured N A R for the winter. Although measured N A R includes effects of dry matter export to the rest of the plant, which can vary as source--sink relations change, and hence is not entirely equivalent to the predicted NAR, the difference for the winter was apparently related to the temporal PAR distribution, as considered next. The high incidence of cloudiness in late fall and winter at the study site caused the measured m o n t h l y averages of total daily PAR on a horiztonal surface to be only 50 to 60% of the PAR for clear days at that time of the year. This average ambient PAR value is similar to the total daffy PAR predicted for a cloudy day, which has only isotropic diffuse PAR. For instance, at the winter solstice the diffuse PAR on a horizontal surface for a cloudy day averaged 45% of the total PAR for a clear day. Thus, the relation used here for diffuse PAR, which is the one conventionally employed (Monteith, 1973; Goudriaan, 1977; Milthorpe and Moorby, 1979; Castillo and Santibaflez, 1981), caused the PAR model to calculate a very low PAR index similar to that for cloudy conditions (Fig. 8F). In reality, however, the m o n t h l y average of total daily PAR in the winter is composed of a combination of bright days with relatively high PAR plus very overcast days where the PAR is actually lower than for the conventionally modeled uniformly overcast days (unpublished observations). For instance, the mean PAR index averaged over all orientation angles at the winter solstice would be 0.01 for the cloudy days incorporated into the model (Fig. 8F), while the same total m o n t h l y PAR caused by 10 clear days (average PAR index of 0.31, Fig. 8E) and 20 very cloudy days (PAR index of 0.00) would be 0.10. Thus, application of the PAR model to the CAM plant O. ficus-indica should be done using day-by-day values of total daffy PAR at the field site (data that are not available for the periods of interest), not m o n t h l y averages of the daily values. A consequence of using the m o n t h l y average values is the underestimating of the PAR index and hence of the predicted N A R in the winter (Fig. 7), when the cloudiness in central Chile is much greater than in the summer. The above effect of temporal PAR distribution is a consequence of the non-linear response of net CO2 uptake b y cacti to total daily PAR (Nobel, 1977; Nobel and Hartsock, 1983). Specifically, the light compensation point occurs at a total daffy PAR of a b o u t 3.5 mol m - 2 . Net CO2 uptake is slightly negative at PAR < 3 . 5 m o l m -2 but increases approximately linearly with PAR from 3.5 to 2 0 m o l m -2, where it reaches nearly 90% of its maximum. Thus, total daily PAR levels below 3.5 mol m -2 lead to a slight loss of CO2, changes in the range of 3.5 to 20 mol m -2 can have major effects, and values above 20 mol m -2 incident on the cladodes do not increase net CO 2 uptake very much. For clear days near the winter solstice, a small fraction of the surfaces of vertical cladodes are oriented such that they intercept 15 or more tool m -2 (Nobel, 1980, 1982b) and thus have a relatively high net CO2 uptake, which leads to net CO2 uptake by the whole plant (the other surfaces have relatively little positive or negative effect on net CO2 uptake). However,
160 for the uniform diffuse conditions on cloudy days near the winter solstice, all surfaces are near light compensation; hence, the NAR for each cladode surface is near zero and productivity by the plant is then predicted to be negligible. The PAR model allowed variation of the spatial distribution of the plants, including stacking adjacent small plants on top of each other to raise the stem area index. The measured productivity of O. ficus-indica for plants of mean age 5.4 years was 1.32 kg m -2 y-1 for an SAI of 1.44 (Acevedo et al., 1983), similar to the value predicted at this stem area index. The predicted net carbohydrate gain reached a m a x i m u m of 3.4 kg m -2 y-1 at an SAI of 7 (Fig. 8), which is a nearly threefold higher productivity than measured or predicted for various CAM plants (Smith, 1929; Lock, 1962; Bartholomew, 1982; Acevedo et al., 1983; Nobel, 1984). This suggests that closer spacing of the plants should increase the annual carbohydrate gain (closer spacing is possible, as the ground cover determined from a polygon circumscribing the most extreme cladodes on these plants was only 32%), although other considerations, such as ease of harvesting, may be of greater practical concern than maximizing productivity. The PAR model was also used to determine the effect on the PAR index of various cladode orientations at different times of the year. Specific orientations can be created by the planting direction of the original cladodes as well as by suitable pruning of the plants. Moreover, unshaded cladodes of O. ficus-indica have a natural t e n d e n c y to face east--west at the study site in Chile (Nobel, 1982b), consistent with the orientation pattern for 23 species of platyopuntias examined worldwide (Nobel, 1982c). For clear days during the main growing season in late spring/summer, the PAR index averaged 0.71 for an east--west orientation, 0.37 for a north--south orientation, and 0.58 half way between (data represent averages for the summer solstice and an equinox for a planar plant of 13 cladodes; Fig. 10); all orientations had the same PAR index for cloudy days. As would be expected, the PAR index of the base cladode was always below the average for the plant. For larger plants of more realistic (non-planar) shape, shadows would tend to reduce the PAR even further for the base cladode, perhaps to the light compensation point, i.e., this region m a y not be photosynthetically active; indeed corky non-photosynthetic tissue generally forms on the surfaces of such cladodes. The PAR model calculated the total daily PAR on the cladode surfaces which, together with the environmental productivity index, enabled prediction of productivity of O. ficus-indica under both actual field conditions as well as hypothetical arrangements that could enhance productivity. Such predictions can be used to m o d i f y the cultivation practices for this and other platyopuntias, which have received little agronomic attention. Also, the PAR model can be extended to consider other complex arrangements of photosynthetic surfaces in space, especially those with regularly repeating units, such as vineyards and orchards.
161
ACKNOWLEDGEMENTS We g r a t e f u l l y a c k n o w l e d g e Mr. O s c a r C a r r a s c o f o r a s s i s t a n c e w i t h fieldw o r k a n d Mr. Moises E s c a f t f o r t h e use o f his f a r m . F i n a n c i a l s u p p o r t was provided by Comisidn Nacional de Investigacion Cientifica y Tecnoldgica ( C O N I C Y T ) o f Chile g r a n t 1 6 8 / 8 2 , D e p a r t a m e n t o d e D e s a r o l l o C i e n t i f i c o d e la U n i v e r s i d a d d e Chile P r o j e c t A 1 2 1 3 / 8 4 4 4 , U n i t e d S t a t e s D e p a r t m e n t of Energy Contract DE-AM03-76-SF00012, and the Laboratory Director's Office Fund of the UCLA Laboratory of Biomedical and Environmental Sciences.
REFERENCES Acevedo, E., Badilla, I. and Nobel, P.S., 1983. Water relations, diurnal acidity changes, and productivity of a cultivated cactus, Opuntia ficus-indica. Plant Physiol., 72: 775--780. Bartholomew, D.P., 1982. Environmental control of carbon assimilation and dry matter production by pineapple. In: I.P. Ting and M. Gibbs (Editors), Crassulacean Acid Metabolism, American Society of Plant Physiologists, Rockville, MD, pp. 278--294. Castillo, H. and Santibanez, F., 1981. Evaluaci6n de la radiacidn solar global y luminosidad en Chile. I. Calibraci6n de f6rmulas para estimar radiaci6n solar global diaria. Agric. Tecn. (Chile), 41: 145--152. Goudriaan, J., 1977. Crop Micrometeorology: a Simulation Study. Pudoc, Wageningen, 249 pp. Le Houerou, H.N., 1970. North Africa: past, present, future. In: H.E. Dregne (Editor), Arid Lands in Transition, Publication 90. American Association for the Advancement of Science, Washington, DC, pp. 227--278. Lock, G.W., 1962. Sisal: Twenty-Five Years Sisal Research. Longmans, London, 355 pp. Metral, J.J., 1965. Les cactes fourrag6res dans le Nord-Est du Brasil plus particuli6rement dans l'~tat du Cear~. Agron. Trop., 20: 248--261. Milthorpe, F.L. and Moorby, J., 1979. An Introduction to Crop Physiology, 2nd edn. Cambridge University Press, Cambridge, 244 pp. Monteith, J., 1973. Principles of Environmental Physics. Edward Arnold, London, 241 pp. Nobel, P.S., 1976. Water relations and photosynthesis of a desert CAM plant, Agave deserti. Plant Physiol., 58: 576--582. Nobel, P.S., 1977. Water relations and photosynthesis of a barrel cactus, Ferocactus acanthodes, in the Colorado Desert. Oecologia, 27: 117--133. Nobel, P.S., 1980. Interception of photosynthetically active radiation by cacti of different morphology. Oecologia, 45: 160--166. Nobel, P., 1982a. Interaction between morphology, PAR interception, and nocturnal acid accumulation in cacti. In: I.P. Ting and M. Gibbs (Editors), Crassulacean Acid Metabolism, American Society of Plant Physiologists, Rockville, MD, pp. 260--277. Nobel, P.S., 1982b. Orientation, PAR interception, and noctural acidity increases for terminal cladodes of a widely cultivated cactus, Opuntia ficus-indica. Am. J. Bot., 69: 1462--1469. Nobel, P.S., 1982c. Orientation of terminal cladodes of platyopuntias. Bot. Gaz., 143: 219--224. Nobel, P.S., 1984. Productivity of Agave deserti: measurement by dry weight and monthly prediction using physiological responses to environmental parameters. Oecologia, 64: 1--7. Nobel, P.S. and Hartsock, T.L., 1978. Resistance analysis of nocturnal carbon dioxide uptake by a Crassulaceanacid metabolismsucculent, Agave deserti. Plant Physiol., 61: 510--514.
162 Nobel, P.S. and Hartsock, T.L., 1983. Relationships between photosynthetically active radiation, nocturnal acid accumulation, and CO 2 uptake for a Crassulacean acid metabolism plant, Opuntia ficus-indica. Plant Physiol., 71 : 71--75. Nobel, P.S. and Hartsock, T.L., 1984. Physiological responses of Opuntia ficus-indica to growth temperature. Physiol. Plant., 60: 98--105. Refiasco, G., 1976. Cultivo de Tunales. Boletl"n divulgativo 44, Servicio Agricola y Gandero, Santiago, 35 pp. Smith, H.H., 1929. Sisal: Production and Preparation. John Bale and Danielsson, London, 384 pp. Varlet-Grancher, C., Chattier, M., Gosse, G. and Bonhomme, R., 1981. Rayonnement utile pour la photosynth~se des v~g~taux en conditions naturelles: caract~risation et variations. Acta Oecol. Oecol. Plant., 2: 189--202.
145
Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
MODELING OF PAR INTERCEPTION AND PRODUCTIVITY BY OPUNTIA FICUS-INDICA VICTOR GARCIA de C O R T A Z A R and EDMUNDO ACEVEDO
Laboratoria Relaciones Suelo-Agua-Planta, Facultad de Agronom}a, Universidad de Chile, Casilla 1004, Santiago (Chile) PARK S. NOBEL*
Department of Biology and Laboratory of Biomedical and Environmental Sciences, University of California, Los Angeles, California 90024 (U.S.A.) (Received July 16, 1984; revision accepted October 11, 1984)
ABSTRACT Garcia de Cortazar, V., Acevedo, E. and Nobel, P.S., 1985. Modeling of PAR interception and productivity by Opuntia ficus-indica. Agric. For. Meteorol., 34: 145--162. A model is described that permits accurate calculation of radiation interception and shadows cast by a set of planar surfaces whose Cartesian coordinates are known. The model is applied to the calculation of interception of photosynthetically active radiation (PAR) by the cladodes (flattened stems) of the widely cultivated cactus, Opuntia ficusindica. Taking into account both direct and diffuse PAR, a PAR index is determined for both sides of the 27 cladodes on two plants. This index has a maximum value of 1.00 when net CO2 uptake by the cladodes is not limited by PAR. The product with similar indices for water status and temperature indicates the fraction of maximum net CO2 uptake expected under particular environmental conditions, the environmental productivity index (EPI). EPI is used to predict the net assimilation rate (NAR) of O. ficus-indica under field conditions in central Chile, where its NAR has been measured. The predicted NAR closely agreed with seasonal trends and average annual values, but underestimated measured NAR in the winter, presumably due to over-representation of the low NAR caused by isotropic diffuse radiation at this cloudy time of the year. Applying the PAR model to different plant spacings, the annual productivitYlPredicted for a stem area index (stem area per ground area) of 1.4 was 1.4 kg m -2 y- , which closely matched field measurements; maximal productivity nearly threefold higher was predicted at a stem area index of 7. The PAR model was also used to analyze a hypothetical plant with all cladodes in a plane so that the influence of cladode orientation on the PAR index at various times of the year for both clear and cloudy days could be determined. Besides indicating PAR distribution within the canopy of the platyopuntias, the PAR model can be used for other three-dimensional distributions of photosynthetic surfaces, especially those that have regularly repeating units in space, such as orchards and vineyards.
INTRODUCTION
Few Crassulacean acid metabolism (CAM) plants are extensively cultivated and relatively little is k n o w n a b o u t their productivity. One o f the m ost *Author for correspondence and reprint requests.
0168-1923/85/$ 03.30
© 1985 Elsevier Science Publishers B.V.
146 widely cultivated is pineapple (Ananas comosus), which can have a net assimilation rate (NAR) (Milthorpe and Moorby, 1979) of 2.0 g dry weight m -2 leaf area d -1 under optimal temperatures in the laboratory; also, it has been predicted to yield 1.2 kg carbohydrate m -2 ground area y- ~ (12 metric tons ha -1 y - l ) in the field in Hawaii when irrigated (Bartholomew, 1982). Field studies with Agave fourcroydes and other fiber-producing agaves in Mexico, Tanzania, and various other countries indicate a maximal productivity of about 1.0 kg leaf dry weight m -2 y-1 for these CAM plants (Smith, 1929; Lock, 1962). Consistent with this, the net productivity of A. deserti in California was 0 . 5 7 k g m -2 over a relatively wet 5-month period (Nobel, 1984). The cactus Opuntia ficus-indica is cultivated on a limited basis for both its fruit and its cladodes (flattened stems) in tropical and subtropical areas as well as in h o t regions of the temperate zone. Total biomass productivity of 5.0kg wet weight m -2 y-1 has been observed in North Africa (Le Houerou, 1970) and 9 . 3 k g wet weight m -2 y-1 in Brazil (Metral, 1965), with a fruit productivity of 1.6 kg wet weight m -2 y-1 measured in central Chile (Reflasco, 1976). Recently, a dry weight productivity of 1.0 kg m -2 y-1 for cladodes and 0 . 3 k g m -2 y-1 for fruit has been measured for O. ficus-indica in Chile (Acevedo et al., 1983). Whether this 1 . 3 k g m -2 y-1 approaches the maximal annual productivity of CAM plants is not known. Opuntia ficus-indica has also been studied under controlled laboratory conditions, and so the responses of net CO2 uptake to photosynthetically active radiation (PAR), air temperature, and soil water status are known. Most CO2 uptake by O. ficus-indica and other CAM plants occurs at night, and so net CO2 uptake is n o t easily related to the instantaneous value of PAR. Rather, it has proved useful to relate net CO2 uptake b y CAM plants to the total dally PAR. Although there is some dependence on PAR distribution during the day as well as on temperature, 90% PAR saturation for O. ficus-indica occurs near a total daily PAR of 2 0 m o l m -2 (Nobel and Hartsock, 1983, 1984), just as for many other CAM plants (Nobel, 1982a). Maximal net CO2 uptake over a 24-h period occurs for relatively low nighttime air temperatures of 11 to 1 2 ° C (Nobel and Hartsock, 1984); daytime temperatures are less important for net dally CO2 uptake by O. ficus-indica as well as by other CAM plants (e.g., Nobel and Hartsock, 1978). Under well-watered conditions, optimal temperatures, and saturating PAR, net CO2 uptake by O. ficus-indica over a 24-h period is 344 mmol m- 2 (Nobel and Hartsock, 1983, 1984). If this all were carbohydrate, it would correspond to a N A R of 10.3 g m -2 d- 1. However, NAR values measured in the field for O. ficus-indica averaged only 3.3 g m-2d -1 over 1.5-year period for plants initially 0.5 year old and 3.1 g m -2 d -1 for those initially 1.5 years old (Acevedo et al., 1983 and unpublished observations; initial age refers to when a mature cladode is placed in the ground for these vegetatively propagated plants). Since temperature and water status do not appear to be far from optimal in the commercial plantations of O. ficus-indica in Chile, especially since they are irrigated during the late spring/summer dry period,
147 the factor limiting productivity m a y be PAR. However, it has been difficult to estimate or model the PAR interception under field conditions, because of the complex three
Plant material and field site Opuntia ficus-indica (L.) Miller (Cactaceae) was studied at a commercial plantation in Til Til, Chile (33 °2'S, 70°54'W, 570 m above sea level) about 50 km north-northwest of Santiago. The two representative, adjacent field plants analyzed were 1.5 years old and had a total of 27 cladodes. Air temperatures and rainfall were obtained from the Rungue meteorological station (700 m elevation) located 10 km north-northeast of the study site. Annual rainfall was 467 m in 1980 and 326 m m in 1981, the two years when the net assimilation rate (NAR) was measured in the field. Additionally, the fields were irrigated three times during late spring/summer with a water depth of about 80 m m each time. Fractional attenuation of photosynthetically active radiation (PAR, 400 to 700 nm) by clouds was equated to the fractional attenuation of global shortwave radiation measured at the A n t u m a p u meteorological station in Santiago. PAR model A computer model was developed to predict the PAR intercepted by each side of all cladodes for two adjacent plants having a total of 27 cladodes. The morphology of the plants was described by the Cartesian coordinates of the proximal and the distal ends along the longitudinal axis of each cladode and of each side of the width at the widest place. The outline of the cladode surface was then generated from an empirical relation of relative width versus relative length along the longitudinal axis determined from 20 measurements along each of six cladodes of various sizes: width/widthmax = -- 3.24 (length/ lengthmax) 2 + 3.38 length/lengthmax + 0.11, r 2 = 0.89, where length was measured from the proximal end and hence lengthmax was the total length
148 along the longitudinal axis. C l a d o d e area f o r each planar side averaged 0 . 7 2 5 x lengthmax x widthmax and t h e lengthm~x/widthm~x ratio was 1.94 + 0.34 ( s t a n d a r d d e v i a t i o n f o r 27 cladodes). A r e c t a n g u l a r parallelepiped or " c e l l " just enclosing t h e t w o plants o c c u p i e d 0.89 m in t h e n o r t h - - s o u t h (x) d i r e c t i o n , 1 . 0 9 m in t h e e a s t - - w e s t ( y ) d i r e c t i o n , and 0 . 9 8 m in height (z d i r e c t i o n ) . T h e t o t a l area o f b o t h sides o f all 27 cladodes was 2.54 m 2 : b o t h sides m u s t be i n c l u d e d , since t h e c l a d o d e s are o p a q u e and h e n c e t h e c h l o r e n c h y m a o n each side relates t o a d i f f e r e n t surface f o r P A R interc e p t i o n . F o r t h e cell just enclosing the t w o plants, t h e g r o u n d area was 0.97 m 2 and h e n c e the stem area i n d e x S A I (total area o f b o t h sides o f cladodes per unit g r o u n d area) f o r t h e cell was 2.62. E a c h c l a d o d e surface was described b y a r e c t a n g u l a r a r r a y o f squares (Figure 1) 1 8 m m o n a side, the c e n t e r o f each square lying within t h e
C
B
\
Fig. 1. Schematic illustration of a three-dimensional "cell" containing a plant with four cladodes. Cladode surfaces are divided into squares (actual model has an average of 145 squares for each cladode side). Direct solar irradiation is indicated by rays that are incident on a cladode (ray A), incident on the ground (ray B), and exiting the cell (ray C). The exiting ray enters an adjacent identical cell, which is equivalent to re-entering at the opposite side of the same cell (ray C'), and is intercepted by a cladode near the middle of the plant.
149 parabola defining the cladode outline (an average of 145 squares were used for each cladode surface). The direct solar beam was represented by 5000 equally spaced rays in a rectangular array orthogonal to the propagation direction, all such rays entering the t op of the cell. A particular ray was either intercepted by one of the squares of a cladode (ray A in Fig. 1), was incident on th e ground (ray B), or passed o u t of the side o f the cell (ray C). This latter ray could then enter a neighboring identical cell, which is equivalent to re-entering the opposite side o f the same cell (with suitable allowance for change in z if the cells are n o t adjacent), and perhaps strike a square in the surface of an underlying cladode (ray C' in Fig. 1). To determine how m uch o f each cladode surface was exposed to the sun at a particular time of day, a new c oor di nat e system was created having a rectangular grid of 5000 squares in the x ' - y ' plane (corresponding t o the 5000 rays) with the direct solar beam traveling along the z' axis. All the center points from the squares o f the cladode surfaces were placed in this new system and their location in the squares of the new rectangular grid noted. If points from different cladodes o ccurred in the same grid square, then the cladode with the highest z' intercepted the ray and the ot her or others were in its shadow. The direct PAR on a cladode surface was then calculated as the fraction o f the center points of a particular cladode surface intercepting rays times the PAR in a plane perpendicular to the direct solar beam times the cosine o f the angle between the normal to the cladode surface and th e direct solar beam (orientation of the normal to each of t he two sides o f a cladode was det er m i ned f r o m t he cross p r o d u c t o f a vector along the longitudinal axis with a vector f r om the cladode base to one of t he points o f the m a x i m u m width). Diffuse PAR f r o m the sky and reflected f r o m t h e ground was also determined for each cladode surface, assuming radiation from each source to be isotropic. Diffuse PAR from t he sky equaled the view factor of a cladode surface toward the sky corrected for occlusion by overlying cladodes times t h e diffuse PAR on an unshaded horizontal surface. The diffuse PAR on an unshaded horizontal surface for clear days was assumed to be 13% of total PAR when the sun was overhead, 16% for a sun elevation angle of 45 °, and 32% at 15 ~ (Goudriaan, 1977). For clear days the global shortwave irradiation (direct plus diffuse) in W m -2 for sun elevation angle ~ was set equal to 1360 sin f i e -°'30/sin~, corresponding to the locally measured atmospheric transmissivity o f e -°'3° or 0.74 for an optical air mass of uni t y (Castillo and Santibafiez, 1981). A shortwave irradiation of 1 . 0 0 M J was assumed to correspond to 2 . 0 2 m o l p h o t o n s from 400 to 700 nm (VarletGrancher et al., 1981). For a c o m p l e t e l y overcast day, PAR was entirely diffuse and based on local measurements was assumed to equal 22% of the radiation incident on t he earth's a t m o s p h e r e (Castillo and Santibafiez, 1981). Diffuse PAR reflected f r o m the ground was equat ed t o the view factor o f a particular cladode surface t ow a r d the ground times the total PAR on a horizontal surface (including effects of shading by cladodes) times the
150 measured reflectivity of the ground for PAR (0.11). Direct and diffuse PAR were calculated for b o t h surfaces of all 27 cladodes for hourly positions of the sun and integrated to give the total daily PAR for b o t h clear and overcast days.
Environmental productivity index Net CO2 uptake by O. fieus-indica in the field was predicted from its response to water status, temperature, and PAR measured under controlled conditions in the laboratory (Nobel and Hartsock, 1983, 1984). An index value was assigned to indicate the fraction of maximal net CO2 uptake expected for each factor individually (Nobel, 1984). For instance, when the soil water potential was above the chlorenchyma osmotic potential (-- 0.5 MPa) (Nobel and Hartsock, 1984), the water status index was assigned a value of 1.00, indicating that water was then not limiting net CO2 uptake. Since the soil particle size distribution and the water retention curve for soil from the field site (Acevedo et al., 1983) were similar to that for soil from a site in the western Sonoran Desert near Palm Desert, California (Nobel, 1976), the relation between rainfall and soil water potential (e.g., Nobel, 1977) from the latter site was used. The relation between drought length (number of days when ~so~ < _ 0.5 MPa in the r o o t zone) and the fraction of maximal net CO2 uptake determined with O. ficus-indica in the laboratory (Nobel and Hartsock, 1984) was used to calculate the water status index when ~so~ was below -- 0.5 MPa. Hence, an average water status index could be determined for the periods of interest. Since nighttime temperatures are more important for net CO2 uptake by desert CAM plants than daytime temperatures (Nobel and Hartsock, 1978), the temperature index was based on mean monthly minimum nighttime temperatures (Nobel, 1984). Field measurements indicated that the average nighttime cladode chlorenchyma temperature of O. ficus-indica was 2°C above the minimum nighttime air temperature at the Rungue meteorological station. Hence, the temperature status index was determined from the net CO2 uptake response to temperature determined for O. ficus-indica in the laboratory (Nobel and Hartsock, 1984) adjusted to a nighttime cladode chlorenchyma temperature 2°C above the m o n t h l y minimum nighttime air temperature obtained from the Rungue meteorological station. The temperature status index was 1.00 for a nocturnal chlorenchyma temperature of 14 ° C, higher or lower temperatures reducing net CO2 uptake. The total daily PAR incident on each side of each cladode was determined b y the PAR model. The PAR index representing the fraction of maximal net CO2 uptake by O. ficus-indica at saturating total daily PAR (Nobel and Hartsock, 1983) could then be determined for each cladode surface for both clear and cloudy days. Based on the measured m o n t h l y attenuation of global shortwave irradiation by clouds, the actual PAR index for each cladode surface was obtained by linearly interpolating between the
151
clear and the cloudy (overcast) conditions. This cladode PAR index times the corresponding cladode surface area summed over both surfaces of all cladodes and then divided by the total cladode surface area gives the PAR index for the plant. The product of the indices for water status, temperature, and PAR, the environmental productivity index EPI (Nobel, 1984), was assumed to reflect the influence of the physical factors of the environment on productivity. EPI times the maximum net CO2 uptake over a 24-h period under ideal conditions (344 mmol m-2; Nobel and Hartsock, 1983, 1984) indicates the predicted daily CO2 uptake per unit stem area. Assuming that such net CO2 uptake can be equated to carbohydrate gain, productivity in mass per unit stem area per unit time (i.e., NAR) can be calculated. This value times the stem area index indicates the productivity per unit ground area. RESULTS
Testing the PAR model Because determination of the shadows is crucial for predicting the PAR intercepted by cladodes of O. ficus-indica, the ability of the model to predict shadows for four geometrically simple objects at various orientations in space was tested first. The model closely predicted the percentage of the rectangles shaded over the entire range from no shading to complete shading (Fig. 2.). Next, the model was used to predict the area available for the tO0
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0
i
I
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20
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Measured shading (%) Fig. 2. C o m p a r i s o n o f p r e d i c t e d w i t h m e a s u r e d s h a d i n g o f f o u r rectangles at various angles a n d l o c a t i o n s in s p a c e for d i f f e r e n t solar a z i m u t h s a n d elevations. E a c h r e c t a n g l e was 1 8 c m b y 3 6 c m , leading t o a n area similar t o t h a t o f a cladode. T h e solid line r e p r e s e n t s c o m p l e t e a g r e e m e n t b e t w e e n m e a s u r e m e n t a n d t h e P A R model.
152 0.5 ~.__ E
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Fig. 3. Effective area of the cladodes directed toward the solar beam at various times during a day. The unshaded area of the cladodes was projected in the direction of the solar beam for the two plants with a total of 27 cladodes using the PAR model ( ~ ) and field measurements (-- ---~-- --) on 22 December 1983. i n t e r c e p t i o n o f d i r e c t P A R b y t h e t w o p l a n t s w i t h a t o t a l o f 27 cladodes. T h e area was p r o j e c t e d i n t o t h e d i r e c t i o n o f t h e d i r e c t solar b e a m a n d t h e n c o m p a r e d w i t h s u c h values m e a s u r e d in t h e field at h o u r l y intervals (Fig. 3). E x c e l l e n t a g r e e m e n t was o b t a i n e d b e t w e e n t h e m o d e l a n d m e a s u r e m e n t , t h e average h o u r l y d i s c r e p a n c y b e i n g o n l y 6% ( d i f f e r e n c e s a p p e a r to be r a n d o m a n d t h e m o d e l values w e r e a b o v e t h e m e a s u r e d values f o r 5 o f t h e 10 h o u r s a n d b e l o w f o r t h e o t h e r 5). T h e t w o - f o l d l o w e r values f o r t h e c l a d o d e area p e r p e n d i c u l a r t o t h e solar b e a m at n o o n c o m p a r e d t o d a w n (Fig. 3) is a c o n s e q u e n c e o f t h e a p p r o x i m a t e l y vertical o r i e n t a t i o n f o r t h e m a j o r i t y o f t h e c l a d o d e s t h a t o c c u r s f o r O. ficus-indica, as well as f o r o t h e r p l a t y o p u n t i a s (Nobel, 1982c).
P A R distribution Once the coordinates of the cladodes were known, the cladode surface a r e a at a n y p a r t i c u l a r h e i g h t interval c o u l d b e r e a d i l y d e t e r m i n e d b y t h e m o d e l (Fig. 4). T h e s u r f a c e area was s y m m e t r i c a l l y d i s t r i b u t e d vertically, with a maximum near the center of the canopy. Cladode surface area per h e i g h t interval d e c r e a s e d t o a p p r o x i m a t e l y zero at t h e t o p o f t h e c a n o p y (1 m ) a n d at g r o u n d level (Fig. 4). As w o u l d be e x p e c t e d f o r essentially v e r t i c a l l y o r i e n t e d surfaces, t h e p r e d i c t e d t o t a l daily P A R p e r u n i t c l a d o d e area was g r e a t e s t at t h e t o p of t h e c a n o p y a n d p r o g r e s s i v e l y d e c r e a s e d t o w a r d t h e g r o u n d as c l a d o d e - c l a d o d e shading increased (Fig. 5). C o m p a r e d to t h e t o p o f t h e c a n o p y , w h e r e t h e average t o t a l daily P A R o n t h e c l a d o d e s j u s t e x c e e d e d 20 m o l m - 2 d-1 at t h e s u m m e r solstice, t h e t o t a l daily P A R was a p p r o x i m a t e l y halved at
153
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Fig. 5. Average total daily PAR incident on cladode surfaces at various canopy heights. Height intervals correspond to those in Fig. 4. Simulations were done for clear days at the indicated times of the year. the 0.1-to-0.2 m height intervals for the summer solstice and the equinox. At t h e w i n t e r s o l s t i c e , w h e n t h e u n i f o r m l y d i s t r i b u t e d d i f f u s e P A R is o f g r e a t e r f r a c t i o n a l i m p o r t a n c e , p r e d i c t e d t o t a l d a i l y P A R was a t t e n u a t e d b y o n l y 36% f r o m t h e t o p t o t h e b o t t o m o f t h e c a n o p y (Fig. 5).
Environmental productivity index and field productivity The various components of the environmental productivity index were d e t e r m i n e d f o r a 1 9 8 0 / 1 9 8 1 p e r i o d f o r w h i c h field d a t a o n t h e N A R o f
154
O. ficus-indica are available. In the field the base cladodes were 0.5 m apart in the east--west direction (the basic " cel l " with the t w o plants having 27 cladodes considered above) and the base cladodes of t w o adjacent plants were 1 m away in the n o r t h - - s o u t h direction, forming a rectangular array of 4 plants. These arrays were repeated at 4 m intervals in the east--west direction and at 5 m intervals in the n o r t h - - s o u t h direction, and so for modeling purposes t w o identical cells each enclosing two of the four plants were similarly spaced at 4 m repeating distances in the east--west direction and at 5 m repeating distances in t he n o r t h - - s o u t h direction. Using the PAR model, the PAR incident on each surface of the 54 cladodes o f the f o u r plants was calculated. A PAR index was then assigned to each surface based on the response of daily net CO2 upt ake to PAR, and an overall PAR index value f or the four plants was det erm i ned (Fig. 6A). This index ranged f r o m a low of 0.15 near the winter solstice to a high of 0.56 near the summer solstice, indicating t hat PAR was varying considerably and indeed limiting the net CO2 upt a ke by O. ficus-indica under field conditions. Attenuation o f total daily PAR on a horizontal surface by clouds t ended to be less during th e s u mm e r (e.g., 20% in November 1980 and 17% in January 1981) i
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Fig. 6. S e a s o n a l p a t t e r n o f c o m p o n e n t e n v i r o n m e n t a l i n d i c e s a n d t h e overall EPI f o r n e t CO 2 u p t a k e . D a t a were c a l c u l a t e d f o r m o n t h l y values o f e n v i r o n m e n t a l p a r a m e t e r s averaged a t a p p r o x i m a t e l y t w o - m o n t h intervals c e n t e r e d o n t h e p o i n t i n d i c a t e d .
155
and greater during the late fall and winter (e.g., 49% in May 1980, 47% in May 1981, and 46% in July 1980). The water status index ranged from 0.70 to 0.98 (Fig. 6B); the relatively high value from November 1980 to February 1981 was a consequence of the three irrigations, since the rainfall in this late spring/summer period was only 27 mm. The least variation occurred in the temperature index, which ranged from 0.80 to 0.98 (Fig. 6C). During essentially the entire observation period, the m o n t h l y minimum nighttime temperatures and hence cladode temperatures were at or below the optimal temperature for net CO2 uptake, e.g., the monthly minimum air temperatures ranged from 1.3°C in July 1981 to 10.0°C in February 1981. The environmental productivity index EPI equals the product of the three individual indices in Fig. 6A--C. EPI (Fig. 6D) times the net daily CO2 uptake under ideal conditions (344 mmol m -2 d -1 ) indicates the net CO2 uptake predicted for field conditions, which can be converted to the units of N A R (g dry weight m -2 stem area d -1) by assuming that the CO2 is converted to carbohydrate. In this way, a predicted N A R can be compared to the NAR measured for O. ficus-indica in the field in the 1980/1981 period (Fig. 7). Although there were differences between predicted and measured NAR, the seasonal pattern was similar, i.e., the lowest values occurred in the winter and the highest in the summer. In the summer (here considered as November--February), the model predicted an average NAR of 5.03 g m -2 d -1 and the measurements yielded 5 . 1 0 g m -2 d -~ (Fig. 7). However, the average N A R for the winter (May--August) for 1980 and 1981 was predicted
it
/I ~l Measured
I
Predicted
I I 0
M
I d
I d
I A
1980
I S
I O
L N
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d
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I M
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1981
Fig. 7. N e t assimilation rate p r e d i c t e d f r o m the e n v i r o n m e n t a l p r o d u c t i v i t y i n d e x and measured in the field. Measured values were means f o r plants i n i t i a l l y 0.5 or 1.5 years old
(differences between two ages averaged 10%; Acevedo et al., 1983 and unpublished observations), which is comparable in age to the 1.5-year-old plants used to develop the PAR model.
156 t o b e 1.46 g m -2 d-1 w h e r e a s t h e m e a s u r e d average was 2 . 7 4 g m - 2 d-1. T h e average p r e d i c t e d N A R f o r J u l y 1 9 8 0 to J u l y 1981 was 3 . 1 6 g m -2 d -~, c o m p a r e d w i t h t h e average m e a s u r e d N A R f o r similarly s p a c e d p l a n t s o f a p p r o x i m a t e l y t h e s a m e size o f 3 . 3 2 g m -2 d- 1 (Fig. 7).
Predicted annual productivity versus stern area index T h e P A R m o d e l was n e x t used to v a r y t h e spacing o f cells and t h e r e b y to g e n e r a t e " f i e l d s " o f O. ficus-indica w i t h d i f f e r e n t s t e m area indices. T h e daily N A R was c a l c u l a t e d as f o r Fig. 7. T h e a n n u a l p r o d u c t i v i t y per u n i t g r o u n d area c o u l d t h e n b e p r e d i c t e d b y i n t e g r a t i n g daily N A R d e t e r m i n e d f o r c o n d i t i o n s a p p r o p r i a t e f o r J u l y 1 9 8 0 t o J u l y 1981 a n d m u l t i p l y i n g b y t h e SAI ( t h e l a t t e r t o c o n v e r t p r o d u c t i v i t y f r o m a s t e m area basis to a g r o u n d area basis). T h e m a x i m u m p r e d i c t e d a n n u a l p r o d u c t i v i t y o f 3.4 kg m - 2 y-1 o c c u r r e d n e a r an SAI o f 7 (Fig. 8). P r o d u c t i v i t y d r o p p e d o f f r a p i d l y at l o w e r SAI's, r e f l e c t i n g l o w e r s t e m areas available f o r CO2 u p t a k e . A t S A I ' s a b o v e 7, p r o d u c t i v i t y p e r u n i t g r o u n d area was r e d u c e d even t h o u g h t h e r e was m o r e s t e m area available (Fig. 8); t h e r e d u c t i o n o c c u r r e d b e c a u s e t h e P A R p e r u n i t s t e m area d e c r e a s e d , leading t o an even greater f r a c t i o n a l d e c r e a s e in n e t CO2 u p t a k e .
Angular dependence of P A R index T o see t h e e f f e c t o f c l a d o d e o r i e n t a t i o n o n P A R i n t e r c e p t i o n a n d h e n c e o n t h e P A R i n d e x f o r n e t CO2 u p t a k e , t h e P A R m o d e l was used to a n a l y s e a h y p o t h e t i c a l flat p l a n t w i t h 13 c l a d o d e s o f t h e s a m e t o t a l a r e a as t h e average f o r t h e t w o p l a n t s in t h e field ( 1 . 2 7 m 2 ; Fig. 3). Such p l a n a r p l a n t s w e r e s p a c e d 2 m a p a r t in r o w s w i t h all o f t h e i r c l a d o d e s vertical a n d aligned along t h e row. R o w s w e r e s p a c e d 0.5 m a p a r t , a n d so t h e s t e m area i n d e x was 1.27. /
6'c
2
t
g g
I
0
2
4
6 8 Slem area index
I0
12
14
Fig. 8. Annual productivity predicted for fields of different stem area indices. SAI's greater than 2.62, a value obtained by placing the cells just enclosing the 27 cladodes on the 2 plants adjacent to each other, were created by stacking such cells on top of each other. NAR data were obtained for time intervals of two months for environmental conditions appropriate for July 1980 to July 1981 (Fig. 7) and then integrated to obtain annual values.
157 ~'~-- 0.5 m - - I ~
/
Fig. 9. H y p o t h e t i c a l p l a n t w i t h all 13 c l a d o d e s in a single, vertical plane. T h e 9 t e r m i n a l c l a d o d e s were 36 c m l o n g ( m a x i m u m w i d t h was h a l f t h e l e n g t h for all t h e cladodes), t h e 3 i n t e r m e d i a t e c l a d o d e s were 40 c m long, a n d t h e base c l a d o d e was 46 c m long w i t h half b e l o w g r o u n d level. T o p a n d base c l a d o d e s are indicated.
PAR indices were calculated for three times of the year (winter solstice, equinox, and summer solstice) for five angles of rotation ranging from 0 ° (plants and hence cladodes facing east--west) to 90 ° (cladodes facing north-south) for both clear days and cloudy days. The total daily PAR calculated by the model for an unshaded horizontal surface was 5 5 . 9 m o l m -~ on the summer solstice, 3 8 . 5 m o l m -2 on the equinox, and 1 6 . 7 m o l m -2 on the winter solstice for the clear days and 19.0, 14.0, and 7 . 5 m o l m -2, respectively, for the cloudy days. For a clear day on the summer solstice, the PAR index averaged for both surfaces of all cladodes decreased nearly fourfold as the plants were rotated from facing east--west to facing north--south (Fig. 10A). A gradual decrease occurred for such rotation on a clear day at the equinox (Fig. 10C), while s u c h rotation from facing east--west to north--south on the winter solstice increased the PAR index about 2-fold (Fig. 10E). Indeed, facing north--south on a clear day at the winter solstice led to a higher PAR index than facing north--south on the summer solstice. For cloudy days represented by isotropic diffuse PAR, the PAR index was independent of direction; it averaged 0.24 on the summer solstice (Fig. 10B), 0.12 on the equinox (Fig. 10D), and only 0.01 on the winter solstice (Fig. 10F). The low value for the winter solstice on cloudy days was a consequence of the low PAR, averaging only 3.8 mol m -2 over the cladode surface, which is essentially the light compensation value for net COs uptake by O. ficus-indica (Nobel and Hartsock, 1983). On both clear and cloudy days at the three times of the year considered, the PAR index for the t o p m o s t central cladode (Fig. 9) was always above the average for the plant and that of the base cladode was always below the average (Fig. 10). The effect of shadows accounts for the increase in PAR index of the base cladode upon rotation of these geometrically regular plants from 0 ° to 22.5 ° at the summer solstice on clear days and its substantial decrease for this rotation on an equinox (Fig. 10A and C).
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Fig. 10. I n f l u e n c e o f angle of r o t a t i o n o f vertical cladodes for plant in Fig. 9 on the P A R index p r e d i c t e d for three different times of the year for clear and c l o u d y days. The solid lines represent the average for all 13 cladodes o f the plant in Fig. 9, the dashed lines are for the t o p cladode, and the d o t t e d lines are for the base cladode. An angle of r o t a t i o n of 0 ° corresponds to facing east-west and 90 ° to facing north-south. DISCUSSION
The PAR model incorporating the trajectory of 5000 equally spaced rays in a rectangular grid proved extremely accurate for calculating the shadows from b o t h geometrically simple and also complex shapes. Using the coordinates at the proximal and distal ends and at the t w o extremes of the width for each of 27 obovate cladodes of Opuntia ficus-indica, a three-dimensional architecture was created that determined which portions of underlying cladodes were in shadow for various times of the day. The direct PAR incident on each surface of each cladode plus the diffuse PAR from the sky and reflected from the ground, including the effects of occlusion by other cladodes, allowed determination of the total PAR intercepted over an entire day. For example, the model showed that the PAR intercepted by the cladodes decreased most rapidly with height near midcanopy, where the greatest cladode surface area per unit height occurred (Fig. 4). From the predicted PAR interception and the influence of total daily PAR on net CO2 uptake by O. ficus-indica (Nobel and Hartsock, 1983, 1984), a PAR index was determined that together with those for water status and temperature (Nobel, 1983) allowed the prediction o f the net assimilation rate of O. ficus-indica under field conditions. The predicted N A R agreed quite favorably with
159 previously measured N A R (Acevedo et al., 1983 and unpublished observations) with respect to seasonal trends and average values. However, the predicted N A R tended to underestimate the measured N A R for the winter. Although measured N A R includes effects of dry matter export to the rest of the plant, which can vary as source--sink relations change, and hence is not entirely equivalent to the predicted NAR, the difference for the winter was apparently related to the temporal PAR distribution, as considered next. The high incidence of cloudiness in late fall and winter at the study site caused the measured m o n t h l y averages of total daily PAR on a horiztonal surface to be only 50 to 60% of the PAR for clear days at that time of the year. This average ambient PAR value is similar to the total daffy PAR predicted for a cloudy day, which has only isotropic diffuse PAR. For instance, at the winter solstice the diffuse PAR on a horizontal surface for a cloudy day averaged 45% of the total PAR for a clear day. Thus, the relation used here for diffuse PAR, which is the one conventionally employed (Monteith, 1973; Goudriaan, 1977; Milthorpe and Moorby, 1979; Castillo and Santibaflez, 1981), caused the PAR model to calculate a very low PAR index similar to that for cloudy conditions (Fig. 8F). In reality, however, the m o n t h l y average of total daily PAR in the winter is composed of a combination of bright days with relatively high PAR plus very overcast days where the PAR is actually lower than for the conventionally modeled uniformly overcast days (unpublished observations). For instance, the mean PAR index averaged over all orientation angles at the winter solstice would be 0.01 for the cloudy days incorporated into the model (Fig. 8F), while the same total m o n t h l y PAR caused by 10 clear days (average PAR index of 0.31, Fig. 8E) and 20 very cloudy days (PAR index of 0.00) would be 0.10. Thus, application of the PAR model to the CAM plant O. ficus-indica should be done using day-by-day values of total daffy PAR at the field site (data that are not available for the periods of interest), not m o n t h l y averages of the daily values. A consequence of using the m o n t h l y average values is the underestimating of the PAR index and hence of the predicted N A R in the winter (Fig. 7), when the cloudiness in central Chile is much greater than in the summer. The above effect of temporal PAR distribution is a consequence of the non-linear response of net CO2 uptake b y cacti to total daily PAR (Nobel, 1977; Nobel and Hartsock, 1983). Specifically, the light compensation point occurs at a total daffy PAR of a b o u t 3.5 mol m - 2 . Net CO2 uptake is slightly negative at PAR < 3 . 5 m o l m -2 but increases approximately linearly with PAR from 3.5 to 2 0 m o l m -2, where it reaches nearly 90% of its maximum. Thus, total daily PAR levels below 3.5 mol m -2 lead to a slight loss of CO2, changes in the range of 3.5 to 20 mol m -2 can have major effects, and values above 20 mol m -2 incident on the cladodes do not increase net CO 2 uptake very much. For clear days near the winter solstice, a small fraction of the surfaces of vertical cladodes are oriented such that they intercept 15 or more tool m -2 (Nobel, 1980, 1982b) and thus have a relatively high net CO2 uptake, which leads to net CO2 uptake by the whole plant (the other surfaces have relatively little positive or negative effect on net CO2 uptake). However,
160 for the uniform diffuse conditions on cloudy days near the winter solstice, all surfaces are near light compensation; hence, the NAR for each cladode surface is near zero and productivity by the plant is then predicted to be negligible. The PAR model allowed variation of the spatial distribution of the plants, including stacking adjacent small plants on top of each other to raise the stem area index. The measured productivity of O. ficus-indica for plants of mean age 5.4 years was 1.32 kg m -2 y-1 for an SAI of 1.44 (Acevedo et al., 1983), similar to the value predicted at this stem area index. The predicted net carbohydrate gain reached a m a x i m u m of 3.4 kg m -2 y-1 at an SAI of 7 (Fig. 8), which is a nearly threefold higher productivity than measured or predicted for various CAM plants (Smith, 1929; Lock, 1962; Bartholomew, 1982; Acevedo et al., 1983; Nobel, 1984). This suggests that closer spacing of the plants should increase the annual carbohydrate gain (closer spacing is possible, as the ground cover determined from a polygon circumscribing the most extreme cladodes on these plants was only 32%), although other considerations, such as ease of harvesting, may be of greater practical concern than maximizing productivity. The PAR model was also used to determine the effect on the PAR index of various cladode orientations at different times of the year. Specific orientations can be created by the planting direction of the original cladodes as well as by suitable pruning of the plants. Moreover, unshaded cladodes of O. ficus-indica have a natural t e n d e n c y to face east--west at the study site in Chile (Nobel, 1982b), consistent with the orientation pattern for 23 species of platyopuntias examined worldwide (Nobel, 1982c). For clear days during the main growing season in late spring/summer, the PAR index averaged 0.71 for an east--west orientation, 0.37 for a north--south orientation, and 0.58 half way between (data represent averages for the summer solstice and an equinox for a planar plant of 13 cladodes; Fig. 10); all orientations had the same PAR index for cloudy days. As would be expected, the PAR index of the base cladode was always below the average for the plant. For larger plants of more realistic (non-planar) shape, shadows would tend to reduce the PAR even further for the base cladode, perhaps to the light compensation point, i.e., this region m a y not be photosynthetically active; indeed corky non-photosynthetic tissue generally forms on the surfaces of such cladodes. The PAR model calculated the total daily PAR on the cladode surfaces which, together with the environmental productivity index, enabled prediction of productivity of O. ficus-indica under both actual field conditions as well as hypothetical arrangements that could enhance productivity. Such predictions can be used to m o d i f y the cultivation practices for this and other platyopuntias, which have received little agronomic attention. Also, the PAR model can be extended to consider other complex arrangements of photosynthetic surfaces in space, especially those with regularly repeating units, such as vineyards and orchards.
161
ACKNOWLEDGEMENTS We g r a t e f u l l y a c k n o w l e d g e Mr. O s c a r C a r r a s c o f o r a s s i s t a n c e w i t h fieldw o r k a n d Mr. Moises E s c a f t f o r t h e use o f his f a r m . F i n a n c i a l s u p p o r t was provided by Comisidn Nacional de Investigacion Cientifica y Tecnoldgica ( C O N I C Y T ) o f Chile g r a n t 1 6 8 / 8 2 , D e p a r t a m e n t o d e D e s a r o l l o C i e n t i f i c o d e la U n i v e r s i d a d d e Chile P r o j e c t A 1 2 1 3 / 8 4 4 4 , U n i t e d S t a t e s D e p a r t m e n t of Energy Contract DE-AM03-76-SF00012, and the Laboratory Director's Office Fund of the UCLA Laboratory of Biomedical and Environmental Sciences.
REFERENCES Acevedo, E., Badilla, I. and Nobel, P.S., 1983. Water relations, diurnal acidity changes, and productivity of a cultivated cactus, Opuntia ficus-indica. Plant Physiol., 72: 775--780. Bartholomew, D.P., 1982. Environmental control of carbon assimilation and dry matter production by pineapple. In: I.P. Ting and M. Gibbs (Editors), Crassulacean Acid Metabolism, American Society of Plant Physiologists, Rockville, MD, pp. 278--294. Castillo, H. and Santibanez, F., 1981. Evaluaci6n de la radiacidn solar global y luminosidad en Chile. I. Calibraci6n de f6rmulas para estimar radiaci6n solar global diaria. Agric. Tecn. (Chile), 41: 145--152. Goudriaan, J., 1977. Crop Micrometeorology: a Simulation Study. Pudoc, Wageningen, 249 pp. Le Houerou, H.N., 1970. North Africa: past, present, future. In: H.E. Dregne (Editor), Arid Lands in Transition, Publication 90. American Association for the Advancement of Science, Washington, DC, pp. 227--278. Lock, G.W., 1962. Sisal: Twenty-Five Years Sisal Research. Longmans, London, 355 pp. Metral, J.J., 1965. Les cactes fourrag6res dans le Nord-Est du Brasil plus particuli6rement dans l'~tat du Cear~. Agron. Trop., 20: 248--261. Milthorpe, F.L. and Moorby, J., 1979. An Introduction to Crop Physiology, 2nd edn. Cambridge University Press, Cambridge, 244 pp. Monteith, J., 1973. Principles of Environmental Physics. Edward Arnold, London, 241 pp. Nobel, P.S., 1976. Water relations and photosynthesis of a desert CAM plant, Agave deserti. Plant Physiol., 58: 576--582. Nobel, P.S., 1977. Water relations and photosynthesis of a barrel cactus, Ferocactus acanthodes, in the Colorado Desert. Oecologia, 27: 117--133. Nobel, P.S., 1980. Interception of photosynthetically active radiation by cacti of different morphology. Oecologia, 45: 160--166. Nobel, P., 1982a. Interaction between morphology, PAR interception, and nocturnal acid accumulation in cacti. In: I.P. Ting and M. Gibbs (Editors), Crassulacean Acid Metabolism, American Society of Plant Physiologists, Rockville, MD, pp. 260--277. Nobel, P.S., 1982b. Orientation, PAR interception, and noctural acidity increases for terminal cladodes of a widely cultivated cactus, Opuntia ficus-indica. Am. J. Bot., 69: 1462--1469. Nobel, P.S., 1982c. Orientation of terminal cladodes of platyopuntias. Bot. Gaz., 143: 219--224. Nobel, P.S., 1984. Productivity of Agave deserti: measurement by dry weight and monthly prediction using physiological responses to environmental parameters. Oecologia, 64: 1--7. Nobel, P.S. and Hartsock, T.L., 1978. Resistance analysis of nocturnal carbon dioxide uptake by a Crassulaceanacid metabolismsucculent, Agave deserti. Plant Physiol., 61: 510--514.
162 Nobel, P.S. and Hartsock, T.L., 1983. Relationships between photosynthetically active radiation, nocturnal acid accumulation, and CO 2 uptake for a Crassulacean acid metabolism plant, Opuntia ficus-indica. Plant Physiol., 71 : 71--75. Nobel, P.S. and Hartsock, T.L., 1984. Physiological responses of Opuntia ficus-indica to growth temperature. Physiol. Plant., 60: 98--105. Refiasco, G., 1976. Cultivo de Tunales. Boletl"n divulgativo 44, Servicio Agricola y Gandero, Santiago, 35 pp. Smith, H.H., 1929. Sisal: Production and Preparation. John Bale and Danielsson, London, 384 pp. Varlet-Grancher, C., Chattier, M., Gosse, G. and Bonhomme, R., 1981. Rayonnement utile pour la photosynth~se des v~g~taux en conditions naturelles: caract~risation et variations. Acta Oecol. Oecol. Plant., 2: 189--202.