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 CORTAZAR 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 inter- ception 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 ficus- indica. 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 produc- tivity 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 known about their productivity. One of the most *Author for correspondence and reprint requests. 0168-1923/85/$ 03.30 © 1985 Elsevier Science Publishers B.V.