Veterinary Science Collected Works - Theses
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ItemSome calculations of potential photosynthetic yield( 1979)Detailed calculations of light relations and seasonal potential photosynthesis are carried out for models of leaf canopies of closed trellis orchard design, with the object of comparing the effectiveness of light capture and usage in canopies of various fork angles and various values of leaf area index. It is assumed that all canopies have adequate water, carbon dioxide and nutrients, a condition satisfied in practical orchards. After examination of a very simple model, a detailed model is set up to take full account of direct sunlight, diffuse skylight and light scattered diffusely by foliage. Irradiance at leaf surfaces of various orientations is calculated from first principles, since in a canopy whose geometry is not independent of azimuth there is no straightforward way of assessing diffuse irradiance. An analytical expression is derived for rate of photosynthesis averaged over sunlit leaves randomly oriented in azimuth at any given isotropic diffuse irradiance. The calculated field of photosynthetically active radiation is used to estimate canopy net photosynthesis during the fruit-filling season for peach orchards. In such canopies the foliage-scattered diffuse light is found to make a relatively small contribution (about 10 percent) to net canopy photosynthesis. It is found that for any given value of leaf area index the seasonal potential photosynthesis, whether net or gross, increases as canopy fork angle increases, in the range of angles from 40 degrees to 180 degrees. The estimated absolute harvest yield of peaches in a 60 degree canopy is found to be lower than the mean value of published measured yields by about one standard deviation. Reasons for this are discussed. The low estimated yield does not affect the validity of theoretical comparison between the various canopies. One of several possible causes of an underestimate of potential photosynthesis is neglect of penumbral effects. A theoretical framework is developed for estimation of the error introduced in photosynthesis calculations by the assumption that incident direct solar radiation is a perfectly parallel beam of light. The calculations of Miller and Norman (1971) on distribution of direct sunlight flux density along transects in sunflecks are discussed. The present theory is developed in terms of probabilities of irradiation by full sun and by partially shaded sun and the probability of umbra at any level in a leaf canopy. Analytical expressions are derived for probability density with respect to fraction of the full sun radiant flux density for partial shading by a straight edge, a circular disk, and a thin strip. It is shown that solar limb darkening may be neglected for the present purpose. The geometry of umbra and penumbra due to crossed shading edges is discussed and quantified. The developed theory is applied to hypothetical canopies of randomly dispersed horizontal circular leaves and to randomly oriented and dispersed vertical leaves. A parameter called the characteristic leaf area index is introduced; this parameter, which includes foliage density and leaf dimensions, may be used in assessing the error in estimated canopy photosynthesis due to neglect of penumbra. Application of the theory to the effects of vertical distribution of foliage on canopy photosynthesis is briefly discussed. The underestimate of potential canopy photosynthesis in a peach tree canopy due to neglect of penumbra is found to be of order 5 percent.