Cases with relatively high ground cover fractions and uniformly arranged plants showed good agreement between the 1D and 3D models regardless of whether the assumption of leaf isotropy was made. As the canopies became more heterogeneous in space, agreement between the models generally declined. Although Potato-Uniform and Potato-Row had identical leaf area indices and leaf angle distributions, the regular distribution of plants within the canopy in Potato Uniform resulted in better agreement between the 1D and 3D models compared to Potato-Row. Despite all cases having highly anisotropic leaf inclination distributions, the assumption of leaf anisotropy had relatively small impact for all cases except for the Grape E-W case. Any effects of heterogeneity or anisotropy tended to decrease as the day of year became further away from the summer solstice. Toward the end of the year , the 1D and 3D models were in fairly good agreement for all canopy cases.The diurnal flux of radiation intercepted by the canopy for an hourly time step on Julian day 153 is shown in Fig. 2.6, plastic gardening pots with corresponding fractions of total radiation intercepted by the canopy shown in Fig. 2.7. The fraction of total radiation intercepted on Julian day 253 and 305 are shown in Figs. 2.8 and 2.9, respectively.
For the homogeneous canopy cases, the assumptions of vegetation homogeneity and isotropy were closely satisfied, and therefore, the 1D model was in very good agreement with the 3D model regardless of leaf density . For the crop canopy cases, the 1D model consistently over estimated light interception as compared to the 3D model, except for Grape E-W and Potato-Row on Julian day 305. For all but the grape cases, eliminating the isotropic assumption resulted in little improvement of agreement between the 1D and 3D models, indicating that errors arose primarily from heterogeneity in these cases. For the Grape N-S, Almond, and Potato cases, errors between the 1D and 3D models were largest near midday when sunlight could most readily reach the ground by penetrating through gaps in vegetation. For Grape E-W, the largest discrepancies occurred at early and late times of the day. The effect of row orientation on diurnal interception patterns for the grape cases was dramatic, as this completely changed the character of interception at different times of the year . The potato cases also illustrated the pronounced effect of heterogeneity in planting pattern on diurnal interception patterns.Figure 2.10 depicts vertical profiles of the absorbed radiation flux at 8:00, 10:00, and 12:00 hours on Julian day 153 for Grape N-S, Grape E-W, Almond, and Corn. Errors in absorbed fluxes for Grape N-S were relatively consistent with height, where errors at a given height were most closely related to the magnitude of the absorbed flux at that height. This was also roughly the case for Almond, except that there was the potential for some under estimation of absorption in the lower canopy when the 1D model was used, which was most pronounced for larger solar zenith angles.
For Grape E-W, the 1D model tended to shift the peak in the absorbed flux deeper into the canopy, which was most pronounced for larger solar zenith angles. In the corn canopy, the vertical pattern in radiation interception differed significantly between the 1D and 3D models. There were up to 50% differences between 1D and 3D fluxes at a given vertical level, with irregular patterns of over or under estimation. In the lower canopy, there was a peak in absorption in the 3D model, which was largely absent in the 1D model, leading to under prediction of absorption by the 1D model in the lower canopy. This is likely due to the substantial over prediction of absorption by the 1D model in the upper canopy, which removes the necessary energy needed to produce a secondary peak in absorption in the lower canopy.If leaf azimuth is uniformly distributed, this effectively reduces the impact of anisotropy in leaf inclination on the projected area fraction G. Since a leaf with a certain elevation angle could be parallel to the sun at one azimuth and perpendicular to the sun at another, an integration over all azimuths can smear out the effects of leaf inclination alone. As in the virtual canopies of this study, field measurements have shown that leaf inclination distributions are usually highly anisotropic. The azimuthal distribution of leaves may be strongly anisotropic within a single plant, but for relatively dense canopies, the azimuthal distribution is often fairly isotropic. In these cases, the assumption of leaf isotropy is likely to result in minimal errors. However, sparse, row-oriented crops such as vineyards may have highly anisotropic azimuthal distributions, in which case it may be necessary to explicitly calculate G based on measurements.
These types of canopies are becoming increasingly prevalent in agricultural applications, due in part to the improved access to mechanical harvesters that a trellised or hedgerow canopy provides.Plant spacing and the resulting heterogeneity had the most pronounced effect on errors resulting from the use of Beer’s law. For the Grape N-S case, the assumption of heterogeneity resulted in an overestimation of the total daily absorbed radiation by 28%, 30%, and 36% on Julian days153, 232, and 305, respectively, with larger instantaneous over estimation near midday. For the Grape E-W case, the assumption of heterogeneity also resulted in overestimating the total daily absorbed radiation by 74%, 51%, and 5% on Julian days 153, 232, and 305, respectively. This was not simply an effect related to L, as was illustrated by the two potato cases. By simply rearranging the potato plants from a uniformly spaced into a row-oriented configuration, errors in the 1D model increased substantially. It is possible that the effect of horizontal heterogeneity can vary in the vertical direction, which appeared to be the case with the Corn canopy. This significantly altered the performance of the 1D model at any given height, although the canopy was dense enough overall that the 1D model performed well when predicting whole-canopy radiation absorption. This could have important implications if the radiation model is coupled with other biophysical models such as a photosynthesis model. The response of photosynthesis to light is nonlinear and asymptotic, so although whole-canopy absorption may be well-represented in some cases by a 1D horizontally homogeneous model, it is unclear if that will result in significant errors in total photosynthetic production given the non-linearity of its response to light. A limitation of this study is that results are only applicable under clear sky conditions. However, results can provide some insight regarding diffuse sky conditions by simultaneously considering all canopy geometries and simulated sun angles. Under a uniformly overcast sky, equal energy originates from all directions. A particular combination of sun angle and leaf orientation bias was required in order to observe a pronounced effect of leaf anisotropy. Thus, for diffuse solar conditions, it is speculated that the impact of leaf anisotropy will be decreased. Sun angle had an important effect on the instantaneous impact of leaf heterogeneity, blueberry pot size and most commonly it was observed that low sun angles resulted in a decreased impact of heterogeneity. Therefore, it is likely that highly diffuse conditions will reduce the impact of heterogeneity near midday because a significant fraction of incoming radiation will originate from directions nearer to the horizon. Estimating light interception with Beer’s law is based on the assumption that canopies are homogeneous. This inherently means that the rate of radiation attenuation along a given path is linearly related to the flux at that location. As the canopy becomes sparse, there are pathways for radiation propagation that allow radiation to penetrate the entire canopy without any probability of interception, which fundamentally violates the assumptions behind Beer’s law or a turbid medium. Therefore, the non-random leaf dispersion in canopies limits the ability of Beer’s law to link light interception to simple bulk measures of plant architecture.
It is well-known that this heterogeneity or “clumping” of vegetation usually results in decreased radiation interception as compared with an equivalent homogeneous canopy. A common means of dealing with this problem without significantly increasing model complexity is to add a “clumping coefficient” W to the argument of the exponential function in Beer’s law. While this is a simple and practical means of reducing the amount of radiation attenuation predicted by Beer’s law, the challenge in applying the clumping coefficient approach is that W is a complex function of nearly every applicable variable, and thus is it is difficult to mechanistically specify. Another approach is to use a model that explicitly resolves plant-level heterogeneity, as it may not be necessary to explicitly resolve every leaf if within-plant heterogeneity is small.Row orientation played an important role when estimating light interception from Beer’s law, particularly when the rows were widely spaced. For sparse, row-oriented canopies, the effective path length of the sun’s rays through vegetation can change dramatically with changes in sun azimuth. For East-West rows, absorption is significantly reduced early and late in the day because the rows are close to parallel with the sun’s rays, whereas North-South rows are perpendicular to the sun at this time. As the day of year progresses further from the summer solstice, the sun spends more time closer to the horizon and thus the impact of heterogeneity in an East-West row orientation increased. For the East-West row configuration, G and light interception were surprisingly constant throughout much of the day, which resulted in 41% and 36% less absorption on Julian days 153 and 232, respectively, compared to North-South rows. In some climates, it may be desirable to maximize sunlight interception, whereas in others it may be desirable to mitigate effects of excess sunlight to reduce temperatures and water use.Despite the simplified assumptions in Beer’s law regarding scattering, there was good agreement between predicted radiation interception using the 1D and 3D models in the PAR band. Scattering did not significantly influence light interception in this band because most of the incident radiation received by individual leaves was absorbed. However, in the NIR band, scattering introduced significant over estimation of absorption using the standard 1D model, since leaves are poor absorbers in this band. Using an ad hoc correction to account for reflection only reduced this over estimation of absorption. An additional correction to account for both reflection and transmission resulted in over correction, and a net under prediction of total radiation absorption.The objective of this work was to evaluate common assumptions used in estimating radiation absorption in plant canopies, namely assumptions of homogeneity or isotropy of vegetation. Our results demonstrated that for relatively dense canopies with azimuthally symmetric leaves, a 1D model that assumes homogeneity and isotropy of vegetation generally produced relatively small errors. As plant spacing became large, the assumptions of homogeneity break down and model errors became large. In the case of a vineyard with rows oriented in the East-West direction, errors in daily intercepted radiation were up to ⇠ 70% due to heterogeneity alone, with much larger instantaneous errors occurring during the day. If leaves were highly anisotropic in the azimuthal direction, there was also the potential for large errors resulting from the assumption of vegetation isotropy which had the potential to increase errors above 100%. Day of year had an impact on model errors, which was that overall errors tended to decline with time from the summer solstice. In cases of canopies where the plant spacing starts to approach the plant height, it is likely necessary to use a plant-resolving radiation model in order to avoid substantial over prediction of absorbed radiative fluxes. Additionally, if vegetation is highly anisotropic in terms of both elevation and azimuthal angle distributions, it is also likely necessary to explicitly calculate the projected area fraction G based on measurements and the instantaneous position of the sun.Recent shifts in climatic patterns have influenced the frequency, timing, and severity of heat waves in many wine grape growing regions, which has introduced challenges for viticulturists. Growing the same varieties under these altered climatic conditions often requires mitigation strategies, but quantitative, generalized understanding of the impacts of such strategies can be difficult or time consuming to determine through field trials. This work developed and validated a detailed three-dimensional model of grape berry temperature that could fully resolve spatial and temporal heterogeneity in berry temperature, and ultimately predict the impacts of potential high berry temperature mitigation strategies such as the use of alternative trellis systems.