These results highlighted the need to use a 3D radiation model to account for complex canopies because these models can represent the vertical and horizontal variability in the canopy and its effect on light interception accurately. Chapter 3 develops a 3D model that can accurately resolve spatial and temporal heterogeneity in berry temperature. The spatially-explicit nature of the model allows for robust representation of varying canopy architectures and their effect on berry temperature. The high model complexity is afforded by performing calculations in parallel on the computer’s graphic processing unit . This ability to resolve the geometry of the vineyard is critical in this particular study because it means the model is robust to changes in row spacing, trellis system, row height, etc. To generate data for validation of the 3D grape berry temperature model, field and laboratory experiments were conducted. Validation results demonstrated that by accurately representing the 3D vine structure, the model was able to closely replicate measured spatial and temporal fluctuations in berry temperature. Chapter 4 aims to explore whether elevated berry temperature can be mitigated by designing and managing vineyards in a way that effectively creates a favorable microclimate for berry development. Identifying strategies that have the potential to reduce elevated temperatures in a warming climate is of great interest to grape growers. However, raspberry container growing given the extremely large number of interacting variables that determine berry temperature it is not feasible to independently vary all of these parameters in field experiments. Thus, to study the interactions between these variables that might yield favorable results, Chapter 4 expands the model developed and validated in Chapter 3 by incorporating the effects of shade cloth on berry temperature.
The model was used to ultimately predict the efficacy of potential mitigation strategies for high berry temperature. The results of this study provided new insights into the effect of fruit zone shading to control berry temperature for the establishment of new vineyards and targeting the management of existing vineyards.Light interception in plant canopies is most commonly estimated using a simple one dimensional turbid medium model . Inherent in this class of models are assumptions that vegetation is uniformly distributed in space and in many cases that vegetation orientation is uniformly distributed . It is known that these assumptions are violated in a wide range of canopies, as real canopies commonly have heterogeneity at multiple scales and almost always have highly anisotropic leaf angle distributions. However, it is not quantitatively known under what conditions these assumptions become problematic given the difficulty of robustly evaluating model results for a range of canopy architectures. In this study, assumptions of vegetation homogeneity and isotropy were evaluated under clear sky conditions for a range of virtually-generated crop canopies with the aid of a detailed three-dimensional, leaf-resolving radiation model. Results showed that Beer’s law consistently over predicted light interception for all canopy configurations. For canopies where the plant spacing was comparable to the plant height, Beer’s law performed poorly, and over predicted daily intercepted sunlight by up to 115%. For vegetation with a highly anisotropic leaf inclination distribution but a relatively isotropic leaf azimuth distribution, the assumption of canopy isotropy resulted in relatively small errors. However, if leaf elevation and azimuth were both highly anisotropic, the assumption of canopy isotropy could introduce significant errors depending on the orientation of the azimuthal anisotropy with respect to the sun’s path.
Solar radiation is a primary driver of most plant biophysical processes, including energy transfer, turbulent transport, evapotranspiration, photosynthesis, and phenology. Fluxes of absorbed radiation in plant canopies have strong gradients in the vertical direction, and potentially in horizontal directions in the case of heterogeneous canopies. Capturing these high gradients through direct measurement is often challenging, and therefore models are frequently used to predict absorbed radiative flux distributions. For practical purposes, relatively simple models are frequently used to estimate light interception in plant canopies. For example, crop models have become important tools for studying agricultural system, yet they commonly utilize relatively simple models for light interception given the frequent lack of detailed architectural inputs. The most commonly used approach for estimating light interception treats the canopy as a homogeneous medium of unresolved vegetation , which allows for the use of a simple exponential model for radiation attenuation commonly know as Beer’s law, Beer-Lambert law, or Beer-Lambert-Bouguer law. Beer’s law calculates the probability of radiation interception as an exponentially increasing function of the leaf area projected in the direction of radiation propagation and the distance travelled through the canopy.The form of Beer’s law given in Eq. 2.1 functions under two main assumptions. The first assumption is that leaves are randomly distributed both vertically and horizontally in a continuous medium where leaves are relatively small. The second assumption is that leaves absorb all incident radiation, which may be reasonable for photosynthetically active radiation bands where leaves absorb roughly 90% of incident radiation, but is likely a poor assumption in other bands such as the near-infrared where absorption is low.
Equation 2.1 also requires specification of G, which is most commonly set to be equal to 0.5 based on the assumption that leaves are isotropic. Leaf area density typically varies sharply in the vertical direction. Many natural plant canopies have considerable horizontal heterogeneity such as savannas, or heterogeneity due to natural or man-made disturbances. Crop canopies also commonly have a sparse, row-oriented configuration that creates high heterogeneity in light interception. Furthermore, it is rare to find canopies with isotropic leaf angle distributions, as this is typically not the most efficient configuration for light interception. Despite the known limitations of Beer’s law in the above cases, it is still frequently applied in these systems due to its simple, tractable form. However, there is a general lack of quantitative understanding of the errors resulting from the application of these simplified models in various canopy architectures, primarily because it is difficult to quantify light interception from field measurements for a range of architectures. The objective of this study is to better understand and quantify errors in modeled radiation absorption under assumptions of vegetation heterogene-ity or isotropy for various canopy configurations. The authors’ hypothesis is that Beer’s law will perform well for relatively dense, closed canopies provided that G is specified appropriately. For sparse canopies, it is hypothesized that assumptions of vegetation homogeneity will result in significant model errors, thus necessitating a more complicated model. Since accurately measuring the distribution of absorbed radiation in space and time is often unfeasible using traditional experimental approaches, we used a sophisticated 3D radiation model along with virtually-generated canopies to evaluate Beer’s law under different simplifying assumptions. Virtual canopies with varying levels of heterogeneity, sparseness, and leaf orientation distributions were generated to evaluate assumptions of vegetation homogeneity or isotropy in terms of absorption of direct solar radiation. A considerable advantage of using virtually generated canopies is that the input parameters in Eq. 2.1 can be calculated exactly from the virtual canopies. When combined with a detailed 3D radiation model, this resulted in a robust means for evaluating the performance of simplified models for a range of canopy architectures.For simulating plant light interactions, blueberry plant pot detailed 3D geometric models were used to describe the architecture of the canopy. Agricultural crops were chosen for the plant types because: many 3D models are readily available, they have sufficient yet regular heterogeneity that limited the degrees of freedom when generating the canopies, and they represent an economically important practical application of the use of Beer’s law. The chosen crop canopies were grape, almond, potato, and corn, which were represented in the 3D model using a mesh of rectangular and triangular elements.
To minimize the number of elements needed to describe their complex geometries, images with a transparency channel could be overlaid on these basic elements, where the transparency channel is used to remove a portion of the element’s surface. Virtually-generated plants were either read from a polygon file , or created using the procedural plant generator described by Weber and Penn .Parameters used to quantify canopy architecture are given in Table 2.1. The procedural model used to generate the grape and almond plants had a random component to each architectural parameter, making each plant unique. Each corn and potato plant was identical, therefore a random azimuthal rotation was applied to each plant to decrease regularity of the canopy. Plants were placed in a marked row structure to form a canopy. Two grape canopy cases were considered: one with a North-South row orientation and one with an East-West row orientation . Two potato canopies were considered in which plants were arranged in either a East-West row-oriented pattern , or a uniformly spaced planting pattern . In all cases, the size of the 3D scene was chosen such that further increasing the total number of plants did not have an impact on results. To test the model in the case of homogeneous and isotropic vegetation, a set of canopies were created with uniformly distributed leaves in space with three different leaf area index values: L =1.5, which consisted of 100,000 leaves; L =3.1, which consisted of 200,000 leaves; and L =6.2, which consisted of 400,000 leaves. The surface area of each leaf was 0.006 m2. Each leaf angle was set by randomly drawing from a spherical distribution. To characterize the plant geometry, L and the leaf inclination angle probability density function were calculated for all five generated canopies, and the leaf azimuthal angle PDF was calculated for the Grape N-S and Grape E-W cases . The L was calculated by summing the one-sided area of all leaves in the canopy and dividing by the total canopy footprint area. The leaf inclination angle and leaf azimuthal angle were calculated for each of the elements from the surface normal of the leaf, and a PDF was formed by weighting each element’s contribution to the PDF by its surface area, then normalizing such that the PDF integrates to unity. The corn model had predominantly vertically oriented leaves, while the almond and potato models had leaves closer to horizontal on average . Grape leaf inclination skewed toward vertical, and leaf azimuth tended to be oriented parallel with the row , which is supported by previous manual and LiDAR measurements. The gap fraction was calculated from the 3D models by computing the fraction of direct sunlight not intercepted when qs = 0 . Gap fraction values ranged from 80% in the grape canopy cases down to 21% for the corn canopy case. Although both potato canopy cases had the same L, their gap fractions were 22% for uniformly spaced plants and 36% for row-oriented plants.The incoming radiation data used to drive the radiation absorption simulations in this study was generated following the REST-2 model of Gueymard. The hourly incoming radiation was calculated based on the assumed virtual site longitude , latitude , offset from UTC , atmospheric pressure , air temperature near ground level , atmospheric turbidity coefficient , relative humidity , and Julian day of the year . It is noted that the precipitable water in the REST-2 model was specified using the model of Viswanadham. The direction of the sun for any time of day at the virtual site was calculated following the approach outlined by Iqbal. In cases where scattering was included, two radiative bands were considered – one character-istic of efficient absorption by leaves such as the photo synthetically active band , and another characteristic of high scattering such as the solar near-infrared band . The total incoming solar flux was partitioned as 47% in the PAR band and 53% in the NIR band. In the PAR band, r was set to 0.056 and t to 0.042, while in the NIR band, r was set to 0.425 and t to 0.334.Results for the daily total light interception on Julian days 153, 232, and 305 are listed in Table 2.2, and shown graphically in Fig. 2.5. For the homogeneous canopy cases, very close agreement was found between the 1D and 3D models regardless of L, which indicated that the approach used to compare the 1D and 3D models was consistent and that leaf-scale heterogeneity created by discrete leaf surfaces did not create significant errors.