A new three-dimensional energy balance model for complex plant canopy geometries: Model development and improved validation strategies

Abstract

Canopy microclimate is a critical component of most biophysical processes in plants. Understanding the role of microclimate across scales in canopies with complex, heterogeneous architectures is challenging, as it is difficult to represent the relevant range of scales. In this study, a model was developed and validated to accurately predict the three-dimensional distribution of microclimate-related quantities (e.g., net radiation, surface temperature, evapotranspiration, flux partitioning) in complex canopy geometries. The modeling strategy was to aggregate individual leaves into isothermal sub-volumes, as resolving all leaves over whole-canopy scales is unfeasible. The model takes leaf-level models for convection, evapotranspiration, and radiative absorption/emission and integrates them over a discrete volume using the leaf angle probability distribution function. The model is built on a framework designed to utilize graphics processing units (GPUs) in order to offset the expense associated with model complexity, which can allow for the simulation of canopy-scale problems at sub-tree resolution. Additional cost-saving strategies are also suggested. Three-dimensional canopy energy transfer models have traditionally been difficult to validate. Two validation experiments were designed to simultaneously measure virtually all model outputs, often using multiple methods at many spatial locations. The model was able to reproduce point, 3D distributed, and bulk measurements at high accuracy, with average model errors within expected measurement errors. living on or within plant tissues. These processes can have high sensitivity to 4 leaf temperature, as temperature differences of only a degree can have critical 5 implications on physiological function (Jones, 2004). 6 Leaf temperature can vary dramatically over short spatial distances due to 7 step changes in radiation interception. In dense, closed canopies, radiative fluxes 8 are relatively homogeneous in horizontal directions, which results in average 9 temperature distributions that are primarily one-dimensional (Monteith and 10 Unsworth, 2008). Many canopy energy models have been successfully developed 11 which treat the canopy as a single 'big leaf ' (e.g., Sinclair et al., 1976; Sellers 12 et al., 1996), or several layers of big leaves (e.g., Leuning et al., 1995; Dai et al., 13 2004). However, in heterogeneous landscapes (e.g., urban canopies, savannas), 14 temperature can vary in the horizontal direction by 10 • C or more within a 15 single tree crown (Tyree and Wilmot, 1990). This necessitates a fully three-16 dimensional (3D) description of leaf temperature in these types of canopies. 17Modeling 3D canopy microclimate presents several challenges, the foremost 18 of which is accurately predicting net radiation fluxes, as radiation drives leaf 19 temperature. As a result, leaf temperature is very sensitive to errors in pre-20 dicted net radiation. During the day, radiative fluxes are usually very large, 21 and dominate the leaf energy balance....

The evolution and sensitivity of katabatic flow dynamics to external influences through the evening transition

“…The ground heat flux, H G , is computed as the sum of the heat flux estimated at a depth of 50 mm from the vertical temperature gradient, computed from T G at the surface, 50 and 250 mm, and the storage term estimated from the temporal temperature gradient evaluated at 50 mm (Eq. A.2 in Bailey et al , ). The latent heat flux ( H L ) is then calculated using the FAO Penman–Monteith equation (Eq.…”

HydroShoot: a functional-structural plant model for simulating hydraulic structure, gas and energy exchange dynamics of complex plant canopies under water deficit - application to grapevine (Vitis vinifera L.)

“…(e.g. Dauzat et al, 2001;Bailey et al, 2016;Ngao et al, 2017). It is hence unclear in literature how the simulation of leaf water status of individual leaves affects the predicted gas-exchange rates and leaf temperature distribution in FSPMs under water deficit and this matter needs to be assessed if FSPMs are to be used under water deficit conditions.…”

“…In addition, longwave energy exchange among leaves from the one hand, and between leaves and the surrounding elements from the other hand, were disregarded, which makes the application of this model to open field conditions not suitable since sky and soil longwave energies substantially affect leaves temperature (Nobel, 2005). This has been solved in two models that link a complete energy budget with gas-exchange in perennials (Bailey et al, 2016 for Vitis vinifera L. and Acer x fremanii; Ngao et al, 2017 for Malus pumila Mill.) Yet again, both models were built at the leaf-cluster scale which does not allow accounting for the location of individual leaves in plant hydraulic structure necessary to calculate local leaf water status.…”

A reverse ray-tracing method for modelling the net radiative flux in leaf-resolving plant canopy simulations

“…Using forward methods to model emission in the case of small geometric elements presents similar problems when modelling shortwave radiation, although they may be more severe in the case of emission. Bailey et al (2016) noted that using a forward tracing method with very small elements resulted in significant sampling errors unless a very large number of rays were used, which could result in substantial errors in the modeled net radiative flux. When coupled with the energy balance equation, it was also noted that very large errors in temperature could result, which led to problematic violations of the second law of thermodynamics.…”