Light exchanges in discrete directions as an alternative to raytracing and radiosity

Abstract

Introduction
Light modelling at the scale of organs is essential to account accurately for the complex interactions between biophysical processes such as photosynthesis, stomatal conductance and energy balance. Yet, the calculation of radiative exchanges at fine scales is computationally-intensive and it remains a hindrance to a widespread use of FSPMs despite advances in light modelling using either radiosity (Chelle and Andrieu, 1998) or raytracing (Bailey, 2018). This study shows that simplifications based on the discretization of radiative fluxes allow processing radiative exchanges in a natural environment while maintaining good accuracy on the simulation of biophysical processes such as carbon assimilation.

Material and Methods
The present study is based on biophysical simulations performed using the ARCHIMED model. Incident radiation is depicted as a set of specular fluxes (i.e. parallel rays) in discrete directions using the sun direction for direct radiation and predefined “turtle” directions for the diffuse radiation. The “turtle” directions are obtained by splitting the sky hemisphere into sectors of equal solid angle (Dauzat et al, 2001). Optionally, direct radiation can be distributed in neighboring "turtle" sectors (turtle only). For each direction, the scene is projected on an image plane and the interception of incident light is deduced from rasterized pixel projections. Additionally, Z-Buffering gives the overlay of scene objects and, in this regard, pixels can be viewed as rays traced from outside down to the ground level. Light scattering can thus be processed similarly to raytracing. In the case of Lambertian objects, we further assume that all rays scattered by an object carry the same energy whatever the “turtle” direction. Net assimilation (An) is calculated with Farquhar’s model (Farquhar et al. 1980), stomatal conductance with Medlyn’s model (Medlyn et al. 2011) and the leaf temperature is found by solving the energy balance of the system.
Simulations are run on a dense three-dimensional scene including two palms (Elaeis guineensis) with the following configuration: latitude= 15°, Day of year 71, time steps of 30mn, clearness index Kt= 0.5. A “toricity” option is used to generate a virtually infinite canopy. The number of “turtle” directions is set to 6, 16, 46 or 136. The sun position is either integrated into the turtle or separately computed. The pixel density ranges from 341 to 6821 pixels m-2. The reference outputs are obtained with the highest number of directions and pixels.
* Scene metrics: plot= 15.9m*9.2m, meshes= 24 863, triangles= 571 934, LAI= 3.2, leaflets= 24 493

Results and Discussions
Figure 1 (left) illustrates the effect of the number of discrete light directions on the estimation of biophysical processes in comparison with the reference of 136 directions. Sampling the sun direction provides best results since direct radiation largely contributes to the PAR irradiance, the energy load of leaflets and, finally, their assimilation. Bias remain low when the sun direction is not sampled except when the number of “turtle” directions is decreased to six. The dispersion of residuals remains quite limited for 46 directions, meaning that reliable values can be obtained at leaflet scale for such configuration.
Figure 1 (right) shows that a low pixel density (682 pixels m-2, i.e. 50 000 pixels) is sufficient to get a relatively unbiased estimation of carbon assimilation at plot level, but a higher density is necessary to get reliable estimation at leaflet scale.

The reference configuration in the left pane of Fig. 1 generates 68.5M rays for each time step and, since several hits are recorded per ray (6 on average) this generates about 5 sub-rays that are used for the calculation of light scattering.
Running the complete simulation with the reference configuration from the right pane of Fig. 1 lasts ~3.4 min for each time step (23M rays). This time can be decreased to only 2 seconds per step by storing partial scene illumination for each direction, but this preliminary step can be time-consuming, mainly during the multiple scattering for the PAR and NIR ranges. A considerable shortening is expected by treating light exchanges using directional form factors between pairs of objects instead of propagating scattered light by individual rays.

Conclusion
Using discrete ordinates allows performing accurate and unbiased simulations of light interception. Biases arise when decreasing the number of directions but with limited consequences on carbon assimilation. Larger biases occur when pixel density is too low to sample correctly individual leaflets. A configuration with 46 turtle directions for depicting both direct and diffuse radiation and a pixel density of 682 pixels m-2 allows fast computations while providing sufficient information to get precise light budget at fine scales.

References
Bailey, 2018, Ecological Modelling. 368:233-245, doi: 10.1016/j.ecolmodel.2017.11.022.
Chelle and Andrieu, 1998, Ecological Modelling 111:75-91, doi: 10.1016/S0304-3800(98)00100-8
Dauzat et al., 2001, Agric. & Forest Met. 109(2)143-160, doi: 10.1016/S0168-1923(01)00236-2
Farquhar et al., 1980, Planta. 149:78-90, doi: 10.1007/BF00386231
Medlyn et al., 2011, Global Change Biology. 17:2134-2144, doi: 10.1111/j.1365-2486.2010.02375.x

Full text

Light exchanges in discrete directions as an alternative to raytracing and radiosity
Light budget in 3D plant stands under natural conditions
Irradiance in PAR and NIR at scale of individual scene items (e.g. leaves , soil patches…)
Calculation of temperature, carbon assimilation and transpiration for each leaf
Shortens computations in comparison to ray-tracing or radiosity
Does not require high computer memory
This allows repetitive simulations for monitoring evolution of eco-
physiological variables over time or for performing response curves over
physical and physiological variables
Rémi Vezy1, Raphaël Perez2, François Grand1, Jean Dauzat1
Strength of the approach
Running a single simulation with 46 directions and 1 million of pixels
per direction lasts about 3.4 min with the sole use of CPU
This duration can be decreased to only 2 seconds for subsequent
simulations after storing the scene illumination for each direction
Weakness
Very small items are poorly sampled compared to big ones
Aim and
Scope
For a given direction
Rasterized projection of items
Each pixel equivalent to a ray
Several hits along a ray obtained with Z-
buffer
Interception of incident light by uppermost
objects
Scattering calculated between pairs of items
Interception
proportional to
number of hits
Principle of discretization
Light interception and scattering in
discrete “turtle” directions
Direct radiation
•interception calculated either in sun
direction or distributed in turtle sectors
Diffuse light split into directional fluxes
compliantly with “turtle model”
Incident solar radiation
Scene
Two palms (Elaeis guineensis)
Toricity option
24 863 meshes, 571 934
triangles, 24 493 leaflets, LAI=
3.2
Simulation runs
Infinite canopy with “toricity” option
Rays pathway are stored and used as
long the scene is not modified
The “toricity” option generates an
infinite canopy by virtually duplicating
the scene
Tips and tricks
Results
1) CIRAD, UMR AMAP, F‐34398 Montpellier, France.AMAP, Univ Montpellier, CIRAD, CNRS, INRAE, IRD, Montpellier, France
2) CIRAD, UMR AGAP, F-34398 Montpellier, France. AGAP, Univ Montpellier, CIRAD, INRAE, Montpellier SupAgro, Montpellier, France
Sum intercepted energy for all mesh
facets of the item
Distribute scattered energy to rays
Transfer energy to other items
along the rays pathway
Light scattered by a Lambertian item
is proportional to its apparent area
which is approximated by the
number of hits
Energy transfer
Example of “turtle” with
46 directions
Sun course Direct and
diffuse radiation
Error (%) for An, PAR and Energy relatively for experiments A and B. The reference is 136 directions + sun for A and 1 million pixels for B
Experiment A
•Best results are obtained with the option
turtle only= false (blue). In this case, the
turtle directions are only used for
calculating diffuse and scattered light
•When using the option turtle only= true,
(red) the % error increases for small
numbers of turtle directions (6 or 16)
and the biases becomes important
Experiments
Exp.A (0.5 M pixels in all cases)
6, 16, 46 or 136 turtle directions
plus sun direction when option
“turtle only” = false
Ex. B (46 directions)
50 000 pixels to 1 million pixels
Implementation
Java; ARCHIMED software
Experiment B
•The % error increases when
decreasing the number of
pixels
•Biases remain small as long
as the number of pixels is >
500 000 (i.e. 342 pixels per
m2
Computer
6 cores, Intel Xeon W2133
3.60 GHz, RAM 32Go
Conclusion
FSPM2020, 5-9 October 2020
Bailey, 2018, Ecological Modelling. 368:233-245, doi: 10.1016/j.ecolmodel.2017.11.022.
Chelle and Andrieu, 1998, Ecological Modelling 111:75-91, doi: 10.1016/S0304-3800(98)00100-8
Dauzat et al., 2001, Agric. & Forest Met. 109(2)143-160, doi: 10.1016/S0168-1923(01)00236-2
Yin et al, Remote Sensing of Environment 135 (2013) 213–223
https://archimed-platform.github.io/archimed-phys-user-doc/