Computational Models Growth & Development

1D light models as accurate are as 3D at estimating dry matter

Researchers compare trade-offs between simplicity and accuracy when modelling greenhouse cucumber canopies.
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Light changes with the angle of the sun.  It bounces off clouds and leaves and scatters, reducing its intensity. A gradient is created as it penetrates the depth of the canopy. Leaf light interception is critical to determining plant productivity through computational modelling, but it is not simple to describe in detail.

There are two approaches to simulating light-plant interactions. One-dimensional (1D) light models are simple and robust tools for estimating light interception of homogeneous canopies. In the most simplified model, light comes from a single overhead source; solar angle is not considered. Light extinction through the canopy is incorporated in this model.

More complex tree-dimensional (3D) models make it possible to capture feedbacks between canopy architecture and light environment. These models capture solar angle changes throughout the day and multiple sources of diffuse light. They incorporate light rays that interact with 3D virtual canopies, reflecting off plant surfaces and diffusing as it moves through the canopy. With this complexity comes an increase in computational requirements and analytical intractability that restrict customization.

In a new article published in in silico Plants, Yi-Chen Pao of Leibniz Universität Hannover and her coauthors examine the trade-offs between simplicity and accuracy of methods by simulating light-plant interaction and its influence on long-term leaf-level photosynthetic acclimation and plant-level dry matter accumulation. The authors compared two methods: a 1D light model and a 3D ray tracing model within an existing dynamic model of greenhouse cucumber, constructed in a 3D modelling platform called GroIMP (see figure 1).

Diagram of 1D and 3D model data flow of the dynamic plant model of greenhouse cucumber.

First, the authors needed to collect the input values to run the models. Most of these were collected experimentally. Cucumber plants were grown in greenhouses for model evaluation. Light interception, biomass partitioning, photosynthesis, and plant architecture were measured. Additional measurements for model input were photosynthetically active radiation, temperature, nitrogen supply, and relative humidity in the greenhouse.

One value required to simulate light-plant interaction is light extinction coefficient k, which depicts how much light penetrates through the canopy and how it decreases towards the ground. k varies depending on solar position, leaf angle, and clumping, as well as canopy development and configuration. While the value of k needed to be input into the 1D model, the 3D model is able to compute the values of k in silico.

Determining the variation of k experimentally through the season as canopy leaf area increases can be difficult. To determine how much error would be introduced into the simulation using an incorrect k value, the authors tested how sensitive the 1D model predictions were to the k value used. Simulation of the 1D model were run using different constant value for k. The output was highly dependent upon k – a difference of 0.2 in k resulted in up to 27% loss in accuracy for shoot dry matter (see figure 2).

Effect of light extinction coefficient k
Effect of light extinction coefficient k on accuracy of predicting plant dry matter for the 1D model.

To overcome this obstacle, the authors used the 3D light model to simulate artificial scenarios of canopy configurations to estimate k for use in the 1D light model.

The authors then ran the two models and compared their predictive accuracies. They found that the shoot dry matter and photosynthetic estimates using both the 1D and 3D model were comparable to measured data (see figure 3).

Model evaluation by comparing simulated shoot dry matter from 1D and 3D models to measured data obtained in experiments.
Model evaluation by comparing simulated shoot dry matter from 1D and 3D models to measured data obtained in experiments.

According to Pao, “these results suggested that, with the assistance of the 3D plant structure and light model, the 1D light model was able to provide efficient estimations and predictions for agronomic purposes with reduced the computational demand.”


Yi-Chen Pao, Katrin Kahlen, Tsu-Wei Chen, Dirk Wiechers, Hartmut Stützel, How does structure matter? Comparison of canopy photosynthesis using one- and three-dimensional light models: a case study using greenhouse cucumber canopies, in silico Plants, 2021; diab031,

This manuscript is part of in silico Plant’s Functional Structural Plant Model special issue.

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