Simplifying a complex computer model: Sensitivity analysis and metamodelling of an 3D individual-based crop-weed canopy model

Abstract

Complex biological models such as mechanistic research models often need to extend their current use to a broader audience. Simplification and faster simulations would increase their use. Here, a step-by-step methodology was developed and applied to partially metamodel, hence accelerate, the mechanistic model FlorSys. This is a process-based, multiannual and multispecies model ("virtual field") which simulates crop growth and weed dynamics and allows users to assess cropping systems for crop production and biodiversity. The model is relatively slow, which makes it difficult to test numerous and diverse cropping systems needed to identify those reconciling crop production and biodiversity. Here, we (1) identified the slowest submodel of FlorSys, i.e. the 3D voxelized light interception submodel, (2) identified and applied a relevant methodology to metamodel this submodel in the simplest situation, i.e. we predicted light interception and absorption directly at the scale of the plant instead of the voxel for a single plant in a field, and (3) extrapolated the method to more complex situations, i.e. a plant in diverse and heterogeneous crop:weed canopies, (4) replaced the original process-based FlorSys submodel by the metamodels, which required additional equations and decision rules, (5) evaluated the metamodelled FlorSys with independent field observations, showing an adequate prediction quality combined with an increased speed at fine-grained scale since the metamodelled version was 28 times faster than the process-based version. For steps 2 and 3, we used the global sensitivity method based on a truncated Legendre polynomial chaos expansion (PCE) whose coefficients were estimated by Partial Least Squares (PLS) regression to simultaneously (i) rank inputs with respect to their polynomial and total effects on outputs via the so-called PCE-PLS sensitivity indices, and (ii) provide metamodels predicting light interception and absorption at the plant level. These metamodels were then shortened into parsimonious metamodels via a LASSO-PLS method. The study showed that there was a trade-off between speed gain due to the metamodelled 3D light submodel and the speed loss due to the additional functions for neighbourhood effects. The metamodelled version is best used for testing complex systems where plant location must be modelled precisley (e.g., precision agriculture, intercropping with precision sowing) whereas the voxelized version with a large voxel size is better for simpler cropping systems. The present step-by-step process may be helpful for investigating and speeding up other complex simulation models with interacting objects/agents. It notably uses a hybrid approach, using a process-based (albeit simplified) approach for the most sensitive plant stage (newly emerged tiny plants) and separate sampling plans and metamodels to ensure that the more sensitive stages/components are adequately covered (small plants).