Modeling Carbon and Leaf Area Allocation in Plant Canopies Using Optimization.

Modeling the distribution of carbon among leaves in plant canopies is important in order to accurately simulate light interception, growth, and nutrient requirements.   However, many explanatory crop models simulate whole organ classes instead of individual organs.  For example, many models simulate all leaves and stems in a plant canopy by using a single big leaf and big stem approach that aggregates all carbon (C) and leaf area together.  This approach greatly simplifies simulation of light interception, daily growth rate, and carbon partitioning among roots, stems, leaves, and reproductive organs, but may not adequately simulate dynamic responses to nutrient and water stress and effects of global warming and elevated atmospheric carbon dioxide concentration (CO2).   The USDA-ARS has developed mathematical subroutines to simulate appearance, growth, and gas exchange of individual leaves in various plant canopies.  However, due to the ability of leaves to export and import photosynthate, it is difficult to accurately simulate the distribution of carbon and incremental increases in leaf area among each leaf using traditional partitioning coefficients.  An alternate approach is to use an optimization algorithm where C is distributed among plant leaves in order to maximize a specific objective function, such as light interception or photosynthetic rate.   Such a strategy was tested using a model-based predictive control approach configured to optimally allocate C among leaves so as to maximize photosynthetic rate over the next 24 hour period.  The Nelder-Nead method was used to find local solutions to the resulting optimization problem.  Simulated results were compared with experimental data from controlled environment studies with potato.  Effects of varying controller output horizons and model parameters were evaluated.