A model development approach to ensure identifiability of a simple mass balance model for photosynthesis and respiration in a plant growth chamber

A model development approach, which aims to build sufficiently simple models so as to ensure parameter identifiability, is presented and used to develop a dynamic mass balance model of photosynthesis and respiration reactions. The model was developed for the control of a highly automated plant growth chamber within the context of the MELiSSA project, a European Space Agency program which aims to develop technology for a future regenerative life support system. Simple, identifiable models are required for this application and are also valuable for other prediction and control applications, which could include the operation of greenhouses or other controlled environment agricultural systems in the future. Experiments were conducted on lettuce (Lactuca sativa cv. Lively) and red beet (Beta vulgaris cv. Detroit Medium Red) in sealed environment plant growth chambers. Environmental variables (including CO2 uptake data) were recorded throughout growth, while biomass and leaf area measurements were taken before transfer to the chamber and at harvest. The model development approach was iterative, with assessments of model reliability throughout. Major metabolic reactions with respect to plant growth were first selected and corresponding mass balance equations were written, taking structural identifiability into account. The kinetic model was selected, from several potential rate laws, based on an analysis of the fit of the model (on identification and independent validation datasets) and the reliability of the parameter estimates (practical identifiability). The application of this systematic model development approach yielded a very simple model of plant growth in which all parameters were identifiable based on the available experimental data (a unique value could be identified for each). The approach could be applied to many other crop modelling problems to obtain simple, identifiable and reliable models.