于强的BLOG

Basic knowledge for mathematicians

Background

Photosynthetic rate (Pn) is determined by light, temperature, atmospheric CO2, leaf water and nutrients. It can be calculated using a set of equations with input of these variables.

The models

There are lots of photosynthesis models, in which biochemical model can be responsive to climatic variables and is sound in mechanism. The model includes,

(1)    Light response (e.g., non-rectangle equation); and

(2)    Temperature, CO2, water and nutrient response of parameters in light response equations.

The model calculation

(1)    Static model

The photosynthesis model is normally static, which means no dynamic (time-related) process in the model. The Pn is only functions of light, temperature, CO2 etc at the same time. We do not intend to use differential equations.

(2)     Model input

The calculation of Pn will need model parameters, and input variables, such as light, temperature, and CO2.

The data and model validation

(1)    We have data of light and CO2 response for different plant species, and will have data of temperature response;

(2)     Method for model validation can be based on comparison between simulated and measured photosynthetic rate. Least square method can be used.

The questions

The main challenge to develop (improve) photosynthesis model is the non-linear response of Pn to temperature, and water, which can result in errors in simulation. That will need us to improve the model, to validate the model and to apply the model to predict climate change impact on plant photosynthesis. We may simplify the question by assuming amply water supply. We may have questions as follows,

(1)    How to optimise model parameters from observation data for a model?

(2)    How to evaluate model soundness in its simulation using parameter optimisation tools (e.g., Lingo)?

(3)    How to require photosynthesis observation according to model parameterisation?