Synthesis of an optimal radiation model of plant growth according to the criterion of the minimum of integral solar radiation transmitted to the soil

Abstract

Relevance. Based on satellite remote sensing data, it has been suggested that there is a linear relationship between NDVI and FPAR. However, the significant influence of seasonal factors of a particular ecosystem on this relationship creates uncertainty in the assessment of plant productivity by remote sensing. This uncertainty in the estimates of total grown products (GPP) by the indicator calculated as the ratio of GPP to photosynthetically active radiation absorbed by vegetation can be explained by daily changes in incoming optical radiation both in composition and magnitude. It is shown that the GPP indicator can be determined indirectly by calculating the extremum of the heat flow of the soil coming from the outside.

Methods. A new approach to the synthesis of the optimal radiation regime of plant growth based on the methodology of optimization of isomorphic-holonomic systems is proposed. The basis of the proposed method for the synthesis of the radiation regime of plant growth is taking into account the total radiation coming from above to the crown of the plant, the peculiarity of this approach is to find a minimum of that part of the externally incoming photosynthetically active radiation that reaches the soil and is not spent on photosynthesis, provided that the production of the initially specified product is guaranteed. The optimization problem of achieving an extreme value of the total radiation coming from outside into the soil is formulated in the form of an unconditional variational optimization problem with a common target optimization functional. An approximate solution of the optimization problem is given, in which the target functional reaches a minimum, i.e. the maximum amount of external radiation is spent on the photosynthesis process.

Results. A solution is obtained at which the target functional reaches a minimum, i.e. the maximum amount of external radiation is spent on the photosynthesis process. It is shown that the application of the known method of unconditional variational optimization with a guaranteed given value of GPP allows us to determine the optimal radiation regime of plant growth.