Modelling the greenhouse environment and the growth of cucumbers (Cucumis sativus L.) : a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Agricultural Engineering at Massey University
Mathematical models which describe the greenhouse environment, and the
growth of a crop of cucumbers, in that environment, have be en developed and
tested. The models have been used to predict: the response of the
greenhouse to varying weather conditions, the growth of the crop leaf
canopy, and the weight and number of fruit harvested
The greenhouse environment has been modelled using a system of non-linear
differential equations, derived from a consideration of the energy and mass
balances of the glazing, internal structure, crop canopy, root media,
fl oor, deep soil layers, and the greenhouse air space. The equations have
been solved for five minute time steps, using measured values of outside
weather conditions and control inputs as boundary values.
Entry of solar radiation into the greenhouse, and absorption by various
surfaces, has been determined using transmission tables generated using a
"ray-tracing" light transmission model. The light transmission model has
been calibrated in a separate experiment. The incoming solar radiation has
been partitioned between diffuse, direct, photosynthetically active and
near infra-red radiation, for use in the crop model.
Validation experiments have been performed to test the greenhouse
environment simulation model. The results of the validation exercise showed
that the model was capable of predicting the temperatures in the
greenhouse, within a few degrees. The mean errors were smaller for the crop
canopy, root medium, and floor, than for the glazing or air temperature.
Prediction errors for relative humidity and carbon dioxide concentration
were more variable.
An existing model of cucumber development rate, and leaf expansion, has
been modified and validated. This gave good results when adequate account
was taken of leaf senescense, and initiation of lateral growths.
Sub-models for photosynthesis, respiration, and assimilate partitioning
have been develope d , and c ombined with the greenhouse environment and leaf
expansion models. The combined model has been used to predict the course of
growth of a cucumber crop over one growing season, and the number and
weight of fruit harvested. The predictions have been compared to results
from a test crop. This revealed that while the total number of fruit
harvested was accurately predicted, the total weight of harvested fruit was
The models are intended to be used in the s tudy of optimal control of the