Crop Growth

This is the first of four conversation Gudrun had during the
British Applied Mathematics Colloquium which took place 5th – 8th
of April 2016 in Oxford.


Josie Dodd finished her Master's in Mathematical and Numerical
Modelling of the Atmosphere and Oceans at the University of
Reading. In her PhD project she is working in the Mathematical
Biology Group inside the Department of Mathematics and Statistics
in Reading. In this group she develops models that describe plant
and canopy growth of the Bambara Groundnut - especially the plant
interaction when grown as part of a crop. The project is
interdisciplinary and interaction with biologists is encouraged
by the funding entity.


Why is this project so interesting? In general, the experimental
effort to understand crop growth is very costly and takes a lot
of time. So it is a great benefit to have cheaper and faster
computer experiments. The project studies the Bambara Groundnut
since it is a candidate for adding to our food supply in the
future. It is an remarkably robust crop, draught tolerant and
nitrogent inriching, which means the production of yield does not
depend on fertilizer. The typical plant grows 150 days per year.
The study will find results for which verfication and paramater
estimations from actual green house data is available. On the
other hand, all experience on the modelling side will be
transferable to other plants up to a certain degree. The
construction of the mathematical model includes finding equations
which are simple enough but cover the main processes as well as
numerical schemes which solve them effectively.


At the moment, temperature and solar radiation are the main input
to the model. In the future, it should include rain as well.
Another important parameter is the placement of the plants -
especially in asking for arrangements which maximize the yield.
Analyzing the available data from the experimental partners leads
to three nonlinear ODEs for each plant. Also, the leave
production has a Gaussian distribution relationship with time and
temperature. The results then enter the biomass equation. The
growth process of the plant is characterized by a change of the
rate of change over time. This is a property of the plant that
leads to nonlinearity in the equations.


Nevertheless, the model has to stay as simple as possible, while
firstly, bridging the gap to complicated and more precise models,
and secondly, staying interpretable to make people able to use it
and understand its behaviour as non-mathematicians. This is the
main group for which the models should be a useful tool.


So far, the model for interaction with neighbouring plants is the
computational more costly part, where - of course - geometric
consideration of overlapping have to enter the model. Though it
does not yet consider many plants (since green house sized
experimental data are available) the model scales well to a big
number of plants due to its inherent symmetries. Since at the
moment the optimizaition of the arrangements of plants has a
priority - a lot of standardization and simplifying assumptions
are applied. So for the future more parameters such as the input
of water should be included, and it would be nice to have more
scales. Such additional scales would be to include the roots
system or other biological processes inside the plant.


Of course, the green house is well controlled and available field
data are less precise due to the difficulty of measurements in
the field.


During her work on the project and as a tutor Josie Dodd found
out that she really likes to do computer programming. Since it is
so applicable to many things theses skills open a lot of doors.
Therefore, she would encourage everybody to give it a try.
Literature and additional material

Crops for the Future website

Asha Sajeewani Karunaratne: Modelling the response of Bambara
groundnut (Vigna subterranea (L.) Verdc) for abiotic stress, PhD
thesis, University of Nottingham (2009).

A.S. Karunaratne e.a.: Modelling the canopy development of
bambara groundnut, Agricultural and Forest Meteorology 150, (7–8)
2010, 1007–1015.