The Effects of Climate Variation on Cocoa Farming in Ghana
Lead Research Organisation:
University of Bath
Department Name: Mathematical Sciences
Abstract
For many years, Ordinary Differential Equations have been an essential tool used in the modelling of several physical phenomena. Even though these model produce some reasonable results, it is observed that the models do not take into account the reality of a number of events when being applied. A good example of this is in applying these models to population dynamics- where it can be observed that there are pauses in the population's response to change in the environment.
As such, a more realistic model is sought after to describe many physical events and this has led to the birth of the Delay Differential Equation. A major characteristic that differentiates the Delay Differential Equation from the Ordinary Differential Equation is the inclusion of the delay term that helps to account for the effect of delays in responses. This therefore, makes the equation more suitable for the event which experiences delay or time lag in responses- especially in relation to epidemics, automation, traffic flow and particularly agricultural practices where a time lag can be observed before the yield and harvesting process.
Hence, for the purpose of this research, the Delay Differential Equation will be used to construct a mathematical model to determine the effect of climate variation on cocoa farming in Ghana. In this case, the delay in response can be found in the period of time that the cocoa pods are ripening before harvest.
The objective of this research therefore, is to use the Delay Differential Equation to build a mathematical model- which will be linked with the data on cocoa production and local climate variation. This model will be applied in the context of cocoa production in order to understand the climatic factors that influence the temporal and spatial variation of cocoa production.
This research will be practically applied in a chocolate company which requires a resiliant cocoa supply chain for the future of chocolate production. This research will provide farmers with adequate information about the farming process, location and period which the growing should be implemented to ensure maximum yield during the harvesting phase. This will therefore, lead to sustainability of the crop for continuous industrial use.
As such, a more realistic model is sought after to describe many physical events and this has led to the birth of the Delay Differential Equation. A major characteristic that differentiates the Delay Differential Equation from the Ordinary Differential Equation is the inclusion of the delay term that helps to account for the effect of delays in responses. This therefore, makes the equation more suitable for the event which experiences delay or time lag in responses- especially in relation to epidemics, automation, traffic flow and particularly agricultural practices where a time lag can be observed before the yield and harvesting process.
Hence, for the purpose of this research, the Delay Differential Equation will be used to construct a mathematical model to determine the effect of climate variation on cocoa farming in Ghana. In this case, the delay in response can be found in the period of time that the cocoa pods are ripening before harvest.
The objective of this research therefore, is to use the Delay Differential Equation to build a mathematical model- which will be linked with the data on cocoa production and local climate variation. This model will be applied in the context of cocoa production in order to understand the climatic factors that influence the temporal and spatial variation of cocoa production.
This research will be practically applied in a chocolate company which requires a resiliant cocoa supply chain for the future of chocolate production. This research will provide farmers with adequate information about the farming process, location and period which the growing should be implemented to ensure maximum yield during the harvesting phase. This will therefore, lead to sustainability of the crop for continuous industrial use.
Planned Impact
The impact of the SAMBa CDT will occur principally through the following two pathways:
1. Direct engagement with industrial partners, leading to PhD projects that are collaborative with industry, and that are focussed on topics with direct industrial impact.
2. The production of PhD graduates with
(a) the mathematical, statistical and computational technical skill sets that have been identified as in crucial demand both by EPSRC and by our industrial partners, coupled to
(b) extensive experience of industrial collaboration.
The underlying opportunity that SAMBa provides is to train graduates to have the ability to combine complex models with 'big data'. Such people will be uniquely equipped to deliver impact: whether they continue with academic careers or move directly to posts in industry, through quantitative modelling, they will provide the information that gives UK businesses competitive advantages. Our industrial partners make it clear to us that competitiveness in the energy, manufacturing, service, retail and financial sectors is increasingly dependent on who can best and most quickly analyse the huge datasets made available by the present information revolution.
During their training as part of SAMBa, these students will have already gained experience of industrial collaboration, through their PhD projects and/or the Integrated Think Tanks (ITTs) that we propose, that will give all SAMBa students opportunities to develop these transferable skills. PhD projects that involve industrial collaboration, whether arising from ITTs or not, will themselves deliver economic and social benefits to UK through the private companies and public sector organisations with which SAMBa will collaborate.
We emphasise that Bath is at the forefront of knowledge transfer (KT) activities of the kind needed to translate our research into impact. Our KT agenda has recently been supported by KT Accounts and Impact Acceleration Accounts from EPSRC (£4.9M in total) and a current HEFCE HEIF allocation of £2.4M. Bath is at the forefront of UK activity in KTPs, having completed 150 and currently holding 16 KTP contracts worth around £2.5M.
The SAMBa ITTs are an exciting new mechanism through which we will actively look for opportunities to turn industrial links into research partnerships, supported in the design of these projects by the substantial experience available across the University.
More widely, we envisage impact stemming from a range of other activities within SAMBa:
- We will look to feed the results of projects involving ecological or epidemiological data directly into environmental and public health policy. We have done this successfully many times and have three REF Case Studies describing work of this nature.
- Students will be encouraged to make statistical tools available as open source software. This will promote dissemination of their research results, particularly beyond academia. There is plenty of recent evidence that such packages are taken up and used.
- Students will discuss how to use new media to promote the public understanding of science, for example contributing to projects such as Wikipedia.
- Students will be encouraged to engage in at least one outreach activity. Bath is well known for its varied, and EPSRC-supported, public engagement activities that include Royal Institution Masterclasses, coaching the UK Mathematics Olympiad team, and reaching 50 000 people in ten days with an exhibit at the Royal Society's 350th Anniversary Summer Exhibition in 2010.
1. Direct engagement with industrial partners, leading to PhD projects that are collaborative with industry, and that are focussed on topics with direct industrial impact.
2. The production of PhD graduates with
(a) the mathematical, statistical and computational technical skill sets that have been identified as in crucial demand both by EPSRC and by our industrial partners, coupled to
(b) extensive experience of industrial collaboration.
The underlying opportunity that SAMBa provides is to train graduates to have the ability to combine complex models with 'big data'. Such people will be uniquely equipped to deliver impact: whether they continue with academic careers or move directly to posts in industry, through quantitative modelling, they will provide the information that gives UK businesses competitive advantages. Our industrial partners make it clear to us that competitiveness in the energy, manufacturing, service, retail and financial sectors is increasingly dependent on who can best and most quickly analyse the huge datasets made available by the present information revolution.
During their training as part of SAMBa, these students will have already gained experience of industrial collaboration, through their PhD projects and/or the Integrated Think Tanks (ITTs) that we propose, that will give all SAMBa students opportunities to develop these transferable skills. PhD projects that involve industrial collaboration, whether arising from ITTs or not, will themselves deliver economic and social benefits to UK through the private companies and public sector organisations with which SAMBa will collaborate.
We emphasise that Bath is at the forefront of knowledge transfer (KT) activities of the kind needed to translate our research into impact. Our KT agenda has recently been supported by KT Accounts and Impact Acceleration Accounts from EPSRC (£4.9M in total) and a current HEFCE HEIF allocation of £2.4M. Bath is at the forefront of UK activity in KTPs, having completed 150 and currently holding 16 KTP contracts worth around £2.5M.
The SAMBa ITTs are an exciting new mechanism through which we will actively look for opportunities to turn industrial links into research partnerships, supported in the design of these projects by the substantial experience available across the University.
More widely, we envisage impact stemming from a range of other activities within SAMBa:
- We will look to feed the results of projects involving ecological or epidemiological data directly into environmental and public health policy. We have done this successfully many times and have three REF Case Studies describing work of this nature.
- Students will be encouraged to make statistical tools available as open source software. This will promote dissemination of their research results, particularly beyond academia. There is plenty of recent evidence that such packages are taken up and used.
- Students will discuss how to use new media to promote the public understanding of science, for example contributing to projects such as Wikipedia.
- Students will be encouraged to engage in at least one outreach activity. Bath is well known for its varied, and EPSRC-supported, public engagement activities that include Royal Institution Masterclasses, coaching the UK Mathematics Olympiad team, and reaching 50 000 people in ten days with an exhibit at the Royal Society's 350th Anniversary Summer Exhibition in 2010.
Organisations
People |
ORCID iD |
| Chris Budd (Primary Supervisor) | |
| Oluwatosin BABASOLA (Student) |