Verifying optimality of rainfed agriculture using a stochastic model for drought occurrence

It may be paradoxical but subsistence rainfed agriculture is the predominant source of food in Sub-Saharan Africa where the production uncertainty is associated with the stochastic nature of rainfall. This paper attempts to comprehend the rationale of this situation by a mathematical approach. Consi...

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Bibliographic Details
Published in:Stochastic environmental research and risk assessment 2016-05, Vol.30 (5), p.1503-1514
Main Authors: Sharifi, Erfaneh, Unami, Koichi, Yangyuoru, Macarius, Fujihara, Masayuki
Format: Article
Language:English
Subjects:
Agricultural production
Agriculture
Aquatic Pollution
Chemistry and Earth Sciences
Computational Intelligence
Computer Science
Crops
Drought
Droughts
Earth and Environmental Science
Earth Sciences
Environment
Irrigation water
Math. Appl. in Environmental Science
Mathematical models
Optimal control
Optimization
Original Paper
Physics
Probability Theory and Stochastic Processes
Rainfed farming
Risk assessment
Statistics for Engineering
Stochastic models
Stochastic processes
Stochasticity
Waste Water Technology
Water Management
Water Pollution Control
Water stress
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Summary:It may be paradoxical but subsistence rainfed agriculture is the predominant source of food in Sub-Saharan Africa where the production uncertainty is associated with the stochastic nature of rainfall. This paper attempts to comprehend the rationale of this situation by a mathematical approach. Considering the level of drought severity as the zero-reverting Ornstein–Uhlenbeck process, optimality of rainfed agriculture is investigated in the context of stochastic control theory. Occurrence of drought terminating growth of crops is modelled with the concept of first exit time. A stochastic control problem allowing for virtual cost of irrigation, water stress to crops, and benefits of farming is formulated with irrigation effort as the control variable. The Hamilton–Jacobi–Bellman equation governing the optimal control is studied to identify the set of cost functions optimizing rainfed agriculture in an inverse problem approach. Data and information were collected in the coastal savanna agro-ecological zone of Ghana, to identify model parameters, formulate the stochastic control problem, solve the inverse problem, and then verify optimality of rainfed agriculture. The results indicated that rainfed agriculture is not optimal when the crop is more tolerant to water stress.
ISSN:1436-3240
1436-3259
DOI:10.1007/s00477-015-1129-y