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

Erfaneh Sharifi, Koichi Unami, Macarius Yangyuoru, Masayuki Fujihara

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1503-1514
Number of pages12
JournalStochastic Environmental Research and Risk Assessment
Volume30
Issue number5
DOIs
Publication statusPublished - 1 May 2016

Keywords

  • Drought
  • Hamilton–Jacobi–Bellman equation
  • Inverse problem
  • Minor rainy season
  • Rainfed agriculture
  • Zero-reverting Ornstein–Uhlenbeck process

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