Optimal control solutions to sodic soil reclamation

Yair Mau*, Amilcare Porporato

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We study the reclamation process of a sodic soil by irrigation with water amended with calcium cations. In order to explore the entire range of time-dependent strategies, this task is framed as an optimal control problem, where the amendment rate is the control and the total rehabilitation time is the quantity to be minimized. We use a minimalist model of vertically averaged soil salinity and sodicity, in which the main feedback controlling the dynamics is the nonlinear coupling of soil water and exchange complex, given by the Gapon equation. We show that the optimal solution is a bang-bang control strategy, where the amendment rate is discontinuously switched along the process from a maximum value to zero. The solution enables a reduction in remediation time of about 50%, compared with the continuous use of good-quality irrigation water. Because of its general structure, the bang-bang solution is also shown to work for the reclamation of other soil conditions, such as saline-sodic soils. The novelty in our modeling approach is the capability of searching the entire "strategy space" for optimal time-dependent protocols. The optimal solutions found for the minimalist model can be then fine-tuned by experiments and numerical simulations, applicable to realistic conditions that include spatial variability and heterogeneities.

Original languageEnglish
Pages (from-to)37-45
Number of pages9
JournalAdvances in Water Resources
Volume91
DOIs
StatePublished - 1 May 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Ltd.

Keywords

  • Amelioration
  • Irrigation
  • Optimal control
  • Reclamation
  • Rehabilitation
  • Salinity
  • Sodicity

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