Skip to main content
SpringerLink
Log in

Probability Analysis of Crop Water Stress Index: An Application of Double Bounded Density Function (DB-CDF)

  • Published:
Water Resources Management Aims and scope Submit manuscript

Abstract

Soil moisture is an uncertain variable due to rainfall randomness. Furthermore, its density function is hybrid in nature, with spikes at maximum and minimum soil moisture (saturation and field capacity). Both of these properties are also considered for crop water stress index. The crop water stress index can be used to show the sensitivity of a crop to deficit irrigation. In this paper, a new methodology is proposed to probability analysis of water stress index using Double Bounded Density Function (DB-CDF) and moment analysis of crop water stress index. For this purpose, two equations were developed for the first and second moments of water stress index. To find out the value of the proposed moment equations, they are used as constraints in a stochastic model of crop water allocation as developed previously by Ganji and Shekarrizfard (Water Resour Manage 25:547–561, 2010). After verification of the model, the DB-CDF of soil moisture stress index was estimated using the value of proposed moments in the growing periods. The results show that in case of deficit irrigation, the probability of crop water stress occurrence is high and as a consequence, any unpredictable water shortage leads to yield reduction. The application of the proposed methodology is novel and has not been reported in the literature to date.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Alizadeh H, Mousavi SJ (2013) Coupled stochastic soil moisture simulation-optimization model of deficit irrigation. Water Resour Res, Accepted Article

  • Brumbelow K (2005) Stochastic net profit-water functions: assessing changes in irrigation needs and farm profits to public policy and climate variability. World Water and Env Resour Congress, Anchorage

    Google Scholar 

  • Chen JY, Tang CY, Sakura Y, Kondoh A, Shen YJ, Song XF (2004) Measurement and analysis of the redistribution of soil moisture and solutes in a maize field in the lower reaches of the Yellow River. Hydrol Process 18:2263–2273

    Article  Google Scholar 

  • English MJ (1981) The uncertainty of crop models in irrigation optimization. Trans ASAE 24(4):917–921

    Google Scholar 

  • English M, James L, Chen CF (1990) Deficit irrigation II: observation in Columbia Basin. J Irrig Drain Eng 116:413–426

    Article  Google Scholar 

  • Fereres E, Soriano MA (2007) Deficit irrigation for reducing agricultural water use. Special issue on integrated approaches to sustain and improve plant production under drought stress. J Exp Bot 58:147–159

    Article  Google Scholar 

  • Fletcher SG, Ponnambalam K (1996) Estimation of the reservoir yield and storage distribution using the moment analysis. J Hydrol 182:259–275

    Article  Google Scholar 

  • Ganji A, Shekarrizfard M (2010) A modified constrained state formulation of soil moisture for stochastic irrigation scheduling. Water Resour Manag 25:547–561

    Article  Google Scholar 

  • Ganji A, Shekarrizfard M (2012) A simple model of fuzzy irrigation depth control: an application of an intelligent state dropping (ISD) mechanism. Irrig Drain 61(5):596–603

    Article  Google Scholar 

  • Ganji A, Ponnambalam K, Khalili D, Karamouz M (2006a) A new stochastic optimization model for deficit irrigation. Irrig Sci J 25(1):63–73

    Article  Google Scholar 

  • Ganji A, Ponnambalam K, Khalili D, Karamouz M (2006b) Grain yield reliability analysis with crop water demand uncertainty. Stoch Env Res Risk A 20(4):259–277

    Article  Google Scholar 

  • Geerts S, Raes D (2009) Deficit irrigation as an on-farm strategy to maximize crop water productivity in dry areas. Agric Water Manag 96:1275–1284

    Article  Google Scholar 

  • Geerts S, Raes D, Garcia M, Condori O, Mamani J, Miranda R, Cusicanqui J, Taboada C, Vacher J (2008) Could deficit irrigation be a sustainable practice for quinoa (Chenopodium quinoaWilld.) in the Southern Bolivian Altiplano? Agric Water Manag 95:909–917

    Article  Google Scholar 

  • Heermann DF, Wallender WW, Bos M (1990) Irrigation scheduling. In: Martin DL, Stegman EC, Fereres E (eds) ASAE. pp 149–175

  • Kang S, Zhang L, Liang Y, Hu X, Cai H, Gu B (2002) Effects of limited irrigation on yield and water use efficiency of winter wheat in the Loess Plateau of China. Agric Water Manag 55:203–216

    Article  Google Scholar 

  • Kipkorir EC, Raes D (2002) Transformation of yield response factor into Jensen’s sensitivity index. Irrig Drain Syst 16:47–52

    Article  Google Scholar 

  • Kloss S, Pushpalatha R, Kamoyo KJ, Schütze N (2012) Evaluation of crop models for simulating and optimizing deficit irrigation systems in arid and semi-arid countries under climate variability. Water Resour Manag 26(4):997–1014

    Article  Google Scholar 

  • Kumaraswamy P (1980) A generalized probability density function for double-bounded random processes. J Hydrol 46:79–88

    Article  Google Scholar 

  • Laio F, Porporato A, Fernandez-Illescas CP, Rodriguez-Iturbe I (2001) Plants in water-controlled ecosystems: active role in hydrological processes and response to water stress IV. Discussion of real cases. Adv Water Resour 24(7):745–762

    Article  Google Scholar 

  • Mannocchi F, Mecarelli P (1994) Optimization analysis of deficit irrigation systems. J Irrig Drain Eng 120:484–502

    Article  Google Scholar 

  • Paul S, Danda SN, Nagesh Kumar D (2000) Optimal irrigation: a multilevel approach. J Irrig Drain Eng 126(3):149–154

    Article  Google Scholar 

  • Porporato A, Laio F, Ridolfi L, Rodriguez-Iturbe I (2001) Plants in water-controlled ecosystems: active role in hydrological processes and response to water stress III. Vegetation water stress. Adv Water Resour 24(7):725–744

    Article  Google Scholar 

  • Ramirez JA, Bras RL (1985) Conditional distribution of Neyman-Scott models for storm arrivals and their use in irrigation scheduling. Water Resour Res 21(3):317–330

    Article  Google Scholar 

  • Regulwar DG, Gurav JB (2011). Irrigation planning under uncertainty—a multi objective fuzzy linear programming approach. 25(5):1387–1416

  • Rodriguez-Iturbe I, Porporato A, Ridolfi L, Isham V, Cox D (1999) Probabilistic modelling of water balance at a point: the role of climate, soil and vegetation. Proc Roy Soc Lond Ser A Math Phys Eng Sci 455:3789–3805

    Article  Google Scholar 

  • Sunantara J, Ramfrez J (1997) Optimal stochastic multicrop and inteaseasonal irrigation control. Water Resour Plan Manag 123(1):39–48

    Article  Google Scholar 

  • Tsakiris GP (1982) A method for applying crop sensitivity factors in irrigation scheduling. Agric Water Manag 5:335–343

    Article  Google Scholar 

  • Vico G, Porporato A (2013) Probabilistic description of crop development and irrigation water requirements with stochastic rainfall. Water Resour Res 49(3):1466–1482

    Article  Google Scholar 

  • Yoo C, Kim S, Juan Valdes B (2005) Sensitivity of soil moisture field evolution to rainfall forcing. Hydrol Process 19:1855–1869

    Article  Google Scholar 

  • Zhang H, Oweis T (1999) Water-yield relations and optimal irrigation scheduling of wheat in the Mediterranean region. Agric Water Manag 38:195–211

    Article  Google Scholar 

  • Zhang X, Pei D, Chen S (2004) Root growth and soil water utilization of winter wheat in the North China Plain. Hydrol Process 18:2275–2287

    Article  Google Scholar 

  • Zhang WH, Wei CF, Zhou J (2010) Optimal allocation of rainfall in the Sichuan Basin, Southwest China Zhang. Water Resour Manag 24(15):4529–4549

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département des Sciences de la Terre et de l’Atmosphère, Université du Québec à Montréal, Montréal, QC, Canada

    Arman Ganji

  2. College of Agriculture, Shiraz University, Shiraz, Iran

    Sara Kaviani

Authors
  1. Arman Ganji
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sara Kaviani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arman Ganji.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ganji, A., Kaviani, S. Probability Analysis of Crop Water Stress Index: An Application of Double Bounded Density Function (DB-CDF). Water Resour Manage 27, 3791–3802 (2013). https://doi.org/10.1007/s11269-013-0381-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11269-013-0381-5

Keywords

Search

Navigation