Agricultural Water Management 137 (2014) 68–74 Contents lists available at ScienceDirect Agricultural Water Management jou rn al hom epage: www.elsevier.com/locat e/agwat A proposed method to determine yield response factors of different crops under deficit irrigation using inverse formulation approach N.K. Garg a,∗ , Sushmita M. Dadhich b a Department of Civil Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India b Division of Agricultural Engineering, Sher-e-Kashmir University of Agricultural Sciences and Technology-Jammu, Srinagar 180009, Jammu & Kashmir, India a r t i c l e i n f o Article history: Received 15 September 2013 Accepted 7 February 2014 Available online 5 March 2014 Keywords: Deficit irrigation Crop yield response factor Additive approach Multiplicative approach a b s t r a c t Yield response factors of a given crop can be determined following the FAO approach (Doorenbos and Kas- sam, 1979. Yield response to water. FAO Irrigation and Drainage Paper no. 33. Rome, Italy, pp. 1–40) either by applying deficit irrigation throughout the whole growing period, or at one stage of the crop growth while maintaining full irrigation at the other stages. In this study, an inverse formulation methodology is proposed to determine the stage wise yield response factors (modified k yi values) for eight crops in the Lower Indus Basin. The proposed inverse formulation was based on the multiplicative (Jensen, 1968. Water consumption by agricultural plants. Chapter 1. In: T.T. Kozlowski (Ed.) Water Deficits and Plant Growth Vol. II (pp 1–22). Academic Press, New York) and additive (Stewart et al., 1977. Determination and utilization of water production functions for principal California crops. W-67 California Contributory Project, University of California) approaches to determine yield response factors. To illustrate the appli- cability of the proposed inverse formulation, the widely used seasonal k y values of FAO Irrigation and Drainage Paper No 33 (Doorenbos and Kassam, 1979. Yield response to water. FAO Irrigation and Drainage Paper no. 33. Rome, Italy, pp. 1–40) were used to generate a data set of yields and evapotranspirations for the crops under study after applying theoretical levels of deficit irrigation at different growth stages using climatic and soil data of the Lower Indus Basin. This data set was then used to estimate the modified k yi values separately for the additive and the multiplicative approaches from the inverse formulations. Mod- ified k yi values were found to be different for additive and multiplicative approaches but there was a good agreement between the relative yield reductions using modified k yi values and seasonal k y values. How- ever, there was a complete mismatch between relative yield reductions using FAO 33 stage wise k yi values and using FAO 33 seasonal k y values. Modified k yi values, based on the proposed inverse formulation, may be more representative by taking into account the effects of deficit irrigation on crop production. © 2014 Elsevier B.V. All rights reserved. 1. Introduction The world population is increasing day by day and it is pro- jected to reach 8.9 billion by 2050 (World Population, 2004). The main effect of the projected population would be an increase in the demand for food and it would further raise immense demand on limited water resources. Therefore, water management has become an important aspect of irrigated crop production. It is a big challenge to produce more food with less water and deficit irrigation can be considered as a possible alternative in this regard. Deficit irrigation has been prac- ticed in different parts of the world (English, 1990; English and ∗ Corresponding author. Tel.: +91 9868486296; fax: +91 11 2658 1117. E-mail addresses: nkgarg123@yahoo.com, nkgarg@civil.iitd.ac.in (N.K. Garg), sushmita.iitd@gmail.com (S.M. Dadhich). Raja, 1996; Pandey et al., 2000; Fabeiro et al., 2001; Oktem et al., 2003; Karam et al., 2005; Girona and Mata, 2005; Zhang et al., 2004; Payero et al., 2006; Igbadun et al., 2007; Bekele and Tilahun, 2007; Ali et al., 2007). It is the practice of deliberately under irrigat- ing crops to reduce water consumption while minimizing adverse effects of extreme water stress on yield (Dag’delen et al., 2006). The resulting yield reduction may be small compared with the benefits gained through diverting the saved water to irrigate other crops for which water would normally be insufficient under traditional irrigation practices (Kirda, 2000). The adoption of deficit irrigation requires knowledge on the response of the different crops to water stress applied at vari- ous growth stages. Reduction in yield due to water stress can be expressed by a curve, drawn between the relative yield reduc- tion and the relative evapotranspiration reduction. The slope of this curve is known as crop yield response factor. Deficit irrigation applied at a given stage of the crop growth determines the http://dx.doi.org/10.1016/j.agwat.2014.02.008 0378-3774/© 2014 Elsevier B.V. All rights reserved.