Evapotranspiration estimation by inverse soil water flow modelling


Crop evapotranspiration (ETc) and crop coefficient (Kc) estimation are important in irrigation scheduling. Evapotranspiration estimation is mostly done by Penman–Montieth method. Though Penman–Montieth method is adopted for drip irrigation, there are possibilities of uncertainty due to the non-availability of experimentally verified crop factor values. Hence the estimation of ETc directly in fields by installing soil moisture sensors is becoming one of the reliable methods. In the present work, soil moisture sensors were installed for paddy crop under drip irrigation. Richards’ equation was used to represent the unsaturated flow in the root zone and a model namely Inverse Soil Water Flow Model (ISWFM) was developed. The average daily ETc and Kc for paddy were estimated using the model. The crop coefficient for drip irrigated Paddy estimated using ISWFM results were higher by 7–20% compared to the crop coefficient values reported in the literature (Allen et al. 1998). The developed model was validated by estimating soil water balance components in the modeled domain. Total water balance error of modeling was estimated to be 8%. The results proved that the soil moisture sensing methodology is useful in the determination of crop coefficient values.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16


  1. Ahmad M, Chakraborty D, Aggarwal P, Bhattacharyya R, Singh R (2018) Modelling soil water dynamics and crop water use in a soybean-wheat rotation under chisel tillage in a sandy clay loam soil. Geoderma 327:13–24

    Article  Google Scholar 

  2. Allen GR, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration: guidelines for computing crop water requirements. FAO Irrigation and drainage paper No. 56

  3. Allen RG, Pereira LS, Howell TA, Jensen ME (2011) Evapotranspiration information reporting: I. Factors governing measurement accuracy 98(6):899–920

    Google Scholar 

  4. Andreu L, Hopmans JW, Schwankl LJ (1997) Spatial and temporal distribution of soil water balance for a drip-irrigated almond tree. Agric Water Manag 35:123–146

    Article  Google Scholar 

  5. Angaleeswari M, Ravikumar V (2019) Estimating evapotranspiration parameters by inverse modelling and non-linear optimization. Agric Water Manag 223:105681

    Article  Google Scholar 

  6. Arif C, Setiawan BI, Sofiyuddin HA, Martief LM, Mizoguchi M, Doi R (2012) Estimating crop coefficient in intermittent irrigation paddy fields using excel solver. Rice Sci 19:143–152

    Article  Google Scholar 

  7. Buckingham E (1907) Studies on the movement of soil moisture. Agic. Bur, Soils Bull, p 38

    Google Scholar 

  8. Campbell scientific (2002) CS616 and CS625 water content reflectometers. Instruction manual 2006

  9. Coelho FE, Or D (1996) A parametric model for two-dimensional water uptake intensity by corn roots under drip irrigation. Soil Sci Soc Am J 60:1039–1049

    CAS  Article  Google Scholar 

  10. Dong X (2016) How to put plant root uptake into a soil water flow model: A documentation with complete computer code. F1000Research 5: 43

  11. Doorenbos J, Kassam AH (1979) Yield response to water. FAO Irrigation and drainage paper No. 33

  12. Doorenbos J, Pruitt WO (1977) Crop water requirement. FAO Irrigation and Drainage paper No. 24

  13. FAO report (2017) Water for Sustainable Food and Agriculture- A report produced for the G20 Presidency of Germany Food and Agriculture Organization of the United Nations

  14. Fares A, Alva AK (2000) Soil Water Components Based on Capacitance Probes in a Sandy Soil. Soil Sci Soc Am J 64:311

    CAS  Article  Google Scholar 

  15. Ghiberto PJ, Libardi PL, Brito AS, Trivelin PCO (2011) Components of the water balance in soil with sugarcane crops. Agric Water Manag 102:1–7

    Article  Google Scholar 

  16. Green SR, Kirkham MB, Clothier BE (2006) Root uptake and transpiration: from measurements and models to sustainable irrigation. Agric Water Manag 86:165–176

    Article  Google Scholar 

  17. Guderle M, Hildebrandt A (2015) Using measured soil water contents to estimate evapotranspiration and root water uptake profiles—a comparative study. Hydrol Earth Syst Sci 19:409–425

    Article  Google Scholar 

  18. Hwan S, Won M (2006) Estimation of paddy rice crop coefficients for Penman-Monteith and FAO modified Penman method. Paper presented at the 2006 ASAE Annual Meeting

  19. Kutilch M, Neilson DR (1994) Soil hydrology. Geoecology textbook. Catena-Vert, Cremligen-Destedt, Hannover

    Google Scholar 

  20. Montazar A, Rejmanek H, Tindula G, Little C, Shapland T, Anderson F, Snyder RL (2017) Crop coefficient curve for paddy rice from residual energy balance calculations. J Irrig Drain Eng 143(2):04016076

    Article  Google Scholar 

  21. Moratiel R, Bravo R, Saa A, Tarquis AM, Almorox J (2020) Estimation of evapotranspiration by the Food and Agricultural Organization of the United Nations (FAO) Penman-Monteith temperature (PMT) and Hargreaves-Samani (HS) models under temporal and spatial criteria–a case study in Duero basin (Spain). Nat Hazard 20(3):859–875

    Article  Google Scholar 

  22. Naranjo JB, Weiler M, Stahl K (2011) Sensitivity of a data-driven soil water balance model to estimate summer evapotranspiration along a forest chronosequence. Hydrol Earth Syst Sci 15(11):3461

    Article  Google Scholar 

  23. Odhiambo LO, Murty VVN (1996) Modeling water balance components in relation to field layout in lowland paddy fields. I Model development Agric Water Manag 30:185–199

    Article  Google Scholar 

  24. Radcliffe DE, Šimůnek J (2010) Soil Physics with Hydrus: Modelling and Applications. CRC press

  25. TNAU Report (2013) New crop varieties and agricultural implements. Tamil Nadu Agricultural University

  26. Reuss JO (1980) Matching cropping systems to water supply using an integrative model: Water Management Research Project. Engineering Research Center

  27. Soman P (2012) Drip Irrigation and Fertigation Technology for Rice Cultivation Session 6b: Tools. Techniques, Innovations

    Google Scholar 

  28. Soman SS, Amol C (2018) Evaluation of the performance of aerobic rice using drip irrigation technology under tropical conditions. International Journal of Agriculture Sciences 10(10):6040–6043

    CAS  Google Scholar 

  29. Tomar V, O’toole J, (1979) Evapotranspiration from rice fields. IRRI Research Paper Series Committee 34:1–15

    Google Scholar 

  30. Wu J, Zhang R, Gui S (1999) Modeling soil water movement with water uptake by roots. Plant Soil 215:7–17

    CAS  Article  Google Scholar 

  31. Zuo Q, Zhang R (2002) Estimating root-water-uptake using an inverse method. Soil Sci 167(9):561–571

    CAS  Article  Google Scholar 

Download references


The Authors acknowledge the research funds used for conducting this research from the scheme namely, “Fertigation Scheduling for Paddy by Simulation Modelling” funded by Indian Council of Agricultural Research of Natural Resources Management Division, New Delhi. Also, we would like to thank "Tamil Nadu Agricultural University, Agricultural Engineering College & Research Institute, Kumulur, Trichy" for providing the facilities to conduct the research works. The Authors also wish to acknowledge the reviewers for their suggestions and comments that helped in significantly improving the quality of the manuscript.

Author information



Corresponding author

Correspondence to M. Angaleeswari.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Angaleeswari, M., Ravikumar, V. & Kannan, S.V. Evapotranspiration estimation by inverse soil water flow modelling. Irrig Sci (2021). https://doi.org/10.1007/s00271-021-00734-2

Download citation