Advertisement

Earth Science Informatics

, Volume 11, Issue 3, pp 325–340 | Cite as

Calibration and spatial modelling of daily ET0 in semiarid areas using Hargreaves equation

  • Francisco Gomariz-CastilloEmail author
  • Francisco Alonso-Sarría
  • Francisco Cabezas-Calvo-Rubio
Research Article

Abstract

Evapotranspiration is difficult to measure and, when measured, its spatial variability is not usually taken into account. The recommended method to estimate evapotranspiration, Penman-Monteith FAO, requires variables not available in most weather stations. Simplified but less accurate methods, as Hargreaves equation, are normally used. Several approaches have been proposed to improve Hargreaves equation accuracy. In this work, 14 calibrations of the Hargreaves equation are compared. Three goodness of fit statistics were used to select the optimal, in terms of simplicity and accuracy. The best option was an annual linear regression. Its parameters were interpolated using regression-kriging combining Random Forest and Ordinary Kriging. Twelve easy to obtain ancillary variables were used as predictors. The same approach was used to interpolate Hargreaves and Penman-Monteith-FAO ET0 on a daily basis; the Hargreaves ET0 layers and the parameter layers were used to obtain calibrated ET0 estimations. To compare the spatial patterns of the three estimations the daily layers were integrated into annual layers. The results of the proposed calibration are much more similar to Penman-Monteith FAO results than those obtained with Hargreaves equation. The research was conducted in south-east Spain with 79 weather stations with data from 01/01/2003 to 31/12/2014.

Keywords

Evapotranspiration Hargreaves equation Allen calibration Spatial interpolation Random forest 

Notes

Acknowledgements

This study was funded by the Segura Hydrographic Confederation, MAPAMA (Government of Spain), within the framework of the Research Project Scientific Support Activities for the Hydrological Planning and European Cooperation Process.

This study was funded in part by the Seneca Foundation, Science and Technology Agency of the Murcia Region (Ref. 19325 / PI / 2015), project The Role of Water Markets in Integrated Water Resources Management in Watersheds.

References

  1. AENOR (2004) Automatic weather stations networks: guidance for the validation of the weather data from the station networks real time validation. Tech. rep. Asociaciȯn Espaṅola de Normalizaciȯn y CertificaciȯnGoogle Scholar
  2. Aguilar C, Polo MJ (2011) Generating reference evapotranspiration surfaces from the Hargreaves equation at watershed scale. Hydrol Earth Syst Sci 15(8):2495–2508.  https://doi.org/10.5194/hess-15-2495-2011 CrossRefGoogle Scholar
  3. Allen RG (1995) Evaluation of procedures for estimating mean monthly solar radiation from air temperature. Tech. rep. Report submitted to the United Nations Food and Agricultural Organization, FAO. Rome, ItalyGoogle Scholar
  4. Allen RG, Jensen ME, Wright JL, Burman RD (1989) Operational estimates of evapotranspiration. Agron J 81:650–662CrossRefGoogle Scholar
  5. Allen RG, Smith M, Perrie M, Pereira LS (1994) An update for the calculation of reference evapotranspiration. ICID Bull 43(2):35–92Google Scholar
  6. Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration: guidelines for computing crop requirements. 56, FAO  https://doi.org/10.1016/j.eja.2010.12.001
  7. Bautista F, Bautista D, Delgado-Carranza C (2009) Calibration of the equations of Hargreaves and thornthwaite to estimate the potential evapotranspiration in semi-arid and subhumid tropical climates for regional applications. Atmosfera 22(4):331–348Google Scholar
  8. Bennett ND, Croke BFW, Guariso G, Guillaume JHA, Hamilton SH, Jakeman AJ, Marsili-Libelli S, Newham LTH, Norton JP, Perrin C, Pierce SA, Robson B, Seppelt R, Voinov AA, Fath BD, Andreassian V (2013) Characterising performance of environmental models. Environ Modell Softw 40:1–20.  https://doi.org/10.1016/j.envsoft.2012.09.011 CrossRefGoogle Scholar
  9. Berengena J, Gavilán P (2005) Reference evapotranspiration estimation in a highly advective semiarid environment. J Irrigation Drain Eng 131(2):147–163.  https://doi.org/10.1061/(ASCE)0733-9437(2005)131:2(147) CrossRefGoogle Scholar
  10. Bȯhner J, Antoniċ O (2009) Chapter 8 land-surface parameters specific to topo-climatology. In: Hengl T, Reuter HI (eds) Developments in soil science, vol 33. Elsevier, pp 195–226, DOI  https://doi.org/10.1016/S0166-2481(08)00008-1
  11. Breiman L (2001) Random forests. Mach Learn 45(1):5–32.  https://doi.org/10.1023/A:1010933404324 CrossRefGoogle Scholar
  12. Brutsaert W (1991) Evaporation into the atmosphere. Theory, history and applications D. Reidel Publishing Company, BostonGoogle Scholar
  13. Dalezios NR, Loukas A, Bampzelis D (2002) Spatial variability of reference evapotranspiration in greece. Phys Chem Earth 27(23-24):1031–1038.  https://doi.org/10.1016/S1474-7065(02)00139-0 CrossRefGoogle Scholar
  14. Di Stefano C, Ferro V (1997) Estimation of evapotranspiration by Hargreaves formula and remotely sensed data in semi-arid mediterranean areas. J Agric Engng Res 68:189–199.  https://doi.org/10.1006/jaer.1997.0166 CrossRefGoogle Scholar
  15. Droogers P, Allen RG (2002) Estimating reference evapotranspiration under inaccurate data conditions. Irrig Drain Syst 16:33–45.  https://doi.org/10.1023/A:1015508322413 CrossRefGoogle Scholar
  16. Er-Raki S, Chehbouni A, Khabba S, Simonneaux V, Jarlan L, Ouldbba A, Rodriguez JC, Allen RG (2010) Assessment of reference evapotranspiration methods in semi-arid regions: can weather forecast data be used as alternate of ground meteorological parameters? J Arid Environ 74(12):1587–1596.  https://doi.org/10.1016/j.jaridenv.2010.07.002 CrossRefGoogle Scholar
  17. Fox J, Monette G (1992) Generalized collinearity diagnostics. J Am Stat Assoc 87(417):178–183.  https://doi.org/10.1080/01621459.1992.10475190 CrossRefGoogle Scholar
  18. Gavilȧn P, Lorite IJ, Tornero S, Berengena J (2006) Regional calibration of Hargreaves equation for estimating reference et in a semiarid environment. Agric Water Manag 81(3):257–281.  https://doi.org/10.1016/j.agwat.2005.05.001 CrossRefGoogle Scholar
  19. Gomariz-Castillo F, Alonso-Sarri̇a F (2013) An r script to model monthly climatic variables with glm to be used in hydrological modeling in river segura basin. In: The 9th international R user conference. Castilla-La Mancha, AlbaceteGoogle Scholar
  20. Hȧntzschel J, Goldberg V, Bernhofer C (2005) Gis-based regionalisation of radiation, temperature and coupling measures in complex terrain for low mountain ranges. Meteorol Appl 12(1):33–42.  https://doi.org/10.1017/S1350482705001489 CrossRefGoogle Scholar
  21. Hargreaves GH (1989) Accuracy of estimated reference evapotranspiration. J Irrig Drain Eng 115(6):1000–1007.  https://doi.org/10.1061/(ASCE)0733--9437(1989)115:6 CrossRefGoogle Scholar
  22. Hargreaves GH (1994a) Defining and using reference evapotranspiration. J Irrig Drain Eng 120(6):1132–1139.  https://doi.org/10.1061/(ASCE)0733-9437(1994)120:6(1132) CrossRefGoogle Scholar
  23. Hargreaves GH (1994b) Simplified coefficients for estimating monthly solar radiation in north america and europe. Tech rep. Utah State University, LoganGoogle Scholar
  24. Hargreaves GH, Allen RG (2003) History and evaluation of Hargreaves evapotranspiration equation. J Irrig Drain Eng-Asce 129(1):53–63.  https://doi.org/10.1061/(ASCE)0733-9437(2003)129:1(53) CrossRefGoogle Scholar
  25. Hargreaves GH, Samani ZA (1985) Reference crop evapotranspiration from temperature. Appl Eng Agric 1(2):96–99.  https://doi.org/10.13031/2013.26773 CrossRefGoogle Scholar
  26. Hengl T, Heuvelink GBM, Stein A (2004) A generic framework for spatial prediction of soil variables based on regression-kriging. Geoderma 120(1-2):75–93.  https://doi.org/10.1016/j.geoderma.2003.08.018 CrossRefGoogle Scholar
  27. Hofierka J, Su̇ri M (2002) The solar radiation model for open source gis: implementation and applications. In: Proceedings of the open source GIS - GRASS users conference. Trento, pp 1–19Google Scholar
  28. Jensen DT, Hargreaves GH, Temesgen B, Allen RG (1997) Computation of eto under non-ideal conditions. J Irrig Drain Eng 123(5):394–400.  https://doi.org/10.1061/(ASCE)0733-9437(1997)123:5(3) CrossRefGoogle Scholar
  29. Kidron GJ, Zohar M (2010) Spatial evaporation patterns within a small drainage basin in the negev desert. J Hydrol 380(3–4):376–385.  https://doi.org/10.1016/j.jhydrol.2009.11.012 CrossRefGoogle Scholar
  30. Kuhn M, Johnson K (2013) Applied predictive modeling. Springer-Verlag, New YorkCrossRefGoogle Scholar
  31. Legates DR, McCabe GJ (1999) Evaluating the use of ’goodness-of-fit’ measures in hydrologic and hydroclimatic model validation. Water Resour Res 35(1):233–241.  https://doi.org/10.1029/1998WR900018 CrossRefGoogle Scholar
  32. Liu BYH, Jordan RC (1960) The interrelationship and characteristic distribution of direct, diffuse, and total solar radiation. Sol Energy 4:1–19.  https://doi.org/10.1016/0038-092X(60)90062-1 CrossRefGoogle Scholar
  33. Lȯpez-Urrea R, Martín de Santa Olalla F, Fabeiro C, Moratalla A (2006) Testing evapotranspiration equations using lysimeter observations in a semiarid climate. Agricul Water Manag 85(1-2):15–26.  https://doi.org/10.1016/j.agwat.2006.03.014 CrossRefGoogle Scholar
  34. Lu J, Sun G, McNulty SG, Amatya DM (2005) A comparison of six potential evapotranspiration methods for regional use in the southeastern united states. JAWRA J Amer Water Resour Assoc 41(3):621–633.  https://doi.org/10.1111/j.1752-1688.2005.tb03759.x CrossRefGoogle Scholar
  35. Mardikis MG, Kalivas DP, Kollias VJ (2005) Comparison of interpolation methods for the prediction of reference evapotranspiration—an application in greece. Water Resour Manag 19(3):251–278.  https://doi.org/10.1007/s11269-005-3179-2 CrossRefGoogle Scholar
  36. Marti̇nez-Cob A, Tejero-Juste M (2004) A wind-based qualitative calibration of the Hargreaves et0 estimation equation in semiarid regions. Agric Water Manag 64(3):251–264.  https://doi.org/10.1016/S0378-3774(03)00199-9 CrossRefGoogle Scholar
  37. McCullagh P, Nelder J (1989) Generalized linear models. Chapman & Hall/CRC, Boca RatonCrossRefGoogle Scholar
  38. Mendicino G, Senatore A (2013) Regionalization of the Hargreaves coefficient for the assessment of distributed reference evapotranspiration in Southern Italy. J Irrig Drain Eng 139(5):349–362.  https://doi.org/10.1061/(ASCE)IR.1943-4774.0000547 CrossRefGoogle Scholar
  39. Monteith JL (1965) Evaporation and the environment, Cambridge University Press, SwanseaGoogle Scholar
  40. Orang MN, Grismer ME, Ashktorab H (1995) New equations estimate evapotranspiration in delta. Calif Agric 49(3):19–21.  https://doi.org/10.3733/ca.v049n03p19 CrossRefGoogle Scholar
  41. Ray SS, Dadhwal VK (2001) Estimation of crop evapotranspiration of irrigation command area using remote sensing and gis. Agric Water Manag 49:239–249.  https://doi.org/10.1016/S0378-3774(00)00147-5 CrossRefGoogle Scholar
  42. Raziei T, Pereira LS (2013) Estimation of eto with Hargreaves–samani and fao-pm temperature methods for a wide range of climates in iran. Agric Water Manag 121(Supplement C):1–18.  https://doi.org/10.1016/j.agwat.2012.12.019 CrossRefGoogle Scholar
  43. Samani Z, Pessarakli M (1986) Estimating potential crop evapotranspiration with minimum data in arizona. Trans ASAE 29(2):522–524.  https://doi.org/10.13031/2013.30184 CrossRefGoogle Scholar
  44. Samani ZA (2000) Estimating solar radiation and evapotranspiration using minimum climatological data. J Irrig Drain Engi 126(4):265–267.  https://doi.org/10.1061/(ASCE)0733-9437(2000)126:4(265) CrossRefGoogle Scholar
  45. Sendanayake S, Miguntanna NP (2014) Estimating incident solar radiation in tropical islands with short term weather data. Eur Sci J 10(3):401–412Google Scholar
  46. Shahidian S, Serralheiro R, Serrano J, Teixeira J, Haie N, Santos F (2012) Chapter 4 Hargreaves and other reduced-set methods for calculating evapotranspiration. In: Irmak A (ed) Evapotranspiration - remote sensing and modeling, vol 33. InTech, pp 59–80, DOI  https://doi.org/10.5772/18059
  47. Shahidian S, Serralheiro RP, Serrano J, Teixeira JL (2013) Parametric calibration of the Hargreaves-samani equation for use at new locations. Hydrol Process 27(4):605–616.  https://doi.org/10.1002/hyp.9277 CrossRefGoogle Scholar
  48. Subburayan S, Murugappan A, Mohan S (2011) Modified Hargreaves equation for estimation of et0 in a hot and humid location in Tamilnadu State, India. Int J Eng Sci Technol 3(1):592– 600Google Scholar
  49. Trajkovic S (2005) Temperature-based approaches for estimating reference evapotranspiration. J Irrig Drain Eng 131(4):316–323.  https://doi.org/10.1061/(ASCE)0733-9437(2005)131:4(316) CrossRefGoogle Scholar
  50. Vanderlinden K, Giraldez JV, Meirvenne MV (2004) Assessing reference evapotranspiration by the Hargreaves method in Southern Spain. J Irrig Drain Eng 130(3):184–191.  https://doi.org/10.1061/(ASCE)0733-9437(2004)130:3(18) CrossRefGoogle Scholar
  51. Vicente-Serrano SM, Lanjeri S, Lȯpez-Moreno JI (2007) Comparison of different procedures to map reference evapotranspiration using geographical information systems and regression-based techniques. Int J Climatol 28(8):1103–1118.  https://doi.org/10.1002/joc.1460 CrossRefGoogle Scholar
  52. Wood S (2006) Generalized additive models: an introduction with R. Chapman & Hall/CRC, Boca RatonGoogle Scholar
  53. Xu CY, Singh VP (2000) Evaluation and generalization of radiation-based methods for calculating evaporation. Hydrol Processes 14(2):339–349.  https://doi.org/10.1002/(SICI)1099-1085(20000215)14:2<339::AID-HYP928>3.0.CO;2-O CrossRefGoogle Scholar
  54. Xu CY, Singh VP (2001) Evaluation and generalization of temperature-based methods for calculating evaporation. Hydrol Process 15(2):305–319.  https://doi.org/10.1002/hyp.119 CrossRefGoogle Scholar
  55. Xu CY, Singh VP (2002) Cross comparison of empirical equations for calculating potential evapotranspiration with data from Switzerland. Water Resour Manag 16(3):197–219.  https://doi.org/10.1023/A:1020282515975 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Euro-mediterranean Water InstituteMurciaSpain
  2. 2.Institute for Water and EnvironmentUniversity of MurciaMurciaSpain

Personalised recommendations