Simplify the triangle method for estimating evapotranspiration and its use in agrometeorological modeling

Daniela Fernanda da Silva Silva Fuzzo, Jansle Vieira Rocha


An aim of this paper was to assess the accuracy in estimating soybean yield proposed by DOORENBOS and KASSAM over a region in Brazil using the evapotranspiration fraction (EF) obtained from a simplified version of the triangle model, the counties analyzed were Toledo, Vera Cruz do Oeste, Cascavel, Campo Bonito, Medianeira and Serranópolis Iguaçu, in Paraná state, for crop years 2002/03 to 2011/12. A high accuracy of the data was found, the model values for the parameter d1 ("d1" modified Willmott) were between 0.8 and 0.95 in most counties, whereas the root mean squared error showed that there was low variation between 149,60 to 358,60 (kg ha-1). This means that the average of the data from the modified model (using the remotely determined evapotranspiration fraction) were statistically equal the average of the measured soybean crop data. The remote sensing input can be used as tools in the absence of surface information, serving as input data for assisting in agrometeorological modeling in order to estimate agricultural productivity of soybean.


crop yield; MODIS image; remote sensing; vegetation index.

Full Text:



BRUNSELL, N. A.; ANDERSON, M. C. Characterizing the multi–scale spatial structure of remotely sensed evapotranspiration with information theory. Biogeosciences, v.8, p.2269-2280, 2011.

CARLSON, T. N. An overview of the "Triangle Method" for estimating surface evapotranspiration and soil moisture from satellite imagery. Sensors v.7, p.1612–|1629, 2007.

CARLSON, T. N. Triangle models and misconceptions. International Journal of Remote Sensing Applications. v.3, p.155-158, 2013.

DOORENBOS, J.; KASSAM, A. H. Yield response to water. Rome, FAO, 1979. 197p.

SILVA-FUZZO, D. F.; PRELA-P ANTANO, A. CAMARGO. M. B. P. Modelagem agrometeorológica para estimativa de produtividade de soja para o vale do Médio Paranapanema-sp. Irriga, v.20, p.490-501, 2015a.

SILVA-FUZZO, D. F.; PRELA-PANTANO, A.; CAMARGO, M. B. P. Risco Climático e produtividade da soja no Médio Paranapanema–SP. Uso de modelos agrometeorológicos para estimativa de produtividade agrícola da soja. Saarbrücken/Alemanha - Novas Edições Acadêmicas. 2015b. 87p.

GARCIA, M.; FERNÁNDEZ, N.; VILLAGARCÍA, L.; DOMINGO, F.; Puigdefábregas, J.; Sandholt, I. Accuracy of the temperature–vegetation dryness index using MODIS under water-limited vs. energy-limited evapotranspiration conditions. Remote Sensing of Environment, v149, p.100–117, 2014.

JIANG, L.; ISLAM, S. Estimation of surface evaporation map over southern Great Plains using remote sensing data. Water Resources Research, v.37, p.329-340, 2001.

JOHANN, J. A. Calibração de dados agrometeorológicos e agrícolas de verão no estado do Paraná. 2012. 201p. (Tese de Doutorado) – Faculdade de Engenharia Agrícola UNICAMP, Campinas.

MKHABELA, M. S.; BULLOCK, S. R.; WANG, Y. Y. Crop yield forecasting on the Canadian Prairies using MODIS NDVI data. Agricultural and Forest Meteorology, v.3, p .385–393, 2011.

PETROPOULOS, G.; CARLSON, T.N.;WOOSTER, M.J.; ISLAM, S. A review os Ts/VI remote sensing based methods for the retrieval of land surfasse energy fluxes and soil surface moisture. Progress in Physical Geography, v. 33, p. 224–250, 2009.

REN, J.; CHEN, Z.; ZHOU, Q.; TANG, H. Regional yield estimation for winter wheat with MODIS-NDVI data in Shandong, China. International Journal of Applied Earth Observation and Geoinformation, v.10, p.403-413, 2008.

TIAN, J.; HONGBO, S.; XIAOMIN, S.; SHAOHUI, C.; HONGLIN, H. E.; LINJUN, Z. Impacto of the Spatial Domain Size on the performance of the Ts-VI triangle method in terrestrial evapotranspiration estimation. Remote Sensing, v 5, p.1998-2013, 2013.

THORNTHWAITE, C. W.; MATHER, J. R. The water balance. In: Centerton, N. J. (ed), Climatology, v.8, n. 1 1955.104p.

WILLMOTT, C. J.; ACKLESON, S. G.; DAVIS, J. J.; FEDDEMA, K. M.; KLINK, D. R. Statistics for the evaluation and comparison of models. Journal of Geophysical Research, v.90, p.8995- 9005, 1985.

Comments on this article

View all comments