Evaluation of mathematical equations for estimating leaf area in rapeseed

Genei Antonio Dalmago, Cleusa Adriane Menegassi Biachi, Samuel Kovaleski, Elizandro Fochesatto


The aim of this study was to evaluate estimations of leaf area in rapeseed (Brassica napus L.) and the potential for application to different genotypes, environmental conditions and types of crop management. In experiments conducted during 2013, 2014, 2016 and 2017, three genotypes of rapeseed, five doses of nitrogen and three sowing dates were used. Leaves were randomly collected from different plants and positions on the plants. The leaf area (LA), and maximum width (W) and length (L) were determined for each leaf, and the product of L and W (LxW) was calculated. Fifty-six equations for estimating LA in rapeseed, where the independent variables were W, L or LxW, were compiled from the bibliography and evaluated in this work. The evaluation was made using the following statistics: significance of the linear (a) and angular (b) coefficients of the regression around the 1:1 line, concordance index (d), bias index (BIAS), mean absolute error (MAE), mean relative error (MRE), random mean squared error (MSEr) and systematic mean squared error (MSEs). Only 11 equations showed the a and b coefficients as not being different from 0 and 1 respectively. However, only 10 were suitable, as they displayed the lowest values for d, BIAS, MAE and RME, and the MSEs was smaller than the MSEr. The MAE ranged from 5.4 cm² to 16.2 cm², well within the error range for generating the equations. LA in rapeseed can be estimated by general biometric equations without considering the specificity of the genotype or the morphological type of the leaf.


Brassica napus; Colza; Modelling; Leaf area index

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ALVARES, C. A. et al. Köppen’s climate classification map for Brazil. Meteorologische Zeitschrift, v. 22, n. 6, p. 711-728, 2013.

BOUCHET, A. S. et al. Nitrogen use efficiency in rapeseed: a review. Agronomy for Sustainable Development, v. 36, n. 38, p. 1-20, 2016.

CARGNELUTTI FILHO, A. et al. Estimação da área foliar de canola por dimensões foliares. Bragantia, v. 74, n. 2, p. 139-148, 2015.

CARGNELUTTI FILHO, A. et al. Estimativa da área foliar de nabo forrageiro em função de dimensões foliares. Bragantia, v. 71, n. 1, p. 47-51, 2012.

CHAVARRIA, G. et al. Índice de área foliar em canola cultivada sob variações de espaçamento e de densidade de semeadura. Ciência Rural, v. 41, n. 12, p. 2084-2089, 2011.

FIALHO, G. S. et al. Predição da área foliar em abobrinha-italiana: um método não destrutivo, exato, simples, rápido e prático. Revista Brasileira de Agropecuária Sustentável, v. 1, n. 2, p. 59-63, 2011.

FOCHESATTO, E. et al. Interception of solar radiation by the reproductive structures of canola hybrids. Ciência Rural, v. 46, n. 10, p. 1790-1796, 2016.

FOX, D. G. Judging air quality model performance. Bulletin of the American Meteorological Society, v. 62, n. 5, p. 599-609, 1981.

JULLIEN, A. et al. Characterization of the interactions between architecture and source–sink relationships in winter oilseed rape (Brassica napus) using the Green Lab model. Annals of Botany, v. 107, n. 5, p. 765-779, 2011.

KIRKEGAARD, J. A. et al. Physiological response of spring canola (Brassica napus) to defoliation in diverse environments. Field Crops Research, v. 125, n. 18, p. 61-68, 2012.

KRÜGER, C. A. M. B. et al. Rapeseed population arrangement defined by adaptability and stability parameters. Revista Brasileira de Engenharia Agrícola e Ambiental, v. 20, n. 1, p. 36-41, 2016.

LEITE, H. G.; ANDRADE, V. C. L. Um método para condução de inventários florestais sem o uso de equações volumétricas. Revista Árvore, v. 26, n. 3, p. 321-328, 2002.

LIMA, R. T. de et al. Modelos para estimativa da área foliar da mangueira utilizando medidas lineares. Revista Brasileira de Fruticultura, v. 34, n. 4, p. 974-980, 2012.

MALDANER, I. C. et al. Modelos de determinação não-destrutiva da área foliar em girassol. Ciência Rural, v. 39, n. 5, p. 1356-1361, 2009.

MISLE, E. et al. Leaf area estimation in muskmelon by allometry. Photosynthetica, v. 51, n. 4, p. 613-620, 2013.

NANDA, R.; BHARGAVA, S. C.; RAWSON, H. M. Effect of sowing date on rates of leaf appearance, final leaf numbers and areas in Brassica campestris, B. juncea, B. napus and B. carinata. Field Crops Research, v. 2, n. 2/3, p. 125-134, 1995.

PIÑEIRO, G. et al. How to evaluate models: observed vs. predicted or predicted vs. observed? Ecological Modelling, v. 216, n. 3/4, p. 316-322, 2008.

PINTO, D. G. et al. Correlations between spectral and biophysical data obtained in canola canopy cultivated in the subtropical region of Brazil. Pesquisa Agropecuária Brasileira, v. 52, n. 10, p. 825-832, 2017.

R CORE TEAM. R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing, 2018. Disponível em: . Acesso em: 04 out. 2018.

RICHTER, G. L. et al. Estimativa da área de folhas de cultivares antigas e modernas de soja por método não destrutivo. Bragantia, v. 73, n. 4, p. 416-425, 2014.

SMITH, E. P.; ROSE, K. A. Model goodness-of-fit analysis using regression and related techniques. Ecological Modelling, v. 77, n. 1, p. 49-64, 1995.

STEFANOWSKA, M. et al. Low temperature affects pattern of leaf growth and structure of cell walls in winter oilseed rape (Brassica napus L., var. oleifera L.). Annals of Botany, v. 84, n. 3, p. 313-319, 1999.

STRECK, E. V. et al. Solos do Rio Grande do Sul. 2. ed. Porto Alegre: EMATER/RS - ASCAR, 2008. 220 p.

TARTAGLIA, F. de L. et al. Modelos não destrutivos para determinação da área foliar em canola. Revista Brasileira de Engenharia Agrícola e Ambiental, v. 20, n. 6, p. 551-556, 2016.

TOEBE, M. et al. Modelos para a estimação da área foliar de feijão de porco por dimensões foliares. Bragantia, v. 71, n. 1, p. 37-41, 2012.

WILLMOTT, C. J. et al. Statistics for the evaluation and comparison of models. Journal of Geophysical Research, v. 90, n. C5, p. 8995-9005, 1985.

WILLMOTT, C. J. Some comments on the evaluation of model performance. Bulletin American Meteorological Society, v. 63, n. 11, p. 1309-1313, 1982.

WILLMOTT, C. J.; MATSUURA, K. Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Climate Research, v. 30, n. 1, p. 79-82, 2005.

ZHANG, L.; LIU, X. Non-destructive leaf-area estimation for Bergenia purpurascens across timberline ecotone, southeast Tibet. Annales Botanici Fennici, v. 47, n. 5, p. 346-352, 2010.

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