Leaf Area Estimation of Garden Boldo From Linear Dimensions

The objective of this work was to determine a mathematical equation using linear measures that allows estimating a leaf area of the specie Plectranthus barbatus Andrews, a plant with medicinal properties popularly known as garden boldo. For this was performed a direct measurement of the leaf blade considering the length (L) along the midrib and the maximum width (W) perpendicular to the midrib of 500 leaves of different specimens and the observed foliar area (OLA), which were obtained by digitized images. A regression study with linear, quadratic, potential and exponential models was performed using a random sample of 400 from the evaluated leaves using OLA as a function of L, W or LW and then obtaining the estimated leaf area (ELA) of each model. From the remaining 100 leaves a validation of the tested models was performed using ELA as a function of OLA in a simple linear regression. From the residues between ELA and OLA the root-square-mean error and Willmot index (d) was obtained and the normality was verified. The parameters used for validation were: statistically linear and angular coefficient equal to zero and one respectively; coefficient of determination closest to the unit; RQME closer to zero; d index closest to the unit; normal distribution of residues. The equation that best represents the estimated leaf area of the garden boldo is ELA = 0.1389 + 0.6779 (LW).

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LEAF AREA ESTIMATION IN LITCHI BY MEANS OF ALLOMETRIC RELATIONSHIPS

Revista Brasileira de Fruticultura ◽

10.1590/0100-29452017403 ◽

2017 ◽

Vol 39 (spe) ◽

Cited By ~ 2

Author(s):

PABLO SOUTO OLIVEIRA ◽

WILTON SILVA ◽

ADRIANA APARECIDA MATTA COSTA ◽

EDILSON ROMAIS SCHMILDT ◽

EDNEY LEANDRO DA VITÓRIA

Keyword(s):

Linear Regression ◽

Leaf Area ◽

Linear Regression Equation ◽

Allometric Relationships ◽

Linear Quadratic ◽

Maximum Width ◽

Quadratic Potential ◽

Area Estimation ◽

Linear Dimensions ◽

The One

ABSTRACT Obtaining leaf area is critical in several agronomic studies, being one of the important instruments to assess plant growth. The aim of this study was to estimate equations and select the most appropriate in determining leaf area in litchi (Litchi chinensis Sonn.). From the linear dimensions of length (L) and maximum width (W) of leaf limb, equations were estimated using linear, quadratic, potential and exponential models. The linear regression equation using the product of the length by maximum width, given by Y = 0.2885 + 0.662 (L.W) is the one that best expresses the leaf area estimation of litchi tree.

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Mathematical Modeling for Leaf Area Estimation From Papaya Seedlings ‘Golden THB’

Journal of Agricultural Science ◽

10.5539/jas.v11n5p496 ◽

2019 ◽

Vol 11 (5) ◽

pp. 496

Author(s):

Vinicius de Souza Oliveira ◽

Karina Tiemi Hassuda dos Santos ◽

Thainá de Jesus Ambrósio ◽

Jéssica Sayuri Hassuda Santos ◽

Weslley do Rosário Santana ◽

...

Keyword(s):

Mathematical Modeling ◽

Leaf Area ◽

Regression Models ◽

Leaf Blade ◽

Coefficient Of Determination ◽

Suitable Model ◽

Linear Regression Models ◽

Maximum Width ◽

Area Estimation ◽

Linear Dimensions

The aim of this study was to select the most suitable model for leaf area estimation from papaya seedlings cv. ‘Golden THB’ using linear dimensions of leaves with unilobular and trilobular morphology. It was used leaves of 60 seedlings with 30 days after sowing produced in nursery of the Fazenda Santa Teresinha which belongs to company Caliman Agrícola S.A., in the municipality of Linhares, state of Espírito Santo, in March 2016. The measurement of the length (L) was performed along the midrib, the maximum width (W) of the leaf blade, the product of the length by the width (LW) and the observed leaf area (OLA). From these results, first degree and power linear regression models was adjusted. From the proposed regression models, the validation was performed with a leaves sample of 60 seedlings produced in June 2016, obtaining, thus, the estimated leaf area (ELA). The following criteria were used to choose the best model: the highest coefficient of determination (R2), the values do not significant of the comparison of means of OLA and ELA and values of MAE and RMSE closer to zero. The leaf area estimation from papaya seedlings cv. ‘Golden THB’ can be represented through equation ELA = -0.402619 + 0.612525(LW) for trilobular leaves and through equation ELA = 0.623355 + 0.610552(LW) for unilobular leaves.

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Alometric Model for Estimation of Leaf Area of Garcinia brasiliensis Mart. Through Non-destructive Method

Journal of Agricultural Science ◽

10.5539/jas.v11n10p154 ◽

2019 ◽

Vol 11 (10) ◽

pp. 154

Author(s):

Vinicius de Souza Oliveira ◽

Cássio Francisco Moreira de Carvalho ◽

Juliany Morosini França ◽

Flávia Barreto Pinto ◽

Karina Tiemi Hassuda dos Santos ◽

...

Keyword(s):

Leaf Area ◽

Linear Equations ◽

Absolute Error ◽

Coefficient Of Determination ◽

Maximum Width ◽

Linear Dimensions ◽

Length Width ◽

Independent Variable ◽

The Mean ◽

Non Destructive

The objective of the present study was to test and establish mathematical models to estimate the leaf area of Garcinia brasiliensis Mart. through linear dimensions of the length, width and product of both measurements. In this way, 500 leaves of trees with age between 4 and 6 years were collected from all the cardinal points of the plant in the municipality of São Mateus, North of the State of Espírito Santo, Brazil. The length (L) along the main midrib, the maximum width (W), the product of the length with the width (LW) and the observed leaf area (OLA) were obtained for all leaves. From these measurements were adjusted linear equations of first degree, quadratic and power, in which OLA was used as dependent variable as function of L, W and LW as independent variable. For the validation, the values of L, W and LW of 100 random leaves were substituted in the equations generated in the modeling, thus obtaining the estimated leaf area (ELA). The values of the means of ELA and OLA were tested by Student’s t test 5% of probability. The mean absolute error (MAE), root mean square error (RMSE) and Willmott’s index d for all proposed models were also determined. The choice of the best model was based on the non significant values in the comparison of the means of ELA and OLA, values of MAE and RMSE closer to zero and value of the index d and coefficient of determination (R2) close to unity. The equation that best estimates leaf area of Garcinia brasiliensis Mart. in a way non-destructive is the power model represented by por ELA = 0.7470(LW)0.9842 and R2 = 0.9949.

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Estimation of leaf area of Erythroxylum citrifolium from linear leaf dimensions

Bioscience Journal ◽

10.14393/bj-v35n6a2019-41743 ◽

2019 ◽

Vol 35 (6) ◽

Author(s):

João Everthon da Silva Ribeiro ◽

Ester dos Santos Coêlho ◽

Francisco Romário Andrade Figueiredo ◽

Sérgio de Faria Lopes ◽

Manoel Bandeira de Albuquerque

Keyword(s):

Leaf Area ◽

Leaf Blade ◽

Information Criterion ◽

Coefficient Of Determination ◽

Concordance Index ◽

R And D ◽

Linear Dimensions ◽

Bias Index ◽

Linear Leaf ◽

Leaf Dimensions

Erythroxylum citrifolium is a neotropical plant species recorded in all regions of Brazil. Determining leaf area is of fundamental importance to studies related to plant propagation and growth. The objective was to obtain an equation to estimate the leaf area of E. citrifolium from linear dimensions of the leaf blade (length and width). A total of 200 leaf blades were collected in Parque Estadual Mata do Pau-Ferro in the municipality of Areia, state of Paraíba, Northeast Brazil. The models evaluated were: linear, linear without intercept, quadratic, cubic, power and exponential. The best model was determined by the criteria of: high coefficient of determination (R²), low root mean square error (RMSE), low Akaike information criterion (AIC), high Willmott concordance index (d) and a BIAS index close to zero. All of the models constructed satisfactorily estimated the leaf area of E. citrifolium, with coefficients of determination above 0.9050, but the power model using the product between length and width (L*W) ŷ = 0.5966 * LW1.0181 was the best, with the highest values of R² and d, low values of RMSE and AIC, and a BIAS index closest to zero.

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Regression models for prediction of leaf area in purple ipe [Tabebuia impetiginosa (Mart.)]

Australian Journal of Crop Science ◽

10.21475/ajcs.20.14.04.p2291 ◽

2020 ◽

pp. 654-659

Author(s):

Jéssica Sayuri Hassuda Santos ◽

Karina Tiemi Hassuda dos Santos ◽

Vinicius de Souza Oliveira ◽

Gleyce Pereira Santos ◽

Luis Fernando Tavares de Menezes ◽

...

Keyword(s):

Leaf Area ◽

Regression Models ◽

Linear Models ◽

Regression Equations ◽

Linear Quadratic ◽

Maximum Width ◽

Quadratic Potential ◽

Area Estimate ◽

Non Destructive

Besides its medicinal and ornamental use, Tabebuia impetiginosa is also very economically important. The achievement of accurate and easy-to-perform tools to determine its leaf area is fundamental for understanding the interaction between the plant and the environment. The objective of this work was to obtain regression equations by using several models that use allometric measurements of the fifth leaflet and to select the most accurate one to determine the leaf area of composite leaves of Tabebuia impetiginosa Mart. in a non-destructive way. By using the dimensions of the fifth leaflet such as - length (LFL in cm), maximum width (WFL in cm) and the product between LFL and WFL (LWFL) of leaf limb, the equations were estimated for linear, quadratic, potential and exponential linear models. The results showed that the determination of leaf area could be performed with excellent precision for leaves of different sizes of this species, using the product of the measurements of length and width of the fifth leaflet. The equation that best expresses the leaf area estimate of the composite leaf of Tabebuia impetiginosa is ELACL = 8.7772 + 2.3840 (LWFL).

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A NON-DESTRUCTIVE METHOD FOR ESTIMATING LEAF AREA OF Ceiba glaziovii (Kuntze) K. Schum.

FLORESTA ◽

10.5380/rf.v50i1.61088 ◽

2019 ◽

Vol 50 (1) ◽

pp. 1063

Author(s):

João Everthon da Silva Ribeiro ◽

Francisco Romário Andrade Figueiredo ◽

Ester Dos Santos Coêlho ◽

Walter Esfrain Pereira ◽

Manoel Bandeira de Albuquerque

Keyword(s):

Leaf Area ◽

Regression Models ◽

Information Criterion ◽

Coefficient Of Determination ◽

Linear Measurements ◽

Maximum Width ◽

Bias Index ◽

Different Shapes ◽

Non Destructive

The determination of leaf area is of fundamental importance in studies involving ecological and ecophysiological aspects of forest species. The objective of this research was to adjust an equation to determine the leaf area of Ceiba glaziovii as a function of linear measurements of leaves. Six hundred healthy leaf limbs were collected in different matrices, with different shapes and sizes, in the Mata do Pau-Ferro State Park, Areia, Paraíba state, Northeast Brazil. The maximum length (L), maximum width (W), product between length and width (L.W), and leaf area of the leaf limbs were calculated. The regression models used to construct equations were: linear, linear without intercept, quadratic, cubic, power and exponential. The criteria for choosing the best equation were based on the coefficient of determination (R²), Akaike information criterion (AIC), root mean square error (RMSE), Willmott concordance index (d) and BIAS index. All the proposed equations satisfactorily estimate the leaf area of C. glaziovii, due to their high determination coefficients (R² ≥ 0.851). The linear model without intercept, using the product between length and width (L.W), presented the best criteria to estimate the leaf area of the species, using the equation 0.4549*LW.

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Mathematical Models for Leaf Area Estimates of Guava

Journal of Agricultural Science ◽

10.5539/jas.v10n12p272 ◽

2018 ◽

Vol 10 (12) ◽

pp. 272

Author(s):

Edney L. da Vitória ◽

Ismael L. de J. Freitas ◽

Tamara Locatelli ◽

Elcio das G. Lacerda ◽

Juliana M. Valle ◽

...

Keyword(s):

Regression Analysis ◽

Leaf Area ◽

Digital Imaging ◽

Linear Regression Analysis ◽

Linear Quadratic ◽

Leaf Discs ◽

Linear Dimensions ◽

Power Models ◽

Scanned Images ◽

Guava Leaf

The aim of this work was to compare methods of determining the leaf area of guava (leaf discs and scanned images) and to model leaf area as a function of linear dimensions. Four areas of guava ‘Paluma’ were selected (12, 15, 20 and 24 months of age) for the experiment in the municipality of Pedro Canário, ES, Brazil. We randomly collected samples from 15 plants in each area. Ten leaves were chosen among the lower, middle and upper thirds of each plant to ensure that leaves of all sizes were collected, for a total of 600 leaves. Subsequently, we determined the leaf area by the methods of digital imaging and leaf discs. Linear regression analysis and correlation analysis were used to compare the methods. Linear, quadratic and power models of leaf area, as a function of the length or width and/or the product of length and width were adjusted. The methods of leaf discs and scanned images are discordant. The method of digitised images was a better fit to the width of the leaf, while the method of leaf discs was a better fit for length.

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Perbandingan Model Regresi untuk Pengukuran Luas Daun Gandum di Daerah Tropis

Paspalum: Jurnal Ilmiah Pertanian ◽

10.35138/paspalum.v9i2.302 ◽

2021 ◽

Vol 9 (2) ◽

pp. 150

Author(s):

Fiky Yulianto Wicaksono ◽

Muhamad Kadapi

Keyword(s):

Leaf Area ◽

Equation Model ◽

Regression Equation ◽

Plant Production ◽

Coefficient Of Determination ◽

Regression Equations ◽

Linear Quadratic ◽

Area Index ◽

Net Assimilation ◽

Materials Used

The growth of wheat plants can be determined by measuring leaf area index and net assimilation rate. Both measurements require leaf area data. Measurement of leaf area of wheat in Indonesia requires a method that is not only accurate, but also easier and cheaper. One of them is the regression method. The purpose of this study was to determine an accurate regression equation model in predicting wheat leaf area. This research was conducted from March to June 2021 at the Experimental Station and Plant Production Technology Laboratory, Faculty of Agriculture, UNPAD, Jatinangor, Sumedang. The materials used in this study were various leaf area printing papers from wheat plants aged 14 days after planting (DAP), 28 DAP, and 42 DAP. The regression equation was assembled from the relationship between leaf area with leaf width and length, then compared with the actual leaf area that measured by scanning. The results showed that the linear, quadratic, cubic, and logarithmic regression equations had a coefficient of determination of more than 90% to predict leaf area, at the age of 14, 28, and 42 DAP, as well as all plant ages. Quadratic regression had a limit of data that can be entered, so it needed circumspection in using the formula. Cubic regression tended to have better accuracy in predicting leaf area at 14, 28, and 42 DAP, but the accuracy was the same as other regression equations at all plant ages.

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Mathematical Modeling to Estimation Leaf Area of Pimenta dioica from Linear Dimensions

International Journal of Plant & Soil Science ◽

10.9734/ijpss/2019/v28i230104 ◽

2019 ◽

pp. 1-8

Author(s):

Vinicius De Souza Oliveira ◽

Lucas Caetano Gonçalves ◽

Amanda Costa ◽

Karina Tiemi Hassuda dos Santos ◽

Jéssica Sayuri Hassuda Santos ◽

...

Keyword(s):

Leaf Area ◽

Linear Equations ◽

Selection Criterion ◽

Absolute Error ◽

Coefficient Of Determination ◽

Regression Equations ◽

Maximum Width ◽

Independent Variable ◽

Pimenta Dioica ◽

Non Destructive

The objective of this work was to obtain regression equations and to indicate the most appropriate from different mathematical models for the estimation of the leaf area of Allspice (Pimenta dioica) by non - destructive method. 500 leaves of plants located in the municipality of São Mateus, North of Espírito Santo State, Brazil, were collected, 400 of which were used to adjust the equations and 100 for validation. The length (L) along the main midrib, the maximum width (W), the product of the length with the width (LW) and the observed leaf area (OLA) were measured from all leaves. We fitted models of linear equations of first degree, quadratic and power, where OLA was the dependent variable in function of L, W and LW. From the 100 sheets intended for validation, and using the adjusted equations for each mathematical model, the estimated leaf area (ELA) was obtained. Subsequently, a simple linear regression was fitted for each model of the proposed equation in which ELA was the dependent variable and OLA the independent variable. The mean absolute error (MAE), the root mean square error (RMSE) and Willmott's index d also determined. The best fit had as selection criterion the non-significance of the comparative means of ELA and OLA, MAE and RMSE values closer to zero and value of the coefficient of determination coefficient (R2) close to one. Thus, the power model (ELA = 0.7605(LW)0.9926, R2 = 0.9764, MAE = 1.0066, RMSE = 1.7759 and d = 0.9950) based on the product of length and width (LW) is the most appropriate for estimating the leaf area of Pimenta dioica.

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ESTIMATION OF LEAF AREA IN WHEAT FROM LINEAR DIMENSIONS

Canadian Journal of Research ◽

10.1139/cjr39c-028 ◽

1939 ◽

Vol 17c (9) ◽

pp. 300-304 ◽

Cited By ~ 3

Author(s):

J. W. Hopkins

Keyword(s):

Least Squares ◽

Leaf Area ◽

Spring Wheat ◽

Standard Error ◽

Leaf Blade ◽

Statistical Relation ◽

Stages Of Development ◽

Individual Leaf ◽

Linear Dimensions ◽

Median Width

Measurements of 80 to 90 leaves of each of four varieties of spring wheat at various stages of development indicate a fairly close statistical relation between area, and length and width, of the leaf blade. This relation was found to be essentially the same for all four varieties, and from a knowledge of length (L) and median width (W½), the area of an individual leaf was given by the Least Squares relation log. A = 0.0094 + 0.934 log. L + 1.071 log. W½, with a standard error of 4.2% of the antilog. Inclusion of a third measurement, width at three-quarters of the distance from base to tip (W¼), led to the relation log. A = − 0.0438 + 0.970 log. L + 0.880 log. W½ + 0.189 log. W¼, giving estimated values having a standard error of 3.7% of the actual area per leaf.This method of estimating leaf areas (i) is rapid in execution and (ii) does not necessitate removing the leaves from experimental plants, which may accordingly be maintained intact for a series of physiological observations.

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