Allometric models for leaf area estimation and ceptometer validation in assessing the leaf area index of ‘Cabernet Franc’ and ‘Malbec’ grape cultivars produced under cycle inversionAbstract:
Leaf area is an important parameter for analyzing the growth and development of grapevines, which has been obtained using direct non-destructive methods and mathematical models based on the relationship between assessed and estimated leaf area. This study aimed to adjust and validate mathematical equations for estimating the leaf area of ‘Cabernet Franc’ and ‘Malbec’ grape cultivars trained to a three-wire vertical trellis and submitted to the cycle inversion technique in São Roque - SP. In addition, the use of the AccuPAR® ceptometer was validated to determine the leaf area index. Leaves of different sizes wererandomly collected, and the central and lateral veins were measured, obtaining leaf area using the WinRHIZO® system. Linear and non-linear models were tested, and the quadratic equation for ‘Cabernet Franc’ grape and the power equation for‘Malbec’ grape had the best fits, with determination coefficients = 90%. In thevalidation, all models showed correlation and no statistical differences with the evaluated leaf area. It was, therefore, possible to obtain leaf area data using a simpleand non-destructive method. For ‘Cabernet Franc’ grape, the suggested equation was y = 0.5215 x2 – 4.473 x + 32.235, and for ‘Malbec’ grape, y = 0.5428 x1.8599.When the leaf area index was indirectly obtained using the AccuPAR® ceptometer, LAI values obtained at the ripening stage were underestimated.
Index terms
Vitis vinifera; Double pruning; Winter wines; Non-destructive method; Mathematical models
Resumo:
A área foliar é um parâmetro importante para a análise do crescimento e do desenvolvimento da videira. Métodos não destrutivos diretos são utilizados para obtenção desta, através de modelos matemáticos estabelecidos na relação entre a área foliar avaliada e a estimada. Desta forma, o objetivo do estudo foi porta ajustar e validar equações matemáticas para estimativas de área foliar das cultivares Cabernet Franc e Malbec, sustentadas em espaldeira e submetidas à técnica deinversão de ciclo, em São Roque – SP, além de validar o uso do ceptômetro AccuPAR® na determinação do índice de área foliar. Para tanto, foram coletadas, aleatoriamente, folhasde diferentes tamanhos, e as nervuras centrais e laterais de cada uma foram mensuradas,sendo a área foliar real obtida pelo sistema WinRHIZO®. Foram testados modeloslineares e não lineares, nos quais a equação quadrática para ‘Cabernet Franc’ e de potência para ‘Malbec’ tiveram os melhores ajustes, com coeficientes de determinação = 90%. Na validação, todos os modelos apresentaram correlação e sem diferenças estatísticas com a área foliar avaliada. Portanto, foi possível obter dados da área foliar utilizando métodosimples e não destrutivo. Para ‘Cabernet Franc’, a equação sugerida foi (y = 0,5215 x2 –4,473 x + 32,235), e para ‘Malbec’ (y = 0,5428 x1,8599). Com relação à obtenção do índice de áreafoliar de modo indireto com o uso do ceptômetro AccuPAR, os valores de IAF fornecidos no estádio de maturação foram subestimados.
Termos para indexação
Vitis vinifera; Dupla-poda; Vinhos de inverno; Método não destrutivo; Modelos Matemáticos
Introduction
The grapevine canopy characteristics are commonly analyzed by the physiological parameter of leaf area index (LAI), which is correlated with production, photosynthetic capacity, growth and development indications, translocation of photoassimilates, water absorption and evapotranspiration, water requirements, among many other variables (TEIXEIRA and LIMA FILHO, 1997; REYNOLDS and VANDEN HEUVEL, 2009; BUTTARO et al., 2015; SANCHEZRODRIGUEZ et al., 2016).
Assessing leaf area in the field can be performed using destructive, indirect, non-destructive, or direct non-destructive methods.
The first model involves the removal of leaves and subsequent reading on specific meters/programs, but it has the disadvantage of damaging plants and being time-consuming and laborious. Using the indirect method, it is possible to use remote detection or remote sensing (DOBROWSKI et al., 2002) and digital imaging (LEITE et al., 2021). With regard to the direct method, portable meters, or data obtained through the relationship between leaf area and linear measurements, are capable of providing information using equations already established in literature.
The mathematical models developed are usually accurate and perform faster field evaluations (CARBONNEAU, 1976; TREGOAT et al., 2001; JUNGES and ANZANELLO, 2021; SAUTCHUK et al., 2024). However, due to leaf morphological variations, specific and adjusted equations are needed for different species, cultivars, training and supporting systems. Several authors have described the establishment of mathematical equations in cultivated plants that can be carried out using measurements of central veins and leaf width (MONTERO et al., 2000; DEMIRSOY et al., 2004; BUTTARO et al., 2015; SACHET et al., 2015), as well as other methods, such as leaf diameter (PERMANHANI et al., 2014) or involving lateral veins (CARBONNEAU, 1976).
Like leaf area, LAI is also measured using destructive and non-destructive methods, with the same advantages and disadvantages.
Non-destructive methods involve specific equipment or established mathematical equations to estimate LAI.
Examples of indirect methods for obtaining indices include the use of thermal images (BANERJEE et al., 2018), UAV (unmanned aerial vehicle) images (VÉLEZ et al., 2021), remote sensing and the portable ceptometer sensor (AccuPAR® L-80, Decagon Devices, USA).
In the region of São Roque, state of São Paulo, there are no studies validating universal mathematical equations or developing new models that estimate leaf area in vines submitted to the cycle inversion technique, from which winter harvest wines are produced.
Likewise, the AccuPAR® ceptometer, as one of the technologies used in research involving photosynthetically active radiation and indirectly obtaining LAI, needs to be validated for this new pruning system.
Thus, the aim of this study was to adjust and validate mathematical models to estimate the leaf area for ‘Cabernet Franc’ and ‘Malbec’ grape cultivars, supported on espaliers and with cycle inversion in the municipality of São Roque – state of São Paulo, as well as to validate the use of the AccuPAR® equipment to determine the leaf area index.
The mathematical models for estimating leaf area were adjusted using leaves from ‘Cabernet Franc’ (clone 214) and ‘Malbec’ (clone 596) grape cultivars collected in a non-irrigated commercial vineyard in the municipality of São Roque - SP, located at 23°35’37.5’’ S and 47°9’ 40’’ W, altitude of 890 m above sea level and climate according to Koppen, Cfb - humid subtropical climate with no dry season and temperate summer (ALVARES et al., 2013), with average temperatures varying between 23.1°C and 15.5°C (ABRAMIDES et al., 2019). To build the models, leaves from ‘Cabernet Franc’ and ‘Malbec’ grape cultivars were collected from a vineyard planted in 2011 on Paulsen 1103 rootstock, with spacing of 1.5 m between plants and 2.5 m between rows. All cultivars were trained to a three-wire vertical trellis with the low wire 0.9 m above ground and two spur cordons per vine and submitted to cycle inversion.
Canopy management consisted of removing leaves around the bunches during stage 73 (groat-size) according to the Biologische Bundesanstalt für Land und Forstwirtschaft, Bundessortenamt und Chemische Industrie (BBCH) scale (LORENZ et al., 1995), no stripping and use of white anti-hail screen around the bunches from the color change stage (BBCH 81) to protect against pests and wild animals.
During the ripening stage, 200 complete, healthy leaves of different sizes for each cultivar were randomly collected from the vineyard in the 2021, 2022 and 2023 seasons (BBCH 83-85). Exsiccates of all the material sampled were prepared, without the petioles, and stored for later evaluations.
Leaves with veins ≤ 3 cm were not used, as recommended by Lopes and Pinto (2000).
The central (CV) and lateral (LV1 and LV2) veins were measured using a graduated ruler (in mm) (Figure 1), while leaf area was measured using the WinRHIZO® computer program. Linear and non-linear models were assessed using the relationship between the leaf area of each leaf assessed and the CV length between assessed leaf area and CV2; between assessed leaf area and the sum of LV1 and LV2 (Σ LV); between the assessed leaf area and the square of the average LV length (x̄LV2). The selected models were adjusted using the Akaike Information Criterion (AIC), Determination Coefficient (R2), Mean Square Error (MSE), Predicted Residual Sum of Squares (PRESS) and Willmott’s Index of Agreement (d).
Leaves and dimensions evaluated for ‘Cabernet Franc’ (A) and ‘Malbec’ (B) grape cultivars, trained to a three-wire vertical trellis and submitted to the cycle inversion technique, São Roque -SP.
To validate the mathematical regression models for each cultivar, 31 healthy leaves (BBCH 83-85), complete and of different sizes, were randomly collected in the 2023 season. After exsiccation, the leaf area of all leaves was measured using WinRHIZO® and estimated using the best fit mathematical model for each cultivar. The general model proposed by Carbonneau (1976) was also tested using the formula: LA = (0.305 x SLV2) + (1.605 x SLV) – 6.885; where LA = leaf area and SLV = sum of lateral veins.
The ceptometer (AccuPAR® L-80) used mainly to determine photosynthetically active radiation through sunlight interception also indirectly estimates the leaf area index. Readings were taken on five plants of each cultivar in the 2021 and 2023 seasons, between 11 a.m. and 1 p.m. at the ripening stage (BBCH 81-83), using the external sensor. Readings were taken parallel to the pruning line (spur cord) (adapted from WURZ et al., 2019), with each value obtained from the average of three readings.
The leaf area index was calculated using the average of all readings.
The actual leaf area index was determined by selecting a branch from the central part of each plant in the 2021 and 2023 seasons (BBCH 81-83), in order not to damage the entire plant. In this way, all healthy and whole leaves were collected from the branch and evaluated using the WinRHIZO® equipment. The total leaf area per plant was obtained from the ratio between the total leaf area per branch under the occupied surface area [average space between one spur and another (0.08 m), and the average width of the double wire (0.18 m), totaling an area of 0.0144 m2 per branch] and the total plant area [average spur cord length (1.5 m) and the average double wire width (0.18 m), occupying an area of 0.27 m2]. The leaf area index per plant was based on the equation defined by Watson (1947), calculated using the formula: LAI = total leaf area m2.0.27 m-2.
Mathematical models were developed using regression analysis with the best fit.
To validate the equations, data collected were transformed (log x) and submitted to the Shapiro Wilk normality test and analysis of variance, followed by comparison of means between assessed and estimated leaf area and the general model proposed by Carbonneau (1976), using the Tukey test at 5% probability and the R® software.
To validate the ceptometer, the leaf area index data for both cultivars obtained by destructive and non-destructive methods were submitted to analysis of variance and Tukey test at 5% probability.
There was a relationship between leaf area and leaf vein length for ‘Cabernet Franc’ and ‘Malbec’ cultivars submitted to cycle inversion, according to the determination coefficient. The best relationship occurred through the sums of lateral veins, represented by non-linear models for both cultivars (Table 1).
High determination coefficients indicate finer adjustments in the developed models.
In this work, the R2 selected is high and is close to or within what is expected for this type of study, as seen in the work by Permanhani et al. (2014) and Junges and Anzanello (2021), with coefficients above 90%. For ‘Cabernet Franc’, the best model was quadratic, with R2 of 0.903. Although ẍ LV2 also had the same R2, it was chosen due to the simplification of the equation and mathematical calculations. The same situation occurred with the ‘Malbec’ cultivar, but the power model was selected, with R2 of 0.913. AIC, MSE, PRESS, and d parameters also collectively contributed to the selection of the best models. The goal was to identify models with low AIC, MSE, and PRESS values, and high d values.
Based on the measurements of lateral veins, the leaf area estimated using the equations that represent the best fit (Figure 2) are consistent and highly accurate.
Quadratic and power equations of models for estimating leaf area (cm2) of ‘Cabernet Franc’ and ‘Malbec’ cultivars, trained to a three-wire vertical trellis and submitted to the cycle inversion technique, São Roque - SP.
The comparison of means between assessed and estimated leaf area (Table 2), using leaves collected for validation and equations suggested for ‘Cabernet Franc’ (y = 0.5215 x2 – 4.473 x + 32.235) and ‘Malbec’ (y = 0.5428 x1.8599), as well as a universal equation proposed by Carbonneau (1976), (y = 0.305 x2 + 1.605 x – 6.885), in which “x” represents the sum of the length of lateral Cabernet Franc veins, showed no significant differences.
This result validates the general equation proposed by Carbonneau (1976), which had not been previously used in a system with differentiated pruning. It also supports the new proposal, providing an additional and specific method for determining leaf area in the field of vines submitted to the cycle inversion technique.
In several other studies, non-linear models have also been proposed, such as the power model indicated for ‘Chardonnay’, ‘Cabernet Sauvignon’ and ‘Merlot’ cultivars growing on vertical trellis and horizontal trellis systems in the region of Serra Gaúcha (JUNGES and ANZANELLO, 2021), ‘Cabernet Sauvignon’ and ‘Sauvignon Blanc’, grown on vertical trellis system in São Joaquim - SC (BORGHEZAN et al., 2010), as well as other crops such as pornunça (Manihot sp.) (LEITE et al., 2021), banana (Musa spp.) (VIEIRA et al., 2022) and cassava (Manihot esculenta Crantz) (TRACHTA et al., 2020). However, other models also suitable for each region and cropping system can be found, such as linear models for litchi tree (Litchi chinensis Sonn.) in Linhares - ES (OLIVEIRA et al., 2017) and ‘Niagara Rosada’ grape in Cardoso Moreira - RJ (PERMANHANI et al., 2014); as well as the logarithmic model for papaya (CAMPOSTRINI and YAMANISH, 2001), among other possibilities.
Using the total leaf area, the LAI value can be obtained as a function of a specific area. However, modern techniques can be used to obtain LAI indirectly and non-destructively, such as the portable sensor ceptometer. Using ceptometer, the question is whether the data provided are consistent with the canopy being assessed.
Comparative data between assessed leaf area index (LAIa) and the leaf area index using ceptometer (LAIc) (Table 3) showed underestimated values with the use of the ceptometer for both cultivars under study.
The average LAIa values were 6.25 for ‘Cabernet Franc’ and 6.81 for ‘Malbec’ cultivars, slightly more than twice the values found using LAIc, which were 2.86 and 2.90, respectively. This situation was also observed in a study on permanent pasture, in which both AccuPAR® and LAI-2200C® sensors found underestimated values (KLINGLER et al., 2020). The reading error caused by the sensor must be taken into account, since it depends on the leaf position.
If leaves overlap, as in the case of grapevines at the ripening stage when conducted on vertical trellis, the amount of shade projected would be similar, even with an increase in the number of leaves. The loss of sensitivity at higher LAI due to small changes in shade is reported by the manufacturer itself, requiring adjustments to the positioning of the sensor bar, such as the position in relation to the sun and the structure and orientation of plants and their leaves, in order to reduce error rates.
The position of the sun influences the reliability of LAI data as a function of shading.
Protocols and correction factors have been developed and studied for different crops to reduce interference in results. The creation of correction factors or the application of adjustment formulas have also been observed in other studies, such as the use of canopy height in soybeans, sugarcane and maize as a calibration measure to avoid overestimating LAI values (GONÇALVES et al., 2020).
Although the use of the ceptometer, under the protocol used in this work and in a different pruning system - cycle inversion, causes LAI values to be lower than expected and not validated, as its use is still a quick alternative for obtaining results throughout the crop cycle.
The leaf area of ‘Cabernet Franc’ and ‘Malbec’ grape cultivars submitted to the cycle inversion technique in the municipality of São Roque - SP can be estimated by the direct non-destructive method using measurements of lateral veins. Both equations suggested for ‘Cabernet Franc’ (y = 0.5215 x2 – 4.473 x + 32.235) and ‘Malbec’ (y = 0.5428 x1.8599), as well as the universal equation proposed by Carbonneau (1976), (y = 0.305 x2 + 1.605 x – 6.885), proved to be suitable for estimating leaf area.
The use of AccuPAR® ceptometer to obtain LAI in an indirect and non-destructive way underestimates the real LAI values under the conditions of the established protocol.
Acknowledgments
This study was financially supported by “Coordenação de Aperfeiçoamento de Pessoal de Nível Superior” (CAPES) - Finance Code 001. We wish to thank the Vitivinícola Góes Ltda. for allowing this study to be carried out in part of its vineyards.
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Edited by
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Scientific Editor
Alexandre pio Viana
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Associate Editor
Alessandro Dal´Col Lucio
