Improving indirect measurements of the leaf area index using canopy height

The objective of this work was to evaluate the use of plant height as a calibration variable for improving indirect measurements of the leaf area index (LAI). Three experiments were conducted with different crops – corn (Zea mays), soybean (Glycine max), and sugarcane (Saccharum officinarum) –, to compare the performance of the LAI measured indirectly (LAIind) and corrected by the calibration variable with the LAI measured directly (LAIref). Without the proposed correction, the LAIind tended to be overestimated by 20%, on average, compared with the LAIref, for the three crops. After crop height was used to adjust the LAIind, a strong positive relationship was observed between the LAIref and the corrected LAIind (R2 = 0.96); overestimation was reduced to 4% and the mean square error decreased to 0.07 m2 m-2. The variable canopy height is promising for the correction of the LAI of the soybean, corn, and sugarcane crops.


Introduction
The leaf area index (LAI) is defined as the ratio of the total leaf area per unit area exploited by the crop (Miller, 1967) and is a key variable in a range of processes including gas and energy exchange, water and nutrient cycling, canopy health, and primary production (Fang et al., Pesq. agropec. bras., Brasília, v.55, e01894, 2020 DOI: 10.1590/S1678-3921.pab2020.v55.01894 2018; Yan et al., 2019). It can be evaluated by: direct methods, such as planimeters, area integrators, and specific relationships (Chianucci & Cutini, 2013); and indirect methods, as dry mass and electronic devices to assess the light intercepted by the canopies (Gonsamo et al., 2018;Fang et al., 2019). An accurate quantification of the LAI is, therefore, important for crop growth and development (Addai & Alimiyawo, 2015).
Of these optical instruments, the LAI-2200C Plant Canopy Analyzer and its predecessor, the LAI-2000, are among the most used worldwide (Kobayashi et al., 2013;LI-COR, Inc., 2015), and their algorithms are based on the approaches proposed by Miller (1986). In the case of the LAI-2000 analyzer, the manufacturer alerts that there may be divergences in LAI estimates when the plants have a large amount of dead and/or senescent material and recommends that calibrations be made using direct LAI determinations to improve the results (Sbrissia & Silva, 2008).
Although indirect methods to estimate the LAI have already been compared in previous researches, large uncertainties still remain and the use of multiple instruments has revealed a considerable variability and uncertainty in the taken measurements (Ariza-Carricondo et al., 2019). In some cases, it is recommended to combine the LAI-2000 instrument with another method for the correct estimation of the LAI (Ryu et al., 2010a(Ryu et al., , 2010b.
The objective of this work was to evaluate the use of plant height as a calibration variable for improving indirect measurements of the leaf area index.

Materials and Methods
Three experiments were carried out with the corn, soybean, and sugarcane crops in the experimental area of Escola Superior de Agricultura Luiz de Queiroz of Universidade de São Paulo (22°41'53"S, 47°38'35"W, at 538 m above sea level). The climate, according to Köppen, is Cwa, described as humid subtropical with a rainy summer and a dry winter . All experiments were irrigated using center-pivot i-Wob UP3 sprinklers (Senninger Irrigation, Clermont, FL, USA), managed by a crop water balance based on data acquired from an automatic agrometeorological station installed in the same experimental area, in order to assure the maximum evapotranspiration rates for all the crops. Each experiment was conducted under conditions to guarantee potential yield (Ittersum et al., 2013;Fischer, 2015), without biotic or abiotic stresses (Fritsche-Neto & Borém, 2012), and preventive actions were taken against pests and diseases. The soils were classified as Oxisols (Peters et al., 2014) in the soybean and sugarcane crop sites and as a Chromic Acrisol Nitisol  in the corn crop site. The biometric data samples consisted of: leaf length and height for corn; dry green leaf mass for sugarcane; and direct and indirect LAI determinations and canopy height measurements for all crops. The period of experimental data collection, number of observations, and a summary of the meteorological conditions are presented in Table 1.
The P-4285YH corn hybrid was sown on 5/16/2016 and harvested on 9/29/2016. The experimental design was randomized complete blocks with four replicates. Each replicate consisted of 96-m 2 plots, 3.2 m wide (four rows spaced at 0.8 m) and 30 m long (288 m 2 per hybrid), resulting in a population of 60,000 plants per hectare. For fertilization, 30 kg ha -1 nitrogen, 90 kg ha -1 P 2 O 5 , and 50 kg ha -1 K 2 O were applied, as well as 80 kg ha -1 nitrogen topdressed. The biometric data The RB867515 sugarcane variety was planted on 5/10/2018, using nearly 9.7 buds per square meter, at a row spacing of 1.4 m. The experimental design was randomized complete blocks with four replicates. From the end of August to the beginning of October 2018, the soil was prepared and received 500 kg ha -1 reactive natural phosphate. Fertilization at planting consisted of 50 kg ha -1 N, 75 kg ha -1 P 2 O 5 , and 75 kg ha -1 K 2 O enriched with 0.3% B and 0.5% Zn. Two cover fertilizations were performed: the first in January 2019, with 177 kg ha -1 N as urea and 186 kg ha -1 K as potassium oxide ( The samples used for the LAI measured directly (LAI ref ) and indirectly (LAI ind ) were collected on the same dates as those for biometrics. For the soybean crop, the LAI ref was estimated with the aid of the Quant scanning and processing software, version 1.0.2 (Richter et al., 2014), used to calculate leaf area. For the corn crop, the LAI ref (Vieira Junior et al., 2006) was based on measuring the width and length of green leaves, multiplied by a shape correction factor of 0.7 (Marin et al., 2005). For the sugarcane crop, the LAI ref was obtained by the leaf disk method (Pierozan Junior & Kawakami, 2013). For the corn and soybean crops, 5 sample plants were randomly selected among the blocks, totalizing 20 plants, for LAI ref determinations. For the soybean and sugarcane crops, 5 sample plants -20 and 25 in total, respectively -were collected among the blocks to determine the LAI ref by the destructive method.
For the indirect measurements of the LAI ind , the LAI-2200C electronic analyzer (LI-COR, Inc., Lincoln, NE, USA), with an embedded algorithm, was used; the theoretical background of this device is fully described in Kuusk (2016). Following the manufacturer's recommendations (LI-COR, Inc., 2015), all LAI measurements were taken in the late afternoon or at sunrise to avoid the incidence of direct sunlight, at a 45° angle view. It should be noted that, although not performed in this work, measurements under open-sky conditions are also allowed (Pearse et al., 2016). Besides each LAI ind , crop canopy height was measured using a ruler.
In theory, electronic retrievers work based on notions of probability, that is, the LAI-2200C analyzer measures the probability (PΘ) that radiation will not be intercepted by the canopy, through the following equation (Ryu et al., 2010a;LI-COR, Inc., 2015): where G (Θ) is the foliage projection fraction, μ is leaf density, and S (Θ) is the distance from the top of the canopy to soil surface. S (Θ) is, therefore, a relationship between canopy height and the cosine of the angle defined between the canopy projection line and its normal (Jones, 2013). The LAI ind data were statistically compared with those obtained for the LAI ref and canopy height, using as agreement measures: Nash & Sutcliffe's modeling efficiency (Ritter & Muñoz-Carpena, 2013), the correlation index, the mean squared error (MSE) (Wilks, 2006), and Wilmott's index of agreement (Willmott et al., 2012).

Results and Discussion
The LAI ind was overestimated by about 20% compared with the LAI ref for soybean, corn, and sugarcane ( Figure 1), but it expressed well the time variation of the LAI for the three crops (Table 2). Based on a theoretical model and on the gap fraction measurements from 41 sites, Kobayashi et al. (2013) reported that the effective LAI must be quantified using a second approach and that, in some cases, the LAI is overestimated up to 30% at the studied sites. Particularly for the soybean crop, the LAI-2200C analyzer was not able to estimate satisfactorily the LAI at the end-of-cycle sampling (71 days after sowing), as found by Jesus et al. (2001). As in the study of Malone et al. (2002), the results probably indicate that the estimates of LAIs with defoliation below 2.0 were likely skewed by a greater proportion of pods, stems and petioles, resulting in higher values than those obtained for the directly measured LAI. Similar results were found by Liu et al. (2008) for soybean crops, since the indirect measurement overestimated the LAI by 12.5% at 96 days after sowing. However, the LAI ref values are consistent with those reported by Heiffig et al. (2006)  The LAI ind (Figure 2 A), compared with the LAI ref , showed good accuracy for all three crops evaluated, as observed by Welles & Norman (1991) and Jonckheere et al. (2004) when using the LAI-2000 analyzer to estimate the LAI in homogeneous canopies such as those of soybean, wheat (Triticum aestivum L.), and grass. This is probably related to the fact that, although they are not the same devices, the successors of LAI-2000 use the same theoretical background, with Pesq. agropec. bras., Brasília, v.55, e01894, 2020 DOI: 10.1590/S1678-3921.pab2020.v55.01894 some improvements (Yan et al., 2019). The obtained coefficient of determination (R 2 ) ranged from 0.46 to 0.88, with higher values for sugarcane and corn and a lower precision for soybean (Table 3). The lower R 2 value for the soybean crop may be explained by the gap fraction highly sensitive to canopy structure, leaf distribution, and leaf plasticity (López-Lozano et al., 2007). Although Willmott's index of agreement showed satisfactory efficiency, a way to improve the correlation between the LAI ref and LAI ind data was still sought. In addition, the canopy height values obtained for the studied crops were considered consistent with those found by Doná et al. (2019), Shioga et al. (2015), and Oliveira et al. (2010) for similar soybean, corn, and sugarcane cultivars, respectively (Table 2); the observed peaks tended to coincide with the maximum LAI values.
After canopy height was used as a calibration variable, R 2 and Willmott's index of agreement showed better performance (Figure 2 B). R 2 ranged from 0.95 to 0.99, and MSE decreased considerably from 2.87 to 0.19 for soybean. In this way, there was a positive contribution to improving estimation, and all p-values were <0.01, except the one for soybean (Table 4). Galzerano et al. (2012) and Coêlho et al. (2014) also found a good correlation between canopy height and determinations of the LAI; however, these authors evaluated tropical grasses.
Inserting canopy height as a secondary input variable in regression reduced the error of both Willmott's index of agreement and R 2 ; therefore, the variable contributed positively to the accuracy of the used   (Table 3). Although canopy height improved the verified correlation, it is possible that other factors influence LAI-2200C measurements, mainly in the crop reproductive stage due to a logical relationship, which implies that other plant structures, such as stems and pods, are considered as leaf area (Malone et al., 2002). This process seems to have occurred for the soybean cultivar evaluated in the present work (Figure 2 B). Welles & Norman (1991) reported another source of uncertainty in the theory behind analyzers, highlighting that the electronic indirect method fails to distinguish senescent or dead tissue from living tissue, increasing the discrepancy in the LAI readings, as in the case of the soybean crop. To improve measurements, Nilson (1971) suggests relating clumping to the size of vegetative elements and to the distance between them. Kucharik et al. (1998) compared the variation of this parameter in a homogeneous canopy and found that the LAI, under these conditions, only varies as a function of canopy height. Canopy height proves to be a promising calibration variable for use in the corn and sugarcane crops. One of the reasons is that, since the LAI can be determined throughout the crop cycle by indirect measurements, more reliable data can be obtained. In both crops, correcting by canopy height resulted in a more accurate LAI because these plants have a higher proportion of leaves than other structures, when compared with soybean (Argenta et al., 2001).   Pesq. agropec. bras., Brasília, v.55, e01894, 2020 DOI: 10.1590/S1678-3921.pab2020.v55.01894

Conclusions
1. The values of the leaf area index (LAI) estimated by the LAI-2200C electronic device are overestimated for the soybean (Glycine max), corn (Zea mays), and sugarcane (Saccharum officinarum) crops.
2. Canopy height as a calibration variable can correct indirect LAI measurements and improve agreement with direct LAI measurements.