# Estimating Vertical Distribution of Leaf Water Content within Wheat Canopies after Head Emergence

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## Abstract

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^{2}= 0.82 and 0.84, respectively). By taking into account the effects of wheat spikes and the interrelationship of vertical LWC within canopies, an indirect induction strategy was developed for modeling the upper-LWC and bottom-LWC. It was found that the indirect induction models based on the WI-4 and NDWSI-4 indices were more effective than the models obtained from conventional direct estimation method, with R

^{2}of 0.78 and 0.81 for the upper-LWC estimation, and 0.75 and 0.74 for the bottom-LWC estimation, respectively.

## 1. Introduction

_{red edge}) could sense the chlorophyll content of the upper seven to nine leaf layers, when employing a hierarchical regression. From the results of Luo et al. [25], leaf nitrogen (N) content of reed in the top three layers can be accurately quantified based on canopy reflectance. The interrelationship of vertical leaf N distribution within the canopy was simulated by a statistical method and used for the estimation of leaf N content for the whole canopy. In addition, a physically based multiple-layer canopy reflectance model was proposed by Wang et al. [21], and was successfully tested in depicting vertical profiles of leaf variables for winter wheat [26]. They suggested that the penetration characteristics and sensitivity of spectral bands used in the spectral indices should also be considered. Based on these results, several wavebands in the NIR and SWIR regions were identified as effective wavelengths for building spectral indices or estimation models for assessing the vertical leaf N distribution [20,22,27].

## 2. Materials and Methods

#### 2.1. Field Experiments

^{6}plants ha

^{−1}and a row spacing of 25 cm, which included Lumai21, Jing411, Jingken49, Jing9843, Jingdong12, 9158, 6211, I-93, Laizhou3279. Nitrogen fertilizer as urea was applied at the pre-planting and the stem elongation stages; 345 kg ha

^{−1}compound fertilizer consists of 15% nitrogen, 15% phosphorus and 15% potassium were used prior to sowing. Each cultivar was planted in a plot with an area of 45 × 10.8 m

^{2}. Experiment 2 (Exp. 2) was conducted in 2017. Two cultivars of Lunxuan167 and Jingdong18 were investigated. Four N fertilization rates were applied for all cultivars: 0 (N0), 150 kg ha

^{−1}(N150), 300 kg ha

^{−1}(N300), and 450 kg ha

^{−1}(N450). Each cultivar was grown in plots of 15 m × 9 m size, on a silty clay loam soil.

#### 2.2. Canopy Spectral Reflectance Measurement

^{2}) were randomly selected, canopy spectral reflectance was measured at a height of about 1 m above wheat canopies from the nadir direction. Notably, in Exp. 2, after collecting spectral reflectance of entire canopy, all of wheat spikes in the subplot were carefully cut off, and the spectral reflectance of the remaining canopy without spikes was measured. Each spectral measurement of the two experiments was preceded by a dark current measurement and a white reference measurement was taken before and after canopy spectral measurement, using a 99% white Spectralon

^{®}(Labsphere, Inc., North Sutton, NH, USA) reference panel. Ten scans were determined and averaged to obtain the spectral reflectance of the entire canopy or canopy without spikes for each subplot. Three averaged subplots’ spectra were used to represent the reflectance of entire canopy or canopy without spikes for each plot.

#### 2.3. Vertical Leaf Water Content Distribution Measurement

#### 2.4. Published Spectral Indices

#### 2.5. Construction of New RRD Type of Spectral Indices

_{i}and b

_{i}are not unique, they depend on different sample datasets of $\overline{{R}_{k}}$ used [43].

_{i}and b

_{i}will be eliminated, thus be insensitive to the sample datasets. Therefore, it can be expressed in Equation (5) as well.

^{2}). All the calculations were implemented using MATLAB 8.3 (The MathWorks, Inc., Nat-ick, MA, USA). From our result, λ3 = 1350 nm for WI-3, λ3 = 1200 nm for NDWSI-3, λ3 = 825 nm and λ4 = 1013 nm for WI-4 and NDWSI-4, so the four new narrow-band spectral indices were:

#### 2.6. Data Analysis

^{2}) between LWC in vertical layers and published spectral indices, derived from spectral reflectance of the entire canopy with or without spikes, were calculated, which were referred to as R

^{2}

_{entire}

_{canopy}and R

^{2}

_{canopy}

_{without spikes}, respectively. A relative variation rate (R

_{v}, %) was used to compare the performance of each spectral index with respect to vertical LWC before and after spike removal, which was formulated as Equation (14). A higher Rv of R

^{2}suggests a higher degree of variations in spectral indices, i.e., effects of spikes, on vertical LWC estimation.

_{v}of R

^{2}(%) indicates the change of the accuracy of estimation models for LWC in a given vertical layer before and after spike removal. The R

_{v}of R

^{2}(%) > 0 represents an increase in model accuracy after removing spikes, whereas the R

_{v}of R

^{2}(%) < 0 represents a decrease.

_{Middle-LWC}indicates the LWC in the middle-layer, SI indicates the spectral indices used, coefficients a and b indicate the slope and intercept of estimation model for middle-LWC.

^{2}and root mean square error (RMSE) were employed to test the performance of the models in vertical LWC prediction, the relative error (RE) and Nash–Sutcliffe efficiency (NSE, calculated as Equation (16)) were used to evaluate the predictive ability of models, which were classified into four and three categories respectively by researchers [45,46], as shown in Table 2.

## 3. Results

#### 3.1. Vertical Variation of LWC within Wheat Canopies

#### 3.2. Effects of Wheat Spikes on Canopy Spectral Reflectance

#### 3.3. Effects of Wheat Spikes on Relationships between Published Spectral Indices and LWC in Vertical Layers

^{2}

_{entire canopy}and R

^{2}

_{canopy without spikes}of linear regression analyses for the relationships between published spectral indices and LWC in the upper-, middle- and bottom-layer are summarized in Table 3. In general, for all vertical layers, the values of R

^{2}

_{entire canopy}were all lower than the corresponding R

^{2}

_{canopy without spikes}, except for the CWI and NIDI, suggesting that the presence of wheat spikes negatively affects the accuracy of spectral indices in assessing the vertical LWC variation. This may present a convincing evidence for the decreased accuracy of leaf biochemical estimation models when the data obtained after the heading stage were pooled [47]. To further quantify the attenuation influence of spikes on LWC estimation in each vertical layer, we calculated the Rv between R

^{2}

_{entire canopy}and R

^{2}

_{canopy without spikes}of each spectral index for the three vertical layers. The results are shown in Figure 5. An important information revealed by Figure 5 is that the spikes had significant, but different, effects on the sensitivity of spectral indices to changes in the vertical LWC within canopies, depending on the vertical layers. Specifically, for almost all spectral indices, the Rv of R

^{2}in the middle layer yielded the smallest values compared with the upper- and bottom-layer, apart from the WBI/NDVI, LWI and NDII, whose Rv of R

^{2}in the middle layer ranked the second place. These results indicated that the assessment of middle-LWC was less susceptible to the effect of spikes, whereas the estimation of upper-LWC or bottom-LWC was relative strongly influenced.

^{2}in the relationship with respect to the middle-LWC, whereas the weakest relationships were found in the bottom layer. In consideration of the significant relationships between middle-LWC vs. upper-LWC and middle-LWC vs. bottom-LWC (Figure 3c,d), it was expected that the LWC in the upper and bottom layers could be indirectly assessed by the remote estimation model of middle-LWC at the late stage of wheat, as a result, reducing the variability due to the wheat spikes and improving vertical LWC estimates within canopies.

#### 3.4. Estimation of Vertical LWC Distribution of Wheat Using a Method of Indirect Induction

^{2}values larger than 0.56, while Rv of R

^{2}values less than 30%. Since the formulas and band combinations of the WI, WBI and FWBI1 showed remarkable consistency (Table 1), we used the WI as a representation. Given the fact that both the additive and multiplicative effects exist in canopy reflectance measurements across different wheat cultivars over growth stages, the WI and NDWSI were optimized by adding the third or/and forth wavebands to construct the four new RRD type of indices, expecting to reduce those effects on LWC estimation based on the MSC theory. Reflectance of each waveband or a large number of two-band combinations over the range of 400–2500 nm, were tested as the ${R}_{\lambda 3}$ or ${R}_{\lambda 3}$ and ${R}_{\lambda 4}$ combination in WI-3, NDWSI-3, WI-4 and NDWSI-4 equations (i.e., Equations (6)–(9)), then related to the middle-LWC. The R

^{2}value was used to evaluate which waveband or band combination should be selected to develop the best performing RRD type of indices (Figure 6). As shown in Figure 6a,b, in the selection of the third waveband used in the WI-3 and NDWSI-3, the high significance area all appeared in NIR region. It was worth noting that there are two peaks, $\lambda 3=1350\mathrm{nm}$ in the WI-3 and $\lambda 3=1200\mathrm{nm}$ in the NDWSI-3, achieving the highest R

^{2}values for determination of middle-LWC.

^{2}contour maps of the two four-band RRD indices showed similar patterns (Figure 6c,d). The indices that consisted of red-NIR region or NIR-NIR region as $\lambda 3$ and $\lambda 4$, i.e., WI-4 indices with $\lambda 3$: 685–700 nm and $\lambda 4$: 1450–1500 nm, $\lambda 3$: 770–850 nm and $\lambda 4$: 1000–1110 nm, as well as $\lambda 3$: 1415–1425 nm and $\lambda 4$: 1480–1525 nm; NDWSI-4 indices with $\lambda 3$: 620–700 nm and $\lambda 4$: 1450–1490 nm, $\lambda 3$: 790–895 nm and $\lambda 4$: 1000–1115 nm, as well as $\lambda 3$: 1415–1425 nm and $\lambda 4$: 1480–1540 nm, revealed high determination of coefficients relating to the middle-LWC (R

^{2}> 0.65). Maximum R

^{2}appeared in $\lambda 3=825\mathrm{nm}$ and $\lambda 4=1013\mathrm{nm}$ for both the WI-4 and NDWSI-4 indices.

^{2}values by 10% and 41%, while the NDWSI-3 $(({R}_{850}-{R}_{970})/({R}_{850}+{R}_{970}-2{R}_{1200}))$ and NDWSI-4 $((({R}_{850}-{R}_{825})-({R}_{970}-{R}_{1013}))/(({R}_{850}-{R}_{825})+({R}_{970}-{R}_{1013})))$ were superior over the NDWSI with increase of R

^{2}values by 3% and 38%, respectively. Being more effective than the three-band RRD indices, the two four-band RRD indices reduced the saturation of spectral indices to some degree and increased the accuracy of LWC estimation, where the WI-4 and NDWSI-4 explained 82% and 84% of the variation in middle-LWC at the late stages.

#### 3.5. Validation of Vertical LWC Distribution Models

^{2}< 0.6), which had led to very higher coefficients of determination (R

^{2}≥ 0.74). Specifically, for the middle-layer, we have found a very consistent agreement between LWC values measured and those estimated by WI-4 and NDWSI-4, with R

^{2}and NSE values higher than 0.8, and REs lower than 10%. The NDWSI-4 models performed the best in estimating the LWC in the top two layers, which explained 83% and 81% the variations in middle-LWC and upper-LWC, respectively. For the bottom layer, the WI-4 and NDWSI-4 produced similar result, with R

^{2}of 0.75 and 0.74. However, the NDWSI-4 estimate was more preferable, since it generated lower RMSE and RE values, as well as larger NSE, expressing distribution of scattering points being closer to the one-to-one line than the WI-4 estimate.

^{2}from 0.66 to 0.78 and from 0.77 to 0.81 for the models based on the WI-4 and NDWSI-4 for the upper-LWC, while the increase in R

^{2}from 0.68 to 0.75 and from 0.67 to 0.74 for the bottom-LWC, respectively.

## 4. Discussion

^{2}higher than 0.81 in middle-LWC assessment). These four new spectral indices were designed by adding one or two NIR bands into the WI and NDWSI on the basis of RRD formulation. Their advantage probably relies on the compensation of additive and multiplicative effects resulted from different canopy structures, anisotropic multiply scattering and soil background by using the MSC method, because the effects are common in the measurements of canopy spectral reflectance but have nothing to do with leaf biochemical parameters, i.e., LWC in this study. Similarly, the formula of RRD was also used by researchers to develop spectral indices, such as the modified SR $(mS{R}_{705}=({R}_{750}-{R}_{445})/({R}_{705}-{R}_{445}))$ and modified NDVI $(mN{D}_{705}=({R}_{750}-{R}_{705})/({R}_{750}+{R}_{705}-2{R}_{445}))$, the MERIS terrestrial chlorophyll index $(MTCI=({R}_{754}-{R}_{709})/({R}_{709}-{R}_{681}))$, the structure-insensitive pigment index $(SIPI=({R}_{800}-{R}_{445})/({R}_{800}-{R}_{680}))$ and the modified difference ratio $(MDR=({R}_{1271}-{R}_{410})/({R}_{1342}-{R}_{410}))$ [7,56,57,58], they all have been proven to be an improvement in terms of sensitivity to leaf pigment and leaf water contents when applied across a wide range of plant species, leaf structures and growth stages. From the comparison results between methods of the indirect induction and the conventional direct estimation (Figure 9), we concluded that the newly proposed approach contributed to achieve the higher potential of canopy spectra obtained from the nadir direction in monitoring vertical profiles of LWC after head emergence of wheat. Due to the limitation of samples, this method needs to be further studied by more experimental data and crop cultivars with different geometry types in the future. Although an increasing number of optical satellite images are freely available, the use of space-based imaging spectroscopy to quantify the vertical LWC distribution within crop canopies is still relatively challenging, because of the limited spatial and spectral resolutions. However, the application of narrow-band spectral indices to detect leaf biochemical parameter details has been an intended goal for studies of canopy physiology and ecology, our results provides support for the selection of spectral bands to design future sensors, and eventually to advance the identification and mapping of the vertical LWC from satellite data.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Vertical profiles of LWC within wheat canopies (

**a**) at different growth stages; (

**b**) under different N treatments at the head emergence stage (Z54), error bars represent standard deviation of vertical LWC measurements; the relationships between (

**c**) the middle-LWC vs. the upper-LWC and (

**d**) the middle-LWC vs. the bottom-LWC for both experiments.

**Figure 4.**Spectral reflectance of the entire wheat canopy and the canopy without spikes (

**a**) at different growth stages under the N300 treatment, and (

**b**) under different N treatments at the milk-filling stage (Z73).

**Figure 5.**The relative variation rate (R

_{v}) of R

^{2}of relationships between published spectral indices and LWC in the upper-, middle- and bottom-layer before and after removing spikes.

**Figure 6.**The R

^{2}curves between middle-LWC vs. (

**a**) the WI-3 and (

**b**) NDWSI-3 indices when using each waveband over 400–2500 nm as the third band ($\lambda 3$); R

^{2}contour maps between middle-LWC vs. (

**c**) the WI-4 and (

**d**) NDWSI-4 indices when using all possible combinations over 400–2500 nm as the third ($\lambda 3$) and forth bands ($\lambda 4$).

**Figure 7.**Scattering plots of relationships between the optimal RRD type of indices/the corresponding published spectral indices and the middle-LWC for the entire canopy. Subplots (

**a**–

**c**) show the relationships between the WI, WI-3, WI-4 and middle-LWC respectively, subplots (

**d**–

**f**) show the relationships between the NDWSI, NDWSI-3, NDWSI-4 and middle-LWC respectively.

**Figure 8.**Validation of estimation models derived from the WI-4, NDWSI-4 and NDWSI for the middle-LWC (

**green point**), the upper-LWC (

**blue diamond**) and the bottom-LWC (

**black star**). The black solid lines indicate linear fits, black dash lines indicate 1:1 line, red dash lines indicate the 95% confidence intervals of prediction.

**Figure 9.**Comparison of validation models between measured LWC and estimated LWC in the upper-layer (

**blue diamond**and

**red**

**diamond**) and bottom-layer (

**black star**and

**red star**) using the indirect induction and direct estimation methods. The four subplots in the first line are validation results based on the WI-4 for the upper- and bottom-layer, whereas the four subplots in the second line are validation results based on the NDWSI-4 for the upper- and bottom-layer.

Spectral Index | Formula | Reference |
---|---|---|

Water index (WI) | $WI=\frac{{R}_{900}}{{R}_{970}}$ | [14] |

Normalized difference water index (NDWI) | $NDWI=\frac{{R}_{860}-{R}_{1240}}{{R}_{860}+{R}_{1240}}$ | [15] |

Moisture stress index (MSI) | $MSI=\frac{{R}_{1600}}{{R}_{820}}$ | [34] |

Water band index (WBI) | $WBI=\frac{{R}_{970}}{{R}_{900}}$ | [35] |

WBI/normalized difference vegetation index (WBI/NDVI) | $WBI/NDVI=\frac{{R}_{970}}{{R}_{900}}/\frac{{R}_{800}-{R}_{680}}{{R}_{800}+{R}_{680}}$ | [14] |

Normalized difference infrared index (NDII) | $NDII=\frac{{R}_{850}-{R}_{1650}}{{R}_{850}+{R}_{1650}}$ | [36] |

Reciprocal of moisture stress index (RMSI) | $RMSI=\frac{{R}_{860}}{{R}_{1650}}$ | [36] |

Simple ratio water index (SRWI) | $SRWI=\frac{{R}_{860}}{{R}_{1240}}$ | [16] |

Maximum difference water index (MDWI) | $MDWI=\frac{{R}_{\mathrm{max}1500-1750}-{R}_{\mathrm{min}1500-1750}}{{R}_{\mathrm{max}1500-1750}+{R}_{\mathrm{min}1500-1750}}$ | [37] |

Composite water index (CWI) | $CWI={R}_{1660}\times {R}_{1820}$ | [13] |

Leaf water index (LWI) | $LWI=\frac{{R}_{1300}}{{R}_{1450}}$ | [38] |

Normalized different water stress index (NDWSI) | $NDWSI=\frac{{R}_{850}-{R}_{970}}{{R}_{850}+{R}_{970}}$ | [39] |

Novel image-derived index (NIDI) | $NIDI=\frac{{R}_{1529}}{{R}_{1416}}$ | [40] |

Floating-position water band index (FWBI1) | $FWBI1=\frac{{R}_{900}}{{R}_{\mathrm{min}930-980}}$ | [41] |

Floating-position water band index (FWBI2) | $FWBI2=\frac{{R}_{920}}{{R}_{\mathrm{min}960-1000}}$ | [42] |

Excellent | Good | Fair | Unsuitable | |
---|---|---|---|---|

RE | <10% | 10%–20% | 20–30% | >30% |

NSE | ≥0.9 | 0.5–0.8 | - | 0.1–0.4 |

**Table 3.**The R

^{2}

_{entire canopy}and R

^{2}

_{canopy without spikes}between published spectral indices and the LWC in different vertical layers. Colors correspond to the level of performances of spectral indices, from light blue for minimum R

^{2}value to red for maximum R

^{2}value.

Spectral Index | R^{2}_{entire canopy} | R^{2}_{canopy without spikes} | ||||
---|---|---|---|---|---|---|

Upper-Layer | Middle-Layer | Bottom-Layer | Upper-Layer | Middle-Layer | Bottom-Layer | |

WI | 0.39 | 0.47 | 0.29 | 0.53 | 0.61 | 0.4 |

NDWI | 0.36 | 0.44 | 0.28 | 0.53 | 0.61 | 0.4 |

MSI | 0.32 | 0.4 | 0.28 | 0.46 | 0.55 | 0.39 |

WBI | 0.38 | 0.47 | 0.29 | 0.52 | 0.6 | 0.4 |

WBI/NDVI | 0.36 | 0.41 | 0.28 | 0.39 | 0.48 | 0.36 |

NDII | 0.34 | 0.41 | 0.3 | 0.48 | 0.56 | 0.39 |

RMSI | 0.36 | 0.45 | 0.31 | 0.53 | 0.6 | 0.39 |

SRWI | 0.37 | 0.45 | 0.32 | 0.55 | 0.62 | 0.4 |

MDWI | 0.27 | 0.38 | 0.24 | 0.4 | 0.49 | 0.32 |

CWI | 0.46 | 0.38 | 0.44 | 0.11 | 0.17 | 0.09 |

LWI | 0.29 | 0.39 | 0.25 | 0.41 | 0.49 | 0.27 |

NDWSI | 0.44 | 0.5 | 0.37 | 0.58 | 0.65 | 0.41 |

NIDI | 0.32 | 0.34 | 0.26 | 0.08 | 0.12 | 0.06 |

FWBI1 | 0.38 | 0.5 | 0.33 | 0.57 | 0.63 | 0.42 |

FWBI2 | 0.38 | 0.48 | 0.33 | 0.56 | 0.63 | 0.44 |

**Table 4.**The R

^{2}between published spectral indices derived from spectral reflectance of the entire canopy and the LWC for the three vertical layers by using datasets from Exp. 1 and 2. Colors correspond to the level of performances of spectral indices, from light blue for minimum R

^{2}value to red for maximum R

^{2}value.

Spectral Index | Upper-Layer | Middle-Layer | Bottom-Layer |
---|---|---|---|

WI | 0.56 | 0.58 | 0.54 |

NDWI | 0.47 | 0.47 | 0.45 |

MSI | 0.40 | 0.42 | 0.38 |

WBI | 0.55 | 0.58 | 0.54 |

WBI/NDVI | 0.42 | 0.49 | 0.44 |

NDII | 0.42 | 0.44 | 0.41 |

RMSI | 0.41 | 0.41 | 0.40 |

SRWI | 0.46 | 0.47 | 0.45 |

MDWI | 0.47 | 0.50 | 0.46 |

CWI | 0.01 | 0.05 | 0.03 |

LWI | 0.45 | 0.46 | 0.44 |

NDWSI | 0.59 | 0.61 | 0.58 |

NIDI | 0.33 | 0.38 | 0.30 |

FWBI1 | 0.56 | 0.56 | 0.52 |

FWBI2 | 0.53 | 0.54 | 0.50 |

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## Share and Cite

**MDPI and ACS Style**

Kong, W.; Huang, W.; Ma, L.; Tang, L.; Li, C.; Zhou, X.; Casa, R.
Estimating Vertical Distribution of Leaf Water Content within Wheat Canopies after Head Emergence. *Remote Sens.* **2021**, *13*, 4125.
https://doi.org/10.3390/rs13204125

**AMA Style**

Kong W, Huang W, Ma L, Tang L, Li C, Zhou X, Casa R.
Estimating Vertical Distribution of Leaf Water Content within Wheat Canopies after Head Emergence. *Remote Sensing*. 2021; 13(20):4125.
https://doi.org/10.3390/rs13204125

**Chicago/Turabian Style**

Kong, Weiping, Wenjiang Huang, Lingling Ma, Lingli Tang, Chuanrong Li, Xianfeng Zhou, and Raffaele Casa.
2021. "Estimating Vertical Distribution of Leaf Water Content within Wheat Canopies after Head Emergence" *Remote Sensing* 13, no. 20: 4125.
https://doi.org/10.3390/rs13204125