# Combining Vegetation Indices to Identify the Maize Phenological Information Based on the Shape Model

Huizhu Wu, Bing Liu, Bingxue Zhu, Zhijun Zhen, Kaishan Song, Jingquan Ren

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Huizhu Wu, Bing Liu, Bingxue Zhu, Zhijun Zhen, Kaishan Song, et al. Combining Vegetation Indices to Identify the Maize Phenological Information Based on the Shape Model. Agriculture, 2024, 14 (9), pp.1608. 10.3390/agriculture14091608. [https://doi.org/10.3390/agriculture14091608]

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Article

# Combining Vegetation Indices to Identify the Maize Phenological Information Based on the Shape Model

Huizhu Wu<sup>1,2</sup>, Bing Liu<sup>1</sup>, Bingxue Zhu<sup>2,*</sup>, Zhijun Zhen<sup>3,4</sup>●, Kaishan Song<sup>2</sup> and Jingquan Ren<sup>5</sup>

**Abstract:** Maize is the world's largest food crop and plays a critical role in global food security. Accurate phenology information is essential for improving yield estimation and enabling timely field management. Yet, much of the research has concentrated on general crop growth periods rather than on pinpointing key phenological stages. This gap in understanding presents a challenge in determining how different vegetation indices (VIs) might accurately extract phenological information across these stages. To address this, we employed the shape model fitting (SMF) method to assess whether a multi-index approach could enhance the precision of identifying key phenological stages. By analyzing time-series data from various VIs, we identified five phenological stages (emergence, seven-leaf, jointing, flowering, and maturity stages) in maize cultivated in Jilin Province. The findings revealed that each VI had distinct advantages depending on the phenological stage, with the land surface water index (LSWI) being particularly effective for jointing and flowering stages due to its correlation with vegetation water content, achieving a root mean square error (RMSE) of three to four days. In contrast, the normalized difference vegetation index (NDVI) was more effective for identifying the emergence and seven-leaf stages, with an RMSE of four days. Overall, combining multiple VIs significantly improved the accuracy of phenological stage identification. This approach offers a novel perspective for utilizing diverse VIs in crop phenology, thereby enhancing the precision of agricultural monitoring and management practices.

**Keywords:** optical remote sensing; crop phenology; land surface water index (LSWI)

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**Citation:** Wu, H.; Liu, B.; Zhu, B.; Zhen, Z.; Song, K.; Ren, J. Combining Vegetation Indices to Identify the Maize Phenological Information Based on the Shape Model. *Agriculture* **2024**, *14*, 1608. https://doi.org/10.3390/agriculture14091608

Academic Editors: Marcus Randall, James Montgomery and Andrew Lewis

Received: 22 August 2024
Revised: 9 September 2024
Accepted: 12 September 2024
Published: 14 September 2024

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**Copyright:** © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## 1. Introduction

Crop phenology refers to stages in plant growth and development that are affected by climate and seasonal changes [1–4]. The accurate identification of phenological stages is crucial in modern agriculture. It provides essential data for scheduling agricultural machinery, precise yield estimation, and timely harvesting [5]. Farm managers can accurately manage irrigation, fertilizer, and pesticide applications based on phenological stages to save energy and increase production [6,7].

Early phenological observations were based on ground observation stations, agricultural surveys, meteorological observations, and field surveys by botanists. These methods required extensive human and material resources, and their spatiotemporal coverage was limited, complicating regional-scale phenology studies [8,9]. With the development of remote sensing technology, regional-scale crop phenology information can now be obtained

<footnote n="1">¹ School of Computer Science and Engineering, Changchun University of Technology, Changchun 130012, China; wuhuizhu@iga.ac.cn (H.W.); liubing@ccut.edu.cn (B.L.)</footnote>

<footnote n="2">² State Key Laboratory of Black Soils Conservation and Utilization, Northeast Institute of Geography and Agroecology, Chinese Academy of Sciences, Changchun 130102, China; songkaishan@iga.ac.cn</footnote>

<footnote n="3">³ College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China; zhenzj18@mails.jlu.edu.cn</footnote>

<footnote n="4">⁴ CESBIO, Université de Toulouse, UT3-Paul Sabatier/CNES/CNRS/INRAE/IRD, 18, Avenue Edouard Belin, 31401 Toulouse, France</footnote>

<footnote n="5">⁵ Institute of Meteorological Science of Jilin Province, Changchun 130062, China; gaoyuang00@stu.hrbnu.edu.cn</footnote>

<footnote>* Correspondence: zhubingxue@iga.ac.cn</footnote>
from satellite remote sensing data. Threshold-based, function-fitting, and phenology-matching methods have been proposed to estimate phenological stages using optical vegetation index (VI) time-series data [10–14].

Threshold-based methods use absolute or relative thresholds. An absolute threshold is when a VI reaches a fixed value, whereas a relative threshold refers to the dates of a given amplitude of seasonal changes in VI values [15]. For example, Boschetti et al. estimated key phenological stages of rice in Italy using time-series data of the normalized difference vegetation index (NDVI) derived from Moderate Resolution Imaging Spectrometer (MODIS) data [16]. The emergence was defined as the date when the NDVI first increased, and the difference between the minimum and maximum NDVI values on the left was 10%. The heading stage was defined as the midpoint between the 90% values on the left and right on the NDVI curve. Function-fitting methods use logistic functions [17], asymmetric Gaussian functions [18], Savitzky-Golay filters [19], quadratic functions [20], nonlinear spherical models [21], and other mathematical functions to simulate VI time-series data. The phenological date is determined by detecting changes in the VI time-series curve, such as the point with the largest derivative, the inflection point with the local extreme in the first derivative, or the rate of change of curvature. Zhang et al. used a piece-wise logistic function to fit MODIS VI time-series data and defined the times of the four inflection points (i.e., curvature changes) in the curve as four phenological events (i.e., greening, maturation, senescence, and dormancy) [17]. Although the characteristic points of the fitted VI time-series curve can be used to determine changes in vegetation color, these points differ from the phenological stages of crop plants [22,23]. Most maize phenology studies utilized the start of season (SOS), end of season (EOS), and several phenological stages, such as the emergence, silking, maturity, and harvest stages [23–26]. However, a lack of information exists on the precise extraction of maize's key phenological stages, such as the three-leaf, seven-leaf, and jointing stages [27]. These periods are crucial for decision-making regarding fertilization, water management, and pest and disease control.

In practical applications, accurate agricultural phenological information is crucial for optimizing farming practices. This includes precise data on the timing of key crop growth stages, such as emergence, flowering, and maturity, which allows for better decision-making in areas such as irrigation, fertilization, and pest management. The researchers identified phenological information by matching time-series VI data with crop phenological periods. One classic approach is the shape model fitting (SMF) based on the shape model proposed by Sakamoto, Wardlow [28]. This method involves averaging multi-year vegetation index (VI) time-series data with ground-based phenological observations to generate reference curves and reference phenology. A shape model is then constructed and used to match with VI time series of the same crop type, allowing for the identification of key phenological stages of crops. It has been used to detect the phenological stages of multiple crops [14,23,28–30]. However, this method has two shortcomings: it assumes that the relative positions of different phenological stages in the VI time series for target pixels of a single crop are consistent and that the spacing between any two pairs of phenological stages changes synchronously. These assumptions are unrealistic [31]. Liu et al. addressed both limitations by developing the shape model fitting by the separate phenological stage method (SMF-S) [32]. They improved the fitting function and iteration of the SMF to match the shape model and the VI time series of each phenological cycle using an adaptive local window. They successfully identified the phenological stages of winter wheat in the North China Plain.

Although the SMF has significant advantages in extracting phenological stages, the estimation accuracy differs for different phenological stages. For instance, estimating crop growth has a larger error during the early stage than the later stage. Furthermore, most SMF-S utilize the NDVI and enhanced vegetation index (EVI) as reference curves [23,28,31,32], whereas other indicators are rarely used. Although the NDVI and EVI provide good results for identifying phenological stages, they have limitations. The NDVI suffers from inherent nonlinearity as a ratio-based index and is influenced by additive noise effects,
such as atmospheric path radiance. It also exhibits scaling problems and saturation under
high-biomass conditions [33]. This saturation is particularly noticeable in crops such as
maize during the mid-to-late growing season, when the leaf area index (LAI) exceeds three
to four, limiting the NDVI's sensitivity to further increases in canopy cover [34]. As a
result, the NDVI becomes less effective in distinguishing between dense vegetation cover,
leading to underestimation of growth during key reproductive stages, such as silking
and tasseling [35]. Furthermore, the NDVI is highly sensitive to variations in canopy
background, particularly in cases of very bright backgrounds [36]. Although the EVI is not
as prone as the NDVI to image saturation in high-biomass areas, its calculation is more
complicated, and it requires more bands. The atmospheric correction of the blue band is
difficult and provides variable results, and the EVI values differ for different sensors [37].
The water demand of maize increases during the rapid growth stage (from the emergence
stage to the jointing stage) and reaches the highest values during the tasseling and silking
stages. The land surface water index (LSWI) is highly sensitive to soil and leaf moisture
contents due to its shortwave-infrared (SWIR) band [38,39]. It has been widely used in
crop and soil moisture monitoring and crop mapping [40,41]. However, it is rarely used to
determine the phenological stage.

Considering the complex characteristics of maize growth, we select five maize agronomic
phenology periods to carry out identification research, including the emergence, seven-leaf,
jointing, flowering, and maturity stages. Taking Jilin Province as an example, the reference
curves of maize phenological feature extraction in different regions are established.

We compare the time series of the NDVI, normalized differential phenology index (NDPI), and LSWI extracted from MODIS data during the growing season and derive indicators suitable for extracting different phenological stages. The results are compared with data from ground stations. The performances of the different indices as reference curves are discussed.

The objectives of this study are to (1) use the SMF-S method to identify the emergence, seven-leaf, jointing, flowering, and maturity stages of maize, (2) perform screening of superior VI for each growth stage of maize, and (3) create maps of maize phenology.

**2. Materials and Methods**

2.1. *Study Area*

The research area is situated in Jilin Province (40°50′ N–46°18′ N, 121°38′ E–131°19′ E) in northeastern China, covering an area of 187,400 square kilometers. Jilin Province has a temperate continental monsoon climate characterized by four seasons and rain. The annual average temperature is 3–5 °C, the annual average precipitation is 400–600 mm, the frost-free period is 100–160 days, and the annual sunshine duration is 2200–3000 h. Maize and rice cultivation are predominant in this region. The maize-planting season ranges from 20 April to 15 May, and the crop matures in September. During the growing season, which runs from May to September, the average temperature ranges from 18 °C to 23 °C, providing favorable conditions for crop growth, particularly for key crops, such as maize.

## 2.2. *Datasets and Preprocessing*

2.2.1. Crop Maps

We used the China crop coverage map developed by Luo, Zhang [42]. It includes the harvest area of three major crops (rice, maize, and wheat) in China from 2000 to 2015 and has a resolution of 1 km. We resampled the crop coverage maps from 2003 to 2015 to a spatial resolution of 500 m using nearest neighbor sampling [43] (Figure 1). The green parts show the maize distribution in 2015.
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Map of the study area and sites.</figcaption></figure>

### 2.2.2. Ground-Based Phenological Observations

We obtained data from agricultural meteorological stations in the maize-growing areas of Jilin Province from 2003 to 2019. The locations of these stations are shown in Figure 1. These 29 stations are distributed across 9 cities in Jilin Province. The data provide detailed records of ten key phenological stages of maize, including emergence, seven-leaf, flowering, and maturity stages. Professionals at the agricultural climate monitoring station observe the growth of corn at fixed locations and at regular intervals, recording the Day of Year (DOY) for each phenological stage, which provides reliable information for studying the growth dynamics of maize.

Figure 2 illustrates the phenological stages of maize, which can be divided into two major growth phases: the vegetative growth phase and the reproductive growth phase. During the vegetative growth phase, maize primarily accumulates biomass to support subsequent reproductive development. This phase includes stages such as emergence, seven-leaf, and jointing. During these stages, maize leaves gradually unfold, the root system expands rapidly, and the plant height increases significantly, laying the foundation for photosynthesis and nutrient absorption. The adequacy of vegetative growth directly impacts the yield performance during the reproductive phase.

After the jointing stage, maize enters the reproductive growth phase, transitioning from vegetative growth to reproductive organ development, which leads to kernel formation and maturation. This phase includes key stages, such as flowering and maturity. Flowering is crucial for fertilization, as the female flowers receive pollen during this period.
Following fertilization, the kernels begin to develop, progressing through milk ripening, where they accumulate nutrients. The final stage, maturity, marks the completion of the maize growth cycle, with fully developed kernels ready for harvest.

<table><caption>**Figure 2.** Division of vegetative and reproductive growth stages in maize phenology.</caption><thead><tr><th rowspan="2">stage</th><th colspan="3">Vegetative Stage</th><th colspan="2">Reproductive Stage</th></tr><tr><th>Emergence</th><th>Seven-leaf</th><th>Jointing</th><th>Flowering</th><th>Maturity</th></tr></thead><tbody><tr><td>VE</td><td></td><td>V7</td><td>Vn</td><td>VT-R1</td><td>R6</td></tr></tbody></table>

### 2.2.3. MODIS Data

The MODIS sensor is a crucial remote sensing instrument on NASA's Terra and Aqua satellites, providing rich data for monitoring Earth's surface and atmosphere. MODIS data products range from 2000 to the present, offering long-term information on surface reflectance, surface temperature, cloud cover, and more for scientists and researchers. MODIS data products have high spatial resolution (ranging from 250 m to 1 km) and multi-band coverage (including visible, near-infrared, shortwave-infrared bands, etc.) and have been used for global environmental monitoring, climate studies, natural disaster monitoring, and other applications.

This study used MOD09A1, which is a surface reflectance product with an 8-day synthetic temporal resolution and a 500 m spatial resolution (Table 1). The data, downloaded via Google Earth Engine (GEE) and accessed on 21 March 2024, cover the Jilin Province region. The region corresponds to SIN grid tiles h26v04 and h27v04, as part of the MODIS Sinusoidal projection system. We calculated the NDVI, NDPI, and LSWI to obtain time-series data from 2003 to 2019 based on the MOD09A1 reflectance product (https://lpdaac.usgs.gov/tools/, accessed on 21 March 2024).

<table><caption>**Table 1.** Summary of MODIS band parameters and resolution.</caption><thead><tr><th>Sensor</th><th>Band</th><th>Wavelength</th><th>Revisit Cycle</th><th>Spatial Resolution</th></tr></thead><tbody><tr><td rowspan="5">MODIS</td><td>Red</td><td>620-670 nm</td><td>8 days</td><td>500 m</td></tr><tr><td>NIR</td><td>841-876 nm</td><td>8 days</td><td>500 m</td></tr><tr><td>Blue</td><td>459-479 nm</td><td>8 days</td><td>500 m</td></tr><tr><td>Green</td><td>545-565 nm</td><td>8 days</td><td>500 m</td></tr><tr><td>SWIR</td><td>1628-1652 nm</td><td>8 days</td><td>500 m</td></tr></tbody></table>

### 2.2.4. Vegetation Indices

We selected three VIs to create the reference curves: NDVI [44], NDPI [45], and LSWI [46]. They were calculated as follows:

$$NDVI = \frac{\rho_{NIR} - \rho_{RED}}{\rho_{NIR} + \rho_{RED}} \quad (1)$$
$$NDPI = \frac{\rho_{NIR} - (0.74 * \rho_{RED} + 0.26 * \rho_{SWIR})}{\rho_{NIR} + (0.74 * \rho_{RED} + 0.26 * \rho_{SWIR})} \quad (2)$$

$$LSWI = \frac{\rho_{NIR} - \rho_{SWIR}}{\rho_{NIR} + \rho_{SWIR}} \quad (3)$$

where $\rho_{NIR}$, $\rho_{RED}$, and $\rho_{SWIR}$ are the reflectance values in the near infrared (841–876 nm), red (620–670 nm), and SWIR (1628–1652 nm) bands, respectively. We used the Savitzky–Golay filter to smooth and denoise the data.

## 2.3. Methodology

Sakamoto et al. proposed the SMF to estimate the phenological stages of crop plants [28]. Although this method has advantages in extracting phenological stages of crops [23,29,30], it has two limitations. First, SMF uses a shape model to match the entire growing season of the target VI time series through linear shifts and scaling. This global matching strategy can lead to synchronous changes in the length between two phenological stages. In other words, the value of the target pixel may increase or decrease between any two phenological stages, which is particularly important for crops in the growing season. Second, the SMF assumes that the scaling factor of a phenological stage (i.e., $\frac{1}{xscale}$) is related to the phenological stage. Therefore, the variance of the phenological estimate of the stage depends on that stage [32].

Liu et al. addressed this problem by improving the fitting function and parameter optimization of the SMF [32]. They designed an adaptive window and developed a shape model fitting by the separate phenological stage method (SMF-S) [32]. This method uses the VI time series with ground-based phenological data to obtain the shape model $g(x, p_0^i)$. We used the shape model to estimate seasonal VI time series of the target pixel $h(x, p_0^i)$ for a specific crop type, $\hat{g}(x, p_0^i)$:

$$\hat{g}(x, p_0^i) = g(xscale_i \times (x + tshift_i) + (1 - xscale_i) \times p_0^i), i = 1, \dots, n \quad (4)$$

where the $xscale_i$ and $tshift_i$ are updated by calculating the correlation coefficient between $h(x, p_0^i)$ and $\hat{g}(x, p_0^i)$, which is expressed as:

$$tshift_i, xscale_i = \operatorname*{argmax}_{x \in (p_0^i - tshift_i - w, p_0^i - tshift_i + w)} R(\hat{g}(x, p_0^i), h(x)), i = 1, 2, \dots, n \quad (5)$$

where $w$ represents the half-window width of the local VI time series. The SMF-S estimates the phenological stage $p_0^i$ in $\hat{g}(x)$, as follows:

$$xscale_i \times p_{est}^i + (1 - xscale_i) \times p_0^i + xscale_i \times tshift_i = p_0^i, i = 1, \dots, n \\ p_{est}^i + p_0^i = tshift_i, i = 1, \dots, n \quad (6)$$

### 2.3.1. Generation of Reference Curves

Most shape-fitting models use a single VI as the reference curve [23,28,31,32]. We generated different reference curves for various cities in Jilin Province to extract the phenological stages of maize and investigate the effect of using different VIs as reference curves. We selected sites with comprehensive phenological records in different cities to ensure temporal consistency in calculating the reference curves.

We used MOD09A1 data to calculate the annual time series of the NDVI, NDPI, and LSWI from 2003 to 2014 within a 1 km² area around each site. The twelve-year averages of each vegetation index were calculated, and three reference curves were generated for different regions. The Savitzky–Golay [47] filter was applied to smooth the VI time series, and the reference phenology was generated by calculating the 12-year average of the phenological stages at each site (Figure 3). These reference curves and phenology were used as shape models in the SMF-S method. For Baishan City, due to data availability only
for 2016–2017, we averaged the data from the other eight cities to generate the reference curves and phenology for Baishan.

The reference curves and reference phenology for different cities were used in experiments to extract the phenological stages of maize.

<figure><img src="image_5.png" /><figcaption>Figure 3. Flowchart of phenological period identification.</figcaption></figure>

### 2.3.2. Verification of Maize Phenology

We utilized the coefficient of determination ($R^2$) [48] and the root mean squared error (RMSE) [49] as evaluation metrics. The $R^2$ represents the proportion of the variance in the dependent variable explained by the independent variable, with values ranging from 0 to 1. Higher values indicate a better model fit. The calculation is as follows:

$$R^2 = 1 - \frac{SS_{res}}{SS_{tot}}$$

$$SS_{res} = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$$

$$SS_{tot} = \sum_{i=1}^{n} (y_i - \bar{y}_i)^2 \qquad (7)$$

where $SS_{res}$ represents the sum of squared residuals, $SS_{tot}$ represents the total sum of squares, $y_i$ denotes the observed values of the dependent variable, $\hat{y}_i$ represents the predicted values of the dependent variable by the model, $\bar{y}_i$ is the mean of the observed values of the dependent variable, and n is the sample size.

The RMSE is the square root of the mean of the squared differences between the actual and predicted values. A smaller RMSE indicates a higher predictive accuracy of the model. The calculation is as follows:

$$RMSE = \sqrt{\frac{1}{N} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2} \qquad (8)$$

where $y_i$ represents the actual values, $\hat{y}_i$ represents the predicted values, and n denotes the sample size.

The calculation of the reference curve and the filtering operation of the VI time series in the method were all performed in PyCharm (version 2021.3.3).
## 3. Results

### 3.1. Extraction of Maize Phenological Information

#### 3.1.1. Accuracy of Identifying Phenological Stages

The relationships between field-observed and estimated phenological stages obtained from the three VIs are shown in Figure 4. The RMSE indicated that the overall error for the LSWI was smaller than that for both the NDVI and NDPI. The NDVI performed the best for identifying the emergence and seven-leaf stages, with an RMSE of four days. The LSWI was optimal for the jointing stage (RMSE of four days) and the flowering stage (RMSE of three days). The RMSE was five days for all VIs to identify the maturity stage. Figure 4b,d,f show the results for the data from 2015 to 2019. The RMSE was five days for all three indicators. The NDVI had the best performance for identifying the emergence and seven-leaf stages, with an RMSE of four days. The LSWI performed the best for the jointing and flowering stages (RMSE of four days), and the NDVI was optimal for identifying the maturity stage (RMSE of four days).

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Relationship between field-observed and estimated phenological stages obtained from different indicators and the RMSE. (a,c,e) The data from 2003 to 2014 and (b,d,f) the data from 2015 to 2019. Both the x and y axes represent the DOY.</figcaption></figure>
3.1.2. Comparison of Results in Different Regions

The accuracy of identifying phenological periods differed in different regions. Figure 5 shows the box plots of the identification errors for different indicators in different locations from 2015 to 2018. The box range represents the standard error, and the whiskers represent the maximum and minimum values of the recognition error.

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Box plots of the errors in identifying phenological phases in different regions: (a) emergence, (b) seven-leaf stage, (c) jointing, (d) flowering, and (e) maturity. The errors are represented by residuals, with positive values indicating delayed predictions and negative values indicating earlier predictions.</figcaption></figure>

The NDVI provided the highest accuracy during the emergence, seven-leaf, and maturity stages. The LSWI showed superior performance during the jointing and flowering stages. In the emergence and seven-leaf stages, the errors were lower in Taobei, Gongzhuling, and Liaoyuan and higher in Nongan for all three indices. Increased rainfall during this period led to different precipitation levels in various regions, resulting in significant differences in the recognition errors. Crops grow rapidly during the jointing and flowering stages, and their reflectance peaks in the flowering stage. Plants require more water in this phase. Thus, the LSWI was more suitable for capturing water variations, resulting in its superior recognition performance. The water demand of plants decreases in the maturity stage as plants begin to wither. The reflectance values of the LSWI and NDPI were lower than that of the NDVI. Therefore, the NDVI exhibited better performance in different regions during this stage. Lower errors were observed in Changchun, Nanguan, Shulan, and Daan, and higher errors occurred in Liaoyuan.
3.1.3. Comparison of Results of Different VIs in the Same Area

To better observe the fitting performance of different VIs as reference curve shape models, we plotted the shape model fitting results at the same pixel location in Baicheng, Jilin Province, for 2019. As shown in Figure 6, the orange curve represents the reference curve for Baicheng, the blue curve represents the time series of different VIs for maize at the target pixel, and the green curve represents the deformed reference curve after fitting. The scatter points on the orange curve indicate the phenological stages in Baicheng, while those on the green curve indicate the estimated phenological stages. The first, second, and third columns represent the fitting results using the NDVI, NDPI, and LSWI as reference curves, respectively.

<figure><img src="image_8.png" /><figcaption>Figure 6. The target curve fitting reference curve in Baicheng City, Jilin Province, in 2019, where the orange curve is the reference curve, the blue curve is the target curve, and the green curve is the</figcaption></figure>
reference curve after deformation by the fitting function. In the subplots, (a,d,g,j,m) represent the fitting cases where NDVI is used as the reference curve for the shape model, (b,e,h,k,n) represent the cases with NDPI as the reference curve, and (c,f,i,l,o) represent the cases with LSWI as the reference curve, with each subplot labeled accordingly.

During the maize emergence stage (Figure 6a-c), the estimated phenological stages for all three VIs were two days earlier. Using the NDVI as the reference curve shape model showed a leftward shift overall compared to the other two VIs, moving closer to the target curve. This trend was also observed during the seven-leaf stage (Figure 6d-g), where the identification error for all three VI shape models was five days, indicating that using the NDVI as the reference curve shape model was more sensitive to the emergence and seven-leaf stages than the other two VIs.

During the jointing stage of maize (Figure 6g-i), the identification errors were seven days for the NDVI, six days for the NDPI, and five days for the LSWI, with the LSWI performing the best. A similar pattern was observed during the flowering stage (Figure 6j-l), where the identification errors were six days for the NDVI and five days for both the NDPI and LSWI. From the graphs, the deformed curve using the LSWI as the reference was closer to the target curve, suggesting that the LSWI captured changes in these two stages better, while the deformed curves for the NDVI and NDPI were farther from the target pixel curve, possibly leading to higher estimation errors for these two VIs.

During the maize maturity stage, the NDVI reference curve shape model accurately identified the phenological stages of the target pixel, with an error of zero days. The NDPI reference curve shape model also successfully extracted the phenological stages, with an error of one day. However, the LSWI reference curve shape model had a larger error of five days. The NDVI reference curve shape model was closer to the target pixel curve, capturing the changes during the maturity stage better, while the LSWI reference curve shape model was farther from the target curve, resulting in a larger error.

In conclusion, for the early (emergence and seven-leaf stages) and late growth stages (maturity stage) of maize, using the NDVI as the reference curve shape model provided better identification accuracy than the other two VIs. For the middle growth stages (jointing and flowering stages), using the LSWI as the reference curve shape model yielded the best identification accuracy, consistent with the previous analysis.

## 3.2. *Spatial Distribution of Maize Phenological Stages*

Figure 7 shows the spatial distribution of the five phenological stages of maize from 2015 to 2018. The maps were derived from SMF-S using the LSWI as a reference curve. Jilin Province has higher elevations in the southeast and lower elevations in the northwest. Most of the maize is grown in the northwestern part of Jilin Province, and less maize is planted in the southeastern region. The maize-planting areas in Jilin Province exhibited a similar spatial pattern, with delays in the growth stages from southeast to northwest. These spatial observations are consistent with the results from the ground stations. Differences in temporal patterns were observed across different years. From 2015 to 2017, the phenological period tended to be earlier. Maize emergence occurred at 135-150 DOY in 2015 and at 130-145 DOY in 2016 and 2017. The subsequent four phenological stages also occurred earlier each year. Maize emergence occurred at the same time in 2015 and 2018, with a DOY range of 135-150. In contrast, maize emergence in the central region of Jilin Province occurred 5-10 days earlier in 2019.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Spatial distribution of the five phenological stages of maize obtained from the LSWI as a reference curve.</figcaption></figure>

**4. Discussion**

A significant number of crop phenology studies have been conducted using remote sensing data. The SMF and the use of thresholds are the two mainstream approaches using optical data [23,28,50–52]. The threshold method has provided accurate results for identifying phenological stages with distinct growth characteristics. For example, the maximum NDVI was used to identify the peak growth period [52], whereas others have used the EOS and SOS [51]. The SMF-S utilizes growth curve fitting to reduce the error and noise in the VI time series and objectively estimate changes in phenological stages over time. This method allows for the acquisition of comprehensive spatiotemporal information on the start, duration, and end of crop growth, enabling the identification of detailed phenological information. Since most studies on the SMF-S have used shape fitting [28,32], they did not consider the importance of index selection and the matching of advantageous periods. However, a lingering question remains: can a single VI in the SMF-S identify all phenological stages? To address this question, we compared the performance of three commonly used VIs in extracting phenological stages using the SMF-S. Our results indicated that combining different VIs improved the accuracy of identifying maize phenological stages during the growing season.
4.1. *The Advantages of Combining Multiple Indicators*

The comparison of the three VIs in the SMF-S indicated that a single VI was insufficient for identifying all phenological stages during the growing season. The VIs exhibited significant differences in their effectiveness in identifying phenological stages. The NDVI showed slightly higher performance for identifying the emergence and seven-leaf stages than the LSWI and NDPI. The rising and falling trends and the width of the peak were similar for the NDVI and NDPI. In contrast, the LSWI reference curve exhibited a single, narrow peak. The LSWI demonstrated higher accuracy in identifying phenological stages near the peak, whereas the NDVI and NDPI exhibited higher accuracy in identifying phenological stages at lower maize canopy coverage (Figure 8).

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Reference curves of different VIs in Jilin City.</figcaption></figure>

The accuracy of identifying several phenological stages can be improved by using
several VIs. The NDVI is highly sensitive to changes in vegetation cover during the early
growth stages [53]. As the vegetation cover increases, the red light reflectance decreases,
and the NIR reflectance increases, resulting in a significant increase in NDVI [54]. Therefore,
the NDVI's variation is closely related to vegetation cover, especially during the transition
from sparse to moderate vegetation density. The NDPI is based on plant phenology and
well suited for distinguishing phenological changes, such as germination, flowering, and
leaf fall. However, maize has a relatively consistent background color in different stages;
therefore, the NDPI is not advantageous. Our results indicated that the NDVI values
coincided with the reference curve during the emergence stage in most years. The values
were significantly higher than those of the reference curve in some years (Figure 9a).
The values were also higher during the seven-leaf and subsequent phenological stages.
This consistency resulted in a good alignment of the SMF-S with the shape of the NDVI
time-series curve and favorable results in the early stages of maize growth (Figure 9b). In
contrast to the NDVI, the NDPI exhibited a similar shape of the time-series curve during the
seedling stage and generally had lower values than the reference curve. In the subsequent
phenological stages, the NDPI approached and diverged from the reference curve. This
dissimilarity to the reference curve reduced the NDPI's ability to identify phenological
stages accurately.

On the other hand, the LSWI was more effective in capturing changes in vegetation
moisture content due to its reliance on the SWIR band, which is highly sensitive to wa-
ter. The NDPI combines the RED and SWIR bands but assigns more weight to the RED
band, which is better at indicating chlorophyll content and vegetation growth rather than
moisture content [45]. As a result, the NDPI's sensitivity to changes in plant moisture is
lower compared to LSWI. The lower weight given to the SWIR band in NDPI reduces its responsiveness to water fluctuations, making it less effective at identifying phenological stages where water dynamics play a critical role, such as the jointing and flowering stages. Conversely, the LSWI's focus on the SWIR and NIR bands allows it to better capture the increase in moisture during these stages, providing a clearer reflection of moisture-related physiological changes in maize.

The LSWI values remained consistently close to the reference curve throughout the time series, exhibiting a distinct peak (Figure 9c). During the jointing and flowering stages, the LSWI values closely matched the reference curve, aiding in the identification of these key stages. Maize undergoes rapid growth and experiences high water demand during the jointing and flowering stages, with moisture content significantly increasing to support cell expansion and growth. Since the LSWI incorporates the SWIR band, this index is highly sensitive to vegetation moisture content [38,39]. The jointing stage marks a period of rapid growth for maize, with increased water demand resulting in higher LSWI values. The flowering stage, which marks the beginning of the reproductive phase, brings even greater water demand, causing moisture levels to peak, as reflected by the LSWI.

During the maturity stage, maize undergoes visible changes in moisture and leaf color, resulting in similar values of the three indices relative to the reference curve. Thus, the performance of the three VIs was similar during the maturity stage.

<figure><img src="image_11.png" /><figcaption>**Figure 9.** Reflectance values and reference curves at different phenological stages of different stations. (a) represents the case where the phenological stages of the stations correspond to NDVI values falling on the reference curve, (b) represents the case for NDPI values, and (c) represents the case for LSWI values.</figcaption></figure>

## 4.2. *The Importance of Improving the Identification of Maize Jointing and Flowering Stages*

The proposed method for identifying phenological stages overcomes the limitations of traditional phenological monitoring methods, which focus on single phenological stages. It uses an optimum VI to identify the phenological stages of maize from emergence to maturity. We used the time when maize entered a phenological stage as ground truth and evaluated the accuracy of predicting the time when the maize reached a phenological stage.
This approach increases the difficulty of phenological stage identification. If we focus solely on identifying whether a crop is in a specific growth stage, we can significantly improve the identification accuracy. However, we consider the dates of the phenological growth stage to be more crucial because they are informative for field management.

Accurately identifying and monitoring the jointing and flowering stages using remote sensing data can provide the government with a macro-level understanding of long-term regional crop growth (Figure 7) and extensive data for agricultural research. This information facilitates in-depth studies on maize growth patterns and promotes agricultural scientific research. The data can be used to breed high-yielding, disease-resistant maize varieties that are better adapted to local climates and environments, advancing agricultural technology. Accurately identifying the jointing and flowering stages allows for the timely implementation of protective measures before extreme weather events occur, such as drought or heavy rainfall, reducing crop damage.

In addition to enhancing crop protection, precise phenological stage identification is essential for optimizing irrigation management. One of the most widely used methods is the FAO-56 framework, which calculates crop water requirements by adjusting for each growth stage using a crop coefficient (Kc) [55]. By integrating real-time phenological information obtained through remote sensing, the use of Kc can be refined to reflect the actual water needs of the crop at each stage. This approach ensures that irrigation is applied more efficiently, reducing water waste and enhancing crop water-use efficiency. For example, timely and precise irrigation during the jointing and flowering stages, which are critical for yield formation, can significantly improve water use and ensure better crop performance [56]. Overall, the combination of accurate phenological stage data and tailored irrigation practices promotes sustainable agricultural management.

### 4.3. *Model Uncertainty*

The SMF is an effective approach to monitoring crop phenology using satellite data (VI) time series. It optimizes remote sensing indices by fitting and quantitatively reconstructing the stages from crop initiation to maturity. However, the model does not provide the same performance in all regions due to differences in geographic location, terrain, and climate. The generation of reference curves relies on field data from specific regions. This approach may not be suitable for regions with incomplete or scarce station data or no stations. Therefore, more ground-based data are crucial for improving crop model simulations. In this study, we compared the performance of different VIs as shape models, with each shape model based on a single index. However, in future research, we plan to explore the possibility of combining multiple indices within the shape model to further improve the accuracy of phenological stage identification across different growth stages. Additionally, it is anticipated that reference curves could be automatically generated, using existing reference curves for multi-year station data to produce similar curves for surrounding areas. This method could generate reference curves for several years in regions without station records or data. This strategy will improve the identification accuracy and application scope. Another issue that needs attention is improving the temporal and spatial resolution of the data, particularly in heterogeneous and fragmented agricultural systems. Higher resolution would enhance the accuracy of phenological identification and its practical application value.

## 5. Conclusions

This study utilized the SMF-S method to explore the effectiveness of using different VIs as reference curves for extracting key phenological stages of maize. The research found that different VIs exhibited varying levels of accuracy in identifying these stages. Specifically, using the NDVI as the reference curve resulted in the smallest errors for identifying the emergence, seven-leaf, and maturity stages of maize, with a RMSE of less than five days. In contrast, using the LSWI as the reference curve produced the smallest errors for the jointing and flowering stages, with a RMSE of less than four days. These findings indicated that
selecting the appropriate VI as a reference curve can significantly enhance the accuracy of identifying maize growth stages.

Additionally, the study successfully created phenology maps based on the identified growth stages, offering a spatial representation of maize development. These maps not only provide a visual tool for understanding the spatial variability of maize growth but also serve as a valuable resource for optimizing agricultural management practices. By incorporating both remote sensing data and growth stage predictions, these phenology maps can help inform decisions related to irrigation, fertilization, and harvest timing, further enhancing precision agriculture strategies.

**Author Contributions:** Conceptualization, B.Z. and H.W.; methodology, H.W.; software, H.W.; validation, H.W., B.Z. and K.S.; formal analysis, H.W. and B.L.; investigation, Z.Z., H.W. and J.R.; resources, J.R.; data curation, H.W., J.R. and B.Z.; writing—original draft preparation, H.W.; writing—review and editing, B.Z. and H.W.; visualization, H.W.; supervision, B.Z. and K.S.; project administration, K.S. and B.Z.; funding acquisition, K.S., B.Z. and Z.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Jilin Province Natural Science Foundation (YDZJ202301ZYTS239), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA28050400), and the Jilin Provincial Department of Education project (JJKH20230765KJ).

**Institutional Review Board Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available upon request from the corresponding author.

**Acknowledgments:** We appreciate the valuable comments and suggestions provided by the reviewers.

**Conflicts of Interest:** The authors declare no conflicts of interest.

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