Temporal Variation and Component Allocation Characteristics of Geometric and Physical Parameters of Maize Canopy for the Entire Growing Season

Abstract

The accurate monitoring of crop parameters is important for crop yield prediction and canopy parameter inversion from remote sensing. Process-based and semi-empirical crop models are the main approaches to modeling the temporal changes in crop parameters. However, the former requires too many input parameters and the latter has the problem of poor portability. In this study, new semi-empirical geometric and physical parameters of the maize canopy model (GPMCM) crop model adapted to northeast China were proposed based on a time-series field datasets collected from 11 sites in the Nong’an and Changling Counties of Jilin Province, China, during DOY (day of year) 163 to DOY 278 in 2021. The allocation characteristics of and correlations between each maize canopy parameter were investigated for the whole growing season using the 22 algorithms of crop parameters, and the following conclusions were obtained. (1) The high correlation coefficient ($R$ mean = 0.79) of LAI with other canopy parameters indicated that it was a good indicator for predicting other parameters. (2) Better performance was achieved by the regression method based on the two-stage simulation. The root-mean-squared error ($RMSE$) of geometric parameters including maize height, stem long radius, and short radius were 12.91 cm, 0.74 mm, and 0.73 mm, respectively, and the $RMSE$ of the physical parameters including the FAGB, AGB, VWC, and RWC of the stems and leaves, ranged from 0.05 kg/m² to 4.24 kg/m² (2.0% to 12.9% for mean absolute percentage error ($MAPE$)). (3) The extension of the field-scale GPMCM to the 500 m MODIS-scale still provided a good accuracy ($MAPE$: 11% to 18.5%) and confirmed the feasibility of the large-scale application of the GPMCM. The proposed CPMCM can predict the temporal dynamics of maize geometric and physical parameters, and it is helpful to establish the forward and reverse models of remote sensing and improve the inversion accuracy of crop parameters.

1. Introduction

Crop canopy parameters are important for the quantitative inversion of ecological remote sensing, providing regulatory and decision support for environmental change, yield prediction, and agricultural management [1,2]. Crop models, as a key monitoring tool in agricultural research, have the advantages of cost-effectiveness, efficiency, and stability, and can therefore effectively simulate the crop canopy parameters [3]. The crop canopy parameters, as a description of crop growth status, are classified into geometric, physical, and chemical categories. The analysis of crop growth status usually requires crop models to simulate the allocation characteristics of each crop component [4,5,6]. Therefore, an accurate crop model describes the crop growth stages continuously, and this capability is essential for the real-time prediction, monitoring, and evaluation of crop canopy parameters [7,8,9].

Geometric parameters such as crop height and stem radius and chemical parameters such as chlorophyll content and photosynthetic capacity play key roles in describing the growth status and physiological processes. Lähivaara et al. [10] obtained tree heights from 3D models built from airborne laser-scanning datasets and used Bayesian inversion approaches to calculate the simulated values. In research on crop chemical parameter inversion, Le Maire et al. [11] estimated the chlorophyll content of the crop canopy using the radiative transfer model PROSPECT. Geometry parameters describe the crop size and range, while chemical parameters indicate the crop photosynthetic efficiency during the growth season, which is difficult to determine.

Generic process-based crop models have been widely used in describing physical parameters equally such as the leaf area index (LAI), fresh above ground biomass (FAGB), above ground biomass (AGB), and vegetation water content (VWC). Generic crop models (such as World Food Studies (WOFOST) [12,13], Simple Universal CROp Simulation (SUCROS) [14], and Simulateur mulTIdisciplinaire pour les Cultures Standard (STICS) [15] mainly describe the process of crop growth, development and photosynthesis, but there are still problems in cross-regional applications due to the spatial and temporal variability of the natural environment and the difficulty of obtaining initial values (such as the planting density and crop variety) [16,17,18]. The STICS model was validated for output parameters in French maize and wheat crops, and the results indicated that the simulation accuracies for AGB and VWC were stable and the errors were maintained at about 15% [19]. The WOFOST assimilates the AGB results of components such as stems and leaves according to the growth status of the crop at different growth stages [12,13]. However, the specific maize models improved from the generic crop models such as Crop Environment Resource Synthesis (CERES-Maize) [20], AquaCrop [21,22], and PolyCrop [23] can be more effective in analyzing the maize parameters and allocation characteristics of crop components [5,24]. The CERES-Maize model simulated maize parameters such as the LAI, FAGB, and AGB for the entire growing season, and the simulations showed correlations of 0.47, 0.54, and 0.77, respectively [20]. Parades et al. [22] performed a parametric analysis of AquaCrop using the field observation datasets of maize in Ribatejo, Portugal, and the root-mean-squared error ($RMSE$) of the simulated AGB improved from 6.14 t/ha to 3.49 t/ha. Nana et al. [23] simulated the daily maize growth status in PolyCrop using environmentally driven parameters (temperature, precipitation, and solar radiation) in two study areas in Italy. The results showed that the LAI simulated by PolyCrop was able to describe the dynamics of maize, and the $RMSE$ was 1.03. These previous works using crop models have shown the potential of simulating the crop canopy parameters.

Globally, maize holds an important position in terms of food security and sustainable development [2,25,26]. The generic crop model describes the growth process of the crop, while the special maize model is mostly improved from the field observation datasets. There are relatively few crop models with physical and geometric parameters developed specifically for maize. Yang et al. [5] combined the maize growth functions of CERES-Maize and the photosynthetically driven functions of the generic model WOFOST to establish a Hybrid-Maize model, simulating maize’s physical parameters including the LAI and AGB. Ferrazzoli and Guerriero proposed a maize model serving remote-sensing inversion in the radiative transfer process. It could simulate and describe the maize component allocation characteristics for the entire growing season [27,28]. This model established linear piecewise equations through relationships between the input maize height and other canopy parameters, and simulated the physical and geometric parameters including the LAI, stem radius, and VWC.

In this study, the geometric and physical parameters of the maize canopy model (GPMCM) were proposed to simulate geometric parameters including maize height and stem radius and physical parameters including the FAGB, AGB, VWC, and relative water content (RWC). The localization of GPMCM using field observation datasets is necessary to accurately describe the growth state of maize and to improve the simulation accuracy for the entire growing season [29]. The localization process reduces errors from variations in the environment and maize variety. Meanwhile, the precise canopy parameter relationship coefficients and the initial input values such as planting density can be obtained to improve the accuracy of the model simulation. The relationships between different maize canopy parameters have been analyzed to optimize the maize model, and the reasonable input parameters can effectively describe the state of maize [18,29]. In previous studies, LAI was expressed as a canopy parameter that can effectively describe crop growth states [30,31]. The maize geometric and physical parameters displayed obvious allocation characteristics throughout the whole growing season; the LAI, FAGB, and RWC showed an increasing trend in the early stages of maize growth and a decreasing trend in the later stages due to the effects of wilting leaves. The maize models of Ferrazzoli and Guerriero divided the entire growing season into three stages using maize height as the threshold, with CERES-Maize dividing it into five stages including developmental stages [5,20,27]. Therefore, the piecewise function simulation is an effective approach to represent the different growth stages, and the piecewise points were determined by analyzing the relationships between the maize canopy parameters in this study.

The GPMCM model is mainly based on the two-stage regression approach for analyzing the growth states and establishing simulation algorithms. Many studies have demonstrated the significant potential of crop parameter datasets and the feasibility of estimating the crop parameters [32]. Mohsen et al. used a machine learning algorithm to predict the allocation characteristics of multiple crop parameters, which was mainly based on the empirical relationships between the simulated crop parameters and the input parameters [33]. In research on the fusion of multiple models to predict biomass, Jin et al. evaluated and extracted representative algorithms from 16 crop models among which APSIM was used as a standard model to integrate specific algorithms from other models to estimate the yield of maize crop [34]. Meanwhile, Jin et al. indicated that a specific crop model could implement more explicit information on the crop parameters to describe the variation characteristics [34]. Therefore, a regression model with specific empirical relationships, GPMCM, proposed in this study using field observation datasets for the entire growing season, can be representative and applicative for the description of crop status. This approach also provides a new approach to the simulation of parameters for other crops. This study had two major objectives. First, to collect numerous maize canopy parameters and construct the datasets of the canopy parameters over the entire growing season. The datasets from the field observations are beneficial for the analysis of the LAI in relationships with other canopy parameters and to evaluate the feasibility of the LAI as the input parameter. Next, the GPMCM was established and localized after integrating the canopy parameter relationships of the field observation datasets. Eventually, the high accuracy simulation of the maize canopy parameters with continuous simulation capability was achieved.

2. Materials and Methods

2.1. Sites Description

Maize crop parameters were measured by collecting maize samples in the field for improvement and validation purposes. The two study areas belong to the Changchun Jingyuetan Remote Sensing Experiment Station of the Chinese Academy of Sciences, located in Nong’an County, 105 km north, and Changling County, 100 km west of Changchun City, Jilin Province, China. The study region has four sites in Kao Shan Town and one in Donglalatun Town in Nong’an County. There are three sites in Shuangchengpu Town, Changling County, and one site in Taipingshan Town, Longwang Town, and Chenjiadian Town, respectively (Figure 1). The 11 sites in the study area of approximately 5 ha each were planted with annual maize at DOY (day of year) 125 and harvested at DOY 288, approximately.

The region is characterized by a mid-temperate continental monsoon climate with four distinct seasons and precipitation concentrated in the summer. In this region, the average annual temperature is 4.4 °C, the average maximum temperature is from mid-June to mid-August (30 °C), and the minimum temperature is from mid-December to mid-February (−24 °C). The average annual precipitation is 520 mm. The proportion of farmland in this area is over 90%, and the main crop is maize [35]. In addition, the study region plays a key role in food production and development as one of the four major black soil regions in the world [36,37].

2.2. Measurements of Maize Canopy Parameters

The maize was monitored throughout the entire growing season from DOY 125 to DOY 288 in 2021, with geometric and physical parameters including planting density, maize height, stem radius, the LAI, FAGB, AGB, VWC, and RWC collected (

Table 1. The canopy parameter observation datasets for the entire maize growing season in 2021.

Parameters		Units	Numerical Range	Number of Samples
LAI		*	0.2–4.8	214
Height		cm	25.4–291.2	207
Stem long radius		mm	5.9–17.0	208
Stem short radius		mm	3.4–14.4	208
FAGB	Stems	kg/m2	0.04–4.11	214
	Leaves	kg/m2	0.06–1.75	214
	Green leaves	kg/m2	0.06–1.75	48
	Wilted leaves	kg/m2	0.26–0.58	48
AGB	Stems	kg/m2	0.01–0.91	214
	Leaves	kg/m2	0.01–0.68	214
	Green leaves	kg/m2	0.01–0.53	48
	Wilted leaves	kg/m2	0.19–0.49	48
VWC	Stems	kg/m2	0.04–3.31	214
	Leaves	kg/m2	0.05–1.25	214
RWC	Stems	%	69.48–90.33	214
	Leaves	%	24.28–82.53	214

* LAI is a dimensionless parameter.

). The datasets were measured on DOY 173, 198, 230, 242, 254, 266, 273, and 278 in Nong’an and on DOY 163, 175, 194, 218, 233, 247, and 266 in Changling. The maize parameters at each site were measured, three plants simultaneously, and averaged, which is an approach that effectively reduces the measurement errors and represents the maize growth status of the region.

Maize column and row spacings were measured three times at each site and averaged. The diversity of planting tools for the maize caused variability in column and row spacings at different sites. Thus, the unit area per maize varied from 0.17 m² to 0.22 m² and the density of the maize planted per unit area varied from 4.5 to 6.0 n/m².

Maize height was measured as the length of the maize stem from root to top, without the length of the maize tassel. Stem bending occurred at later stages of maize growth and segmented measurements were used to reduce errors. Most maize stems are oval in section, and the long and short radius need to be measured to ensure a reasonable representation of the maize growth state. The maximum height was 291.2 cm on DOY 218, while the maximum stem radii were 17.0 mm and 14.4 mm (Table 1).

The LAI is an important index to evaluate the photosynthesis, evapotranspiration, and transpiration of crops, as it is a dimensionless parameter equal to the ratio of the total area of crop leaves to the unit area [31,38]. The LAI was calculated after measuring each leaf by using the LI-3000C Portable Leaf Area Meter recording the number of leaves in field measurements. The wilting parts of leaves were manually clipped at DOY 266, 273, and 278 in the late growing season of maize in order to obtain accurate and realistic measurements of the LAI values. As leaves grow and wilt during maize growth, the LAI and leaf number showed roughly symmetrical upward and downward trends throughout the growing season. The maximum LAI was 4.8 on DOY 233, while the maximum number of leaves was 14 (Table 1).

The collected maize samples were divided into three parts—leaves, stems, and fruits—and the fruits were not considered in this study. The AGB means the total mass of organic matter per unit area of the maize at a certain time, which is an important indicator of productivity in the ecosystem. The most accurate approach to measuring the authentic values of AGB is to obtain the weight by destructive harvesting [39]. The FAGB was obtained by weighing each part separately before measuring the physical parameters of the maize, where the wilted parts of the maize leaves were removed in the late growing season. Then, the parts were dried at 85 °C for 24 h and weighed to obtain the AGB. Maize loses moisture in the drying process, hence the VWC of each part of the maize is calculated by Equation (1), while RWC is calculated by Equation (2). The VWC depends on the LAI to directly reflect the crop growth status and the degree of drought stress [30,40].

$$VW{C}_i=FAG{B}_i-AG{B}_i$$

(1)

$$RW{C}_i=\frac{VW{C}_i}{FAG{B}_i}$$

(2)

where $RWC$ is the relative water content of each component of maize and $i$ represents the maize stem or leaf components.

2.3. Localization Methods for GPMCM

Selecting the LAI as the input to the GPMCM was reasonable after the analysis of the relationships between the geometric and physical parameters of the field observation datasets. The maize height and stem radius increased with the LAI in the pre-growing season, with a nonsignificant decreasing trend in the late-growing season. The FAGB and VWC showed an increasing trend followed by a decreasing trend throughout the growing season (Figure 2). The coefficients of the simulated canopy parameters in the maize model proposed by Ferrazzoli and Guerriero were obtained mainly based on the empirical relationships from the field observation datasets, and maize height was used as the only input parameter to the model [27,28]. Using the maize height as the input to simulate other maize canopy parameters is inappropriate. First, maize height is difficult to obtain throughout the growing season; the main method to obtain maize height data is still field measurements. Second, the weak variation in maize height in the later stages of growth makes it difficult to simulate other canopy parameters as the input (Figure 2b). However, the temporal variation of LAI was shown to be effective in expressing the growth states of the maize crop [30]. The LAI increased with the number and area of maize leaves in the pre-growing season, and decreased with the wilting of leaves in the post-growing season. Therefore, the GPMCM was established using the LAI as the input parameter. The fitted relationships between the LAI and maize canopy parameters such as FAGB indicated that LAI could effectively simulate other parameters during the later stages of maize growth (Figure 2c). Meanwhile, various LAI remote-sensing products can provide data support on a large scale.

The geometric and physical parameters of the maize canopy need to be represented as piecewise functions in order to accurately describe the status of maize growth at different stages of the entire growing season. Moreover, the overlap of the same values is not conducive to expressing the parameters’ changes throughout the growing season (Figure 2b). The single variable of the input parameter will have multiple corresponding values throughout the growth process due to maize development and wilting. The approach of piecewise simulation is related to the allocation characteristics of the input LAI. Therefore, the entire growing season was divided into two stages to simulate the geometric and physical parameters. The approach to determine the piecewise point in GPMCM first involves finding the peak point of the fitted curve of LAI and selecting the field-observed LAI value near the DOY corresponding to that peak point. The fitted region represented as multiple values in the fitted relationships of LAI with other observed parameters is shown in the box in Figure 2c. The next step is to calculate the correlations between the LAI and other canopy parameters for the two stages, assuming that each LAI is selected as the piecewise point. Finally, the LAI with the best-fitting relationships is selected as the piecewise point for each canopy parameter. The maize model is influenced by environmental parameters such as planting density and by genotype factors such as the maize variety. Hence, there is a necessity to localize the GPMCM to improve its simulation accuracy throughout the growing season [29]. This study achieved localization through the fitted relationships established by the field observation datasets. The LAI values of each day were conveniently expressed using DOY, and the piecewise points of FAGB and VWC for the stem and leaf were DOY 218, the maize height and stem diameter were DOY 230, and the AGBs for the stem and leaf were DOY 233 (

Table 2. The piecewise points of the maize canopy parameters for the entire growing season corresponding to the DOY and the fitted equations at the two growth stages.

Parameters	Piecewise Point	Equation of Pre-Stage	R of Pre-Stage	Equation of Post-Stage	R of Post-Stage
Height	DOY 230	$y=58.07x+19.89$	0.98	$y=3.95x+254.07$	0.53
Long radius	DOY 230	$y=3.28\times \ln x+11.29$	0.97	$y=0.13x+13.33$	0.25
Short radius	DOY 230	$y=2.7\times \ln x+9.37$	0.96	$y=-0.07x+12.54$	0.14
FAGB of stems	DOY 218	$y=0.9x-0.12$	0.99	$y=0.29x+1.95$	0.71
FAGB of leaves	DOY 218	$y=0.34x+0.14$	0.98	$y=0.29x+0.1$	0.95
AGB of stems	DOY 233	$y=0.14x+0.06$	0.96	$y=-0.004x+0.75$	0
AGB of leaves	DOY 233	$y=0.09x+0.1$	0.95	$y=-0.09x+0.8$	0.75
VWC of stems	DOY 218	$y=0.75x-0.18$	0.98	$y=0.3x+1.2$	0.83
VWC of leaves	DOY 218	$y=0.26x+0.04$	0.98	$y=0.21x+0.03$	0.98
RWC of stems	DOY 218	$y=-1.73x+89.98$	0.87	$y=2.69x+65.28$	0.81
RWC of leaves	DOY 218	$y=-3.29x+83.74$	0.93	$y=13.37x+9.53$	0.95

where $y$ is the maize canopy parameters and $x$ is the LAI.

).

2.4. Evaluation Indicators

Four statistical indicators are used to quantify the accuracy performance of GPMCM: the root-mean-squared error ($RMSE$), $Bias$, correlation coefficient ($R$) and mean absolute percentage error ($MAPE$). The $RMSE$ is used to describe the accuracy between the simulated and actual values (Equation (3)). The $Bias$ is used to measure the deviation of the overall simulated results (Equation (4)). $R$ describes the performance of the linear correlation between the simulated and actual values (Equation (5)). The mean absolute percentage error ($MAPE$) represents the average error ratio between the simulated and true values (Equation (6)).

$$RMSE=\sqrt{E[{(M{P}_{simu}-M{P}_{true})}^2]}$$

(3)

$$Bias=E[M{P}_{simu}]-E[M{P}_{true}]$$

(4)

$$R=\frac{{\displaystyle {\sum }_{i=1}^n(M{P}_{sim{u}_i}-E[M{P}_{simu}])(M{P}_{tru{e}_i}-E[M{P}_{true}])}}{\sqrt{{\displaystyle {\sum }_{i=1}^n{(M{P}_{sim{u}_i}-E[M{P}_{simu}])}^2{\displaystyle {\sum }_{i=1}^n{(M{P}_{tru{e}_i}-E[M{P}_{true}])}^2}}}}$$

(5)

$$MAPE=\frac{1}{n}{\displaystyle {\sum }_{i=1}^n\left|\frac{M{P}_{simu}-M{P}_{true}}{M{P}_{true}}\right|}\times 100\%$$

(6)

where $E[.]$ is the mean value; $M{P}_{simu}$ is the simulated value of the GPMCM; and $M{P}_{true}$ are the actual values of the measured maize samples’ parameters.

3. Results

3.1. Geometric Parameters Simulation Results in GPMCM

The relationships between the LAI and maize canopy parameters were fitted to analyze the temporal variation and component allocation characteristics of each canopy parameter separately for the entire growing season. The LAI values at the piecewise points for each canopy parameter were determined by the selection of the optimal fit relationships that create the two growth stages. The high correlations of the LAI with other maize canopy parameters indicated the feasibility of using it as an input parameter, replacing the maize height. During the pre-growing season, the LAI increased with geometric parameters such as maize height and stem radius. The increase in maize height was accompanied by an increase in stem radius, with the maize stem radius growing rapidly at a LAI of less than 1. The geometric parameters of maize showed a weak trend in the later stages due to maize wilting, alongside a decrease in the LAI, and this phenomenon caused the insensitivity of geometric parameters to the LAI in the GPMCM (Figure 3).

The GPMCM of localization with the LAI as the input was established by analyzing the fitting relationships between the LAI and maize canopy parameters in the field datasets. The GPMCM in this study achieved the localization and piecewise simulation processes, which enabled the simulated canopy parameters to effectively reflect the authentic maize growth status in the region. The simulation results showed favorable accuracies compared to the field measurements for the maize height and stem long radius and short radius, with $RMSE$ values of 12.91 cm, 0.74 mm, and 0.73 mm, respectively. The simulated errors compared to the field observations demonstrated a $MAPE$ of 4.9%, 3.4%, and 4%, respectively (

Table 3. The indicators of the simulated maize height and stem radius in the maize canopy parameters compared to the field-measured values.

Parameters	Units	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	$\mathit{B}\mathit{i}\mathit{a}\mathit{s}$	$\mathit{R}$	$\mathit{M}\mathit{A}\mathit{P}\mathit{E}$
Height	cm	12.91	0.44	0.99	4.9
Long radius	mm	0.74	$-$0.09	0.96	3.4
Short radius	mm	0.73	$-$0.74	0.96	4.0

). The high-accuracy simulation results indicated that the GPMCM-simulated maize geometric parameters are representative at the regional scale (Figure 4).

3.2. Allocation Characteristics of Simulated Biomass

The allocation characteristics of the FAGB and AGB of the maize leaves and stems throughout the entire growing season were analyzed in this study. The FAGB of the maize stems and leaves increased with the LAI in the pre-growing season and showed a decreasing trend in the post-growing season (Figure 5a). The allocation characteristics of the AGB were significantly different from the FAGB in the late-growing season, with the stems showing a steady trend with decreasing LAI while the leaves were increasing. This indicated that the leaves’ AGB continuously accumulated for the entire growing season, while the stems’ AGB accumulated only in the pre-growing season (Figure 5b). This phenomenon of LAI as an important indicator of the growth status is consistent with the growth and wilting process of maize. However, the proportional relationships between the biomass contributions of maize leaves and stems were significantly different throughout the growing season. During the early-growing season, the rapid growth of maize stem radius leads to rapid growth in the stem volume and biomass (Figure 3b). The biomass accumulation in maize stems was greater than in the leaves, despite the concomitant increase in the LAI, indicating that the stems were the main part of the maize biomass composition. In the middle of the growing season with LAI greater than 4, the proportion of the FAGB and AGB contributions from the maize stems and leaves gradually stabilized, with leaves accounting for 43.6% and 61.1% of the FAGB and AGB in stems, respectively (Figure 5c,d). The contribution ratios of the maize leaves and stem components changed again, accompanied by water loss during the wilting process. The FAGB of the leaves decreased with LAI, indicating that the leaves wilted more rapidly than the stems (Figure 5c). Moreover, the characteristics of the variations in AGB demonstrated that the dry matter accumulation in the maize leaf and stem components were approximately equal (Figure 5d).

The simulation of the maize FAGB was better than that of AGB for both the stems and leaves. The $MAPE$ for the maize FAGB in the leaves and stems were 7% and 5.7% compared to 12.8% and 11.1% for the AGB, respectively (

Table 4. The simulation accuracy indicator results for the FAGB and AGB in the simulated values of the maize stems and leaves compared to the field-measured values, respectively.

Parameters	Units	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	$\mathit{B}\mathit{i}\mathit{a}\mathit{s}$	$\mathit{R}$	$\mathit{M}\mathit{A}\mathit{P}\mathit{E}$
FAGB of stems	kg/m2	0.27	$-$0.017	0.98	7.0
FAGB of leaves	kg/m2	0.10	0	0.98	5.7
AGB of stems	kg/m2	0.11	0.001	0.91	12.8
AGB of leaves	kg/m2	0.07	0	0.91	11.1

). The two stages of the FAGB and AGB with an LAI at DOY 218 and DOY 233 as piecewise points in the GPMCM showed high simulation accuracies. The FAGB of the stems and leaves at $RMSE$ was 0.27 kg/m² and 0.11 kg/m², with $R$ correlations of 0.98 and 0.97, respectively (Figure 6a,b). The simulation results of the AGB showed overestimation in the early stage and underestimation in the later stage. The correlations between the simulated and measured AGB values were 0.91 for both the stems and leaves. The stem AGB was not sensitive to the variation in the LAI in the post-growing season, with slightly better simulation results for the leaves (Figure 5b). The accuracy of the AGB simulations for the stems and leaves showed $RMSE$ values of 0.11 kg/m² and 0.07 kg/m², respectively (Figure 6c,d).

3.3. Temporal Characteristics of Simulated VWC and RWC

The VWC increased with the maize height and LAI in the pre-growing season. The change in the percentage of the VWC mass in the maize stems and leaves was similar to that of the FAGB. Additionally, the water storage capacity of stems was found to be significantly better for leaves at a LAI greater than 4, and the VWC in the maize leaves was about 38.1% that of the stems. The change in the VWC was obviously different from the AGB in the late-growing season (Figure 7a). The rate of moisture loss from the leaves was significantly faster than that from the stems while the stems and leaves wilted. This phenomenon caused the main water content of maize to be concentrated in the stems (Figure 7c).

The RWC is more capable of expressing moisture variation in each component of maize (Equation (2)). Similarly, the percentages of water in the stems and leaves were obtained separately from the RWC to determine the growth of maize. The entire growing season was divided into two stages, namely, growth to stability and stability to wilting. The results revealed a linear trend of the RWC stems with approximately the same slope in both growth stages. The stems, as the support structure and moisture transport channel for maize, remained at approximately 69.5% RWC, even at the end of the growing season. The RWC of the maize leaves also showed a linear trend in both growth stages. However, the rate of moisture loss increased with leaf wilting in the post-growing season and the rate of variation was about 4.1 times higher than that in the pre-growing season (Figure 3b).

The maize VWC values were measured based on destructive experiments, and the VWC values of the stems and leaves were measured separately before and after drying. The correlations for the VWC of the simulations of the stems and leaves in GPMAM were 0.98 and 0.99, respectively. Meanwhile, the $MAPE$ values of the simulated VWC stems and leaves were 12.9% and 7.6%, as shown by the $RMSE$ of 0.2 kg/m² and 0.05 kg/m² for the stem and leaves, respectively (

Table 5. The evaluation indicators of the simulated and field-measured values of the VWC and RWC in the maize stems and leaves.

Parameters	Units	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	$\mathit{B}\mathit{i}\mathit{a}\mathit{s}$	$\mathit{R}$	$\mathit{M}\mathit{A}\mathit{P}\mathit{E}$
VWC of stems	kg/m2	0.20	0.01	0.98	12.9
VWC of leaves	kg/m2	0.05	0	0.99	7.6
RWC of stems	%	2.10	0.02	0.95	2.0
RWC of leaves	%	4.24	0	0.97	5.7

). Simulation results for RWC of maize leaves and stems displayed better performance with $MAPE$ of 2.0% and 5.7%, respectively. These high-accuracy simulation results indicated that the status of the water content of maize was effectively described (Figure 8).

4. Discussion

4.1. Accuracy of Simulated Maize Canopy Parameters by Incorporate MODIS LAI Product

The LAI was used as the input to establish and improve the GPMCM to simulate the maize geometric and physical parameters. The accuracy of the simulation mainly relies on the piecewise point of the LAI to determine two growth stages in the growing season. The continuous measurement and acquisition of the LAI in the field still face some difficulties, while the remote-sensing product datasets of the LAI have the advantages of continuity and accessibility [41]. The simulation accuracy of the LAI remote-sensing products as input parameters was analyzed to improve the applicability of the GPMCM. Satellite remote sensing provides effective support for obtaining LAI datasets in the region. The resolution of the remote-sensing product was considered to match the measurement sites, and the Moderate Resolution Imaging Spectroradiometer (MODIS) LAI was selected. The spatial resolution was 500 m and the revisit time was 4 days [42,43,44].

The LAI product datasets for the six areas were obtained by combining the resolution of the MODIS LAI product and the distribution of the field observation region (Figure 1). The MODIS LAI datasets were represented by polynomial fits for the analysis and comparison of the LAI features (Figure 9). The temporal variations in the MODIS LAI were consistent with the field experiment datasets over the entire growing season, but the extreme points of the LAI were significantly different. The extreme points of the MODIS LAI fitted curves were used as the piecewise points for the maize growing season. Figure 9 shows the piecewise points calculated for the six areas of Kaoshan, Donglalatun, Taipingshan, Shaungchengpu, Longwang, and Chenjiadian at DOY 214, 219, 225, 229, 222, and 218, respectively. The time-series MODIS LAI products have a higher frequency of observations compared to ground-based measurements, thus they potentially have more specific piecewise points. The MODIS LAI as input also has higher spatial resolution, making it easier to obtain the LAI for multiple sites than the GPMCM based on the study region after localization.

The piecewise points of the MODIS LAI at different sites ranged from DOY 214 to DOY 229, which was different from the field measurements. The results of the MODIS LAI as input with piecewise points of the field-measured datasets were simulated to further validate the applicability of the GPMCM in this study.

Table 6. The accuracy results of the simulated maize canopy parameters were compared to the field-measured datasets separately, based on two methods of dividing the entire growing season into two stages using the MODIS-product LAI values and the field-observed values of the extreme value points.

Piecewise Point	Index	Height	Long Radius	Short Radius	FAGB of Stems	FAGB of Leaves	AGB of Stems	AGB of Leaves	VWC of Stems	VWC of Leaves
		cm	mm	mm	————————— kg/m2 —————————
MODIS LAI fitted	$RMSE$	28.1	2.06	1.72	0.52	0.22	0.12	0.13	0.46	0.16
	$Bias$	3.17	0.11	0	$-$0.01	$-$0.02	$-$0.01	$-$0.05	0	0
	$R$	0.95	0.57	0.63	0.90	0.89	0.85	0.85	0.90	0.91
	$MAPE$	11.0	12.4	12.4	14.7	14.6	17.5	17.9	18.5	16.5
Field observations fitted	$RMSE$	28.09	1.90	1.61	0.52	0.21	0.12	0.13	0.47	0.16
	$Bias$	4.89	0.26	0.11	$-$0.02	$-$0.03	$-$0.01	$-$0.04	$-$0.02	$-$0.01
	$R$	0.95	0.63	0.68	0.90	0.89	0.85	0.83	0.89	0.89
	$MAPE$	11.5	11.4	11.4	15.5	13.5	16.8	17.6	20.6	16.5

shows the accuracy indicators of the simulation results on the premise of two piecewise point methods: the extreme points of the LAI values fitted to the MODIS products and field-measured values. The DOYs of the piecewise points were 218, 230, and 233 for the field observations according to the maize canopy parameters (Table 2). The simulated values were underestimated when using the piecewise points of the field observation datasets because the field observation piecewise points for simulating the FAGB and VWC of the maize stem and leaf components were on DOY 218, which was earlier than the DOY of the piecewise points from the MODIS LAI values. Similarly, the same phenomenon exists for the AGB parameter, which was confirmed by the deviations in the simulation results (Table 6).

The feasibility and applicability of the GPMCM was verified by taking the 4 day LAI product of MODIS instead of the field LAI as the input. After matching the MODIS product with the field measurement DOY, the accuracy of MODIS LAI was found to be representative of the study area and showed a high correlation with an $R$ of 0.95 (Figure 10a). Considering the accuracy of the MODIS LAI values, the simulation results of the maize height were favorable, with a $Bias$ of 3.17 cm and $MAPE$ of 11% (Figure 10b). The simulation results for the maize stem long and short radius had $R$ values of 0.57 and 0.63, respectively (Figure 10c). The allocation characteristics of the maize stem radius showed a steady change in the late-growing season (Figure 3b). This phenomenon suggests a reduction in the sensitivity of the maize radius to the LAI and in simulating features in the maize stem radius (Figure 10c).

The FAGB, AGB, and VWC simulations for each component of maize showed favorable correlations and accuracy. The simulation accuracy of the leaf component was better than the stem in the canopy parameters of FAGB and VWC. The $MAPE$ for the FAGB and stem VWC components were 14.7% and 18.5%, while for the leaf component they were 14.6% and 16.5%, respectively (

Table A1. The evaluation indicators of the accuracy in the canopy parameters simulated by the MODIS LAI as the input parameter were compared with the field observations for each site and all sites separately.

Site	Index	LAI	Height	Long Radius	Short Radius	FAGB of Stems	FAGB of Leaves	AGB of Stems	AGB of Leaves	VWC of Stems	VWC of Leaves
			cm	mm	mm	————————— kg/m2 —————————
Kaoshan	$RMSE$	0.54	9.92	1.58	1.12	0.27	0.16	0.10	0.12	0.23	0.10
	$Bias$	$-$0.39	2.57	0.91	0.53	0.07	$-$0.06	$-$0.01	$-$0.05	0.11	$-$0.02
	$R$	0.96	0.99	0.51	0.68	0.95	0.89	0.86	0.86	0.96	0.93
	$MAPE$ *	14.0	4.8	11.3	9.1	7.8	11.1	15.6	18.6	11.3	13.3
Donglalatun	$RMSE$	0.51	32.25	2.83	2.22	0.51	0.23	0.16	0.14	0.40	0.15
	$Bias$	$-$0.02	3.09	$-$0.96	0.11	0.03	0.04	0.07	0.05	$-$0.02	$-$0.02
	$R$	0.94	0.97	0.79	0.84	0.90	0.86	0.82	0.36	0.90	0.90
	$MAPE$	26.56	22.01	17.92	24.40	20.38	21.86	26.65	43.31	34.57	36.86
Taipingshan	$RMSE$	0.54	46.85	2.63	2.74	0.81	0.30	0.16	0.11	0.67	0.17
	$Bias$	0.39	24.52	$-$1.23	$-$1.43	$-$0.14	0	0	$-$0.06	$-$0.28	$-$0.01
	$R$	1	0.91	0.34	0.24	0.81	0.81	0.75	0.73	0.85	0.91
	$MAPE$	16.6	22.7	16.3	19.1	23.2	22.7	24.1	23.6	21.9	18.1
Shuangchengpu	$RMSE$	0.31	20.25	1.57	1.11	0.54	0.24	0.08	0.11	0.50	0.19
	$Bias$	$-$0.13	9.44	$-$0.67	$-$0.87	$-$0.05	$-$0.09	$-$0.01	$-$0.07	0	$-$0.03
	$R$	0.98	0.96	0.30	0.71	0.87	0.96	0.93	0.62	0.89	0.87
	$MAPE$	8.0	6.6	8.9	6.7	13.9	12.6	9.4	17.9	15.0	12.3
Longwang	$RMSE$	0.26	12.88	1.5	1.18	0.45	0.18	0.07	0.09	0.46	0.20
	$Bias$	0.21	$-$9.10	0.79	0.66	0.09	0.07	$-$0.03	$-$0.05	0.14	0.12
	$R$	0.99	0.99	0.83	0.84	0.94	0.95	0.96	0.88	0.92	0.92
	$MAPE$	8.6	5.0	8.9	8.20	12.7	9.8	10.8	14.9	19.5	14.6
Chenjiadian	$RMSE$	0.48	37.36	2.24	1.47	0.47	0.17	0.15	0.06	0.42	0.12
	$Bias$	$-$0.34	$-$14.59	1.59	1.11	$-$0.11	$-$0.11	$-$0.09	$-$0.05	0	$-$0.06
	$R$	0.99	0.94	0.85	0.92	0.95	0.97	0.88	0.97	0.94	0.97
	$MAPE$	10.6	15.9	13.2	10.2	14.2	11.7	22.7	15.0	14.6	8.6

* The mean absolute percentage error ($MAPE$) with units in percentage (%).

). The simulated values of the AGB for the maize stems and leaves were slightly underestimated in the late-growing season when the MODIS LAI products were used as input parameters (Figure 10e). The simulated results of the AGB in maize stems were consistent with the low correlation to LAI (Figure 5b). There were obvious biases in the MODIS LAI values for the Taipingshan and Chenjiadian sites, with a $Bias$ of 0.39 and $-$0.34, respectively, which caused the dispersion of the overestimated and underestimated simulated values of the canopy parameters (Table A1).

Due to the fact that the LAI datasets of MODIS products are discontinuous, the differences in piecewise points indicated that the accuracy of the simulation results were not significantly affected by comparing the field measurement datasets separately. The comparison of previous studies revealed that the $R$ values of the FAGB and AGB simulated by CERES-Maize were 0.54 and 0.77, respectively, while the input results of the GPMCM for both the field-observed LAI and MODIS LAI had $R$ values greater than 0.83 [20]. The simulation results of AquaCrop showed an $RMSE$ of 0.349 kg/m² for the simulated AGB, while the GPMCM revealed stem and leaf AGB values with a $RMSE$ less than 0.13 kg/m² [22]. The MODIS LAI products were used as input parameters for the entire growing season, showing favorable simulation accuracy and correlation and demonstrating the applicability and feasibility of the GPMCM.

4.2. Effect of Wilted Leaves on Simulated Accuracy of Canopy Parameters

The LAI decreased as the leaves wilted in the late-growing season. The combination of field observations found that the wilting of the leaves is mainly a gradual process, manifesting as gradual wilting from the edge to the middle of the leaves or random spotted wilting on a single leaf area [25]. The wilting process is caused by shading of the leaves, which prevents the photosynthesis of the bottom leaves of the maize [45]. In the vertical direction, the leaves of maize usually wilted from the lowermost leaves, and the rate of wilting showed a decreasing trend with maize height. However, the wilted leaves did not fall off immediately, which caused an overestimation of the observed parameters such as LAI. However, it is important to obtain an accurate crop green-leaf area for the assessment of crop growth status [46]. At the later stage of field observation in this study, the LAI dataset was obtained manually via the LI-3000C leaf-area scanner after removing the wilted parts or spots from the leaves, and the plants were measured leaf-by-leaf. The FAGB and AGB values were recorded separately for wilted and green leaves during the laboratory processing of maize samples.

The effects of wilted leaves on the FAGB and AGB cannot be neglected after the fit and analysis of maize leaf features for the whole growing season. The FAGB of the maize leaves decreased with the LAI during the late-growth stage (Figure 2c). The FAGB of the wilted leaves increased significantly with the growth process, indicating that the lack of removed wilted leaf parts in the field observations during the later stages would cause an overestimation of the FAGB (Figure 11a). For the entire growing season, the FAGB of the wilted leaves accounted for 9% of the total stems and leaves in the maize per unit area (

Table 7. The contributions of the green and wilted leaves of maize to the FAGB, AGB and VWC, respectively.

Component of Leaves	FAGB	AGB	VWC
Green leaves	0.91%	0.87%	0.97%
Wilted leaves	0.09%	0.13%	0.03%

). The AGB of the leaves was continuously accumulated despite the moisture loss in the maize stems and leaves. The allocation characteristics in the AGB of the wilted leaves showed an opposite tendency to the LAI, meaning that the rapidly increasing wilted leaves accelerated the rate of the LAI decrease. The temporal variation of the green and wilted leaves was analyzed separately, revealing that the effects of wilted leaves on the LAI were obvious, while the presence of wilted leaves indicated that the LAI was not symmetric in the two growth stages. The contribution of the wilted leaves to the AGB gradually increased in the late growing stage of the maize, and accounted for 13% of the contribution from the maize stems and leaves for the entire growing season (Table 7). The characteristics of the AGB in maize leaves were specifically shown as three processes of the increase, stability, and re-increase during the whole growing season (Figure 11b). However, the effect of wilted leaves on the VWC was not significant because of the reduced moisture contained in the wilted leaves. However, this indicates that there still exists an error of approximately 3% in the simulation accuracy of wilted leaves in the FAGB, and this error is difficult to estimate in the GPMCM of this study (Table 7).

4.3. Applicability Analysis of the GPMCM

The specific maize crop model provides an effective approach for cropland productivity prediction and remote-sensing parameter inversion studies. In this study, the entire growing season was divided into two growth stages for the regression simulation based on the allocation characteristics of the maize crop parameters. Previous studies have shown that it is feasible to establish simulation relationships for different crop growth stages. The CERES-Maize model divides the growing season into five stages, while the IN-TERCOM model divides it into two [20,47]. However, the excessive delineation of growth stages has the problems of insufficient fitted data and difficulty in delineating the growing season boundaries. Meanwhile, conducting the localization process using field observation datasets is essential, and can capture the allocation characteristics of each crop parameter throughout the growing season. This is important for establishing the expression forms of the crop parameter relationships in the model. The proposed GPMCM model provides an effective reference for the maize crop model construction method.

The main factors that affect the applicability of the GPMCM are the maize varieties, growth period, and planting density. The maize varieties directly determine the thresholds of the geometric and physical parameters of the maize crop, which are the main factors affecting the scalability of the GPMCM model. The FAGB of the stems of green-fed maize was much higher than the FAGB of leaves [48]. More sunshine and the higher annual accumulation of temperature at low latitudes allow for maize to be grown in two or three seasons a year. The shorter growing season leads to temporal variation and biomass allocation characteristics that do not correspond to the annual cycle in the GPMCM. The variability of planting densities in different regions also leads to differences in the characteristics of crop geometry and the physical parameters. These factors reduce the applicability of crop models in different countries and hemispheres. However, the applicability of the GPMCM model to the maize crop in northeastern China reflects the advantages of the modeling approach in this study and provides the feasibility of solving the influences in different regions. The applicability of the GPMCM model to other study regions still needs further analysis.

5. Conclusions

In this study, a new semi-empirical geometric and physical parameter of the maize canopy model (GPMCM) based on field observation datasets was proposed. The GPMCM achieved the simulation of multiple crop geometrical and physical parameters and moreover proposes a characterization of the crop geometry and biomass allocation. Meanwhile, the allocation characteristics of the biomass and water content between different components of the crop were demonstrated. The field datasets were observed 15 times for the entire growing season including the geometric parameters (such as the LAI, maize height, stem long and short radius) and physical parameters (such as the FAGB, AGB, VWC, and RWC of the stem and leaf components, respectively). The GPMCM analyzed the fitted relationships between the maize canopy parameters, and LAI was selected as the input to simulate the allocation characteristics of the maize canopy parameters. The allocation characteristics and variation rates of the maize geometric and physical parameters at the growth and wilting stages were different. Thus, the piecewise functions can effectively describe the maize growth and wilting processes. The piecewise points for each canopy parameter were determined by the temporal variation of the LAI and the fitted relationships between the LAI and the other canopy parameters. The GPMCM-simulated FAGB and AGB were more accurate using the quantitative separation of wilted leaves. Compared to field observation datasets, the simulation results for the maize geometric and physical parameters showed high accuracy, with a $MAPE$ ranging from 3.4% to 12.9%. The establishment of the GPMCM provides a feasible tool for monitoring the maize canopy parameters and improving the remote-sensing inversion process. Additionally, this regression-based, two-stage approach for crop model construction is more reasonable. The input parameter LAI as a commonly used crop index was combined with other crop models or remote-sensing data in the present research. The simulation results combined with the MODIS LAI products indicated a $MAPE$ ranging from 11% to 18.5%. This indicates that the GPMCM model has the basis for wide application. However, its applicability needs further analysis due to the effects of crop variety, growth period, and planting density. In this study, the influence of wilted leaves on the biomass and water content was analyzed and found to play a non-negligible role. The long-term research objectives based on the GPMCM model are (1) to establish crop models of other species (such as soybean and rice) with the consideration of the crop characteristics and growth patterns, and (2) to increase the field observations of wilted leaves and analyze the temporal variation of the biomass.