Constructing and Validating Estimation Models for Individual-Tree Aboveground Biomass of Salix suchowensis in China

Abstract

Biomass serves as a crucial indicator of plant productivity, and the development of biomass models has become an efficient way for estimating tree biomass production rapidly and accurately. This study aimed to develop a rapid and accurate model to estimate the individual aboveground biomass of Salix suchowensis. Growth parameters, including plant height (PH), ground diameter (GD), number of first branches (NFB), number of second branches (NSB) and aboveground fresh biomass weight (FW), were measured from 892 destructive sample trees. Correlation analysis indicated that GD had higher positive correlations with FW than PH, NFB and NSB. According to the biological features and field observations of S. suchowensis, the samples were classified into three categories: single-stemmed type, first-branched type and second-branched type. Based on the field measurement data, regression models were constructed separately between FW and each growth trait (PH, GD, NFB and NSB) using linear and nonlinear regression functions (linear, exponential and power). Then, multiple power regression and multiple linear regression were conducted to estimate the fresh biomass of three types of S. suchowensis. For the single-stemmed plant type, model M1 with GD as the single parameter had the highest adj R², outperforming the other models. Among the 16 constructed biomass-estimating equations for the first-branched plant type, model M32 FW = ^0.010371 × PH^1.15862 × GD^1.250581 × NFB^0.190707 was found to have the best fit, with the highest coefficient of determination (adj R² = 0.6627) and lowest Akaike Information Criterion (AIC = 5997.3081). When it comes to the second-branched plant type, the best-fitting equation was proved to be the multiple power model M43 with PH, GD, NFB and NSB as parameters, which had the highest adj R² value and best-fitting effect. The stability and reliability of the models were confirmed by the F-test, repeated k-fold cross-validation and paired-sample t-tests. The models developed in this study could provide efficient tools for accurately estimating the total aboveground biomass for S. suchowensis at individual tree levels. The results of this study could also be useful for optimizing the economic productivity of shrub willow plantations.

1. Introduction

Global warming is a worldwide environmental crisis, with carbon dioxide identified as the primary contributor. The extensive use of fossil fuels for heat and electricity production, as well as for transportation, accounts for approximately 80% of global greenhouse gas emissions [1,2]. The escalating issues of global warming and climate change have garnered interest in the use of green biomass, particularly woody plants, due to their ecological and environmental benefits [3]. Biomass energy is green, renewable, abundant and widely distributed, playing an important role in alleviating energy shortages, optimizing energy structures and improving the ecological environment [4]. Consequently, the development and utilization of biomass energy is an inevitable strategy for achieving a low-carbon economy and sustainable development [5,6]. Among various renewable biomasses, forest biomass stands out due to its rich reserves and diverse utilization forms, making it an ideal alternative to fossil fuels [7]. Biomass directly reflects plant growth and serves as a crucial indicator for evaluating plant productivity. It also forms the basis of ecosystem matter and energy dynamics [8]. The timely and accurate estimation of forest biomass is essential for assessing biomass resources and carbon stocks, formulating biomass energy policies and conducting climate change studies [9].

Shrubs play a significant role in ecosystems and are vital components of forest resources, characterized by well-developed root systems, high biological productivity and wide ecological adaptability [10,11]. The well-developed root systems of shrubs and the abundance of inter-root microorganisms enhance the production, decomposition and accumulation of soil humus, which is the major driver of ecosystem productivity and diversity [12]. Although shrubs constitute a smaller proportion of forest ecosystems compared to trees, they are better-adapted to harsh climatic conditions and contribute significantly to environmental and ecological conservation in fragile areas such as deserts, plateaus and regions prone to rocky desertification. They prevent wind erosion, stabilize sand, conserve soil and water, and ameliorate saline and alkaline soils [13]. Despite their importance, research on shrub biomass modeling remains limited due to the smaller size and proportion of shrubs, the vast diversity of species and significant morphological and structural differentiation [14]. Previous studies have often overlooked the biomass and carbon stocks of shrubs and young forests, likely due to the absence of predictive equations for shrub biomass, which hindered the accurate quantification of forest biomass and its carbon stocks [9].

Salix suchowensis is a deciduous shrub of the genus Willow in the Populus family, with a wide distribution range, rapid growth and easy reproduction, which is not only an important urban and landscape greening tree species, but also an important energy and industrial tree species [15]. S. suchowensis grows fast and can reach the height of about 3 m, and efficiently converts solar energy into biomass [16]. Compared with many other annual energy crops, S. suchowensis has a short growing period and can regenerate from stumps after cutting, allowing for multiple harvests from the same plants, thus making it an excellent short-rotation coppice [17]. However, research on the biomass performance and growth model of S. suchowensis is scarce. There is a need to develop biomass estimation models for S. suchowensis across various ecological zones to support decision-making in natural resource management [18].

Traditional plant biomass measurements involve manually weighing the fresh weight of trees, a method that is both destructive and irreversible, and thus suitable only for small sample sizes [19]. In contrast, indirect modeling methods use simple, easily measurable indicators, such as diameter at breast height and plant height to establish biomass prediction models. This approach overcomes the limitations of the harvesting method and enables large-scale biomass assessments [20]. Currently, most studies, both domestic and international, estimate forest tree biomass and develop estimation models using related phenotypic parameters [21]. There are various mathematical models for predicting shrub biomass, including linear models, polynomial models and power exponential allometric growth models. Common predictive indicators include the diameter, height, crown width and number of branches, as well as composite factors like cross-sectional area (diameter squared) and plant volume (product of diameter squared and height). For instance, an allometric growth model for the aboveground biomass of four bamboo species was established using a power function with plant height, diameter at breast height and age as the input parameters [22]. Another study used diameter, tree height, wood density and crown width to develop a biomass estimation model [23]. Additionally, the allometric growth relationship between the dry biomass of the aboveground tree and diameter at breast height during individual tree development has also been reported [24].

In this study, we analyzed the variation in plant height, ground diameter, fresh weight biomass, number of first and second branches, and the ratio of the main stem to branches for S. suchowensis. The fresh weight biomass prediction models were established for S. suchwensis seedlings by performing linear, nonlinear and stepwise regression analyses using plant height, ground diameter, number of primary branches and number of secondary branches as the input parameters, and the F-test, repeated k-fold cross-validation and paired-sample T-test were applied on the model to test the generality of the model, thus providing a reference for the implementation of rapid biomass measurements of S. suchowensis.

2. Materials and Methods

2.1. Field Trial

An F1 population consisting of 892 S. suchowensis individuals was established and planted at the Baima Base of Nanjing Forestry University (31°36′46″ N, 119°9′16″ E) in Nanjing, China (Figure 1). This location is situated in the northern subtropical monsoon climate zone, characterized by yellow loam, an average annual temperature of 16.4 °C and an average annual precipitation of 1204.3 mm, with four distinct seasons (

Table 1. Environmental conditions of the experimental field.

Site	Longitude (E)	Latitude (N)	Annual Temperature/°C	Min Temperature/°C	Max Temperature/°C	Annual Rainfall/mm	Soil Type	Plant Space/m	Trial Size
Nanjing	119°9′16″	31°36′46″	16.4	−10	37	1204.3	yellow loam	0.5 × 0.5	892

). Seeds obtained from the hybridization of SB48 × SB13 were sown in March 2023. Seedlings were transported to the Baima base for potting on 30 April 2023, and subsequently transplanted to the field on 20 May 2023, with a planting configuration of 0.5 m × 0.5 m. To minimize edge effects, protective rows were set up around the experimental plots.

On 12 March 2024, the plant height and ground diameter of S. suchowensis were measured using a height measurement pole (precision 0.1 cm) and a vernier caliper (precision 0.01 mm), respectively. Additionally, the number of first and second branches was investigated. The aboveground parts of the plants were then harvested, and the samples were immediately transported to the laboratory. The fresh weight of the whole plant, the main stem and branches were measured manually on the same day.

2.2. Data Processing and Analysis

Firstly, the obtained data were screened to remove abnormal data, such as dead or missing plants. Key parameters were measured, including plant height (PH, the distance from the plant shoot tip to the ground, in cm), ground diameter (GD, the diameter of the plant at 5 cm above the ground, in mm), number of first branches (NFB) and number of second branches (NSB).

Before data analysis and model construction, based on the biological characteristics of S. suchowensis and the results of the field investigation, we classified the samples into three categories according to the plant type (Figure 2), namely, single-stemmed type, containing only the main stem; first-branched type, consisting of the main stem and the first branches occurring directly from the main stem; and second-branched type, consisting of the main stem, the first-order branches and the second-order branches. Then, the four parameters, PH, GD, NFB and NSB, were selected as independent variables, and the fresh weight (FW) of S. suchowensis was selected as the dependent variable, and the R software was utilized to conduct the collinearity tests, correlation analyses, linear and nonlinear regression analyses, and cross-validation.

To construct the estimation models of S. suchowensis fresh weight biomass, it was essential to perform collinearity tests on the independent variables. Initially, the correlation coefficients between the independent variables were calculated, followed by the computation of the variance inflation factor (VIF). If the VIF value is over 10, the collinearity between independent variables is considered to exist; if the VIF value is less than 10, the collinearity between the independent variables can be ignored for subsequent analyses. The equation used was as follows:

$$\mathrm{V}\mathrm{I}\mathrm{F}={\displaystyle \frac{1}{1-r^2}}$$

(1)

where r is the correlation coefficient between independent variables. Furthermore, the correlation between biomass and each factor was tested as well.

2.3. Model Fitting and Evaluation

We used the R software (v.4.4.0) to calculate the basic statistics for the phenotypic data and conduct the regression analysis, including linear regression, multiple nonlinear regression and multiple linear regression. The unitary regression models applied a linear function y = a + bx, the power function y = ab^x, and the exponential function y = ae^bx for a total of three types of functions. The multiple power models applied the power function y = ax₁^bx₂^cx₃^dx₄^e, where: y is the predictor variable (fresh weight biomass); x is the fitted variable (PH, GD, NFB, NSB); a is the regression constant; and b, c, d and e are the regression coefficients. The parameters of the models were estimated by the nonlinear least-squares (NLS) method using the “gslnls” package (v.1.3.2) [25], and the “MASS” package (v.7.3-61) [26] was used to perform multiple linear stepwise regression analyses on the following indicators: plant height, ground diameter, number of first branches and number of second branches, respectively. Box plots, line plots and scatter plots were produced using the “ggplot2” R package (v.3.5.1) [27].

To assess model performance, we selected the adjusted coefficient of determination (adj R²), Akaike Information Criterion (AIC), absolute mean residual (AMR) and root mean square error (RMSE). Higher adj R² values and lower AIC, AMR and RMSE values generally indicate a better model fit. The specific equations used for evaluation are as follows:

$$adj R^2=1-\left[{\displaystyle \frac{\sum _{i=1}^n (y_i-{\widehat{y}}_i{)}^2/(n-k-1)}{\sum _{i=1}^n (y_i-{\overline{y}}_i{)}^2/(n-1)}}\right]$$

(2)

$$\mathrm{AIC}=n\ln {\displaystyle \frac{\sum _{i=1}^n (y_i-{\widehat{y}}_i{)}^2}{n}}+n+n\ln \left(2\pi \right)+2\mathrm{k}$$

(3)

$$\mathrm{AMR}={\displaystyle \frac{1}{n}}\sum _{i=1}^n \left(\left|y_i-{\widehat{y}}_i\right|\right)$$

(4)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\begin{array}{c}{\displaystyle \frac{1}{n-k}}\sum _{i=1}^n {\left(y_i-{\widehat{y}}_i\right)}^2\\ \end{array}}$$

(5)

where n is the number of samples; y_i is the measured value of biomass; ŷ_i is the predicted value of sample i; ȳ_i is the mean of the measured value; and k is the number of parameters of the fitted equation.

2.4. Validation and Significance Tests

After fitting the biomass prediction models, we conducted the F-test, the repeat k-fold cross-validation and the paired-sample T-test on the regression models to accurately assess the generalization ability of the model and avoid overfitting and underfitting problems of the prediction models. The F-test helps determine whether the differences between models or data are significant or not, thus providing a statistical basis for model selection and data analysis. Repeated k-fold cross-validation involves splitting the data into multiple subsets (folds), with one subset used for model training and the remaining subsets for validation. This iterative process ensured that each data point is used for both training and validation, thereby enhancing the reliability and generalization of the models. The paired-sample T-test is able to determine whether the means under the two conditions are significantly different or not. Data processing and analysis for cross-validation were performed by the ‘caret’ R package (v.6.0-94) [28].

3. Results

3.1. Variations in the Growth Phenotypes

Initially, the total sample size for biomass calculations included 892 individuals. Following the exclusion of missing and non-viable data points, the refined dataset used for analysis comprised 885 individuals. The frequency distributions of directly measured phenotypic traits of S. suchowensis (FW, PH, GD, NFB) exhibited a well bell-shaped curve, except for NSB, which showed a skewed normal distribution (Figure 3). The statistics for biomass-related phenotypic data are presented in

Table 2. Growth statistics of the Salix suchowensis F1 full-sib family.

Parameter	Sample Size	Min.	Max.	Range	Mean	SD	CV/%
PH (cm)	885	103.00	235.00	132.00	181.44	17.74	9.78
GD (mm)		5.98	19.62	13.64	13.24	2.01	15.19
FW (g)		22.25	375.95	353.70	157.82	60.76	38.50
WMS (g)		11.55	170.75	159.20	80.77	23.67	29.31
WTB (g)		0.00	301.65	301.65	77.04	49.51	64.27
WFB (g)		0.00	299.20	299.20	75.17	48.30	64.25
WSB (g)		0.00	49.65	49.65	1.86	4.41	236.82
NFB		0.00	23.00	23.00	6.44	3.87	60.16
NSB		0.00	11.00	11.00	0.68	1.41	206.77
WMS/FW		0.17	1.00	0.83	0.55	0.17	30.63
WTB/FW		0.00	0.83	0.83	0.45	0.17	37.85

Note: PH, plant height, in cm; GD, ground diameter, in mm; FW, fresh weight of the aboveground biomass, in g; WMS, weight of main stem, in g; WTB, weight of total branches, in g; WFB, weight of first branches, in g; WSB, weight of second branches, in g; NFB, number of first branches, in count; NSB, number of second branches, in count; WMS/FW, the ratio of WMS to FW; WTB/FW, the ratio of WTB to FW; SD, the standard deviation, in g; CV, the coefficient of variation.

. Plant height and ground diameter are important parameters in describing plant growth and are integral to establishing biomass prediction models. The data revealed that PH had a mean value of 181.44 ± 17.74 cm, with a coefficient of variation (CV) of 9.78%, while GD averaged 13.24 ± 2.01 mm, with a CV of 15.19%. The fresh weight (FW) ranged from 22.25 g to 375.95 g, with a mean of 174.60 g and a CV of 38.50%, indicating considerable variability compared to PH and GD. Additionally, weights such as the weight of the main stem (WMS), total branches (WTB), first branches (WFB) and second branches (WSB) were also determined, serving as significant indicators of biomass accumulation and growth, all demonstrating large variation. The number of first branches (NFB) and second branches (NSB) exhibited large differences among individuals within the sample. Moreover, the fresh weight of the stem and branches are both important components of the aboveground fresh weight of the stand, accounting for 55% and 45% of the aboveground biomass, respectively, which are essential components of biomass prediction models.

3.2. Correlation and Multicollinearity Analyses

The construction of prediction models was based on the significant correlations between the dependent and independent variables. Four factors were selected to analyze the correlation with biomass. As is vividly shown in Figure 4, FW was significantly correlated with all independent variables. The correlation coefficients of GD and NFB with FW exceeded 0.5, which were 0.730 and 0.531, respectively. All of the factors can be used for biomass prediction model construction. PH exhibited a positive correlation with GD but a negative correlation with NFB and NSB. This suggested that an increase in ground diameter correlates with increased plant height, while an increase in branch number tended to suppress the height growth of S. suchowensis. NFB had a positive correlation with NSB, and GD was positively correlated with NFB and NSB.

To ensure the accuracy of the regression analysis, collinearity tests were conducted on the independent variables for multiple linear regression. The VIF values among the four independent variables are presented in

Table 3. VIF values for the PH, GD, NFB and NSB of Salix suchowensis.

Value	Parameter	PH	GD	NFB	NSB
VIF value	PH	-	1.313	1.001	1.001
	GD	1.313	-	1.134	1.033
	NFB	1.001	1.134	-	1.055
	NSB	1.001	1.033	1.055	-

. All of the VIF values were less than 10, ranging from 1.001 to 1.313, indicating that multicollinearity among the variables is negligible and does not compromise the predictive accuracy of the regression model. Thus, the multiple power regression and the multiple stepwise regression analyses could be carried out.

3.3. Construction of Biomass Models with a Single Variable

Using FW as the dependent variable and PH, GD, NFB and NSB as single independent variables, respectively, we chose three types of regression equations (linear, exponential and power functions) to establish the fresh weight biomass prediction models for S. suchowensis. After fitting the equations, we evaluated the goodness of fit using the adjusted R², absolute mean residual (AMR), root mean square error (RMSE) and Akaike Information Criterion (AIC) of the fitted model. The model parameters and evaluation indicators are presented in

Table 4. Construction and evaluation of the aboveground biomass model based on linear and nonlinear regression method with a single variable.

Plant Type	Number of Models	Variable	Function	Model	adj R2	AMR	RMSE	AIC
Single-stemmed	M1	GD (mm)	linear	−89.254 + 14.994 × GD	0.7547	8.2753	11.5529	139.5674
	M2	PH (cm)	linear	−89.2289 + 0.9011 × PH	0.4799	12.5228	16.8229	152.3449
	M3	GD (mm)	power	0.5717 × GD2.0313	0.7520	7.9675	11.6163	139.7537
	M4	PH (cm)	power	0.001256 × PH0.474703	0.4940	11.9686	16.5939	151.8788
	M5	GD (mm)	exponential	11.66273 × e0.16778×GD	0.7415	8.1886	11.8608	140.4619
	M6	PH (cm)	exponential	10.458999 × e0.010688×PH	0.5034	11.7908	16.4386	151.5592
First-branched	M7	GD (mm)	linear	−118.0284 + 20.4825 × GD	0.5373	30.3384	38.0425	6188.4420
	M8	PH (cm)	linear	−138.2263 + 1.5877 × PH	0.2460	37.9849	48.5632	6486.8093
	M9	NFB (count)	linear	105.2827 + 7.3416 × NFB	0.2203	39.3610	49.3842	6507.2940
	M10	GD (mm)	power	1.38538 × GD1.81498	0.5423	30.0709	37.8377	6181.8457
	M11	PH (cm)	power	0.00597 × PH0.15643	0.2421	38.1137	48.6885	6489.9570
	M12	NFB (count)	power	93.07986 × NFB0.28511	0.2254	39.4878	49.2232	6503.3047
	M13	GD (mm)	exponential	26.392691 × e0.130215×GD	0.5392	30.3318	37.9664	6185.9965
	M14	PH (cm)	exponential	20.2828 × e0.01067×PH	0.2356	38.2771	48.8970	6495.1793
	M15	NFB (count)	exponential	115.4 × e0.04135×NFB	0.2031	39.6735	49.9256	6520.6188
Second-branched	M16	GD (mm)	linear	−131.94 + 22.79 × GD	0.4641	36.9922	45.7992	2703.0155
	M17	PH (cm)	linear	−126.9487 + 1.7016 × PH	0.2137	42.8030	55.4764	2801.5444
	M18	NFB (count)	linear	116.6239 + 8.3883 × NFB	0.2731	42.3882	53.3412	2781.3707
	M19	NSB (count)	linear	164.133 + 7.529 × NSB	0.0345	49.5459	61.4762	2854.3284
	M20	GD (mm)	power	1.822 × GD1.7505	0.4672	36.7482	45.6676	2701.5364
	M21	PH (cm)	power	0.02423 × PH1.71461	0.2123	42.8130	55.5273	2802.0162
	M22	NFB (count)	power	91.59733 × NFB0.34908	0.2717	42.2365	53.3912	2781.8525
	M23	NSB (count)	power	168.49783 × NSB0.11372	0.0344	49.3556	61.4801	2854.3606
	M24	GD (mm)	exponential	33.425143 × e0.121141×GD	0.4628	36.8447	45.8564	2703.6568
	M25	PH (cm)	exponential	32.738980 × e0.00938×PH	0.2082	42.9067	55.6729	2803.3622
	M26	NFB (count)	exponential	131.2 × e0.0404×NFB	0.2601	42.9116	53.8176	2785.9410
	M27	NSB (count)	exponential	166.05339 × e0.03769×NSB	0.0335	49.5853	61.5089	2854.6016

and Figure 5, Figure 6 and Figure 7.

For the single-stemmed plants, models using PH as the independent variable, the three functions yielded adj R² values ranging from 0.4799 to 0.5034, with corresponding AIC values ranging from 151.5592 to 152.3449. For the GD biomass prediction models, the best fit was observed with the linear regression, achieving the highest adj R² value of 0.7547 and the smallest AIC value of 139.5674, with an RMSE value of 11.5529. Moreover, the models constructed with GD were better than models constructed with PH, mainly due to higher correlation with FW. For the first-branched plants, it is always the regression model constructed by GD that had a better fit when compared to models established by PH and NFB. Of the nine functions for estimating first-branched plant biomass, the GD power model acts better than any other models, achieving an adj R² value of 0.5423, slightly better than the 0.5373 and 0.5392 of linear and exponential functions. When it comes to the second-branched models with four single indicators, models constructed with GD as a single variable still outperformed other indexes, showing a better fit. Furthermore, among the three regression functions, the power function was more appropriate for the fresh weight biomass estimation for S. suchowensis.

3.4. Construction of Biomass Models with the Multiple Power Regression Model

Combining the biological growth pattern of woody plants and the results of the biomass equations constructed with different growth indicators as single parameters, we chose four growth indicators, namely, PH, GD, NFB and NSB, and used the power function equation as the basic regression function for constructing the multiple regression models of the aboveground fresh biomass of S. suchowensis. The regression results were presented in

Table 5. Construction and evaluation of the aboveground fresh biomass model based on the multiple power function.

Plant Type	Number of Models	Variable	Model	adj R2	AMR	RMSE	AIC
Single-stemmed	M28	PH, GD	0.65878 × PH−0.04224 × GD2.06403	0.7330	8.0541	11.2208	141.7487
First-branched	M29	PH, GD	0.04184 × PH0.76849 × GD1.62038	0.5669	29.2461	36.7479	6149.1357
	M30	PH, NFB	0.0013373 × PH2.143829 × NFB0.2907575	0.4984	30.5206	39.5453	6238.7903
	M31	GD, NFB	1.85901 × GD1.59945 × NFB0.15714	0.6099	27.4503	34.8724	6085.1222
	M32	PH, GD, NFB	0.010371 × PH1.15862 × GD1.250581 × NFB0.190707	0.6627	25.5405	32.3746	5997.3081
Second-branched	M33	PH, GD	0.05619 × PH0.77712 × GD1.5353	0.5021	34.7678	43.9728	2685.1083
	M34	PH, NFB	0.006992 × PH1.822947 × NFB0.346552	0.5089	33.4632	43.6738	2681.6003
	M35	PH, NSB	0.01443 × PH1.79633 × NFB0.13901	0.2716	40.5132	53.1880	2782.9024
	M36	GD, NFB	2.20095 × GD1.49342 × NFB0.24835	0.6033	31.2947	39.2517	2626.7298
	M37	GD, NSB	2.01224 × GD1.70305 × NSB0.03917	0.4704	36.4646	45.3533	2700.9963
	M38	NFB, NSB	90.48203 × NFB0.33657 × NSB0.05557	0.2792	41.9256	52.9091	2780.1999
	M39	PH, GD, NFB	0.01798 × PH1.07279 × GD1.18201 × NFB0.2701	0.6680	27.4081	35.7664	2581.9485
	M40	PH, GD, NSB	0.04731 × PH0.84888 × GD1.44434 × NSB^0.05774	0.5110	34.2005	43.4058	2681.4509
	M41	PH, NFB, NSB	0.005093 × PH1.879635 × NFB0.329125 × NSB0.083416	0.5295	32.3366	42.5757	2671.5259
	M42	GD, NFB, NSB	2.240458 × GD1.485723 × NFB0.246951 × NSB0.007962	0.6019	31.2828	39.1635	2628.5872
	M43	PH, GD, NFB, NSB	0.01635 × PH1.10962 × GD1.14101 × NFB0.26604 × NSB0.02936	0.6695	27.3795	35.5435	2581.7529

Note: PH, plant height, in cm; GD, ground diameter, in mm; NFB, number of first branches, in count; NSB, number of second branches, in count.

. The fitted model for single-stemmed plants comprised PH and GD, the adj R² value of which was 0.7330 and the RMSE value was 11.2208. For the first-branched type, model M32 obtained an adj R² value of 0.6627 and the RMSE value was 32.3746, which consisted of three variables, showing a better-fitting effect than models constructed by two variables. Furthermore, the established models with GD as parameters, including model M29 and M31, indicated a better-fitting effect than model M30. For second-branched type, the best-fitting effect was achieved by M43, which consisted of four variables and had the highest adj R² and lowest RMSE value, at 0.6695 and 35.5435, respectively. The second fit model was M3,9 constructed by PH, GD and NFB. Compared to other two-variable models, M36 with GD and NFB as independent variables performed better.

3.5. Construction of the Biomass Model with the Multiple Linear Regression Model

The multiple linear regression models for S. suchowensis aboveground biomass are presented in

Table 6. The multiple linear regression models for aboveground biomass prediction.

Plant Type	Number of Models	Variable	Model	adj R2	AMR	RMSE	AIC
Single-stemmed	M1	GD	−89.254 + 14.994 × GD	0.7547	8.2753	11.5529	139.5674
	M44	PH, GD	−92.31803 + 14.42325 × GD + 0.05036 × PH	0.7366	8.0453	11.1464	141.5227
First-branched	M7	GD	−118.0284 + 20.4825 × GD	0.5373	30.3384	38.0425	6188.4420
	M45	GD, NFB	−111.1329 + 18.1047 × GD + 3.992 × NFB	0.5955	28.1244	35.5126	6107.3536
	M46	GD, NFB, PH	−200.504 + 14.22424 × GD + 4.74834 × NFB + 0.7471 × PH	0.6329	26.9029	33.7758	6049.0851
Second-branched	M16	GD	−131.94 + 22.79 × GD	0.4641	36.9922	45.7992	2703.0155
	M47	GD, NFB	−135.1219 + 19.6094 × GD + 6.0419 × NFB	0.5991	31.6873	39.4557	2629.3932
	M48	GD, NFB, PH	−255.6368 + 15.2791 × GD + 6.62 × NFB + 0.9682 × PH	0.6538	28.4586	36.5250	2592.7359
	M49	GD, NFB, PH, NSB	−262.7903 + 14.6867 × GD + 6.4681 × NFB + 1.0191 × PH + 3.1043 × NSB	0.6592	28.1342	36.0939	2589.6514

Note: PH, plant height, in cm; GD, ground diameter, in mm; NFB, number of first branches, in count; NSB, number of second branches, in count.

. The constructed multiple linear model M44 obtained an adj R² value of 0.7366, which was lower than model M1 with GD as the single variable. Except for the single-stemmed plant type, with the introduction of each independent variable, the adj R² of the regression model gradually increased and the RMSE and AIC values gradually decreased, thus the model fit improved. The best model fitting effect for first-branched type was M46, which was established by GD, NFB and PH, and had the adj R² value of 0.6329. For the second-branched plants, the optimal multiple linear regression model incorporated four variables GD, NFB, PH and NSB to construct an optimal stepwise regression model with an adj R² value of 0.6592, an RMSE value of 36.0939 and an AIC value of 2589.6514.

3.6. Validation of the Optimal Biomass Prediction Model

As shown in

Table 7. Significance test for the intercept and coefficient of the linear regression equation against the y = x line.

Plant Type	Number of Models	Regression Equation	Intercept	Coefficient	adj R2
Single-stemmed	M1	0.7854x + 17.7427	p < 0.001	0.1	0.8074
Single-stemmed	M28	0.7777x + 18.4189	p < 0.001	0.1	0.8086
Single-stemmed	M44	0.7860x + 17.6952	p < 0.001	0.1	0.8077
First-branched	M10	0.5443x + 68.2393	p < 0.001	p < 0.001	0.7506
First-branched	M32	0.67136x + 49.10486	p < 0.001	p < 0.001	0.7722
First-branched	M46	0.63528x + 54.62628	p < 0.001	p < 0.001	0.7675
Second-branched	M20	0.47162x + 96.03041	p < 0.001	p < 0.001	0.7486
Second-branched	M43	0.67697x + 58.68191	p < 0.001	p < 0.001	0.7786
Second-branched	M49	0.66585x + 60.72916	p < 0.001	p < 0.001	0.7758

and Figure 8, the adj R² values between the predicted and measured value of the regression models were all over 0.7. The slopes of the linear equations of the regression model for the single-stemmed type did not have a significant difference from the slopes of y = x, while the intercepts and slopes of the other equations were all significantly different, which indicated that there was a significant difference between the predicted and the actual values of the model. This indicated that the constructed models did not fit the data perfectly. Consequently, to better evaluate the predictive performance of the models, we conducted cross-validation of the selected models and paired-sample T-tests of the observed values against the predicted values of the models.

To further explore the predictive and practical performance of the models, repeated 10-fold cross-validation was conducted to assess the stability and reliability of the models. As can be seen from the cross-validation results in

Table 8. Cross-validation of the aboveground biomass prediction models for Salix suchowensis.

Plant Type	Number of Models	Function	Variable	adj R2	AMR	RMSE	AIC
Single-stemmed	M1	linear	GD	0.7582	8.2899	12.9620	125.2333
Single-stemmed	M28	multiple power	PH, GD	0.7409	8.0984	13.3771	126.6291
Single-stemmed	M44	multiple linear	PH, GD	0.7433	8.1061	13.3424	126.6930
First-branched	M10	power	GD	0.5423	30.0711	37.9619	5564.0003
First-branched	M32	multiple power	PH, GD, NFB	0.6629	25.5261	32.5833	5397.9424
First-branched	M46	multiple linear	PH, GD, NFB	0.6331	26.8934	33.9949	5444.5853
Second-branched	M20	power	GD	0.4673	36.7384	46.0272	2431.7251
Second-branched	M43	multiple power	PH, GD, NFB, NSB	0.6703	27.3385	36.2197	2323.7875
Second-branched	M49	multiple linear	PH, GD, NFB, NSB	0.6598	28.0965	36.7975	2331.1340

, the adj R², AMR values and RMSE values obtained from cross-validation had little difference from the original model. Compared with the original model, the difference in adj R² of model M1 was less than 0.0025 and the difference in RMSE was less than 1.4091; the difference in adj R² of multiple power regression model M32 and model M43 was less than 0.0002 and 0.0008, respectively; the difference in the adj R² of model M46 was less than 0.0002 and the difference in the RMSE was less than 0.2191; the difference in the adj R² of model M49 was less than 0.0006 and the difference in the RMSE was less than 0.7036. These results proved the stability and predictive capability of the constructed models. The differences observed between the original and cross-validated metrics indicated that our models are reliable and well-suited for predicting the biomass of S. suchowensis. Furthermore, paired-sample T-tests were performed to determine whether there is a significant difference between the predicted values of the constructed models and the sample means of the observations. As can be seen in Figure 9, the results indicated no significant difference between the mean predicted and observed values of any of the nine regression models selected.

4. Discussion

The development and application of biomass energy can not only achieve the harmless, reduced and resourceful utilization of various organic wastes, thus improving the ecological environment, but also contribute to optimizing the energy structure, and realizing the synergy between carbon peaking, carbon neutrality and environmental pollution control [29]. Bioenergy derived from S. suchowensis biomass is more economically competitive than many other shrub species due to its sustainable high production, multiple harvest cycles and the high input–output ratio of energy exchange, making it an excellent short-rotation coppice (SRC) species [3,15,30,31]. However, the lack of reliable biomass estimation models hinders the utilization of biomass energy of S. suchowensis. The estimation of forest biomass basically relies on two methods: the direct measurement method and the indirect estimation method. The direct measurement method, known as the harvesting method, has the advantage of high measurement accuracy, but with the disadvantage of large effort, unrecoverable damage to the environment and high cost [32,33]. Consequently, indirect modeling methods are usually used to estimate biomass. Consequently, indirect modeling methods, particularly allometric growth models, are preferred for biomass estimation, having been applied across various tree species [21,34,35]. Sangsuree et al. employed allometric models to estimate the seedling biomass in the tropical dry evergreen forests of Thailand [36]. The biomass of Pinus radiata, Eucalyptus globulus and Eucalyptus nitens were estimated by the measured phenotypic data. Therefore, to maximize the S. suchowensis biomass, it is necessary to excavate its biomass model. The main objectives of this study were to accurately determine the fresh aboveground biomass of S. suchowensis in Nanjing, China, by traditional harvesting and weighing methods. Firstly, the samples were classified into three types by plant type and the branching conditions. Then, the phenotypic data were analyzed to assess the correlation and collinearity between biomass and variables to test the accuracy of biomass prediction by dynamic variables and equations, and to screen out and cross-validate species-specific prediction equations suitable for estimating the fresh weight biomass of S. suchowensis in subtropical regions of Nanjing.

GD and PH are important indicators for assessing tree biomass, reflecting radial growth and longitudinal growth, and demonstrating strong correlations with biomass accumulation. Many studies have selected PH, GD or the combined parameter (GD² × PH) as independent variables to predict the biomass of different organs or the whole plant [37]. In this study, all parameters exhibited highly significant correlations with fresh weight biomass, which were suitable for fitting the biomass prediction model. Consistent with previous studies, the results of the single-variable model showed that GD is the most suitable measure for biomass prediction equations for S. suchowensis in Nanjing, demonstrating that S. suchowensis biomass production was mainly related to radial growth. Several studies have reported that the aboveground biomass estimation models constructed with GD alone or composite variables based on GD have good predictive abilities [30]. For instance, ground diameter, plant height and wood density were used to model the optimal biomass of 205 seedlings of 20 species in Thailand [36]. Zeng et al. found that the bivariate (D and H) model was slightly better than the univariate model in estimating single wood biomass of five conifers [21]. Similarly, the function y = aD^bH^c was found to be the most significant model for estimating the aboveground biomass of Larix sibirica in the forest steppe of Mongolia [38]. In line with previous studies, power function models constructed based on GD or parameters with GD included fitted well in this study. These findings collectively highlight the good predictive ability of GD and its derivative indexes in aboveground biomass prediction. There are several key factors contributing to this situation. (1) Morphologically, trees usually resemble cylinders or cones, whose volume is related to height and diameter, and the power function can well describe this heavy geometry. In shrubs, when the shrub growth reaches a certain height, its growth transforms into radial growth [39]. (2) The growth of woody plants follows a certain biological pattern that often manifests as a power relationship between various growth indexes [40]. (3) The growth process of an organism is often complex and multi-scaled, and the power function is sufficiently scale-invariant to capture this complexity succinctly [41].

However, compared to trees, shrubs have more complex morphological characteristics, with more clumped branches and lateral branches, which must be considered when establishing prediction models for the aboveground biomass of shrubs [42,43]. Accurate predictions of shrub biomass are challenging due to the abundant sprouts, branches and the dispersed characteristics [33,44,45]. In estimating the aboveground biomass of Rhododendron mariesii and Eurya muricata, incorporating crown area or the crown volume into the models increased prediction accuracy, which could reflect the morphological and structural characteristics of shrubs better than using D, H and D²H alone [46]. Therefore, selecting appropriate independent variables specific to particular species and regions is crucial for optimizing the shrub biomass prediction accuracy. During the investigation of field phenotypes, we found that S. suchowensis exhibits a higher number of lateral branches compared to other shrubs with pronounced main stem effects. Therefore, based on biological features and field observations, the samples were classified into three categories: single-stemmed type, first-branched type and second-branched type. Subsequently, the single-variable linear and nonlinear regression, as well as multiple power and multiple linear regression was conducted to figure out the effects of branches on aboveground biomass and refine the prediction model. Table 4 illustrates that the fitted models differ across various strain or branching types, even when the independent variables are the same. Furthermore, in the multiple regression analysis of first-branched and second-branched types, the inclusion of more variables generally increased the adj R² value, indicating an improvement in the predictive ability of the models, which acted a similar function with the crown area [32]. These findings underscored the importance of considering lateral branches alongside traditional metrics when modeling shrub biomass, thereby improving the accuracy of biomass prediction models for S. suchowensis.

Indirect measurement methods for estimating biomass through constructing biomass equations based on easily measurable traits have been widely used to predict forest productivity and carbon sinks, with little environmental damage and great economic accuracy [37,38]. Forest biomass and carbon stocks could be effectively quantified using dynamic equations [35]. Many mathematical functions have been utilized in biomass estimation, such as the logarithmic, exponential, power and quadratic functions, and the most commonly used model is the power function (allometric growth function) [24]. Previous studies have demonstrated that the power function with GD² × PH as the predictive variable was one of the best models to estimate the forest biomass [23,24]. In this study, three types of linear and nonlinear functions, including linear, exponential and power functions, as well as the multiple power and multiple linear regression were utilized to develop the predictive model for the aboveground biomass of S. suchowensis within a single growing period. The effectiveness of these mathematical equations varied across different parameters. Our findings indicated that the most suitable equations for fitting univariate parameters varied, where the linear equation with GD as the predictive indicator was most suitable for estimating the aboveground biomass of the single-stemmed plant type, while the power function was optimal for aboveground biomass estimation using GD, exhibiting a higher adj R² value than other parameters, consistent with previous studies. Although single-variable function models have been suggested for estimating tree aboveground biomass [8,18], research has shown that the inclusion of more variables could enhance the accuracy of modeling shrub biomass. The predictive accuracy of the model improves as its complexity increases [46]. Zeng et al. estimated the biomass of organs and the total plants of four shrubs [11]. They found that the quadratic model with D² (breast diameter) as the independent variable was the best predictive model for the total biomass of Loropetalum chinense and Gardenia jasminoides, while the best predictive quadratic model for white oak biomass involved V (D²H) as the independent variable. In our study, to improve the predictive ability of biomass models, we conducted multiple power regression and multiple linear regression on the aboveground biomass estimation of three plant types. The results showed that, except for the single-stemmed multi-parameter model, which performed similarly to the unitary model, the fitting effect of the other two plant types was superior to the other models with fewer parameters. This may be attributed to the complex biological characteristics of S. suchowensis.

To assess the applicability of the constructed biomass prediction models, we employed the F-test, repeated k-fold cross-validation and the paired-sample T-tests on the selected models. As obviously seen from Table 7 and Table 8, Figure 8 and Figure 9, although the significance test showed that there were significant differences between the regression function of predicted value and measured value and y = x function, which meant the predictive models could not perfectly predict the aboveground biomass, the paired-sample T-tests showed that there was little difference between the mean value of the predicted value and the measured value. Additionally, the cross-validation indicated that the selected models for three kinds of plant types of S. suchowensis exhibited good stability and predictive ability to estimate the aboveground biomass of S. suchowensis. Consequently, these models can be applied to make predictions for fresh biomass of the fresh aboveground portion of S. suchowensis. Furthermore, factors influencing plant biomass production are divided into environmental and genetic factors. Environmental factors include interregional climate and soil differences, while genetic factors contain photosynthetic efficiency, energy conversion efficiency and other endogenous factors [47]. The photosynthesis and growth of trees are strongly influenced by these factors, which in turn affects tree biomass, resulting in biomass modeling that is highly site-specific [48,49]. The models developed in this study are based on measurements and calculations of aboveground biomass of S. suchowensis within the study area; thus, validation is necessary before applying these models to regions with different terrains and climatic conditions [14].

5. Conclusions

Forests are the main carbon sequestration system around the world, and shrubs play a crucial role in ecological restoration due to their good fuel properties and carbon storage capacity. Numerous studies have proven the high biomass and carbon storage potential of shrubs. This study aimed to develop a non-destructive estimation model for predicting the aboveground biomass of S. suchowensis in subtropical China. The study identified correlations between the aboveground biomass and GD, PH, NFB and NSB. Additionally, S. suchowensis was classified into three plant types based on the morphological characteristics and the number of branches. By comparing the fitting results of linear regression, nonlinear regression and multiple power and multiple linear regression, the optimal model for estimating the aboveground biomass of S. suchowensis in three plant types was identified. For the single-stemmed plant type, the linear model M1 with GD as a single variable was the most appropriate. On the other hand, for the first-branched type, the multiple power model M32 was better for the biomass estimation, which included more indexes. Furthermore, the best biomass prediction model M49 for the second-branched type was established using multiple power regression analysis with PH, GD, NFB and NSB as variables. The stability and predictive accuracy of these models were verified through the F-test, cross-validation and paired-sample T-test. It is hoped that this study offers a reference for exploring shrub aboveground biomass in regions with similar climate and soil conditions to the study area. Future research should incorporate climate and environmental factors into the model construction to explore the variations in the prediction models across different regions, and expand the applicability and predictive capacity of the developed models.