Optimizing crown density and volume estimation across two coniferous forest types in southern China via Boruta and Cubist methods

Abstract

Quantifying forest stand parameters is crucial in forestry research and environmental monitoring because it provides important factors for analyzing forest structure and comprehending forest resources. And the estimation of crown density and volume has always been a prominent topic in forestry remote sensing. Based on GF-2 remote sensing data, sample plot survey data and forest resource survey data, this study used the Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) and Pinus massoniana Lamb. as research objects to tackle the key challenges in the use of remote sensing technology. The Boruta feature selection technique, together with multiple stepwise and Cubist regression models, was used to estimate crown density and volume in portions of the research area’s stands, introducing novel technological methods for estimating stand parameters. The results show that: (i) the Boruta algorithm is effective at selecting the feature set with the strongest correlation with the dependent variable, which solves the problem of data and the loss of original feature data after dimensionality reduction; (ii) using the Cubist method to build the model yields better results than using multiple stepwise regression. The Cubist regression model’s coefficient of determination (R²) is all more than 0.67 in the Chinese fir plots and 0.63 in the P. massoniana plots. As a result, combining the two methods can increase the estimation accuracy of stand parameters, providing a theoretical foundation and technical support for future studies.

摘要

基于Boruta和Cubist方法的中国南方两种针叶林林分参数的估算

林分参数是林业调查和生态环境监测中不可或缺的因子，也是研究森林结构和了解森林资源的重要参数。郁闭度和蓄积量的估测一直是林业遥感研究的热点方向。本研究以福建省将乐国有林场为研究区，以杉木(Cunninghamia lanceolata (Lamb.) Hook.)和马尾松(Pinus massoniana Lamb.)为研究对象，基于高分二号(GF-2)遥感数据、样地调查数据以及森林资源二类调查数据，引入Boruta特征选择算法，结合多元逐步和Cubist回归模型，对研究区部分区域的林分郁闭度和每公顷蓄积量进行估算，为探索林分参数估测提供新的技术方法。结果表明，使用Boruta算法可以选择出与因变量相关性最强的特征集合，将其用于建模会优于使用所有特征建模，不仅解决了数据冗余问题，而且避免降维后的原始特征数据缺失。运用Cubist方法进行模型构建，均得到比多元逐步回归更优的效果。其中，在杉木样地中，Cubist回归模型的决定系数R²均在0.67以上；在马尾松样地中，Cubist回归模型的决定系数R²均在0.63以上。上述结果表明，两种方法的结合使用，可以提高林分参数的估测精度，为后续研究提供理论依据和技术支撑。

INTRODUCTION

Stand parameters are critical components of forestry research and ecological environment monitoring, and they can help us better comprehend the relationship between ecosystem function and forest information. The traditional survey method directly obtains stand parameters by field survey, but it has limitations such as low efficiency, lengthy time to get information, time-consuming and difficult. With the application and development of remote sensing technology, an increasing number of researchers are beginning to estimate stand parameters using remote sensing photos (Zhang et al. 2022). Domestic and international researchers have mostly focused on estimating stand crown density, extracting information from tree height and crown breadth, and inverting volume and biomass using machine learning (Sun 2013; Yan et al. 2019). However, estimating crown density and volume has long been a hot topic in forestry remote sensing research, and it is crucial to forest inquiry and monitoring (Wang et al. 2019a; Xie 2018). The ratio of canopy projection area to woodland area in a stand is referred to as crown density, while volume is the total volume of all standing trees in a stand. Both are crucial markers of forest structure and quantitative traits, as well as key determinants in determining forest growth status (Meng 2006). Furthermore, using remote sensing technology to study these stand parameters can effectively solve the problems associated with traditional stand parameter acquisition, such as relying primarily on manual investigation and a lengthy information acquisition cycle, by providing technical and methodological references for the rapid acquisition of large-scale stand parameters. However, due to the inherent limitations in capturing information through imagery, optical images exhibit certain constraints in estimating forest parameters. This is particularly true for low-resolution remote sensing data, which is characterized by poor spectral sensitivity and lower saturation points. Therefore, utilizing higher-resolution optical images provides significant advantages in offering richer spatial details, improving stand classification accuracy and enhancing feature recognition accuracy compared with low-resolution optical images. These benefits lead to an increase in the accuracy and reliability of forest parameter estimation.

The key to remote sensing estimation of stand parameters, as we all know, is the extraction of valuable information and parameters from vast amounts of remote sensing data, as well as the selection of models for operation (Liang 2009). When estimating stand parameters using optical remote sensing images, remote sensing factors are extracted and feature selection is performed, i.e. modeling factors are optimally picked, which is a necessary step before continued modeling. Gao et al. (2012), e.g., employed field investigation crown density data and performed correlation analysis with the mean value of DN (Digital Number) in each band in the SPOT-5 image, and devised a method of inverting crown density with different band combinations, achieving good results. Liu et al. (2017) employed the principal component analysis method to lower the dimension of the data, and then the linear regression method for modeling to develop a good-fitting estimation model of forest volume. Shi and Wang (2019) performed a correlation analysis between various modeling factors and crown density, eliminating those with weak correlation. They then used principal component analysis to select factors for the crown density estimation model, proving that the estimation accuracy (EA) of a multivariable model is higher than that of a single-variable model. However, current methods for estimating forest parameters still present research gaps. Existing approaches often fail to consider the complex nonlinear relationships between remote sensing data and forest parameters, nor do they adequately address the issues of high dimensionality and multicollinearity within the remote sensing variables. Therefore, exploring more advantageous feature selection and modeling methods can resolve these shortcomings and better capture the intricate relationships inherent in remote sensing data for the estimation of forest parameters.

To ensure the integrity of information and better address issues of data redundancy, this study has incorporated the Boruta feature selection algorithm. The Boruta algorithm is an all-relevant feature selection method capable of identifying and retaining all significant features related to the outcome variable, without relying on an arbitrary cutoff for importance. Unlike other feature selection algorithms, the Boruta algorithm introduces randomness and performs filtering by extracting from a random sample set, aiming to reduce the randomness in volatility and correlation. This ultimately selects all feature sets related to the dependent variable. The algorithm creates shadow features from the original data by randomizing the values within each feature. It then iteratively tests the importance of the original features against these shadow features through a random forest classifier. Features that prove to be more important than the best of the shadow features are deemed relevant. This process continues until all features are either confirmed as relevant or rejected, ensuring no potentially useful information is lost (Kursa and Rudnicki 2010). In this way, researchers can gain a more comprehensive understanding of the factors influencing the dependent variable, enabling them to select features more effectively and efficiently (Chen and Tang 2019). Meanwhile, model selection is equally essential for estimating stand parameters. The Cubist model was presented in this work, which is a composite model that employs nearest-neighbor samples to adjust the rule model’s prediction outcomes and is more accurate than the single rule-based model (John et al. 2018). Furthermore, currently, there are few studies that combine the Boruta feature selection algorithm with the Cubist model for the estimation of forest stand parameters. Therefore, the combination of these two methods is not only crucial for accurately estimating forest stand parameters but also has a significant impact on improving the efficiency of forest resource monitoring.

In this study, native tree species of Jiangle County in Fujian Province, namely Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) and Pinus massoniana Lamb., are chosen as research subjects. Based on the GF-2 satellite remote sensing data, field survey data and forest management inventory data, we estimate the crown density and volume per hectare of some forest stands within the Jiangle State-owned Forest Farm in Fujian Province, southeast China. Furthermore, this article introduces the Boruta feature selection algorithm combined with the Cubist regression model, resulting in an effective technical method for exploring forest stand parameter estimation. This innovative approach seeks to enhance the accuracy and reliability of forest stand parameter estimation, thereby facilitating its application in forest resource monitoring and surveying. Additionally, it aims to investigate the practical application potential of these methods in the field of forest resource management and conservation.

MATERIALS AND METHODS

Study area

The study site illustrated in Fig. 1 is located in the Jiangle State-owned Forest Farm at Jiangle County, northwest Sanming City, southeast China (117°05ʹ–117°40ʹ E, 26°26ʹ–27°04ʹ N), which has jurisdiction over eight towns and five townships. The research area has a subtropical monsoon climate, with an annual average temperature of 16–26°C and an annual average rainfall of 2027 mm. On the one hand, the area is rich in forest resources, with a forest coverage rate of 85.7%, so it is an important forest resource cultivation, forest management demonstration, timber strategic reserve, forestry scientific research and promotion base in Fujian Province. On the other hand, the region has a diversity of tree species, with the primary species including Chinese fir (C. lanceolata (Lamb.) Hook.), P. massoniana Lamb., Phyllostachys edulis (Carrière) J. Houz., Schima superba Gardner & Champ., Cinnamomum camphora (L.) Presl., Fokienia hodginsii (Dunn) A. Henry & H. H. Thomas, among others. Notably, Chinese fir and P. massoniana are not only the two predominant coniferous tree species in terms of planted area within the Jiangle State-owned Forest Farm in Fujian Province but also represent the most widely distributed and largest stock volume of forest ecological species within the farm. The plantations of these two species play a pivotal role in the forest resources of the Jiangle area. As fast-growing species, the plantations of Chinese fir and P. massoniana significantly contribute to increasing timber production and promoting forestry economic development. Moreover, they play an irreplaceable role in water conservation, soil erosion control and the formation and maintenance of the forest ecosystem.

Data and preprocessing

Remote sensing data

The remote sensing data of this study came from Geospatial Data Cloud, one scene of GF-2 L1A level image data on 28 October 2018, were obtained, covering 117.27°–117.57° E, 26.59°–126.85° N, with a width of 6.7 km × 6.7 km, and including one panchromatic band and four multispectral bands. The spatial resolution is 0.81 and 3.24 m, and the overall band range is 0.45–0.89 µm (Fu et al. 2019). In addition, vector maps of forest boundaries and the Digital Elevation Model (DEM) data of 30 m covering the study area were obtained.

The obtained GF-2 remote sensing images were preprocessed, including radiometric calibration, FLAASH atmospheric correction and orthography correction. Then, the processed multispectral and panchromatic images were fused and registered, and the image fusion adopted the GS (Gram–Schmidt) fusion method, which had the best fusion effect on multispectral and panchromatic data and was most suitable for GF-2 image fusion (Sun et al. 2016). Finally, the fusion image is trimmed to obtain the preprocessed remote sensing image.

Plot survey data

The plot survey data were derived from two sources: field measurements and the forest management inventory. The field measurements were investigated in July 2018 and July 2019. A total of 59 pure Chinese fir plots and 23 pure P. massoniana plots were established, with each plot size of 20 m × 30 m. Survey parameters such as tree species, diameter at breast height, tree height, crown width and crown density were recorded, along with the geographical coordinates of the four corners of each plot using a handheld GPS device. Additionally, some forest management inventory data for the study area were obtained as auxiliary data for the plot surveys (Wang et al. 2019b), including 161 pure Chinese fir stands and 217 pure P. massoniana stands, with the subcompartment areas of these pure stands being appropriately sized for data accuracy. In summary, a total of 220 pure Chinese fir stands and 240 pure P. massoniana stands were obtained, all of which were accessible for surveying and evenly distributed within the Jiangle State-owned Forest Farm, with the distribution of plots illustrated in Fig. 1.

According to the binary standing tree volume table of Fujian Province, the single tree volume in the sample plot was calculated. According to the following formulas:

In the formulas, V₁ and V₂ represent the individual volume of Chinese fir and P. massoniana plots; D₁ and D₂ represent the individual diameter at breast height of Chinese fir and P. massoniana plots; H₁ and H₂ represent the individual tree heights of Chinese fir and P. massoniana plots.

The single tree volume of various plots of Chinese fir and P. massoniana obtained was summarized, respectively, to obtain the total stock volume of various plots in the research area, which was the stock volume per hectare/(m³/hm²) in this study.

Extraction of remote sensing factors

Spectral information

The single-band spectral information of remote sensing was extracted from the preprocessed GF-2 remote sensing image, including four bands, namely band 1 (blue band), band 2 (green band), band 3 (red band) and band 4 (near infrared band). By using ArcGIS 10.3 software, the sample site and the center point of the small class were superimposed on the image map of each band to obtain the band information of each point in the sample site.

Texture features

The research shows that the texture features reflect the visual roughness of ground objects through the spatial variation and repeatability of grayscale, fully reflect the characteristics of remote sensing images, and can provide relevant information on forest structure and geometric properties, which is helpful for the study of forest crown density and stand volume (Cutler et al. 2012; Gou et al. 2019). There are many texture feature extraction methods, such as statistical analysis, structural analysis, model analysis and spectral analysis. The most widely used texture statistical analysis method is the Gray Level Co-occurrence Matrix (Haralick et al. 1973; Sun and Ma 2010; Weszka et al. 1976). There are eight commonly used texture features of the gray co-occurrence matrix, namely: Mean, Variance, Homogeneity, Contrast, Dissimilarity, Entropy, Second Moment and Correlation (Pu 2019). In this study, 8 texture features of 4 bands were extracted by ENVI 5.3.1 software, and 32 texture factors were finally obtained as subsequent modeling factors.

Vegetation index

A single-band information is difficult to accurately describe the vegetation information in the complex forest research area, while the vegetation index is composed of data from different bands, which can better reflect the characteristics of vegetation. In this study, Band Math in ENVI 5.3.1 software was used to calculate four bands of the preprocessed GF-2 images, and nine common vegetation indices were obtained according to relevant literature screening (Colombo et al. 2003; Hashemi et al. 2013; Qi et al. 1994; Schlerf et al. 2005; Yang et al. 2012; Zhang 2015).

Terrain factor

Topographic factors are one of the main factors affecting stand parameters, such as slope and aspect, which affect forest population distribution, and altitude, which affect the growth state of vegetation, thus affecting the calculation of forest crown density and stand volume (Liu et al. 2020; Ross et al. 1984). In this study, ArcGIS 10.3 software was used to extract three topographic factors, including aspect, slope and elevation, according to DEM data in the study area. After extracting the slope aspect and slope image of the study area, the data of the central position point of the sample plot were superimposed on the image to read the slope aspect and slope data of the pixel where the sampling area is located. Similarly, the elevation data of the pixel where the sample site is located can be obtained from the original DEM image.

Feature selection method

The selection of appropriate independent variables is the key to constructing an estimation model (Shi and Wang 2019), there are many feature factors derived from remote sensing data, and too many variables will lead to data redundancy. To efficiently select the optimal feature subset from a large number of features and establish the estimation model of crown density and stock volume, feature selection is required. Feature selection is to select some features from the original features according to certain criteria or methods. Therefore, the selected features retain the physical significance of the original features while reducing the data dimension and avoiding data loss as much as possible (Du et al. 2012; Han et al. 2020; Jin and Ke 2019).

Boruta algorithm is a kind of feature selection method based on a random forest algorithm. The algorithm can filter out all the independent and dependent variables related to the optimal feature subset, and the poor correlation with the dependent variable features from the original focus, this will help us more comprehensive understanding of the influence factors of the dependent variable, thus help us to more efficiently in feature selection (Han 2020; Kursa et al. 2010; Kursa and Rudnicki 2010). The main steps of the Boruta feature selection algorithm are as follows: (i) The extended dataset is obtained by randomly disordering each original feature and increasing the random components (also called shadow attributes) of all its attributes. (ii) The importance of evaluation features, including real features and shadow features, was obtained by running the random forest method training model on the extended dataset. (iii) By comparing the importance of real features and the maximum importance of shadow features, a hit was recorded for the feature greater than the maximum value of shadow features. (iv) According to the cumulative hit of real features, the feature is marked as ‘important’ or ‘unimportant’, i.e., the maximum value greater than the importance of the shadow feature is judged as ‘important’ and the feature is retained, the maximum value lower than the importance of the shadow feature is judged as ‘unimportant’ and will be excluded from the subsequent operation. (v) Repeat the above steps. When the attribute comparison of all features is completed, or the algorithm reaches the preset random forest running times, the algorithm stops running (Guo et al. 2018; Han et al. 2020; Kursa et al. 2010; Lu et al. 2019). The resulting feature set is divided into two categories: ‘important’ and ‘unimportant’, and the ‘important’ feature set is used for subsequent model construction.

Establishment of stand parameter estimation model

Since the modeling method adopted in this study is regression based on machine learning, the test set and training set need to be divided according to a unified standard (Yang 2019). This article adopts the traditional method of dividing training and testing datasets, i.e., 70% of samples are used for training and 30% of samples are used for testing. Divided by tree species, in pure Chinese fir forest plots, 154 sample plots were obtained to participate in model construction, and 66 samples were used for verification. For the pure plots of P. massoniana, 168 plot data were obtained to participate in model construction, and 72 samples were used for verification. Furthermore, to assess the model’s sensitivity to different feature variables, a sensitivity analysis was conducted prior to modeling in this study. Through sensitivity analysis, it was determined which variables, after feature selection, had the most significant impact on model predictive performance, thereby providing guidance for model optimization.

After obtaining the test set and training set, the estimation model of stand parameters was constructed. In this study, multiple stepwise regression and Cubist regression models were used for comparative study. Multiple regression analysis refers to a statistical analysis method in which one variable is regarded as the dependent variable and other variables as independent variables in correlation analysis, and the quantitative relations of linear or nonlinear mathematical models between multiple variables are established and analyzed by using sample data. Stepwise regression is an optimal regression method in multiple linear regression. Its principle is to select the factors that affect the dependent variables greatly from many independent variables, and then establish a regression prediction model (Geng 2017). As the multiple stepwise regression algorithm is mature and simple, it is widely used, and has been applied by scholars in the research area, and achieved good results (Pan and Sun 2018). Therefore, this algorithm is considered to be feasible.

The Cubist algorithm is a piece-wise linear regression model based on rules with overlapping rules, which is an extension of the M5 model tree because it is a composite model i.e. often used in continuous value prediction problems. Cubist regression is implemented by Cubist functions in R, which automatically identifies the role of independent variables and selects the independent variables for node branching and model. The program also gives the utilization of independent variables in branching conditions and linear models (Houborg and Mccabe 2018; Nguyen et al. 2019; Wang 2010; Yang 2018).

Accuracy evaluation method

In this study, five assessment indexes typically used in regression models are utilized to assess the correctness of the developed model (Huang 2019; Li et al. 2019; Pang and Li 2012): (i) Calculating the coefficient (R²), which can be used to assess the model’s fit. The greater the R² number, the greater the correlation between the estimated and measured values, and hence the better the model. (ii) The square root of the ratio of the sum of squares of the variance between the estimated value and the measured value and the estimated times is called the root mean square error (RMSE). The model’s influence is better the lower the RMSE value. (iii) The mean absolute error (MAE) is the average absolute difference between the estimated and measured values. The lower the MAE value, the better the model effect. (iv) Standard error (SE) is used to predict sample data accuracy. The better the model, the smaller the SE. (v) EA, and the higher the EA value, the greater the model’s estimation impact.

RESULTS

Results of Chinese fir sample plots feature selection

In this study, the Boruta software package in R language was used for feature selection of the extracted remote sensing factors, and the feature selection results of the Chinese fir sample plots were finally obtained, as shown in Fig. 2. In the process of operation, Boruta gave a clear definition of the meaning of the dataset, and the initial calculation result of the crown density of the Chinese fir sample plot was as follows: among 51 attribute factors, including 48 remote sensing factors and 3 shadow attributes, 41 were rejected, 8 were confirmed and 2 were designated as tentative. The importance of the temporary factor was so close to the best-shaded attribute that Boruta could not make an obvious judgment for the time being, and made another comparison judgment for the temporary factor until all attributes were compared. Finally, the results of feature selection for crown density of the Chinese fir plot were obtained. Among 51 feature factors, 8 features were identified as ‘important’. The eight feature factors are further screened, and seven factors with higher importance values are selected, which are band 3, band 4, b1_Mean, b2_Mean, b4_Mean, ARVI and DEM, whose importance is shown in Table 1.

Similarly, 10 factors were identified as ‘important’ in Boruta feature selection for the volume of Chinese fir plots, among which the importance values of some factors were significantly lower than those of rejected factors, such as b4_Con, b2_Con and b2_SM. The average importance of some factors, such as b3_Var, b3_Ent and DEM, is higher than that of the rejected factor (b2_SM). Further screening of feature factors is carried out, and seven feature factors with higher importance values are finally selected, which are as follows: b1_Var, b1_Ent, b3_Var, b3_Ent, b4_Hom, b4_Ent and DEM, their importance is shown in Table 1.

Results of feature selection of P. massoniana plots

Similarly, Boruta feature selection results of P. massoniana sample plots were obtained as shown in Fig. 3. For their crown density, a total of 11 factors were identified as ‘important’. For the GNDVI factor, although it was larger than the average value of rejected factor DVI, it was smaller than the median value, and the importance values of b2_Cor and band 4 are lower than DVI. Then the feature factors were further screened, and eight feature factors with higher importance values were selected, which were b2_Cor, b4_Cor, NDVI, RVI, MSAVI, TVI, EVI and GNDVI. For their volume, seven factors were selected for their high importance, namely, b1_Mean, b2_Mean, b3_Mean, b4_Mean, ARVI, Slope and DEM. Finally, the selected characteristic factors of P. massoniana plots were summarized, and their importance is shown in Table 2.

Regression model construction

This study employs multiple stepwise regression and the Cubist method to construct models, using feature factors selected after feature selection and sensitivity analysis as independent variables, with crown density and volume as dependent variables, randomly drawing 70% of the data. Since the Cubist algorithm is combined with a series of piece-wise linear models after its judgment conditions are given in R language, the subsequent accuracy evaluation results can be directly achieved, so the modeling regression model is not described here. Finally, the multiple stepwise regression modeling equations of Chinese fir and P. massoniana plots were obtained (Table 3). As can be seen from Table 3, for Chinese fir sample plots, factors selected by the crown density model include elevation factor (DEM) and texture mean of the first band (b1_Mean), and factors selected by the volume model include elevation factor (DEM) and variance of the first band (b1_Var). The results showed that the altitude factor had a great influence on the estimation of stand parameters of the Chinese fir sample plot, and the effect was better combined with the blue band texture information. For P. massoniana plots, the crown density model for factor includes the normalized difference vegetation index (NDVI) and the correlation of the fourth band (b4_Cor), and the volume model for factor contains the altitude factor (DEM) and the first band texture average (b1_Mean). The results showed that the texture characteristics had a great influence on the estimation of stand parameters in P. massoniana plots, and the effect was more significant when combined with vegetation index or altitude factors.

Accuracy evaluation results

The remaining 30% of data were substituted into the modeling equation, namely 66 Chinese fir plots and 72 P. massoniana plots, to obtain the estimated crown density and volume. Then, combined with the actual measured data, scatter plots of measured and estimated values of multiple stepwise regression and Cubist model are drawn, respectively, as shown in Figs 4 and 5.

As can be seen from Fig. 4, when the multiple stepwise regression model is used to estimate stand parameters, the fitting effect of the measured value and the predicted value is poor, and the determination coefficient R² is below 0.65. It can be seen from Fig. 5 that when estimating stand parameters using the Cubist regression model, there is a good linear fitting relationship between measured and predicted values. Among them, the crown density fitting effect of the Chinese fir sample plot is better, determining coefficient R² is 0.7820; The fitting effect of the P. massoniana plot is relatively poor, and the determining coefficient R² is 0.6377.

The accuracy of the model was further evaluated by five indexes, including R², RMSE, MAE, SE and EA, of the measured and estimated values of the model. The specific evaluation indexes are shown in Table 4. As shown in Table 4, the estimated results obtained by using the Cubist regression model are better than those obtained by multiple stepwise regression. In addition, the estimation effect of crown density was better than that of the amount in the estimation of stand parameters of Chinese fir and P. massoniana plots.

DISCUSSION

Overall result analysis

The estimation results for forest stand parameters indicate that the models derived using both the Boruta and Cubist methods exhibit good accuracy. In the extraction of remote sensing factors, feature variables that are significantly correlated with crown density and volume are generally chosen for modeling inversion. However, in reality, the more feature variables incorporated into modeling, the higher the complexity of the model, the longer the runtime, and even the occurrence of overfitting phenomena. Screening feature variables can greatly reduce model development time, enhance model EA and improve model interpretability and applicability. In this study, 48 factors were retrieved from optical remote sensing data and screened for feature variables using the Boruta approach. The highly linked parameters with crown density and volume were identified. This aligns with the conclusions drawn by Montesinos-López et al. (2023), who posited that Boruta exhibits significant improvements in accuracy when environmental covariates are relevant to the outcome and are optimally included, suggesting its potential advantage in scenarios requiring the identification of all-relevant features. Thus, compared with other feature selection methods, the Boruta algorithm not only ensures a comprehensive evaluation of feature importance, aiding in the capture of important features that might be overlooked by other methods, but also helps in reducing model complexity and the risk of overfitting, thereby enhancing the model’s generalization ability (Gasmi et al. 2023).

Overall, regardless of the plot type, the distribution of the fitting plot for crown density is consistently better than that for volume. This can be attributed to, on the one hand, the measurements of crown density being more accurate than those of volume in plot surveys, coupled with a smaller range of variation for crown density, leading to smaller errors between observed and predicted values, and consequently, a more uniform distribution in the fitting plot for crown density as compared with volume. On the other hand, it may also be related to the feature selection process. Crown density, being a variable i.e. easier to measure precisely, may have its related features exhibit less variability in the dataset. The Boruta feature selection method is capable of optimizing for such features with low variability, allowing for better capture of the patterns of change in crown density when utilizing the Cubist model, thereby enhancing the quality of the fit.

Additionally, in the processing and analysis of GF-2 remote sensing data, we employed a 7 × 7 computation window, utilizing the pixels within this window for calculations and analyses to extract the image’s texture features. When dealing with remote sensing images that feature complex terrain and vegetation distribution, selecting an appropriate computation window size is crucial for the effective extraction of texture information. Furthermore, different window sizes result in varying proportions of canopy and shadow within the window, leading to differences in the extracted texture information. As demonstrated in the research by Hu et al. (2018), larger computation windows yield higher modeling accuracy. However, overly large windows may overlook local details, resulting in greater errors in information extraction. Therefore, a 7 × 7 window size is often a compromise solution, capable of capturing sufficient texture information without neglecting local details due to excessive window size. This holds practical significance for the effective extraction of texture information in this region.

Modeling results of different forest types

There are substantial variances in stand variables for different plot data and forest types, and the internal components of the stand are typically complicated and diverse, so employing the same estimation model may affect the accuracy (Zhang 2020). On the one hand, the Cubist model was utilized in this work to get different combinations of influencing elements in the estimate equation for the estimation of crown density in Chinese fir and P. massoniana plots. The Chinese fir plots included both altitude factors and vegetation indices, whereas the P. massoniana plots included a variety of vegetation indices. This indicates that the estimation model for Chinese fir plots is capable of integrating a wider range of environmental variables, such as the physiological properties of the soil or variations in terrain elevation, which play significant roles in the growth and development of Chinese fir stands. On the other hand, in terms of estimating volume, the Chinese fir sample plots’ determination coefficient R² and EA were higher than those of the P. massoniana plots, while the RMSE, MAE and SE were lower, indicating that the volume of the Chinese fir sample plots was more stable than that of the P. massoniana plots. In summary, the inclusion of elevation as an influencing factor in the Chinese fir plot estimation model suggests that terrain and ecological conditions have a more significant impact on the growth of Chinese fir compared with P. massoniana. Therefore, in areas with complex terrain and diverse ecological environments, estimation models that can integrate these factors will be more applicable. In other words, this method is more suitable for broader application within Chinese fir plot regions in the area. Furthermore, texture features account for a very big proportion in the two sample plots in the feature selection findings, although different tree species and age groups of forest land demonstrate significant variances in texture features, which influences later modeling. As a result, developing relevant models and estimating methods for various forest types and tree species merits additional investigation.

Limitations and future works

From the estimation results, it is observed that despite the overall relative superiority in the accuracy of models derived using both the Boruta and Cubist methods, instances of ‘low-value overestimation’ and ‘high-value underestimation’ still occur, a common phenomenon in the remote sensing estimation of stand parameters. Furthermore, the accuracy of volume estimations obtained in this study is not as high compared with crown density accuracy. To address these phenomena and issues, considerations must be made from various aspects for improvement. First, there is a need to research and develop more precise model algorithms, as these algorithms can better handle nonlinear relationships and extreme value problems within the data. New algorithms in machine learning and deep learning could offer improved generalization capabilities, reducing estimation errors. Moreover, utilizing ensemble learning methods such as random forests, gradient boosting machines or stacked models can enhance overall prediction accuracy by combining predictions from multiple models and reducing the bias of single models.

Second, future research could utilize higher-resolution optical images or microwave radar and LiDAR data to obtain information about the internal structure of forests (Liu et al. 2022). Combining multiple sources of remote sensing data, integrating the advantages of both active and passive remote sensing technologies, and jointly inverting stand parameters using optical imagery, Synthetic Aperture Radar (SAR) imagery and other remote sensing data can provide more comprehensive surface information. This helps to improve the accuracy and robustness of estimations and more precisely estimate stand parameters.

Additionally, the computation window is an important process in the extraction of texture features from optical remote sensing data, directly affecting the effectiveness of texture analysis and the accuracy of its application. Different window sizes and positions may lead to variations in the extracted texture information, as the ground reality covered by the window changes. In practical applications, selecting an appropriate window size should be based on specific analysis goals and image characteristics. Therefore, subsequent research should focus on the extraction of texture features using different windows, exploring the impact of various windows on stand parameter estimation to enhance modeling accuracy.

CONCLUSIONS

Drawing upon GF-2 remote sensing data, field survey data and forest management inventory data, this study leveraged the Boruta feature selection method and the Cubist regression model to estimate crown density and volume per hectare for selected stands within the Jiangle State-owned Forest Farm in Fujian Province. The analysis revealed that the Cubist regression model significantly outshines conventional multiple stepwise regression models in terms of accurately determining stand parameters through the congruence of measured and predicted values. Specifically, in the Chinese fir sample plots, the Cubist model yielded determination coefficients (R²) exceeding 0.67 and EA surpassing 60%. Similarly, for the P. massoniana sample plots, the model achieved determination coefficients (R²) over 0.63 and EA above 56%. However, the values obtained from the multiple stepwise regression model are all lower than those derived from the Cubist regression model, indicating that the stand parameter estimation based on the Cubist regression model yielded superior results compared with the multiple stepwise regression model. This further demonstrates the advantages and applicability of the Cubist regression model.

In summary, after employing the Boruta algorithm to select features encompassing single-band information, texture features, vegetation indices and terrain factors, the estimation model established using the Cubist method identified a combination of vegetation indices, texture features and terrain factors as the feature factors related to stand parameters. Not only were these feature factors readily collectible, but the model also delivered commendable outcomes. Consequently, this research introduces an innovative methodology for accurately assessing crown density and volume, promising valuable insights for future endeavors in the promotion and widespread adoption of such models.

Funding

This research was supported by the project of the National Technology Extension Fund of Forestry, ‘Forest Vegetation Carbon Storage Monitoring Technology Based on Watershed Algorithm’ ([2019]06) and the National Natural Science Foundation of China, ‘Study on Crown Models for Larix olgensis Based on Tree Growth’ (31870620).

Acknowledgements

We appreciate the data provided by the Jiangle State-owned Forest Farm in Fujian Province. We would also like to thank the editors and anonymous reviewers.

Conflict of interest statement. The authors declare that they have no conflict of interest.

REFERENCES