Meteorological-Data-Driven Rubber Tree Powdery Mildew Model and Its Application on Spatiotemporal Patterns: A Case Study of Hainan Island

Abstract

Given that rubber is an important strategic material and the prevalence of rubber tree powdery mildew (RTPM) is a serious issue, the study of RTPM is becoming increasingly significant in aiding our understanding and managing rubber plantations. By enhancing our understanding, we may improve both the yield and quality of the rubber produced. Using meteorological station and reanalysis data, we employed factor expansion and three different feature-selection methods to screen for significant meteorological factors, ultimately constructing a data-driven RTPM disease index (RTPM-DI) model. This model was then used to analyze the spatiotemporal distribution of RTPM-DI in Hainan Island from 1980 to 2018, to reproduce and explore its patterns. The results show that (1) the RTPM-DI is dominantly negatively influenced by the average wind speed and positively affected by days with moderate rain; (2) the average wind speed and the days with moderate rain could explain 71% of the interannual variations in RTPM-DI, and a model established on the basis of these can simulate the changing RTPM-DI pattern very well (RMSE = 8.2511, MAE = 6.7765, MAPE = 0.2486, KGE = 0.9921, MSE = 68.081, RMSLE = 0.0953); (3) the model simulation revealed that during the period from 1980 to 2018, oscillating cold spots accounted for 72% of the whole area of Hainan Island, indicating a declining trend in RTPM-DI in the middle, western, southwestern, and northwestern regions. Conversely, new hot-spots and oscillating hot-spots accounted for 1% and 6% of the entire island, respectively, demonstrating an upward trend in the southeastern and northern regions. Additionally, no discernible pattern was observed for 21% of the island, encompassing the southern, eastern, and northeastern regions. It is evident that the whole island displayed significant spatial differences in the RTPM-DI pattern. The RTPM-DI model constructed in this study enhances our understanding of how climate change impacts RTPM, and it provides a useful tool for investigating the formation mechanism and control strategies of RTPM in greater depth.

1. Introduction

Powdery mildew is a prevalent disease in rubber trees and can cause extensive harm. The powdery mildew fungus grows and reproduces inside plant cells, leading to cellular fragility, apoptosis, and loss of function in the infected area, resulting in a white powdery substance covering the rubber leaves, which ultimately leads to significant leaf fall and crown failure, consequently reducing the yield of rubber trees [1,2]. Powdery mildew is a fungal infection transmitted through air and direct contact [3], and generally occurs under conditions of high humidity and moderate temperature [2]. However, the effective prevention and control of this disease remain challenging, and currently, available interventions have not been entirely satisfactory [4]. Therefore, investigating the mechanisms underlying its occurrence and transmission is imperative to develop an effective and science-based strategy for prevention and control. Rubber tree powdery mildew (RTPM) remains a significant focus of global research. A comprehensive understanding and deep research on RTPM can contribute to more effective protection of rubber resources and enhance farmers’ economic benefits [5].

Many studies have been conducted both domestically and internationally in the field of RTPM, with a primary focus on elucidating the influencing factors of RTPM and constructing RTPM models [1,6,7]. The findings from studies on influencing factors have unveiled a strong association between RTPM incidence and environmental factors such as temperature, humidity, and light intensity [7,8]. Moreover, meteorological factors exhibit intricate interactions with one another in RTPM occurrence [9,10]. However, in selecting influencing variables, scholars often fail to fully consider multiple factors and instead tend to focus only on a few for analysis [3,5]. Moreover, they seldom thoroughly screen relevant factors [3,11], resulting in insufficient research on various pathogenic meteorological factors.

In this study, we not only comprehensively considered a variety of meteorological factors related to RTPM, but also provided more detailed categorization of these factors. For instance, days with an average temperature above 25 °C, days with a minimum temperature below 10 °C, days with light rain, days with moderate rain, etc., were further identified to select factors with stronger correlations for model development.

In terms of model building, both traditional mathematical statistical methods and machine learning methods are widely used [7,12]. Initially, multiple regression analysis, logistic regression models, and partial least-squares regression models were used for modeling [3,5,6]. Later, machine learning methods such as artificial neural networks, maximum entropy models, random forests, backpropagation neural networks, and support vector machines were adopted [7,12,13]. The development and integration of machine learning methods have significantly advanced the field of RTPM modeling, allowing for more sophisticated analysis and prediction capabilities [12,13]. Machine learning, being data-driven, can automatically learn features and patterns [14]. It can handle complex nonlinear relationships [15] and objectively reveal the connections between data [16], providing a more accurate understanding of the occurrence and development of RTPM. While traditional research has also achieved relatively accurate results, it has both advantages and disadvantages. For example, although maximum entropy models can be applied to predict RTPM, they may be limited when facing complex nonlinear relationships [17] and require many features and indicators to support model construction [18]. The machine learning approach proposed in this study requires only a minimum number of indicators, yet it can effectively predict RTPM, providing accurate decision support for farmers and experts.

Unfortunately, no scholars have studied RTPM spatially, let alone conducted large-scale spatiotemporal analysis, which limits our ability to gain an in-depth understanding and effectively control RTPM. Through large-scale spatiotemporal analysis, relevant data can be collected and integrated, enabling a comprehensive understanding of the evolving trends of RTPM over time and space [19,20]. Subsequently, this facilitates the evaluation of RTPM’s impact and the resulting losses on rubber plantations. These findings have excellent application potential and have been utilized in various studies [20,21]. Moreover, performing large-scale spatiotemporal analyses can offer a scientific foundation for developing prevention and control tactics, thus significantly mitigating the negative impact of RTPM. Hence, in future investigations, it is crucial to delve into more sophisticated analysis techniques, integrate remote sensing technology and geographic information systems, and conduct more inclusive sample data collection and processing to comprehensively enhance the research outcomes in respect of RTPM.

To address these challenges, we established the RTPM disease index (RTPM-DI) model utilizing meteorological factors, replicated RTPM data from Hainan Island over multiple years, and performed a thorough spatial-temporal analysis to offer valuable insights and guidance for RTPM prediction and mitigation efforts. We employed novel approaches by utilizing factor expansion and feature selection methods to screen meteorological factors, integrating six meteorological factors to construct an optimizable ensemble model, and employing emerging hotspot analysis technology combined with remote sensing (RS) and geographic information system (GIS) technologies for spatial analysis, resulting in innovative progress. Although the RTPM-DI model constructed in this study cannot be directly applied to simulate other plant diseases, these innovative methods and techniques will provide research directions and modeling approaches that are more relevant to the monitoring and simulation of other plant diseases. This will help with assessing the occurrence and spread of various plant diseases more accurately and provide more comprehensive support for the sustainable development of vegetation.

The Association of Natural Rubber Producing Countries (ANRPC) reports that China is ranked fifth in the world in terms of rubber production, with an estimated total output of 850,000 tons. Significantly, Hainan Island boasts rubber production that commands approximately 41% (340,000 tons) of China’s total output, highlighting its noteworthy contribution to the country’s rubber industry [22]. However, rubber plantations are often vulnerable to disease and pest infestations, with powdery mildew being considered one of the most serious threats to the health of rubber trees, possibly affecting growth and yield [23]. Research has shown that powdery mildew was first reported on rubber trees in Hainan Island during the late 1950s, and subsequently spread to other areas of China where rubber trees are commonly grown [24].

Therefore, exploring the temporal and spatial distributions of RTPM in Hainan Island is crucial for improving the rubber industry’s development environment and enhancing related prevention and control management. The aim of this study is to provide practical recommendations for the future monitoring and management of RTPM in the region by developing innovative methods through which to assess RTPM and investigating its spatiotemporal variability.

In short, we aim to reproduce the historical RTPM in Hainan Island and examine its spatiotemporal variability using a meteorological-data-driven model. The results of this research will offer practical recommendations and future research prospects in related fields.

2. Materials and Methods

2.1. Study Area

Hainan Island, situated in southern China (18°10′04″ N~20°0′40″ N, 108°30′43″ E~111°2′33″ E), belongs to the subtropical zone characterized by prolonged periods of warmth and humidity. The island is abundant in precipitation, with an annual range of 1000~2500 mm, and experiences a relatively high average wind speed. Additionally, the average temperature ranges from 23 °C to 29 °C annually. The area of rubber plantations on Hainan Island is 7269.66 km², accounting for nearly a quarter of the island’s forest area. Rubber plantations in Hainan are primarily situated in the western, northern, and east-central regions [25,26]. In recent years, there has been a trend of increasing plantations in the north with decreasing plantations in the south [27]. The central, southern, and southeastern areas face higher meteorological disaster risks, as they are vulnerable to typhoons and cold damage, which may provide suitable environments for pest and disease infection [28].

2.2. Materials

2.2.1. RTPM-DI

The RTPM-DI is a multidimensional index designed to evaluate the severity, transmission trend, and future development of an RTPM epidemic. It comprises two factors: the degree of disease and the number of diseased plants. The formula for calculating this index is as follows:

$$\mathrm{D}\mathrm{I}=\left[\frac{{\sum }_{i=0}^5\left(n_i\times i\right)}{\mathrm{N}\times i_{max}}\right]\times 100$$

(1)

where DI is the disease index of RTPM, N is the total number of plants, n is the number of diseased plants at each level, i is the level of disease, and i_max is the highest level [29].

The number of diseased plants at each disease level, disease severity, the total number of plants investigated, and the highest disease level were obtained through historic field investigations. Specifically, data from 1962 to 2003 were derived from the Hainan agricultural reclamation rubber tree records for diseases and pest control [30], while data from 2004 to 2009 were sourced from field surveys conducted by the Hainan Land Reclamation Bureau [31]. The data presented in this study (Table S1) are based on rigorous investigations and provide strong scientific evidence. In this study, we utilized the DI as the index for evaluating the condition of RTPM and analyzed its spatiotemporal distribution pattern in Hainan Island.

2.2.2. Meteorological Data

We utilized data obtained from the National Climate Center, which comprised daily records of average, maximum, and minimum temperature, precipitation, average wind speed, relative humidity, and sunshine hours at seven stations located in Hainan Island, spanning the period 1961 to 2009. We employed factor expansion and feature selection techniques to identify meteorological factors that had a significant impact on RTPM.

Additionally, we acquired precipitation and average wind speed data from the Chinese Meteorological Forcing Dataset (CMFD) of the Tibetan Plateau Data Center (TPDC), spanning the period 1979 to 2018, with both high spatial resolution (0.1 degrees) and temporal resolution (3 h), albeit with inevitable inherent errors.

In our study, we converted the raw data from a three-hour time resolution to a daily resolution. The process involved two steps. Firstly, we summed multiple three-hour precipitation data from the same day to obtain the total daily precipitation. Secondly, we averaged all three-hour wind speeds from the same day to obtain the daily average wind speed. These daily data were utilized in the spatiotemporal simulation of the RTPM-DI.

2.3. Methods

2.3.1. Factor Expansion

Factor Expansion is a useful technique to uncover the influence of preceding meteorological conditions on disease incidence. Its application can enhance the precision and reliability of simulations [32]. There are typically three approaches employed for factor expansion, including the square method, the anomaly square method, and the linear combination method. Among these, the linear combination method has been found to be particularly effective for meteorological factors [33]. This method involves the summation of factors with similar characteristics from adjacent meteorological time periods to derive new factors. Let x₁, x₂, …, x_m represent factors of the same nature, and assume that m time periods are arranged in sequential order as fundamental meteorological periods. The process of factor expansion can be described as follows, expanding the m time periods into m (m + 1)/2 [34]:

$$x_1,x_2,...,x_m$$

(2)

$$x_1+x_2,x_2+x_3,...,x_{m-1}+x_m$$

(3)

$$x_1+x_2+x_3,x_2+x_3+x_4,...,x_{m-2}+x_{m-1}+x_m$$

(4)

In this study, the factor expansion methodology was utilized to extract the characteristics of 16 meteorological variables, designated as m1~m16 in consecutive order. These variables comprise the following indicators: average temperature (m1), days with an average temperature above 15 °C (m2), days with an average temperature above 20 °C (m3), days with an average temperature above 25 °C (m4), average maximum temperature (m5), days with a maximum temperature above 30 °C (m6), average minimum temperature (m7), days with a minimum temperature below 10 °C (m8), total precipitation (m9), days with light rain (m10), days with moderate rain (m11), days with heavy rain (m12), days with a rainstorm (m13), hours of sunshine (m14), relative humidity (m15), and average wind speed (m16). Since the incidence, progression, and prevalence of RTPM are intimately linked to meteorological variables during the winter and spring seasons, the period spanning from October of the previous year until April of the current year was deemed appropriate for expanding the scope of factors [6]. The 16 meteorological factors were combined into 448 groups using continuous time periods of one month, two months, up to seven months, and the mean values of each time period were subsequently computed.

The factors are denoted by a combination of the meteorological factor number, the start month, and the end month, following the format m16s11d4. In this notation, m16 denotes the average wind speed, while s11d4 represents the period from November of the previous year to April of the current calendar year.

The correlation coefficients between meteorological factors and RTPM-DI were calculated separately for each period. A two-tailed t-test was subsequently conducted to assess the significance of the results. Key factors that significantly impacted RTPM-DI in Hainan Island were then identified and screened out at a significance level of 0.01.

2.3.2. Feature Selection Methods

Feature selection, which is also referred to as factor screening, can decrease the dimensionality of factors and significantly enhance the performance of machine learning algorithms. Moreover, through the adoption of this technique, the model’s accuracy is not diminished but rather maintained at a high level [35].

In this study, a total of 51 factors were screened out using the factor expansion technique, and min-max normalization was applied to this set. Furthermore, three distinct feature selection algorithms, namely relevance relaxation factorization (RReliefF), minimum redundancy maximum relevance (MRMR), and F-test, were employed to select the top 5 to 15 factors from the 51 factors. By marking separate selections, along with 10-fold cross-validation and 100 iterations, each method will obtain an optimal model. The three optimal models obtained were trained, respectively, using the top 6, 10, and 7 factors selected using the three feature selection methods. The coefficient of determination (R²) values for these models were 0.45, 0.51, and 0.46, with root-mean-squared error (RMSE) values of 11.278, 10.653, and 11.194, respectively. However, due to the presence of shared factors, the final total number of factors was 14.

By individually considering these 14 factors according to the ranking provided by the three feature-selection methods, selecting the top 5–13 factors, and utilizing 48-fold cross-validation and parameter adjustment to improve the model’s simulation capability, we ultimately obtained the optimal model when employing RReliefF to select the top 6 factors. Moreover, these 6 factors also received high scores in the other two feature selection methods, indicating that they are the key climate factors. The calculation formulas for the three feature selection methods are presented below.

The calculation formulas of RReliefF are as follows [36]:

$${\mathrm{P}}_{diff\mathrm{A}}=\mathrm{P}\left(different value of \mathrm{A} | nearest instances\right)$$

(5)

$${\mathrm{P}}_{diff\mathrm{C}}=\mathrm{P}\left(different prediction | nearest instances\right)$$

(6)

$${\mathrm{P}}_{diff\mathrm{C}|diff\mathrm{A}}=\mathrm{P}\left(diff.prediction | diff.value of \mathrm{A} and nearest instances\right)$$

(7)

$$\mathrm{W}\left[\mathrm{A}\right]=\frac{{\mathrm{P}}_{diff\mathrm{C}|diff\mathrm{A}}{\mathrm{P}}_{diff\mathrm{A}}}{{\mathrm{P}}_{diff\mathrm{C}}}-\frac{\left(1-{\mathrm{P}}_{diff\mathrm{C}|diff\mathrm{A}}\right){\mathrm{P}}_{diff\mathrm{A}}}{1-{\mathrm{P}}_{diff\mathrm{C}}}$$

(8)

where A represents the set of attributes, W[A] represents the importance of attribute A to the prediction result, and P represents the probability.

The calculation formulas for MRMR are as follows [37,38]:

$$\mathrm{J}{\left(f\right)}^1=\mathrm{I}\left(f;c\right)-\frac{1}{\left|\mathrm{S}\right|}\sum _{s\in \mathrm{S}}\mathrm{I}\left(f;s\right)$$

(9)

$$\mathrm{J}{\left(f\right)}^2=\frac{\mathrm{I}\left(f;c\right)}{\frac{1}{\left|\mathrm{S}\right|}{\sum }_{s\in \mathrm{S}}\mathrm{I}\left(f;s\right)}$$

(10)

where S represents the selected feature subset, |S| represents the number of features, the mutual information I (f; c) of feature f and category c represent the correlation, and the mutual information I (f; s) stands for redundancy.

The calculation formulas for F-test are as follows [39]:

$$\mathrm{F}=\frac{{\mathrm{S}}_B^2}{{\mathrm{S}}_W^2}$$

(11)

$${\mathrm{S}}_B^2=\sum _{i=1}^k\frac{{n_i\left({\overline{\mathrm{X}}}_i-\overline{\mathrm{X}}\right)}^2}{\left(k-1\right)}$$

(12)

$${\mathrm{S}}_W^2=\sum _{i=1}^k\sum _{j=1}^{ni}\frac{{\left({\mathrm{X}}_{ij}-{\overline{\mathrm{X}}}_i\right)}^2}{\left(\mathrm{N}-k\right)}$$

(13)

where k represents the number of groups, n_i represents the number of samples in the ith group, ${\overline{\mathrm{X}}}_i$ represents the mean of the ith group, $\overline{\mathrm{X}}$ represents the mean of all samples, X_ij represents the value of the jth sample in the ith group, and N represents the total number of samples.

2.3.3. Optimizable Ensemble Model

The optimizable ensemble model is a machine learning approach developed to enhance predictive capabilities through the combination of multiple models. The term “optimizable” pertains to the fine-tuning process of the hyperparameters in the algorithms using the Bayesian optimization technique to augment their classification performance [40].

Using the regression learner in MATLAB R2022b, we developed an RTPM-DI ensemble model through 48-fold cross-validation, incorporating the 6 prominent meteorological factors that heavily influence the RTPM-DI on Hainan Island.

To assess the model’s efficacy, we computed several metrics including the coefficient of determination (R²), root-mean-squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), Kling–Gupta efficiency (KGE), mean squared error (MSE), and root-mean-squared log error (RMSLE). These metrics were evaluated using the respective formulae mentioned below:

$${\mathrm{R}}^2=1-\frac{{\sum }_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}{{\sum }_{i=1}^n{\left(y_i-\overline{y}\right)}^2}$$

(14)

$$\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{{\sum }_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}{n}}$$

(15)

$$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{n}\sum _{i=1}^n\left|y_i-{\widehat{y}}_i\right|$$

(16)

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}=\frac{100\%}{n}\sum _{i=1}^n\left|\frac{y_i-{\widehat{y}}_i}{y_i}\right|$$

(17)

$$\mathrm{K}\mathrm{G}\mathrm{E}=1-\sqrt{{\left(r-1\right)}^2+{\left(a-1\right)}^2+{\left(b-1\right)}^2}$$

(18)

$$\mathrm{M}\mathrm{S}\mathrm{E}=\frac{1}{n}\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2$$

(19)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{L}\mathrm{E}=\sqrt{\frac{1}{n}\sum _{i=1}^n{\left(\log \left(1+y_i\right)-\log \left(1+{\widehat{y}}_i\right)\right)}^2}$$

(20)

where y_i is the actual observed value, $\widehat{y_i}$ is the model predicted value, $\overline{y}$ is the mean observed value, n is the sample size, r is the correlation coefficient, a is the ratio of standard deviations, and b is the ratio of means [41,42,43,44,45,46].

2.3.4. Emerging Hotspot Analysis

Emerging hotspot analysis is a spatial analysis technique that utilizes geographic information technology and data mining methods to identify the spatial and temporal distribution patterns of various events or phenomena categories within a specific geographic area during a given timeframe. The method also identifies hotspot areas and cold spot areas within the region. Compared with traditional hotspot analysis methods, this technique can effectively detect the spatiotemporal dynamic evolution characteristics of geographic phenomena [47]. We conducted a spatiotemporal analysis of RTPM-DI in Hainan Island from 1980 to 2018 and evaluated hot- and cold-spot trends using the Getis–Ord method and Mann–Kendall trend test, respectively [48,49].

By conducting Mann–Kendall trend analysis, we obtained the Z value and P value. A Z value greater than 1.65 indicates an upward trend in the time series, implying increasing severity of the RTPM-DI over the years. Conversely, a Z value less than −1.65 suggests a downward trend and decreasing severity of the RTPM-DI over the years. A Z value close to zero implies no significant changes in the severity of the RTPM-DI with respect to the time series. The significance level is determined based on the range of P values. Based on the obtained Z- and P-values, we divided the significance of the hot- and cold-spot trends of RTPM-DI intensity into 16 different patterns [50].

2.4. Study Process

Using daily meteorological data from seven meteorological stations in Hainan Island spanning from 1961 to 2009, we utilized factor expansion and three feature-selection techniques to identify the key meteorological factors, and used them in conjunction with the RTPM-DI for model training. By inputting reanalysis meteorological data into the model, we were able to conduct long-term time series simulations and emerging hotspot analysis of RTPM’s temporal and spatial distribution and evolution in Hainan Island during the period 1980 to 2018. The technical route is illustrated in Figure 1.

3. Results

3.1. Meteorological Factors Affecting RTPM-DI

Using factor expansion, we selected 51 meteorological factors that significantly impact RTPM-DI at a significance level of 0.01, as shown in

Table 1. Meteorological factors with high correlation with RTPM-DI screened using factor expansion.

Factors	R	Factors	R	Factors	R
m1d1	0.384	m11s10d4	−0.414	m16d2d3	−0.511
m1s12d1	0.433	m15s10	−0.464	m16d3d4	−0.496
m1s11d1	0.402	m15s11	−0.403	m16s10s12	−0.594
m1s10d1	0.417	m15s10s11	−0.521	m16s11d1	−0.625
m3d1	0.462	m15s11s12	−0.437	m16s12d2	−0.614
m3s12d1	0.466	m15s10s12	−0.529	m16d1d3	−0.575
m3s11d1	0.407	m15s10d1	−0.394	m16d2d4	−0.508
m3s12d2	0.375	m16s10	−0.378	m16s10d1	−0.639
m3s10d1	0.408	m16s11	−0.426	m16s11d2	−0.631
m5s12d1	0.386	m16s12	−0.596	m16s12d3	−0.607
m5s11d1	0.402	m16d1	−0.583	m16d1d4	−0.558
m5s10d1	0.425	m16d2	−0.453	m16s10d2	−0.638
m7d1	0.424	m16d3	−0.499	m16s11d3	−0.634
m7s12d1	0.401	m16s10s11	−0.510	m16s12d4	−0.594
m11s10s11	−0.401	m16s11s12	−0.566	m16s10d3	−0.645
m11s10s12	−0.415	m16s12d1	−0.636	m16s11d4	−0.626
m11s10d1	−0.390	m16d1d2	−0.576	m16s10d4	−0.642

. Subsequently, three feature-selection methods were employed to further screen these factors, leading to the identification of six meteorological factors with a greater impact. These factors consist of two types of meteorological elements: the average wind speed (0.1 m/s) and the days with moderate rain (d). The significance of each factor in the three feature-selection methodologies is presented in

Table 2. The importance of meteorological factors in three feature-selection methods.

Factors	RReliefF	MRMR	F-Test
m16d3	0.0212	0.1384	10.7856
m16s11d4	0.0111	0.2111	9.1235
m16s11d2	0.0097	0.0445	4.6479
m11s10d1	0.0097	0.0000	3.1585
m11s10s11	0.0075	0.1483	2.9856
m16s11d1	0.0057	0.0631	8.1169

.

To explore the influence of individual factors on DI, we carried out further analysis and depicted the outcomes using the partial dependence plots (PDPs) in Figure 2. The plots demonstrate strong nonlinear relationships between all factors and the predicted DI. The highest DI values are observed when the values of m16d3 and m16s11d4 are below 40, showing a clear downward trend beyond this threshold. Conversely, m16s11d2 and m16s11d1 lead to a significant increase in DI at this threshold. If the values of all four wind speed factors exceed 45, DI remains relatively stable. Nonetheless, m11s10s11 generally has a negative impact on DI. DI initially rises and then falls when the value of m11s10d1 ranges from 6 to 9, while it remains relatively stable for other values.

3.2. RTPM-DI Model

The RTPM-DI model trained in this study is an ensemble model boosted by least squares. Figure 3 shows that the observed values are in proximity to the perfect prediction line, denoting a strong simulation capacity achieved by the model. The indicator scores (R² = 0.71, RMSE = 8.2511, MAE = 6.7765, MAPE = 0.2486, KGE = 0.9921, MSE = 68.081, RMSLE = 0.0953) suggest that the model performs well with respect to all evaluation indicators and effectively simulates the RTPM-DI of Hainan Island.

3.3. Temporal and Spatial Distribution of RTPM-DI

In this study, a spatial analysis was conducted on the RTPM-DI in Hainan Island spanning a period of 39 years, from 1980 to 2018. The findings of this analysis are shown in Figure 4. During the 1980s, the DI in the southwestern part of Hainan Island was relatively high, contrasting with the comparatively low levels in the northeastern part. However, by the 1990s, the DI levels across most regions of the island experienced a significant rise, peaking from 1993 to 1995, with most areas showing a DI of over 40%. Between 2000 and 2004, there was a brief decline in DI in the central region, followed by a severe outbreak of RTPM across the entire island in 2005 and 2006. Since then, the DI has gradually decreased, with the northeastern regions displaying a downward trend from 2007 to 2008, followed by a steady decline throughout most areas from 2009 to 2018. However, the DI of the southeastern region has consistently increased since 2013 and is currently more severe than in other areas. In summary, the western, southwestern, northwestern, and northeastern regions of Hainan Island have witnessed a downward trend in DI, whereas the southeastern and northern regions have seen an upward trend.

3.4. Spatiotemporal Dynamic Evolution of RTPM-DI

The emerging hotspot analysis of RTPM-DI spatiotemporal patterns in Hainan Island over the past 39 years is presented in Figure 5. A total of three spatiotemporal patterns were identified in Hainan Island, comprising 1% with new hotspots, 6% with oscillating hotspots, 72% with oscillating cold spots, and 21% with no discernible pattern. The central and western parts of Hainan Island exhibit oscillating cold spots, indicating intermittent RTPM outbreaks that alternate between hot- and cold-spots, with recent years being cold. The southeastern part, on the other hand, is dominated by oscillating hotspots and new hotspots, suggesting recent severe RTPM infections and making it the main outbreak area on the island. The northeast region of the island shows a small number of oscillating cold spots with little variation, indicating a minor impact of RTPM in this area. Overall, the island displays significant pattern differences, with decreasing infection levels in the western, northwestern, and southwestern regions, and increasing levels in the southeastern and northern regions, while no significant change is evident in the northeastern and eastern regions.

4. Discussion

4.1. Analysis of Meteorological Factors Affecting RTPM

Based on current research, meteorological factors play a crucial role in affecting RTPM. Temperature, precipitation, humidity, and wind speed are among the significant factors that have a significant impact on RTPM-DI [51,52]. In this study, we employed factor expansion and three feature-selection methods to identify two meteorological factors (average wind speed and precipitation) that have the greatest impact on RTPM-DI. Our findings align with the conclusions drawn from previous studies. However, there are certain limitations in using these two methods for factor screening. Factor expansion and feature selection methods assume a linear relationship or independence between factors and variables [34,38], while the relationship between meteorological factors and RTPM-DI may be nonlinear, so we may not capture the nonlinear relationship, leading to reduced accuracy in the results. Additionally, these methods only consider known meteorological factors and may overlook other unconsidered variables that could potentially influence RTPM-DI, resulting in an incomplete understanding of the mechanisms by which various factors affect RTPM. Furthermore, different meteorological factors may have varying degrees of impact on RTPM-DI, while factor expansion assumes an equal impact of factors on all variables [34], which may underestimate the factors with significant influence and overestimate those with minor influence on RTPM-DI.

The incorporation of variables such as maximum temperature, relative humidity, average temperature, precipitation, and average wind speed in our study aligns with previous research [6,12,53], thereby enhancing the robustness and rationality of our approach. Our study suggests a negative correlation between the average wind speed from November of the previous year to April of the current year and RTPM occurrence, while the days with moderate rain from October of the previous year to January of the current year show a positive correlation with RTPM occurrence. These findings are in line with the existing research [54,55]. To analyze the seasonal impact of selected meteorological factors on RTPM-DI and assess the risk zones, we derived the average values of the six meteorological factors for multiple years (1980–2018), as shown in Figure 6. Based on Table 2 and Figure 2, m16d3 and m16s11d4 are the two major influencing factors, with higher DI values when their values range from 20–40 and 35–40, respectively. According to the selected range determined using factor expansion, the average wind speed from November to March has the greatest impact on RTPM, indicating that the average wind speeds in the late leaf-falling period and early leafing period of rubber trees have the most significant influence on RTPM. Combining Figure 6, we can infer that during this period, the average wind speeds in the southwestern, southern, southeastern, and northeastern regions of Hainan Island are more favorable for the growth and spread of powdery mildew spores, thus increasing the likelihood of rubber tree susceptibility to powdery mildew. Additionally, days with moderate rain in the pre-leafing period may result in some areas experiencing powdery mildew infestation, although the impact is relatively small. However, our analysis may be limited in its ability to capture seasonal variations in the influence of different factors on RTPM-DI due to the selective inclusion of data within a specific time range. Moreover, there is a potential risk of overlooking unforeseen weather events or extreme climatic conditions that may have a significant impact on RTPM-DI [31].

Although we acknowledge that various climatic parameters, such as average temperature, maximum temperature, and relative humidity, may play a role in influencing RTPM-DI [5,6,53], our factor screening analysis did not reveal a significant correlation with these variables, which could be attributed to the intricate and strong interactions among these factors, potentially masking their individual effects on RTPM-DI. These findings underline the challenges and limitations faced in selecting and studying meteorological factors when investigating RTPM-DI models. Further research and analysis are necessary to comprehend these complex relationships, such as collecting more detailed data, enhancing the models, or exploring alternative potential factors. Additionally, our analysis suggests that variables such as minimum temperature, sunshine hours, and days with rainstorms may not be the primary drivers of RTPM-DI.

4.2. Spatial Distribution Mechanism of RTPM

In order to investigate the influence mechanism of selected meteorological factors on RTPM-DI across the island, we analyzed two years, 1980 and 2008, with significant regional differences in RTPM-DI. Spatially, RTPM-DI generally exhibits a pattern of higher values in the southern regions and lower values in the northern regions. However, there are more pronounced spatial differences in 1980 and 2008, with a noticeable pattern of higher values in the southwest and lower values in the northeast (Figure 4). These findings underscore the likelihood that powdery mildew, influenced by meteorological factors, is contributing to the recent trend of a decrease in rubber trees in the southern regions and an increase in the northern regions [27]. To delve deeper into the relationship between meteorological factors and RTPM-DI, we compared six meteorological factors that influence the disease in areas with high DI (above 40%) and low DI (less than 30%) in 1980 and 2008 (Figure 7).

Areas with high DI levels exhibit lower wind speeds and higher precipitation, while regions with low DI levels tend to have higher wind speeds and lower precipitation. This finding supports previous research, wherein low wind speeds facilitate the spread of powdery mildew conidia and lead to a greater incidence of the disease. Conversely, high wind speeds make it difficult for the spores to attach to trees, thereby reducing the incidence of powdery mildew [56]. Further, high humidity levels create an ideal environment for powdery mildew spores to germinate and reproduce, while rainfall not only boosts humidity, but also transports the spores to distant areas, thereby expanding the spread of the disease and increasing both the transmission speed and severity of RTPM [2]. However, as shown in Figure 2, there exists a nonlinear relationship between average wind speed, days with moderate rain, and RTPM-DI. Consequently, when investigating the influence of meteorological factors on RTPM, it is imperative to consider multiple variables comprehensively to precisely analyze the occurrence and spread of RTPM [53,57].

4.3. Suggestions for Future Research

The meteorological data for Hainan Island and RTPM-DI used in this study are prone to inherent errors that could influence the model’s development and simulation results. The analysis relied on limited meteorological station data from only seven stations on Hainan Island, which may not adequately represent the island’s overall meteorological characteristics. In addition, the timeframe of the station data from 1961 to 2009 may limit the analysis and exploration of earlier or more recent data. Considering the temporal variations in meteorology and RTPM dynamics [58], it would be beneficial to analyze and discuss data from a longer or more up-to-date timeframe. Furthermore, the accuracy and reliability of the CMFD reanalysis data are subject to the availability of in situ data, and the 0.1° spatial resolution and 3-h temporal resolution of the data may not capture fine-scale meteorological changes, making it challenging to analyze localized diseases like RTPM with great accuracy [2,59]. In future studies, using higher-resolution meteorological data would allow for a more precise simulation of RTPM [60]. Moreover, the RTPM-DI data used in the study were obtained through manual measurements with relative accuracy. However, they may have some form of uncertainty arising from measurement methods, data collection errors, or human factors. While the data covers a long timeframe (1962–2009), they may not sufficiently reflect the current or future RTPM conditions due to climate change [7], alterations in agricultural practices [61], and advancements in disease control methods [62]. Additionally, the RTPM-DI data do not provide detailed information for all regions of Hainan Island, which restricts comprehensive inferences about the overall RTPM situation on the island.

Furthermore, RTPM is not solely influenced by meteorological factors but also correlates with other factors such as wintering patterns, leaf age, and tree species [63,64,65]. In this study, we only accounted for average wind speed and precipitation, which could be a contributing factor in the RTPM-DI model’s explanatory rate of 71%. In addition, our model has inherent errors or uncertainties, leading to situations where lower values are overestimated and higher values are underestimated, exhibiting a tendency towards averaging (Figure 3). In future research, it is recommended that the analysis of RTPM should not only focus on meteorological factors, but should also include a comprehensive analysis of various influencing factors using methods such as structural equation modeling, principal component analysis, and deep learning [66,67,68]. These approaches will ensure a better understanding of the impact mechanism of RTPM. Additionally, we employed 48-fold cross-validation (leave-one-out method) to evaluate the performance of the time series model that incorporates 48 years of data. The leave-one-out method allows each year’s data to serve as an independent validation set, while the remaining years are used for training [69]. By observing the model’s performance on different years’ data, we can accurately assess its stability and reliability. However, this method also has certain limitations, including a higher computational cost, increased training time requirements, and applicability only to datasets with longer time spans [70,71]. We believe that adopting the leave-one-out method can provide valuable insights when evaluating time series models. Moreover, the availability of higher-resolution reanalyzed meteorological data and longer time-series simulated meteorological data under different scenarios can pave the way for large-scale, long-term time-series analysis, simulation, and forecasting research on RTPM [72,73], given the advancement of science and technology.

5. Conclusions

Based on meteorological station data and the RTPM-DI in Hainan Island, we employed factor analysis and three feature-selection methods to identify significant meteorological factors affecting RTPM. Subsequently, we developed a meteorological data-driven model and reproduced and analyzed the RTPM-DI in Hainan Island from 1980 to 2018 on a larger scale. From our analysis, we can draw the following main conclusions.

The RTPM-DI is influenced by average wind speed and moderate rainfall days, with the former negatively impacting DI and the latter positively affecting it. The RTPM-DI model developed in this study accurately captures changes in Hainan’s RTPM-DI and serves as an efficient tool for simulating RTPM.

From 1980 to 2018, there has been a gradual increase in RTPM-DI in Hainan Island, with a spatial trend moving from the northwest, southwest, and western regions towards the southeastern part. The southeastern part has emerged as a recent hotspot for RTPM occurrence, while there have been no significant changes observed in the northeastern part.

The results of our study can aid farmers and scholars in understanding the influencing mechanisms and spatial distribution of RTPM on Hainan Island, which can provide a scientific foundation and technical means for the prevention, control, and management of RTPM.