The Application of Machine Learning to Model the Impacts of Extreme Climatic Events on the Productivity of Dwarf Green Coconut Trees in the Eastern Amazon

Abstract

The coconut crop (Cocos nucifera L.) is essential in humid tropical regions, contributing to the economy and food security. However, its perennial nature makes it sensitive to climate variability, particularly extreme events that affect productivity. This study evaluated the impacts of extreme climatic events on the productivity of dwarf green coconut in northeastern Pará, analyzing rainy (PC—December to July) and less rainy (PMC—August to November) periods between 2015 and 2023. Meteorological and experimental data were used, including extreme climate variables such as maximum temperature (HT) and precipitation (HEP), defined by the 90th percentiles, and low precipitation (LP, 10th percentile). Predictive models, such as Multiple Linear Regression (MLR) and Random Forest (RF), were developed. RF showed better performance, with an RMSE equivalent to 20% of the average productivity, while that of MLR exceeded 50%. However, RF struggled with generalization in the test set, likely due to overfitting. The inclusion of lagged productivity (productivity t-1) highlighted its significant influence. During the PC, extreme high precipitation (HEP) events and excessive water surplus (HE) occurring after the fifth month of inflorescence development contributed to increased productivity, whereas during the PMC, low-precipitation (LP) events led to productivity reductions. Notably, under certain circumstances, elevated precipitation can mitigate the negative impacts of low water availability. These findings underscore the need for adaptive management strategies to mitigate climatic impacts and promote stability in dwarf green coconut production.

1. Introduction

Climate change has profoundly impacted agriculture, directly affecting crop production and bringing significant implications for the global economy [1]. Climate projections indicate a gradual and consistent increase in global temperatures over the coming decades, with estimates of a rise between 1.5 and 2.5 °C in the annual average temperature across much of the tropics [2]. As agriculture heavily depends on variables such as temperature and precipitation [3], it is among the most vulnerable sectors to these changes [4]. Increasing climate variability and intensifying extreme events, such as prolonged droughts and heat waves, threaten global food security, exacerbating the challenges associated with population growth and shifting precipitation patterns [5]. These extreme climatic events can drastically reduce crop yields, even when favorable conditions return afterward [6].

Among the crops most sensitive to climate change, the coconut palm (Cocos nucifera L.) stands out due to its socioeconomic importance in tropical countries and its vulnerability to climatic variations [7]. Together, countries like Indonesia, the Philippines, India, Sri Lanka, and Brazil account for 82.9% of global coconut production, with an annual average of 62 million tons [8]. Although the coconut palm exhibits high adaptability, its perennial nature and indeterminate growth pattern make it susceptible to thermal and water stresses, particularly during critical stages of its production cycle, such as floral primordia initiation and fruit development [3].

Climatic variables, such as temperature, precipitation, relative humidity, and solar radiation, directly influence coconut fruiting. Optimal conditions include temperatures between 25 °C and 30 °C and annual precipitation exceeding 1500 mm [9,10]. However, deviations from these conditions during the period between inflorescence opening and fruit maturation—estimated at approximately seven months—can lead to premature fruit drop and underdevelopment, resulting in significant productivity losses [9,11,12,13].

Recent research [3,10] has sought to evaluate the relationship between climatic variables and agricultural productivity, emphasizing connections between variables such as temperature and precipitation and crop yields. However, there is a growing recognition of the need to further explore this relationship by considering additional factors, such as extreme climatic events during critical crop development stages [14]. For instance, refs. [7,14] analyzed the impact of climatic extremes on the productivity of coconuts, soybeans, and wheat, finding that these events can cause significant and specific impacts depending on the crop, development stage, and regional climatic conditions.

In this context, forecasting agricultural productivity has proven to be an essential tool for mitigating the impacts of climate variability [15]. Traditional statistical models, such as Multiple Linear Regression (MLR), have been widely used to establish relationships between productivity and climatic variables [16]. However, advanced machine learning (ML) techniques, including artificial neural networks, Random Forest, and Gradient Boosting algorithms, have stood out for their accuracy and robustness in modeling agricultural systems [17,18]. These methods have been successfully applied to predict the productivity of crops like soybeans and coffee, demonstrating great potential in analyzing complex datasets [19,20].

The results of this study aim to contribute significantly to understanding the relationships between extreme climatic variables and agricultural productivity, emphasizing the need to integrate these conditions into agricultural planning. By providing valuable insights for farmers and policymakers, this research seeks to reinforce the importance of adaptive management strategies that account for the impacts of extreme climatic events. These strategies can mitigate the negative effects of climate change, promoting resilience and sustainability in dwarf green coconut production while ensuring market stability.

2. Materials and Methods

2.1. Study Area

This study was conducted in a 2500-hectare commercial area at Fazenda Reunidas da Sococo S/A—Agroindústrias, located in the municipality of Santa Isabel do Pará (−01°12′36″ S, −48°04′48″ W), at an altitude of 24 m, during the 2015–2023 growing season (Figure 1). This region is recognized as one of the main producers of dwarf green coconut in northern Brazil, emphasizing the economic importance of this crop. The climate in the study area is classified as tropical hot and humid (Am) according to the Köppen classification [21]. It is characterized by a predominant rainy season from December to July and a less rainy period from August to November. The annual average precipitation is approximately 2000 mm, while the annual average temperature is 26 °C. The region’s soil is predominantly Quartzarenic Neosol, known for its low natural fertility and high susceptibility to erosion [22].

2.2. Productivity Data

The productivity data of dwarf green coconut were obtained from monthly production estimates conducted by the company from 2015 to 2023. This activity involves counting harvested fruits in the plots marked in Figure 1. Based on the number of fruits and the area occupied, the productivity of each plot was calculated, which was grouped by plantation ages ranging from 4 to 8 years. It is important to note that the plants are arranged in an equilateral triangular pattern with a spacing of 7.5 m × 7.5 m, resulting in a planting density of approximately 205 plants per hectare.

In this study, analyses were performed considering the fruiting phase duration of the coconut palm as 210 days, equivalent to seven months. This phase includes different stages of fruit growth and development, which, according to [9,23,24], can be sequenced as follows: (1) initial growth and mesocarp development in the first two months after flower pollination; (2) endocarp lignification and liquid endosperm formation between the third and fourth months; (3) an increase in the sugar concentration in the liquid endosperm and the subsequent formation of solid endosperm in the fifth and sixth months; and finally, (4) fruit harvest (Figure 2).

2.3. Models Input Variables

Daily meteorological data for maximum air temperature (Tmax, °C) and precipitation (PP, mm) were used, obtained from a weather station located in the cultivation area. Additionally, the water balance (WB) was calculated based on the method described in [25], using an available water capacity set at 130 mm and a crop coefficient established in [26], which determined a value of 1.1. This calculation allowed for the determination of two key elements: the water deficit (DEF), representing the shortage of water in the soil–plant-atmosphere system (mm), and the water surplus (EXC), indicating the excess water in the system (mm).

Based on these basic variables, extreme climatic events were incorporated as input variables for the models. High-temperature days were defined as those when the maximum air temperature (Tmax) exceeded the 90th percentile of the daily distribution during the reference period (1995–2015). Intense precipitation events were characterized as days when precipitation exceeded the 90th percentile, while low-precipitation events were defined as those with precipitation below the 10th percentile of the daily distribution. These definitions followed the guidelines of the IPCC Fourth Assessment Report [27]. Additionally, days with high water deficits and surpluses were included as relevant variables.

Tmax values were aggregated as monthly averages, while extreme climatic events were grouped as monthly totals. For days with intense precipitation, the monthly sum of corresponding daily values was calculated. Furthermore, a lagged productivity variable (productivity t-1, referring to the previous month) was included as a predictor to capture potential autocorrelation effects in the data and improve the explanatory power of the models.

The input variables for the models were comprehensively organized, including both basic climatic elements and indicators of extreme events. For example, Tmax_1 represented the maximum temperature recorded in the first month after inflorescence opening, with the same logic applied to Tmax_2 through Tmax_7. This approach was extended to other variables, such as the number of occurrences of extreme low-precipitation (LP) and high-temperature (HT) events. In total, eight main variables were considered, seven of which were analyzed over the seven months following inflorescence opening, resulting in a dataset with 50 input variables. A complete list of these variables is detailed in

Table 1. Predictor variables used for Random Forest Regression and Multiple Linear Regression Analysis.

Variable	Unit	Description
Tmax	°C	Maximum temperature from month 1 (Tmax_1) to month 7 (Tmax_7)
HT		High-temperature extreme event from month 1 to month 7
HEP		Heavy precipitation extreme event from month 1 to month 7
LP		Low-precipitation extreme event from month 1 to month 7
HEP_sum	mm	Sum of heavy precipitation from month 1 to month 7
HD		High water deficit extreme event from month 1 to month 7
HE		High water excess extreme event from month 1 to month 7
p_t-1	Fruits ha−1	Productivity of the previous month

.

2.4. Development and Validation of Predictive Models

The analyses began with the selection of the variables listed in Table 1 using Spearman’s correlation method. The aim of this analysis was to remove variables with a low association with productivity. Variables that showed a significant relationship with productivity during the rainy period (PC) and the less rainy period (PMC) were included in the model construction.

Regression models were initially developed using the stepwise method, which allowed for the selection of the most relevant predictor variables to explain productivity. Subsequently, the models were refined based on the Variance Inflation Factor (VIF) and the correlation matrix to mitigate potential multicollinearity issues among the independent variables. The performance of the models was evaluated using the adjusted coefficient of determination (adjusted R²), ensuring reliable and robust predictions.

The data were split into 80% for training and 20% for validation using the train_test_split method from the Scikit-learn library in the Python environment (version 3.10.9). During cross-validation, the adjusted models were evaluated on the validation set, and the predicted values were compared with the observed values in a scatter plot. An ideal trend line (X = Y) was used as a reference to analyze the accuracy and dispersion of the results, ensuring the reliability of the model.

In addition to Multiple Linear Regression (MLR) models, machine learning (ML) algorithms were incorporated to enhance predictive capacity. Among these, Random Forest Regressor (RFR) stood out as a robust ensemble learning method, utilizing multiple decision trees to increase prediction accuracy. The model was fine-tuned using the grid search technique (GridSearchCV), testing different parameter combinations, including the number of trees (n_estimators, ranging from 50 to 150), tree depth (max_depth, ranging from 5 to 20), and the number of variables considered per split (max_features, fixed at 2).

The optimal set of parameters was identified after 5-fold cross-validation, ensuring a robust model resistant to overfitting and capable of capturing complex interactions between meteorological variables and productivity. This approach enabled the identification of non-linear relationships, resulting in more precise estimates aligned with the characteristics of the dataset and the study objectives.

The optimized parameters and the variables selected for each model are presented in

Table 2. Optimized parameters and adjusted values of the Random Forest model for productivity forecasting.

Model	Parameters	Values Tested	Defined Values (PC)	Defined Values (PMC)
RF	n_stimators max_depth max_features	50, 100, 150 5, 10, 15, 20 2	50 15 2	150 15 2

, providing a detailed overview of the adopted configurations. The models’ ability to reflect the impacts of climatic conditions on productivity is further discussed in the context of their predictive performance.

2.5. Analysis of Models’ Performance

The performance of the statistical and machine learning models was evaluated using three assessment metrics: the root mean square error (RMSE, ton ha⁻¹), the coefficient of determination (R²), and the mean absolute error (MAE), respectively, to measure the accuracy, precision, and bias of the models. A lower RMSE (Equation (1)) indicates better model estimation performance, while a lower MAE (Equation (2)) reflects a reduced bias tendency in the model predictions.

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^N{(Y_{obs}-Y_{est})}^2}{N}}},$$

(1)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{{\sum }_{i=1}^N\left|Y_{obs}-Y_{est}\right|}{N}},$$

(2)

where Y_obs is the observed productivity (fruits ha⁻¹), Y_est is the estimated productivity (fruits ha⁻¹), N is the number of observed productivity data points, and k is the number of features in the input layer.

2.6. The Interpretation of the ML Model

Considering that insufficient interpretability is one of the main limitations in using machine learning algorithms, we employed a SHAP analysis to quantify the contribution of input variables to the results of the RF model’s estimates and identify the variables that most influenced productivity estimates. Based on game theory, this analysis constructs combinations of different input variables to clarify the importance of a specific variable by comparing the average change in the model’s output when that input variable is included or excluded [28]. The SHAP value for each input variable is calculated as the weighted average of that variable’s marginal contribution.

3. Results and Discussion

3.1. Time Series of Extreme Climatic Events

An analysis of climatic dynamics in the study area revealed that the most frequent extreme events over the nine years evaluated were low-precipitation events, highlighted by the red bars in Figure 3B. When comparing maximum temperature events (Figure 3A) with high-precipitation events (Figure 3B), greater variability and fluctuations were observed in high-precipitation events throughout the period, reflecting the seasonal and interannual dynamics of climatic conditions.

The accumulated precipitation during high-intensity events (HEP_sum) and maximum temperature (Tmax) showed significant seasonal variations (Figure 3). The maximum temperature ranged from 27.8 °C to 35.1 °C, with an overall average of 31.8 °C (Figure 3A,B). The months of September to November stood out as the hottest, especially in 2015 and 2020, when average temperatures reached 33.5 °C. In contrast, the months from January to April recorded milder maximum temperatures, with an average of 30.3 °C.

Regarding the accumulated precipitation during high-intensity events, the monthly average was 121.8 mm, with values ranging from 0 mm to 497.8 mm in specific months. The rainiest months were concentrated between February and May, with 2020 and 2022 standing out, accounting for about 50% of the annual precipitation. Conversely, the least rainy months occurred between August and October, with 2015 being particularly critical, accumulating only 803 mm of annual precipitation, while 2020 and 2022 exceeded 2000 mm. These results highlight the behavior of extreme event occurrences and their interannual variations.

3.2. Productivity of Dwarf Green Coconut

Regarding the commercial productivity of dwarf green coconut, it exhibited an average of 1652.1 fruits ha⁻¹ over the nine years evaluated, with a notable monthly variation ranging from 10.1 to 7763.9 fruits ha⁻¹. An increase in production was observed between March and May, with averages varying between 2000 and 2600 fruits ha⁻¹ (Figure 4), with 2020 standing out for recording the highest values. In contrast, productivity showed a significant reduction between August and November, a period characterized by greater dispersion and the occurrence of outliers, possibly associated with extreme climatic events.

This pattern aligns with the results obtained by the authors of [11], who reported significant seasonal variations in fruit production and the development of dwarf green coconut. According to the authors, the liquid endosperm mass, an important commercial component, is higher during the rainy season, reinforcing the direct influence of climatic conditions on crop productivity.

A significant annual fluctuation in the productivity of dwarf green coconut was observed over the years. In 2016, there was a drastic reduction, with drops of approximately 64% and 83% in the harvests of April and November, respectively. These results reflect the crop’s high sensitivity to adverse climatic conditions, highlighting the importance of continuous monitoring and mitigating the impacts caused by extreme climatic events.

In the context of this study, the significant decline in productivity observed in 2016 can be attributed to the severe drought associated with the 2015–2016 El Niño event, a phenomenon that also impacted other crops, such as cocoa, as demonstrated in [29]. This scenario reflects the growing influence of climate change, characterized by an increase in the frequency and intensity of extreme events, such as heavy rainfall and high temperatures, which have had substantial impacts on agricultural production.

The studies conducted in [30] highlight that adverse climatic events negatively affect coconut productivity, especially when they occur during the first four months after inflorescence opening—a critical phase for fruit development [7]. These findings emphasize the need for adaptive management strategies to minimize the harmful effects of climatic extremes on the productivity of this crop.

3.3. Impact of Extreme Climatic Events on Coconut Productivity

The relationship between fruit productivity and the frequency of extreme climatic events, such as maximum temperature (HT), high precipitation (HEP), and low precipitation (LP), during the rainy period (PC) and the less rainy period (PMC) is presented in Figure 5. During the PC, productivity was consistently higher and less variable, even in the presence of extreme HT and HEP events. In contrast, during the PMC, average productivity values were lower and exhibited greater dispersion, highlighting the crop’s sensitivity to adverse climatic conditions. In this period, extreme low-precipitation (LP) events had a more severe impact, resulting in lower productivity and higher variability, emphasizing the vulnerability of coconut trees during periods of water scarcity.

The impact of extreme climatic events on coconut productivity was initially evaluated by the authors of [7] in three climatic zones of Sri Lanka (dry, intermediate, and wet). While previous studies, such as [10], demonstrated that temperature increases and precipitation variations during the fruit production cycle exert a significant negative impact, limited attention has been given to the specific effects of extreme climatic events. Ref. [31] further highlighted the critical role of phenological stages by observing that extreme high-temperature events after flowering had the greatest negative influence on wheat yields, underscoring the vulnerability of crops to climatic extremes during key developmental phases.

Building on the findings of [7], the results of this study reaffirm that extreme events, such as high precipitation and elevated temperatures, significantly affect coconut productivity, particularly during critical stages of the production cycle. These findings reinforce the urgent need for adaptive management strategies to mitigate the adverse impacts of extreme climatic conditions, enhancing the resilience of crops in the context of climate change.

3.4. Correlation Between Coconut Productivity and Predictor Variables

Spearman’s univariate correlations between coconut productivity and climatic variables during the fruiting stage showed distinct patterns and varying intensities in the rainy period (PC) and the less rainy period (PMC), as presented in Figure 6 and Figure 7, respectively. During the PC, high-precipitation events (HEPs) and water surplus (HE) starting from the fifth month after inflorescence opening—a critical phase for increasing sugar concentration in coconut water and fruit volume—demonstrated moderately positive correlations, ranging from 0.31 to 0.53. On the other hand, high-temperature (HT) events exhibited predominantly negative correlations, highlighting the adverse impacts of elevated temperatures during this stage of fruit development.

Similar results were reported by the authors of [14] in soybean yield, where thermal and hydro-meteorological parameters showed negative and positive correlations, respectively. These findings highlight the importance of water availability for proper fruit development, as water supply favors the retention of volume inside the fruit, especially during the formation of liquid endosperm [23]. Additionally, ref. [32] emphasizes that adequate water supply meets the physiological demands of the plant, promoting growth, stimulating the production of female flowers, regulating transpiration, and reducing premature fruit drop. Ref. [33] further reinforces that temperature and precipitation exert the greatest effects on crop productivity, underscoring the critical influence of climatic variables in determining agricultural outcomes.

On the other hand, the maximum and average temperatures showed inverse relationships with productivity during the fruit maturation and harvest phases. These results align with previous studies that associated thermal stress with reduced coconut production due to the abortion of fruits and female flowers [3,12,30]. High temperatures intensify transpiration, compromising plant metabolism and negatively affecting fruit yield. Our results correlate with previous research, suggesting that rising heat stress due to climate change, as highlighted in [34], will significantly affect wheat yield and production, further reinforcing the vulnerability of crops to elevated temperatures.

In the PMC, the correlations displayed distinct patterns throughout the fruiting cycle (Figure 7). The accumulated precipitation during high-intensity events (HEP_sum) and water surplus (HE) showed positive correlations in the first four months after inflorescence opening, highlighting the importance of water availability during this initial period for proper fruit development. However, temperature extremes did not show strongly significant correlations.

In contrast, the occurrence of extreme low-precipitation (LP) events from the third month after inflorescence opening was associated with adverse impacts. Water scarcity during this critical phase can result in smaller, less juicy fruits with a lower water content, compromising their quality, marketability, and economic value [30].

Due to the high water demand during this critical period [26], the practice of irrigation becomes essential to mitigate the impacts of water stress [35]. In their study, the authors of [11] demonstrated that irrigation significantly reduced fruit production losses, highlighting that proper water management can improve the productivity of the green dwarf coconut palm.

Considering the significant variables identified in the correlation analyses, productivity estimation models were developed for the rainy and less rainy harvest periods. The estimates were performed using Multiple Linear Regression (MLR) models and advanced machine learning algorithms, such as Random Forest (RF).

3.5. Productivity Prediction Models for the Green Dwarf Coconut Palm

The regression model (R-sq = 50%) for the relationship between coconut productivity in the PC and the predictor variables (

Table 3. Coefficients of the predictor variables in the regression model for the rainy period.

Variable	Coefficient	SE Coef	T-Value	p-Value	VIF
const	1453.62	58.37	24.90	<0.001	1.01
p_t-1	557.02	65.08	8.56	<0.001	1.13
HEP_6	195.39	72.01	2.71	0.007	1.55
HE_7	227.39	67.60	3.36	0.001	1.40

) is as follows:

$$p=1453.62+557.02 p_t-1+195.39 HEP\_6+227.39 HE\_7$$

(3)

The adjusted regression model to predict productivity during the rainy period (PC), based on extreme climatic events, showed low VIF (Variance Inflation Factor) values, indicating no multicollinearity among the predictor variables. Among the analyzed variables, p_t-1 had the greatest impact, while HEP_6 and HE_7 also contributed positively and significantly to productivity.

The estimated productivity values for the PC were compared with the observed values for each harvest in the training and test sets (Figure 8A and Figure 8B, respectively). To evaluate the agreement and dispersion between the model-predicted and actual values, a trend line was drawn, enabling the visualization of the precision and performance of the estimates.

The analysis of the dispersion between the observed and predicted values revealed a tendency toward underestimation, even in the most accurate models. The results obtained through Multiple Linear Regression (MLR) showed moderate performance, with R² = 0.49, RMSE = 747.1 fruits ha⁻¹, and MAE = 536.7 fruits ha⁻¹ in the training set, calculated according to Equation (2), suggesting a limited ability of the model to explain data variability. In the test set, the results were comparable, with R² = 0.50, RMSE = 775.6 fruits ha⁻¹, and MAE = 512.7 fruits ha⁻¹. Although the RMSE value increased slightly in the test set, the results indicate a general consistency in model performance across datasets, as shown in Figure 8. However, the persistence of errors suggests that, despite its stability, MLR requires further refinement to enhance its accuracy in estimating productivity.

To compare the MLR results with a more robust model, Random Forest (RF) was applied, showing superior performance in fitting the data. In the training set, RF explained 92% of the variability in productivity (R² = 0.92), with MAE = 232.895 fruits ha⁻¹ and RMSE = 303.119 fruits ha⁻¹ (equivalent to 17.46% of the average yield), demonstrating the model’s high capability in capturing non-linear and complex relationships among the variables.

However, in the test set, the performance of RF showed a reduction, with R² = 0.50, MAE = 577.779 fruits ha⁻¹, and RMSE = 755.775 fruits ha⁻¹. This decline can be attributed to the limited amount of available data, which restricts the model’s ability to generalize patterns observed during training. In contexts with smaller sample sizes, more complex models like RF tend to face challenges in generalization due to the high variability of test data.

Even so, RF maintained performance equivalent to MLR in the test set but with the advantage of being a more robust model and better suited to handling non-linear patterns. As highlighted in [36], increasing the amount of data available for model training would likely enhance the predictive capacity of RF regression, emphasizing the importance of expanding the dataset to improve the performance of this type of model.

The Random Forest (RF) model stands out as the most promising approach due to its high accuracy during training and its ability to capture non-linearities in the data. Although Multiple Linear Regression (MLR) showed more stable performance across datasets, its fitting capacity is limited, making it more suitable for simple applications with straightforward interpretation. The increase in errors observed with RF should be interpreted cautiously, as a larger volume of data could significantly improve its generalization ability. Thus, RF emerges as the best alternative for modeling productivity, particularly in scenarios characterized by high variability and greater data availability.

Previous studies, such as [19,36,37], also highlighted the high accuracy achieved in agricultural productivity prediction using algorithms like Random Forest, Multi-layer Perceptron (MLP), and Support Vector Regression (SVR). Among these approaches, RF has proven particularly effective due to its ability to model non-linear relationships and identify complex patterns between explanatory and response variables, making it a promising and efficient tool for predicting complex crop responses in agricultural systems.

Despite the remarkable accuracy of ML models, their interpretation can be challenging due to their inherent complexity. Therefore, to enhance the interpretability of the RF model, the SHAP (Shapley Additive Explanations) technique was employed to quantify the relative importance of each feature and clarify its influence on the model’s predictions. The relevance of the top ten input variables was determined through the mean absolute SHAP values, as presented in Figure 9.

The results indicate that the variable p_t-1 was the most influential in predicting productivity. Higher values of this variable (indicated in pink) contribute positively to increased productivity, while lower values (in blue) are associated with reduced predictions. This highlights the central role of lagged productivity as a strong indicator of current productivity.

Additionally, variables related to extreme high-precipitation events, such as HEP_5 to HEP_7 and HE_7, showed variable impacts on productivity. Generally, higher values of these variables tend to have positive effects (increasing productivity), as indicated by the predominance of pink points, while lower values exert negative effects (reducing productivity), reflected in blue points.

Maximum temperature variables, represented by Tmax_av4 and Tmax_av6, showed a significant influence on productivity. Higher values of these variables had a moderately positive impact; however, extreme temperatures resulted in a reduction in productivity, suggesting a non-linear relationship and highlighting the sensitivity of productivity to thermal variations. These findings are consistent with those of the authors of [14], who emphasized the impact of extreme temperature events on reducing wheat productivity.

The regression model (R-sq = 53%) for the relationship between coconut productivity in the PMC and the predictor variables (

Table 4. Coefficients of the predictor variables in the regression model for the less rainy period.

Variable	Coefficient	SE Coef	T-Value	p-Value	VIF
const	1458.43	61.39	23.75	<0.001	1.01
p_t-1	633.33	65.11	9.73	<0.001	1.02
LP_7	−226.35	60.85	−3.72	0.007	1.02
HD_4	121.26	55.02	2.20	0.029	1.00

) is as follows:

$$p=1458.43+633.33 p_t-1-226.35 LP\_7+121.26 HD\_4$$

(4)

The adjusted regression model to predict productivity during the less rainy period (PMC), based on extreme climatic events, also showed no multicollinearity, as indicated by the low VIF values. Similarly to the productivity in the rainy period (PC), p_t-1 had the greatest impact. On the other hand, low-precipitation events (LP_7) had a significantly negative impact, indicating the sensitivity of productivity to soil water deficits. The variable water deficit (HD_4), despite representing stress, showed a positive effect, suggesting the complexity of productive responses to adverse conditions.

The results of the Multiple Linear Regression (MLR) and Random Forest (RF) models for estimating productivity during the less rainy period showed distinct performances between the training and test sets, reflecting their fitting and generalization capabilities (Figure 10).

In the training set, the Random Forest (RF) model demonstrated superior performance, explaining 93% of the observed variability (R² = 0.93) with relatively low errors: MAE = 204,850 fruits ha⁻¹ and RMSE = 277,089 fruits ha⁻¹. These results indicate an excellent ability of RF to capture the complex and non-linear relationships between predictor variables and productivity, achieving a highly precise fit to the data. In contrast, the MLR model showed more limited performance, with R² = 0.43, MAE = 595,038 fruits ha⁻¹, and RMSE = 792,181 fruits ha⁻¹, suggesting a more restricted ability to explain data variability.

In the test set, the performance of the RF model dropped significantly, with R² = 0.44, MAE = 607,540 fruits ha⁻¹, and RMSE = 795,451 fruits ha⁻¹. The reduction in R² and the increase in errors indicate a decline in the RF’s generalization ability, possibly due to the limited volume of available data and the greater variability observed during the less rainy period. On the other hand, the MLR model showed improved performance in the test set, with R² = 0.53, MAE = 526,842 fruits ha⁻¹, and RMSE = 750,657 fruits ha⁻¹, outperforming RF in terms of explaining out-of-sample variability.

These results reveal an important contrast between the models. While RF showed significantly superior performance in training, it struggled with generalization in the test set, likely due to overfitting. Similarly, ref. [38] observed that the RFR model performed the best on the training set but exhibited the poorest performance on the validation set, highlighting its poor generalization capabilities. Conversely, MLR, despite its lower accuracy during training, demonstrated greater stability across the two datasets, with more consistent and generalizable performance.

According to the SHAP values of the predictor variables in the RF model for the PMC, as presented in Figure 11, the most influential variable was p_t-1 (lagged productivity), with both significant positive and negative impacts depending on the values of the variable. This highlights that productivity history is one of the main determinants of future productivity, even under conditions of lower precipitation.

Among the extreme climatic variables, LP_7, LP_6, and LP_5, associated with low-precipitation events, stood out. These results show that high values of these variables (in pink) are predominantly associated with reduced productivity, suggesting that extreme low-precipitation events negatively affect the production system during the less rainy period.

The variables HEP_3 and HEP_2, related to extreme high-precipitation events, also stood out. However, their impacts exhibited mixed behavior: while lower values (in blue) tend to reduce productivity, higher values (in pink) contribute positively, indicating that, under certain circumstances, elevated precipitation can mitigate the negative impacts of low water availability.

Overall, the analysis reinforces the importance of water conditions, including potential water balance, accumulated precipitation, and soil water storage, in sustaining productivity under conditions of lower water availability. Furthermore, the impact of lagged productivity highlights the importance of historical factors in modeling coconut productivity during less rainy periods.

4. Conclusions

The results of this study highlight the significant influence of extreme climatic events on dwarf green coconut productivity, varying according to the climatic period. During the rainy period, high-precipitation events and water surplus negatively impacted critical phases of the production cycle. In contrast, during the less rainy period, low precipitation proved to be the main limiting factor for productivity, demonstrating the crop’s vulnerability to extreme climatic conditions.

Furthermore, the comparative analysis of predictive models revealed that Random Forest Regressor (RFR) outperformed Multiple Linear Regression in capturing non-linear and complex patterns, showcasing the robustness of machine learning techniques in agricultural systems. However, the model’s limited performance on the test set emphasizes the need to increase the volume of data available for training, which could enhance the precision of the predictions.

These results underscore the need to consider extreme climatic events in agricultural planning and the development of adaptive management strategies. Investments in research, improvements in climate monitoring, and the expansion of climatic and agronomic data repositories are essential to promote resilience and sustainability in dwarf green coconut production, particularly in the face of climate change scenarios.