1. Introduction

2. Material and Methods

2.5. Grey Model

In this study, the predict of PCDD/Fs emissions from 2023 to 2028 based on data from 2016 to 2022 that employ the 'Grey Model First Order One Variable' (GM (1,1)). This model is particularly useful when dealing with limited and uncertain data. The GM (1,1) model is advantageous due to its simplicity and has short time series data, where traditional statistical methods may not be as effective to be used [39]. This approach involves converting original data into cumulatiove using AGO. Despite its simplicity, this model still achieving excellent prediction results [40]. The concept shown in the figure 1 below, the input data being processed through predictive modeling to output. This model uses feedback mechanisms to adjust predictions based on input data, ensuring accurate and reliable emission forecasts. After gather and order the input data sequencially according to the years then we initiate the model.

Figure 1. GM (1,1) Concept of Feedback Control System.

Figure 1. GM (1,1) Concept of Feedback Control System.

Firstly, the process begins by organizing the input data chronologically. The initial step involves converting the raw data into an accumulative sum to improve the data regularity, which is crucial for handling the exponential growth characteristics typical in grey models. This accumulation helps in smoothing out random fluctuations in the time series data. The first-order differential equation of the model is described in Equation 6. The calculation known as the DAGO from the cumulative data and extrapolate this sequence to predict dioxin emissions.

$${\displaystyle \frac{{dx}^{\left(1\right)}}{dt}}+{ax}^{\left(1\right)}=b$$

(6)

where a and b are parameters estimated using the least squares method applied to the cumulative data series. Continuing with inverse accumulated, time response to predict the future PCDD/Fs emission. x⁽⁰⁾ (1) is the first value of original historical emissions data and k is the time step. This constructed model will forecast future values. By inputting the values of k for the years 2023 to 2028, the model will predict the corresponding PCDD/Fs emissions (equation 7). The Inverse Accumulated Generating Operation (IAGO) is used to convert the predicted accumulated values back to the original scale, providing the forecasted emissions for each year.

$${\widehat{x}}^{\left(1\right)}\left(k+1\right)=\left(x^{\left(0\right)}\left(1\right)-{\displaystyle \frac{b}{a}}\right)e^{-ak}+{\displaystyle \frac{b}{a}}$$

(7)

GM (1,1) performance evaluation is assessed through cross-validation of mean absolute percentage error (MAPE) and Mean Absolute Error (MAE). In equation 8, e_i and Y_i are the error and observation values (here using 3^rd year prediction data) of the ith period. While MAE the is a measure used to quantify the accuracy of a forecasting model by averaging the absolute errors in the predictions show in equation (9).

$$MAPE={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{e_i}{Y_i}}\right|x100$$

(8)

$$MAE={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|e_i\right|$$

(9)

3. Results and Discussion

3.1. Annual Emission and Geographical Distribution

The activity rate of sugarcane crop residue burning is influenced by biomass fuel load (BL), biomass sugarcane consumption (Bb), and the quantity of dry sugarcane residue (Qs). Table S2 provides a comprehensive overview of BL, Bb, and Qs in Indonesian provinces from 2016 to 2022. The data indicates substantial differences of sugarcane residue among the provinces. For instance, D.I. Yogyakarta shows consistently high values in both BL and Bb, with sugarcane residue quantities peaking at 367,918 tonnes/year in 2016 and 340,266 tonnes/year in 2022. Similarly, West Jawa displays significant biomass fuel load and consumption, reaching a Bb of 0.14 kg/m² and Qs of 72,365 tonnes/year in 2022. Compared to Thailand, where the biomass fuel load was 10.15 million tons in 2012 [18], Indonesia's biomass fuel load is significantly smaller, highlighting differences in agricultural practices between the two countries. However, there are other also other factors that influence the activity rate like moisture content mentioned in a simulation study conducted by Spaunhorst, et al. [41] demonstrated that different biomass densities, ranging from 6.1 to 24.2 Mg/ha with 44% moisture content during lower wind speeds, resulted in a smoldering effect. This effect reduced weed emergence by 23% compared to burning postharvest residue with 30% moisture during breezy conditions.

Table 2 summarizes the descriptive statistics of PCDD/Fs emissions across Indonesian provinces from 2016 to 2022. The revised statement based on the data provided in the table would be as follows:

The average PCDD/Fs emission values exhibit significant variation among the provinces. North Sumatra records a mean emission of 232 pg/yr, whereas East Nusa Tenggara displays the lowest mean emission at 187 pg/yr. Notably, East Jawa shows the highest mean emission value at 435 pg/yr, indicating significant variability in emissions between provinces. The standard deviation values also exhibit considerable variation, with D.I. Yogyakarta presenting the highest variability (std = 70), suggesting fluctuating emission levels over the years. In contrast, East Nusa Tenggara has a relatively high standard deviation of 153, but this is based on a limited sample size (n=2), which may affect the reliability of the PCDD/Fs emission inventory. The range of minimum emission values spans from as low as 50 pg/yr in East Nusa Tenggara to 290 pg/yr in D.I. Yogyakarta. Conversely, the maximum values range from 294 pg/yr in East Nusa Tenggara to 487 pg/yr in Gorontalo, illustrating a wide dispersion in emission levels across the provinces. The 50th percentile (median) values align closely with the mean values in most provinces, indicating a symmetrical distribution of emission data. However, provinces like West Nusa Tenggara show a substantial difference between the median (276.5 pg/yr) and the mean (435 pg/yr), hinting at potential outliers or skewed data. The 50th percentile (median) values align closely with the mean values in most provinces, indicating a symmetrical distribution of emission data. However, provinces like West Nusa Tenggara show a substantial difference between the median (276.5 pg/yr) and the mean (435 pg/yr), hinting at potential outliers or skewed data.

As shown in figure 2, the trend of PCDD/Fs emissions at provincial level from 2016 – 2022. The average dioxin from sugarcane residue burning emissions in Indonesia, at approximately 309 pg TEQ/year, are notably lower compared to the emissions reported from the United States in 2001, which included states like Florida, Hawaii, Louisiana, and Texas, each by 37.5 g TEQ/yr [9]. Despite the US utilizing smaller emission factors (ranging from 0.017 to 0.025 ug TEQ/kg), factors such as higher combustion efficiency (90%) and a greater proportion of the harvested area being burned (50%) contribute to these increased emissions. Nonetheless, from all sectors, Indonesia still count as among the top five countries in terms of PCDD/Fs emissions, releasing 1.17 to 2.04 kg TEQ across all sector and all media (atmosphere, soil, and water) [42].

Figure 2. Total Annual Dioxin Emission in Each Province over 2016 – 2022.

Figure 2. Total Annual Dioxin Emission in Each Province over 2016 – 2022.

In this emissions inventory, there are several factors that might influence uncertainty: emission factor, activity rate and model for prediction. Unfortunately, the study of dioxin emission factors remains limited in Indonesia and Southeast Asia. To address this gap, we compare the emission results using factors from several field simulation studies conducted in the USA [31] and Australia [10]. Table 3 presents a comparison of PCDD/Fs emissions (in picograms per year) from sugarcane open burning in Indonesia, utilizing emission factors derived from these field measurements. This approach allows us to utilize established and peer-reviewed emission factors to estimate emissions more accurately, despite the regional limitations of direct local studies.

From the table, it is evident that there are significant differences when using different emission factors. Markly, emissions based on the UNEP factor tend to be higher compared to the other two factors. The UNEP factor, more generic nature, and lack of regional specificity. While The USA and Australia factors might be more accurate for their respective contexts. Sugarcane burning conditions (e.g., temperature, moisture content, combustion efficiency) impact dioxin formation. Variations in field practices, such as pre-harvest burning versus post-harvest burning, contribute to differences. Sugarcane composition varies globally. Factors like sugarcane variety, soil nutrients, and growth conditions affect the chemical makeup. Different compositions lead to varying dioxin emissions. Regarding activity-related uncertainty, it may also stem from the ratio of produced sugarcane to burning residue. In this study, we assume a uniform 33% residue ratio [43] across all provinces, which is higher than the ratio observed in India (20%) according to S. Bhuvaneshwari, et al. [44]. However, variations in this ratio are likely due to different sugarcane varieties and harvest conditions.

Figure 4. Spatial Distribution Dioxin Emission in Each Province over 2016 – 2022.

Figure 4. Spatial Distribution Dioxin Emission in Each Province over 2016 – 2022.

Spatially, certain regions in Indonesia consistently exhibit higher PCDD/Fs emissions. Provinces such as Lampung and South Sumatra, known for their extensive sugarcane agriculture, show persistently elevated levels of PCDD/Fs emissions. This trend is likely driven by intensive agricultural activities and the widespread practice of crop residue burning, which releases significant quantities of dioxins. This trend is likely driven by the intensive agricultural activities and the prevalent practice of crop residue burning as a cost-effective method to prepare land for new plantings. Such practices, while economically beneficial in the short term [45,46], release significant quantities of dioxins, which are known for their persistence in the environment and potential to bioaccumulate. High PCDD/Fs emissions are predominantly observed in agricultural regions. For example, South Sumatra and East Jawa have shown consistently high emissions, often exceeding 400 pg/m².

This pattern is influenced by the extensive cultivation and agricultural practices in these regions. In contrast, while East Jawa and Central Jawa also engage in substantial sugarcane cultivation, their emission profiles vary, with some regions showing spikes in certain periods followed by reductions. Regions like North Sumatra and West Jawa consistently exhibit high emission levels, reflecting the spatial distribution of intensive agricultural activities. However, new regions such as Gorontalo have begun to show increased emissions, reaching higher levels in recent years. This indicates a spatial expansion of high emission areas beyond the traditional agricultural hubs. The spatial distribution maps for 2020 and 2021 reveal continued high emissions in key areas, with some fluctuations. Notably, East Nusa Tenggara exhibited significant emission levels despite fewer data points, suggesting sporadic yet high-intensity emission events. By 2022, there was a noticeable decrease in emission levels across most provinces, except for Gorontalo and parts of East Jawa, which remained hotspots for PCDD/Fs emissions. However, higher emission intensity over the areas cultivated with sugarcane showed in spatial distributions of annual emissions (0.1° x 0.1°) specifically monthly emissions in the dry season [12]. Yearly trends on the maps also reveal sporadic peaks in emissions in certain years could be linked to less stringent enforcement of environmental policies or temporary increases in agricultural production demands.

Given that Indonesia contributes 72.81% of the total PCDDs/PCDFs emissions in the air across all inventories in Southeast Asia, trends analyse from 2003 to 2019 [47]. By examining changes over time (from 2016 to 2022), we can identify patterns, such as increasing or decreasing emissions. Furthermore, regions with consistently high emissions emerge as ‘hotspots,’ which may require targeted interventions. Moreover, the broader environmental impact of these emissions cannot be overstated.

3.3. Emission Prediction

Table 4 offers a compelling predicted emission from 2023 – 2028, presenting an upward trend in some areas, while others show fluctuating or stable patterns. The Grey Model GM(1,1) is particularly suited due to often the case with environmental data collected from diverse geographical locations like Indonesia. North Sumatra, regions traditionally intensive in sugarcane cultivation, is predicted to experience a steady increase in PCDD/Fs emissions unlike South Sumatra and Lampung with a slight decline. This trend may be attributed to expanding agricultural activities and possibly stagnant technological advancements in crop residue management. The sustained increase underscores the urgent need for implementing more robust sustainable agricultural practices in these regions. Most region in Jawa Island show gradually increase in their emission projections except for East Jawa that has slight decline from 416 pg/yr in 2023 to 397 pg/yr in 2028. These variations could reflect intermittent enforcement of agricultural burning regulations or periodic shifts in agricultural practices. Such data suggests that policy interventions need to be adaptable and responsive to the changing dynamics of agricultural practices in these provinces. West Nusa Tengggara indicate a substantial increase from 296 pg/yr in 2023 to 381 pg/ year in 2028. East Nusa Tengggara that start to plant sugarcane in 2021 has a gradual decrease. This might be indicating the lack of data as input in grey model also that can be seen from the higher MAPE and MAE. South Sulawesi, experience a significant decline emission in all projected years. While Gorontalo with the highest emissions still projected to have highest increase emission. The grey model resulted varying performance across regions (as shown in Table 6), with certain areas, particularly Jawa Island, demonstrating more accurate predictions than others. Factors such as data availability (including the lack of data in East Nusa Tenggara), model complexity, and local characteristics might influence these results.

Such data suggests that policy interventions need to be adaptable and responsive to the changing dynamics of agricultural practices in these provinces. West Nusa Tengggara indicate a substantial increase from 296 pg/yr in 2023 to 381 pg/ year in 2028. East Nusa Tengggara that start to plant sugarcane in 2021 has a gradual decrease. This might be indicating the lack of data as input in grey model also that can be seen from the higher MAPE and MAE. South Sulawesi, experience a significant decline emission in all projected years. While Gorontalo with the highest emissions still projected to have highest increase emission. The grey model resulted varying performance across regions (as shown in Table 6), with certain areas, particularly Jawa Island, demonstrating more accurate predictions than others. Factors such as data availability (including the lack of data in East Nusa Tenggara), model complexity, and local characteristics might influence these results.

Figure 5 complements these insights by visualizing the spatial distribution of emissions across the provinces, emphasizing the diverse emission trajectories. For instance, Gorontalo is predicted to maintain high emissions, highlighting it as a persistent hotspot. Conversely, regions like South Sulawesi and East Nusa Tenggara exhibit high-emission events despite an overall downward trend, suggesting that localized interventions are necessary to effectively mitigate emissions. This variation across provinces highlights the necessity for targeted and adaptable policy interventions to support sustainable sugarcane agriculture and effectively manage PCDD/Fs emissions in Indonesia.

The forecast data provided by the Grey Model GM(1,1) serves as a valuable tool for policymakers and environmental managers in Indonesia. However, model improvements might be necessary. The results of the model’s performance (Table 6) highlight varying degrees of prediction reliability. Regions like East Jawa and Central Jawa, which demonstrate exceptional prediction accuracy, could serve as benchmarks for refining the model’s accuracy in other regions with less precise predictions. For instance, East Jawa shows highly precise model predictions with the lowest MAPE of 1.4% and an MAE of 6. In contrast, East Nusa Tenggara, which has only two years of data, and South Sulawesi exhibit the highest MAPE values at 100% and 83%, respectively, paired with substantial MAEs of 186 and 143.

Table 6. Grey Model Performance Evaluation of Dioxin Emission Prediction.

Table 6. Grey Model Performance Evaluation of Dioxin Emission Prediction.

	MAPE (%)	MAE
North Sumatra	36	95
South Sumatra	9	27
Lampung	6	26
West Jawa	18	58
Central Jawa	3	12
D.I. Yogyakarta	78	177
East Jawa	1.4	6
West Nusa Tenggara	42	140
East Nusa Tenggara	100	186
South Sulawesi	83	143
Gorontalo	29	129

However, It is recommended to have monthly emissions profiles that can show local agricultural practices (such as varying harvesting times for different crop types) and seasonal conditions (dry or wet). The emission data generated in this study deliver spatially and temporally , holds valuable potential for air quality modelling studies like several studies [48,49]. By leveraging this data, researchers can assess the impact of current and future emissions on ambient air quality.

4. Conclusions

Supplementary Information

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