A Multi-Model Approach to Pollen Season Estimations: Case Study for Olea and Quercus in Thessaloniki, Greece

Abstract

The accurate prediction of the Main Pollen Season (MPS) is crucial for public health and environmental management, particularly for allergenic and highly abundant taxa such as Olea and Quercus. This study presents a comparative evaluation of multiple predictive models for estimating MPS in Thessaloniki, Greece, from 2016 to 2022. The models examined include cumulative temperature-based approaches, Logistic Models (LM), the Distribution Method (DM), and Machine Learning Techniques (MLTs) such as Random Forest, Neural Networks, and Ensemble Learning. The results indicate that Double-Threshold temperature-based (DT) and LM models effectively capture the end of the pollen season, with differences from observed values ranging from 0 to 7 days. Meanwhile MLTs, particularly Random Forest, exhibit high accuracy in predicting its onset of the season, with deviations ranging from 0 to 10 days. Notably, the DT approach, which incorporates transition ranges, enhances the prediction reliability in complex urban environments. These findings contribute to the development of more robust aerobiological forecasting systems, supporting allergen exposure mitigation strategies and agricultural planning in Mediterranean climates. Future research should focus on multifold cross-validation techniques and advanced deep learning models, such as LSTMs (Long Short-Term Memory models), to further refine the prediction accuracy. These advancements would enable the development of more accurate and generalized forecasting models, contributing into a broader modeling system capable of predicting daily pollen concentrations, further supporting real-time pollen forecasting efforts.

1. Introduction

Allergenic pollen poses a significant health risk to sensitized individuals, contributing to respiratory conditions like asthma and allergic rhinitis [1,2,3]. Affecting up to 40% of the global population [4,5], pollen-induced allergies diminish quality of life, lower productivity, and increase healthcare costs [6,7,8]. In Mediterranean countries, Olea pollen is particularly allergenic, often triggering severe reactions [9,10,11,12]. In contrast, although Quercus pollen is generally regarded as having moderate allergenic potential [13,14], it can still trigger symptoms in areas with dense oak populations [15,16], where substantial quantities of pollen are released [17]. Related reactivity with Olea pollen can exacerbate allergic reactions, intensifying the impact on sensitized individuals [18]. Additionally, Quercus pollen often remains airborne for extended periods due to overlapping flowering times among different oak species [19,20]. Economically, these taxa are also vital: olive trees are integral to the Mediterranean economy, particularly due to their role in olive oil production, and their significance makes agricultural planning and effective crop management essential [21,22,23,24,25]. Quercus species similarly hold substantial value, supporting the timber and livestock industries, and contributing to regional economies [26].

Climate change is profoundly effecting the phenology of allergenic plants, leading to shifts in the timing, duration, and intensity of pollen seasons across various taxa and extending the period of allergenic pollen exposure for individuals [27,28,29,30,31,32,33,34]. These shifts are closely influenced by meteorological conditions such as the rising of the temperature, wind and relative humidity, as well as climatological factors like the soil moisture, as well as CO₂ levels, all of which directly affect pollen emissions [35]. For Olea and Quercus, the effects of climate change manifest uniquely due to their specific reproductive requirements. Olive trees, which flower in late spring and have high thermal requirements, respond to increased temperatures with more intense flowering and higher atmospheric pollen concentrations, while they may also flower earlier [36,37,38]. Quercus species show shifts in reproductive timing with warming trends, often flowering earlier in the season [20,39,40] and producing more frequent pollen peaks [41]. Both Olea and Quercus serve as important bioindicators of climate change: The Olea phenology is particularly sensitive to “spring warming” effects due to its dependence on specific thermal thresholds, making it an effective indicator in the Mediterranean basin [38,42,43,44]. Similarly, Quercus pollen data are valuable for monitoring temperature trends and long-term ecological shifts [20,45,46,47]. Together, the phenological responses of these taxa provide essential insights into broader environmental changes driven by climate variability.

Therefore, the monitoring of airborne pollen has garnered significant attention in recent decades. One of the primary objectives in aerobiological research is to develop predictive models that accurately determine the onset of the pollen season, enabling patients to begin treatment before pollination, thereby ensuring effective medication use and the improved planning of daily activities [48,49]. From a modeling perspective, this objective is interpreted as a predictive task aimed at creating optimized forecasting systems for specific pollen taxa, which can be applied in an operational context [50,51,52]. Numerous studies have focused on forecasting the pollen seasons of various taxa [53,54,55,56,57,58,59]. Nevertheless, defining the pollen season is not straightforward, as it depends on the specific context in which it is considered. For instance, if the objective is to determine the existence of airborne pollen grains, in the air, the pollen season can be defined as the period during which at least one pollen grain per cubic meter is detected for any specific taxon [53]. However, this definition does not necessarily correspond to the period in which sensitized individuals experience pollen-related symptoms, as symptom manifestation appears to be dependent on specific pollen concentration thresholds, which remain incompletely defined. Conversely, if the goal is to delineate the timeframe for administering Allergic Immunotherapy (AIT), where available, strict clinical criteria are applied [60]. Consequently, the time periods established for AIT administration are often subsets of those defined by the pollen detection criteria [61]. To delineate the Main Pollen Season (MPS), i.e., the duration of time when pollen is present in the atmosphere in significant concentrations at a location [62], a range of methodologies has been proposed, including those based on temperature thresholds to determine the start and end dates of the season [53,56,63,64,65,66]. In addition, statistical approaches, such as regression [67,68,69] and logistic models [55,70], have been extensively explored in this context. In recent years, Machine Learning Techniques (MLTs), which have been extensively applied to the analysis of air pollutants and their concentrations [71,72], have begun to gain traction in the study of airborne pollen. These methods utilize meteorological parameters and historical pollen data as predictive features. While MLTs have become increasingly popular for predicting pollen concentrations [73,74,75,76,77], their application to the prediction of MPS remains relatively limited [65,78].

Building on the aforementioned methodologies, several studies have compared different approaches for predicting the MPS across various regions and taxa. For instance, predictive models have been applied to birch and grass pollen in Switzerland [79], including statistical models and MLTs such as random forests and neural networks, as well as Poaceae [80] and Ambrosia [68] in France and Quercus in Poland [81], employing multiple regression and temperature sum approaches, including combinations of growing degree day methods [66,82]. This study extends the application of these methodologies by employing the most diverse and comprehensive set of predictive models, applied for the first time to forecast the MPS of Olea (Olea europaea L.) and Quercus in Thessaloniki, Greece. The models utilized include cumulative temperature-based models, a distribution method (DM), logistic models (LM), and MLTs, including an ensemble approach that combines multiple MLTs methodologies. To address the research gap, we pose the following question: which approach most accurately predicts the onset and end of the MPS for Olea and Quercus in Thessaloniki? By comparing the performance of these models, this study aims to enhance the accuracy of MPS predictions and contribute to the refinement of pollen forecasting techniques. The findings may support the integration of predictive models into real-time pollen monitoring systems and inform decision-making processes in public health, exposure mitigation, environmental management, and agricultural planning.

2. Materials and Methods

The Materials and Methods section includes several subsections. The Materials are detailed in Section 2.1. Area of Study, which explicitly describes the geographical characteristics and climatic conditions of the study area, as well as the pollen spectrum and the abundance of Olea and Quercus trees in the region, and Section 2.2. Pollen and Meteorological Data, where the variables and data sources used in this study are thoroughly explained. Regarding the Methods, Section 2.3. Predictive Models of MPS presents the modeling approaches employed to forecast the Main Pollen Season (MPS), including cumulative temperature models (Section 2.3.1), the Distribution Method (Section 2.3.2), Machine Learning Techniques (Section 2.3.3), and Logistic Models (Section 2.3.4).

2.1. Area of Study

Thessaloniki, located in the northern part of Greece, is the country’s second-largest city, the administrative center of the region of Central Macedonia, and a major cultural and economic hub in the wider Eastern Mediterranean region [83,84], with a population of around 1 million residents (2023, [85]). Geographically, Thessaloniki is positioned at 40.64° N and 22.94° E. Covering an area of approximately 93 km², it is one of the most densely populated cities in Europe [86]. It is bordered by the Thermaikos Gulf to the south, Mount Chortiatis to the north, and the Seich Sou forest to the northeast, giving the area a diverse topography that results in various microclimates and a range of vegetation [87].

The climate in Thessaloniki is typically Mediterranean, characterized by hot, dry summers and mild, rainy winters, while the urban heat island effect further influences the city’s local conditions [88,89]. The prevailing winds generally blow from the northwest and southeast (Figure 1c). The average annual temperature is 16.35 °C, with 2015 being notable in studied years for having both the highest (20.29 °C) and the lowest (10.88 °C) mean temperature (Figure 1b). These climatic conditions support the growth of plant taxa that contribute to the region’s airborne pollen [90,91,92].

The pollen spectrum in Thessaloniki is heavily influenced by a variety of plant taxa, with Cupressaceae being the most dominant contributor (23.2%). Other significant sources include Quercus (20.8%), Urticaceae (10.8%), and Olea (7.6%), which are among the top contributors to the overall pollen load in the region [40]. The Olea pollen, in particular, is known for its high allergenic potential and is a common trigger for allergic reactions among the local population (31.8%) [9]. A positive trend has been observed in the annual variation of airborne pollen levels in Thessaloniki, including notable increases in Olea and Quercus species [93].

The olive trees are extensively cultivated in large areas in the region of Halkidiki, located southeast of Thessaloniki, as well as along the coastal zone to the west of the city, in relation to the Annual Available Pollen (AAP), which defines the amount of pollen produced per vegetation biomass per year [51,67] (Figure 2a). Therefore, studying olive trees is crucial, not only because of their allergenic properties, but also due to the prospect of the long-range transport of their pollen grains [94]. In contrast, oak trees are more abundant in the greater Thessaloniki area compared to olive trees, with the highest AAP recorded in the nearby mountainous regions (Figure 2b). The widespread presence of these taxa underscores the importance of monitoring and understanding their impact on the air quality and public health.

2.2. Pollen and Meteorological Data

Airborne pollen collection in Thessaloniki has been continuously conducted since 1987 using a 7-day Hirst-type volumetric sampler [97] located on the rooftop of the Biology School at Aristotle University of Thessaloniki, positioned approximately 30 m above ground level (40°38′00″ N, 22°57′26″ E), and operated by the Department of Ecology [40,98]. This device, following the European Aerobiology Society’s (EAS) guidelines by the standard method EN16868:2019 [99] and the minimum requirements of the European Aeroallergen Network (EAN) for pollen monitoring described by Galán (2014) [100], ensures consistent and reliable data collection. The data are expressed as daily pollen concentrations (pollen grains/m³), providing detailed and accurate records that are vital for understanding pollen dynamics in the Thessaloniki area.

Daily pollen concentrations from 2016 to 2022, with the exception of 2018 due to unavailable data, were provided by the Municipality of Thessaloniki (MoT (https://envdimosthes.gr/fisika-aerioallergiogona/, accessed on 8 January 2025)). To determine the MPS, the methodology of Wozniak and Steiner (2017) [67] was applied, which filters out minor signals from the dataset potentially caused by counting errors. This was followed by the implementation of the 95% method [101], which defines the MPS as the period during which 95% of the annual pollen total is recorded. Specifically, the MPS begins when 2.5% of the cumulative annual pollen concentration is reached and ends when 97.5% is achieved. This method provides a reliable basis for analyzing the phenological patterns of airborne pollen.

Meteorological data for this study were sourced from ERA5 (https://cds.climate.copernicus.eu/datasets/reanalysis-era5-single-levels?tab=overview, accessed on 8 January 2025), the latest reanalysis product from the European Center for Medium-Range Weather Forecasts (ECMWF), which provides a detailed global record of atmospheric, terrestrial, and oceanic variables from 1950 to the present [102,103] in a resolution of 0.25° × 0.25°. This research utilized hourly and daily predictor variables from ERA5 spanning 2015–2022 (

Table 1. Meteorological and cyclical parameters from European Center for Medium-Range Weather Forecasts (ECMWF) used in the MPS predicting models.

	Variable Name	Unit
Meteorological	2 m mean, minimum, and maximum temperature	°C
	2 m dew point temperature	°C
	10 m U wind component	ms−1
	10 m V wind component	ms−1
	Total precipitation	mm
	Soil temperature level 1	°C
	Total cloud cover	0–1
	Total column water	kg m−2
	Surface air pressure	Pa
	Mean surface downward short-wave radiation flux	Wm−2
Cyclical	Season	1, 2, 3, 4
	Month	1, 2, …, 11, 12
	Week	1, 2, …, 52, 53
	Day of Year	1, 2, …, 365, 366

). Cyclical (temporal) variables were transformed using sine and cosine functions. The wind speed and direction were derived from the 10 m U and V wind components, with the direction also expressed through sine and cosine transformations [104]. The photoperiod was calculated based on the latitude, date, solar declination, and hour angle at sunrise [105], while daily sunshine hours were estimated by multiplying the photoperiod by the fraction of clear sky, determined by the total cloud cover variable. The relative humidity was computed as the ratio of actual vapor pressure (from 2 m dew point temperature) to the saturation vapor pressure (from 2 m mean temperature) [106]. Rainfall duration per day was determined by counting each hour with precipitation exceeding a zero value, thereby yielding the total daily hours of significant rainfall.

2.3. Predictive Models of MPS

A range of predictive models were employed to forecast the MPS for olive and oak trees. Cumulative temperature models (Section 2.3.1), along with DM (Section 2.3.2), MLTs (Section 2.3.3), and LM (Section 2.3.4), offered insights into seasonal pollen dynamics. Together, these approaches enhance the predictive accuracy for pollen season timing.

2.3.1. Cumulative Temperature Approaches

The prediction of the MPS for various pollen taxa has been advanced by utilizing temperature-based methods. Linkosalo et al. (2010) [63] developed a phenological model focused on predicting the main flowering period and pollen release intensity by using a double-threshold temperature (DT) sum approach. This model employs cumulative temperature thresholds that mark both the start and end of the pollen release, thereby allowing for the estimation of the full flowering duration and daily pollen release intensity based on thermal accumulation. The model calculates a cumulative temperature sum, starting from a fixed date (t₀), to estimate the ontogenetic stage of bud development, as determined by Sarvas (1972) [107]. The model specifies two key thresholds: S₁ (°C), marking the onset of the pollen release, also mentioned as SCRIT, and S₂ (°C), indicating its ending. The cumulative pollen release on any given day t, R(t), is calculated based on the temperature sum S(t) accumulated by that day.

$$\mathrm{R}\left(\mathrm{t}\right)={\displaystyle \frac{\mathrm{S}\left(\mathrm{t}\right)-S_1}{S_2-S_1}}$$

(1)

where S(t) is the cumulative temperature from the starting date t₀ up to day t, and the parameters S₁, S₂, and t₀ are optimized using empirical data. This DT model is particularly suited for species with extended flowering periods, where flowering and pollen release can last up to several weeks. It allows not only for the prediction of the onset, but also for the duration of the pollen release by incorporating daily temperature variations.

The model of Sofiev et al. (2013; 2017) [52,64] refines the DT sum approach initially developed by Linkosalo et al. (2010) [63] to provide a more nuanced prediction of the pollen season onset and duration. While it retains the core principles of cumulative temperature thresholds to determine the start and end of the pollen season, the model introduces several modifications aimed at improving the model’s accuracy and adaptability to different climatic conditions.

One of the main enhancements is the addition of a gradual initiation mechanism known as the flowering spin-up period. In contrast to Linkosalo et al. (2010) [63], where the pollen release starts immediately once the first temperature threshold is reached, Sofiev et al. (2013) [64] introduces a transition range, known as δH, which allows for a smoother start to the season. The pollen release begins to intensify as the cumulative temperature approaches the initial threshold H_fs, but it gradually ramps up over the next few days. This process is managed using a blurring function, which adjusts the pollen release intensity across this transitional range. The spin-up mechanism accounts for regional variability in flowering initiation and helps prevent sudden changes in pollen concentrations, thereby offering a more realistic simulation of pollen season onset. The model also applies a similar blurring technique for the end of the pollen season. Rather than ending the pollen release abruptly when the second threshold is reached, the model allows for a gradual decline. This is controlled by an additional parameter, δN, which represents the uncertainty in the pollen release as the season draws to a close. By providing a tapered end to the season, the model can better reflect the prolonged pollen release observed in many taxa, which often continues at reduced levels toward the season’s end. Finally, the model includes a calibration process that refines the start and end thresholds based on multi-annual pollen and temperature data, enabling both regional and temporal customization. The starting H_fs and ending thresholds H_fe are calibrated against cumulative pollen count data, ensuring that model parameters accurately reflect local flowering conditions. This fitting procedure enhances the model’s adaptability across diverse climates and taxa.

In addition to the cumulative temperature approaches, the Cordero et al. (2021) [65] method offers an alternative approach to predicting the MPS by utilizing the concept of the state of forcing heat (Sf). This cumulative measure of daily temperatures above a set threshold T_b, expressed in non-dimensional forcing units, quantifies cumulative heat as a driver for biological processes like bud growth and pollen release, and it has been widely applied for determining the start of the pollen season. Sf is calculated as follows:

$$Sf\left(t\right)=\sum _{i=1}^{n}f\left(T_{avg}\left(i\right),d,c\right)$$

(2)

where T_avg denotes the daily average temperature, n represents the cumulative number of days up to day t starting when T_avg > T_b, and d and c are parameters with negative and positive values, respectively. When T_avg falls below c, the contribution to Sf is minimal, but it rises substantially on days when it exceeds c.

The base temperature T_b is first computed as the average temperature over all of the years, representing the conditions just before the pollen season onset. An initial Sf is calculated, followed by a non-linear least square fit to fine-tune parameters c and d. This optimization minimizes the Mean Absolute Error (MAE) between the observed and predicted Sf values, allowing the identification of a critical Sf threshold that marks the start of the pollen season, known as the day of year (DOY) when Sf reaches this critical value. By fitting these parameters, the method enables a precise prediction of MPS onset based solely on daily temperatures, offering a robust means of forecasting the timing of the pollen release.

Base and/or threshold temperatures essential for predicting phenological stages, such as the MPS, can vary widely based on the regional climate and the specific ecological and geographical traits of the area under investigation [54]. For olive trees, temperature thresholds are critical, as shown by extensive studies in the Mediterranean region, particularly the Iberian Peninsula, where these range from 0 °C to 12.5 °C [38,108,109,110]. Meanwhile, due to limited data, a base temperature of 5 °C has been adopted for Olea in this study. This selection represents a mid-range value well-suited for the thermal requirements of olive trees in temperate climates and is consistent with prior studies on similar taxa in Mediterranean climates, such as Galán (2005) [54], Tesar (1984) [111], Frenguelli et al. (1989) [112], and Alba and Díaz De La Guardia (1998) [113]. For Quercus, studies suggest a base temperature threshold typically between 6 °C and 11 °C, based on extensive work in Spain and other Mediterranean regions [48,114]. Specific studies on Quercus robur and Quercus pyrenaica, for instance, highlight that these thresholds are aligned with the tree’s phenological responses to temperature cues, which trigger pollen release and flowering events after dormancy [19,115]. The base temperature for oak trees in this study has been set at 3.5 °C. This choice aligns with the thermal requirements for bud development and subsequent pollen release, and is consistent with base temperatures used for similar forest species across Mediterranean climates, where heat accumulation following dormancy is essential, as supported by Sofiev et al. (2013) [64].

2.3.2. Distribution Method (DM)

The DM, as outlined by Wozniak and Steiner (2017) [67], is a phenological modeling approach that utilizes Gaussian distribution to simulate the pollen release over time. This approach is particularly suitable for species with identifiable start and end points in their MPS. The method uses observed pollen counts to construct a Gaussian curve that reflects the daily release of pollen, with the peak representing the day of the maximum pollen concentration. In this model, the mean and half-width of the Gaussian curve determine the overall shape and duration of the pollen season. These parameters are empirically derived from observed data, allowing the model to adapt to various taxa with different seasonal timings.

The start day of the year (sDOY) and end day of the year (eDOY) for the MPS are calculated using historical pollen data and the percentage method (Section 2.2). Once the sDOY and eDOY are identified, the Gaussian curve is used to model the pollen emission cycle. Linear regressions based on the Previous-Year Annual Average Temperature (PYAAT) are utilized to refine the prediction of sDOY and eDOY, with the temperature serving as a primary explanatory variable. This temperature-based adjustment is crucial for predicting seasonal shifts and accounting for climatic variability from one year to the next. The fit parameter a is introduced in the Gaussian function to convert empirical phenological dates based on pollen count thresholds into a standardized emission curve. This parameter adjusts the width of the curve to accurately reflect the intensity and duration of the pollen season and is set to a value of 3 [51]. By calibrating the model to observational data, the DM provides a predictive framework for assessing both the onset and ending of the pollen release, making it a valuable tool for forecasting pollen exposure and understanding seasonal pollen dynamics.

2.3.3. Machine Learning Techniques (MLTs)

For predicting the onset and ending of the MPS, several MLTs were employed, including Artificial Neural Networks (ANNs), a Multi-Layer Perceptron (MLP), Naive Bayes (NB), a Random Forest (RF), Linear Discriminant Analysis (LDA), and an Ensemble approach. In addition, ANNs and a Light Gradient-Boosting Machine (LightGBM) were used specifically for predicting the peak of the pollen season, due to their capability to model non-linear relationships and capture complex temporal patterns. The models were trained using two distinct approaches. The Simple Training Approach involved training the models on all available data, except for the final year, which was reserved for testing [116]. In contrast, the Walk-Forward Approach trained the models on data from two consecutive years and then tested them on the subsequent year [117,118,119]. This process was repeated iteratively for the subsequent two years to enhance the generalization of the model and evaluate its robustness over time. In addition, the sine of the Julian day was included as a feature to capture the seasonal periodicity of the pollen release during testing.

A Genetic Algorithm (GA) was applied in this study for feature selection and model optimization, as selecting relevant input variables is essential for improving the model performance. Irrelevant or noisy features can negatively impact the training process, leading to a complex model structure with poor generalization capabilities. Genetic algorithms, which are heuristic optimization techniques, have proven effective in air quality forecasting applications and work by identifying optimal solutions based on an objective function [74,120,121,122]. In a GA, a population of potential solutions, represented as binary-encoded feature subsets, is initialized randomly. This population evolves through genetic recombination, selection, and mutation, whereby fitter individuals are chosen to produce the next generation, while less fit ones are replaced. Over successive generations, individuals that better approximate the solution are selected, with the process continuing until a predefined stopping criterion, such as a maximum number of generations, is reached. To further enhance the model performance, hyperparameter tuning was conducted using GridSearchCV from Scikit-learn (https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html, accessed on 8 January 2025). While the GA optimized the feature selection, GridSearchCV systematically explored different hyperparameter combinations to identify the optimal settings for each model. Hyperparameter tuning is crucial, as suboptimal choices can lead to overfitting, underfitting, or inefficient learning. Each combination of hyperparameters was evaluated through cross-validation, ensuring that the best configuration was selected based on performance metrics such as the Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE).

ANNs are computational models inspired by biological neural networks, consisting of interconnected layers of nodes or “neurons”. They are widely used in predictive modeling for their ability to capture complex, non-linear relationships within data, allowing them to adapt to patterns effectively. These models are well-suited to handle large datasets and can achieve high predictive accuracy when appropriately configured and trained [71,78,123,124,125]. These networks typically contain an input layer, one or more hidden layers, and an output layer. In this study, a Deep Feedforward Neural Network (DFNN) was initially used in Python 3.0, which included, after tuning, 8 input layers, 300 hidden layers with the ReLU (Rectified Linear Unit) activation function, and a single output layer with a sigmoid activation function. The network was trained over 500 epochs with a batch size of 64, using a validation split of 30%, and the Stochastic Gradient Descent (SGD) optimizer. MLP is another type of ANN with fully connected layers, where each neuron in one layer is connected to every neuron in the following layer. MLP is effective for supervised learning tasks and is commonly applied in classification and regression problems. For this study, the MLP was configured with a maximum of 1000 iterations and a fixed random state to ensure reproducibility. Both ANNs (the DFNN and the MLP) learn by adjusting weights across their layers through backpropagation, which minimizes the error between predicted and actual outcomes over multiple iterations [126,127].

NB is a probabilistic classifier based on Bayes’ theorem [128], assuming conditional independence between features that are used for their simplicity, interpretability, and efficiency, especially in classification tasks [129,130]. This method is particularly effective for high-dimensional data, where each feature contributes independently to the outcome. For this study, a Gaussian Naive Bayes model was implemented with cross-validation (cv = 5) and accuracy as the scoring metric. RF, on the other hand, is an ensemble learning method that constructs multiple decision trees during training and outputs the mode of the classes (classification) or mean prediction (regression) of individual trees. By averaging the results of many trees, RF models enhance the predictive accuracy and reduce overfitting [131,132]. The RF configuration included a step size of 1, and five-fold cross-validation. Each tree is built from a random subset of the training data, which provides robustness to noise and improves generalization. RF models excel in handling non-linear data structures and can provide feature importance scores, helping to identify the most influential variables for prediction tasks [127,133,134].

LDA is a widely used classification technique that identifies linear combinations of features to optimally separate two or more classes. Particularly effective when data distributions are close to Gaussian, LDA works by developing a discriminant function that maximizes the ratio of between-class variance to within-class variance, thus establishing robust decision boundaries. This approach results in a latent variable, called a canonical variate, which serves as the primary axis for class separation. For a dataset with k classes, LDA can calculate up to k − 1 canonical functions, each enhancing the discrimination between defined categories [127,135]. This method’s ability to highlight class differences makes it well-suited for capturing distinct seasonal phases within the data [136]. LightGBM captures non-linear relationships and is highly effective with complex features. Its unique leaf-wise tree growth with depth constraints allows for the efficient handling of sharp changes in pollen counts, which are critical for accurately identifying peak periods. As an ensemble method in itself, LightGBM combines several boosted decision trees to generate predictions, enhancing its robustness and predictive power [65,137]. In addition, an ensemble model was constructed by combining the predictions from all MLTs used. The ensemble approach averaged the predictions, providing a balanced forecast that capitalizes on the strengths of each model. This consensus-based approach minimizes the limitations of individual models, leading to improved accuracy and robustness in predicting the timing and intensity of the MPS [50].

2.3.4. Logistic Models (LM)

The LM by Ribeiro et al. (2007) [70] and Cunha et al. (2015) [55] utilize non-linear logistic regression to predict pollen season dynamics by modeling the cumulative pollen emission over time. Both models employ a logistic growth curve to represent the seasonal progression of pollen release, fitting parameters that allow for the identification of key phenological dates, such as the beginning and ending of the MPS.

Ribeiro’s (2007) [70] model is specifically focused on allergenic pollen and calculates the MPS by applying a sigmoid function to the accumulated daily airborne pollen concentration, thereby creating a smooth progression between the start and end of the season. The model equation is defined as:

$$y\left(t\right)=a{\displaystyle \frac{1}{1+e^{-\beta (t-\gamma )}}}+\epsilon \left(t\right)$$

(3)

where y(t) represents the cumulative pollen amount up to day t. In this equation, α denotes the difference between the upper and lower asymptotes, indicating the total annual pollen concentration, while β expresses the accumulated pollen concentration influencing the timing of the MPS, and γ marks the inflection point (IP) where the pollen release rate is at its maximum. The first derivative of the model equation gives the value of the IP (Equation (4)). The error term, ϵ(t), accounts for random variation. Ribeiro et al.’s (2007) [70] model determines the start and end of MPS by fitting a logistic curve to the accumulated pollen data and identifying points where the cumulative pollen concentration diverges significantly from the curve’s asymptotes.

$$\left(IP\right)=\left(-{\displaystyle \frac{\widehat{\beta }}{\widehat{\gamma }}};{\displaystyle \frac{\widehat{\alpha }}{2}}\right)$$

(4)

In contrast, Cunha et al. (2015) [55] developed a logistic model, originally within the context of viticulture, but adaptable to pollen modeling, which similarly uses a logistic function to capture cumulative pollen emissions. However, it includes distinctive features that differentiate it from Ribeiro et al.’s (2007) [70] approach. An added layer to the model is its reliance on second and higher-order derivatives of the logistic function, which enables the model to estimate the acceleration and deceleration of the pollen release throughout the MPS. By examining these higher-order derivatives, the model can identify where the pollen release transitions from rapid growth to stabilization, providing more granular insights into pollen season dynamics. In addition, the model incorporates environmental variables such as temperature and precipitation, which influence the shape of the pollen release curve. This refinement allows the model to account for inter-annual climatic variability, making it more adaptive to changes in local conditions.

3. Results

3.1. Pollen Season Analysis

For the studied period (2016–2022), Figure 3 presents the time series of the Olea and Quercus daily pollen concentrations in Thessaloniki, Greece. The MPS for Olea typically begins from mid-to-late March and ends in early June. The highest daily pollen concentration during the studied period was recorded in 2019, with a peak value of 152 pollen grains/m³ on May 28. This peak appears to be an isolated incident and no consistent diurnal pattern in the Olea pollen concentrations was observed across the years [138]. In contrast, the lowest peak concentration occurred in 2021, reaching only 28 pollen grains/m³. The Olea pollen peak commonly occurs during the second half of May, as also suggested by Tasioulis et al. (2022) [61]. The earliest onset and simultaneous earliest ending of the MPS were observed in 2022, with the season starting on April 2 and ending on June 10, resulting in a duration of 69 days. In comparison, the shortest MPS was recorded in 2017, lasting only 55 days.

The Quercus MPS, compared to that of Olea, starts and ends slightly later, typically extending from mid-April to mid-June. As one of the most abundant pollen taxa in Thessaloniki [40], Quercus exhibited high daily concentrations during the studied period, with the highest values recorded in 2016 (670 pollen grains/m³) and 2021 (654 pollen grains/m³) [139]. The peak concentrations for Quercus commonly occur near the end of April. The lowest recorded concentrations occurred in 2022, with a peak of only 142 pollen grains/m³. The longest MPS was observed in 2016, lasting 55 days from March 23 to May 17. In contrast, the shortest season was recorded in 2017, with an MPS duration of only 38 days.

3.2. Performance of Predictive Models for MPS

Table 2. Observed (Obs.) and predicted DOYs for the start and end of the MPS for Olea (Ol.) and Quercus (Quer.) during the study period (2016–2022). Predictions were generated using DT approaches from Linkosalo (2010) [63], Sofiev (2013) [64], and Cordero (2021) [65], DM from Wozniak and Steiner (2017) [67], and LM approaches from Ribeiro (2007) [70] and Cunha (2015) [55].

		MPS
		2016		2017		2019		2020		2021		2022
Start		Ol.	Quer.	Ol.	Quer.	Ol.	Quer.	Ol.	Quer.	Ol.	Quer.	Ol.	Quer.
	Obs.	94	83	100	95	99	102	98	105	89	97	92	111
	DTa	88	91	101	104	99	98	102	104	95	100	110	113
	DTb	85	84	100	99	102	98	101	100	93	93	108	108
	DTc	97	83	105	89	116	116	120	102	119	93	99	98
	DM	92	86	95	100	96	103	96	103	95	101	95	97
	LMa	90	81	97	94	95	95	97	103	90	105	91	108
	LMb	95	96	107	96	114	104	97	109	90	115	96	111
End
	Obs.	142	138	155	133	157	150	154	149	151	147	161	158
	DTa	145	138	153	147	155	149	157	149	152	146	156	151
	DTb	140	140	151	132	155	148	153	152	150	143	158	159
	DTc	153	135	151	144	156	150	160	145	154	149	157	146
	DM	144	139	154	146	156	148	156	148	155	147	152	145
	LMa	145	140	159	135	157	152	152	149	148	146	158	160
	LMb	144	133	151	135	154	156	150	147	154	150	163	148

DT_a [63], DT_b [64], DT_c [65], LM_a [70], LM_b [55]. Bold values indicate predictions within ±2 days of the observed DOYs.

presents the analysis of various predictive models for estimating the DOYs corresponding to the start and end of the MPS for Olea and Quercus. The observed values (Obs.) are included for comparison with the predicted values from each model, highlighting the accuracy of the models in forecasting the pollen seasons. The predictive approaches applied in this analysis include DT, DM, and LM models, which are evaluated across the entire study period (2016–2022).

The performance of the predictive models for determining the start and end of the MPS for both Olea and Quercus shows notable variations compared to observed values. The models generally capture the inter-annual variability of the MPS, but exhibit varying degrees of accuracy depending on the model and the specific taxon. The deviations between the predicted and observed start dates range from zero days to a maximum of ±30 days across all models and years. For Olea, the models demonstrate a better performance in predicting the end of the MPS than the start. The DT_b model, in particular, exhibits the closest alignment with observed values for the start date, while the DM and LM_a models show the best performance for predicting the end date. The largest discrepancies occur with the DT_c model, which tends to overestimate the start of the MPS. For Quercus, the models perform more consistently for both the start and end of the MPS. The DT_b and DM approaches yield the most accurate predictions for the start date, while the DM and LM_a models provide better estimates for the end date. The smallest discrepancies are observed in the DT_b model. However, the DT_c model again shows the largest deviations, particularly overestimating both the start and end of the MPS for several years.

For the DT_a and DT_b approaches, two thermal thresholds were used to estimate the start and end of the MPS for Olea and Quercus. For Olea, the threshold for the start (S₁/H_fs) is 463 °C, while the threshold for the end (S₂/H_fe) is 1139 °C. For Quercus, the corresponding thresholds are 490 °C for the start and 1037 °C for the end. In the DT_b approach, the transition range (δH), which represents the duration of the flowering spin-up, was estimated at 6% for Olea, with the transition range for cumulative forcing (δN) set at 20%, in accordance with the study by Sofiev (2013) [64]. For Quercus, δN remains at 20%, while δH was calculated at 8%. Regarding the DT_c approach, the mean base temperature (T_b) across all studied years was determined to be 16.43 °C. The fitted parameters, optimized through a non-linear least square algorithm, were set at c = 16.93 and d = −6.06 for Olea, and c = 15.42 and d = −6.35 for Quercus. Additionally, the critical state of forcing heat (Sf_critic) was calculated to be 0.1 forcing units for Olea and 1.17 forcing units for Quercus.

Regarding the LM approaches, the parameters obtained for each year (

Table 3. Estimated parameter values for the MPS of Olea and Quercus using LM approaches, including the parameter estimates (α, β, γ), the coefficient of determination (R²), and the IP coordinates (x, y) for each year.

		Parameters Estimates				IP
Taxon	Year	α	β	γ	R2	x	y
Olea	2016	354.89	−20.59	0.15	0.99	130	177
	2017	250.01	−27.38	0.20	0.99	140	125
	2019	500.52	−34.58	0.24	0.99	144	250
	2020	353.24	−14.23	0.11	0.99	129	177
	2021	270.28	−13.72	0.10	0.99	132	135
	2022	288.22	−13.85	0.09	0.98	141	144
Quercus	2016	4647.77	−23.62	0.22	0.99	107	2324
	2017	4104.12	−21.57	0.19	0.99	108	2052
	2019	2681.33	−15.20	0.12	0.99	123	1341
	2020	2026.19	−25.29	0.21	0.99	121	1013
	2021	5916.88	−30.06	0.24	0.99	125	2958
	2022	1145.02	−25.82	0.21	0.99	121	573

) from Equation (3), along with the coefficient of determination (R²) and the Inflection Point (IP) from Equation (4), were essential for the determination of the MPS. The models explained more than 98% of the observed variation in pollen season timing across the study period. Notably, the parameters exhibited inter-annual variability, particularly for Olea. Furthermore, the parameters β and γ demonstrated comparable statistical behavior across both taxa, indicating similar underlying dynamics in the modeled processes.

The graphical representations of the adjusted pollen emission models using the one-derivative approach [70] are shown in Figure 4a,b. These figures illustrate the accumulated pollen curves across all studied years, demonstrating that the model effectively captures inter-annual variability in pollen emissions for both taxa, including the highest and lowest recorded emission rates. In Figure 4c,d, the corresponding adjusted curves obtained from the four-derivative method [55] are presented. These figures provide a representative example of the years with the highest pollen concentrations, specifically 2019 for Olea and 2016 for Quercus.

In addition to the predictive methods outlined in Table 2,

Table 4. Observed DOYs and predicted deviations from observed values using MLTs for the start and end of the MPS for Olea and Quercus.

Taxon			MPS
	Start		Obs.	DFNN	MLP	NB	RF	LDA	Ensemble
Olea		‘22	92	+3	+5	−2	+3	+2	−1
		sin ‘22		+1	−2	−1	−1	+1	0
		Walk-Forward
		‘19	99	−3	0	0	0	+8	+1
		sin ‘19		+9	0	−7	−5	+5	−7
		‘22	92	−2	−2	−2	0	−5	−2
		sin ‘22		+1	−3	+2	−4	−1	−1
Quercus		‘22	111	−5	−4	−6	+3	+11	−4
		sin ‘22		+6	+3	+1	+5	−9	+1
		Walk-Forward
		‘19	102	−2	−5	−4	−6	−10	−6
		sin ‘19		−2	−3	−3	−10	−8	−5
		‘22	111	−1	+2	−6	−1	−2	−4
		sin ‘22		−3	+2	−3	+3	−10	−2
	End		Obs.	DFNN	MLP	NB	RF	LDA	Ensemble
Olea		‘22	161	+4	+1	−8	−5	−1	−2
		sin ‘22		−3	−5	−10	−7	0	−5
		Walk-Forward
		‘19	157	−1	−7	−3	−5	−5	−4
		sin ‘19		−1	+3	−6	−8	−2	−3
		‘22	161	+6	−1	−5	−7	+2	−1
		sin ‘22		−2	0	−8	−1	−2	−3
Quercus		‘22	158	−7	+8	−10	−7	−12	−9
		sin ‘22		+5	−7	−7	−9	−9	−6
		Walk-Forward
		‘19	150	−4	−1	−5	−6	−9	−5
		sin ‘19		−4	−1	−4	−9	−7	−5
		‘22	158	−4	+2	−4	−2	−11	−4
		sin ‘22		−5	−3	−3	−7	−9	−6

Bold values indicate predictions within ±2 days of the observed DOYs.

presents the results from the application of MLTs, incorporating five distinct methods: DFNN, MLP, NB, RF, and LDA, as well as an ensemble model combining these approaches. The table illustrates a straightforward predictive approach, where the year 2022 (denoted as ‘22) is used for validation, while the models are trained on data from the years 2016 to 2021. Additionally, the sine transformation of the Julian day is included as an extra feature in the models to assess its impact on the prediction accuracy, referred to as sin ‘22 in the table. Beyond the simple approach, a walk-forward validation method is also employed, as described in Section 2.3.3. This approach allows for the continuous model adaptation and evaluation across different years.

The performance of the MLTs (Table 4) in predicting the start and end of the MPS for Olea and Quercus shows variability across the models. For Olea, the ensemble method consistently provides the most accurate predictions for both the start and end of the pollen season, showing minimal deviations from observed values across all approaches, including the walk-forward validation and sine-transformed models. The NB and RF methods also perform well, particularly for the start of the MPS, with deviations generally smaller compared to other models. Conversely, the MLP and LDA approaches show larger deviations in certain years, indicating a lower predictive accuracy for some periods. For Quercus, the RF model demonstrates the highest accuracy in predicting both the start and end of the MPS across most validation approaches. The ensemble method also performs well, particularly in minimizing errors for the start dates. However, the LDA and NB show larger deviations, especially for the end of the seasons, indicating less reliable predictions for this taxon. The inclusion of the sine-transformed Julian day as an additional feature enhances the performance of most models, particularly in reducing deviations for the start dates in both taxa.

Following the application of MLTs, Figure 5 presents the predicted peak DOYs for the MPS using DFNN and LightGBM models. The predictions are shown for both the simple and walk-forward approaches, enabling a comparative assessment of the model performance. The comparison between the predicted and observed peak DOYs indicates that the LightGBM model outperforms DFNN for both Olea and Quercus, closely aligning with the observed values and demonstrating smaller deviations, though slightly larger for Quercus than for Olea. The DFNN model, while providing reasonably accurate predictions, exhibits larger deviations, with discrepancies reaching up to 10 days, which is suboptimal for precise forecasting. However, both models show minimal deviations of ±2 days in certain cases, suggesting a good predictive accuracy in years with regular seasonal patterns. The superior performance of LightGBM compared to DFNN may also be attributed to its robustness with smaller, structured datasets. In contrast, DFNN likely requires larger and more diverse datasets to generalize effectively, which may explain its higher variability in the prediction accuracy.

4. Discussion

The accurate prediction of the MPS for taxa, such as Olea and Quercus, is essential for both public health management and agricultural planning. The application of both traditional phenological models and MLTs in this study demonstrates the importance of using diverse approaches to capture the variability in pollen season timing. The results highlight that different models exhibit varying levels of accuracy depending on the taxon and the specific phase of the pollen season being predicted.

Among the applied methods, the DT_b approach demonstrated a strong performance for both Olea and Quercus, particularly in predicting the end of the MPS, with deviations ranging from 0 to 7 days, making it one of the most reliable models in this study, compared to past research in the Mediterranean, which reported an average prediction error of 10 days [52]. For Olea, this improved accuracy in predicting the end of the season may be attributed to the fact that the peak pollen concentrations typically occur after the midpoint of the season (Figure 3), while the start of the season is characterized by lower, more sporadic daily pollen counts. The DT_b approach outperformed the simpler DT_a model due to the incorporation of transition ranges, which enhanced the model’s ability to account for gradual changes in pollen emission dynamics. This modification allows DT_b to better capture the variability of the pollen season, especially in complex urban environments like Thessaloniki. Figure 6a presents a detailed comparison between the observed and predicted pollen concentrations for Olea in 2019, utilizing the DT_b approach. This particular year was selected for analysis as it exhibited the highest pollen concentrations among all studied years. The time series analysis reveals minor discrepancies in the timing of the onset and conclusion of the pollen season, with the most pronounced deviations occurring at the beginning. Notably, in 2022, the predicted start of the season differed, highlighting the challenges associated with modeling early-season dynamics (Figure 6b). These results emphasize the capability of DT_b in handling the complexities of late-season predictions, while also pointing to the need for further refinements to improve its accuracy in capturing the onset of the pollen season.

The DM approach, while effectively capturing the end of the Olea MPS with a maximum deviation of +5 days and the start of the Quercus MPS with +7 days, requires a longer time series of daily pollen concentrations and more geographically diverse study sites to be considered a robust and reliable method for MPS prediction. Longer datasets would help account for the influence of PYAAT and better reflect the impact of the temperature and climate change on these taxa. The absence of extended time series data limits the optimization of critical parameters, such as c and d in the state of the forcing heat method (DT_c), which currently shows a poor performance in predicting the MPS for Thessaloniki. These findings contrast with studies conducted in Madrid, where 22 years of pollen data were available [65], and in the United States, where the DM approach was tested across 96 sites using only 7 years of data [67]. The geographical diversity and longer time series in these studies likely contributed to more reliable results. Therefore, to fully evaluate the performance and reliability of the DM and DT_c approaches in Thessaloniki, the availability of a larger and more comprehensive dataset would be essential.

Alongside the DT_b approach, the LM_a model also performs satisfactorily for both Olea and Quercus (Table 2), demonstrating a superior performance compared to the LM_b model, which can delay the start of the season by up to 18 days. In contrast, a study conducted in Portugal reported deviations ranging from 5 to 10 days, though it was based on a longer study period of up to 19 years [55]. This outcome suggests that incorporating additional derivatives does not significantly enhance the accuracy of predicting the onset and end of the pollen season. Instead, higher-order derivatives may be more relevant for modeling specific phenological phases of the trees rather than seasonal pollen dynamics. In the present case, the use of a single derivative proves sufficient for accurate predictions. The satisfactory performance of the LM_a model is further illustrated in Figure 7, which depicts the time series of observed and predicted daily pollen concentrations for Quercus in 2016, the year with the highest recorded values. The figure highlights the model’s ability to closely align with the observed values, underscoring its reliability for the MPS prediction in the studied taxa.

The parameters of the models are inherently influenced by the climatic conditions of the sampling site, as these conditions strongly shape the behavior of the MPS (Table 3). The parameter α reflects the total pollen emissions, representing local pollen dynamics and the total annual pollen amount of each taxon. Consequently, α is higher for Quercus compared to Olea, as it aligns with the pollen index, which is typically greater for Quercus. The parameter γ, which describes the rate of the pollen increase, remains relatively consistent across the studied years, with the exception of 2019—a year characterized by notably high daily pollen concentrations for Olea and low concentrations for Quercus. Additionally, the IP provides a valuable metric for capturing the inter-annual variability and could potentially be utilized for forecasting the MPS in future years.

In the case of MLTs, the results were satisfactory for the prediction of the MPS characteristic for both Quercus and Olea with models like RF providing consistently good results, with deviations ranging from 0 to 10 days. In all cases, the end of the pollen season was a parameter that proved to be more difficult to model. For the next step, the multifold cross validation method leaving every time one year out will be employed, estimating MPS characteristics as mean values over multiple validation rounds. Moreover, the addition of new features (to result from feature engineering) as well as the involvement of new algorithmic approaches like XGBoost (eXtreme Gradient Boosting) as well as LSTM (Long Short-Term Memory) Neural Networks are expected to enhance the modeling performance.

5. Conclusions

This study provides an in-depth evaluation of various modeling approaches for predicting the MPS of Olea and Quercus in Thessaloniki, Greece, addressing the research question: which approach most accurately predicts the onset and end of the MPS? The findings highlight the strengths and limitations of different predictive techniques, emphasizing that DT sum approaches and LMs are particularly effective in capturing the end of the pollen season, while MLTs, especially RF, offer improved accuracy in predicting its onset. However, challenges remain in modeling early-season dynamics, as observed in 2022, where discrepancies in the predicted start date underline the complexity of pollen season forecasting. The absence of pollen data for 2018 represents a limitation, as it has restricted a more continuous evaluation of the inter-annual variability. Although this gap did not significantly affect the model performance, future studies incorporating longer and more complete datasets would enhance the model validation and improve the forecasting accuracy. Additionally, the state of forcing heat approach (DT_c) demonstrated limited effectiveness, suggesting that longer time series and diverse geographic datasets are necessary for refining the prediction accuracy.

Future research should focus on enhancing the feature selection, integrating deep learning methodologies, and expanding datasets across multiple climatic regions to improve the adaptability of forecasting models. These advancements would allow for more accurate and generalized forecasting models, contributing to improved aerobiological monitoring and allergen exposure management. Moreover, this study could be incorporated into a broader modeling system capable of predicting daily pollen concentrations, further supporting real-time pollen forecasting efforts. The findings of this study provide valuable insights for researchers developing pollen forecasting methodologies and for policymakers seeking to implement evidence-based strategies for mitigating pollen-related health risks in the Mediterranean and other pollen-sensitive regions.