# Forcing experiment and model integration to validate an olive tree phenological model

Omar Abou-Saaid, Bouchaib Khadari

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Omar Abou-Saaid, Bouchaib Khadari. Forcing experiment and model integration to validate an olive tree phenological model. Agricultural and Forest Meteorology, 2025, 373, pp.110752. 10.1016/j.agrformet.2025.110752. hal-05208118

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# Forcing experiment and model integration to validate an olive tree phenological model

Omar Abou-Saaid<sup>a,b,c</sup> <sup>id</sup>, Bouchaib Khadari<sup>a,d,1,*</sup> <sup>id</sup>

## ARTICLE INFO

**Keywords:**

Olea europaea L.

PhenoFlex framework

Forcing experiment

Endodormancy, Olive phenological model

Picholine Marocaine

Dynamic model

## ABSTRACT

Accurate assessment of chill and heat requirements is a fundamental challenge in phenological modeling of perennial fruit species, especially in the current climate change setting. Such models are typically calibrated and validated on the basis of long-term phenological and temperature records, without the integration of forcing experiments to highlight endodormancy release dates. Here we investigated olive tree flowering date modeling by combining a statistical approach and forcing experiments on the Picholine Marocaine cultivar with the aim of developing an olive phenological model for accurate assessment of chill and heat requirements. We initially assessed the endodormancy release date using a forcing experiment in 2021 and 2022 by comparing floral bud fresh weights under natural field conditions and after forcing conditions in a climate-controlled growing chamber. Subsequently, we used the PhenoFlex framework to calibrate and validate the model based on 31 years of flowering date and temperature data. We obtained an optimal model following nine calibrations with distinct season onset dates, and the latter were similar to the chilling onset date determined through a previous partial least squares regression approach. We also used endodormancy release dates to improve our model calibration by fitting the predicted flowering date to the observed value according to the recalibrated chill and heat requirement values. Finally, we validated the model based on six years of flowering date and temperature data. Our findings highlighted that the model calibrated solely via phenological records was less accurate than that calibrated based on a combination of phenological records and forcing experiment data. Our investigations broaden the scope for future applications of phenological olive tree modeling to accurately assess chill and heat requirements, which is currently a challenging issue facing olive growing in Mediterranean areas under climate warming.

## 1. Introduction

Temperate perennial species undergo a winter dormancy period where the trees remain inactive until the environmental conditions become suitable for growth (Fadon et al., 2020). Trees require low temperatures during the first stage of dormancy to be able to flower, while warm conditions are essential during the second phase, i.e. known as endo- and eco-dormancy, respectively (Campoy et al., 2011; Lang, 1987). Budburst and subsequent bloom can occur once the chill and heat requirements have both been fulfilled. In the global warming context, the winter chill temperature gradually decreases, causing insufficient chill in forest and fruit trees, which may lead to heterogeneous budburst

and bloom, asynchrony between pollen donors and pollen receptors in self-incompatible species, in turn hampering fruit set (Atkinson et al., 2013; Luedeling et al., 2011; Tominaga et al., 2022). As a key driver of tree dormancy and flowering, chill requirements may become a limiting factor under future scenarios in many regions worldwide (Egea et al., 2022; Rodríguez et al., 2021). Investigating the response of winter-dormant trees to cold temperatures is a scientific challenge, as the buds do not visibly exhibit any changes during the endodormancy phase and the temperature has a dual effect on bud development.

Thermal requirements to overcome dormancy can be estimated experimentally through forcing experiments (Campoy et al., 2019; Fernandez et al., 2019; Ruiz et al., 2007, 2018) or by modeling

<footnote><sup>a</sup> AGAP Institute, Université de Montpellier, CIRAD, INRAE, Institut Agro, 34398 Montpellier, France</footnote>

<footnote><sup>b</sup> INRA, UR Amélioration des Plantes, Marrakech 40005, Morocco</footnote>

<footnote><sup>c</sup> Centre d'Agrobiotechnologie et Bioingénierie, URL-CNRST 05, Université Cadi Ayyad, Marrakech 40010, Morocco</footnote>

<footnote><sup>d</sup> CBNMed, AGAP Institute, 34398 Montpellier, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: bouchaib.khadari@cirad.fr (B. Khadari).</footnote>

<footnote n="1">¹ b.khadari@cbnmed</footnote>
long-term phenology records (Chuine et al., 2016; Fadón et al., 2021; Fernandez et al., 2022; Luedeling et al., 2021). Several models have been developed in the last three decades to predict budburst and flowering dates of several perennial tree species (Chuine, 2000; Chuine et al., 2016; Darbyshire et al., 2016; Erez et al., 1989; Pope et al., 2014). These models differ by the dormancy phases they consider, i.e. either only ecodormancy, or both endo- and ecodormancy, and the reaction norms of bud development to temperature during each phase (Chuine et al., 2013). Models that consider only the ecodormancy phase, or so-called one-phase models, are based on the assumption that endodormancy is always broken before the climatic conditions for bud cell growth are suitable. Models that consider both the endo- and ecodormancy phases, or so-called two phase-models, predict the endodormancy release date, which varies from year to year depending on the temperature conditions during the endodormancy phase.

Since one-phase models do not consider what happens prior to eco-
dormancy, it is unlikely that they could generate accurate predictions in
future climate conditions (Chuine, 2010; Legave, 2008; Vitasse et al.,
2011). Two-phase models can predict budburst and flowering dates by
assessing the endodormancy release date and quantifying the chill and
heat requirements. These two phase-models mostly differ in the ways the
endodormancy and ecodormancy phases can overlap or not as the re-
lationships between the two accumulation processes are highly uncer-
tain (Hanninen, 1990). They are classified as sequential accumulation, i.
e. chill followed by heat (Ashcroft et al., 1977), parallel accumulation,
where chill and heat accumulate at the same time (Landsberg, 1974),
and overlapping chill and heat accumulation (Cannell and Smith, 1983).

Luedeling et al. (2021) thereby developed PhenoFlex, which is a phenological model whereby the two chill and heat phases are implemented through a flexible approach that allows for the testing of sequential, overlapping and even parallel relationships between chill and heat. The model uses the Dynamic model for the chill phase, which is currently the most reliable model for quantifying chill requirements (Fernandez et al., 2020), and the Growing Degree Hours (GDH) model for quantifying heat (Anderson et al., 1986). PhenoFlex has proven to perform well for modeling apple trees growing under a range of temperatures reflecting the climatic conditions that prevail in temperate growing areas (Luedeling et al., 2021). However, two major parameters are overlooked in these two-phase models that are closely related to chill and heat accumulation onset. Chill onset usually assumed to be arbitrary. In some studies, the authors consider that heat onset occurs once the chill requirements have been fulfilled (Legave et al., 2013). In other investigations, the authors consider that the chill and heat accumulation periods overlap. The extent of overlapping can be set before the modelling (Darbyshire et al., 2016; Pope et al., 2014).

Links between chill and heat phases are still misunderstood and are
likely variable among perennial fruit species. The interaction between
chill and heat accumulation could vary according to cultivars or groups
of cultivars, and the overlapping pattern could be cultivar specific
(Benmoussa et al., 2017a; 2017b; Diez-Palet et al., 2019). The use of
forcing tests to assess endodormancy dates could be a highly effective
approach, as demonstrated by Chuine et al. (2016). Without information
on the endodormancy dates, chill assessment can be over- or under-
estimated as chill and heat can compensate each other (Darbyshire et al.,
2016). Empirical determination of endodormancy release via forcing
experiments addresses a key limitation of purely statistical calibra-
tions—subjectively optimized parameters (e.g., y<sub>c</sub>, z<sub>c</sub>). This approach is
especially critical for olive trees, where regional and cultivar-specific
responses diverge from temperate fruit trees (Aguilera et al., 2014).
By combining long-term phenological records with experimental data,
we bridge the gap between model flexibility and biological process.

All of the above knowledge derives from investigations on forest and fruit species in temperate regions, while less is known on those growing in Mediterranean areas. The present study focused on olive—an emblematic species of the Mediterranean Basin. Unlike deciduous trees in which the meristem transition occurs within the bud prior to winter

dormancy onset, the olive tree bud morphology remains undifferenti-
ated (i.e. vegetative or reproductive) until dormancy release (Haberman
et al., 2017). This feature could explain the lack of knowledge on the
links between flowering and chill temperatures in olive trees. While the
dormancy model is well-established for deciduous fruit trees (Campoy
et al., 2011; Fadon et al., 2020), it has yet to be clearly understood with
regard to olive trees (Haberman et al., 2017; Hackett and Hartmann,
1967; Rallo and Martin, 1991; Rubio-Valdés et al., 2022). Based on the
overall hypothesis that olive trees require sufficient winter chilling fol-
lowed by warm temperatures, various attempts have been made to es-
timate the thermal requirements for budburst and flowering, and forcing
experiments have been found to be highly informative in this quest
(Ramos et al., 2018; Rubio-Valdés et al., 2022). Most prior investigations
on olive trees were based on a sequential model, yet compensation be-
tween chill and heat phases could occur when there has not been suf-
ficient chill (Demeloabreu, 2004; Elloumi et al., 2020; Hartmann and
Porlingis, 1957; Malik and Bradford, 2005). Picornell et al. (2023)
recently used the PhenoFlex framework to develop an olive tree
phenology model based on pollen data collected in Portugal over a
25-year period.

Here we aimed to develop an olive tree phenology model using the PhenoFlex framework based on long-term flowering date records and linked temperatures compiled for the Picholine Marocaine (PM) olive cultivar. We calibrated the model by testing the effects of season onset and integrated endodormancy release dates using forcing experiments. Compared to the findings of previous studies, we demonstrated that seasonal chill accumulation onset is a key factor for a robust phenology model. Furthermore, as discussed by Chuine et al. (2016), we demonstrated that modeling chill and heat requirements with the aim of predicting phenological stages such as budburst or blooming is inefficient without the assessment of experimental data on the endodormancy release dates via forcing experiments.

## 2. Material and methods

Full PM flowering dates over a 31 year period with associated tem-
perature data were used to calibrate and validate the recently developed
PhenoFlex phenology model framework (Luedeling et al., 2021). In a
first step, the calibration was performed using phenological data from
1986 to 2013, with data missing between 1992 and 1996 (23 years of
data overall). Then a second calibration was conducted on endo-
dormancy release and full flowering data obtained over 2 years (2021
and 2022) of forcing experiments carried out on shoot explants under
controlled and natural conditions. Two versions of the model with and
without the second level of calibration were then validated on the 6
years of phenological data recorded between 2014 and 2019 (see the
 workflow in Fig. 1).

2.1. *Site and plant material*

This study was performed on 88 PM olive trees grown in the
Worldwide Olive Germplasm Bank of Marrakech (WOGBM) at the Tas-
saout research station of the National Institute of Agricultural Research
(INRA) in Morocco. The site is located 60 km northeast of Marrakech, at
31°49'10" N 7°25'58" W (CRS: WGS84-EPSG:4326) and 465 m elevation
(Figure S1). Semi-arid climatic conditions prevail, with average annual
precipitation and temperatures of 255.5 mm and 19.05 °C, respectively,
as recorded over the 1985 to 2022 period (Figure S2). The trees were
cultivated under the same pedoclimatic conditions using the same hor-
ticultural practices, including drip irrigation, annual pruning, fertiliza-
tion and plant protection.

## 2.2. *Temperature and full flowering data*

Recorded hourly temperatures were obtained from the INRA mete-
orological station located in the same research station. This
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Overview of the modelling workflow process used in this study. Data preparation involved compiling full flowering dates for Picholine Marocaine olives from 1986 to 2022, with missing data noted over the 1992–1996 period and in the year 2020. The 1986–2013 period was designated as the initial calibration dataset for the PhenoFlex framework. The y_c and z_c parameters were subsequently recalibrated using endodormancy release dates obtained by forcing experiments carried out during 2021 and 2022, along with observed full flowering dates determined in the field for the same years. Two model validations were conducted: one prior to and another after the recalibration of y_c and z_c. These validations were carried out using full flowering date data for the 2014–2019 external period. Hourly temperatures recorded directly at the study site were used for this purpose. chillR was used to generate missing values, as described in (Luedeling, 2018).</figcaption></figure>

Meteorological station is operated by Pessl Instruments GmbH (Austria) and the data can be downloaded directly from their website. The temperature data were then quality checked to ensure that there were no missing data. For periods when the data recording had failed, the missing values were then estimated by generating hourly temperatures based on daily extremes via the Linvill (1990) algorithm, implemented in ChillR package (Luedeling et al., 2023). Phenological data on PM full flowering dates collected over the 1986–2019 period were derived from previous studies (Abou-Saaid et al., 2022; El Yaacoubi et al., 2014). The observations were based on the BBCH scale for olive, stage 65 (Full Flowering) (Sanz-Cortes et al., 2002).

## 2.3. Forcing experiment

The forcing experiment consisted of evaluating floral bud development to determine potential endodormancy release dates by weighting floral buds directly sampled in olive orchards and other ones excised from shoot explants subjected to artificial forcing conditions over 1–3 weeks (El Yaacoubi et al., 2016; Ramos et al., 2018; Ruiz et al., 2007; Tabuenca, 1964). This method was used for the first time on cv. Manzanilla olive trees (Ramos et al., 2018), and recently on cv. Arbequina olive trees (Rubio-Valdés et al., 2022). The forcing experiment proved to be effective in assessing endodormancy release dates in olive trees by comparing the results with those obtained in experiments

carried out on whole potted trees under artificial conditions (Rubio-Valdés et al., 2022).

Using two trees with off-bearing status in the previous year, eight shoot explants (≈ 15 cm height and ≈ 2 cm dia.) were sampled randomly once a week from early January to late March during each year of the experiment. Five floral buds were then excised from each of three shoots and directly weighed with a precision balance to measure the fresh weight for the unforced bud set. The five remaining shoots were then put in a pot containing water, incubated in forcing conditions in a climate-controlled growing chamber at 24 °C, with a 16/8 h light/dark photoperiod and constant ≈70 % RH for 7 consecutive days. Three separate repetitions were conducted, with five floral buds excised from their bases using a scalpel in each repetition, while using the same procedure as that applied for the first unforced bud set. The excised floral buds were weighed to measure the fresh weight for the forced bud set. Shoots were freshly cut at their bases every 2 days to ensure water transport throughout the shoot. A comparison of the forced and unforced sets at each sampling date was performed using a T-test. We considered the endodormancy release date, when the fresh weights in the forced set were significantly greater than those in the unforced set at "p < 0.05" (Figure S3).
## 2.4. PhenoFlex framework calibration based on flowering date and temperature data

A framework for modeling phenological data using the Dynamic and GDH models as sub-models was developed by (Luedeling et al., 2021). The authors called it the PhenoFlex framework because of its flexibility for testing sequential, overlap and parallel models for chilling and heat accumulation through a sigmoidal conversion function by a sigmoidal function for conversion to determine the transition between the two phases. This modeling approach is implemented in the chillR package (Luedeling et al., 2023).

Twelve parameters have to be fitted in the PhenoFlex framework, including six parameters of the Dynamic model for chill accumulation developed initially based on an experiment on peach (Erez et al., 1989), three parameters of the Growing Degree Hours model also developed for peach (Richardson et al., 1974), and three parameters to determine the link between the two phases. For chill accumulation, the Dynamic model assumes that there are basically two steps to fulfill. The first is a dormancy release (x) precursor that is converted under a given temperature into a dormancy release factor (y). The precursor transformation is dynamic and is described by the following equation:

$$K_{0.1} = A_{0.1} \exp^{E_{0.1}/T(t)}$$

with $k_0$ and $k_1$ being formation and destruction rate constants, $A_0$ and $A_1$ respectively being time-independent amplitudes of the formation and destruction of x measured in $(h^{-1})$, $E_0$ and $E_1$ respectively being time-independent activation energies of production and destruction measured in kelvin (K), and $T(t)$ being the time-dependent temperature in K. The two steps are described by a sigmoidal function with slope S measured in $K^{-1}$ under temperature $T_f$. Once one unit of x is transformed to y, the accumulation is redeemed irreversible (Fishman et al., 1987a; 1987b; Luedeling et al., 2021).

The heat phase is described by the GDH model, where at base temperature $T_b$ heat starts accumulating and reaches optimum accumulation at temperature $T_u$, then the accumulation process stops once the temperature exceeds threshold $T_c$. The heat accumulated in the PhenoFlex framework is referred to as $z_c$ and is related to a critical amount of chill $y_c$, represented by sigmoidal function with slope $S_1$. At high $S_1$ values, $y_c$ and $z_c$ accumulation tends to be sequential and at lower values the two submodels are parallel (Luedeling et al., 2021).

The GenSA algorithm was used to fit all twelve parameters, i.e. $y_c$, $z_c$, $S_1$, $T_u$, $A_0$, $A_1$, $E_0$, $E_1$, $T_f$, $T_c$, $T_b$ and the slope. The optimization process takes parameters bounded by an optimization interval as input values and the fitted parameter domain is then truncated with the values reported in (Fernandez et al., 2022) (see details in Supplementary materials).

The limit of the PhenoFlex framework, as acknowledged by the authors (Luedeling et al., 2021), is the determination of the chilling accumulation onset date. To our knowledge, this date is usually subjectively chosen by authors (Elloumi et al., 2022; Fernandez et al., 2022; Luedeling et al., 2021; Picornell et al., 2024). We sought to overcome this shortcoming in the PhenoFlex framework by performing a multiple set of calibrations with different season onsets. Overall, nine calibrations were conducted, starting from September to January with a 2-week interval. For each season, the optimization process was conducted with the same methodology as that reported by Fernandez et al. (2022) (see Supplementary materials). In the first run, we started using the default parameters outlined in (Urbach et al., 2021) and (Fernandez et al., 2022), with an optimization interval. We repeated the same procedure in the following run using the same parameters as in the previous run. To assess the calibration procedure performance, the root mean squared error of prediction (RMSEP) between the predicted and the observed flowering date data was computed at each run until the RMSEP value remained constant between the two last runs. Among the nine calibrated models, the best calibration showing the best potential season onset was

chosen based on the lowest RMSEP value.

## 2.5. PhenoFlex framework calibration based on endodormancy release dates

The best model was then subjected to a second calibration level. Using the endodormancy release date derived from the forcing experiment as well as the observed full flowering dates of the two years 2021 and 2022, the amounts of accumulated $y_c$ and $z_c$ delineated by the calibrated model from the first step were recalibrated according to the experimentally assessed endodormancy release dates and to the recorded full flowering dates. The aim of this second validation was to compare the amounts of $y_c$ and $z_c$ delineated by the calibrated model and the endodormancy release and full flowering dates determined experimentally and on the basis of field observations, respectively. The mean absolute error (MAE) between the predicted and observed flowering dates during the 2 years was calculated to assess the model performance at this second calibration level (see details in Supplementary materials). While historical data (23 years) capture interannual variability, forcing experiments (2021–2022) provide empirical anchors for the chill-heat transition. The latter constrained $y_c$ and $z_c$ to biologically plausible ranges, reducing compensation artifacts inherent in purely statistical optimization.

## 2.6. PhenoFlex validation

Two validation sets were performed to assess the interest of using the potential endodormancy release date determined experimentally in the calibration of the amount of $y_c$ and $z_c$ in the PhenoFlex framework. The first validation was done directly after the first calibration process, using six years (2014 to 2019) of full flowering dates (20.6 % of data without the two years of forcing experiments). The second validation was done on the same set of full flowering data after recalibrating the amount of $y_c$ and $z_c$ using the experimentally assessed endodormancy release dates for 2021 and 2022. RMSEP and the MAE between the predicted and observed flowering dates were calculated to assess the model performance in the validation process.

## 2.7. Reproducibility, data analysis and model application

All statistical analyses, including model application and performance assessment were performed in the R software environment (R Core Team, 2024). Libraries in the tidyverse framework (Wickham et al., 2019) were mainly used for data preparation and figure generation. All data and codes used to perform and reproduce the analyses are available upon request in a GitHub repository.

# 3. Results

## 3.1. Dynamic response to the forcing experiment

The measurement of floral bud weights over time highlighted the dynamic response of bud weights under forced and unforced conditions throughout the 2-years study. Notably, the endodormancy release date differed between the two years, i.e. it occurred on 20th February and 1st March, respectively, in 2021 and 2022, as shown in Fig. 2. These disparities were attributed to the natural conditions, especially the different temperature variations between the two years (Fig. 2). Despite differing endodormancy release dates, CP values were similar (~55 CP), supporting the Dynamic Model’s physiological relevance.

## 3.2. A first PhenoFlex calibration according to the chill accumulation onset date

The calibrated models were systematically evaluated for different season onset dates. A comprehensive overview of the key metrics and
Picholine Marocaine

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Dynamics of floral bud weights for two treatments over two consecutive years (2021 and 2022), with 1st January as start date each year. The green line depicts the progression of floral bud weights under natural conditions, while the red line represents the floral bud weight dynamics under forced conditions. The term “endodormancy release” denotes the point at which a t-test comparison of mean floral bud weights between the two treatments became significant and maintained this significance for subsequent sampling dates, as indicated here with the blue vertical dashed line. The middle panel showcases the variation in minimum, maximum and mean temperatures for the two 2020–2021 and 2021–2022 seasons, spanning the period from early January to late March. The bottom panel shows the accumulation of chill portions until the observed endodormancy release dates (20th February: 53 CP; 1st March 2022: 58.5 CP).</figcaption></figure>

values for each configuration are provided in Table 1. Notably, varia-
tions in $y_c$, $z_c$, $S_1$, $T_u$, $E_0$, $E_1$, $A_0$, $A_1$, $T_f$, $T_c$, $T_b$ and slope were observed
across the different onset dates. According to different season onset
dates, we observed distinct shifts in the model parameters, thereby
highlighting the sensitivity of these parameters to the season onset
timing. While few changes were observed in $E_0$, $E_1$, $A_0$, with $A_1$ values
remaining constant, no parameter variation trends were highlighted
across the season onset dates. The RMSEP values for all other season
onsets ranged from 9.5 days to 8.1 days. The single best predictive model
showing an RMSEP value of 5.8 days was founded on a chill accumu-
lation period starting January 1st

3.3. A second PhenoFlex calibration based on the endodormancy release dates assessed by forcing experiments

The best-calibrated model from the initial calibration process, using
1st January as the season onset date, exhibited significant disparities
between the chill accumulation end date assessed by PhenoFlex
modeling and the endodormancy release date assessed by forcing ex-
periments (Fig. 3). Similar disparities were noted between the model
predicted heat accumulation end date and the full flowering dates
observed in the field (Fig. 3). This suggests that the model structure was
not yet aligned with the empirically determined endodormancy release
dates (end of chill) and the observed full flowering date (end of heat).

Upon recalibration of both $y_c$ and $z_c$ for the years 2021 and 2022
(Fig. 3), we obtained a good fitting between the modeling and
<caption>**Table 1**</caption>

PhenoFlex framework: first calibration based on the 23 years of full flowering date data for the Picholine Marocaine olive cultivar recorded between 1986–2013, with different season onset dates from 1st September to 1st January (see material and methods for the parameter descriptions).

<table><thead><tr><th rowspan="2"></th><th colspan="9">Season onset dates</th></tr><tr><th>1st Sept.</th><th>15th Sept.</th><th>1st Oct.</th><th>15th Oct.</th><th>1st Nov.</th><th>15th Nov.</th><th>1st Dec.</th><th>15th Dec.</th><th>1st Jan.</th></tr></thead><tbody><tr><td>Number of runs</td><td>3</td><td>10</td><td>8</td><td>8</td><td>3</td><td>2</td><td>2</td><td>2</td><td>7</td></tr><tr><td>yc</td><td>77.19</td><td>84.58</td><td>88.17</td><td>60.63</td><td>62.35</td><td>78.66</td><td>64.55</td><td>73.48</td><td><strong>82.83</strong></td></tr><tr><td>zc (h)</td><td>975.94</td><td>476.04</td><td>934.23</td><td>722.03</td><td>671.52</td><td>490.99</td><td>396.05</td><td>397.03</td><td><strong>487.60</strong></td></tr><tr><td>s1</td><td>0.98</td><td>0.99</td><td>0.20</td><td>1.00</td><td>0.97</td><td>0.99</td><td>0.18</td><td>0.17</td><td><strong>0.80</strong></td></tr><tr><td>Tu (°C)</td><td>14.16</td><td>20.36</td><td>13.39</td><td>15.59</td><td>15.31</td><td>19.33</td><td>20.15</td><td>20.26</td><td><strong>26.82</strong></td></tr><tr><td>E0 (K)</td><td>3 013.10</td><td>3 018.81</td><td>3 014.31</td><td>3 015.72</td><td>3 018.99</td><td>3 018.79</td><td>3 237.14</td><td>3 235.12</td><td><strong>3 241.00</strong></td></tr><tr><td>E1 (K)</td><td>9 575.19</td><td>9 572.72</td><td>9 577.91</td><td>9 554.69</td><td>9 563.45</td><td>9 569.42</td><td>9 867.73</td><td>9 874.58</td><td><strong>9 921.81</strong></td></tr><tr><td>A0 (h<sup>-1</sup>)</td><td>6 046.60</td><td>6 001.94</td><td>6 255.42</td><td>6 005.05</td><td>6 041.37</td><td>6 049.49</td><td>6 066.02</td><td>6 415.73</td><td><strong>6 867.30</strong></td></tr><tr><td>A1 (h<sup>-1</sup>)</td><td>5.94·10<sup>13</sup></td><td>5.94·10<sup>13</sup></td><td>5.94·10<sup>13</sup></td><td>5.94·10<sup>13</sup></td><td>5.94·10<sup>13</sup></td><td>5.94·10<sup>13</sup></td><td>5.94·10<sup>13</sup></td><td>5.94·10<sup>13</sup></td><td><strong>5.94·10<sup>13</sup></strong></td></tr><tr><td>Tf (°C)</td><td>3.87</td><td>2.78</td><td>5.98</td><td>5.30</td><td>5.23</td><td>3.11</td><td>3.07</td><td>3.97</td><td><strong>7.49</strong></td></tr><tr><td>Tc (°C)</td><td>39.34</td><td>20.40</td><td>39.01</td><td>29.66</td><td>28.20</td><td>21.65</td><td>20.17</td><td>20.84</td><td><strong>34.28</strong></td></tr><tr><td>Tb (°C)</td><td>9.86</td><td>9.53</td><td>10.36</td><td>10.83</td><td>11.24</td><td>9.58</td><td>9.68</td><td>8.73</td><td><strong>2.96</strong></td></tr><tr><td>Slope (K<sup>-1</sup>)</td><td>5.68</td><td>1.64</td><td>2.81</td><td>2.10</td><td>1.82</td><td>0.92</td><td>3.30</td><td>16.09</td><td><strong>3.56</strong></td></tr><tr><td>RMSEP calibration</td><td>9</td><td>9.5</td><td>8.7</td><td>8.5</td><td>8.9</td><td>9</td><td>8.2</td><td>8.1</td><td><strong>5.8</strong></td></tr></tbody></table>

A

<figure><img src="image_5.png" /></figure>

B

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 3.** Illustration of chill and heat accumulation patterns predicted by the two sub-models within the fitted PhenoFlex framework for the Picholine Marocaine olive cultivar in the two years of forcing experiments (2021 and 2022). The panels on the left (A) represent the thermal accumulation progression patterns for 2021 and 2022, which is required in the calibrated PhenoFlex framework without endodormancy dates. The panels on the right (B) represent the thermal accumulation progression patterns for the 2021 and 2022, which is required in the calibrated PhenoFlex framework using endodormancy dates. The vertical blue and green dashed lines indicate the predicted chill requirement fulfillment date and the experimentally delineated endodormancy release date, respectively. Similarly, the vertical red and orange dashed lines represent the predicted heat requirements fulfillment date and the observed full flowering dates, respectively. In both panels, the horizontal blue and red lines indicate the chill and heat requirements, respectively.</figcaption></figure>

experimentally assessed chill accumulation end dates. This alignment was achieved with $y_c$ values ranging from 53 to 58.5 chill portions (CP) and $z_c$ values ranging from 670 to 795 growing degree hours (GDH), for the years 2021 and 2022, respectively. This contrasted with the 82.8 and

487.6 values obtained for $y_c$ and $z_c$, respectively, using the initial calibrated model. Following this recalibration, the lowest MAE for $y_c$ and $z_c$ values from an optimization over the two years was 5.7 days. Notably, the final model values for $y_c$ and $z_c$, in accordance with the best full
flowering date prediction for the 2 years, were 58 CP and 785 GDH, respectively (see Figure S4).

### 3.4. Model validation

The two model versions were fully validated using a dataset spanning six years (2014 to 2019). The first version of the model, which had an RMSEP of 7.8 days, set the foundations (Figure S5). A second variant followed with a significantly shorter RMSEP of 5.6 days (Fig. 4). The main change in this enhanced model validation resulted from the recalibration of two crucial parameters, i.e. $y_c$ and $z_c$, while all other parameters remained identical to those of the first version of the model. Forcing experiments precisely guiding this recalibration had a significant impact on the model performance. These findings show how adjusting model parameters based on forcing experiments can markedly enhance the model performance.

The validated model and its parameters, including the standard error (SE), derived by a bootstrap, are described in the Table 2. Each parameter's fitted value is depicted as the value ± SE, which reflects the estimation precision. The minimum limit (Min. Limit) and the maximum limit (Max. Limit) columns refer to the optimization margins set in the process, delineating the parameter ranges within which the model was optimized. This table can thus serve as a reference for understanding the interplay of parameters that jointly enable the model to effectively capture and predict PM full flowering dates.

### 3.5. Temperature response of the model

Relationships between temperature and the response of two distinct sub-models within the validated PhenoFlex framework for olive trees are described in Fig. 5. Regarding the chill model, the temperature accumulation process started at 5.6 °C, with a gradually increasing pattern. Notably, there was a pivotal juncture as the accumulation peaked, which

<caption>Table 2</caption>

Optimized model parameters, standard error (SE) from the bootstrap procedure and the minimum and maximum limits of the optimization margins.

<table><thead><tr><td>Model parameter</td><td>Fitted value ± SE</td><td>Min. limit</td><td>Max. limit</td></tr></thead><tbody><tr><td>y<sub>c</sub></td><td>58.00 ± 15.39</td><td>20</td><td>90</td></tr><tr><td>z<sub>c</sub> (h)</td><td>785.00 ± 66.15</td><td>100</td><td>900</td></tr><tr><td>S1</td><td>0.80 ± 0.25</td><td>0.1</td><td>1</td></tr><tr><td>Tu (°C)</td><td>26.82 ± 2.15</td><td>0</td><td>30</td></tr><tr><td>E0 (K)</td><td>3 241.00 ± 32.51</td><td>3000</td><td>4000</td></tr><tr><td>E1 (K)</td><td>9 921.81 ± 35.80</td><td>9000</td><td>10,000</td></tr><tr><td>A0 (h<sup>-1</sup>)</td><td>6 867.30 ± 306.19</td><td>6000</td><td>7000</td></tr><tr><td>A1 (h<sup>-1</sup>)</td><td>5.9410<sup>13</sup> ± 3.1210<sup>8</sup></td><td>5.0010<sup>13</sup></td><td>6.0010<sup>13</sup></td></tr><tr><td>Tf (°C)</td><td>7.49 ± 1.48</td><td>0</td><td>10</td></tr><tr><td>Tc (°C)</td><td>34.28 ± 4.58</td><td>0</td><td>40</td></tr><tr><td>Tb (°C)</td><td>2.96 ± 1.43</td><td>0</td><td>12</td></tr><tr><td>S (K-1)</td><td>3.56 ± 11.73</td><td>0.05</td><td>50</td></tr></tbody></table>

occurred in the 8 °C to 12 °C temperature range. The response exhibited a discernible decline, in line with the absence of accumulation observed >18 °C.

The temperature response of the heat model was initiated at ~4 °C, then the response gained momentum as the temperature increased, culminating in an optimal response in the 24–25 °C range. As the temperature progressed beyond this range, the response decreased, with an absence of accumulation >34 °C.

The temperature reactions of these two models highlight the intricacies of temperature-driven responses within chill and heat sub-models. The visual narrative illustrated in Fig. 5 showcased the distinct optimal accumulation zones for each sub-model in the PhenoFlex framework. It also provided an enhanced understanding of the behavior of olive trees in relationship with temperature variations, while underscoring the critical thresholds beyond which responses attenuate.

<figure><img src="image_9.png" /><figcaption>Fig. 4. Observed and predicted flowering dates generated by the fitted PhenoFlex framework, thereby offering insight into model performance throughout the calibration and validation steps. RMSE<sub>calib</sub> and MAE<sub>calib</sub> respectively correspond to the root mean square error and the mean absolute error obtained during the calibration process. Similarly, RMSE<sub>valid</sub> and MAE<sub>valid</sub> represent the root mean square error and the mean absolute error obtained in the validation process, respectively.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 5.** Illustration of the temperature response of the two sub-models for chill and heat accumulation within PhenoFlex framework over a 1200 h period under constant temperature of between -5 °C to 60 °C. In the left panel, the response of the chill sub-model initiated at a temperature of 5.6 °C, then peaking around 8.2 °C and 12 °C. Subsequently, it declined rapidly at 16 °C, with no response observed >18.5 °C. The right panel showcases the response of the heat sub-model, starting from 4.2 °C and gradually gaining momentum until 25.6 °C. At this point, it sharply dropped to 0 °C, with no accumulation observed >33.4 °C.</figcaption></figure>

**4. Discussion**

Estimating thermal requirements in temperate fruit trees has always been a challenging issue. The chill and heat requirements concept was developed based on the hypothesis that the dormancy release process in temperate fruit trees requires chill to break endodormancy and then heat to overcome the ecodormancy phase and enable flowering (Lang, 1987). Rubio-Valdés et al. (2022) put forward the assumption that endodormancy and ecodormancy phases are key drivers of olive tree flowering. Various researchers have made numerous attempts to estimate these hidden phases using modeling or experimental approaches focused on various fruit tree species such as almond, pistachio and walnut (Benmoussa et al., 2017a; 2017b; Diez-Palet et al., 2019; Guo et al., 2013; Luedeling et al., 2013). Predictive modeling using PhenoFlex (Luedeling et al., 2021) seems to be a reliable approach for delineating chill and heat accumulation in given cultivars, as it incorporates two chill and heat accumulation sub-models to predict reproductive phenological stages. However, two major parameters have been overlooked in the model calibration. The first is the chill accumulation onset date, which here we call 'season onset'—to our knowledge no previous studies have investigated this parameter for model calibration (Darbyshire et al., 2016; De Melo-Abreu et al., 2004; Luedeling et al., 2021; Picornell et al., 2023). The second is the integration of endodormancy dates in calibration frameworks structurally similar to PhenoFlex. As discussed by (Chuine et al., 2016), integrating endodormancy breaking dates can greatly improve the performance of models that incorporate both chill and heat phases for the purpose of phenology prediction.

Here we examined, for the first time, the chill accumulation onset date and the integration of endodormancy release dates in calibrating the PhenoFlex framework. Hereafter we discuss our results with regard to chill accumulation onset and endodormancy release dates, i.e. the two parameters we focused on in this study.

**4.1.** *Chill accumulation onset is a key parameter to obtain the best predictive model*

In previous investigations, modelers focused on determining appropriate season onset dates. Typically, the solution has been to subjectively select a chill accumulation onset date (Chuine et al., 2016; Darbyshire et al., 2016; De Melo-Abreu et al., 2004). In the case of PhenoFlex, authors have identified early September as the season onset date, including Luedeling et al. (2021), who developed the PhenoFlex framework in Appel and Peach, and Fernandez et al. (2022), who studied the effects of extreme seasons on the overall PhenoFlex performance. With the aim of tailoring PhenoFlex for future trend analyses in olive trees, Picornell et al. (2023) applied PhenoFlex using main pollen season (MPS) data with a season onset of 1st October, while relying on the phases determined via partial least squares (PLS) analysis.

Subjectively selecting a season onset can markedly alter the model structure, especially the transition period between the chill and heat phases. As we demonstrated with PhenoFlex, the chill accumulation onset date can directly influence the amount of chill and heat calibrated for the same flowering dates and the same cultivar, which range from 60.63 CP to 84.58 CP for chill and 396.05 GDH to 975.94 GDH for heat as the chill onset date changes. Despite the fact that many authors of previous studies have set the season onset date between October and November, including studies involving olive trees (De Melo-Abreu et al., 2004; Picornell et al., 2023), in our study 1st January proved to be the optimal season onset for the PM cultivar. This finding was perfectly in line with the chilling phase described in our previous study on olive thermal requirements (Abou-Saaid et al., 2022), as indicated by an RMSE ranging from 9 to 8 days for all tested season onset dates, with 5.8 days being the RMSE obtained using 1st January as the season onset. We firmly believe that the choice of season onset is cultivar specific, as demonstrated by PLS in our previous study involving a set of 286 olive cultivars (Abou-Saaid et al., 2022).
## 4.2. Incorporating experimentally assessed endodormancy release dates in model calibration is another key parameter to obtain the best predictive model

Many phenology prediction models varying in structure and complexity have been discussed in the literature. Multiple environmental cues have been incorporated in these one-phase (ecodormancy model) or two-phase (endo- and ecodormancy model) models, see (Chuine et al., 2013) for a review. Two-phase models proved their efficacy compared to one-phase and correlative models, as shown by (Asse et al., 2020; Chuine et al., 2016). The advantage of using PhenoFlex is that it enables calibration of DM and GDH models with a possibility of overlapping the phases, as compared to other previously described model frameworks that used the two sub-models sequentially (De Melo-Abreu et al., 2004; Gaeta et al., 2018) or with a fixed percentage of overlap (Darbyshire et al., 2016; Pope et al., 2014). The compensation effect between phases is also accounted for within the PhenoFlex framework (Darbyshire et al., 2014; Harrington et al., 2010; Pope et al., 2014). Yet the framework lacks the option of incorporating endodormancy in the calibration process, which may compromise its effectiveness in providing plausible chill units and hamper endodormancy date prediction. The model performance could be enhanced by including endodormancy dates in the model calibration (Chuine et al., 2016). When calibrating PhenoFlex without any endodormancy date information, we found that the extent of chill $y_c$ rendered by the model exceeded the experimentally determined endodormancy date (see Fig. 3A), which is inconsistent with the hypothesis that the endodormancy date corresponds to the chill end date. Furthermore, providing plausible endodormancy dates allowed for more accurate calibration of the amounts of $y_c$ and $z_c$, thereby improving the performance of the calibrated PhenoFlex model by rendering an RMSE of 5.7 days instead of 7.3 days (Fig. 4 and S5).

Chuine et al. (2016) reported that a two-phase model calibrated for apricot, peach, and walnut without including endodormancy dates had lower RMSE values during calibration compared to a model where the chill phase was calibrated using fixed parameters with endodormancy dates. However, the validation results showed higher RMSE for the model calibrated without endodormancy dates. Our methodology differed from that of (Chuine et al., 2016) as we chose to retain the chill model from the initial calibration, which was based solely on full flowering dates. This decision was necessary because data on endodormancy release dates were available for only 2 years. Such a limited dataset was insufficient for reliably recalibrating the chill phase parameters. We calibrated the amounts of $y_c$ and $z_c$ using the endodormancy dates of the two years of data, while selecting values that would give the lowest MAE for those two years. Despite the differences in the approaches, we obtained the lowest RMSE for validation as that reported in Chuine et al. (2016) for the model calibrated using endodormancy dates.

Asse et al. (2020) reported RMSE values of around 8 days for a two-phase process-based model, i.e. similar to our findings before the incorporation of endodormancy dates but with different parameters and different species. Asse et al. (2020) tested a model using data collected through a citizen-science program, while incorporating endodormancy dates for larch trees (Larix sp.)—this so-called forward calibrated model performed better in the validation dataset than in the calibration process, with RMSE values of 8.7 and 9.9 days, respectively. Our model outperformed the unified model used in Picornell et al. (2023) on MPS data, with RMSE values of 7.8 days used in the calibration process and 14.7 days in the validation phase.

In previous model validations on apple and pear (Luedeling et al., 2021), PhenoFlex performed better than in our olive tree study, with RMSE values of 3.82 and 3.98 days, respectively. In olive, low RMSE values have also been reported by De Melo-Abreu et al. (2004) where they tested a sequential two-phase model on the flowering dates of five different cultivars, and they obtained RMSE values of ≈ 3 days.

Furthermore, Picornell et al. (2023) reported an RMSE for validation of 3.5 days in a recent study using PhenoFlex. Although it included pollen data, this study represented a benchmark for comparison with our study. The higher RMSE obtained in our study, despite the model performance improvement achieved with the inclusion of endodormancy release dates, was probably related to the quality of our data as they were collected over a 3 to 4 day interval (Abou-Saaid et al., 2022).

Overall, integrating experimentally obtained endodormancy release dates so as to recalibrate the amount of chill and heat markedly improved the model performance. This could be a potential future model fitting strategy. However, further studies are needed to confirm the efficacy of forcing experiments in enhancing the model performance, and they should be conducted over subsequent years in order to assess the temporal variability.

## 4.3. Chill and heat sub-model interactions and potential compensation

PhenoFlex and PLS are valuable tools for estimating plant responses to temperature. Both approaches involve data-driven modeling to assess how plants respond to different temperature conditions. In the previous study (Abou-Saaid et al., 2022), we delineated the two chill and heat accumulation phases for PM olives. The chill phase, as indicated by the fitted PhenoFlex model, roughly spanned from 1st January to 11th February in 2021 and to 13th February in 2022, compared to the PLS-derived period which was from 31st December to 21st February.

However, a key difference has been noted regarding the connection between the chill and heat phases. In previous investigations, this link was often assumed to be sequential (Luedeling et al., 2013). However, subsequent applications of the PLS approach using the DM and GDH models as explanatory variables revealed cases of overlap and even gaps between the chill and heat phase transitions, thereby highlighting the main limits in using PLS when characterizing the link between both phases (Diez-Palet et al., 2019). In Abou-Saaid et al. (2022), we assessed the two phases independently as the main objective was to characterize the chilling requirements of a set of cultivars, and PLS proved to be a valuable tool in this assessment (Luedeling et al., 2013). The sequential framework has been widely used in predictive modeling with the two sub-models. However, the sequential framework might not be well suited for application in the Mediterranean area where mild winters prevail or in current climate change setting, which can hamper the availability of chill (Luedeling et al., 2011). Recent almond and apple flowering phenology modeling efforts revealed the effectiveness of including some overlapping and a partially compensatory relationship between chill and heat accumulation was noted. Pope et al. (2014) and Darbyshire et al. (2016) used the DM and GDH sub-models and suggested a 75 % overlap between chill and heat based on the exponential relationship between phases while fitting three parameters and testing different percentages of overlap. The compensation effect between phases integrated in PhenoFlex is much more flexible (Luedeling et al., 2021). Fernandez et al. (2022) reported $S_1$ parameter values of between 0 and 1, and values close to 1 indicates less overlap and a trend towards a sequential relationship. In our fitted PhenoFlex model, this link was characterized by a slope of ≈ 0.80±0.35 (see Table 2). This suggests that there was some overlap after the critical amount of chill required for heat accumulation was reached (see Fig. 3). $S_1$ values obtained in a study conducted on olive MPS data were similar to those obtained in our study, with a slope of 0.75±0.19 (Picornell et al., 2023).

Note here that the $y_c$ and $z_c$ calibration approach was quite similar to that used by Darbyshire et al. (2016), where they tested a range of chill values to determine the most suitable heat accumulation level. However, when selecting a chill value range subjectively without including the endodormancy dates (minimum chill accumulation end date), the compensatory effect between phases can yield lower RMSE values with different $y_c$ and $z_c$ combinations compared to selection using endodormancy dates.
## 4.4. Proposing a PhenoFlex framework tailored for olive using endodormancy dates and flowering data for calibration

The dynamic sub-model in the PhenoFlex framework has consistently been applied in several studies due to its high performance compared to existing chill estimation models (Fernandez et al., 2020; Luedeling et al., 2013). Users often ignore the model developer's recommendation for pre-use calibration due to the lack of an accessible calibration platform. PhenoFlex now provides calibration access within its framework, thereby facilitating comparison of our fitted dynamic sub-model with the default dynamic model described by (Fishman et al., 1987a; 1987b).

Significant differences have been noted between the fitted and the default dynamic sub-models across all parameters. In the fitted DM sub-model, both T<sub>f</sub> and the slope were greater than in the default DM sub-model, with T<sub>f</sub> values of 7.9 °C and a slope of 8 for the fitted dynamic sub-model and T<sub>f</sub> of 4 °C and 1.6 K<sup>-1</sup> for the default dynamic sub-model. These differences account for the variations in chill amounts documented for PM in a previous study (Abou-Saaid et al., 2022), with y<sub>c</sub> of 27.9 ± 6.1 CP reported in Abou-Saaid et al. (2022) versus 58.00 ± 15.39 CP reported here, even with the same season onset. Note that the default DMs used in previous studies regarding olive chill requirements were underestimated (Abou-Saaid et al., 2022; Elloumi et al., 2020).

The fitted parameters for the dynamic sub-model in the PhenoFlex framework in our study was quite similar to the values reported by Picornell et al. (2023), except for the slope. In our case, the slope was 3.56±8.42, i.e. less than the 43.70±8.82 values reported for the same parameter in the study of Picornell et al. (2023). However, T<sub>f</sub> was similar to that obtained in our study, i.e. ≈7 °C. Despite the earlier season onset reported in Picornell et al. (2023) (1st October) and the steeper slope, implying more rapid chill accumulation when T<sub>f</sub> is reached. The chill amounts estimated in Picornell et al. (2023) were lower, with y<sub>c</sub> of 47.09 ±2.01 CP vs. 58.00 ± 15.39 CP in our case. These disparities could be explained by the temperature differences between the two contrasted sites, suggesting that in Alentejo the temperatures did not reach optimum for chill accumulation or that the endodormancy dates were earlier. There could also be a compensatory effect between phases that may alter the exact amounts of y<sub>c</sub> as this study did not include endodormancy dates for of y<sub>c</sub> and z<sub>c</sub> calibration. Note also that, when calibrating the PhenoFlex model with its multiple parameters, many variations can arise in the fitting procedure. This indicates that comparing parameters across studies may not be the best approach. For instance, the extent of chill noted in our study may not be the same as that noted in another study.

The temperature threshold in the GDH sub-model was quite similar to the ranges obtained when applying the default model (Anderson et al., 1986), with critical temperature at which accumulation starts being lower than that of the default model (~3 °C vs 4 °C). The same result was obtained when Picornell et al. (2023) tailored PhenoFlex for olive, except for T<sub>c</sub>, i.e. the critical temperature at which heat accumulation stops, which was higher (40±2.16 °C) compared to that noted in our study (34.28±4.6 °C).

Unlike deciduous trees, olive buds remain undifferentiated until dormancy release (Haberman et al., 2017), and chill requirements are lower (e.g., 58 CP vs. 80+ CP in apples). Additionally, olive dormancy is more sensitive to fluctuating winter temperatures (Rallo and Martin, 1991), necessitating cultivar-specific calibration. Our forcing experiments and PhenoFlex adaptation address these unique traits. The chill accumulation range obtained by DM in our study was similar to thresholds previously reported by (Hackett and Hartmann, 1967), who identified an optimal chill range of 7 °C to 16 °C, compared to our study where it was between 6 °C and 18 °C. A similar flower initiation pattern has also been observed in Manzanillo and Ascolano olive cultivars, with a minimum of 2 °C and a maximum of 15 °C (Hartmann and Whisler, 1975).

In warmer Mediterranean regions (e.g., Morocco, Tunisia), delayed

chill accumulation (December–January) reflects marginal winter temperatures (Fraga et al., 2019). Under climate change, such areas may face insufficient chill, exacerbating flowering asynchrony (Abou-Saaid et al., 2022). Our model's cultivar-specific calibration (58 CP for PM) offers a template to identify climate-resilient cultivars. Suboptimal chilling (<58 CP for PM) may lead to erratic budbreak and floral abortion (Ben Dhiab et al., 2017). In warmer regions, low-chill cultivars such as 'Arbequina' (~12 CP, Abou-Saaid et al. (2022) could be a promising candidate for future adaptation. However, the assessment methodology has to be taken with caution as it was based on the Dynamic Model using default parameters developed for peach by (Erez et al., 1990). We demonstrated that the default DMs used in previous studies regarding olive chill requirements were underestimated (Abou-Saaid et al., 2022). Therefore, our model's thresholds provide a more tailored approach for identifying suitable cultivars under changing climatic conditions.

## 5. Conclusion

PhenoFlex calibration requires careful consideration of key parameters such as the season onset and endodormancy dates. The efficacy of using 1st January as the season onset for the prediction of flowering dates in the PM cultivar, supported by PLS analysis findings that indicated the same chill onset, underscores the importance of this parameter in the calibration process. The potential of obtaining misleading results due to the compensatory effects between y<sub>c</sub> and z<sub>c</sub> in PhenoFlex calibration process should be kept in mind, while highlighting the need for incorporating endodormancy dates in the model.

By validating a model for the PM cultivar, we provide a useful tool for predicting flowering dates and set a benchmark for future research. This model should be further tested for its applicability on a larger scale and across different cultivars so as to pave the way for ongoing investigations and phenological modeling enhancement.

## Funding

This research was funded through Labex AGRO 2011 - LABX-002, ClimOliveMed project n° 2003-001 (under the I-Site Muse 658 framework) coordinated by Agropolis Foundation. It was conducted as part of the PhD thesis of Omar Abou-Saaid, who was funded by a grant co-financed by INRAE/Initiative TSARA and by the ClimOliveMed project.

## CRediT authorship contribution statement

**Omar Abou-Saaid:** Conceptualization, Writing – review & editing, Writing – original draft, Methodology, Data curation, Formal analysis, Visualization, Software, Validation. **Bouchaib Khadari:** Conceptualization, Methodology, Writing – review & editing, Supervision, Validation, Project administration, Funding acquisition.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper

## Acknowledgments

We warmly thank Adnane El Yaacoubi and Ahmed El Bakkali for advice and help in conducting the forcing test experiments. We also thank Hayat Zaher, Magalie Delalande and Adnane El Yaacoubi for their comments on the first draft of the paper. We acknowledge Eike Lüdeling for helpful comments on the latest version, and David Manley for the English corrections—he is a professional scientific English native speaking translator and reviser.
## Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.agrformet.2025.110752.

## Data availability

Data will be made available on request.

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