{"paper_id":"09554dae-55fe-490a-bde7-985f4bd87e7b","body_text":"Alternative modelling approaches significantly differ in simulating summer crops phenology in Mediterranean Europe | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Alternative modelling approaches significantly differ in simulating summer crops phenology in Mediterranean Europe Giovanni Maria Poggi, Marco Vignudelli, Francesca Di Cesare, Francesca Ventura This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7650147/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 09 Jan, 2026 Read the published version in International Journal of Biometeorology → Version 1 posted 4 You are reading this latest preprint version Abstract Variations in temperature trends are considerably impacting plants’ phenology. Most predictive models share the concept of Growing Degree Days (GDDs). Among available formulations, the ones not considering the effects of high temperatures on plants’ development seem no longer adequate, due to the increasing frequency of heat waves, leading to misinterpretation of climate effects. The aim of the present work is to compare six different degree-days models, in order to assess which of them could give the best results in terms of GDDs calculation for summer crops in Mediterranean Europe. Specifically, average method, single triangle method (with also three different cut-off techniques: horizontal, vertical, intermediate) and beta-distribution function method were tested. For this purpose 22 years of phenological data were used, comparing “standard years” and “warm years” (defined as those in which average temperature during June – August was below and above, or equal to, the median value of the 22-years period, respectively). Models were compared via Root Mean Square Error (RMSE) and Diebold-Mariano test, to assess differences in their predictive performance. Results showed that the use of models considering the negative effects of high temperatures in the ripening period significantly boost predictive accuracy. Among these approaches, the physiologically based beta-distribution function provided the best results. However, simpler methods, which could facilitate the acquisition of modelling novelty in operational contexts, having the advantage of being easy-to-use also proved to be significantly improving, such as intermediate cut-off technique, which among geometrical models can be considered the best approximation of crops physiological response. Degree-days calculation climate change cut-off techniques thermal thresholds Beta-distribution function. Figures Figure 1 Figure 2 Figure 3 Introduction Plants’ phenological development, referring to the periodically recurring events throughout their life cycle (Lieth 1974 ) primarily depends on air temperature, which is recognized as its major driving force (Schwartz 2003 ). The connection between air temperature and plants phenology has been translated into the Growing Degree Days (GDDs) concept, defined as the thermal time accumulated during a period of time, generally a day (24 hours) (Mcmaster and Wilhelm 1997 ). This agrees with the evidence that physiological processes related to progression of the life cycle in poikilotherm organisms are temperature-dependent, as the enzymes’ functionality and the alterations in their conformation are induced by thermal variations (Sharper and Demichele 1977). The concept of thermal time accumulation was firstly introduced in the 18th century by de Reaumur, who found a proportionality between plant development and the temperature sum over time (de Reaumur R.A.F., 1735). Since then, various modeling approaches have been developed to simulate plants phenology through GDDs accumulation. Most of these models share the assumption that a plant starts cumulating thermal time once temperatures rise above a minimum threshold (base temperature - T base ), required to transition between phenological stages, and ceases accumulation when temperature exceeds an upper threshold (T up ) (Mcmaster and Wilhelm 1997 ; Chuine and Régnìere 2017 ; Piao et al. 2019 ). The consideration that plant’s development is constrained by a minimum (T base ) and maximum (T up ) cardinal temperature reflects the fact that each species has a specific ‘thermal kinetic window’, i.e. a temperature range ensuring optimal enzyme activity. Outside this window, enzyme denaturation can occur, in turn disrupting metabolic reactions (Burke, Mahan, and Hatfield 1988 ). The simplest approach to predict plant phenology is the so-called “rectangle” or “average” method (Arnold 1960 ), which consists in calculating GDDs as the difference between daily average air temperature (T avg ) and T base , constrained to zero when T avg < T base (Stewart, Dwyer, and Carrigan 1998). However, this approach presents several weaknesses, due to its excessive simplification. Notably, it assumes a linear relationship between temperature and GDDs across the whole range of temperatures with T > T base , despite the recognized evidence that the temperature response of poikilotherm organisms is inherently nonlinear (Maiorano 2012 ). Modified approaches consider that phenology rates linearly increase from T base to the optimal temperature (T opt ) and simulate a nonlinear decrease once daily temperature exceeds T opt , down to zero when temperature is higher than T up (Yin et al. 1995 ). Another limitation of the average method is the lack of consideration of daily temperature fluctuations, which cause large variations on developmental rates with respect to constant temperatures in poikilotherm organisms (Worner 1992 ). Most advanced models solve these limitations by adopting the beta distribution function, which requires defining T base , T opt and T up . According to this approach, thermal time is set to zero when T < T base or T > T up , and reaches its maximum at T = T opt , with nonlinear decrease in the range T opt - T up . This function can be computed with hourly temperature data as input, explicitly considering the whole range of daily temperature fluctuations (Zhou and Wang 2018 ). Other easy-to-use methods for estimating GDDs accumulation are employed in field-operational contexts, requiring daily T min and T max as input. These methods assume that the daily temperature variation can be approximated by a geometrical shape, such as in the single triangle method (Snyder et al. 1999 ). By representing the 24-hour temperature profile as a triangle, the cumulative GDDs are estimated based on the area of the triangle, serving as an approximation of the integral under the daily temperature curve. Moreover, to account for the negative effects of temperatures higher than T opt , the single triangle method can be adapted using various “cut-off” approaches (horizontal, vertical, intermediate). In these modified methods, the degree-day calculation area is adjusted based on an upper threshold temperature. Depending on the chosen strategy, the GDDs rate begins to decrease if the threshold is set to T opt , or stops entirely when threshold is set to T up (University of California, www.ipm.ucdavis.edu/WEATHER/ddconcepts.html ). Given these premises, GDDs calculation methods not considering negative effects of high temperatures may perform well under ‘standard’ climate. However, they can become inadequate in the context of climate change where the increasing frequency of heat waves may lead to misinterpretations of climate effects on actual phenological responses. This is because the assumption of a linear relationship between temperature and developmental rate introduces significant errors as temperatures approaches extreme values (Maiorano et al. 2012 ; Zhou and Wang 2018 ). Climate change has indeed greatly shifted the timing of major phenological events, with strong impacts on crops development, yield and quality(Piao et al. 2019 ; Poggi et al. 2022 ; Fornaciari et al. 2023 ), paving the way to manifold phenology model comparison studies (Chuine and Régnìere 2017 ). However, even today, phenological models assuming a linear developmental rate above T base are widely used, especially in field-operational contexts. This widespread use is due to the fact that these models often produced satisfactory results under intermediate temperature conditions(Zhou and Wang 2018 ), and therefore continue to be routinely applied despite the challenges posed by the current climate change scenario. The lack of long and robust phenological observation datasets often hampers the assessment of the magnitude of errors done by these models in reproducing specific phenophases, and the possible improvements from the adoption of alternative models. Furthermore, since phenology is influenced not only by temperature but also by other environmental-specific factors, it is important that such investigations are carried out for each area of interest (Stewart, Dwyer, and Carrigan 1998; Schwartz 2003 ). The aim of the present work is to compare the performance of alternative modeling approaches in simulating the phenology of summer crops in Mediterranean Europe in the current climate change scenario. Materials and methods Phenological observations and weather data The observation dataset used in this study has been collected over 22 years (2003–2024), and has been derived from the phenological bulletins weekly released by the Department of Agricultural and Food Sciences (DISTAL), University of Bologna. Three relevant summer crops for Mediterranean Europe were chosen: maize ( Zea mays , L.), sorghum ( Sorghum vulgare Pers.) and sunflower ( Helianthus annuus L.). Phenological surveys were carried out according to the Phenagri protocol (Pasquini 2006) in Cadriano (Bologna, Italy) (44◦ 330 0300’ N, 11◦ 240 3600 E). Crop phenology phases were collected following the BBCH scale (Biologische Bundesanstalt, Bundessortenamt, and CHemical industry), which encodes plants’ development stages using a double-digit code from sowing (00) to harvest (99). This scale consists of ten main stages (0– 9), each divided into ten secondary stages (Meier 1997). Weather data for GDDs calculation (daily maximum and minimum and hourly temperatures) were provided by DISTAL agrometeorological station, sited within the agro-phenological station. Degree-Days models Six degree-days models were compared in this study. The first method is the average method (Arnold 1960 ): $$\\:GDD=\\frac{Tmax+Tmin}{2}-Tbase\\:$$ Where $$\\:Tmin=Tbase\\:if\\:Tmin\\:Tup\\frac{\\frac{}{}}{\\frac{}{}}\\end{array}\\right.$$ where HTT is Hourly Thermal Time and T h is hourly air temperature. Input data and parameters requested by each model are schematically presented in Table 1 Table 1 Input data and parameters requested by each degree-days model considered in the present study. Tmin is minimum daily temperature, Tmax is maximum daily temperature, Th is hourly air temperature, Tbase, Topt and Tup are respectively crop minimum, optimum and maximum cardinal temperatures. Tmin Tmax Th Tbase Topt Tup Average ✓ ✓ ✓ Single triangle ✓ ✓ ✓ Horizontal cut-off ✓ ✓ ✓ ✓ Intermediate cut-off ✓ ✓ ✓ ✓ Vertical cut-off ✓ ✓ ✓ ✓ Beta-distribution function ✓ ✓ ✓ ✓ Modeling test and statistical analysis To evaluate the effects of high temperature regimes on degree-days models for summer crops (maize, sorghum and sunflower), weather data were categorized into “standard” and “warm” years, following Fornaciari et al. ( 2023 ). Specifically, “standard” and “warm” years were defined as those in which the average temperature during June – August was below and above (or equal to) the median value of the 22-years period, respectively. The first step of the analysis consisted in the models calibration using data from “standard” years. For each crop and model, the Cumulated Growing Degree Days (CGDD) required to reach BBCH 65 (full flowering) and BBCH 89 (full maturity) were calculated, in order to define the thermal requirements to reach these phenological phases in standard years. In the second phase, models were validated using data from “warm” years to evaluate their performance under elevated temperature scenario. Each model was applied to simulate the Days After Sowing (DAS) when BBCH 65 and BBCH 89 were reached using calibrated CGDD from the first step. These simulations were then compared with field-observed DAS from phenological bulletins, using Root Mean square Error (RMSE) as accuracy metric. To verify whether the models showed a significantly different predictive capacity, the Diebold-Mariano test was conducted (p value = 0.05). All statistical analyses were performed in R (R Development Core Team 2021 ), using packages rstatix (Alboukadel Kassambara 2023) and forecast (Hyndman and Khandakar 2008). Results The classification of years in “standard” and “warm” categories is presented in Table 2 . CGDD to reach BBCH stages 65 and 89 in “standard” years are reported for each degree-days model and crop in Table 3 . Table 2 Classification of the 22-year period into “standard” and “warm” years based on average temperature from June to August. T = temperature. Median climatic value 2003–2024 period (°C) 24.5 standard years average T in June - August trimester (°C) warm years average T in June - August trimester (°C) 2004 23.5 2003 26.8 2005 22.8 2009 24.5 2006 22.4 2012 25.9 2007 23.7 2015 25.1 2008 24.0 2017 26.1 2010 24.0 2018 24.9 2011 24.4 2019 26.0 2013 23.8 2021 24.9 2014 23.0 2022 25.6 2016 23.9 2023 24.9 2020 24.2 2024 26.0 Table 3 Calibrated thermal threshold (CGDD) to reach BBCH 65 and BBCH 89 in “standard” years for each degree-day model and crop. Degree-days model Crop CGDDs for BBCH 65 CGDDs for BBCH 89 Average Maize 840 1742 Sorghum 908 1632 Sunflower 1213 2390 Single Triangle Maize 837 1757 Sorghum 909 1633 Sunflower 1215 2392 Vertical cut-off Maize 837 1757 Sorghum 909 1633 Sunflower 1215 2392 Horizontal cut-off Maize 835 1755 Sorghum 905 1615 Sunflower 1212 2373 Intermediate cut-off Maize 835 1721 Sorghum 901 1596 Sunflower 1210 2354 Beta-distribution Maize 1122 2176 Sorghum 1179 2001 Sunflower 1569 2897 With regard to the flowering phase, for all crops, based on RMSE values and the results of Diebold-Mariano test (Fig. 2 a and Fig. 3 ), no significant differences emerged among the tested models in their ability to predict BBCH 65. BBCH 89 showed different results (Fig. 2 b and Fig. 3 ). The prediction of the DAS for the reaching of BBCH 89, with average, single triangle and vertical cut-off methods showed similar RMSE, for the three crops and when considered as average of all species. On the contrary, horizontal cut-off method resulted in a significant improvement with respect to average, single triangle and vertical cut-off. However, horizontal cut-off method resulted to be more imprecise respect to intermediate cut-off, since this latter cut-off technique showed a lower RMSE (7.4, 11.2, 7.3 for maize, sunflower and sorghum, respectively) and a significantly better predictive performance when subjected to Diebold-Mariano test compared to the horizontal cut-off method. Finally, beta-distribution resulted to be more precise than any other method analyzed. Specifically, it showed the best results for all crops, with RMSE equal to 5.5, 9.2, and 6.4 for maize, sunflower and sorghum, respectively and significantly better predictive performance compared to all other models analyzed. Discussion No significant differences emerged among the tested models in their ability to predict BBCH 65. This is probably because during “warm years”, full flowering was, on average, reached on 25th June for maize, 4th July for sunflower and 27th June for sorghum. This phenological stage was then reached before the onset of high summer temperatures, which explains the small differences in CGDD between models, disregarding the consideration of an upper threshold temperature. In specific, the vertical cut-off method obtained the same CGDD than the single triangle method as the upper threshold temperature (40°C) was never reached in the explored conditions. Please note that RMSE presented are in DAS, meaning that the differences for BBCH65 are at most 5 days. The frequency with which phenological observations are made in the agrophenological station is weekly, and therefore this RMSE is lower than the sampling frequency. In practice, the error is lower than the resolution of the measurements. The prediction of the DAS for the reaching of BBCH 89, with average, single triangle and vertical cut-off methods showed similar results. This is not surprising. In fact, both average and single triangle methods do not consider any upper thresholds, and, as previously observed by (Maiorano 2012 ), in the modelling of GDDs cumulation for poikilothermic organisms, vertical cut-off does not consider any slowdown of GDDs cumulation above T opt , until T up is reached. Therefore, by setting T up equal to 40°C, the results obtained were superimposable to the single triangle method without adopting cut-off techniques, given the low frequency with which a temperature at least equal 40°C was recorded in the summer trimester for the considered years (5 times in total, all in 2003 summer season). On the contrary, horizontal cut-off method resulted in a significant improvement with respect to average, single triangle and vertical cut-off, as it takes into account that, above T opt , the linear relationship between air temperature increase and GDDs cumulation is interrupted. However, this method resulted to be more imprecise respect to intermediate cut-off. In fact, the first one is still incorrect for temperatures higher than optimal, assuming that development continues at a constant rate above the upper threshold, thus not considering the detrimental effect of excessive temperatures on plant development. Thus, intermediate cut-off method can be considered a better approximation of the physiological response of the crop, considering that plant development slows at temperatures above the upper threshold (fixed equal to T opt ). Finally, beta-distribution, taking into account daily temperature fluctuation (using hourly temperature input data) and being physiologically-based, resulted to be more precise than any other method analyzed, as in previous phenological studies (Maiorano 2012 ; Zhou and Wang 2018 ). Thus, considering the results of all crops together, intermediate cut-off proved to be the best among geometrical cut-off techniques, and beta-distribution showed the overall best results. Conclusions This study compared alternative degree-days models to identify the most accurate for GDDs calculation in summer crops under climate change conditions in Mediterranean Europe, using a long term phenological and weather dataset for calibration and validation. Considering that oversimplified degree-days models (such as average method) are still frequently employed in field-operational contexts, Decision Supporting Systems (DSS) and regional services, physiologically-based beta-distribution function method and cut-off techniques applied to single triangle method were considered to take into account the detrimental effects of high thermal regimes associated with climate change. In particular, geometrical approximation methods require specific validation, as their performance can deeply vary in function of the time of the year, the geographical location and the biology of the crop under consideration. For these reasons, case study such the one here presented are precious source of information about the possibility of successfully employ cut-off techniques for the modelling of GDDs cumulation in this specific area. In addition, this work allows phenological data sharing, which is gaining more and more importance in the scientific community in the framework of climate change, as this challenging global phenomenon has already greatly shifted the timing of major phenological events, having critical impacts on agroecosystems functions, crop management schemes and both qualitative and quantitative yield aspects (Piao et al. 2019 ; Mereu et al. 2021 ; Poggi et al. 2022 ). Hence, present work showed that in the Mediterranean Europe area, in the context of climate change, for key spring crops such as maize, sorghum and sunflower, while modelling solutions such as average and single triangle method do not yet produce significant errors in the estimation of full flowering, their overshoot becomes essential for the estimation of full maturity. The physiologically based beta-distribution function method provided the best results; however, geometrical cut-off, simpler than beta-distribution function method, also proved to be significantly improving, such as, in particular, intermediate cut-off technique, which among geometrical models can be considered the best approximation of the physiological response of crops. This method could facilitate the acquisition of modelling novelty in field-operational contexts and DSS, having the advantage of being easy-to-use (using as input minimum and maximum daily temperature instead of hourly temperature). Rising temperatures in the Mediterranean, recognized as a hotspot for climate change, highlight the urgent need for adaptive strategies of the agroecosystems. In this framework, enhancing the accuracy of key-crop modeling through improved GDDs calculation is vital for optimizing agronomic practices and guarantee satisfactory and stable yields in the next future, as well as for enabling data-driven decisions and promoting climate-smart agriculture, clarifying, through precise quantification, the relationships between ongoing climate change and the adaptive phenological response of crops. Declarations Competing Interests The authors have no relevant financial or non-financial interests to disclose. Funding financial support was received from ARPAE (Regional Agency for Prevention, Environment and Energy of Emilia-Romagna), which funded the agro-phenological station from which data used in this study were collected. Author contributions Conceptualization: Giovanni Maria Poggi, Francesca Ventura ; Methodology: Giovannni Maria Poggi; Formal analysis and investigation: Giovanni Maria Poggi, Marco Vignudelli, Francesca di Cesare; Writing - original draft preparation: Giovanni Maria Poggi; Writing - review and editing: Francesca Ventura ; Funding acquisition: Francesca Ventura ; Supervision: Francesca Ventura Acknowledgements Authors acknowledge ARPAE (Regional Agency for Prevention, Environment and Energy of Emilia-Romagna) for funding the agro-phenological station from which the data used in this study were collected. References Alboukadel Kassambara. (2023) Rstatix R Package. Arnold CY (1960) Maximum-Minimum Temperatures as a Basis for Computing Heat Units. Proceedings. American Society for Horticultural Science 76 Burke JJ, Mahan JR, Hatfield JL (1988) Crop-Specific Thermal Kinetic Windows in Relation to Wheat and Cotton Biomass Production. 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Environ Entomol 21(4):689–699. https://doi.org/https://doi.org/10.1093/ee/21.4.689 Yin X, Kropff MJ, Mclaren G, Romeo MV (1995) AGRICULTURAL AND FOREST METEOROLOGY A Nonlinear Model for Crop Development as a Function of Temperature. Agric For Meteorol. 77 Zhou G, Wang Q (2018) A New Nonlinear Method for Calculating Growing Degree Days. Sci Rep 8(1):1–14. https://doi.org/10.1038/s41598-018-28392-z Cite Share Download PDF Status: Published Journal Publication published 09 Jan, 2026 Read the published version in International Journal of Biometeorology → Version 1 posted Reviewers agreed at journal 25 Sep, 2025 Reviewers invited by journal 20 Sep, 2025 Editor assigned by journal 18 Sep, 2025 First submitted to journal 18 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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09:11:27\",\"extension\":\"html\",\"order_by\":24,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"acdc-reference\",\"size\":99081,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"earlyproof.html\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7650147/v1/c31f8fef244ebc7871b9e947.html\"},{\"id\":92580172,\"identity\":\"cac841e4-4852-42a0-9d32-5b49982bbcaa\",\"added_by\":\"auto\",\"created_at\":\"2025-10-01 09:11:27\",\"extension\":\"png\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":355267,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003e\\u003cem\\u003eDegree-days models based on geometrical approximations used in this study: single triangle (a) (with no cut-off), horizontal cut-off (b), intermediate cut-off (c), vertical cut-off (d). Tbase = crop base temperature. Tup = crop upper threshold temperature, Tmax = maximum daily temperature, Tmin = minimum daily temperature. Solid line represents daily temperature dynamic.\\u003c/em\\u003e\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure1.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7650147/v1/d70d2332f5a235b468877bfa.png\"},{\"id\":92580423,\"identity\":\"49e2fccd-3f3b-4d0f-81aa-9d86c192ca6b\",\"added_by\":\"auto\",\"created_at\":\"2025-10-01 09:19:27\",\"extension\":\"png\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":1272826,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003e\\u003cem\\u003eComparison of the performance of tested degree days models in reproducing BBCH stages 65 (a) and 89 (b). Histograms show RMSE between observed and simulated DAS for each crop.\\u003c/em\\u003e\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure2.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7650147/v1/cec985febcd41b76031ee2a1.png\"},{\"id\":92580421,\"identity\":\"014d346a-fc04-40f9-a4f1-edd3fb44d5a3\",\"added_by\":\"auto\",\"created_at\":\"2025-10-01 09:19:27\",\"extension\":\"png\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":835697,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003e\\u003cem\\u003eComparison of alternative degree days models. Histograms show the RMSE between simulated and observed Days After Sowing (DAS) of BBCH stages 65 (left) and 89 (right) for the three tested crops. Different letters indicate statistically significant differences in predictive performance among models, based on the Diebold-Mariano test (p \\u0026lt; 0.05).\\u003c/em\\u003e\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"Figure3.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7650147/v1/fb1b66ae4347d7f345c35e3a.png\"},{\"id\":100069156,\"identity\":\"3a8a9b09-9ff2-4f04-923f-bc9c22d08b8a\",\"added_by\":\"auto\",\"created_at\":\"2026-01-12 16:10:54\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":2802100,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7650147/v1/deabf757-0736-4b9c-b951-69c8d07fad77.pdf\"}],\"financialInterests\":\"\",\"formattedTitle\":\"Alternative modelling approaches significantly differ in simulating summer crops phenology in Mediterranean Europe\",\"fulltext\":[{\"header\":\"Introduction\",\"content\":\"\\u003cp\\u003ePlants\\u0026rsquo; phenological development, referring to the periodically recurring events throughout their life cycle (Lieth \\u003cspan class=\\\"CitationRef\\\"\\u003e1974\\u003c/span\\u003e) primarily depends on air temperature, which is recognized as its major driving force (Schwartz \\u003cspan class=\\\"CitationRef\\\"\\u003e2003\\u003c/span\\u003e). The connection between air temperature and plants phenology has been translated into the Growing Degree Days (GDDs) concept, defined as the thermal time accumulated during a period of time, generally a day (24 hours) (Mcmaster and Wilhelm \\u003cspan class=\\\"CitationRef\\\"\\u003e1997\\u003c/span\\u003e). This agrees with the evidence that physiological processes related to progression of the life cycle in poikilotherm organisms are temperature-dependent, as the enzymes\\u0026rsquo; functionality and the alterations in their conformation are induced by thermal variations (Sharper and Demichele 1977). The concept of thermal time accumulation was firstly introduced in the 18th century by de Reaumur, who found a proportionality between plant development and the temperature sum over time (de Reaumur R.A.F., 1735). Since then, various modeling approaches have been developed to simulate plants phenology through GDDs accumulation. Most of these models share the assumption that a plant starts cumulating thermal time once temperatures rise above a minimum threshold (base temperature - T\\u003csub\\u003ebase\\u003c/sub\\u003e), required to transition between phenological stages, and ceases accumulation when temperature exceeds an upper threshold (T\\u003csub\\u003eup\\u003c/sub\\u003e) (Mcmaster and Wilhelm \\u003cspan class=\\\"CitationRef\\\"\\u003e1997\\u003c/span\\u003e; Chuine and R\\u0026eacute;gn\\u0026igrave;ere \\u003cspan class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e; Piao et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e). The consideration that plant\\u0026rsquo;s development is constrained by a minimum (T\\u003csub\\u003ebase\\u003c/sub\\u003e) and maximum (T\\u003csub\\u003eup\\u003c/sub\\u003e) cardinal temperature reflects the fact that each species has a specific \\u0026lsquo;thermal kinetic window\\u0026rsquo;, i.e. a temperature range ensuring optimal enzyme activity. Outside this window, enzyme denaturation can occur, in turn disrupting metabolic reactions (Burke, Mahan, and Hatfield \\u003cspan class=\\\"CitationRef\\\"\\u003e1988\\u003c/span\\u003e).\\u003c/p\\u003e\\n\\u003cp\\u003eThe simplest approach to predict plant phenology is the so-called \\u0026ldquo;rectangle\\u0026rdquo; or \\u0026ldquo;average\\u0026rdquo; method (Arnold \\u003cspan class=\\\"CitationRef\\\"\\u003e1960\\u003c/span\\u003e), which consists in calculating GDDs as the difference between daily average air temperature (T\\u003csub\\u003eavg\\u003c/sub\\u003e) and T\\u003csub\\u003ebase\\u003c/sub\\u003e, constrained to zero when T\\u003csub\\u003eavg\\u003c/sub\\u003e \\u0026lt; T\\u003csub\\u003ebase\\u003c/sub\\u003e (Stewart, Dwyer, and Carrigan 1998). However, this approach presents several weaknesses, due to its excessive simplification. Notably, it assumes a linear relationship between temperature and GDDs across the whole range of temperatures with T\\u0026thinsp;\\u0026gt;\\u0026thinsp;T\\u003csub\\u003ebase\\u003c/sub\\u003e, despite the recognized evidence that the temperature response of poikilotherm organisms is inherently nonlinear (Maiorano \\u003cspan class=\\\"CitationRef\\\"\\u003e2012\\u003c/span\\u003e). Modified approaches consider that phenology rates linearly increase from T\\u003csub\\u003ebase\\u003c/sub\\u003e to the optimal temperature (T\\u003csub\\u003eopt\\u003c/sub\\u003e) and simulate a nonlinear decrease once daily temperature exceeds T\\u003csub\\u003eopt\\u003c/sub\\u003e, down to zero when temperature is higher than T\\u003csub\\u003eup\\u003c/sub\\u003e (Yin et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e1995\\u003c/span\\u003e). Another limitation of the average method is the lack of consideration of daily temperature fluctuations, which cause large variations on developmental rates with respect to constant temperatures in poikilotherm organisms (Worner \\u003cspan class=\\\"CitationRef\\\"\\u003e1992\\u003c/span\\u003e). Most advanced models solve these limitations by adopting the beta distribution function, which requires defining T\\u003csub\\u003ebase\\u003c/sub\\u003e, T\\u003csub\\u003eopt\\u003c/sub\\u003e and T\\u003csub\\u003eup\\u003c/sub\\u003e. According to this approach, thermal time is set to zero when T\\u0026thinsp;\\u0026lt;\\u0026thinsp;T\\u003csub\\u003ebase\\u003c/sub\\u003e or T\\u0026thinsp;\\u0026gt;\\u0026thinsp;T\\u003csub\\u003eup\\u003c/sub\\u003e, and reaches its maximum at T\\u0026thinsp;=\\u0026thinsp;T\\u003csub\\u003eopt\\u003c/sub\\u003e, with nonlinear decrease in the range T\\u003csub\\u003eopt\\u003c/sub\\u003e - T\\u003csub\\u003eup\\u003c/sub\\u003e. This function can be computed with hourly temperature data as input, explicitly considering the whole range of daily temperature fluctuations (Zhou and Wang \\u003cspan class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e). Other easy-to-use methods for estimating GDDs accumulation are employed in field-operational contexts, requiring daily T\\u003csub\\u003emin\\u003c/sub\\u003e and T\\u003csub\\u003emax\\u003c/sub\\u003e as input. These methods assume that the daily temperature variation can be approximated by a geometrical shape, such as in the single triangle method (Snyder et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e1999\\u003c/span\\u003e). By representing the 24-hour temperature profile as a triangle, the cumulative GDDs are estimated based on the area of the triangle, serving as an approximation of the integral under the daily temperature curve. Moreover, to account for the negative effects of temperatures higher than T\\u003csub\\u003eopt\\u003c/sub\\u003e, the single triangle method can be adapted using various \\u0026ldquo;cut-off\\u0026rdquo; approaches (horizontal, vertical, intermediate). In these modified methods, the degree-day calculation area is adjusted based on an upper threshold temperature. Depending on the chosen strategy, the GDDs rate begins to decrease if the threshold is set to T\\u003csub\\u003eopt\\u003c/sub\\u003e, or stops entirely when threshold is set to T\\u003csub\\u003eup\\u003c/sub\\u003e (University of California, \\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003ewww.ipm.ucdavis.edu/WEATHER/ddconcepts.html\\u003c/span\\u003e\\u003c/span\\u003e).\\u003c/p\\u003e\\n\\u003cp\\u003eGiven these premises, GDDs calculation methods not considering negative effects of high temperatures may perform well under \\u0026lsquo;standard\\u0026rsquo; climate. However, they can become inadequate in the context of climate change where the increasing frequency of heat waves may lead to misinterpretations of climate effects on actual phenological responses. This is because the assumption of a linear relationship between temperature and developmental rate introduces significant errors as temperatures approaches extreme values (Maiorano et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2012\\u003c/span\\u003e; Zhou and Wang \\u003cspan class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e). Climate change has indeed greatly shifted the timing of major phenological events, with strong impacts on crops development, yield and quality(Piao et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e; Poggi et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e; Fornaciari et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e), paving the way to manifold phenology model comparison studies (Chuine and R\\u0026eacute;gn\\u0026igrave;ere \\u003cspan class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e). However, even today, phenological models assuming a linear developmental rate above T\\u003csub\\u003ebase\\u003c/sub\\u003e are widely used, especially in field-operational contexts. This widespread use is due to the fact that these models often produced satisfactory results under intermediate temperature conditions(Zhou and Wang \\u003cspan class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e), and therefore continue to be routinely applied despite the challenges posed by the current climate change scenario. The lack of long and robust phenological observation datasets often hampers the assessment of the magnitude of errors done by these models in reproducing specific phenophases, and the possible improvements from the adoption of alternative models. Furthermore, since phenology is influenced not only by temperature but also by other environmental-specific factors, it is important that such investigations are carried out for each area of interest (Stewart, Dwyer, and Carrigan 1998; Schwartz \\u003cspan class=\\\"CitationRef\\\"\\u003e2003\\u003c/span\\u003e). The aim of the present work is to compare the performance of alternative modeling approaches in simulating the phenology of summer crops in Mediterranean Europe in the current climate change scenario.\\u003c/p\\u003e\"},{\"header\":\"Materials and methods\",\"content\":\"\\u003cdiv id=\\\"Sec3\\\" class=\\\"Section2\\\"\\u003e\\n \\u003ch2\\u003ePhenological observations and weather data\\u003c/h2\\u003e\\n \\u003cp\\u003eThe observation dataset used in this study has been collected over 22 years (2003\\u0026ndash;2024), and has been derived from the phenological bulletins weekly released by the Department of Agricultural and Food Sciences (DISTAL), University of Bologna. Three relevant summer crops for Mediterranean Europe were chosen: maize (\\u003cem\\u003eZea mays\\u003c/em\\u003e, L.), sorghum (\\u003cem\\u003eSorghum vulgare\\u003c/em\\u003e Pers.) and sunflower (\\u003cem\\u003eHelianthus annuus\\u003c/em\\u003e L.). Phenological surveys were carried out according to the Phenagri protocol (Pasquini 2006) in Cadriano (Bologna, Italy) (44◦ 330 0300\\u0026rsquo; N, 11◦ 240 3600 E). Crop phenology phases were collected following the BBCH scale (Biologische Bundesanstalt, Bundessortenamt, and CHemical industry), which encodes plants\\u0026rsquo; development stages using a double-digit code from sowing (00) to harvest (99). This scale consists of ten main stages (0\\u0026ndash; 9), each divided into ten secondary stages (Meier 1997). Weather data for GDDs calculation (daily maximum and minimum and hourly temperatures) were provided by DISTAL agrometeorological station, sited within the agro-phenological station.\\u003c/p\\u003e\\n\\u003c/div\\u003e\\n\\u003ch3\\u003eDegree-Days models\\u003c/h3\\u003e\\n\\u003cp\\u003eSix degree-days models were compared in this study. The first method is the average method (Arnold \\u003cspan class=\\\"CitationRef\\\"\\u003e1960\\u003c/span\\u003e):\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equa\\\" class=\\\"Equation\\\"\\u003e\\n \\u003cdiv class=\\\"mathdisplay\\\" id=\\\"FileID_Equa\\\" name=\\\"EquationSource\\\"\\u003e$$\\\\:GDD=\\\\frac{Tmax+Tmin}{2}-Tbase\\\\:$$\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003e\\u003cem\\u003eWhere\\u003c/em\\u003e\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equb\\\" class=\\\"Equation\\\"\\u003e\\n \\u003cdiv class=\\\"mathdisplay\\\" id=\\\"FileID_Equb\\\" name=\\\"EquationSource\\\"\\u003e$$\\\\:Tmin=Tbase\\\\:if\\\\:Tmin\\u0026lt;Tbase$$\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003ewhere GDD is the daily accumulated degree-days, T\\u003csub\\u003emin\\u003c/sub\\u003e and T\\u003csub\\u003emax\\u003c/sub\\u003e are the minimum and maximum daily temperatures (\\u0026deg;C), and T\\u003csub\\u003ebase\\u003c/sub\\u003e is crop minimum cardinal temperature (\\u0026deg;C).\\u003c/p\\u003e\\n\\u003cp\\u003eThis study also considered the so-called geometric methods, taking into consideration daily temperature fluctuation, assuming that daily temperature profile can be approximated to a specific geometrical shape. Specifically, single triangle method with and without cut-off techniques were tested. The single triangle method and the different cut-off techniques are presented in Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e. Briefly, the standard single triangle method does not consider any upper threshold, thus GDDs cumulation proceeds up to daily T\\u003csub\\u003emax\\u003c/sub\\u003e (Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003ea). The horizontal cut-off method considers that development continues at a constant rate when temperature exceeds the upper threshold (Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003eb). The intermediate cut-off method assumes that development slows (but does not stop) at temperatures above the upper threshold (Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003ec). The vertical cut-off method considers that development totally stops over the upper threshold (Fig. \\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003ed). Considering the conceptualization of the different cut-off techniques, the upper threshold was set equal to crop T\\u003csub\\u003eopt\\u003c/sub\\u003e for horizontal and intermediate strategies, and equal to crop T\\u003csub\\u003eup\\u003c/sub\\u003e for vertical cut-off. Maize and sorghum T\\u003csub\\u003ebase\\u003c/sub\\u003e, T\\u003csub\\u003eopt\\u003c/sub\\u003e and T\\u003csub\\u003eup\\u003c/sub\\u003e adopted were 8\\u0026deg;C, 30\\u0026deg;C and 40\\u0026deg;C respectively, while for sunflower, 4\\u0026deg;C, 30\\u0026deg;C and 40\\u0026deg;C were used (Singh et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e; Zhou and Wang \\u003cspan class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e; Raes et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e).\\u003c/p\\u003e\\n\\u003cp\\u003eThe most refined approach considered in the present study is the physiologically-based degree-day modeling solution (based on the beta-distribution function), developed by (Yin et al. \\u003cspan class=\\\"CitationRef\\\"\\u003e1995\\u003c/span\\u003e), in the form proposed by (Zhou and Wang \\u003cspan class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e):\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equc\\\" class=\\\"Equation\\\"\\u003e\\n \\u003cdiv class=\\\"mathdisplay\\\" id=\\\"FileID_Equc\\\" name=\\\"EquationSource\\\"\\u003e$$\\\\:GDD=(\\\\sum\\\\:_{1}^{24}HTT)/24$$\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003e\\u003cem\\u003eWhere\\u003c/em\\u003e\\u003c/p\\u003e\\n\\u003cdiv id=\\\"Equd\\\" class=\\\"Equation\\\"\\u003e\\n \\u003cdiv class=\\\"mathdisplay\\\" id=\\\"FileID_Equd\\\" name=\\\"EquationSource\\\"\\u003e$$\\\\:HTT=\\\\:\\\\left\\\\{\\\\begin{array}{c}\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:0\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:if\\\\:\\\\:\\\\:\\\\:\\\\:Th\\\\:\\u0026lt;\\\\:Tbase\\\\frac{}{\\\\frac{}{\\\\frac{}{}}}\\\\frac{}{}\\\\\\\\\\\\:{\\\\left(\\\\frac{Th\\\\:-\\\\:Tbase}{Topt\\\\:-Tbase}\\\\right)\\\\left(\\\\frac{Tup\\\\:-\\\\:Th}{Tup\\\\:-\\\\:Topt}\\\\right)}^{\\\\frac{Tup\\\\:-\\\\:Topt}{Topt\\\\:-\\\\:Tbase}}\\\\left(Topt\\\\:-\\\\:Tbase\\\\right)\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:if\\\\:\\\\:\\\\:\\\\:\\\\:Tbase\\\\:\\\\le\\\\:\\\\:Th\\\\:\\\\le\\\\:\\\\:Tup\\\\:\\\\:\\\\:\\\\\\\\\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:0\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:\\\\:if\\\\:\\\\:\\\\:\\\\:\\\\:Th\\\\:\\u0026gt;\\\\:Tup\\\\frac{\\\\frac{}{}}{\\\\frac{}{}}\\\\end{array}\\\\right.$$\\u003c/div\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003e\\u003cbr\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003ewhere HTT is Hourly Thermal Time and T\\u003csub\\u003eh\\u003c/sub\\u003e is hourly air temperature.\\u003c/p\\u003e\\n\\u003cp\\u003eInput data and parameters requested by each model are schematically presented in Table\\u0026nbsp;\\u003cspan class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e\\u003c/p\\u003e\\n\\u003cdiv class=\\\"gridtable\\\"\\u003e\\n \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\"\\u003e\\u003cbr\\u003e\\u003c/div\\u003e\\n \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\"\\u003e\\u003cbr\\u003e\\u003c/div\\u003e\\n \\u003ctable id=\\\"Tab1\\\" border=\\\"1\\\"\\u003e\\n \\u003ccaption language=\\\"En\\\"\\u003e\\n \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 1\\u003c/div\\u003e\\n \\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\n \\u003cp\\u003eInput data and parameters requested by each degree-days model considered in the present study. Tmin is minimum daily temperature, Tmax is maximum daily temperature, Th is hourly air temperature, Tbase, Topt and Tup are respectively crop minimum, optimum and maximum cardinal temperatures.\\u003c/p\\u003e\\n \\u003c/div\\u003e\\n \\u003c/caption\\u003e\\n \\u003cthead\\u003e\\n \\u003ctr\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eTmin\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eTmax\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eTh\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eTbase\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eTopt\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003cth align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eTup\\u003c/p\\u003e\\n \\u003c/th\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/thead\\u003e\\n \\u003ctbody\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eAverage\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eSingle triangle\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eHorizontal cut-off\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eIntermediate cut-off\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eVertical cut-off\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003ctr\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003eBeta-distribution function\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003ctd align=\\\"left\\\"\\u003e\\n \\u003cp\\u003e✓\\u003c/p\\u003e\\n \\u003c/td\\u003e\\n \\u003c/tr\\u003e\\n \\u003c/tbody\\u003e\\n \\u003c/table\\u003e\\n\\u003c/div\\u003e\\n\\u003cp\\u003e\\u003cbr\\u003e\\u003c/p\\u003e\\n\\u003ch3\\u003eModeling test and statistical analysis\\u003c/h3\\u003e\\n\\u003cp\\u003eTo evaluate the effects of high temperature regimes on degree-days models for summer crops (maize, sorghum and sunflower), weather data were categorized into \\u0026ldquo;standard\\u0026rdquo; and \\u0026ldquo;warm\\u0026rdquo; years, following Fornaciari et al. (\\u003cspan class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e). Specifically, \\u0026ldquo;standard\\u0026rdquo; and \\u0026ldquo;warm\\u0026rdquo; years were defined as those in which the average temperature during June \\u0026ndash; August was below and above (or equal to) the median value of the 22-years period, respectively.\\u003c/p\\u003e\\n\\u003cp\\u003eThe first step of the analysis consisted in the models calibration using data from \\u0026ldquo;standard\\u0026rdquo; years. For each crop and model, the Cumulated Growing Degree Days (CGDD) required to reach BBCH 65 (full flowering) and BBCH 89 (full maturity) were calculated, in order to define the thermal requirements to reach these phenological phases in standard years. In the second phase, models were validated using data from \\u0026ldquo;warm\\u0026rdquo; years to evaluate their performance under elevated temperature scenario. Each model was applied to simulate the Days After Sowing (DAS) when BBCH 65 and BBCH 89 were reached using calibrated CGDD from the first step. These simulations were then compared with field-observed DAS from phenological bulletins, using Root Mean square Error (RMSE) as accuracy metric. To verify whether the models showed a significantly different predictive capacity, the Diebold-Mariano test was conducted (p value\\u0026thinsp;=\\u0026thinsp;0.05).\\u003c/p\\u003e\\n\\u003cp\\u003eAll statistical analyses were performed in R (R Development Core Team \\u003cspan class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e), using packages rstatix (Alboukadel Kassambara 2023) and forecast (Hyndman and Khandakar 2008).\\u003c/p\\u003e\"},{\"header\":\"Results\",\"content\":\"\\u003cp\\u003eThe classification of years in \\u0026ldquo;standard\\u0026rdquo; and \\u0026ldquo;warm\\u0026rdquo; categories is presented in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e. CGDD to reach BBCH stages 65 and 89 in \\u0026ldquo;standard\\u0026rdquo; years are reported for each degree-days model and crop in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab2\\\" border=\\\"1\\\"\\u003e\\u003ccaption language=\\\"En\\\"\\u003e\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 2\\u003c/div\\u003e\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\u003cp\\u003eClassification of the 22-year period into \\u0026ldquo;standard\\u0026rdquo; and \\u0026ldquo;warm\\u0026rdquo; years based on average temperature from June to August. T\\u0026thinsp;=\\u0026thinsp;temperature.\\u003c/p\\u003e\\u003c/div\\u003e\\u003c/caption\\u003e\\u003ccolgroup cols=\\\"5\\\"\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e\\u003cthead\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colspan=\\\"3\\\" nameend=\\\"c3\\\" namest=\\\"c1\\\"\\u003e\\u003cp\\u003eMedian climatic value 2003\\u0026ndash;2024 period (\\u0026deg;C)\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c5\\\" namest=\\\"c4\\\"\\u003e\\u003cp\\u003e24.5\\u003c/p\\u003e\\u003c/th\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003estandard years\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eaverage T in June - August trimester (\\u0026deg;C)\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003ewarm years\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003eaverage T in June - August trimester (\\u0026deg;C)\\u003c/p\\u003e\\u003c/th\\u003e\\u003c/tr\\u003e\\u003c/thead\\u003e\\u003ctbody\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2004\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e23.5\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003e2003\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e26.8\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2005\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e22.8\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003e2009\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e24.5\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2006\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e22.4\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003e2012\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e25.9\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2007\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e23.7\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003e2015\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e25.1\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2008\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e24.0\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003e2017\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e26.1\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2010\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e24.0\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003e2018\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e24.9\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2011\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e24.4\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003e2019\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e26.0\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2013\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e23.8\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003e2021\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e24.9\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2014\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e23.0\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003e2022\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e25.6\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2016\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e23.9\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003e2023\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e24.9\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2020\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e24.2\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003e2024\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e26.0\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003c/tbody\\u003e\\u003c/colgroup\\u003e\\u003c/table\\u003e\\u003c/div\\u003e\\u003c/p\\u003e\\u003cp\\u003e\\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab3\\\" border=\\\"1\\\"\\u003e\\u003ccaption language=\\\"En\\\"\\u003e\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 3\\u003c/div\\u003e\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\u003cp\\u003eCalibrated thermal threshold (CGDD) to reach BBCH 65 and BBCH 89 in \\u0026ldquo;standard\\u0026rdquo; years for each degree-day model and crop.\\u003c/p\\u003e\\u003c/div\\u003e\\u003c/caption\\u003e\\u003ccolgroup cols=\\\"4\\\"\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e\\u003cthead\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003eDegree-days model\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eCrop\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003eCGDDs for BBCH 65\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003eCGDDs for BBCH 89\\u003c/p\\u003e\\u003c/th\\u003e\\u003c/tr\\u003e\\u003c/thead\\u003e\\u003ctbody\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003eAverage\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMaize\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e840\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e1742\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSorghum\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e908\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e1632\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSunflower\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e1213\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e2390\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003eSingle Triangle\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMaize\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e837\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e1757\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSorghum\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e909\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e1633\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSunflower\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e1215\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e2392\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003eVertical cut-off\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMaize\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e837\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e1757\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSorghum\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e909\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e1633\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSunflower\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e1215\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e2392\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003eHorizontal cut-off\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMaize\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e835\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e1755\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSorghum\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e905\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e1615\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSunflower\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e1212\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e2373\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003eIntermediate cut-off\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMaize\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e835\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e1721\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSorghum\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e901\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e1596\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSunflower\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e1210\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e2354\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003eBeta-distribution\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMaize\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e1122\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e2176\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSorghum\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e1179\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e2001\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eSunflower\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e1569\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e2897\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003c/tbody\\u003e\\u003c/colgroup\\u003e\\u003c/table\\u003e\\u003c/div\\u003e\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eWith regard to the flowering phase, for all crops, based on RMSE values and the results of Diebold-Mariano test (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003ea and Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e), no significant differences emerged among the tested models in their ability to predict BBCH 65.\\u003c/p\\u003e\\u003cp\\u003eBBCH 89 showed different results (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003eb and Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e). The prediction of the DAS for the reaching of BBCH 89, with average, single triangle and vertical cut-off methods showed similar RMSE, for the three crops and when considered as average of all species. On the contrary, horizontal cut-off method resulted in a significant improvement with respect to average, single triangle and vertical cut-off. However, horizontal cut-off method resulted to be more imprecise respect to intermediate cut-off, since this latter cut-off technique showed a lower RMSE (7.4, 11.2, 7.3 for maize, sunflower and sorghum, respectively) and a significantly better predictive performance when subjected to Diebold-Mariano test compared to the horizontal cut-off method. Finally, beta-distribution resulted to be more precise than any other method analyzed. Specifically, it showed the best results for all crops, with RMSE equal to 5.5, 9.2, and 6.4 for maize, sunflower and sorghum, respectively and significantly better predictive performance compared to all other models analyzed.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\"},{\"header\":\"Discussion\",\"content\":\"\\u003cp\\u003eNo significant differences emerged among the tested models in their ability to predict BBCH 65. This is probably because during \\u0026ldquo;warm years\\u0026rdquo;, full flowering was, on average, reached on 25th June for maize, 4th July for sunflower and 27th June for sorghum. This phenological stage was then reached before the onset of high summer temperatures, which explains the small differences in CGDD between models, disregarding the consideration of an upper threshold temperature. In specific, the vertical cut-off method obtained the same CGDD than the single triangle method as the upper threshold temperature (40\\u0026deg;C) was never reached in the explored conditions. Please note that RMSE presented are in DAS, meaning that the differences for BBCH65 are at most 5 days. The frequency with which phenological observations are made in the agrophenological station is weekly, and therefore this RMSE is lower than the sampling frequency. In practice, the error is lower than the resolution of the measurements.\\u003c/p\\u003e\\u003cp\\u003eThe prediction of the DAS for the reaching of BBCH 89, with average, single triangle and vertical cut-off methods showed similar results. This is not surprising. In fact, both average and single triangle methods do not consider any upper thresholds, and, as previously observed by (Maiorano \\u003cspan citationid=\\\"CR8\\\" class=\\\"CitationRef\\\"\\u003e2012\\u003c/span\\u003e), in the modelling of GDDs cumulation for poikilothermic organisms, vertical cut-off does not consider any slowdown of GDDs cumulation above T\\u003csub\\u003eopt\\u003c/sub\\u003e, until T\\u003csub\\u003eup\\u003c/sub\\u003e is reached. Therefore, by setting T\\u003csub\\u003eup\\u003c/sub\\u003e equal to 40\\u0026deg;C, the results obtained were superimposable to the single triangle method without adopting cut-off techniques, given the low frequency with which a temperature at least equal 40\\u0026deg;C was recorded in the summer trimester for the considered years (5 times in total, all in 2003 summer season).\\u003c/p\\u003e\\u003cp\\u003eOn the contrary, horizontal cut-off method resulted in a significant improvement with respect to average, single triangle and vertical cut-off, as it takes into account that, above T\\u003csub\\u003eopt\\u003c/sub\\u003e, the linear relationship between air temperature increase and GDDs cumulation is interrupted. However, this method resulted to be more imprecise respect to intermediate cut-off. In fact, the first one is still incorrect for temperatures higher than optimal, assuming that development continues at a constant rate above the upper threshold, thus not considering the detrimental effect of excessive temperatures on plant development. Thus, intermediate cut-off method can be considered a better approximation of the physiological response of the crop, considering that plant development slows at temperatures above the upper threshold (fixed equal to T\\u003csub\\u003eopt\\u003c/sub\\u003e).\\u003c/p\\u003e\\u003cp\\u003eFinally, beta-distribution, taking into account daily temperature fluctuation (using hourly temperature input data) and being physiologically-based, resulted to be more precise than any other method analyzed, as in previous phenological studies (Maiorano \\u003cspan citationid=\\\"CR8\\\" class=\\\"CitationRef\\\"\\u003e2012\\u003c/span\\u003e; Zhou and Wang \\u003cspan citationid=\\\"CR24\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e).\\u003c/p\\u003e\\u003cp\\u003eThus, considering the results of all crops together, intermediate cut-off proved to be the best among geometrical cut-off techniques, and beta-distribution showed the overall best results.\\u003c/p\\u003e\"},{\"header\":\"Conclusions\",\"content\":\"\\u003cp\\u003eThis study compared alternative degree-days models to identify the most accurate for GDDs calculation in summer crops under climate change conditions in Mediterranean Europe, using a long term phenological and weather dataset for calibration and validation. Considering that oversimplified degree-days models (such as average method) are still frequently employed in field-operational contexts, Decision Supporting Systems (DSS) and regional services, physiologically-based beta-distribution function method and cut-off techniques applied to single triangle method were considered to take into account the detrimental effects of high thermal regimes associated with climate change. In particular, geometrical approximation methods require specific validation, as their performance can deeply vary in function of the time of the year, the geographical location and the biology of the crop under consideration. For these reasons, case study such the one here presented are precious source of information about the possibility of successfully employ cut-off techniques for the modelling of GDDs cumulation in this specific area. In addition, this work allows phenological data sharing, which is gaining more and more importance in the scientific community in the framework of climate change, as this challenging global phenomenon has already greatly shifted the timing of major phenological events, having critical impacts on agroecosystems functions, crop management schemes and both qualitative and quantitative yield aspects (Piao et al. \\u003cspan citationid=\\\"CR12\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e; Mereu et al. \\u003cspan citationid=\\\"CR11\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e; Poggi et al. \\u003cspan citationid=\\\"CR13\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e).\\u003c/p\\u003e\\u003cp\\u003eHence, present work showed that in the Mediterranean Europe area, in the context of climate change, for key spring crops such as maize, sorghum and sunflower, while modelling solutions such as average and single triangle method do not yet produce significant errors in the estimation of full flowering, their overshoot becomes essential for the estimation of full maturity. The physiologically based beta-distribution function method provided the best results; however, geometrical cut-off, simpler than beta-distribution function method, also proved to be significantly improving, such as, in particular, intermediate cut-off technique, which among geometrical models can be considered the best approximation of the physiological response of crops. This method could facilitate the acquisition of modelling novelty in field-operational contexts and DSS, having the advantage of being easy-to-use (using as input minimum and maximum daily temperature instead of hourly temperature). Rising temperatures in the Mediterranean, recognized as a hotspot for climate change, highlight the urgent need for adaptive strategies of the agroecosystems. In this framework, enhancing the accuracy of key-crop modeling through improved GDDs calculation is vital for optimizing agronomic practices and guarantee satisfactory and stable yields in the next future, as well as for enabling data-driven decisions and promoting climate-smart agriculture, clarifying, through precise quantification, the relationships between ongoing climate change and the adaptive phenological response of crops.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003e\\u003ch2\\u003eCompeting Interests\\u003c/h2\\u003e\\u003cp\\u003eThe authors have no relevant financial or non-financial interests to disclose.\\u003c/p\\u003e\\u003c/p\\u003e\\u003ch2\\u003eFunding\\u003c/h2\\u003e\\u003cp\\u003efinancial support was received from ARPAE (Regional Agency for Prevention, Environment and Energy of Emilia-Romagna), which funded the agro-phenological station from which data used in this study were collected.\\u003c/p\\u003e\\u003ch2\\u003eAuthor contributions\\u003c/h2\\u003e\\u003cp\\u003eConceptualization: Giovanni Maria Poggi, Francesca Ventura ; Methodology: Giovannni Maria Poggi; Formal analysis and investigation: Giovanni Maria Poggi, Marco Vignudelli, Francesca di Cesare; Writing - original draft preparation: Giovanni Maria Poggi; Writing - review and editing: Francesca Ventura ; Funding acquisition: Francesca Ventura ; Supervision: Francesca Ventura\\u003c/p\\u003e\\u003ch2\\u003eAcknowledgements\\u003c/h2\\u003e\\u003cp\\u003eAuthors acknowledge ARPAE (Regional Agency for Prevention, Environment and Energy of Emilia-Romagna) for funding the agro-phenological station from which the data used in this study were collected.\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\u003cli\\u003e\\u003cspan\\u003eAlboukadel Kassambara. 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Environ Entomol 21(4):689\\u0026ndash;699. \\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003ehttps://doi.org/https://doi.org/10.1093/ee/21.4.689\\u003c/span\\u003e\\u003cspan address=\\\"10.1093/ee/21.4.689\\\" targettype=\\\"DOI\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/li\\u003e\\u003cli\\u003e\\u003cspan\\u003eYin X, Kropff MJ, Mclaren G, Romeo MV (1995) AGRICULTURAL AND FOREST METEOROLOGY A Nonlinear Model for Crop Development as a Function of Temperature. Agric For Meteorol. 77\\u003c/span\\u003e\\u003c/li\\u003e\\u003cli\\u003e\\u003cspan\\u003eZhou G, Wang Q (2018) A New Nonlinear Method for Calculating Growing Degree Days. Sci Rep 8(1):1\\u0026ndash;14. \\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003ehttps://doi.org/10.1038/s41598-018-28392-z\\u003c/span\\u003e\\u003cspan address=\\\"10.1038/s41598-018-28392-z\\\" targettype=\\\"DOI\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/li\\u003e\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"international-journal-of-biometeorology\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"ijbm\",\"sideBox\":\"Learn more about [International Journal of Biometeorology](http://link.springer.com/journal/484)\",\"snPcode\":\"484\",\"submissionUrl\":\"https://www.editorialmanager.com/ijbm/default2.aspx\",\"title\":\"International Journal of Biometeorology\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false},\"keywords\":\"Degree-days calculation, climate change, cut-off techniques, thermal thresholds, Beta-distribution function.\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-7650147/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-7650147/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eVariations in temperature trends are considerably impacting plants\\u0026rsquo; phenology. Most predictive models share the concept of Growing Degree Days (GDDs). Among available formulations, the ones not considering the effects of high temperatures on plants\\u0026rsquo; development seem no longer adequate, due to the increasing frequency of heat waves, leading to misinterpretation of climate effects. The aim of the present work is to compare six different degree-days models, in order to assess which of them could give the best results in terms of GDDs calculation for summer crops in Mediterranean Europe. Specifically, average method, single triangle method (with also three different cut-off techniques: horizontal, vertical, intermediate) and beta-distribution function method were tested. For this purpose 22 years of phenological data were used, comparing \\u0026ldquo;standard years\\u0026rdquo; and \\u0026ldquo;warm years\\u0026rdquo; (defined as those in which average temperature during June \\u0026ndash; August was below and above, or equal to, the median value of the 22-years period, respectively). Models were compared via Root Mean Square Error (RMSE) and Diebold-Mariano test, to assess differences in their predictive performance. Results showed that the use of models considering the negative effects of high temperatures in the ripening period significantly boost predictive accuracy. Among these approaches, the physiologically based beta-distribution function provided the best results. However, simpler methods, which could facilitate the acquisition of modelling novelty in operational contexts, having the advantage of being easy-to-use also proved to be significantly improving, such as intermediate cut-off technique, which among geometrical models can be considered the best approximation of crops physiological response.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Alternative modelling approaches significantly differ in simulating summer crops phenology in Mediterranean Europe\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2025-10-01 09:11:22\",\"doi\":\"10.21203/rs.3.rs-7650147/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"reviewerAgreed\",\"content\":\"\",\"date\":\"2025-09-25T04:57:57+00:00\",\"index\":0,\"fulltext\":\"\"},{\"type\":\"reviewersInvited\",\"content\":\"\",\"date\":\"2025-09-21T00:55:16+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2025-09-19T00:12:31+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"International Journal of Biometeorology\",\"date\":\"2025-09-18T09:27:02+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"international-journal-of-biometeorology\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"ijbm\",\"sideBox\":\"Learn more about [International Journal of Biometeorology](http://link.springer.com/journal/484)\",\"snPcode\":\"484\",\"submissionUrl\":\"https://www.editorialmanager.com/ijbm/default2.aspx\",\"title\":\"International Journal of Biometeorology\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false}}],\"origin\":\"\",\"ownerIdentity\":\"98ff0a41-4358-4e27-b951-ab5757e170f4\",\"owner\":[],\"postedDate\":\"October 1st, 2025\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"published-in-journal\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2026-01-12T16:01:35+00:00\",\"versionOfRecord\":{\"articleIdentity\":\"rs-7650147\",\"link\":\"https://doi.org/10.1007/s00484-025-03066-4\",\"journal\":{\"identity\":\"international-journal-of-biometeorology\",\"isVorOnly\":false,\"title\":\"International Journal of Biometeorology\"},\"publishedOn\":\"2026-01-09 15:57:31\",\"publishedOnDateReadable\":\"January 9th, 2026\"},\"versionCreatedAt\":\"2025-10-01 09:11:22\",\"video\":\"\",\"vorDoi\":\"10.1007/s00484-025-03066-4\",\"vorDoiUrl\":\"https://doi.org/10.1007/s00484-025-03066-4\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-7650147\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-7650147\",\"identity\":\"rs-7650147\",\"version\":[\"v1\"]},\"buildId\":\"8U1c8b4HqxoKbykW_rLl7\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}