Process-based crop simulation models simulate phenological development and aspects of the water, carbon and nitrogen economies of the crop (Boote et al., 1998; Holzworth et al., 2014; Ritchie et al., 1984; Stöckle et al., 2003). They operate at a daily time-step and are widely used to evaluate crop responses to the environment and management practices. Their predictive reliability often reflects the depth of empirical research invested in understanding crop response to abiotic stress, which tends to be better for crops such as soybean, rice, wheat, and maize than for pulses (Hao et al., 2021; Lake et al., 2021). The simulation accuracy of these models is also process-dependent, reflecting variability in both biological complexity and the degree to which the underlying mechanisms are understood. For example, we are better able to simulate crop-soil water balance (Cammarano et al., 2016; Gaydon et al., 2017), in which the underlying biophysics are well established (Penman, 1948), than biologically intricate processes, such as plant dry matter allocation, where modelling relies on coarse empirical partitioning factors because physiological understanding is lacking (Deng et al., 2020; Du et al., 2020; Ratjen et al., 2016; Weiner et al., 2009). Collectively, crop models typically achieve an r² ~ 0.7 in large-scale comparisons of observed and modelled yield, which is sufficient to address many agronomic questions where resource supply is the main source of variation, such as the response of yield to rainfall or nitrogen availability (Asseng et al., 2001; Richetti et al., 2024; Saseendran et al., 2004). Crop models can model different species, as well as cultivar differences (especially phenology), but some environmental stresses, such as the impact of frost and heat on yields, are not modelled.

Early crop models designed for agronomic applications did not explicitly account for the effects of heat and frost stress on crop yield (Barlow et al., 2015). Incorporating these temperature stress effects expands the model’s realm of applicability. For example, augmenting a wheat model with heat stress functions led to a 73% reduction in yield prediction error (RMSE reduction of 1.8 t/ha; Liu et al., 2020). Another example is that by incorporating frost and heat stress response functions into a canola model, reduced the RMSE by 0.2 t/ha (Lilley et al., 2018). In chickpeas, although a cold temperature threshold has been proposed, no dynamic frost response function has been incorporated, limiting the model’s utility in risk assessment (Anwar et al., 2022). Optimal pairing of variety and sowing dates to minimise the combined risk of drought, heat and frost stress is a prime example of applications that require models that account for extreme temperatures (Barlow et al., 2015; Cammarano and Tian, 2018; Flohr et al., 2017; Hunt et al., 2019; Lilley et al., 2019). Extreme temperature events such as frost and heat pose a significant threat to plant metabolism, development, growth, and yield. Their impact depends on their timing, severity, and duration, and they can jeopardise local agricultural economies and global food security (Frederiks et al., 2015; McKersie, 2015). In 2024, widespread frost events in the Riverina region of Australia caused yield losses of up to 90% in canola, wheat, and barley crops, compounding drought-related stress and prompting growers to cut affected crops for hay (Smith, 2024). A late spring frost in Europe in 2017 resulted in economic losses of €3.3 billion (~US$3.8 billion) (Faust and Herbold, 2018). These increasingly frequent extremes add to the pressure on the major cropping systems due to anthropogenic climatic risks occurring earlier than previously anticipated (Jägermeyr et al., 2021). In the US, the combined effect of heat waves and droughts between 1980 and 2004 led to losses of more than US$125 billion, losses sixfold greater than drought alone (<US$18 billion) (Mittler, 2006). It is important to quantify the impact of extreme temperatures, including frost (resulting from minimum temperatures) and heat stress (resulting from maximum temperatures), on grain yield.

Grain yield in annual crops correlated primarily with the number of grains per unit area (Sadras, 2021), which is established during a species-specific developmental window known as the critical period (Carrera et al., 2024; Dreccer et al., 2018; Hunt et al., 2019; Kirkegaard et al., 2018; Sadras and Dreccer, 2015). This window is centred around flowering in cereals, and is centred at podding in canola and pulses (Dreccer et al., 2018). In variable climates, such as those found across broadacre cropping regions in Australia, the United States, Canada, Russia and South America, late-spring frosts during flowering and early grain-filling remain a significant risk (Zheng et al., 2015). Hence, pairing variety phenology and sowing date is a key management approach to managing the risk of yield loss to temperature extremes during this critical period (Chen et al., 2020; Flohr et al., 2017; Hunt et al., 2019; Lilley et al., 2019). These agronomic strategies become more important as climate change is projected to intensify the frequency and unpredictability of extreme temperature events (Lamichhane, 2021).

Numerous reviews have documented the physiological responses of plants to frost and heat stress (Farooq et al., 2011; Fischer, 2011; Frederiks et al., 2011; Grossman, 2023; Hasanuzzaman et al., 2013; Lara et al., 2025; Maqbool et al., 2010; Martino and Abbate, 2019; Sánchez et al., 2014; Younis et al., 2020). However, most insights are from studies at lower levels of biological organisation. These include alterations of gene expression, enzyme activities, photochemical reactions, carbon metabolism, metabolites/ion balance changes, stomatal conductance, chlorophyll content, photosynthetic efficiency, membrane stability, lateral diffusion of lipids, damage in cellular structures, etc (Bañon et al., 2004; Cheong et al., 2019; Hasanuzzaman et al., 2013; Kasuga et al., 1999; Levitt, 1980; Marcum, 1998; Mittler, 2006; Ruelland and Zachowski, 2010; Seetharam et al., 2021; Stitt and Hurry, 2002; Thakur et al., 2010; Theocharis et al., 2012; Thomashow, 1999; Vaultier et al., 2006; Vogg et al., 1998; Wise et al., 2004). While valuable, such perspectives offer limited insight into the impact of frost or heat stress on yield at the canopy or field scales. Bridging this gap requires scaling physiological responses into model-relevant traits such as leaf area index, radiation use efficiency or harvest index.

Several studies have investigated temperature stress impacts on yield in a crop modelling context. Barlow et al. (2015) focused on grain number around anthesis in wheat. Kogo et al. (2019) found only one maize statistical model (not process-based) that explicitly accounted for frost and heat stresses; Hao et al. (2021) reported considerable uncertainty in simulating wheat yield using APSIM Classic under frost, heat, nitrogen and water stress. Lake et al. (2021) identified five key challenges in modelling of frost and heat effects: (i) These events, though biologically and agronomically important, are statistically complex and rare; (ii) Field experiments face practical limitations under realistic stress conditions; (iii) Intra-field phenological variation differs with species, cultivar, management, and environment; (iv) Discrepancies exist between meteorological and canopy-level and finally, (v.) Crop responses to stress depend on the complex interplay between event timing, intensity, duration, recurrence, acclimation and recovery after the event. Arguably, both issues (i) and (iii) are in essence the same, the lack of adequate data. Another issue is that by adding more processes in the modelling framework, the model complexity increases and, consequently, the model’s equifinality also increases (Beven and Freer, 2001; Pasley et al., 2022). Which also contributes to the difficulty in implementing and publishing these improvements.

In light of these challenges, a focused synthesis of temperature stress representation in crop models is timely. This review centres on cool-season grain crop species and does not address intraspecific variation for which data is limited. Yield loss from late-spring frosts is a significant risk during flowering and early grain-filling in many temperate crop production areas worldwide. While frost damage during flowering is unlikely in summer-growing regions, heat stress remains a major concern. Our objective is to critically examine how crop simulation models represent the effects of extreme temperatures and to identify priorities for improving model responsiveness to temperature stress. Highly detailed models that prioritise physiological processes, such as Defraeye et al. (2014) and Zhu et al. (2014) operate at the expense of agronomic relevance and are beyond the scope of this review.

First, we acknowledge that models are based on empirical relationships that represent the physiological processes of crop growth and development, and are validated against real-world data. Therefore, the accuracy of the models, in most cases, will depend on the availability of empirical research to develop the algorithms. Most process-based models do not account for several key physiological processes, such as acclimation – a crop’s adjustment to gradual changes in stress, compensation – growth recovery from suboptimal conditions, pathogen-induced freezing, and psychrophiles – cold-loving microbes that influence rhizosphere dynamics. Moreover, models do not explicitly explain interactions between extreme temperatures and other environmental factors such as solar radiation, water supply and demand, and nitrogen availability. While some of these interactions emerge depending on the model architecture, their representation is rarely mechanistic or generalisable. Lastly, it is important to note that abiotic stresses such as frost, heat, and drought are likely to have combined effects on yields that are not simply additive (Chen et al., 2019; Mahrookashani et al., 2017; Prasad et al., 2011; Stone et al., 1995). For example, a meta-analysis revealed that crops (including barley, canola, rice, wheat, maize, soybean, chickpea, groundnut, pearl millet, lentil, and potatoes) subjected to heat or drought stresses applied as a single-stress factor displayed a 33 and 48% yield reduction on average, respectively. In contrast, the average yield reduction in response to a combination of drought and heat stress was 65% (Cohen et al., 2021). Such findings challenge the assumptions of most existing crop models, which typically treat stress effects independently or additively. Here, we describe several processes supported by empirical literature but not yet incorporated into current models. Building on this, emerging work suggests that combining physiological principles and mathematics could lead to more mechanistically grounded algorithms, enhancing crop models’ predictive and explanatory power (Yin et al., 2021). The following subsections examine a series of specific physiological processes that are currently oversimplified or absent in crop models.

Models used different approaches to simulate the effects of extreme temperatures on crops. Some models include functions that impact crop survival, leaf area index, grain number, grain weight, and overall yield. When scaling plant population density and leaf area index, the effects of extreme temperatures are transferred to yield via the capture of resources such as radiation and water. Scaling of yield and yield components is usually direct, based on empirical “penalty” functions. Overall, these are scalars (0–1) applied as a multiplier to a potential physiological rate, effectively reducing the rate to simulate crop responses under stress. In APSIM, modular penalty functions can be customised and can adjust photosynthesis, phenology and partitioning based on stress indices (Holzworth et al., 2018). In DSSAT, penalty functions are typically multiplicative stress factors applied to potential growth rates (Hoogenboom et al., 2019). In STICS, they are referred to as stress response functions and reduce processes like leaf area development, biomass production, and phenological progression (Brisson et al., 2003). In WOFOST, reduction factors affect assimilation rate, leaf area expansion, and transpiration (de Wit et al., 2019).

Chilling temperature has been defined as ‘any temperature that is cool enough to produce injury but not cool enough to freeze the plant’ (Levitt, 1980), while frost refers to ice formation on crops, usually when the air temperature falls below 0°C. Similarly, heat stress disrupts plant growth and development, particularly during reproductive stages, often leading to yield loss (Shah and Paulsen, 2003; Talukder et al., 2014). Conceptually, frost or heat temperature thresholds mark the critical temperatures where crop damage begins and peaks. These thresholds vary with crop species, cultivar, and development stage with lethal and supra-optimal temperatures differing accordingly. Determining temperature thresholds for heat and frost requires trait vs temperature data, fitted response functions, and inflection points accounting for effects of genotype, environment, management, and their interactions. Several experiments have aimed to develop response functions for crop models. For example, studies on wheat have shown clear reductions in grain number and weight due to brief periods of high-temperature stress (Elía et al., 2018; Prasad et al., 2014). Delahunty et al. (2023) tested lentil response to high temperature (>32°C) using late sowing and partial shading. A field study comparing frost-exposed and frost-protected wheat showed a yield reduction from 2.6 to 1.8 t ha^-1, partly due to a decrease in grain number per spike from 29 to 19 (Ferrante et al., 2024). These experimental designs could be adapted for studies of other crops.

While field studies often report significant damage (e.g. from ANOVA), the inherent temperature variability in field conditions frequently hinders the establishment of clear thresholds. Typically, temperature reporting includes (i) maximum and minimum temperatures and may also include (ii) duration above or below a particular temperature and (iii) the number of extreme temperature events based on a temperature threshold. However, it is the yield loss in the field that models aim to simulate, and field experiments, which capture acclimation and stress interactions, are ideal for model validation, particularly when phenotyping occurs at the level of the processes affected. For example, phenotyping studies with remote sensing that also assess losses due to frost (Nuttall et al., 2019) offer information valuable for modelling. That is, if the model aims to simulate yield loss by accounting for natural variability and interactions between stress, plants and environment, then accurate information on temperature ranges, thresholds and variation from field experiments is essential. Unfortunately, this foundational data is often inaccurate or incomplete.

In this review, we examined the literature and have summarised and calculated relative damage or loss at various temperatures ( Figure 1 ). For example, a grain weight reduction from 40 mg per kernel (control) to 35 mg per kernel (frost/heat treatment) represents a 12.5% loss (1 – 35/40). Total plant or organ kill is assumed to be 100% damage. The inconsistency on reporting prevents an overall summary of yield loss; thus, we aggregated the percent damage on yield-related variables, such as survival, biomass, harvest index, grain weight, grain number (spikelets killed), and final yield. We have summarised a range of temperatures and their impacts across various development stages and organs in different crop species. The various stages where treatment was applied were split into pre- and post-anthesis, anthesis, and the whole plant growth period. Results of the analysis appear in Supplementary Table 1 and are summarised graphically in Figure 1 . Experimental environments were not clearly split in Figure 1 (see supplementary materials for further detail), but it is noted that data from chambers and glasshouses often fail to represent field conditions accurately and need to be interpreted with caution. Field data are more realistic but still face challenges in the removal of confounded environmental effects, such as the association between low vapour pressure deficit and high temperature (Bonada and Sadras, 2015). Methods for measuring frost and heat events across crops are not consistent, and this also reduces the comparability of the data between crops and experiments.

Abiotic stresses culminating in yield reduction are associated with flower abortion (reducing grain number) and grain damage (reducing grain quality and weight). These observations help define the critical period, defined as the developmental stages when crop yield is most susceptible to stress events such as frost and heat: see Dreccer et al. (2018) for cereals and pulses, Lake and Sadras (2014) for chickpea, Monzon et al. (2021) for soybean, Kirkegaard et al. (2018) for canola, and Sadras and Calderini,. (2021) for other major crops. For heat tolerance during flowering in rice, wheat, and maize, see (Liu et al., 2023). Models that capture this time-sensitivity to damage will more likely accurately capture yield losses due to frost and heat.

In his 1980s summary of state-of-the-art in crop modelling, Monteith (1981) concluded that “Progress has not been impeded by lack of ingenuity in model building but rather by the large number of grey areas in our physiological knowledge which modellers have drawn attention to”. This observation remains relevant to the modelling of extreme events in annual crops, for which physiological understanding continues to be a bottleneck. General response functions for setting of maximum grain number pre-flowering and grain size post-flowering appear valid across a range of crops, not only wheat as previously proposed (Barlow et al., 2015). However, deriving the temperature thresholds and response functions for occasional, extreme temperature stress events remains challenging, as experiments designed to capture the required data for modelling are still needed. Most experiments on frost and heat stress are designed for other purposes. For example, studies on barley show significant impacts on yield and other traits (Högy et al., 2013), but these treatments compare elevated vs. ambient temperature making it impossible to define a stress threshold. Furthermore, damage is often assessed visually rather than quantitatively. For example, in a scoring system by (Fiebelkorn and Rahman, 2016), 0 denoted dead, 5 denoted no damage, and scores of 1–4 were based on visual estimation of frost damage. A lack of detailed data hinders objective improvements to crop models. Nonetheless, some studies provide valuable data for developing response functions. For example, Nguyen et al. (2013) and Prasad et al. (2014) explored grain number and weight responses to the timing of high temperature stress, while Martino and Abbate (2019) conducted hypothesis-driven, data-rich studies. The advent of high-resolution phenotyping offers the opportunity to gather quantitative data that can be used in process-based modelling (Nuttall et al., 2019). Although the development of frost damage indices at broad scale through remote sensing (Wang et al., 2020) demonstrates potential to assess damage at a regional scale, such remotely-sensed indices do not necessarily model the processes. Figure 1 summarises data that can facilitate the first steps in the development of response functions for various crops to frost and heat stress. However, a major limitation to modelling crop responses to extreme temperatures is our superficial understanding of the underlying physiological processes.

The current stress and heat multipliers are based on limited data without rigorous optimisation. Furthermore, the multiplier functions are linear, which may over-simplify the biological response. Significant research has been conducted at lower levels of biological organisation, focusing on the effects of frost and heat stress on physiological processes. These effects are only partially understood, particularly at the molecular and cellular levels, ranging from gene expression to short-term metabolic responses (Bañon et al., 2004; Cheong et al., 2019; Hasanuzzaman et al., 2013; Kasuga et al., 1999; Levitt, 1980; Marcum, 1998; Mittler, 2006; Ruelland and Zachowski, 2010; Seetharam et al., 2021; Stitt and Hurry, 2002; Thakur et al., 2010; Theocharis et al., 2012; Thomashow, 1999; Vaultier et al., 2006; Vogg et al., 1998; Wise et al., 2004). Scaling these findings to agronomically relevant processes used in crop simulation models remains a challenge. For this reason, empirical functions are employed to scale processes, but experimental data are insufficient to fully capture the combinations of stress intensity, duration, and timing needed to build robust response curves. While these studies are insightful, they fall short in relevance to agronomic traits such as yield formation over the growing season. This review outlines current knowledge to inform the parameterisation of development stage-based yield-damage functions, which can be integrated into process-based crop models.

Differences between air and canopy temperatures also present a gap that needs addressing. The Stevenson Screen effect, reported to be +2.2°C compared to ground or canopy temperature (Grey, 2014), introduces potential systematic errors in crop models as air temperature data from weather stations is a standard data input. However, since most studies report air temperature impacts on plants, the Stevenson Screen effect may already be embedded in model development. Nonetheless, land surface temperature, particularly from satellite imagery, could provide valuable insights into the spatial-temporal distribution of frost and heat events across landscapes. Satellite products offer better spatial resolution than gridded weather data (e.g. Himawari 8 resolution at 2 km vs. Australian Bureau of Meteorology at 5km). From a crop modelling perspective, methods that deliver finer spatial resolution for daily minimum and maximum air temperature are warranted.

Future developments in crop modelling should incorporate frost and heat response functions. We have expanded and updated the compilation of temperature-damage relationships for wheat (Barlow et al., 2015) to include other crops. In cereals, frost or heat stress during the critical period can reduce grain number due to stress effects on meiosis and flower abortion. Subsequent stress events after the potential grain number is set primarily affect grain weight or can result in grain abortion. Most damage functions simply penalise yield. To improve models, separate response functions could be developed for grain number and grain weight, each linked to developmental stage and temperature thresholds. Based on the assumptions presented in Section 2 and the temperature and damage percentages reported in Section 4, response functions for frost and heat stress could be incorporated into a wide range of crop models to enhance their accuracy under extreme temperature conditions. Additionally, stress-induced leaf senescence from frost and heat effects on foliage may contribute to yield losses by reducing LAI and thus limiting assimilate supply during grain filling. However, this hypothesis remains untested.

When developing and testing models with frost and heat yield reducing components, two key components need consideration; i) yield response to frost and heat events, which depends on the timing (on a phenological scale), intensity (how cold or hot, i.e. temperature) and duration of stress (time spent above or below temperature thresholds); and ii) validation of response functions using experimental data across diverse environments, crops, and genotypes. Furthermore, the development of frost and heat response function should be in the form of elegant and robust equations that achieve both biological rigour and model simplicity, and interact with other stress effects (e.g., heat and drought combined effect). This approach aims to bridge the gap between the understanding of the effects of frost and heat stress effects at the cellular and plant organ level and their agronomically relevant impacts at the field scale.

Lastly, the use of modelling thinking to inform experimental design will facilitate the development of crop models which capture the effects of frost and heat stresses on crop yields (Craufurd et al., 2013; Nuttall et al., 2019; Rötter et al., 2018). This begins with identifying the key physiological processes affected by frost and heat stresses, which are required to conceptualize the processes within a model. Key physiological processes related to reproductive biology include floret initiation, development and growth, and grain formation and abortion. Ideally, field experiments should incorporate diverse combinations of genotypes, environments, and management practices. Temperature-controlled field plots or open-top chambers can facilitate the imposition of frost and heat events alongside natural stress events to capture a range of responses across growth stages (Leske and Biddulph, 2022). Additionally, meteorological data (e.g. canopy temperature, humidity, and radiation) should be systematically recorded in the canopy with high temporal and spatial resolution. This data can help quantify the microclimatic differences and link environmental conditions to crop stress responses. Remote sensing technologies, such as thermal imaging and hyperspectral sensors (Deery et al., 2019), offer valuable tools to enhance data collection by capturing spatial and temporal variability in stress responses. However, field experiments are labour-intensive, and introducing additional requirements might not be feasible. Therefore, promoting data sharing in accordance with the F.A.I.R. principles (Findability, Accessibility, Interoperability, and Reusability) can help generate robust datasets to improve model development (see the example of plant traits in Kattge et al., 2020).

Current process-based modelling approaches face six major challenges: (1) insufficient spatial and temporal resolution for extreme events, (2) non-linear and threshold-based crop responses, (3) complex interactions between phenology and management, (4) cumulative and interacting stress effects throughout development stages, (5) inadequate representation of genotype-specific sensitivities, and (6) dependence on daily temperature data. Using sub-daily climate data, incorporating physiological damage mechanisms, and improving genotype-specific parameterisation will improve the modelling of frost and heat event impacts on the yield of cool-season annual grain crops. To achieve this, more interdisciplinary work between modellers and field experimentalists and data sharing should be encouraged and resourced.