Cold Hardiness Mechanisms and Modeling: Existing Approaches and Future Avenues

Viewpoint
Cold hardiness mechanisms and
modeling: existing approaches
and future avenues
Summary
Cold hardiness models are useful tools to predict cold damage in
plants, such as those produced by unseasonal temperature cycles or
by increased cold exposure. Although development of these models
started about five decades ago, their applications remain limited.
We describe the main paradigms driving the different types of cold
hardiness models (empirical to process-based), their similarities and
differences. Among the existing paradigms, process-based models
are built to translate physiological mechanisms into mathematical
functions over a broad range of climatic conditions, thus making
them more accurate for studying the effect of climate change.
Different approaches have been developed in predicting cold
hardiness: (1) empirical relationships between temperature and cold
hardiness; (2) phenological processes controlling acclimation and
deacclimation rates; (3) phenological and physiological processes
predicting cold hardiness through the osmo-hydric approach; and
(4) molecular regulation driving the metabolic drivers of cold
hardiness. For the first three approaches, we describe the context,
the experimental and field observations that defined their frame-
works as well as their limitations. To increase the realism of cold
hardiness models, we describe the potential of a fourth approach,
based on the perception of environmental signals, how it translates
into cold acclimation/deacclimation and provide recommendations
to develop this framework.
Introduction
In temperate, mountain, and boreal areas, cold hardiness is an
important driver of a plant’s fitness through its survival (essentially
maximum cold hardiness in winter) and reproduction (in relation
to phenology). In the future, climate models predict a temperature
rise of 4–6°C over the next century, contrasting sharply with past
temperature changes when a similar rise took c. 20 000 yr
(IPCC, 2023). These rapid changes are jeopardizing the link
between climate and plant adaptation. One critical yet counter-
intuitive consequence of global warming relates to freezing risks, as
warming trends may impair the cold acclimation process that
enables plants to survive extreme winter temperatures (Charrier
et al., 2015a). How plants will adapt to winter temperatures now
and in the future will help to predict vegetation feedback on climate
(Rammig et al., 2010; Lambert et al., 2022,2023; Wang
et al., 2025).
Simultaneous change in climate mean and variability can have
detrimental effects on vegetation, especially regarding cold stress,
although the threat of freezes depends on the geographical region
(Augspurger, 2013; Zohner et al., 2020; Cohen et al., 2023). On
the one hand, global change would delay cold acclimation and
hasten cold deacclimation under warmer conditions. On the other
hand, an increase in temperature variability would increase the
likelihood of extreme weather events at a given date (Reyer
et al., 2013; Thornton et al., 2014), that would affect vulnerable
plants.
According to Levitt’s (1980) stress physiology paradigm, the
ability to survive low temperature can be divided into two main
processes (Charrier et al., 2011): freeze avoidance (avoidance of
exposing sensitive organs to subzero temperature and limiting ice
formation), and freeze tolerance (ability to withstand subzero
temperatures without suffering damage, cold hardiness hereafter).
The ability of plant water to supercool by limiting ice nucleation
activity within (intrinsic nucleation) or upon (extrinsic nuclea-
tion) their tissues defines freeze avoidance. Although ice
nucleation activity does not exhibit a clear link with plant
physiological or phenological stage, some critical factors have been
identified, such as flavonoids (Kasuga et al., 2008), osmotic
potential (Gusta et al., 2004), structure (Lintunen et al., 2013), ice
nucleation active bacteria (Lindow et al., 1978), and antifreeze
proteins (Griffith & Yaish, 2004). Despite its relevance, especially
with respect to late freeze events, ice nucleation has not been
modeled in plant tissues, but the molecular dynamics of
heterogeneous ice nucleation could provide interesting avenues
(Glatz & Sarupria, 2018). In either case (avoidance or tolerance),
the maximum cold hardiness of tissues is not constitutive and
must be gained through acclimation and lost through deacclima-
tion in a timely manner to survive winters.
Freeze risks can also be categorized according to their period of
occurrence: early, mid-winter, and late freezes. Early freeze damage
can result from cold weather setting in after heat waves in late
summer and early autumn (Charrier & Ameglio, 2011; Ferguson
et al., 2014; Chang et al., 2015; Charrier et al., 2021). In winter,
warm spells induce insufficient acclimation or mid-winter
deacclimation (Kalberer et al., 2006; Kovaleski, 2024). Attempts
to transfer populations from drier and warmer regions to colder
environments through assisted migration have raised concerns
about cold hardiness, for example massive damage to Pinus pinaster
from Portugal introduced in southern France (Benito-Garzon
et al., 2013). Freeze risks in mid-winter are currently the best
integrated into species distribution predictions, as for the
maximum hardiness zones developed by the USDA. The freeze
safety margin, that is the difference between maximum cold
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hardiness and absolute minimum temperature, decreases sharply at
the cold edge of tree species distribution (Baranger et al., 2024).
During late winter and early spring, flushing buds are particularly
susceptible to damage by low temperatures (Gu et al., 2008;
Chamberlain et al., 2019; Kirchhof et al., 2025).
The complexity of the factors involved in cold acclimation has
led to the development of various models in many functional types,
such as grasses, deciduous and evergreen woody perennials. Cold
hardiness models differ in their purpose (e.g. descriptive, under-
standing, or predictive), defining the input and simulated variables
and their underlying paradigms. This viewpoint aims to describe
the concepts of these models and identify their potential and
limitations in predicting freeze risk in unprecedented conditions,
such as those imposed by global change, and propose new
approaches to cold hardiness modeling, notably by analogy with
phenological modeling.
Main concepts of cold hardiness models
Existing models are distributed according to a gradient of
increasing complexity (Fig. 1; Table 1), which is linked to their
degree of realism (the extent to which the model describes and
explains real-life causal phenomena) and generality (the ability of
the model to maintain accuracy across a broad range of input
variables, in different locations and/or over time, particularly
outside the calibration range), as defined by Levins (1966). A first,
more empirical approach relies directly on statistical relationships
and/or historical data to predict cold hardiness (Anisko
et al., 1994). Environmental factors such as air temperature and
photoperiod are used as explanatory variables to directly
estimate cold hardiness or changes in it. A second approach (called
integrated models) incorporates the effect of the phenological cycle
on cold hardiness, thus increasing the realism and generality of the
model (H€anninen, 2016). A third approach focuses on a lower level
of organization, integrating the role of physiological variables on
cold hardiness (Charrier et al., 2013a). A fourth approach has yet to
be developed and could be further downscaled by explicitly
modeling signal perception and transduction, resulting in meta-
bolic changes. This would decouple the phenological cycle from
cold acclimation and facilitate the integration of environmental
signals and the accumulation of their impact throughout the plant’s
life cycle via legacy and memory effects. Finally, all these
approaches predict plant vulnerability to low temperature, which
still need to be compared with stress exposure to predict a realistic
risk of low temperature damage.
Cold hardiness as the response variable
Plant cold hardiness is a phenotypic trait that can be modified by
environmental stimuli, mainly low temperatures and short days
(Welling & Palva, 2006). Cold hardiness thus varies depending on
the season, due to environmentally induced changes in gene
expression, which result in physiological, biochemical, and
anatomical changes primarily through the osmotic control of the
Fig. 1 Approaches developed to model plant cold hardiness across a spectrum of complexity, in relation to the number of intricate processes involved.
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Table 1 Cold hardiness models and their properties. Model type Species Predicted variable Input variables Acclim. Deacc. Reacc.
Thermal time/ phenology
Modulation by phenology Legacy Reversibility Perception Source
Empirical Triticum aestivum Biomass loss Air temperature Sharpley & Williams (1990)
Deciduous woody plants Survival
temperature
Air temperature (sum +mean), day
of year (DOY)
x x x No No No Yes No Ani
sko et al.(1994)
Pinus sylvestris Cold hardiness Air temperature, photoperiod, pH of
cell effusate
x x x No No No Yes No Taulavuori et al.(1997)
Brassica napus, Brassica
rapa
Winter survival Multiple, derived from air and soil
temperatures and precipitation
x x x Yes No No Yes No Waalen et al.(2013)
Prunus cerasus Cold hardiness Air temperature No No No No No Salazar-Guti
errez & Chaves-
Cordoba (2020)
Triticum aestivum,
Triticosecale 9Wittmack
Winter survival Multiple, derived from temperature
and snow depth
x x x No No No No No Rapacz et al.(2022)
Vitis vinifera Cold Hardiness Air temperature x x x No No No Yes No (Jones et al., 2024)
Vitis spp. Cold hardiness Air temperature, DOY No No No Yes No (Wang et al., 2024)
CH-based Phleum pratense Cold hardiness Air temperature, precipitation x x x No No No Yes No (Thorsen & H€
oglind, 2010)
Picea sitchensis Survival
temperature
Crown temperature, photoperiod x No No No Yes No (Cannell et al., 1985)
Pinus sylvestris Cold hardiness Air temperature x x x No No No Yes No (Repo et al., 1990)
Pseudotsuga menziesii Cold hardiness Air temperature x x Yes No No No No (Timmis et al., 1994)
Phenological Malus domestica Cold hardiness Air temperature x x Yes No No Yes No (Winter, 1973)
Cornus sericea Cold hardiness Air temperature x x x Yes Yes No Yes No (Fuchigami et al., 1982;
Kobayashi et al., 1983;
Kobayashi & Fuchigami, 1983a,
1983b)
Triticum aestivum Biomass loss Crown temperature, snow depth,
photoperiod
x x x Yes No No No No (Ritchie, 1991)
Pinus sylvestris Cold hardiness Air temperature, photoperiod x x x Yes Yes No Yes No (Kellom€
aki et al., 1992, Kellomaki
et al., 1995)
Pseudotsuga menziesii Cold hardiness Air temperature, photoperiod x x x No Yes No Yes No (Leinonen et al., 1995)
Triticum aestivum, Secale
cereale
Cold hardiness Air temperature, photoperiod x x x Yes Yes No No No (Fowler et al., 1999)
Medicago sativa Winter survival
and yield loss
Air temperature, photoperiod, snow
depth, solar irradiance, soil moisture, precipitation and plant density
x x x Yes No No Yes No (Kanneganti et al., 1998a,
1998b)
Triticum aestivum, Pisum
sativum
Cold hardiness Air temperature x x x No No No Yes No (Lecomte et al., 2003; Castel
et al., 2017)
Triticum aestivum Cold hardiness Crown temperature, snow depth x x x Yes No Yes No No (Bergjord et al., 2008)
Generic (annual and
perennial crops)
Biomass loss Air temperature Yes No Yes No No (Brisson et al., 2009)
Vitis vinifera, Juglans regia,
Camellia sinensis, Pseudotsuga menziesii
Cold hardiness Air temperature x x x Yes Yes No Yes No (Ferguson et al., 2011,2014;
Charrier et al., 2018b; Kimura
et al., 2021; North et al., 2021;
Stuke et al., 2024)
Triticum aestivum,
Triticosecale 9Wittmack
Biomass loss Air temperature Yes No No No No (Zheng et al., 2014)
Vitis spp. Cold hardiness Air temperature, DOY Yes Yes No Yes No (Londo & Kovaleski, 2017)
Pinus sylvestris, Juglans
regia
Cold hardiness Air temperature, photoperiod x x x Yes Yes No Yes No (Leinonen, 1996; Charrier
et al., 2018b)
Vitis riparia Cold hardiness Air temperature Yes Yes No Yes No (Londo & Kovaleski, 2019) Winter cereals LT50 (individual) Crown temperature, photoperiod x x x Yes Yes ? No (Byrns et al., 2020)
Prunus cerasus Cold hardiness Air temperature, Water content
(WC)
x Yes No No No No (Hillmann et al., 2021)
Vitis spp. Cold hardiness Air temperature Yes Yes No Yes No (Kovaleski et al., 2023)
Physiological Juglans regia Cold hardiness Air temperature, starch, soluble
carbohydrates and water contents
x x x No No Yes Yes No (Poirier et al., 2010)
Deciduous woody plants Cold hardiness Soluble carbohydrates and water
contents
x x x No No Yes Yes No (Charrier et al., 2013a; Baffoin
et al., 2021)
Juglans regia Cold hardiness Air temperature, photoperiod
Starch, soluble carbohydrates and
water contents (for initialization)
x x x Yes Yes Yes Yes No (Charrier et al., 2018a; Charrier &
Am
eglio, 2024)
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intracellular freezing point (Charrier et al., 2013a), plasma
membrane composition (Uemura et al., 2006), and cell wall
thickness (Takahashi et al., 2021).
Depending on the species, cold hardiness per se is not easily
measurable and is sometimes based on the consequences of low
temperature stress after the winter period. This is particularly true
in herbaceous species (e.g. winter cereals and other annual crops),
exhibiting cold damage as a disturbance (sensu Grime, 1973), that is
partial or total loss of biomass. In these species, a good cold
hardiness index thus relates to the survival (or the lack of recovery)
of the whole individual, the destruction of plant tissues, and the
resulting yield (generally referred to as ‘winter kill’).
In woody perennial species, cold hardiness can be measured
regularly during the winter period through different techniques
such as lethal temperature for 50% of the individuals, the
temperature of intracellular exotherm by thermal analysis (LTE),
or progressive damage by relative electrolyte leakage, or visual
scoring. Depending on the measured phenotype, the cold hardiness
index can constitute a threshold that, once exceeded, marks the
development of damage and jeopardizes survival (survival, biomass
loss, LTE). A more quantitative cold hardiness index, as measured
by the electrolyte leakage or visual scoring methods, may allow a
more gradual assessment of damage intensity, therefore predicting
cold damage with a thinner resolution, still missing the link with
survival.
One peculiar case is freezing avoidance, that is the ability to resist
cold temperatures by maintaining supercooled water. The process
of ice nucleation depends on the plant tissue and developmental
stage, as well as the nature of the nucleus (e.g. ice-nucleation-active
bacteria), other biophysical conditions in plants (e.g. solute
concentration, wettability, cell wall properties, and physical
barriers), and atmospheric conditions (Kirchhof et al., 2025).
However, current cold hardiness models consider ice nucleation to
be a deterministic process that occurs at a fixed temperature (e.g. 0,
2, or 4°C), whereas experimental evidence has shown that its
stochasticity depends on both biotic and abiotic factors (Kirchhof
et al., 2025).
Although plant mortality is complex and difficult to measure (see
e.g. Leopold, 1978; Filip et al., 2007; Anderegg et al., 2012, for
drought stress), the ability of meristematic cells, particularly those
in the shoot apical meristem, to divide and form new vegetative
organs is crucial for predicting resilience to stressful events
(Thomas, 2013). Current methods cannot easily determine the
sequence of damage leading to plant mortality; they only allow
measurements after the stressful event has occurred. Nondestruc-
tive monitoring techniques, such as micro-dendrometers or
acoustic emission analysis (Charrier et al., 2017,2021; Lamacque
et al., 2022), are therefore needed to assess low-temperature
damage. This would allow a continuous assessment of damages,
required to elucidate the dual role of freeze intensity and duration as
simulated by the death time model (Faber et al., 2024).
As the mechanisms driving cold hardiness continue to be
elucidated, the effects of variables continue to be quantified
through experimental evidence or modeling efforts. Depending on
the biology of the species and the purpose of the model, cold
hardiness can be modeled at a single point in time (static models,
e.g. Charrier et al., 2013a), dynamically over a short period (less
than a year; Cannell et al., 1985), or over multiple years
(Leinonen, 1996). In perennial species, simulations may require
reinitialization at fixed dates (Cannell et al., 1985; Timmis
et al., 1994). In winter cereals and crops, the dynamics typically
begin at the sowing date and continue until harvest (Bergjord
et al., 2008; Byrns et al., 2020).
Predicting cold hardiness
In static models, cold hardiness is predicted using variables
measured on the same date (Charrier et al., 2013a; Jones
et al., 2024), a few days later (Proebsting, 1963; Andrews &
Proebsting, 1986), or up to several months earlier (Anisko
et al., 1994; Poirier et al., 2010; Rapacz et al., 2022). In multiple
regression analysis, a subset of variables is predefined and measured,
and the most informative index is selected through a calibration
process that requires it to significantly improve prediction accuracy
(stepwise procedure; Anisko et al., 1994). Over the past decade,
partial least squares regressions and machine learning algorithms
have significantly increased the number of variables included in
analyses, even when there is no prior knowledge of their effect. For
example, the NYUS.2 model uses 117 features in its training
process, including cultivar features and hourly temperature-based
features such as daily and cumulative temperature descriptors, as
well as exponential and reverse exponential weighted moving
averages (Wang et al., 2025). While these models generally lead to
highly accurate predictions (RMSE lower than 2°C, and even 1°C
in some cases), they lack realism, which can restrict their validity to
the climate range in which they were developed. Empirical models
also usually lack reversibility, that is the ability to allow
deacclimation and reacclimation throughout the modeled period;
this is only achieved through the fluctuation of driving variables.
Based on a large series of experimental measurements and field
observations, Repo et al.(1990) developed a simple, cold hardiness-
based, dynamic model that integrates reversibility through the
concept of stationary cold hardiness in order to predict realistic cold
hardiness mechanisms (Kalberer et al., 2006). In order to enable
reversibility in simulations, this model uses stationary cold
hardiness and the rate of change in cold hardiness. The prevailing
air temperature determines stationary cold hardiness, and the rate
of change is proportional to the difference between prevailing and
stationary cold hardiness. Based on these assumptions: (1) under a
constant air temperature, cold hardiness attains the stationary level
determined by that temperature; and (2) under fluctuating
temperatures, cold hardiness follows changes in air temperature
(which determine the stationary level). To mitigate the impact of
rapid air temperature fluctuations on cold hardiness, a time
constant (s) governs the rate of change. The higher the value of s,
the slower the predicted changes in cold hardiness. The first-order
model predicts a rapid change that slows for small differences
between the prevailing and stationary cold hardiness levels (Repo
et al., 1990; Leinonen, 1996). Leinonen et al.(1995) introduced a
second-order model using two time constants corresponding to two
stationary levels of cold hardiness to address the exceptionally
complex air temperature response of cold hardiness in Douglas-fir
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during dormancy. The second time constant is called ‘asymptotic
cold hardiness’. As endodormancy progresses, the effect of the
second time constant decreases until it finally vanishes, meaning
that at the beginning of ecodormancy, cold hardiness is again
modeled with one time constant.
Predictor variables driving cold hardiness
The variables used in current models are described according to the
following framework: description of the variable, its perception and
molecular regulation, integration into current models, and
limitations.
Temperature
Air temperature is the most commonly used input variable for
predicting cold hardiness, either directly on the change in cold
hardiness or indirectly through its effect on phenological processes
(Fig. 2). Directly, the signal of low temperatures enhances cold
hardiness, whereas the indirect effect of thermal times (e.g. chill and
growing degree-day accumulation) relates to phenological cycles
and other physiological processes, which then affect the dynamics
of cold hardiness.
As there are no known specific temperature sensors in plants,
temperature perception occurs at multiple levels (Penfield, 2008;
Kerbler & Wigge, 2023). The main perception pathways involve
modulation of plasma membrane fluidity; cytoskeletal stability;
activation of channels that allow calcium (Ca
2+
) to enter the cell;
conformation of certain proteins; enzymatic activity within
different metabolic reactions; and the expression, transcription,
and translation of various genes (Ruelland & Zachowski, 2010).
Cold temperatures, in particular, affect the rigidity of fatty acid
aliphatic chains, thereby exerting physical constraints on mem-
brane proteins such as calcium (Ca
2+
) channels. Calcium can then
trigger a cold response via the expression of C-REPEAT
BINDING/DEHYDRATION-RESPONSIVE ELEMENT BIND-
ING 1 FACTORS (CBF/DREB1), which activate the promoters of
COLD-REGULATED (COR) genes. As acclimation is a process
that occurs against the temperature gradient, it provides an
interesting avenue for studying the effects of temperature sensing.
Although maximum cold hardiness in the middle of winter does
not usually depend on the lowest recorded temperature (Aitken
et al., 1996; Larcher & Mair, 1968; Morin et al., 2007; Charrier
et al., 2013b; however, see Vitra et al., 2017), the direct effect of low
temperatures on the rate of change in cold hardiness has long been
documented (Haberlandt, 1875; Schaffnit, 1910; Irmscher, 1912;
Chandler, 1913; Gassner & Grimme, 1913). The effective
temperature threshold for stem acclimation varies between species
but is generally below 5–10°C (Harvey, 1922; Greer et al., 2000).
The acclimation rate increases with decreasing temperature
(Dantuma & Andrews, 1960; Pogosian & Sakai, 1969), and daily
temperature fluctuations also play a role thanks to the nonlinear
response between temperature and cold hardiness (Wang
et al., 2024). In general, the lesser the cold hardiness (i.e. more
vulnerable), the greater the effect of low temperatures on the rate of
change in cold hardiness (Luoranen et al., 2004) via a nonlinear
relationship (Greer et al., 2000) that depends on the phenological
stage (Tumanov, 1969).
Temperature can also be integrated over extended periods,
creating new variables that are used to model cold hardiness. Warm
temperatures are integrated to simulate a developmental path
(Reaumur, 1735). This metric is referred to as growing degree-days
(GDDs) or growing degree-hours, depending on the timescale of
measurement used for integration, and its accumulation is
associated with ‘forcing’ by the environmental conditions (i.e.
promotion of growth). GDDs are calculated using different
functions, but generally at their simplest as a linear response (with
or without added thermal limits of base temperature and maximum
temperature), or sometimes based on sigmoid or bell-shaped
curves. Similarly, cold temperatures can be integrated over time to
produce a metric referred to as chilling accumulation. Many
methods exist for integration of low temperatures, from simple
sums of time under a threshold (Weinberger, 1950) to more
complex, physiology-informed models that use a combination of
multiple functions (e.g. Dynamic model; Fishman et al., 1987). As
parts of the process are unknown, the timing of start for integration
of warm or cold units remains an arbitrary aspect of the
accumulation, which largely affects multilocation analyses (Fer-
nandez et al., 2020). Both forcing and chilling are often parts of
models to predict shifts in phenology and physiology, such as
endodormancy release and budbreak (see further below), but units
Fig. 2 Seasonal dynamics of biotic and abiotic factors involved in cold
hardiness (CH) during successive phenological stages (Lign, lignification;
EnDI, endodormancy induction; EnDR, endodormancy release; EcoD,
ecodormancy; and growth). Variation occurs across the year in
environmental factors (temperature and photoperiod), sensing of short and
long days (SD, LD), and low, freezing, and warm temperatures (LT, FT, and
WT), leading to changes in water content (WC), starch to soluble
carbohydrates (TSC) interconversion, and conferring cold hardiness to plants.
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