# Regional climate warming increases occurrence and intensity of winter wheat drought risk

Léa Laurent, Albin Ullmann, Thierry Castel

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Léa Laurent, Albin Ullmann, Thierry Castel. Regional climate warming increases occurrence and intensity of winter wheat drought risk. Agricultural and Forest Meteorology, 2025, 366, pp.110493. 10.1016/j.agrformet.2025.110493. hal-04986079

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# Regional climate warming increases occurrence and intensity of winter wheat drought risk

Léa Laurent<sup>a,b,*</sup>, Albin Ullmann<sup>a</sup>, Thierry Castel<sup>a</sup>

## ARTICLE INFO

**Keywords:**

Agro-climatic risk

Drought

Winter wheat

Abrupt warming

Water balance

## ABSTRACT

During the 1960–2021 period, France experienced two rapid increases in 2m air temperature, in 1987/1988 and 2014/2015. Between the periods 1960–1987 and 1988–2014, this induced significant differences in the mean state of the local water cycle climatic components. Evolving climate hazards linked to the water cycle led to water balance modifications, especially in winter bread wheat fields. This work aims to analyze the resulting changes in agro-climatic risk linked to drought after each abrupt warming. For each grid point of the Safran-Isba-Modcou (SIM) dataset and each year, daily values of Relative Extractible Water (REW) under a wheat stress threshold of 40 % are cumulated to obtain a water stress index. For the first time, the modeling of water stress index distributions using Tweedie family distributions allows to disentangle modifications in frequency and intensity of drought events. These display various changes depending on the wheat production basin and the studied period. Overall, the mean water stress index increases in each production basin, with the Nord-Pas-de-Calais and Parisian production basins being particularly impacted by the 1987/1988 abrupt warming. Our results highlight that the modifications of climate hazards lead to harsher hydric stress events over main French wheat production basins. The probability of extreme drought events is rising strongly in several production basins. Changes in agro-climatic risk associated with drought are one of the main factors affecting crop growth cycle and development. As the probability to overcome risk threshold increases, yields may be significantly reduced, leading to increased economic losses. This is of major concern for the agricultural sector, including crop insurers, and underscores the urgent need for adaptation and prevention measures.

## 1. Introduction

After a constant increase in cereal yields during the second half of the 20th century thanks to genetic advances and the use of inputs (Gervois et al., 2008), Europe experiences a decline in this growth trend (Calderini and Slafer, 1998). Several crops encounter a stagnation or even a decreasing trend in their potential yields in some areas of the continent (Grassini et al., 2013; Supit et al., 2010). In France, yields growth has stopped since the 1990s for several crops, such as winter wheat, barley, oats or durum wheat (Schauberger et al., 2018). Several causes have been identified to explain this yield stagnation, such as changes in crop management practices or in legislation on fertilizer use, a slowdown in genetic improvement and climate hazards (Hawkins et al., 2013; Lin and Huybers, 2012).

Wheat is particularly impacted by this yield stagnation, reaching its turning point in the 1990s for many departments (Brisson et al., 2010).

As France is the leading wheat producer in the European Union in 2020, this slowdown of the winter wheat harvest questions the food security of the continent (Agreste, 2021). With the increase in world food requirements, this statement represents a major societal issue (Shiferaw et al., 2013).

Climate hazards are one of the main causes of yield variability in maize and wheat in France (Ceglar et al., 2020). With climate change, the agro-climatic risk is expected to be modified, leading to lower food production (Gaupp et al., 2020). In France, as in the entire Western Europe, over the last sixty years, climate change results in an abrupt increase in surface temperatures, which occurred around 1987/1988 (Brulebois et al., 2015; de Laat and Crok, 2013). Both maximum and minimum temperatures are impacted, and the spring and summer seasons show the largest differences between the 1961–1987 and 1988–2013 periods, with respectively 1.55 °C and 1.31 °C for maximum temperatures in France (Brulebois et al., 2015). Several factors have

<footnote><sup>a</sup> Biogéosciences, UMR 6282 CNRS, université Bourgogne Europe, 6 boulevard Gabriel, 21000 Dijon, France</footnote>

<footnote><sup>b</sup> Direction Actuariat Groupe, Groupama Assurances Mutuelles, 8-10 rue d'Astorg, 75383 Paris Cedex 08, France</footnote>

<footnote>* Corresponding author at: Biogéosciences, UMR 6282 CNRS, université Bourgogne Europe, 6 boulevard Gabriel, 21000 Dijon, France.
E-mail address: lea.laurent@u-bourgogne.fr (L. Laurent).</footnote>
been identified to explain this rapid increase in surface temperature over Western Europe (Robson et al., 2012; Terray and Boë, 2013). The substantial warming of the North Atlantic Ocean due to North Atlantic Oscillation (NAO) variations and the decrease in anthropogenic aerosol emissions coupled with global warming seem to have played a major role in this late 80s regional abrupt warming (Booth et al., 2012; Evan et al., 2009; Sutton and Dong, 2012). After 1988, a slightly positive trend in temperatures until 2000 is followed by a 10-year hiatus due to La Nina conditions (Meehl et al., 2011). This delimits both sides of 1987/1988 two stationary periods of approximately equal duration that differ in their mean temperature. More recently, a new strong surface temperature increase is observed around 2014/2015 years, suggesting a new climate warming process over France (Laurent et al., 2024).

Such rapid warming in surface temperature impacts water cycle through modifications in evapotranspiration (Yao et al., 2020). In France, spring depicts a high increase in evapotranspiration, following the abrupt warming of 1987/1988. But in summer, water constraint is rising significantly, with the emptying of soil water reservoirs. From spring to the beginning of autumn, the increase in potential evapo-transpiration and, in a second step, the lengthening of dry spells, play a major role in the intensification of water constraint (Laurent et al., 2024). These changes in climate hazards linked to the water cycle after the 1987/1988 climate shift are expected to affect agro-climatic risk, as the risk is the combination of hazard and vulnerability. Vegetation cover is highly affected by increased water constraint, leading to a decline in forest growth or yield losses for example (Creed et al., 2015; Daryanto et al., 2016).

In France, wheat water balance is strongly affected by the abrupt changes in climate hazard around 1987/1988, leading to harsher hydric stress events that alter the crop growth cycle (Laurent et al., 2023). As France has been the largest wheat producer in the European Union for several years, the assessment of drought risk on wheat crops is a key issue (Food and Agriculture Organization of the United Nations (FAO), 2022). The assessment of risk parameters and their evolution is crucial for the socio-economic world of agriculture, especially for insurers, policy makers and governments (Dragos et al., 2023). The rapid increase in surface air temperature in France in 1987/1988 delimits along 1960–2014 two periods of 28 and 27 years respectively. This allows a robust assessment of how this structural change in climate hazard affects agro-climatic risk. In France, wheat production is spread over several main production basins with different pedo-climatic characteristics. This provides an opportunity to investigate how agro-climatic regions are affected by climate warming. Furthermore, recent work suggests that a new warming shift occurs over France around 2014/2015 (Laurent et al., 2024). Even if it displays a shorter period of 7 years between 2015 and 2021, dividing the 1988–2021 period into two sub-periods (1988–2014 and 2015–2021), this new rapid warming is of interest to investigate (i) whether the structure of drought risk changes and (ii) whether or not the changes are similar in space and time.

This study aims at estimating the structural changes of the drought risk over the main pedo-climatic wheat production basins in France. More specifically, drought is assessed from the daily computation of water balance for the winter wheat crop, based on a simplified two-reservoirs water balance model (Jacquart and Choisnel, 1995), and from the application of a threshold below which wheat is considered to be under hydric stress. This led us to develop an annual water stress index for winter wheat. The index is computed for each year and for each 8km grid point of the reanalysis of surface climate data covering the six main French winter wheat production basins. As the climate dataset starts in 1959, it is relevant to statistically investigate structural changes in the water stress index and consequently in the drought risk. To this aim, we introduce the use of the Tweedie distribution to model simultaneously the occurrence and the intensity of drought events (Dunn, 2004).

## 2. Material and methods

### 2.1. Study area and datasets

**Table 1:** Agronomic, pedologic and climatic characteristics of the six winter wheat production basins studied. Period 1: 1960–1987; period 2: 1988–2014; period 3: 2015–2021. PET: Potential EvapoTranspiration, PRELIQ: liquid precipitation. Production basins 1, 2, 3, 4, 5, 6 respectively Nord-Pas-de-Calais, Parisian, Poitou-Charentes, Centre, Bourgogne/Rhône-Alpes and Aquitain production basins. * indicates that the difference is significant according to Bayesian differences test (95 % HDI).

The Safran-Isba-Modcou (SIM) model, developed by Météo France (Habets et al., 2008; Soubeyroux et al., 2008), consists of an 8km resolution reanalysis chain combining the Safran meteorological analysis system (Durand et al., 2009), the Isba land surface model (Noilhan and Planton, 1989) and the Modcou hydrogeological model (Ledoux et al., 1989).

All the climatic variables used in this work come from the Safran module. This atmospheric forcing analysis system is based on a robust vertical interpolation method of the main meteorological parameters (Durand et al., 1993). Both the Météo France observation network and the outputs of atmospheric models (Arpège or ECMWF) are used to compute the solar radiation terms using the radiative transfer model described in Ritter and Geleyn (1992). 8 meteorological parameters are analyzed at an hourly time step on more than 9000 grid points (Soubeyroux et al., 2008), including liquid precipitation, which is needed to compute the water balance. Safran offers a continuous and uniform spatial and temporal information covering the entire French territory. The model also computes Potential EvapoTranspiration (PET) using the Penman-Monteith equation (Allen et al., 1998). Several studies account for the relevance of the meteorological analysis in Safran, especially for the precipitation and air temperature fields (Quintana-Seguí et al., 2008; Vidal et al., 2010).

The SIM dataset starts from the 1st of August 1958 and is periodically updated until present time. In this study, a 63-year time period from 1959 to 2021 is selected to model the water balance at a daily time step for each grid point of the French territory using winter bread wheat characteristics. This allows to distinguish three climate regimes based on the rapid temperature warmings of 1987/1988 and 2014/2015.

Required for water balance modeling, the capacity of the soil water content is obtained from the GISSol database (Groupement d'intérêt scientifique sur les sols (France), 2011; Le Bas, 2018). The capacity of the soil water content values, divided into classes, are recalculated at the SIM grid point scale. To do so, the GISSol database and the SIM grid points shapefiles over metropolitan France are crossed using QGis (QGis. org, 2023), and the median of each class of useful soil water content in each grid point is weighted by the proportion of the grid point covered by the class. All the values obtained for each grid point are summed up, giving a unique value of useful soil water content per grid point. Fig. 1 shows the resulting map of the useful soil water content values categorized with the same classes used in the GISSol database.

In this work, the analysis of water stress modifications is carried out for each main winter bread wheat production basin (Fig. 1). The latter are defined by first selecting all the grid points where at least 10 % of the surface is covered by winter bread wheat fields according to the 2019 agricultural survey called Registre Parcellaire Graphique from the French Mapping Agency (Institut National de l'information Géographique et Forestière, 2019). The main production basins are then designed by selecting groups of grid points in French agricultural basins, and approved by field insurance experts. The impact of the abrupt warming on the water stress index is thus assessed for the six main winter wheat production areas: Nord-Pas-de-Calais, Parisian Basin, Poitou-Charentes, Centre, Bourgogne/Rhône-Alpes and Aquitain Basin regions. Each production basin is characterized by its climate, its useful soil water content and its surface covered by wheat fields (Table 1).
<caption>**Table 1**</caption>

Agronomic, pedologic and climatic characteristics of the six winter wheat production basins studied. Period 1: 1960–1987; period 2: 1988–2014; period 3: 2015–2021.
**PET**: Potential EvapoTranspiration, **PRELIQ**: liquid precipitation. Production basins 1, 2, 3, 4, 5, 6 respectively Nord-Pas-de-Calais, Parisian, Poitou-Charentes, Centre, Bourgogne/Rhône-Alpes and Aquitain production basins. * indicates that the difference is significant according to Bayesian differences test (95 %HDI).

<table><thead><tr><th>Production basin</th><th></th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><td colspan="2">Mean percentage of SIM grid point covered by winter wheat fields</td><td>25.9</td><td>24.2</td><td>18.2</td><td>19.3</td><td>14.9</td><td>15.8</td></tr><tr><td colspan="2">Mean useful soil water content (mm)</td><td>161</td><td>165</td><td>125</td><td>95</td><td>126</td><td>100</td></tr><tr><td rowspan="6">Δ period 2 – period 1 (mm)</td><td rowspan="2">Year</td><td><i>PET</i></td><td>99.3*</td><td>100*</td><td>103*</td><td>87.0*</td><td>95.6*</td><td>135*</td></tr><tr><td><i>PRELIQ</i></td><td>80.9*</td><td>25.7*</td><td>3.80</td><td>37.1*</td><td>55.1*</td><td>-12.8*</td></tr><tr><td rowspan="2">Spring</td><td><i>PET</i></td><td>36.8*</td><td>33.9*</td><td>36.1*</td><td>33.3*</td><td>38.2*</td><td>43.3*</td></tr><tr><td><i>PRELIQ</i></td><td>-1.51</td><td>-4.02*</td><td>-8.81*</td><td>-1.87</td><td>9.47*</td><td>2.08</td></tr><tr><td rowspan="2">Summer</td><td><i>PET</i></td><td>80.7*</td><td>82.3*</td><td>76.8*</td><td>72.9*</td><td>78.7*</td><td>94.1*</td></tr><tr><td><i>PRELIQ</i></td><td>19.7*</td><td>4.75*</td><td>-1.98</td><td>12.0*</td><td>15.4*</td><td>3.63*</td></tr><tr><td rowspan="2">Autumn</td><td><i>PET</i></td><td>52.1*</td><td>50.3*</td><td>58.1*</td><td>43.3*</td><td>47.9*</td><td>70.1*</td></tr><tr><td><i>PRELIQ</i></td><td>-0.514</td><td>-11.3*</td><td>-6.98*</td><td>16.2*</td><td>41.3*</td><td>12.1*</td></tr><tr><td rowspan="6">Δ period 3 – period 2 (mm)</td><td rowspan="2">Year</td><td><i>PET</i></td><td>43.4*</td><td>38.2*</td><td>41.2*</td><td>38.6*</td><td>46.3*</td><td>57.4*</td></tr><tr><td><i>PRELIQ</i></td><td>55.2*</td><td>22.9*</td><td>-5.05*</td><td>3.21</td><td>8.93*</td><td>-22.0*</td></tr><tr><td rowspan="2">Spring</td><td><i>PET</i></td><td>-17.8*</td><td>-5.83*</td><td>-10.3*</td><td>27.2*</td><td>70.8*</td><td>17.0*</td></tr><tr><td><i>PRELIQ</i></td><td>-15.4*</td><td>-5.55*</td><td>-6.69*</td><td>-39.0*</td><td>-58.1*</td><td>-7.44*</td></tr><tr><td rowspan="2">Summer</td><td><i>PET</i></td><td>-7.79*</td><td>-9.13*</td><td>-5.81*</td><td>-3.93*</td><td>7.44*</td><td>0.604*</td></tr><tr><td><i>PRELIQ</i></td><td>-5.94*</td><td>3.71*</td><td>6.25*</td><td>8.14*</td><td>6.47*</td><td>-11.3*</td></tr><tr><td rowspan="2">Autumn</td><td><i>PET</i></td><td>-10.1*</td><td>-1.50</td><td>-6.77*</td><td>20.7*</td><td>55.8*</td><td>16.0*</td></tr><tr><td><i>PRELIQ</i></td><td>-30.1*</td><td>-19.3*</td><td>2.89*</td><td>-30.9*</td><td>-24.1*</td><td>-21.1*</td></tr><tr><td rowspan="2">Winter</td><td><i>PET</i></td><td>-11.8*</td><td>-11.5*</td><td>-6.65*</td><td>3.93*</td><td>21.2*</td><td>2.38*</td></tr><tr><td><i>PRELIQ</i></td><td>-6.20*</td><td>5.08*</td><td>-30.2*</td><td>-19.6*</td><td>-43.5*</td><td>-36.0*</td></tr><tr><td rowspan="2"></td><td rowspan="2"></td><td><i>PET</i></td><td>-7.63*</td><td>-11.1*</td><td>-8.50*</td><td>-4.98*</td><td>8.33*</td><td>0.182</td></tr><tr><td><i>PRELIQ</i></td><td>15.9*</td><td>31.4*</td><td>31.1*</td><td>33.5*</td><td>22.3*</td><td>24.5*</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Map of the main winter bread wheat production basins in metropolitan France and associated useful soil water content. The area of each SIM grid point shown is covered by at least 10 % of wheat fields according to the 2019 survey of the Registre Parcellaire Graphique (Institut National de l'information Géographique et Forestière, 2019). Blue colors correspond to classes of useful soil water content (mm, see map legend). Red contours represent main winter bread wheat production basins: 1. Nord-Pas-de-Calais, 2. Parisian Basin, 3. Poitou-Charentes, 4. Centre, 5. Bourgogne/Rhône-Alpes, 6. Aquitain Basin. The background map comes from OpenStreet Map database.</figcaption></figure>

## 2.2. Phenology and water balance modeling

The characteristics and phenology of the crop of interest are taken into account in the water balance model through Maximal Evapo-

Transpiration (MET), corresponding to the amount of water that a given crop can evapotranspirate under optimal soil water content and actual climatic conditions (Allen et al., 1998). MET can be computed by weighting the PET by the crop coefficient, named Kc, which depends on
the phenological stage of the crop, i.e., the development stage.

The start date of each phenological stage is assessed for each SIM grid point by using a growing degree-days (GDD) model developed on R language (R Core Team, 2021). The growing degree-days needs to reach each specific phenological stage of the winter bread wheat crop come from Gate (1995). Growing degree-days are computed on a 0 °C basis, starting from a sowing date on the 1st of November, from 1959 to 2021. When the growing degree-days needs of a phenological stage is reached, the start date of this phenological stage is extracted, allowing a Kc to be assigned to each day. Daily Kc values are used to weight the PET to provide daily MET values for each grid point from 1959 to 2021. Daily MET is required as input for water balance modeling.

In this study, a simplified two-reservoirs water balance model was used to compute the daily water balance of a given crop (Jacquart and Choisnel, 1995). The model uses several input variables: liquid precipitation and MET. The useful soil water content, also called RU, summarizes the soil water reservoir capacity i.e., the maximum extractable water in the soil, and is also required as an input to the model. Although this model does not involve an explicit resolution of the surface energy balance equation, it displays good performance when compared to a model using a surface energy balance equation, such as in the Earth model for example (Choisnel, 1985). The model computes numerically and iteratively, at a daily time step, the variation of soil water content as:

$$ \frac{dW}{dt} = \text{PRELIQ} - \text{AET} - D \qquad (1) $$

where dW is the change in soil water content between two consecutive days (dt), balanced between water input from liquid precipitation (PRELIQ), water loss from actual evapotranspiration (AET) – computed using MET and the filling level of soil water reservoirs –, and water loss as drainage (D).

The model assumes for each grid point that, on January 1st of 1959, its soil water storage on a homogeneous soil texture, called R(t), is full. The lower bound for R(t) is 0 when soil water reservoirs are empty, the upper bound is RU. Thus, for a given day, the available soil water content is given by:

$$ R(t) = \begin{cases} RU & \text{if } R(t-1) + dW > RU \\ R(t-1) + dW & \text{else} \end{cases} \qquad (2) $$

The RU value is fixed for each SIM grid point (see Study area and datasets). The water storage R(t) is managed by decomposing the soil water content into two reservoirs: the surface reservoir (R1(t)) supplied by liquid precipitation and emptying in the deep reservoir (R2(t)) in case of water excess. It gives an accurate representation of the dependence of evaporation on soil water content near the surface and allows to better account for the impact of the succession of dry and wet sequences on water availability, especially during the spring and summer seasons. In the Earth model, the Actual EvapoTranspiration (AET)/MET ratio drops significantly when the R(t)/RU ratio goes below 60% (Choisnel, 1985). Based on these findings, in the simplified two-reservoirs water balance model used in this study, the partition of surface (RU1) and deep (RU2) reservoirs corresponds respectively to 40% and 60% of the total RU. For more details on the simplified two-reservoirs water balance model, see Jacquart and Choisnel (1995), and further details on the water balance modeling methodology of this study, are described in Laurent et al. (2023).

The water balance is computed continuously between 1959 and 2021. Note that 1959 is considered a spin-up and is removed from the statistical analysis.

## 2.3. Water balance analysis

Vegetation cover is considered to be under water stress when the fill rate of soil water reservoirs, or water balance, falls below a threshold (Granier et al., 1999). The threshold at which plant growth and

development starts to diverge from a reference value depends on several factors, such as evaporative demand, root distribution and soil texture (Sadras and Milroy, 1996). For example, in Meyer and Green (1980), leaf growth of winter wheat starts to decrease when 52 to 57% of the RU is used. Wheat evapotranspiration declines when soil water reservoirs are 20 to 30% full, and growth slows down at about 34% of the RU. Another substrate based experiment estimated that the limit of extractable water for wheat is 39.7% (Norikane et al., 2003). Regarding previous findings, this work considers a water stress threshold fixed at 40% of the total RU of each point, below which the growth of winter bread wheat is affected by water stress (Jacquart and Choisnel, 1995).

A useful index that accounts for variability in water storage capacity is the relative extractable water (REW), expressed here as:

$$ \text{REW} = \frac{R(t)}{RU} \quad \text{with } R(t) = R1(t) + R2(t) \qquad (3) $$

where R1(t) and R2(t) are the amount of water in the surface and deep reservoirs, respectively, on day t. The REW daily mean cycle is computed for each SIM grid point along the 1959–2021 period. Spatial and temporal aggregations for each winter bread wheat production basins are computed to analyze the evolution of the REW daily mean cycle with abrupt warmings.

From there, as previously shown, we assume that water stress occurs when REW falls below 40% (REWc i.e., critical REW) of the maximum extractable water (RU). Hence, the daily Soil Water Deficit (SWD, in mm) is computed against this threshold as:

$$ \text{SWD}(t) = \begin{cases} 0 & \text{if } \text{REW}(t) \ge \text{REWc} \\ 0.4 * \text{RU} - R(t) & \text{if } \text{REW}(t) < \text{REWc} \end{cases} \qquad (4) $$

Based on those daily differences, and in order to compare wheat production basins, an index quantifying the water stress experienced by a crop during a given period is required. Such an index may summarize both the duration and intensity of the water stress. Following Granier et al. (1999), we propose a water stress index (Is) that cumulates daily soil water deficit (SWD) on an annual scale. Is is computed as:

$$ \text{Is} = \sum_{t=\text{January1}}^{t=\text{December31}} \text{SWD}(t) \qquad (5) $$

with water stress index (Is) expressed in mm. Is is computed for each of the grid points covering the six winter wheat production basins. From there, for one grid point and for a given year, two cases are possible. First, no water stress is observed (i.e., Is = 0). Second, winter wheat experiences water stress (i.e., Is > 0) of a certain amount. This amount indicates drought.

## 2.4. Modeling drought risk with Tweedie distributions

In order to statistically assess drought risk, it is necessary to simultaneously account for (i) the probability that a drought occurs and (ii) its intensity. The difficulty in modeling drought risk is that water stress is continuous with exact zeros, meaning that its probability distribution is compound (both continuous and discrete). Candidate probabilistic models able to dive with compound distributions include the Tweedie model. The latter has been successful in modeling precipitation (Dunn, 2004) or frost stress (Castel et al., 2017), which are also mixtures of discrete and continuous processes.

Annual water stress index Is distributions – generated using Is values from all years of the studied sub-period and from all grid points in a production basin – can produce various forms of probability density functions, revealing, for example, an inflation of zeros and more or less heavy tails. Poisson-gamma distributions, belonging to the class of Tweedie models (Jørgensen, 1987; Tweedie, 1984), offer a unified framework for modeling zero-inflated asymmetric histograms with heavier or lighter tails. In this work, and to our knowledge for the first
time, we applied such a model to fit the water stress index Is distributions derived for each of the sub-period bounded by the abrupt rises in surface temperature and over each production basin.

Assuming that $SWD(j)$ is the intensity of a daily water stress event $j$, and has a gamma distribution $\text{Gamma}(-\alpha, \gamma)$ (with the mean being $-\alpha\gamma$ and the variance $-\alpha\gamma^2$). Assuming also that the number of water stress events in a year is $N$ and has a Poisson distribution, which implies that some years will have no water stress events ($N = 0$). Then the annual water stress $Is$ can be computed as the Poisson sum of the gamma random variables, so that

$$Is = SWD(1) + SWD(2) + \dots + SWD(N) \quad (6)$$

where $N$ has a Poisson distribution with mean $\lambda$.

According to Dunn (2004), the distribution of $Is$ can be deduced by working with cumulative generating functions by noting that $Is$ given $N$ has the gamma distribution $\text{Gamma}(-N\alpha, \gamma)$. The resulting distribution is called a Poisson-gamma distribution (Smyth, 1996), and its probability function can be written as

$$\log f(y; \mu, \phi, p) = \begin{cases} -\lambda, & y = 0, \\ \frac{y}{\gamma} - \lambda - \log y + \log W(y, \phi, p), & y > 0 \end{cases} \quad (7)$$

where $\gamma = \phi(p-1)\mu^{p-1}$, $\lambda = \mu^{2-p}/[\phi(p-1)]$, and $W$ is expressed as

$$W(y, \phi, p) = \sum_{j=1}^{\infty} \frac{y^{-j\alpha}(p-1)^{j\alpha}}{\phi^{j(1-\alpha)}(2-p)^{j\alpha}\Gamma(-j\alpha)} \quad (8)$$

where $\alpha = (2-p)/(1-p)$. The mean of the distribution is $\mu$ and the variance $\text{var}[Y] = \phi\mu^p$. In these equations, $1<p<2$ is the index that determines which Poisson-gamma distribution is used.

Climatologically, the parametrization in terms of $(\lambda, \gamma, \alpha)$ is useful and best analyzed: according to Dunn, (2004), $\lambda$ refers to the mean number of water stress events per year, and $-\alpha\gamma$ refers to the mean intensity of an event. Then, due to their mathematical properties, the parameters of the fitted distributions allow to infer simultaneously the mean of occurrence and intensity of drought events. The evolution of these two parameters with warming enables us to assess structural changes in drought risk.

# 3. Results

## 3.1. Water balance daily mean cycle modification

As expected, the water balance, or REW, daily mean cycle displays values close to 1 for the fall and winter seasons, when soil reservoirs are full (i.e., at field capacity), while spring and summer values decrease (Fig. 2). A value close to 0 indicates that soil reservoirs are empty, i.e., at permanent wilting point.

In this part, only the results merged for all the grid points of all the production basins are depicted (Fig. 2), in order to illustrate the methodology used to study water stress events. However, the analysis of the REW daily mean cycle on each wheat production basin reveals spatial disparities in the pattern of evolution after the abrupt warmings (Supplementary Figure 1).

Over all the winter wheat production basins, the abrupt warmings of 1987/1988 and 2014/2015 significantly affected water balance cycle (Fig. 2). Minimum water storage occurs in late July/early August during the 1960–1987 period, with an average of 30 % of soil water reservoirs filled, while during the 1988/2014 period, minimum water storage shifts by about a week, with approximately 25 % of reservoirs filled. REW goes below the stress threshold almost 20 days earlier in 1988–2014 than in 1960–1987, and the water stress event (materialized by gray, dot or bar filling) ends 5 days earlier. At the end of June, a strong decrease in REW up to almost 30 % occurs during the 1988–2014 period, but not for the 1960–1987 period. Clearly, climate warming affects more the emptying of the reservoir than its filling.

During the 2015–2021 period, the minimum REW occurs between the 15th and the 20th of July with almost 20 % fill rate. The start date of the hydric stress event occurs one week later in the 2015–2021 period compared to the 1988–2014 period, but no clear shift in the end date of the hydric stress event is detected. This is a preliminary trend that is likely to evolve in the coming years as a function of regional warming conditions.

The 1987/1988 and 2014/2015 abrupt warmings show different effects on the water balance in all the wheat production basins, as well as in each of them independently (Supplementary Figure 1). Fig. 2 shows that the first abrupt warming induced a shift in water stress events, which became longer and more intense on the 1988–2014 period than in the 1960–1987 period. Since the 2014/2015 abrupt warming, the drought trend has led to more intense but slightly shorter water stress events.

<figure><img src="image_5.png" /><figcaption>Fig. 2. Relative Extractible Water (REW) daily mean cycle for all winter bread wheat production basins. Green: daily mean for 1960–1987 period; blue: daily mean for 1988–2014 period; red: daily mean for 2015–2021 period; with associated standard deviations in transparent colors. Black dashed line: stress threshold. Gray, line and point fillings represent the annual cumulative water stress index $Is$ (mm).</figcaption></figure>
To study more precisely the changes in water stress events on both sides of each rapid warming, the water stress index *Is* (represented by gray, dots and points filling on Fig. 2) is computed for each SIM grid point and each year, analyzed through histograms and modeled with Tweedie distributions. This allows us to identify changes in the occurrence and/or the intensity of drought events on each wheat production basin.

## 3.2. Water stress index evolution and drought risk modifications

**Table 2:** Mean occurrence $\lambda$ and intensity $-\alpha\gamma$ of water stress events according to the Tweedie distributions fitted on water stress index *Is* distributions and mean *Is* (mm). Period 1: 1960–1987, period 2: 1988–2014, period 3: 2015–2021. Production basins 1, 2, 3, 4, 5, 6 respectively Nord-Pas-de-Calais, Parisian, Poitou-Charentes, Centre, Bourgogne/Rhône-Alpes and Aquitain production basins.

The rate of cases (i.e. one grid point and one year) with no water stress ($y(x=0)$ on the graph) falls dramatically – divided by two in the 1988–2014 period compared to the 1960–1987 period – on all the wheat grid points (Fig. 3). This rate slightly increases in the 2015–2021 period compared to the 1988–2014 period, but is still below the 1960–1987 value. This latter trend is to be confirmed given the short number of years covered. Fig. 3 displays a shift in non-zero water stress events, which are intensifying with time. The proportion of low water stress index (i.e., *Is* < 500 mm) decreases between each period studied, while the mean value of *Is* increases between the 1960–1987 period and the 1988–2014 period and between the 1988–2014 period and the 2015–2021 period. To study how the water stress index *Is* evolves with abrupt warming in various geographic zones, a similar assessment is applied to each production basin independently (Fig. 4).

It is clear from Fig. 4 that the rate of cases with no water stress ($y(x=0)$ on the graph) decreases in the 1988–2014 period compared to the 1960–1987 period for all the wheat main production basins, except for Poitou-Charentes. However, between the periods 1988–2014 and 2015–2021, the evolution is more contrasted. The Nord-Pas-de-Calais, Parisian Basin and Centre production areas (n°1, 2 and 4) display a slight increase in the proportion of no-stress cases, whereas the Poitou-Charentes, Bourgogne/Rhône-Alpes and Aquitain Basin production areas (n°3, 5 and 6) experience a decrease.

The no-stress cases display various evolutions depending on the production basin (Fig. 4). For almost all production basins, the proportion of water stress events with low intensity (i.e., *Is* < 500 mm) decreases over time. The mean value of the water stress index *Is* seems to shift towards higher values between the 1960–1987 and 1988–2014 periods for the Nord-Pas-de-Calais, Parisian Basin, Centre and Bourgogne/Rhône-Alpes production basins (n°1, 2, 4 and 5), and between the 1988–2014 and 2015–2021 periods for the Centre and Aquitain

Basin production areas (n°4 and 6). Overall, the differences in the distributions of the *Is* drought index between the 1960–1987 and 1988–2014 periods and between the 1988–2014 and 2015–2021 periods are significant according to the Kolmogorov-Smirnov test, for each production basin studied and for all the production basins gathered (Supplementary Table 1). It is worth noting that even if the *Is* index for the 2015–2021 period significantly evolved, this result should be considered in the light of the shorter time frame available for the study, which accentuates the uncertainty surrounding the estimation of the Tweedie-based occurrence and intensity of drought events.

As explained in the 2.4. section (see Modeling drought risk with Tweedie distribution), the Tweedie distributions closely match the *Is* distributions, with the presence of a zero inflation and more or less heavy tails (Figs. 3 and 4). Kolmogorov-Smirnov tests show significant similarities between the distributions of water stress index and the fitted Tweedie distributions for the three studied periods and for all the production basins, with p-values above 0.5 (Supplementary Table 2). Kolmogorov-Smirnov tests on each production basin independently reveal more contrasted correlation results, but many production basins and studied periods exhibit significant similarities between the two distributions. Modeling water stress index distributions provides estimates of the occurrence and intensity of water stress events. This allows to study changes in the distribution parameters on both sides of each abrupt warming in the main wheat production basins, and consequently to assess changes in drought risk. All these parameters are summarized in the Table 2, with the mean value of *Is* for each production basin and period.

The analysis on all the production basins reveals an increase in the occurrence $\lambda$ and intensity $-\alpha\gamma$ of wheat drought risk after the rapid warming of 1987/1988, which conceals subtleties depending on the subperiod of warming considered. The period 1988–2014 shows a strong increase in the occurrence of water stress compared to the period 1960–1987 (about 25 %), but a slight decrease in its intensity (2 %) (Table 2). Opposite trends are observed between the periods 1988–2014 and 2015–2021, with a 7 % decrease in occurrence but a 14 % increase in intensity. Overall, winter wheat production basins experience an important rise in the mean water stress index *Is* of 23 % and 6 % for the 1987/1988 and 2014/2015 abrupt warmings, respectively.

As for the histograms, the distribution parameters of the water stress events display geographical disparities across the country (Table 2). In the Nord-Pas-de-Calais and the Centre production basins, water stress events are more than 50 % more frequent in the 1988–2014 period than in the 1960–1987 period, but also respectively 8 % and 33 % less intense. In the Bourgogne/Rhône-Alpes and Aquitain production basins, hydric stress events are respectively 20 % and 30 % more frequent, but also 4 % and 19 % less intense. Conversely, in the Poitou-Charentes production basin, hydric stress events are 6 % less frequent but 28 % more intense. In the Parisian Basin, hydric stress events are both more

<caption>**Table 2**</caption>

Mean occurrence $\lambda$ and intensity $-\alpha\gamma$ of water stress events according to the Tweedie distributions fitted on water stress index *Is* distributions and mean *Is* (mm). Period 1: 1960–1987, period 2: 1988–2014, period 3: 2015–2021. Production basins 1, 2, 3, 4, 5, 6 respectively Nord-Pas-de-Calais, Parisian, Poitou-Charentes, Centre, Bourgogne/Rhône-Alpes and Aquitain production basins.

<table><thead><tr><th rowspan="2">Production<br>basin</th><th colspan="3">Period 1</th><th colspan="3">Period 2</th><th colspan="3">Period 3</th></tr><tr><th>Number<br>of events λ</th><th>Mean intensity<br>of an event –<br>αγ (mm/event)</th><th>Mean<br>cumulative<br>hydric stress<br>index (mm)</th><th>Number<br>of events λ</th><th>Mean intensity<br>of an event –<br>αγ (mm/event)</th><th>Mean<br>cumulative<br>hydric stress<br>index (mm)</th><th>Number<br>of events λ</th><th>Mean intensity<br>of an event –<br>αγ (mm/event)</th><th>Mean<br>cumulative<br>hydric stress<br>index (mm)</th></tr></thead><tbody><tr><td>All<br>production<br>basins</td><td>2.57</td><td>645</td><td>1660</td><td>3.24</td><td>632</td><td>2050</td><td>3.01</td><td>722</td><td>2180</td></tr><tr><td>1</td><td>1.64</td><td>686</td><td>1120</td><td>2.47</td><td>628</td><td>1550</td><td>2.18</td><td>880</td><td>1920</td></tr><tr><td>2</td><td>2.04</td><td>772</td><td>1580</td><td>2.76</td><td>777</td><td>2140</td><td>2.31</td><td>1057</td><td>2440</td></tr><tr><td>3</td><td>5.11</td><td>440</td><td>2250</td><td>4.78</td><td>563</td><td>2690</td><td>5.43</td><td>410</td><td>2220</td></tr><tr><td>4</td><td>3.92</td><td>385</td><td>1510</td><td>6.13</td><td>257</td><td>1580</td><td>5.25</td><td>395</td><td>2080</td></tr><tr><td>5</td><td>2.37</td><td>476</td><td>1130</td><td>2.84</td><td>457</td><td>1300</td><td>3.09</td><td>529</td><td>1540</td></tr><tr><td>6</td><td>3.59</td><td>462</td><td>1660</td><td>4.69</td><td>373</td><td>1750</td><td>5.74</td><td>301</td><td>1730</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Density histograms of annual water stress index *Is* (mm) of all grid points in all winter bread wheat main production basins and associated Tweedie distributions. Green bars: 1960–1987 period; blue bars: 1988–2014 period; red bars: 2015–2021 period. The first class on the far left (zero water stress) is represented by a thinner bar, the associated density value (exceeding y limits) is written in the corresponding colored text.</figcaption></figure>

frequent (35 %) and slightly more intense (less than 1 %).

Between the periods 1988–2014 and 2014–2015, the Nord-Pas-de-Calais, Parisian Basin and Centre production basins experience a decrease in the frequency of hydric stress events but an increase in their intensity. The Poitou-Charentes and Aquitain production basins encounter an increase in the occurrence of water stress events but a decrease in their intensity, and the Bourgogne/Rhône-Alpes production basin experiences a rise in both occurrence and intensity. These results on the second abrupt warming must be taken carefully, as the temporal depth of the 2015–2021 period is substantially lower than that of the two first periods and is less than 20 years.

Consequently, for both abrupt warmings and for all production basins – except for Poitou-Charentes and Aquitain Basin for the 2014/2015 abrupt warming – the *Is* mean value increases significantly over time. The northernmost production basins experience the highest increases in the 1988–2014 period compared to the 1960–1987 period, with 38 % and 36 % for respectively Nord-Pas-de-Calais and Parisian Basin. The Nord-Pas-de-Calais and Centre production basins show the largest increase in the mean cumulative hydric stress index for the 2015–2021 period compared to the 1988–2014 period, with respectively 24 % and 32 %.

To summarize, modifications in the winter wheat water balance cycle with abrupt warmings led to changes in water stress events and drought risk. Their occurrence $\lambda$ and intensity $-\alpha\gamma$ increase after the 1987/1988 warming shift. However, the results show non-homogeneous changes during the 1988–2021 period. Indeed, the drought risk evolves in various ways depending on the subperiod (1988–2014 or 2015–2021) and on the production basin studied. Overall, the mean value of the water stress index *Is* rises after the rapid increase of the surface air temperature in almost all the French winter wheat main production basin.

### 3.3. Geographical pattern of extreme hydric stress index evolution

To assess spatial changes at a sub-regional scale, this last section

investigates how each SIM grid point of the wheat production basins reacts to changes in the extreme values of the water stress index *Is*. To that end, the 90th percentile of *Is* is determined for the 1960–1987 period and for all the winter wheat SIM grid points using the Tweedie R package (Dunn and Smyth, 2005). Fig. 5 illustrates the proportion of years in which the water stress index overcomes the 90th percentile value described above, for each of the three studied periods.

In all the production basins except the Centre, the rate of SIM grid points exceeding the 90th percentile rises in the 1988–2014 period compared to the 1960–1987 period (Fig. 5a). For many of these SIM grid points, the probability to overcome the 90th percentile increases strongly between period 1 and period 2. The Parisian and Poitou-Charentes production basins experience the most important increase in the probability of exceeding the 90th percentile. In the 1960–1987 period, the grid points of these production basins had between 10 and 30 % chances of overcoming extreme water stress events, whereas, in the 1988–2014 period, some grid points overcame this threshold in more than one out of two years. The grid points of the Bourgogne/Rhône-Alpes and Aquitain production basins almost didn’t encounter extreme water stress events on the 1960–1987 period. On the 1988–2014 period, SIM grid points on these production basins have between 10 and 20 % of chances of exceeding the 90th percentile of the water stress index *Is* of the 1960–1987 period.

Between the periods 1988–2014 and 2015–2021, the probability to exceed the 90th percentile reveals more contrasted changes. The Poitou-Charentes and Aquitain production basins show a decrease in the number of grid points overpassing the 90th percentile, in contrast to the other zones. For the Nord-Pas-de-Calais and Parisian production basins, almost all grid points exceed the threshold at least one out of ten times on the 2015–2021 period. On this period, almost half of the Parisian production grid points have more than 20 % of chances to overcome the 90th percentile. Several grid points of the Parisian, Poitou-Charentes and Centre production basins, exceed the threshold more than 4 times out of 10.

Following the rapid warmings of surface air temperature, French
<figure><img src="image_7.png" /><figcaption>Fig. 4. Same as Fig. 3 but for each winter bread wheat production basin separately.</figcaption></figure>

winter wheat production basins encounter a strong increase in the in-
tensity of water stress events. The northern production basins and the
Poitou-Charentes production basin are particularly impacted by the
1987/1988 abrupt warming, with an important increase in the proba-
bility of experiencing extreme water stress events. The other production
basins reveal more various changes. In addition to changes in the
occurrence and intensity of mean value of the water stress events, the
abrupt surface temperature warmings induced more widespread and
frequent extreme droughts in almost all winter wheat production basins.

4. Discussion

This study proposes to characterize changes in winter wheat water
stress events and drought risk parameters after an abrupt warming using
Tweedie distributions. Statistical distributions of the water stress index
Is display patterns that Tweedie distributions can fit well. These distri-

butions are a combination of discrete (when there is no hydric stress)
and continuous processes, also known as mixed probability distribu-
tions. The 1987/1988 rapid warming of surface air temperature delimits
over the 1960–2014 period two climate subperiods of sufficient and
nearly equal temporal depth to statistically determine structural modi-
fications of drought risk (occurrence and intensity). In this work, we also
try to carry out an initial assessment of the preliminary impact of the
2014/2015 abrupt warming on winter wheat water stress, even if the
temporal depth of the 2015–2021 period is not long enough to robustly
and fully evaluate significant changes in drought risk. However, it al-
lows to show that drought risk evolutions over this last period vary
spatially.

The increase in water demand after the abrupt warmings in France
led to modifications in the climatic water balance, with a significant
increase in water demand leading to a decrease in soil water content
(Chaouche et al., 2010; Laurent et al., 2023). In winter bread wheat
<figure><img src="image_8.png" /><figcaption>Fig. 5. Proportion of years exceeding the 90th percentile of the water stress index *Is* of all the winter bread wheat production basins of the 1960–1987 period. (a) Period 1: 1960–1987; (b) period 2: 1988–2014; (c) period 3: 2015–2021.</figcaption></figure>

production basins, the water balance daily mean cycle reveals various changes. Depending on the production basin considered, the period for which the water balance is below the stress threshold is longer or shifts earlier in the year, or the minimum *REW* daily mean cycle is lower in the post-shift period compared to the pre-shift period. The rapid warming affects reservoir emptying more than filling, which can be due to the fact that after 1987/1988, the spring experienced more important warming than the autumn (Brulebois et al., 2015). Across the country, the 1987/1988 abrupt warming led to longer and slightly more intense periods below the water stress threshold, and the 2014/2015 abrupt warming induced more intense and slightly shorter periods of hydric stress.

Water balance modeling results must be considered in relation to the modeling chain used in the study. As explained in the 2.2. section (see *Phenology and water balance modeling*), crop phenology is modeled using a simple growing degree-day model. Compared to the *REW* coming from a modeling chain using a more complex phenological model, STICS (Simulateur MulTidisciplinaire pour les Cultures Standard, Brisson et al., 2009), the *REW* between March and November seems to be overestimated (Supplementary Figure 2). This could be due to the fact that the crop coefficient reaches its maximum value ($K_c = 1,1$) earlier in the year and for a longer period with the simple growing degree-day phenological model compared to the STICS model (Supplementary Figures 3 and 4). Thus, the choice of the phenological model used in the water balance modeling chain is an important factor affecting the assessment of changes in water balance and hydric stress events. This does not change the impact of warming on drought risk, except in terms of the amplitude of change.

The changes in climatic hazard linked to water balance result in changes in agro-climatic risks, especially drought risk. In this study, we show that the water stress index *Is* distributions are significantly modified in each wheat production basin after the abrupt warmings. Tweedie modeling reveals changes in the occurrence and intensity of water stress events that are not homogeneous over the period considered and also show subtle regional modifications. Some wheat production basins experience an increase in occurrence but a decrease in intensity, others encounter opposite effects, and the latter go through a rise in both occurrence and intensity of water stress. Ultimately, the water stress index increases after both abrupt warmings on every wheat production basin. On average, across all winter wheat production basins, the 1987/1988 abrupt warming increased the number of water stress events, and the 2014/2015 warming led to more intense water stress. Each time, the mean water stress index rises strongly.

Extreme drought events are also impacted by the abrupt increase in surface air temperature over France. The probability to overcome the

90th percentile of the water stress index *Is* of all the wheat production basins is increasing sharply, especially on the Nord-Pas-de-Calais, Parisian and Poitou-Charentes production basins, which are the main production areas. On some grid points of these zones after the abrupt warmings of 1987/1988 and 2014/2015, the probability of experiencing extreme water stress for wheat exceeds 40 %. Note that on some grid points of the Poitou-Charentes and Aquitain production basins, the probability of going through extreme drought events decreases in the 2015–2021 period compared to the 1988–2014 period. This could be explained by the evolution of the annual amount of liquid precipitation and the mean length of dry spell in spring and summer (result not shown). In these seasons, France is divided into two zones with a north-west/south-east axis. To the east of this axis, a lengthening of dry spells is highlighted, whereas to the west of the axis, the mean length of dry spells decreases (Raymond and Ullmann, 2021). This decrease could offset the effects of temperature warming on drought risk evolution. Conversely, to the east of the north-west/south-east axis, the Nord-Pas-de-Calais, Parisian, Centre and Bourgogne/Rhône-Alpes production basins experience an increase in *PET* and a lengthening of dry spells in spring and summer, leading to an increase in the probability to overcome extreme water stress events after the 2014/2015 abrupt warming.

These results are in line with others studies at larger spatial or temporal scales. Spinoni et al. (2018) show that the intensity and occurrence of drought events evolve with climate change over Western Europe. Over the historical period, temperature warming leads to a moderate but almost generalized rise in drought occurrence and intensity at the annual scale in France/Benelux region, with spring being particularly impacted by a strong increase. Future scenarios of temperature warming point out a critical increase in the spatio-temporal characteristics of agricultural drought in France (Vidal et al., 2012). The occurrence and intensity of severe and extreme soil moisture droughts are expected to drastically increase over France and Europe by 2100 (Grillakis, 2019).

Several factors are involved in the impact of climatic shifts on wheat water balance and drought. At the annual scale, the Parisian and Poitou-Charentes production basins experienced an important increase in *PET* between 1960–1987 and 1988–2014 periods, but only a slight increase in liquid precipitation (Table 1). This important climatic water balance deficit – also highlighted on a seasonal scale in spring and summer (Table 1) – could explain the important rise in water stress index *Is* on these zones (Table 2) and the increase in extreme drought events probability (Fig. 5). Aquitain Basin also undergoes an important increase in *PET* after 1987/1988 abrupt warming but a decrease in liquid precipitation (Table 1), but the impact on wheat water stress is less
pronounced (Table 2 and Fig. 5). In this production basin, hydric stress events are not more intense or longer, but shift earlier in the year (Supplementary Figure 1). This could be explained by a shift in the crop growth cycle, with maturity being reached earlier in the year. The strong increase of PET in spring between 1960–1987 and 1988–2014 periods could have fostered the shift in water stress event towards spring (Table 1). The low useful soil water content of the Aquitain Basin could explain the development of water stress already during the 1960–1987 period. The strong increase in PET between 1988–2014 and 2015–2021 periods on the Centre and Bourgogne/Rhône-Alpes production basins at the annual scale and in summer, and the decrease in liquid precipitation (Table 1) enhance the decline in the climatic water balance. Those two processes are identified as possible causes of the strong increase in the *Is* mean value and in extreme drought events probability (Fig. 5).

Such changes in drought events parameters can be correlated with
yield losses, such as for maize and wheat, which are particularly affected
by drought events modifications (Daryanto et al., 2016; Hendrawan
et al., 2022; Mohammed et al., 2022). In Spain for example, wheat yields
are strongly linked to dry spells (Raymond et al., 2018). This study
highlights the role of liquid precipitation in the evolution of drought
events. The absence of liquid precipitation, combined with the increase
in evaporative demand with temperature warming, leads to an increase
in drought risk. In France, Zampieri et al. (2017) show spatial disparities
in the correlation between the Standardized Precipitation Evapotrans-
piration Index and wheat yield anomalies. Mediterranean regions are
more sensitive to drought while northern parts of the country result to be
more sensitive to water excess. It would be interesting to compare the
yield anomalies with the water hydric stress index *Is* computed in this
work. Note that the extreme drought event of 2003 in France and Europe
dramatically affected primary productivity, including crop yields (Ciais
et al., 2005).

Modifications of the drought events characteristics following the abrupt warmings affect different phenological stages of the crop. More intense drought events in summer may alter grain forming and ripening, while longer water stress events may extend into spring and affect bolting development stages (Arvalis Institut du Végétal, 2022). For example, Jamieson et al. (1995) demonstrated that the wheat yield response to drought is mostly associated with grain number, which is determined between June and July. Drought during stem elongation is also a driver of wheat yield stagnation (Le Gouis et al., 2020). Thus, depending on the drought intensity and occurrence changes in each winter wheat production basin, different yield components will be affected, leading to a decrease in wheat harvests.

In the context of climate change, the mean surface temperature is expected to increase continuously more than 5 °C by 2100 under the Radiative Concentration Pathway (RCP) 8.5 scenario in France (IPCC, 2021). As a consequence, the hydrological cycle will intensify, with further increases in evapotranspiration (Douville et al., 2013; Huntington, 2006). In France, these changes are likely to occur mostly in summer (Boé et al., 2009; Chauveau et al., 2013). During this season, evapotranspiration is expected to decrease, leading to an important increase in meteorological and agricultural drought (Dayon et al., 2018). By 2100, the spatial coverage and intensity of agricultural drought events are foreseen to drastically increase (Vidal et al., 2012).

Modifications of the water stress intensity and occurrence after the abrupt warmings in France and their impacts on wheat yields, together with expected future changes in drought events, highlight the need for the agricultural sector to adapt. The agricultural insurance industry, especially crop insurance, is particularly vulnerable to adverse climatic events. Assessing the impact of changes in agro-climatic risk linked to drought on yields and, by extension, on economic losses, is of major concern for crop insurers (Hagenlocher et al., 2019). Some studies tried to link drought indices to economic costs, but few of them have focused on crop insurance losses, especially in France (Charpentier et al., 2022; Fusco et al., 2018; Hagenlocher et al., 2019). The impacts of changes in agro-climatic risks, especially drought events modifications, on the crop

weather insurance loss ratio needs to be investigated more closely in our
country, in order to better adapt the agricultural system to future
challenges.

5. Conclusion

In this work, we explore how the winter bread wheat agro-climatic
risk linked to drought can be modeled using Tweedie distributions,
and how its parameters evolve with abrupt surface temperature warm-
ing. The studied period extends from 1960 to 2021, and is divided into
three sub-periods according to the two rapid warming signals detected
over France: 1987/1988 and 2014/2015. The spatial and temporal
evolution of drought risk is studied by computing a water stress index *Is*
for each SIM grid point and each year from 1960 to 2021. Histograms of
the water stress index for each sub-period and each main winter wheat
production basin result from a mixture of continuous and discrete pro-
cesses (stress or no stress), showing an inflation of zero values (no stress)
and an asymmetry with more or less heavy tails. Tweedie distributions
are able to capture the characteristics of discrete and continuous com-
pound processes, and can be used to model *Is* mixed probability distri-
butions.

Tweedie modeling clearly reports and supports modifications in the
occurrence and intensity of drought events for each winter bread wheat
production basin with abrupt warmings. Changes in both parameters
depend on the production basin studied, and the periods compared.
Overall, the mean water stress index rises for all the zones studied. The
occurrence and intensity of drought events increase on average in all the
winter wheat production basins. The Nord-Pas-de-Calais, Parisian and
Poitou-Charentes production basins experience the most important in-
crease in *Is* after 1987/1988. These production basins also experience a
strong increase in extreme drought events probability, with several grid
points of these zones having more than 4 out of 10 chances to experience
extreme water stress during the 1988–2014 period, compared to 2 or 3
chances out of 10 during the 1960–1987 period. The 2014/2015 rapid
temperature increase also had an impact on drought risk. The Nord-Pas-
de-Calais, Centre and Bourgogne/Rhône-Alpes production basins show
the most important rises in the water stress index *Is* and the extreme
drought events probability.

In this study, we demonstrate that climate hazard evolution at
regional scale, through rapid surface temperature increase over France,
induced modifications of the winter bread wheat water balance, leading
to significant changes in the water stress occurrence and intensity.
Structural drought risk evolution could affect crop growth and devel-
opment, and ultimately alter yields. The resulting economic losses are of
great concern to the agricultural sector, especially the crop insurance
industry. Such abrupt warmings may occur again in the future over
France, accelerating the need for a better knowledge of the evolution of
agro-climatic risk linked to drought and its impacts on yields and in-
surance losses.

CRediT authorship contribution statement

Léa Laurent: Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation.

Albin Ullmann: Writing – original draft, Validation, Supervision, Project administration, Methodology, Funding acquisition, Conceptualization. Thierry Castel: Writing – original draft, Validation, Supervision, Project administration, Methodology, Funding acquisition, Conceptualization.

Declaration of competing interest

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

This work is part of a CIFRE PhD supported by Groupama Rhône-Alpes Auvergne insurance company. In this context, we would like to acknowledge Claude Perrot - head of Domaine Assurance Récolte of the company and scientific manager of the CIFRE PhD student - and Xavier Aubouy - data scientist in the Pricing and Analysis Department of Groupama Assurances Mutuelles company and administrative manager of the CIFRE PhD student - for their help in the methodology development and data collection, and their listening and advices. We also would like to thank Asmat Ullah for proof-reading and correcting our English.

## Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.agrformet.2025.110493.

## Data availability

Data will be made available on request.

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